of5 (45) 2013
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PUBLISHED SINCE MARCH, 2003
Editorial Board Members
Chairman:
V.M. Kolokoltsev – Prof., D. Sc., Rectorof Nosov Magnitogorsk State Technical University.
Honorary Board Members:
A.V. Dub – D.Sc., General Director of JSC Researchand Production Association of Central Scientific
Research Institution of Technical Mechanic Engineering.
D.R. Kaplunov – Prof., D.Sc., Corresponding Memberof Russian Academy of Science.
V.Ph. Rashnikov – Prof., D. Sc., President of LTd«Magnitogorsk Steel and Iron Works Managing Company».
V.M. Schastlivtsev – D. Sc., Chief of laboratory
in Russian Academy of Science , Academician
of Russian Academy of Science.
M. Pietrzyk – Prof. Akademia Gorniczo-Hutnicza,
Krakow, Poland.
K. Mori – Prof. Department of Production Systems
Engineering, Toyohashi Universityof Technology, Japan.
I. Gorlach – PhD in Mechanical Engineering,
Head of Department of Mechatronics, Nelson Mandela
Metropolitan University, South Africa.
H. Dyja – Prof., D. Sc, Director of the Instituteof Metal Forming and Engineering Security, Czestochowa
University of Technology, Poland.
A.B. Nayzabekov – Prof., D.Sc., Memberof the Academy of Sciences, Rector of Rudnensk
Industrial Institute, Republic of Kazakhstan.

R.O. Dusane – Prof., Head of Departmentof Metallurgical Engineering & Materials
Science, Institute of Technology
Bombay, India
Editor-in-chief:
M.V. Chukin – Prof., D.Sc., Vice-rector
for scientific and innovation work
Nosov Magnitogorsk State Technical University.
First deputy chief editor:
G.S. Gun – Prof., D. Sc. Nosov Magnitogorsk
State Technical University.
Deputy chief editor:
A.G. Korchunov – Prof., D.Sc, Vice-rector
for International Relations Nosov Magnitogorsk
State Technical University.
Executive editors:
M.A. Polyakova – Assoc. Prof., Ph.D
Nosov Magnitogorsk State
Technical University.
M.V. Shubina - Assoc. Prof., Ph.D
Nosov Magnitogorsk State Technical
University.
Editor: N.V. Kutekina.
Technical editor: G.N. Lapina.

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CONTENTS
Kolokoltsev V.M., Petrochenko E.V.
Structure features and propertiesof high-alloy white irons .................................................. 3
Vdovin K.N., Gorlenko D.A., Zavalischin A.N.
Structure changes of chromium-nickel
indefinite cast irons in heating ......................................... 9

Logunova O.S., Matsko I.I.,
Posochov I.A.
Integrated system structure of intelligent
management support of multistage
metallurgical processes .................................................. 50

Hamedon Z., Mori K.-I., Maeno T., YamashitaY.
Hot stamping of titanium alloy sheet using
resistance heating ........................................................... 12

Shatokhin I.M., Bigeev V.A.,
Shaymardanov K.R., Manashev I.R.
Investigation of combustionin titanium-ferrosilicon system....................................... 55

Sztangret M., Pietrzyk M.
Applications of plane strain compression
tests for identification of flow stress models
of materials and for physical simulationof metal forming processes ............................................ 16

Parsunkin B.N., Andreev S.M.,
Akhmetov T.U., Mukhina E.Y.
Optimal energy-efficient combustion
process control in heating furnacesof rolling mills ................................................................ 58

Pesin A.M.
Scientific school of asymmetric rollingin Magnitogorsk ............................................................. 23
Kawa ek A., Dyja H.
Analysis of variations in roll separating forces
and rolling moments in the asymmetricalrolling process of flat products ...................................... 28
Chukin M.V., Korchunov A.G., Gun G.S.,
Polyakova M.A., Koptseva N.V.
Nanodimentional structural part formation in highcarbon steel by thermal and deformation processing ..... 33
Satonin .V., orenko .G.,
Nastoyashchaya S.S., Perekhodchenko V.A.
The development of engineering methods
for calculating energy-power parametersof relatively thin strips hot rolling process .................... 36
Borovik P.V.
3d model of cutting by rolling cut type shears ............... 40
Gribkov E.P., Danilyuk V.A.
Mathematical modelling of srtess-strain behavoir
in rolling of the compositions including powdermaterials......................................................................... 42
Tulupov O.N., Moller A.B., Kinzin D.I., Levandovskiy
S.A., Ruchinskaya N.A., Nalivaiko A.V.,
Rychkov S.S., Ishmetyev E.N.
Structural-matrix models for long product rolling
processes: modeling production traceability
and forming consumer properties of products ............... 46

2

Antsupov A.V., Antsupov A.V. (jun),
Antsupov V.P.
Designed assessment of machine element
reliability due to efficiency criteria ................................ 62
Gun G.S., Rubin G. Sh., Chukin M.V.,
Gun I.G., Mezin I.U.,
Korchunov A.G.
Metallurgy qualimetry theory designand development ............................................................ 67
Lutsenko A.N., Rumyantsev M.I.,
Tulupov O.N., Moller A.B., Novitskiy R.V.
Technological reserves: reasonable
implementation of simple solutions
to improve hot rolling technology .................................. 70
Drobny O.F., Cherchintsev V.D.
Development and implementation of measures
to improve environmental situation within
Magnitogorsk industrial hub .......................................... 74
Kolga M., De Smedt V., Van Nerom L.
Planning Principles in Metallurgy .................................. 78
Polikarpova M.G.
Fuzzy-logic-based risk managementof M&A deals outcome: a casy-studya large russian metallurgic holding ................................ 80
The information about the authors ............................. 85—————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013.

5.

Kolokoltsev V.M., Petrochenko E.V.

Kolokoltsev V.M., Petrochenko E.V.

STRUCTURE FEATURES AND PROPERTIES OF HIGH-ALLOY
WHITE IRONS
Abstract. In this paper the regularities of structure formation, mechanical properties and wearability of chrome-vanadium white
cast irons, depending on chemical composition, cooling conditions during solidification have been investigated.
The relation of wearability of chrome vanadium white cast irons with the morphology of carbide phase, types of binary and ternary eutectics, phase and chemical composition of metallic matrix of castings in abrasive wearing-out has been established.
The reasoning of the influence of structure formation features in chrome vanadium white cast irons on the mechanical and special features, forming during crystallization and the following effects of abrasive ambient are represented.
Cast iron classification according to metallic matrix structure, eutectic type and quantity, eutectic morphology, phase morphology, forming any eutectic, is suggested.
Keywords: structure, eutectic compositions, phase structure, phase composition, microhardness, wearability, straining martensitic transformation, classification according to white cast iron morphology.

White cast iron is widely used as a material for tools
and machinery parts, which undergo intensive wear andoxidation. It was traditionally attributed to the class offragile and low-strength materials and this fact significantly limited the area of its use. The progress in the fieldof white irons alloying, achieved in recent years, has significantly changed the ideas about their properties andpossible applications.
Modern white cast irons are complex multicomponent alloys, different in structure and specific properties. They are a separate group of industrial cast irons,
which composite structure is being formed during solidification. It is the group that determines the specific properties of white cast irons in the as-cast state.
Despite the literature readings abundance concerning
the composition optimization of complex alloyed whiteirons of functional purpose, the effect of alloying elements on the crystallization processes and structure formation, mechanical and special (heat resistance, durability) properties of cast irons has not been considerably andsystematically investigated. Especially, it concerns theformation conditions of various eutectic and carbide
phase, containing some carbide-forming elements in ironcomposition.
In this paper the regularities of structure formation,mechanical and specific properties of chrome-vanadium
white cast irons, depending on the chemical composition,
cooling conditions during solidification have been investigated.
The selection of alloying structure and varying limitsof alloying elements and carbon content largely determines
the metallic matrix morphology, quantity, carbide phasetype and eutectic, and, consequently, the alloy properties inwhole and is settled by the following statements.
The most wear resistant, in accordance with Charpy
principle, are cast irons requiring the complete inversion ofphase location. It means the most solid structured constituents should lie in the form of isolated impurities, but themost viscous constituents should form a solid matrix, thatprovides not only high wear-resistant properties, but also
strength, toughness, resistance to thermal cycling, etc.
Such phase arrangement inversion in the structure ofaustenitic-carbide eutectic can be achieved in highchrome cast iron alloying with more than 3% vanadium.
Carbide is the branched phase but austenite or its transformation products are the matrix phase, being in generala cast composite.
Carbon is the main regulator of the carbide phase,
which determines the properties of the present irons. Carbon addition of 3.2-3.6% provides the 7 3 carbides
formation, which improves cast iron wear resistance.
Carbon addition of less than 3.2% leads to the primary austenite quantity increasing. Carbon addition of more than
3.2% leads to the reducing of alloying elements content in
the solid solution, and to the disruption of the cast structure
uniformity at the expense of large branched carbides precipitation. Both negatively affect on cast iron properties.
Chromium can partially replace the iron atoms in theiron carbide (Fe,Cr)3 or it can form chromium carbides,
in which the part of chromium atoms is substituted byiron: trigonal (Cr,Fe)7 3 and cubic (Cr,Fe)23 6. In -ironchromium has unlimited solvency, in -iron chrome dissolves to 14% Cr. Chromium carbides have significantly
higher hardness than chromium alloyed cementite, and it
promotes cast iron durability and mechanical properties.
Cementite carbides in iron form a hard framing ofledeburite eutectic. Criteria of fragile destruction for suchcarbide hard framing are achieved earlier than for eutectic
with carbides (Cr,Fe)7 3. Cast irons with carbides(Cr,Fe)7 3 (chromium content in the iron exceeds 11-14%)
are of maximum wear resistance due to increased microhardness of these carbides and eutectic branched morphology. Carbide (Cr,Fe)23 6 microhardness is 2000 MPa below than carbide (Cr,Fe)7 3 microhardness. It is more crisp
and intent to crushing through the process of coupling withabrasive particles that helps to reduce cast iron durability.
To form complex carbides (Cr,Fe)7 3, giving maximum cast iron durability, chromium levels range from
14,0-20,0% is required. When the chromium content is lessthan 14%, the formation of carbides (Cr,Fe)7 3 along withcarbides (Fe,Cr)3 is possible reducing cast iron durability.
When the chromium content is more than 20.0%, large andfragile carbides (Cr,Fe)23 6 appear in the iron structure,
resulting in wear-resistant properties reducing.
Vanadium in the range of 3.0-9.0% forms special VC
carbides with carbon of high microhardness (~ HV 3000).
Moreover, two types of eutectic are formed in the iron struc-www.vestnik.magtu.ru. ——————————————————————————————————————————————

3

Structure Features And Properties Of High-Alloy White Irons

ture: double austenitic-vanadium-carbide and triple austenitic-chrome-vanadium-carbide, which, being the composite
strengtheners, greatly increase cast iron durability.
Investigations were carried out on Fe - C - Cr - V alloys,
containing 2.6-3.2% C, 14,0-20,0% Cr, 3,0-9,0% V. The
amount of silicon and manganese in the experiment alloys
was at the permanent level: Si (0,4-0,6%); Mn (0,4-0,6%).
The experimental alloys were melted in the induction furnace IST-006 with the basic lining. The cooling rate influence on the structure and wear resistance during crystallization was studied on the iron samples, poured into dry andwet sand and clayed molds (SCM) and casting mold [1, 2].
The chemical composition of the samples was determined by an emission spectrometer «Bird» and by a spectrometer OBLF QSG 750 GOST 18895-97.
The structure and phase composition of cast irons were
examined with the help of metallographic and x-ray methods. X-ray imaging was carried out on a DRON-UM1 diffractometer (in the cobalt
radiation). The diffractometer
was connected to a . Phase analysis was carried out withthe help of XRAYAN program and PDF database.
Quantitative metallographic analysis, automated processing of microhardness measurement results were performed using a Thixomet PRO image analyzer. Microhardness measurement was carried out using a PMT-3
according to GOST 9450-76.
Micro X-ray spectrum studies of phase components
in alloys were carried out using scanning electron microscopes «JEOL» JSM-6460 LV, «TESCAN VEGA IIXMU», «Camscan» with micro X-ray spectrum analyzers.
Comparative tests of alloy and cast iron wear resistance in rubbing with semifixed abrasive particles werecarried out according to GOST 23.208-79. Wear-out was
performed by abrasive particles of various hardness (electrocorundum and periclase), allowing to define various
mechanisms of wear-out. Testing corundum, whose hardness (20-22 hPa) is comparable with vanadium carbide
hardness and exceeds chromium carbide hardness andmartensite-austenite matrix, the main mechanism of surface
destruction is microcutting. Periclase hardness (10-12 hPa)
is lower than vanadium carbide hardness and close to chromium carbide and metallic matrix hardness, therefore coupling iron with periclase plastic ousting is the main wear-out
mechanism.
Phase composition of chromium-vanadium irons in ascast state presents -phase (martensite), -phase (austenite),
vanadium carbide (VC), chromium carbide (Fe, Cr, V)7C3.
The combination of these phases provides two binary eutectics + VC, + (Fe, Cr, V) 7C3 and triple eutectic + (Fe,Cr, V) 7C3 + VC while crystallizing. The oexistence of
carbides of different forms and types is determined by ironcomposition and its crystallizing conditions.
Carbide and metallic matrix composition is variableand depends on chemical composition of the alloy andcooling rate during solidification. Carbides (Fe, Cr, V)7C3
contain 26,0-48,0% iron, 41,0-52,0% chromium,
9,0-22,0% vanadium, vanadium carbide dissolves ironpartially (up to 2,0-5,0%), chromium dissolves iron somemore – (8,0-16,0%) [3].
The determination of vanadium carbide volume quantity was performed on unpickled sections. The determination of the chromium carbide amount and size, the volume4

quantity of eutectics and their dispersity was carried out
on sections after pickling.
Depending on iron composition the following typesof alloy structures are formed (structural classes) [4]:1 – hypoeutectic, consisting of excessive austenite
dendrites (or products of its decomposition) and triple
eutectics + (Fe, Cr, V) 7C3+ VC;
2 – structure, consisting of two eutectics + VC
(spherulitic form) and + (Fe, Cr, V) 7C3 + VC;
3 – structure, consisting of two eutectics + (Fe, Cr,
V) 7C3 and + (Fe, Cr, V) 7C3 + VC;
4 – structure, consisting of pre-eutectic VC carbides andeutectic + (Fe, Cr, V) 7C3 and + (Fe, Cr, V) 7C3 + VC;
5 – structure, consisting of excessive VC carbides (orcarbides (Fe, Cr, V) 7C3) and eutectics + VC, + (Fe,Cr, V) 7C3 + V (Fig. 1).
Eutectics + (Fe, Cr, V) 7C3 and + (Fe, Cr, V) 7C3 +VC are socket-shaped in cross section, and fan-shaped inlongitudinal section.
Composition, structure and carbide phase properties
depend on the ratio of chromium and vanadium in castirons. When the content of carbon and alloying elements
is excessive, massive branched dendrites of primary vanadium carbides are formed (see Fig. 1).
The chromium increasing in the alloy causes vanadium
content reducing in the composition of carbides VC and(Fe, Cr, V) 7C3. It manifests in microhardness decreasing of
vanadium carbide from 22 to 18 GPa and complex chromium carbides from 16 to 10 GPa. The increasing of vanadium and carbon concentration in the alloy reduces iron content in carbides and increases chromium and vanadium
content. As a result, carbide (Fe, Cr, V) 7C3 microhardness
rises up to 16-17 GPa.
The cooling rate increasing leads to the followingchange in carbides composition: reduces chromium content from 10 to 8% in VC carbide, increases iron content
from 37 to 47% and reduces chromium content from 51 to
41% in complex carbide (Fe, Cr, V) 7C3. As a result, thealloying level of metallic matrix increases.
Carbide phase volume in eutectics + (Fe, Cr, V) 7C3
and + (Fe, Cr, V) 7C3 + VC is 28-36%, in eutectic A + VC
the amount of carbides is less – 10-15%. The difference inthe eutectic structure determines their different properties.
Eutectic compositions are crystallized within thetemperature range and have variable phase composition(Table 1), different density (by changing the amount ofcarbides in the eutectic, intercarbide distance) and carbide
phase dispersion, depending on alloy chemical composition and cooling rate during solidification. Eutectic type
and proportion in the structure of iron also depend on thealloy composition and cooling conditions, determining
cast iron mechanical properties and wear resistance inwearing-out by different hardness abrasive.
Table 1
The influence of cooling conditions on the amountof martensite q , austenite q , complex chromium carbides
q1and vanadium q2, %Dry SCM
Wet SCM
Chill moldq q q1 q2 q q q1 q2 qq
q1 q2
67,4 3,5 27,6 1,4 48,1 8,4 40,4 2,1 19,0 31,61 51,1 3,9—————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013.

5.

Kolokoltsev V.M., Petrochenko E.V.

The features of formation of structure and properties of different structural
types (classes) cast irons have been studied. There is one eutectic + (Fe, Cr, V)
7C3 + V in cast iron structure of the firststructural class. Complex (Fe, Cr, V)
7C3 carbide is the predominant phase in
the ternary eutectic.
3% vanadium content is sufficientconcentration when it is not only in thesolid solution and is a part of complex
carbide (Cr, Fe) 7C3, but forms separate
1
2
VC carbides in the form close to spherical.
The maximum size of carbides is 2, 5-6, 8
microns; the average size is 1.0-2.8 microns. Vanadium carbide is on chromium
eutectic carbides.
With increasing chromium, carbon
content and cooling rate, the volume fraction (from 58,8,0 to 27.6%) and primary
austenite dendrites sizes (the average size
from 13.7 to 28.0 mm) decline, the dispersion and the volume fraction of aus33btenite--chromium carbide eutectic increase (Fig. 2a, b). Eutectic microhardness
changes slightly 6.0-6.8 GPa. Hardness
and wear resistance increase.
The cooling rate increasing causes
martensite quantity reduction, butamount of austenite, at the same time,increases. This can be explained by matrix chemical composition changing:
chromium content increases and ironcontent decreases, vanadium content
changes slightly.
The increasing of chromium concen4
4
tration in the alloy is accompanied by
Fig. 1. Types of chrome-vanadium iron structures: 1 – A dendrites and eutectic
chromium content from 10% to 15%+ (Fe, Cr, V) 7C3 + VC; 2 – eutectics + VC and + (Fe, Cr, V) 7C3 + VC;
increasing in the metallic matrix of aus3 – eutectics + (Fe, Cr, V) 7C3 and + (Fe, Cr, V) 7C3 + VC (a - dry SCM;
tenite--chromium carbide eutectic andb - chill); 4 – excessive VC carbides and eutectics + VC (fibrous form),
reducing iron concentration from 87 to+ (Fe, Cr, V) 7C3 + VC; 5 – excessive VC carbides and eutectics + (Fe, Cr,
80%. This causes temperature reducingV) 7C3 and + (Fe, Cr, V) 7C3 + VC
at the martensite start Ms and results inmartensite quantity reduction. Chromium content in
The metallic matrix consists of austenite and marten- chromium carbides increases from 40% to 50%, but vasite, the ratio of these phases depends on the chemical nadium content reduces. Matrix microhardness decreases
composition of metallic matrix, which is defined by alloy from 7.1 to 4.4 GPa. Chromium carbide microhardness
composition and casting mould type. In chill casting decreases from 15.1 to 13.9 MPa.
chromium and vanadium content in
the matrix increases, that causes theincreasing of austenite proportion in
the structure.
Different structural types areformed in cast irons of the following
compositions, %: type 1 – 2,6 C;
14-20 Cr; 3 V and 3,2 C; 14 Cr; 3 V;
type 2 – 2,6 C; 14 Cr; 9 V; 2,6 C;
14-20 Cr; 9 V; 3 type – 3,2 C; 20 Cr;ab
3 V; 4 type –3,2 C; 14 Cr; V 9 andst
2.9 C, 17 Cr , 6 V; 5 type-3,2 C;
Fig.2. Microstructure of the 1 type chrome-vanadium cast irons,
20 Cr; V 9.
poured into dry SCM (a) and chill mold (b), x500
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5

Structure Features And Properties Of High-Alloy White Irons

The phase composition of cast iron samples, containing 3.2% C, 14% Cr, 3% V, depending on the coolingconditions is shown in Table 1.
Durability corundum is small and increases along withthe growing of metallic matrix microhardness and theamount of cast irons carbide phase volume. Durability ofchrome-vanadium cast irons containing periclase insignificantly depends on carbide phase volume and cast ironhardness, but depends on austenite quantity and its metastability towards straining martensitic transformation. Metastable austenite, being transformed into strain martensite
during the wearing, strengthens the surface and improves
durability (Table 2).
High chrome-vanadium cast iron durability underconditions of plastic push-off mechanism wear-out is due
to surface layers hardening because of phase transformations and phase straining hardening.
Table 2The influence of cooling conditions on the amount oftransformed austenite q p, a b ratio and wear resistancein corundum c and periclase p
Mould type

q p,%

a

b*

a

b

p
c
corundum periclase
Dry SCM
0
1,3
1,1
4,2
17,6
Wet SCM
0
1,7
1,3
4,9
43,8
Chill mold 23,0-25,02,22,05,4 108,0* b
a– microhardness of the metallic matrix before and after wear

The absence of straining martensitic transformation incast irons, poured into dry and wet SCM, can be explainedby a large amount of cooling martensite in the metallic matrix structure. Strain martensite formation during cast ironwear-out with corundum and periclase is relieved in the
structure with metastable austenite predominance.

The features of the 2nd and 3d class structure formation. The structure of the 2nd class is formed in castirons, containing 2.6% C; 14-20% Cr and 9% V; thestructure of the 3d class is formed in cast iron composition,%: 3.2 C, 20 Cr; 3 V. Cast iron structure consists of
two eutectics (refer to Fig. 1, 2 and 3). There is lessamount of carbide phase in eutectic + VC than in eutectics + (Fe, Cr, V) 7C3 and + (Fe, Cr, V) 7C3+ VC.
With the help of X-ray mapping concentrated eutectic
irregularities, determining their structure and properties,
were revealed (Fig. 3).
With chromium content of 14% in the alloy the metallic matrix chemical composition in vanadium eutecticof irons of the 2nd structural class is,%: 5,79 V; 11,4 Cr
and 82,0 Fe; ternary eutectic matrix composition is,%: 1,7
V; 13 9 and Cr 83,3 Fe.
The increasing of chromium content in the alloy up to
20,0% alters phase composition. Vanadium content reduces to 2.7% , but chromium content increases to 12.5%
in metallic matrix of eutectic + VC. The amount of vanadium and chromium in eutectic matrix + (Fe, Cr, V)
7C3 + VC increases up to 7.1 and 14.9%. That concerns
not only with chromium quantity increasing in the alloy,
but also with changes of volume fraction and vanadiumand chromium carbide content. The difference in eutectic
matrix compositions is shown in their properties: eutectic
metallic matrix microhardness + (Fe, Cr, V) 7C3 + VC isunder 1200-2000 MPa. Thus, changing the quantitative
ratio of eutectics with different properties it is possible toobtain various properties of the alloy in whole.
The volume fraction and size of binary eutectic varydepending on carbon and alloying elements content andcooling conditions. With increasing chromium content
and the cooling rate the volume fraction of ternary eutectic, dispersion eutectic + (Fe, Cr, V) 7C3 and + (Fe, Cr,
V) 7C3 + VC increase (see Fig. 1, 3a and 3b ).

Fig. 3. Electron micrograph and element distribution in the structural constitutes of cast iron with eutectics+ VC and + (Fe, Cr, V) 7C3 + VC

6—————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013.

5.

Kolokoltsev V.M., Petrochenko E.V.

In increasing cooling rate the density and dispersionof eutectic + VC increase (the number of vanadium carbides increases from 2705 up to 16410 1/mm2, interparticle distance decreases from 62 to 21 microns and carbide
size decreases from 6.5 to 2.8 microns).
Cooling martensite 72,2-90,0% prevails in cast ironstructure of 2nd and 3d classes, filled in dry and wet SCM.
Wear resistance of cast irons with corundum, poured
into SCM is 4,5-10,1 units, with periclase it is 10,8-28,7
units. Wear resistance of cast irons of the 2nd and 3d structural classes is higher than wear resistance of cast irons of
the 1st type. Wear resistance of cast irons of the 2nd classis higher because of the presence of 7,5-9,1% vanadium
carbides in the structure. Wear resistance of cast irons of
the 3d class is higher because of the presence 30,2-72,3%
complex chromium carbides. In the cast irons of the 1stclass volume ratio of vanadium carbides is 0,3-5,2%,
20,0-51,5% of chromium carbides.

In pouring into a mold the austenite proportion in ironstructure increases, straining martensitic transformation takes
place with corundum and periclase wearing-out, resulting insignificantly hardened surface (microhardness increases in
1.5-2.0 times). Wear resistance with corundum increases up
to 9,1-13,0 units and in periclase up to 19,8-60,6 units.
There are dendrites of excessive vanadium carbides inthe structure of irons of the 4th and 5th structural classes.
The structure of irons of the 4th class consists of excessive
VC carbides and eutectic + VC and + (Fe, Cr, V) 7C3 ++VC; of 5th class of excessive VC carbides and eutectic ++ (Fe, Cr, V) 7C3 and + (Fe, Cr, V) 7C3 + VC (see Fig. 1, 4,
5). The structure of the 4th type is formed in cast irons withthe following composition, %: 3,2 C; 14 Cr; V and 2.9 C 9,
17 Cr; 6 V; the structure of the 5th type is formed in cast irons
with the following composition, %: 3,2 C; 20 Cr; V 9.
Using X-ray mapping the element distribution between iron structural components of the 4th and 5th structural classes was detected (Fig. 4, 5).

Fig. 4. Electron micrograph of iron of the 4th structural class and element distribution in structural components

Fig. 5. Electron micrograph of cast iron of the 5th structural class and element distribution in structural components
of cast iron with eutectics + VC and + (Fe, Cr, V) 7C3 + VC
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7

Structure Features And Properties Of High-Alloy White Irons

With cooling rate increasing volume fraction andasizes of vanadium carbides,
binary eutectics decrease, thevolume fraction of ternary
eutectic increases. For example, in cast irons of the 4thclass in casting into dry SCM
volume fractions of structural components are as follows: 11.2% of vanadium
carbides, 53.8% binary eutectic, 34.9% triple eutectic.
In pouring into the mold thevolumetric proportions ofexcessive VC carbides, eutectic+ VC and+ (Fe, Cr, V) 7C3 + VC areb
9,3; 38,5 and 51,7%, accordingly.
In the case of high cooling speed (chill casting) thenature of excessive phasechanges in the alloy structure
containing 2.9% C; 17% Cr;
6% V. Complex carbide (Fe,Cr, V) 7C3 (Fig. 6b) becomesthe excessive phase instead of
vanadium carbide (Fig. 6a).
Wear resistance of castirons of the 4th, 5th structuralFig. 6. Micrographs of irons of the 4th structural class and spectrograms
classes is 8,0-14,0 units withof composition of excessive vanadium carbides (a) and chromium (b), x1000
corundum, 33,0-99,0 units
with periclase.
• eutectics + (Fe, Cr,) 7C3 and + (Fe, Cr, V) 7C3+
As a result of analysis of the chemical composition+VC, having a socket shape in cross-sectional view, and a
and cooling condition effect on the types of chromefan shape in longitudinal section;
vanadium iron structures in the studied concentrated in– according to the phase morphology, forming eutervals laws of morphology of excessive phases, eutectic
tectic:composition and metallic matrix were established, which• branched (fibrous ( + VC));
allowed to offer the classification according to the follow• compact (grained ( + VC));
ing criteria:• rod ( + 7 3).
- according to the metallic matrix type: mainly martensitic and martensitic- austenite;
References- according to the eutectic type:
1. Kolokoltsev V.M., Petrochenko E.V., Molochkov P.A. Complex effect• with eutectic + carbides of M7C3 type;on the structure of wear-resistant white cast irons in order to improve
operational stability of castings Vestnik Magnitogorskogo gosudar• with eutectic + carbides of MC type, such as VC;
stvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of No• with eutectic + M7C3 and MC, example (Fe, Cr)7C3
sov Magnitogorsk State Technical Univeersity]. 2004, no 4, pp. 23-29.
and VC, etc.;
2. Kolokoltsev V.M., Petrochenko E.V., Molochkov P.A. Structure andwear resistance of chrome-vanadium cast irons. Izvestiya vuzov.
– according to the number of eutectics and their
Chernaya metallurgia. [Izvestiya VUZ. Ferrous metallurgy]. 2004,
constitutive phases:
no 7, pp. 25-28.
• cast irons with double and ternary eutectics (3. Petrochenko E.V., Valishina T.S. The influence of the chemical composition, solidification conditions and heat treatment modes on microstructureand+ 3 ; +and ++ 7 3, + 7 3
features, mechanical properties and special properties of chrome vanadiand ++ 7 3);
um white cast irons. Izvestiya vuzov. Chernaya metallurgia. [Izvestiya• cast irons with two double and ternary eutectics
VUZ. Ferrous metallurgy]. 2009, no 2, pp. 39-42.
4. Petrochenko E.V. The relationship of the chemical composition, structure+M3C, + 7 3, + 7 3 +) and others;
and properties of complex-alloyed white irons in the as-cast condition.
– according to the eutectic morphology:
Izvestiya vuzov. Chernaya metallurgia [Izvestiya VUZ. Ferrous metallurgy].
• spherulitic shape eutectic + VC;
2012, no 3, pp. 51-55.

8—————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013.

5.

Vdovin K.N., Gorlenko D.A., Zavalischin A.N.

Vdovin K.N., Gorlenko D.A., Zavalischin A.N.

STRUCTURE CHANGES OF CHROMIUM-NICKEL INDEFINITE CASTIRONS IN HEATING
Abstract. The paper studies the processes taking place in chromium-nickel indefinite cast iron heating. Intervals of these processes and their changes depending on the heating rate were defined.
Keywords: indefinite cast iron, abstraction, phase transformations, carbides, carbon, austenite.

Chromium – nickel cast irons are assigned to theclass of alloy, wear resistant cast irons. Long run service
ability without damage and with minimal wear is the main
requirement for this group of irons [1].
There are considerable shrinkage and thermal stresses
in the castings after solidification and cooling due to the
production large mass and alloy cast iron low thermal
conductivity, which are supplemented by phase strain
hardeningtransformation. Therefore, the productusage in the as-cast condition is not desirable, in view ofpossible product destruction. Long (for about six months)
maturing in storehouses is one of the internal stress relieving methods. This is accompanied by a 30% stress relaxation. That is enough to increase service durability andpreserve production hardness and, consequently, durability. It is not always economically effectually, because
large areas are required. Tempering is the replacement of
natural maturing, wherein the relaxation processes aremuch faster and required time varies from several hours
to several days, depending on the product shape and massiveness. There is no common opinion concerning thetempering temperature. High temperature promotes more
rapid processes and a 70% residual stress relieving, butwherein there is a significant decrease in hardness.
Ageing lower temperature results in only a 30 ... 50%
stress relieving, wherein the hardness and wear resistanceare less reduced, but the possibility of early cracking increases [2, 3]. Therefore, it is necessary to choose theoptimal ratio between the structure, that determines product properties, and stresses by selecting the required tempering temperature.
Therefore, the aim of this work was to study the
structure formation and its properties in cast iron during
the heating after crystallization.
The studies were carried out on iron samples; ironchemical composition is shown in Table 1.
Table 1White iron chemical composition, %
C
Si
Mn
S
P
Cr
Ni
3.05-3.20 0.7-1.0 0.75-0.95 0.015 0.045 1.5-1.85 4.0-4.6
Samples were selected from the castings after crystallization. The microstructure was studied with the help of alight microscope MEIJI 2700 at 50- to1000-fold magnification using an image analyzer Thixomet PRO. The processes, taking place during cast iron heating were determined with the help of a thermal analyzer NETZSCHSTA 449 F3 Jupiter. The sample heating rate was from 5

to 30°C / min. The average microhardness of carbide andmetal base stock was defined using a PMT-3 device, with
100 g load. To fix high-temperature structure, samples
were cooled in water; thereby the secondary phase precipitation and austenite disintegration were mitigated.
Derivatograms exhibits some specific peaks, obtainedin a 5°C / min heating rate, corresponding to the structuraland phase transformations being accompanied by thermal
effects (Fig. 1).

Fig. 1. Derivatogram, obtained in cast iron heating
The first reaction to the heating is observed when thetemperature is in the range of 250-280°C, herewith withheating rate increasing, the range upper limit shifts tohigher temperatures. The second peak at a 5°C / min heating rate occurs when the temperature is in the range of
420 ... 540°C.
With heating speed rising, reaction temperature range
increases, along with the simultaneous temperature rising
proportionally to the heating rate within the intervalboundaries.
The third reaction to the heating is observed when thetemperature is in the range of 700 ... 740°C and the temperature at the beginning and at the end does not significantly depend on the heating rate. The fourth reactionwww.vestnik.magtu.ru. ——————————————————————————————————————————————

9

Structure changes of chromium-nickel indefinite cast irons in heatingtakes place at temperatures above 830°C, and the starting
temperature increases with the heating rate rising.
Exothermic peak at a temperature range of 260 to
280°C agrees with the secondary carbides releasing(Fig. 2a, b).

ab

Endothermic reaction occurring in the temperature
range of 350 to 550°C is in agreement with it (Fig. 1). The
solid graphite mass is proportional to the ageing time andheat temperature.

abcFig. 2. The iron microstructure in as cast state (a), x200
after tempered at 300°C, 15 minutes ageing and quenched(b), x200 volume ratio and carbides average length
dependence upon the heating rate (c)The temperature reduction decreases the diffusionrate, making carbides precipitation difficult, and the abstraction process almost completely stops when the temperature is below 180°C. The most intense secondary carbides precipitation occurs at 10 ... 15°C / min heating
rates (Fig. 2 c). The average microhardness of new extracted carbides increases from 810 to 1490 HV units.
Further heating speed rising produces a decrease insecondary carbides precipitation density, wherein theheating rate does not affect on the secondary carbides
size. The average carbides microhardness decreases dueto the «cast» carbides prevalence (Table 2).
Table 2The base stock and carbides hardness and microhardness
dependence on the heating rate
The average microhardness, HV
Heating rate, Hardness
/ min
HRC
base stockcarbides5
53,6
540…570
810…99010
52,1
520…550
830…1440
15
54,5
490…550
980…1490
20
54,0
440…480
860…110030
53,6
440…490
830…1090

Temperature rising mitigates carbides precipitationand is replaced by a more active process of fine flaky
graphite particles precipitation (Fig. 3a, b).

cFig. 3. The cast iron microstructure in as-cast condition (a)(not pickled.) X500; tempered at 550°C, 30 ageing
and quenched (b), (not pickled.) x500; graphite nodules
volume mass and average diameter dependence upon
the heating rate (c)The precipitation temperature range increasing resultsin the graphite quantity increasing with the heating raterising to 15°C / min, and their average size is reduced,
because of new impurities formation. With further heating
rate increasing, the graphite quantity is reduced due to theprecipitation time decreasing, and the average graphite
size grows at the expense of the precipitation on the existing impurities (Fig. 3 c).
With ageing time increasing, temperature ranges ofcarbides and graphite precipitation collide and their simultaneous formation becomes possible. Therefore, it ispossible to vary the required ratio of these phases by theheating rate and ageing time variation.
Endothermic reaction at the temperature of 720°
agrees withphase transformation, since other transformations and precipitations are mitigated by high heating rates. The subsequent high cooling rate stabilizes austenite and allows austenite and carbides, formed during
crystallization, to be observed in the structure.
Consequently, in heating above 720°C, the cast ironstructure is represented by austenite and carbides (Fig. 4),
which begin to dissolve at the temperature of about
830° , that is in agreement with endothermic reaction in
the curve (see Fig. 1).

10 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Vdovin K.N., Gorlenko D.A., Zavalischin A.N.

Fig.4. The cast microstructure after heating to 740° ,10 minutes ageing and cooled in water, x100aWith heating rate increasing, the temperature of carbides dissolving starting slightly rises and with the increasing of austenitizing temperature and ageing time, carbides
volume fraction decreases from 30.5 to 16.0% (Fig. 5).

bFig.6. Volume fraction (a) and average microhardness (b)of carbides, depending on the temperature
and ageing timeb
Fig. 5. Cast iron microstructure, x100: a – as-cast, b – after
heating up to 1100 , 60 min ageing and cooling in water
Along with the carbides fraction reducing (Fig. 6 a)their microhardness decreases, resulting from elements
redistribution between the eutectic carbides and the basestock (Fig. 6 b).
After 5 minutes ageing at the temperature of 900°C, theaverage microhardness falls from 1050 to 1000 HV units, at
a 30 minutes ageing it reduces to 840 VH units, and it does
not change at the further ageing. Ageing at the temperatures
1000 and 1100°C during one hour leads to the similar reduction of the average microhardness to 660 HV units.
Conclusions
1. Four thermal effects taking place during the process of indefinite chromium - nickel pig iron heating in
the temperature range of 20 to 1100°C are observed in thederivatograms.

2. The first effect at the temperatures of 250 to 280°C
matches to the secondary carbides precipitation. The
graphite releasing takes place at the temperatures of 420
to 540°C. The third thermal effect is observed at the temperatures of 700 to 740°C and is connected withtransformation. The latter effect occurs at the temperatures
above 830°C and agrees with carbides dissolving.
3. With heating rate increasing, temperatures at the
beginning and at the end of thermal effects shift. Temperature at the end of carbide precipitation shifts to the rangeof higher temperatures; temperature and range of graphite
separation boundaries increase, the temperature oftransformation is not significantly dependent on the heating rate, the temperature at the beginning of carbides dissolving increases proportionally to the heating rate.
4. In changing heating rate and temperature it is possible to control the phase relationship in indefinite chromium-nickel cast iron, which allows to adjust the tempering mode in order to obtain the required structures andproperties.
References
1.

2.
3.

Emelyushin A.N., Petrochenko E.V., Nefedjev S.P. Investigation of thestructure and impact-abrasive wear resistance of coatings of Fe-C-Cr-MnSi system, additionally alloyed with nitrogen. Svarochnoe proizvodstvo.
[Welding engineering]. 2011, no 10, pp.18-22.
Vdovin K.N., Gimaletdinov R.H., Kolokoltsev V.M. and others. Prokatnye
valki. [Forming rolls]. Magnitogorsk, 2005, 543 p.
Vdovin K.N., Zaitseva A.A. Heat processing effect on roll-foundry iron,modified with boron. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State
Technical Univeersity]. 2011, no 4, pp. 13-15.

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11

Hot stamping of titanium alloy sheet using resistance heating

Hamedon Z., Mori K.-I., Maeno T., YamashitaY.

HOT STAMPING OF TITANIUM ALLOY SHEET USING RESISTANCEHEATING
Abstract. A hot stamping process of a titanium alloy sheet using resistance heating was developed to improve the productivity.
As the heating temperature increased, the bending load decreased and the titanium alloy sheet was successfully formed at elevatedtemperatures. As the heating temperature increased, the springback of the bent sheet decreased. Although needle-shaped martensite
appeared at a heating temperature of 1050°C, the microstructure at a heating temperature of 880°C was similar to the as-received
sheet. When the heating temperature increased to 880°C, the hardness increased to 370 HV20. It was found that the hot hat-shaped
bending of the titanium alloy sheet using the resistance heating was effective in improving the productivity.
Keywords: Titanium alloy sheet, Ti-6Al-4V, hot stamping, resistance heating, springback.

1200
1000

80
Tensile strength

800
600
400

40
Elongation

0

200

600
800
1000
400
Heating temperature T [ºC]

Fig. 1. Variations of tensile strength and elongationof titanium alloy sheet with heating temperature
obtained by tensile test
The hot hat-shaped bending of the titanium alloy
sheet using the resistance heating is shown in Fig. 2. The
length and width of the sheet were 130 and 20 mm, respectively, and only the regions of 5 mm from both edgesof the sheet were in contact with the electrodes, i.e. insufficient heating. During resistance heating, the sheet is notin contact with the die, punch and blankholders in order toprevent the heating of these tools.

Blankholder

Punch

Electrode clamp
Blank

37.2

Copperelectrode20

An alpha-beta titanium alloy Ti-6Al-4V sheet (Al:
6.0%, V: 4.0%, Fe: 0.4%, O: 0.2%, C: 0.08%, N: 0.05%,
H: 0.015%) having 1.2 mm in thickness was bent at elevated temperatures. The mechanical properties of the titanium sheet were measured in the uniaxial tensile test atdifferent heating temperatures. A 50kN screw driven typeuniversal testing instrument was used in the tensile test.
The variations of the tensile strength and elongationof the titanium alloy sheet with the heating temperature
obtained by the tensile test are given in Fig. 1. As the heating temperature increases, the tensile strength decreases
and the elongation increases, particularly above 560°C.

20

200

2. Procedure of hot stampingof titanium alloy sheet
2.1 Experimental procedure

60

Elongation /%Tensile strength [MPa]1. Introduction
The usage of titanium alloy sheets for airplane parts
increases due to the high strength at high temperatures,
low density and high corrosion resistance, etc. Since thecold formability of the titanium alloy sheets is low, thesheets are generally formed at elevated temperatures. In
coventional hot stamping using a furnace, the productivity
is very low. The heating time of tools is about 2 h, and theheating time of the sheets in the furnace and the forming
time are about several minutes, respectively.
Rapid resistance heating was effective in the hot
stamping, only a time of 2 s to a heating time of 900°C.
Resistance heating is generally employed for preheatingof forging billets. Mori et al. have applied the resistanceheating to the warm and hot stamping of ultra-highstrength steel sheets [1], to the tailor die-quenching in hot
stamping for producing ultra-high strength steel formed
parts having a strength distribution [2], and to the spline
forming of ultra-high strength steel gear drums [3],respectively. In addition, Mori et al. [4] have developed apunching process of ultra-high strength steel sheets using
local resistance heating of a shearing zone. Although
Ozturk et al. [5] applied the resistance heating to hot
stamping of titanum alloy sheets, forming results werehardly shown.
In the present study, a hot bending process of a titanium alloy sheet using resistance heating was performed toincrease the formability and to reduce the forming load.
The springback and hardness of the hot bent sheet werealso measured.

Die

40

Insulator

Fig. 2. Hot hat-shaped bending using resistance heatingof titanium alloy sheet

12 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Hamedon Z., Mori K.-I., Maeno T., Yamashita Y.

Experimental conditions for hot bending
Sheet holder pressure [MPa]0.6Electrode clamping pressure [MPa]4

Bending speed [mm/s]

150

Current density [A/mm2]

12.5

Heating temperature T [ºC]

370 550 690 790 880

Heating time th [s]2.8 4.9 6.1 7.3 8.0

mm]

400
Bending area
200
20

40
60
80
100
Distance from edge [mm]1203. Results of hot stamping of titanium alloy
sheet using resistance heating
3.1 Stamped sheets

The variation of the electrical resistivity of the titanium alloy sheet with the heating temperature is shownin Fig. 3. The variation of the electrical resistivity for thetitanium alloy sheet is relatively small in comparison
with the steel sheet. It is not easy to uniformly heat the
sheet for the constant resistivity. The increase in resistance caused by the rise in temperature in local portions leads to the decrease in current, and thus the increase in temperature in these portions becomes small.
The increase in resistivity has the function of uniform
heating, and thus it is not easy to heat the titanium alloy
sheet.

Electrical resistivity [600

Fig. 4. Temperature distribution for resistance heatingin longitudinal distance of titanium alloy sheet

2.2 Heating behaviour of sheet

2000

800

0

Holding time at bottom dead centre t [s] 0, 3, 6

3000

1000

Heating temperature, T [ºC]

A CNC servo press with a maximum load capacity of
800 kN is synchronised to a DC power supply with capacitors for the resistance heating, and the time interval between the end of heating and the beginning of the bendingis only 0.2 s. The experimental conditions are given in
Table.

The hat-shaped bent sheet for resistance heating at
T = 880°C is compared with that for furnace heating in
Fig. 5. Although the springback and oxidation of the bent
sheet for furnace heating are remarkably large, these arevery small for resistance heating.

2500
Titanium alloy

1500(a) Furnace heating, th = 240 s.

1000
500
0

Steel
200
400
600
800
Heating temperature T [ºC]1000

Fig. 3. Variations of electrical resistivity
with heating temperature of titanium alloyand steel sheets
The distribution of heating temperature in the longitudinal direction of the titanium alloy sheet by the resistance heating is shown in Fig. 4. The heating temperature in the forming area is almost uniform, whereas bothedges of the sheet are not sufficiently heated by the contact with the electrodes.

(b) Resistance heating, th = 8 s.
Fig. 5. Comparison between bent sheets for furnace heating
and resistance heating for T = 880 ºC and t = 3 s

www.vestnik.magtu.ru. ——————————————————————————————————————————————

13

Hot stamping of titanium alloy sheet using resistance heatingcreases, the springback angle and the corner radius decrease. It is found that the hot bending is effective in preventing the springback of the titanium alloy sheet.

[º]

10

11.5
Radius86

11.0
Springback

4

10.5
2
0

400
200
600
800
Heating temperature T [ºC]

Corner radius /mm(a) Example of reflective lighting for cracks

12.0

12

Springback angle

The non-destructive fluorescent penetrant test of the
hat-shaped bent sheets was performed to check the occurrence of cracks. The reflective lighting of the bent titanium alloy sheet is shown in Fig. 6. Since the lighting was
not observed for the bent sheets, no cracks occurred forthe bent sheets.

10.0
1000

Fig. 8. Relationships between springback angle and heating
temperature and between corner radius and heating
temperature for t = 3 s

880 ºC

Fig. 6. Bent sheets during non-destructive fluorescentpenetrant test for t = 3 s

Bending load [kN]

The relationship between the bending load and heating
temperature is given in Fig. 7. Although the titanium sheet
fractured at room temperature due to low ductility, thesheet was successfully formed at elevated temperatures
above for T=370°C. As the heating temperature increases,
the bending load decreases. The bending load for T=880°C
is reduced from 6.5 kN at room temperature to 1.8 kN.

7
6

6

11.0
Radius4

Springback

2
0

3
Holding time t [s]

10.5
10.0
6

Fig. 9. Relationships between springback angle
and holding time and between corner radius and holding
time at bottom dead centre for T = 880°C

Fracture5

3.3 Microstructure and hardness of bent sheet

4

The microstructures of the bent sheet for the different
heating temperatures are shown in Fig. 10. Although needle-shaped martensite having a low strength appears for
T=1050°C, the microstructure for T=880°C is similar tothat for the as-received sheet.

3
2
1
0

Springback angle

3.2 Bending load and springback

Corner radius /mm

790 ºC[º](b) T=560 ºC 690 ºC

The relationships between the springback angle andholding time and the corner radius and holding time at thebottom dead centre for T=880°C are illustrated in Fig. 9.
As the holding time increases, the springback angle andthe corner radius decrease.

50 m

400
200
600
800
Heating temperature T [ºC]1000

Fig. 7. Relationship between bending load and heating
temperature for t=3 s
The relationships between the springback angle andheating temperature and between the corner radius andheating temperature in the hat-shaped bending for t = 3 s
are illustrated in Fig. 8. As the heating temperature in-(a) As-received(b) T = 880 ºC(c) T = 1050 ºC

Fig. 10. Microstructures of bent sheet for different
heating temperatures

14 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Hamedon Z., Mori K.-I., Maeno T., Yamashita Y.

Vickers hardness [HV20]

The distributions of the Vickers hardness in the longitudinal direction for the different heating temperatures areshown in Fig. 11. The hardness at T=550 and 785°C issimilar to that for the as-received sheet. When the heating
temperature increases at 880°C, the hardness increases to
370 HV20. Therefore, the optimum heating temperature is
T=880 ºC due the small springback, high hardness and noappearance of needle-shaped martensite.

400
350
300

880 ºC785 ºC

Bending
area

ContactwithDie
corner electrodex

0

Electrode

Electrode

T=550 ºC

As-received
Punch
corner

250
200
150
100
50

trodes, the coupled thermal-electric analysis of the resistance heating was performed using the commercial
FEM software ANSYS. In the calculation, the homogeneous contact between the sheet and the electrode was assumed. For the parallel electrodes, the distribution oftemperature is not uniform as shown in Fig. 13(a), whereas
the distribution of temperature in the bending area for the
inclined electrodes is almost uniform, 825 ± 20°C as illustrated in Fig. 13(b).

50
30
40
10
20
Distance from centre x [mm]Bendingarea

700
300 500
300 500 700
400 600 [ºC]
400 600 [ºC](a) Parallel electrodes(b) Inclined electrodes60

Fig. 11. Distribution of Vickers hardness in the longitudinal
direction for different heating temperatures

Fig. 13. Distribution of temperature in curved sheet
having thickness of 1.6 mm for current of 750 A.

4. Resistance heating of curved sheet
It is desirable in industry to bend curved sheets. For
the curved sheets, the distribution of current density in theelectrification direction becomes non-uniform as shown in
Fig. 12(a), and thus the distribution of temperature becomes
non-uniform. To obtain the uniform distribution of temperature, the electrodes are inclined as shown in Fig. 12(b).

Low density
High density

Electrode50

50

Electrode

Similardensity

5. Conclusions
The hot hat-shaped bending of the Ti-6Al-4V titanium sheet using resistance heating was carried out. The
productivity of bending of the titanium alloy sheet was
improved by the resistance heating, because the heatingprocess of the dies was eliminated and the heating time ofthe sheet was reduced. Hot bending using resistance heating was also effective in preventing the springback andoxidation of the titanium alloy sheet. The sheet was successfully formed at the elevated temperatures above
370°C and the bending load at a heating temperature 880°C
was reduce from 6.5 kN at room temperature to 1.8 kN. In
heating of the curved titanium alloy sheet, the distributionof temperature became more uniform, 825°C±20°C for
the inclined electrodes by 7°.
References
1.
2.

(a) Parallel electrodes(b) Inclined electrodes

Fig. 12. Distributions of current density in electrification
direction of curved sheet for parallel and inclined
electrodes
To calculate the distributions of heating temperatureof the curved sheet for the parallel and inclined elec-

3.
4.
5.

Mori K., Maki S., Tanaka Y. Warm and hot stamping of ultra-high tensile
strength steel sheets using resistance heating, CIRP Annals – Manufacturing Technology, 54-1 (2005), 209-212.
Mori K., Okuda Y. Tailor die quenching in hot stamping for producing ultrahigh strength steel formed parts having strength distribution, Annals of the
CIRP–- Manufacturing Technology, 59-1 (2010), 291-294.
Mori K., Maeno T., Fukui Y. Spline forming of ultra-high strength gear
drum using resistance heating of side wall of cup, CIRP Annals – Manufacturing Technology, 60-1, (2011), 299-302.
Mori K., Maeno T., Fuzisaka S. Punching of ultra-high strength steel
sheets using local resistance heating of shearing zone, Journal of Materials Processing Technology, 212-2 (2012), 534-540.
Ozturk F., Ece R.E., Polat N., Koksal A. Assessment of electrical resistance heating for hot formability of Ti-6Al-4V alloy sheet, Key Engineering Materials, 473 (2011), 130-136.

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15

Applications of plane strain compression tests for identification of flow stress models of materials and for physical simulation…

Sztangret M., Pietrzyk M.

APPLICATIONS OF PLANE STRAIN COMPRESSION TESTSFOR IDENTIFICATION OF FLOW STRESS MODELS OF MATERIALSAND FOR PHYSICAL SIMULATION OF METAL FORMING PROCESSES
Abstract. Possibility of application of the plane strain compression test (PSC) to the determination of the flow stress was evaluated. It was shown that distributions of strains and stresses are very nonuniform, that makes interpretation of results difficult. Inverse
analysis eliminates effects of inhomogeneities but in the case of the PSC it involves high computing costs. To improve the efficiencyof the analysis PSC was simplified to 2D model. Application of the PSC test to physical simulations of multi pass rolling is discussed
in the paper, as well.
Keywords: plane strain compression, flow stress, identification, physical simulation.

1. Introduction
The design of new industrial forming technologies isfrequently based on numerical and physical simulations [1].
This approach allows to consider a variety of technological variants and to find the best solution in relatively shorttime and with low costs. In the case of metal forming processes the flow stress model used in simulation has an
essential influence on the accuracy of simulations. Problem of selection and identification of the flow stress model has been discussed in numerous publications, see forexample [2-4]. Flow stress models usually contain coefficients, which have to be determined on the basis of plastometric tests. Due to low costs the axisymmetric compression is the most commonly used plastometric test [4,5].
Plane strain compression (PSC) is the test, which have one
important advantage: the state of strains in this test is similar to that occurring in flat rolling processes. On the other
hand, due to very inhomogeneous strains, stresses and temperatures in this test interpretation of results of the planestrain compression is very difficult, what prevent its wide
applications. Discussion of capabilities and limitations of
the PSC test is the main objective of this paper.

ab

2. Plane strain compression
2.1. General idea
Plane strain compression (PSC) is one of the plastometric tests, which is used for determination of the flow
stress. In his test a cuboid sample is compressed between
two flat dies, see Fig. 1a. This test permits large plastic
deformation and the state of strains is similar to that,which occurs in the flat rolling process (Fig. 1b). The planestrain state is obtained due to two factors. The low width of
the sample (b) – to width of the die (w) ratio prevents flowof the material in the width direction. It is similar to the flat
rolling, where low length of contact (L) – to width of the
strip (b) ratio fosters elongation and prevents spread. Influence of the so- called rigid ends is another factor,
which constrains spread and involves plane strain state.
Rigid ends are the parts of the sample beyond the area
under the die. These parts are not compressed, therefore,
they do not have tendency to spread. Moreover, when thesamples are heated by resistance heating (eg. on Gleeble3800) these parts are in lower temperature than the area
under the dies and their resistance to deformation is higher. Due to all these discussed facts PSC is frequently usedas physical simulation of the flat rolling process.

Fig. 1. Schematic illustration of the PCS test (a)and flat rolling process (b)Plane state of strains, which is not reachable in otherplastometric tests, has for years inspired the scientists tovarious applications of the PSC tests. Identification of
the flow stress model is one of such applications andinvestigation of the microstructure evolution is anotherexample. Among several research laboratories involved
in investigations based on the PSC tests a team led byprofessor Sellars at the University of Sheffield should be
mentioned. During 50-ies and 60-ies of the last century
this test was commonly used there for investigation ofmaterials and fundamental works on microstructure evolution [7] and on flow stress models [8] were a result of
this research.

16 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Sztangret M., Pietrzyk M.

It should be emphasized, however, that various disturbances make interpretation of results of PSC tests very
difficult. These tests are characterized by large inhomogeneity of deformation (Fig. 2a), which is caused by complex shape of the deformation zone (Fig. 1a) and by theeffect of friction. Beyond this, heat generated due to plastic work and friction, as well as heat transfer to the tools
and to the surrounding, cause strong inhomogeneity of thetemperature in the sample (Fig. 2b).

sents deformation work [10]. It is seen that minimum of
this work exists for certain height of the sample. Left tothis point an increase of the work is caused by the effectof the friction, which contributes more for lower samples. Right to this point an increase is caused by the effect of the rigid ends, which is larger when the ratio of
the height of these ends with respect to the width of thesample increases.
240

20 s-1aflow stress, MPaa200

0.5 s-1

160

3 s-1

2.5 mm
5 mm
10 mm

120

temperature 300oC
0

b

0.4

0.8

1.2

1.6

2

strain76

PSC testbFig. 2. Distribution of strains (a) and temperatures (b)in the PSC test
Further analysis of the PSC tests has shown that theflow stress determined from this test as ratio of the force(F) with respect to the contact surface (S) is sensitive tothe parameters of the test. It is in contradiction with thetheory of plasticity, which states that for isotropic material the flow stress is a property of this material independent of the type of the test, which was used for determination of this stress [9]. The flow stress calculated as the F/S
ratio in the PSC for aluminium samples with various initial heights is shown in Fig. 3.
Plots in Fig. 3a represent an influence of the height ofthe sample on forces and calculated flow stresses. Carefulanalysis of these plots shows that at the beginning of deformation, when samples are higher, larger stresses areobserved for higher samples. It is due to the effect of therigid ends. When reduction of the height proceeds, thesamples become lower and the effect of friction increases.
In consequence, larger stresses are observed for lower
samples.
Average force plotted in Fig. 3b is calculated as anintegral of the force with respect to the strain and repre-

average force, kN

72

68

64

60

56
0

4

8

12

16

height of the sample, mm
Fig. 3. Stress (F/S) as a function of strain (a) and integral
of force with respect to strain (b) – various heightof the sample
Character of the material flow in the PSC tests is sensitive to the height of the sample, as well [10]. For low
samples (Fig. 4a) a side of this sample after deformation
has the shape of the letter D. For high samples (Fig. 4b)
the material flows easier under the die and, in consequence, side of this sample after deformation has theshape of the Letter B.

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17

Applications of plane strain compression tests for identification of flow stress models of materials and for physical simulation…

ab

Fig. 4. View of the sample after PSC, initialheight 2.5 mm (a) and 15 mm (b)3.2. Sensitivity of the PSC results with respect
to the parameters of the test
The scientists working with the PSC tests have realized inaccuracies and problems connected with interpretation of results of this test, which are caused by inhomogeneity of deformation and temperature. A lot ofeffort was made to development of methods of correction of the PSC test results [7,8,11-16]. In the present
work finite element analysis of strains and stresses in
the PSC test was performed and selected results arepresented in Fig.5.
It is seen in Fig. 5 that the character of the distribution of strains and stresses changes drastically depending on the dimensions of the sample and the die. The
idea of the shape coefficient = w/h, which was introduced in [17], was used in the present work to characterize the dimensions of the deformation zone. Values ofthis coefficient were 2, 1 and 0.5 respectively in Figs 5a,5b and 5c. Decrease of the coefficient leads to more
uniform distribution of strains and stresses in the deformation zone. The effect of friction increases with decreasing. Deformation cross characteristic for compression in flat dies, for example for free forging, is wellseen for high coefficient (Figs 5a and b). Plastic deformation does not penetrate through the whole thickness of the sample in this case. Performed analysis
shows that deformation scheme in the PSC test is very
sensitive to the dimensions of the sample and the die,which makes direct interpretation of results very difficult. Thus, inverse analysis was applied in the present
work to solve this problem.

Fig. 5. Distribution of effective strains (left) and effective
stress (right) in the PSC test, initial sample height – to - widthof the anvil ratio equals 10/5 mm (a), 10/10 mm (b), 5/10 mm (c)18 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Sztangret M., Pietrzyk M.

3. Inverse analysis
Inverse analysis was used to determine the real flow
stress corrected against the effect of friction, rigid ends
and deformation heating in the PSC tests. The algorithm
descibed in [4] was applied. The flow stress values
corresponding to the subsequent strains were determinedusing optimization techniques. The quadratic norm of theerror between measured and calculated compression loads
was used as the objective function, see details in [4].
Inverse procedure requires several simulations of theplane strain compression test. Due to high computing
costs, 3D inverse analysis is practically impossible. As far
as compression of axisymmetrical samples is simulatedusing 2D mesh, plane strain compression requires 3D
mesh, which has to be very fine in the areas of contact
with the edge of the die, see Fig. 8. In consequence, thecosts of the PSC simulations are about hundred times
higher comparing to the axisymmetrical ones.

This correction allowed to use 2D model in simulation of the PSC tests. Analysis of the effectiveness of theinverse solution has shown that even simplified 2D simulation for one PSC test, using FE mesh with 220 elements,
requires about 5-10 min. Assuming that at least threetemperatures and three strain rates are necessary to determine relation of the flow stress on these parameters, nine
simulations of the test are needed for one evaluation of
the objective function. In consequence, full inverse analysis would still require very long computing times. In orderto make the analysis more efficient, the analysis was
performed in two steps [4]. In the first step the stressstrain function was determined in a tabular form for eachtest separately. This function can be considered a propertyof material for isothermal, constant strain rate conditions.
The functions introduced in the finite element program
together with correction for variations of temperature andstrain rate gives perfect agreement between measured andpredicted forces. The correction is given by the following
equation:
m
p

b

m
n

exp

Q 1
R T

1
Tn

,

(1)

where p is flow stress, b is isothermal constant strain
rate value of the flow stress, determined from the inverse analysis, R is gas constant, Q is activation energy,
n , Tn are nominal values of strain rate and temperature
Fig. 8. Finite element mesh in the 3D simulationof the PSC test

for a considered test, , T is current local value of strain
rate and temperature in the finite element node (or in theGauss integration point).
The results given in a tabular form, which were obtained in the first step of the analysis, were approximatedusing equation, which describes flow stress as a functionof strain, strain rate and temperature. The equation proposed in [18] was used:

These long computing times of the objective functionin the PSC tests prevented wide applications of this test
for the inverse analysis and evaluation of the flow stressof materials. Assessment of possibility of decreasing
computing times necessary for the PSC test simulations
and making the inverse analysis more effective is one ofthe objectives of the present work. Tomreach this goal, simulations were sim3 a n exp
exp q
1 exp q asat exp sat
3
, (2)
T
RT
plified to the 2D domain at the crosssection of the sample. A correction
is effective strain rate,
proposed in [19] was used. This correction accounts for where is effective strain,
the slight increase of the contact surface due to spread T is temperature in K.
The coefficients in equation (2) obtained from the apunder the die. This spread influences the current width ofproximation
were used as a starting point for the second
the sample, according to the formula:
stage of the inverse analysis. In this stage coefficients in
0,18
equation (2) were optimization variables. The startinghpoint was very close to the minimum and only few steps
b b0 1 C C,
of the simplex method were needed to find this minimum.
h0
In consequence, a noticeable decrease of the computing
costs was obtainedbf(1)
Inverse analysis was performed for the steel contain1
b0
ing 0.075%C, 1.375%Mn, 0.25%Si, 0.3%Ni, 0.15%Cu,,
C
0,18
0.15%Cr. The samples, which measured 20 25 35 mm,hf
werecompressed in the dies with the width of 16 mm at1h0
temperatures 800, 850, 900, 950, 1000, 1050 and 1100oC
wand at strain rates 0.1, 1 and 10 s-1. Three temperatures
where b0 is initial width, h0 is initial height, bf is final (800, 950, and 1100°C) were used in the identification
width, hf is final height, b is current width, b is current phase and remaining four temperatures were used for theheight, C is coefficient.
validation of the model. All tests were performed on the
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19

Applications of plane strain compression tests for identification of flow stress models of materials and for physical simulation…

Coefficients in equation (2) calculated using inverse
analysis for the investigated steel
A
n
M
asat
q
sat
8.363 3723.3 0.469 0.099 0.0642 7815.1 1.086 0.129
120

good agreement was obtained in a wide range of temperatures and strain rate. It can be concluded that inverse
analysis allows proper interpretation of results of theplane strain compression test and flow stress insensitive tothe inhomogeneities in the test can be determined.

850oC/1 s-1
80

force, kN

Gleeble 3800 simulator in the Institute for Ferrous Metallurgy in Gliwice, Poland. Selected results of force measurements and flow stress determination are shown in Fig. 9.
Coefficients in equation (2) obtained from the second
step of the inverse analysis are given in Table. The final
value of the objective function in the inverse analysis isgiven in the last column of this Table. This value is ameasure of the accuracy of the inverse solution.

950oC/1 s-1
950oC/0.1 s-1

60

1000oC/0.1 s-1
1050oC/0.1 s-1

40

strain rate 1 s-1

1100oC/0.1 s-1

20

100

force, kN

a
80

0
0

60

800oC
850oC
900oC
950oC

20

8

12

Fig. 10. Selected examples of comparison of forces
measured and calculated using FE program withequation (2), with coefficients in Table 1
as the flow stress model

1000oC
1050oC
1100oC

0
0

2

4

6

8

10

die displacement, mm
300

flow stress, MPa4

die displacement, mm

40bcalculations
measurements

200

100

strain rate 1 s-1

0
0

0.2

0.4

0.6

0.8

4. Physical simulation of hot rolling
Plane strain compression test has been for years used
for physical simulation of rolling processes. Temperatureand strain history can be easily reproduced in this test.
Samples can be quenched after each deformation stage
and microstructure can be investigated. However,problems with the interpretation of results of suchphysical simulation are similar to those discussed above
for the single stage compression. Deformation andtemperatures are inhomogeneous and, what is even more
important, the shape coefficient changes during the test
( = 0.667; 0.82; 1.17; 1.55 respectively for stages 1, 2, 3
and 4), what involves changes of the inhomogeneity of
deformation. Thus, the general principle followed by thescientists was to investigate the material in the centre of
the sample, assuming that strains and temperatures at thatlocation are close to the nominal values in the test
calculated as:

1strainFig. 9. Selected examples of recorded forces (a)and flow stress determined using inverse analysisof the PSC tests (b)Comparison of measured forces and those calculatedusing FE program with equation (2), with coefficients inTable 1 as the flow stress model is shown in Fig. 10. Veryhh2ln f ,hi3(3)where hi is initial height, hf is final height.
It seams that FE simulation of the multi stage PSC
test should help interpretation of the results.The 4 stagecompression test performed on the Gleeble 3800 in thetemperatures covering austenitic and ferritic range were
investigated. The samples, which measured 15 20 35 mm,

20 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Sztangret M., Pietrzyk M.

significantly from the homogeneous one (figure 14). It
can be concluded that interpretation of the physicalsimulation based on the PSC tests should be combinedwith the FE simulations of these tests.
1200

1

1000

temperature, oC

were compressed in the dies with the width of 10 mm.
Schematic illustration of the time-temperaturedeformation history is given in Fig. 11. Subsequent
deformations were carried out at temperatures
T1 = 1000°C, T2 = 900°C, T3 = 820°C and T4 = 66680°C.
Description of this test and results of measurements are
given in [20].
Several samples were deformed in the experiment.
The process was interrupted at various stages and samples were quenched to observe microstructure. All pictures of microstructure at the centre of the samples areshown in the publication [20]. Four of these pictures
showing microstructures right after deformation are repeated in Fig. 12. In the present work FE simulations of
the multi stage PSC test were performed, and distribution of strains were evaluated. Results of the 2D finite
element simulations of the 4th experimental stage PSC
test are shown in Fig. 13.
It is seen in Fig. 13 that different distributions ofstrains are observed for different stages of deformation.
The largest inhomogeneity of deformation is observed in
the 2nd stage. The most uniform deformation is in thelast stage. It seams, however, that problem of strain levelin the centre of the sample is even more serious. At thislocation the microstructure was analysed and it wasreferred to the nominal homogeneous strain in thecompression. It is seen that local strains differ

1

2
800

= 0.244= 0.404
3 3 = 0.325
2

4
600

4

= 0.244

quenching

400
200

temperature
deformation

00

100 200 300 400 500 600 700

time, sFig. 11. Schematic illustration of the time-temperaturedeformation history in the investigated multi-stage
PSC test [20]

a

b

c

d

Fig. 12. Microstructure after deformation at 1000°C (a), 900°C (b), 820°C (c) and 680°C (d)www.vestnik.magtu.ru. ——————————————————————————————————————————————

21

Applications of plane strain compression tests for identification of flow stress models of materials and for physical simulation…
8

8

6

6

5

5

4
3

4
3

2

2

1

1

0
0

1

2

stage 2

7

y, mm

y, mm

stage 1
7

3

4

5

6

7

8

0
0

9 10 11

1

2

3

4

5

6

x, mm
8
7

6

5

5

4
3

4
3

2

2

1

1

1

2

3

9 10 11 12 13

stage 4

7

6

0
0

8

8

stage 3
y, mm

y, mm

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

7

x, mm

4

5

6

7

8

0
0

9 10 11 12 13 14 15

1

2

3

4

5

6

7

x, mm

8

9 10 11 12 13 14 15 16x, mm

Fig. 13. Distribution of strains at subsequent stages of the multi-stage PSC test
Conclusions

FE simulations of the PSC tests combined with optimization techniques require very long computing
times. Low efficiency of this approach is its important drawback. Methods of improvement of thisefficiency should be searched in the future. Application of the metamodel, which proved to be efficientfor the axisymmetric tests [21], seems to be a promising solution and it will be an objective of the future
research.
Acknowledgements
Financial assistance of the NCN, project N N508
629 740, is acknowledged.

homogeneousFE

0.8

PSC test has several advantages, connected mainlywith capability to reproduce state of strains, which ischaracteristic for rolling. It is shown in the paper how
multi-stage compression allows to investigate microstructure evolution in multi pass rolling.
Due to inhomogeneity of deformation and temperature interpretation of results of the PSC tests is difficult. It prevents wider application of this test.
Finite element simulation combined with optimization methods allows realistic interpretation of resultsof the PSC test. The application of this solution is
twofold. The first is inverse analysis and identification of the flow stress model. The second is interpretation of results of physical simulations of rolling
processes.

0.7

strain

0.6
0.5
0.4
0.3
0.2
0.1
0
1

2

3

4

stage

Fig. 14. Comparison of the homogeneous strains
with strains in the centre of the sample calculatedby the FE code andReferences
1.
2.
3.
4.
5.

Sztangret ., Milenin A., Sztangret M., Walczyk W., Pietrzyk M., Kusiak J.,
Computer aided design of the best TR forging technology for crank shafts,
Computer Methods in Materials Science, 11, 2011, 237-242.
Grosman F., Application of the flow stress function in programmes forcomputer simulation of plastic working processes, J. Mat. Proc. Techn.,
64, 1997, 169-180.
Bariani, P., Dal Negro, T., Bruschi, S., 2004, Testing and modelling ofmaterial response to deformation in bulk metal forming, Annals of the
CIRP, 53: 573-594.
Szeliga D., Gaw d J., Pietrzyk M., Inverse analysis for identification ofrheological and friction models in metal forming, Comp. Meth. Appl. Mech.
Eng., 195, 2006, 6778-6798.
Hadasik E., Kuziak R., Kawalla R., Adamczyk M., Pietrzyk M., Rheologicalmodel for simulation of hot rolling of new generation steel strips for auto-

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motive industry, Steel Research Int., 77, 2006, 927-933.
Kuc D., Pietrzyk M., Rheological model of the austenitic steel subjected to
hot deformation, accounting for the microstructure evolution, HutnikWiadomo ci Hutnicze, 76, 2009, 607-610.
Sellars C.M., Physical metallurgy of hot working, w: Hot working andforming processes, (ed.), Sellars C.M., Davies G.J., The Metals Soc.,
London, 1979, 3-15.
Davenport S.B., Silk N.J., Sparks C.N., Sellars C.M., Development ofconstitutive equations for the modelling of hot rolling, Mat. Sci. Techn., 16,1999, 1-8.
Szeliga D., Matuszyk P., Kuziak R., Pietrzyk M., Identification of rheological parameters on the basis of various types of plastometric tests, J. Mat.
Proc. Techn., 125-126, 2002, 150-154.
Sztangret M., Pietrzyk M., Próba ciskania próbek p askich jako metoda
symulacji fizycznej procesów przeróbki plastycznej oraz narz dzie do
identyfikacji modeli reologicznych materia ów, Hutnik-Wiadomo ci
Hutnicze, 79, 2012, (in press)
Kowalski B., Method of interpretation of results of plane strain compression tests for evaluation of rheological parameters of materials, Praca
doktorska, AGH, Kraków, 2003.
Pietrzyk M., Lenard J.G., Dalton G.M., A study of the plane strain compression test, Ann. CIRP, 42, 1993, 331-334.
Pietrzyk M., Tibbals J.E., Application of the finite element technique to theinterpretation of the plane strain compression test for aluminum, Mat.

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COMPLAS 4, ed., Owen D.R.J., Onate E., Hinton E., Pineridge Press,
Barcelona, 1995, 889-900.
Silk N.J., Ban Der Winden M.R., Interpretation of hot plane strain compression testing of aluminum specimens, Mat. Sci. Techn., 15, 1999, 295-300.
Kowalski B., Sellars C.M., Pietrzyk M., Development of a computer codefor the interpretation of results of hot plane strain compression tests, ISIJ
Int., 40, 2000, 1230-1236.
Kowalski B., Lacey A.J., Sellars C.M., Correction of plane strain compression data for the effects of inhomogeneous deformation, Mat. Sci. Techn.,
19, 2003, 1564-1570.
Backofen W.A., Deformation Processing, Addison-Wesley 1972.
Gavrus A., Massoni E., Chenot J.L., An inverse analysis using a finite
element model for identification of rheological parameters, J. Mat. Proc.
Techn., 60, 1996, 447-454.
Kowalski B., Wajda W., Pietrzyk M., Sellars C.M., Sensitivity of constitutive
equations on strain and strain rate inhomogeneity determined for FE modeling of plane strain compression tests, Proc. 4th Conf. ESAFORM, ed.,Habraken A.-M., Liege, 2001, 561-564.
Pietrzyk M., Kuziak R., Validation of a model of plastic deformation of CMn steels in the two-phase temperature region, Steel Research International, 80, 2009, 767-778.
Sztangret ., Szeliga D., Kusiak J., Pietrzyk M., Identyfikacja modelu
materia u w prawie konstytutywnym w oparciu o rozwi zanie odwrotne z
metamodelem, Mechanik, 84, 2011, 32-36 (in Polish).

Pesin A.M.

SCIENTIFIC SCHOOL OF ASYMMETRIC ROLLINGIN MAGNITOGORSKAbstract. The article presents some results of studies of Scientific School of Asymmetric Rolling in Magnitogorsk. This paper
presents a classification and practical application of the asymmetric rolling processes. Further development of the asymmetric rolling
process is their use as a severe plastic deformation method for ultra-fine structures of the metal.
Keywords: scientific School, classification, asymmetric rolling, shear deformation, severe plastic deformation, parts of large
bodies of revolution, finite element method modeling.

Over 30 years Metal Forming Department at theHigher Professional Institution «Magnitogorsk State
Technical University» has been developing the scientificdirection of both current and new technologies of asymmetric plate rolling. This direction is headed by V. Salganik and dissertations for Ph. D degree on this theme
were written by A. Pesin (scientific supervisor M. Polyakov), V. Rudakov, V. Lunev, I. Vier, G. Kunitsyn (scientific supervisor V. Salganik), K. Kuranov, D. Chikishev(scientific supervisor A. Pesin), M. Chernyakovsky (scientific supervisors V. Salganik, A. Pesin). A. Pesin,
G. Kunitsyn (scientific advisor V. Salganik) and V. Salganik have written doctorate dissertations.
Since the foundation of Magnitogorsk scholar collaborations with V. Vydrin, L. Ageev (Chelyabinsk school),
V. Potapkin, V. Fedorinov, A. Satonin (Kramatorsk
school), S. Kotsar, V. Tretiakov, J. Mukhin (Lipetsk
school), V. Polukhin, A. Pimenov, V. Skorokhodov,
A. Traino, B. Kucheriaev have been established.
Nowadays several scientific projects have been carriedout together with K. Dyja, A. Kawalek from Technical University in Czestochowa (Poland), K. Mori from Technical
University in Toyohashi (Japan), V. Fedorinov, A. Satoninfrom State Engineering University in Donbass (Ukrain).
Metal Forming Department at the Higher Professional
Institution «Nosov Magnitogorsk State Technical University» has solved the following challenging issues: 1) theprocesses of asymmetric rolling have been classified; 2)statics, geometry and kinetics of vertically asymmetricdeformation site have been described; 3) special cases ofvertically asymmetric rolling have been investigated; 4) a
new integrated process of vertically asymmetric rollingand plastic bend of plate mill has been developed; 5) metal cross-section in horizontal asymmetric rolling has been
investigated; 6) new technical schemes in horizontallyand vertically asymmetric rolling have been found.
These days the research is focused on the following
directions: 1) shape control of the front end of the strip inplate rolling; 2) ultrafine grain structure in asymmetricintensive plastic deformation.
1. The classification processof asymmetric rolling
Due to different criteria, there are various approaches
to the cases, which take place in asymmetric rolling. The
scientists from Magnitogorsk scholar have suggested theclassification containing 3 hierarchal levels [1, 2]. The
upper level regards the causes of asymmetry occurreddeliberately or evoked by any disturbances. The next levelconsiders asymmetry in space in relation to either horizontal or vertical plane or to both of them. Finally, thelower level includes factors that can define asymmetry(geometric, frictional, elastic, kinematic, etc.) Asymmetryof different kinds often occurs simultaneously.
These days the technical approaches to purposeful
asymmetry in the vertical plane are widely spread andwww.vestnik.magtu.ru. ——————————————————————————————————————————————

23

Scientific School of Asymmetric Rolling in Magnitogorsk

promoted. The purposeful asymmetry is determined by
the following main factors:
1) geometric asymmetry specified by roll geometry
and inlet and outlet angles of the rolled stock; 2) kinematic asymmetry related to different velocity of roll periphery; 3) surface asymmetry concerned the quality andproperties of the surface on working rolls and strip and its
firm and rough surface; 4) physical and mechanicalasymmetry caused by different physical and mechanicalproperties between Young’s E-modulus and Poisson’s
ratio in the working rolls as well as mechanical and physical properties of rolled stock through thickness; 5) contact asymmetry developed due to substances that get into
the deformation site between the surfaces of the working
rolls and metal from outside; 6) temperature asymmetry

provoked by nonuniform heating of metal and working
rolls in rolling.
Asymmetry in the vertical plane alters kinematics inthe deformation site i.e. changes in length of backward
and forward creeps in the upper and lower rolls. Considering this fact, the following cases of asymmetric rolling aredepicted:
1) a common case, when the deformation site has got
2 kinematic areas – backward and forward creep but theirlength in the upper and lower areas aren’t equal (Fig. 2a);2) a semi-extreme case when a roll has two areas –backward and forward creeps and the other – only one
area: either backward or forward creep (Fig. 2b);3) an extreme case when one roll has only a backward
area and the other – a forward creep (Fig.2c).

Fig.1. Classification of asymmetric rolling processes

24 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Pesin A.M.

2. Statics, geometry and kinematics of verticallyasymmetric deformation site
Mathematical description of asymmetric deformationsite shows geometric ambiguity – while the radius of rolls
and strip thickness in the inlet and outlet are well-known,
the boundary points of the arc in the inlet and outlet crosssection are not depicted. Their rotation in the center of therolls causes this situation. The asymmetric deformation site
has got an area where friction goes to the opposite sides on
the opposed areas of the arcs. It gives a rotation moment in
the deformation site. As a result we get the above mentioned sectional rotation that is experimentally confirmed.
For a mathematical model of asymmetric rolling thebalance of the whole deformation site that was influenced
by contact loads and tensions of the outer parts of the strip
were very favourable [1-3]. As a result, we received thefollowing contact stresses through the length of the deformation site in common case (Fig. 3), where we observe
all three kinematic areas, including forward, backward
and mixed creeps. Both curves of contact stresses have
two breaks in the cross-section corresponding to neutral
one on each of the rolls. If one break on each curve is apoint of neutral cross-section, the other break is a certain
reaction on the opposite roll.

ab

3. New integrated process of verticallyasymmetric rolling and plastic bendof thick sheetcFig. 2. Scheme of asymmetric deformation site:a – common case, b – semi-extreme case,c – extreme case

The mathematical models enable to calculate an extreme case when the whole deformation site is a mixed
area, as well as a semi-extreme case when the deformationsite has got two areas: either forward and mixed or backward and mixed. The mathematical models were confirmed
experimentally by specialists in Czestochowa Technical
University in Poland [4]. We got the mathematical modelof integrated process of vertically asymmetric rolling andplastic bend for large rotary bodies (Fig. 4) [5-12].

Fig.3. Search of normal contact stresses
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25

Scientific School of Asymmetric Rolling in Magnitogorskab

Fig.4. Integrated process of asymmetric rolling and plastic bend: a – scheme,b – industrial experiment at Mill 4500at the OSJC «Magnitogorsk Iron and Steel Works»
The integrated process has three stages: verticallyasymmetric rolling, when the front end of the sheet does
not touch the detector roll; non-adjusted integrated process of vertically asymmetric rolling and plastic bend,
when the front end of the sheet touches the detector roll;adjusted integrated process of vertically asymmetric rolling and plastic bend, when the front end of the sheet separates from the detector roll.
This technology gives us rotation items as a cylinder segment with 45°-60° angle made of stainless steel
and following parameters: thickness – 40-220 mm,
width – 4300 mm, length – 5000 mm, radius of curve –1850-5000 mm.
The technology of large rotary bodies has been implemented at the OSJC «Magnitogorsk Iron and SteelWorks». The cover units have been manufactured andinstalled for two converters in the oxygen-converter plantat the OSJC «Magnitogorsk Iron and Steel Works». The
economical revenue of this technology is over $1 million.
This technology has a serious drawback such as astrong dynamic blow, when the front end of the sheet
touches and shifts over the fixed detector roll. The upperroll has abrupt rolling process that can damage theequipment. It is caused by rigid fixing of the detector roll.
To solve this problem new ways of this technology havebeen introduced: 1) roller aprons have been fixed to follow the detector roll; 2) the detector roll moves in thetarget track; 3) different speed of rolls have been used toincrease accuracy of the curve .
The mathematical modeling shows the fact that newtechnical and technological changes makes a dangerous
difference of moments decrease to 1.5-2.5 compared to the
fixed detector roll. This work has been supported by the
Grant of Analytical Target Program of the Russian Federation (grant 2.1.2/4390 Scientific development and enhancement of technical systems including new processes ofmetal items of large bodies of the fixed curve and by the
grant «Participation in youth scientific contest» (UMNIK2009) organized by the Fond of Small Business in scientificand technical sphere together with Federal Agency of Science and Innovations and Educational Agency.

4. The shape of the front end in plate rolling
These days Metal Forming Department at the Higher
Educational Institution «Nosov Magnitogorsk State Technical University» studies asymmetric modes to decreaseski-effect in plate rolling at Mill 5000 at the OSJC «Magnitogorsk Iron and Steel Works» (Fig. 5).

Fig.5. Ski-effect in plate rolling at Mill 5000 at the OSJC
«Magnitogorsk Iron and Steel Works»
In plate rolling the rolls, which move at similar speed,
bend vertically the front end of rolled stock. It is caused
by geometrical, frictional and temperature asymmetry
through the height of the deformation site. The rising vertical bend leads to the rolled stock stuck in the rolls ofoutlet table in the machine of preliminary melting. To
decrease the vertical bend of the front end of the rolled
stock in plate rolling it is necessary to apply kinematic
asymmetry – difference in speed of the working rolls.
In plate rolling with different speed of the working
rolls the bend can occur in the direction of the roll withhigher speed or in the direction of the roll with lower
speed. When the sheet decreases in thickness to 8-32 mm,
the impact of different speed of the working rolls can be
ambiguous. In the light draft the bend occurs in the direction of the roll with lower speed; in high draft the bend
occurs in the direction of the roll with higher speed. Moreover, under certain circumstances, there is a neutral point
when the vertical bend of the front end of the sheet does notoccur in rolling with different speeds. Neutral point is a
special point, which is not influenced by different speeds.

26 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Pesin A.M.

The scientists of the scholar developed a finite element mathematical model of stress and deformation metalstate in the asymmetric deformation site with different
temperature. The model was adjusted at Mill 5000 at the
OSJC «Magnitogorsk Iron and Steel Works». New
asymmetric modes of deformation have been elaborated
due to the impact of the shape of the deformation site on
the direction of bend of the front end of the sheet in rolling with different speeds.
5. Ultrafine grain structure in asymmetric intensive plastic deformation
Industrial technologies of flat long rolled stock produced of ultrafine grain materials can be based on the well
- known process of metal forming such as rolling. However, classic symmetric rolling has a number of drawbacks: monotoneness and the lowest level of deformation
so this process cannot be used for ultrafine grain structure.
One of the most efficient methods of intensive plastic
deformation for flat long ultrafine grain metal materials asa strand and sheet is asymmetric rolling. It includes methods of intensive plastic deformation and has the following
essential criteria to get an ultrafine grain structure: 1) highshearing deformation in each stage of treatment;2) high level of accumulated shearing deformation
e=2,0÷4,0; 3) non-monotoneness of deformation; 4) hightension in the deformation site to get flawless metal;
5) simultaneous impact on materials with high deformation of pressure and shift.
In the asymmetric site at the opposite arcs of the contact friction moves to the opposite sides that lead to thechange of cross-sections and shearing deformations which
are necessary for to get ultrafine grain structure. For in-astance, mathematical modeling shows the increase in
shearing deformations throughout the cross-section of thestrand as much 9 times compared to symmetric rolling(Fig. 6) [13]. The extreme cases of asymmetric rolling
have better effect of fine crushing of metal.
On the one hand, asymmetry leads to decreasing infriction negative impact that leads to deformation pressure
increasing. On the other hand, the site has considerable
shearing deformation and strain rate rises (Fig. 7).
Special schemes of mechanical deformation to get anultrafine grain structure can be applied: 1) asymmetric rolling, i.e. common case of asymmetry; 2) rolling-drawing, anextreme and non-extreme case of rolling; 3) deformation
between the fixed element and driven roll that is also an
extreme and non-extreme case of rolling. However, processes of asymmetric rolling belong to those methods ofintensive plastic deformation where initial and final parameters do not coincide and it restricts it application.
The criterion of an ultrafine grain structure in asymmetric rolling: 1) scalar value

2
2 yy2
3

6 xy2 forflat deformation state which characterizes accumulated
intensity of the shift deformation and that is defined by 2
tensor components: pressure deformation yy and shift
deformation

xy ; 2) slope angleof vertical cross sec-tion. Target levels:
2;
45 .
Asymmetric rolling can increase the intensity of shift
deformation through the cross-section of the sheet (up to3.5) and can be used to get an ultrafine grain structure forstrands and sheets.

b

Strain
10%

30%

50%

70%

80%
Fig.6. Distortion of vertical lines of asymmetric and symmetric rollingwww.vestnik.magtu.ru. ——————————————————————————————————————————————

27

Scientific School of Asymmetric Rolling in Magnitogorsk

Fig.7. Field of strain rate in asymmetric and symmetric rolling
References
1.

2.

3.
4.

5.

6.
7.

Pesin
. Modelirovanie i razvitie processov asimmetrichnogo
deformirovanija dlja povyshenija jeffektivnosti listovoj prokatki. Dokt. Diss.
[Modeling and development of the processes of asymmetric deformation
to improve sheet rolling: thesis]. Magnitogorsk, 2003. 395 p.
Salganik V. ., Pesin. Asimmetrichnaja tonkolistovaja prokatka:
razvitie teorii, tehnologii i novye reshenija [Asymmetric rolling of thin sheet:the development of theory, technology and new solutions]. oscow:
MISIS, 1997. 192 p.
Pesin A.M. New technological solutions based on the modeling ofasymmetric rolling. Steel, 2003, no. 2, pp. 66-68.
Dyja ., Pesin A.M., Salganik W.M., Kawalek A. Asymetriczne
walcowanie blacli cienkicli: teoria, teclinologia i nowe rozwiazania: Seria
Monografie nr 137. Wydawnictwo Politechniki Czestochowskiej.
Czestochowa, 2008, 345 p.
Pesin A., Salganik V., Trahtengertz E., Drigun E. Development of theasymmetric rolling theory and technology / Proceedings of the 8-th
International Conference on Metal Forming. Krakow / Poland / 3-7
September, 2000. Metal Forming 2000. Balkema / Potterdam / Brookfield /2000. pp. 311-314.
Pesin A.M., Salganik V. ., E.M. Drigun, Chikishev D.N. Ustrojstvo dlja
asimmetrichnoj prokatki tolstolistovogo metalla. [Device for asymmetricalrolling metal plate]. Patent RF, no. 38646, 2004.
Pesin A.M., Salganik V. ., E.M. Drigun, Chikishev D.N. Ustrojstvo dlja
asimmetrichnoj prokatki tolstolistovogo metalla. [Device for asymmetricalrolling metal plate]. Patent RF, no. 2254943, 2005.

8.

9.

10.
11.

12.

13.

Pesin A., Salganik V., Sverdlik M., Pustovoytov D., Chikishev D.
Theoretical Basis and Technology Development of the Combined Processof Asymmetric Rolling and Plastic Bending. Proceedings of the 2011
International Conference on Mechanical Engineering and Technology UK
ICMET 2011, ASME Press, 2011, USA, pp. 95-98.
Pesin A.M., Salganik V. ., Chikishev D.N. Improvement of production
technology of large parts of bodies of revolution on the basis ofmathematical modeling. Proizvodstvo prokata. [Production of rolled]. 2007,
no. 3, pp. 34-40.
Pesin A.M., Salganik V.M., Dyja H., Chikishev D.N., Pustovoitov D.O.,
Kawalek A. Asymmetric rolling: Theory and Technology. HUTNIKWIADOMOSCI HUTNICZE. 2012, no 5, pp. 358-363.
Pesin A.M., Salganik V. ., Chikishev D.N., Drigun E.M. Razvitie teorii itehnologii poluchenija detalej krupnogabaritnyh tel vrashhenija:
monografija. [The development of the theory and technology of parts oflarge bodies of revolution: monograph]. Magnitogorsk: «NMSTU», 2010,
102 p.
Salganik V. ., Pesin., Chikishev D.N., Lokotunina N.M.,
Pustovoitov D.O. Prilozhenija teorii plastichnosti k razrabotke i analizu
tehnologicheskih processov [Applications of the theory of plasticity in thedesign and analysis process]. Magnitogorsk: «NMSTU», 2012, 251 p.
Pesin A.M., Pustovoytov D. ., Perehogih., Sverdlik. Simulationof shear strain in the extreme case of asymmetric sheet rolling. Vestnik
Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta
im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical
University]. 2013. no 1, pp. 65-68.

Kawa ek A., Dyja H.

ANALYSIS OF VARIATIONS IN ROLL SEPARATING FORCES
AND ROLLING MOMENTS IN THE ASYMMETRICAL ROLLINGPROCESS OF FLAT PRODUCTS
Abstract. The paper presents the results of investigation into the effect of roll peripheral speed asymmetry on the force and energy parameters of the process for the conditions of normalizing rolling of plates in the finishing rolling stand.
Keywords: numerical modelling; asymmetrical rolling; roll rotational speed asymmetry factor.

1. Introduction
An important problem that drives the upgrading ofplate rolling mills are increasing demands on the geometrical dimensions of finished products. These demands
force the manufacturers to implement roll gap control
systems that helps to maintain stability and improve thegeometrical parameters of rolled strip.
Works [1-4] have demonstrated that by using asymmetrical plate rolling process, improvement in the qualityof plate geometry can be achieved. The idea behind theasymmetrical rolling technology consists in taking ad-

vantage of the positive effects of the asymmetrical deformation zone, which include primarily the reduction of thetotal roll separating force and the enhancement of the
product service properties.
The asymmetrical rolling system relies chiefly on a
direct action being exerted on the strip in the deformation
zone, in which, owing to an asymmetry introduced to theworking roll peripheral speed, longitudinal tensile stresses
occur, whose effect is analogous to that of tension andback tension in continuous rolling mills. These stresses
have the effect of reducing the magnitude of unit pressurein the roll gap and enhancing the equalization of the non-28 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Kawa ek A., Dyja H.

uniform distribution of rolled strip thickness, at the costof the elastic properties of the rolling stand itself. At thesame time, the regulation of the distribution of thickness
over the strip length, flatness and the cross-sectional strip
shape occurs at a reduced total roll separating force [5-7].
Reducing the total roll separating force has a direct
effect of decreasing the elastic deflection of the mill housing and rolls, and an indirect effect on the roll gap shapethat determines the cross-sectional shape of rolled flat
products.
2. Selection of the kinetic and initial parametersof the plate hot rolling process

above 40%, whereas in the last passes the strip deformation is only at a level of a few percent. The rolling
moments in the first roll passes exceed the nominal moment value. The driving motors are exposed to overheating. The use of driving motor power in the subsequent rollpasses is lower from nominal, which allows the introduction of a difference in the rotational speeds of individual
working rolls in the range of 4-9% in the intermediate rollpasses and above 15% in the end roll passes.
Therefore, by introducing the asymmetric rolling system in the finishing mill of the Rolling Mill 3600 theachieving of favourable technical and economic effects (areduction of thickness deviations over the band length andan improvement in the flatness of finished plate) should
be fully ensured, despite the non-stationary temperature
distribution in the deformed strip, which occurs under
actual conditions [9].

pm, [kN/mm]

The material used for tests was steel of the S355J2G3
grade. Working rolls of D = 1000 mm diameter and aconstant lower working roll rotational speed equal ton = 50 rpm were assumed for the tests. The asymmetrical rolling process was run by varying the rotational
3. Investigation results and their analysis
speed of the upper roll, which was lower than that of thelower roll. The range of variation of the roll rotational
Figures 1-8 illustrate the effects of the working roll
speed factor, av =vl/vu (where vl, vu – the rotational speed peripheral speed asymmetry factor, av, being variable in theof the lower roll and the upper roll, respectively) was range 1.01-1.15, and of the relative reduction =0.08-0.50,
1.01-1.15. A strip shape factor of h0/D = 0.05-0.018 was for the feedstock thickness range under investigation
assumed. The range of relative rolling reductions applied (h0/D = 0.050-0.018), on the magnitude of unit pressures
was = 0.08-0.50.
p m [kN/mm]. As shown by data in Figs. 1, 4 and 5, forMoreover, the following input data were taken for the feedstock of the greatest thickness, i.e. h0=50 mm
simulation: tool temperature, 60 C; ambient temperature, (h 0/D = 0.050), rolled asymmetrically with asymmetry
20 C; friction coefficient, 0.3; friction factor, 0.7; the factors from the range of av=1.01-1.15, no decrease in thecontact thermal conductivity, tool = 3000 [W/Km2]; and unit pressure, pm, was observed; just the opposite, even aslight increase in its magnitude occurred. This was caused
the heat transfer coefficient, surface = 100 [W/Km2].
The temperature of the rolled strip was varied de- by the non-uniform deformation over the strip height andpending on the initial height h0 within the temperature by the different lengths of the contact arc, ld, as a result of
the large bending of the strip on exit from the deformation
ranges for normalizing rolling:zone. The application of rolling reductions of 0.15 reh0 = 50 mm, the rolling temperature T = 950°C,
sulted in a reduction of unit pressure magnitudes from ah0 = 27 mm, the rolling temperature T = 900°C,
few percent (for =0.20) up to approx. 8% for the larges
h0 = 18 mm, the rolling temperature T = 880°C.
The parameters describing the physical features of values of the asymmetry factor, (Figs.1, 6-8).
steel were adopted based on the
100
material database enclosed to theForge2008® program [8], and90
were as follows: thermal conduc80
tivity, 35.5 W/(m·K); specific heat,
778
J/(kg·K);
steel
density,70
7 850 kg/m3; emissivity, 0.88.
60
In order to implement asymmetrical rolling in the conditions of50
existing Rolling Mill it is necessary
40
to consider conditions prevailing inthat Rolling Mill and apply one of30
the newest, proven numerical
20
methods for analysis.
On the date base given from
10
industrial conditions said, then in0
the finishing mill of the Rolling
1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15
Mill 3600 uneven loading of thedriving motors is used. “Rough”
av
wire rod (i.e. the strip obtained inFig. 1. Effect of the asymmetry factor av on the magnitude of the average roll separating
the break-down stand) in the firstforce pm for different relative rolling reduction values and a constant strip
two passes is deformed with relashape factor of h0/D = 0.050
tive rolling reductions as high as
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29

Analysis of variations in roll separating forces and rolling moments in the asymmetrical rolling process of flat products

For the h0=27 mm thick (h0/D=0.027) feedstockrolled asymmetrically, using the least rolling reductions of=0.08-0.10, no decrease in the unit pressure magnitude
was observed for the entire asymmetry factor range of
av=1.01÷1.15 as a result of introducing asymmetric rolling; quite the opposite, a slight increase in the value of pm
occurred (Figs. 2 and 4). For rolling reductions >0.10, adrop in the unit pressure magnitudes by as much as approx. 11% was found for =0.15 and av=1.15 upon introducing asymmetric rolling (Figs. 2 and 5).
The application of asymmetric rolling for the h0=18 mm

thick (h0/D=0.018) feedstock and asymmetry factors ofav>1.01 resulted in a decrease in the average pressure
magnitude by approx. 8% (for av=1.15) already for thelowest rolling reductions used, i.e. =0.08. After applying
rolling reductions from the range of =0,15-0.30 with
av=1.15, the pressure decrease was even greater, reachingnearly 22% (Figs. 3, 5 and 6). For rolling reductions of=0.40-0.50 and with small asymmetry factor values of
av=1.01-1.03, no pressure force decrease was found,
whereas for av>1.05 a pressure force reduction occurred,
which was greater than 12% (for =0.40), Figs. 3, 7 and 8.

7060

pm , [kN/mm]

50
40
30
20
10
0
1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

av

Fig. 2. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different relativerolling reduction values and a constant strip shape factor of h0/D = 0.027
7060pm, [kN/mm]

50

40

30

20

10

0
1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

av

Fig. 3. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different relativerolling reduction values and a constant strip shape factor of h0/D = 0.018
26

pm , [kN/mm]

23

Ho/D=0.05

Ho/D=0.027

Ho/D=0.018

20
17
14
11
8
5
1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

av

Fig. 4. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different
shape factor of h0/D and relative rolling reduction = 0.08

30 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Kawa ek A., Dyja H.
5045pm , [kN/,mm]40

Ho/D=0.05

Ho/D=0.027

Ho/D=0.018

35
30
25
20
15
10
5
1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

av

Fig. 5. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different
shape factor of h0/D and relative rolling reduction = 0.15
60
55

Ho/D=0.05

pm , [kN/mm]

50

Ho/D=0.027

Ho/D=0.018

45
40
35
30
25
20
15
1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

av

Fig. 6. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different
shape factor of h0/D and relative rolling reduction = 0.30
80

Ho/D=0.05

pm , [kN/mm]

70

Ho/D=0.027

Ho/D=0.018

60

50

40

30

20
1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

av

Fig. 7. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different
shape factor of h0/D and relative rolling reduction = 0.40
95

Ho/D=0,05

pm, [kN/mm]

85

Ho/D=0,027

Ho/D=0,018

75

65

55

45

35
1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

av

Fig. 8. Effect of the asymmetry factor av on the magnitude of the average roll separating force pm for different
shape factor of h0/D and relative rolling reduction = 0.50

www.vestnik.magtu.ru. ——————————————————————————————————————————————

31

Analysis of variations in roll separating forces and rolling moments in the asymmetrical rolling process of flat products

M1, M2, [kNm/mm]

M1, M2, [kNm/mm]

The data in figures 1-8 indicate that for the h0/D strip
shape factor values investigated in this work, the effect of
the applied working roll peripheral speed asymmetry factor on the variation of the unit pressure magnitudes (ascomputed per unit width of rolled strip) is different anddepends on the remaining process parameters, namely thefeedstock thickness and the relative deformation used.
The effect of the asymmetric rolling process on themagnitudes and variations of rolling moments for particular working rolls and the total rolling moment is illustrated in Figs. 9-10.

It can be found from the moment magnitude distributions shown in these figures that the moment on the rollwith higher peripheral speed (the lower roll) is always
positive. This roll is always a driving roll. The rolling
moment on the roll with lower peripheral speed (the upperroll) may either be negative (then it becomes a drivenroll), have a zero value, or be positive. The introduced
asymmetry of roll peripheral velocities has a substantial
influence on the value of the rolling moments M1 and M2.
The greater feedstock thickness h0, the greater moment isrequired for carrying out the rolling process. This is dueto the greater absolute rolling reduction h in
the case of rolling thicker strips, at the same
3.00
M1, M2,
magnitude of relative rolling reductions in
2.75
av=1.00
particular passes. Depending on the magniM1, av=1.01
2.50
tude of the asymmetry factor av, at the same
2.25
M2, av=1.01
magnitude of the relative rolling reduction ,2.00
M1, av=1.02
the magnitudes of M1 and M2 change. The
1.75
M2, av=1.02
presented results of the investigation of the
1.50
M1, av=1.03
effect of asymmetric rolling process parame1.25
ters on the magnitudes of total roll separating
M2, av=1.03
1.00
forces (the average pressure per unit strip
M1, av=1.05
0.75
width) and the rolling moment distributions
M2, av=1.05
0.50
on particular working rolls were obtained on
M1, av=1.08
0.25
assuming a constant rotational (peripheral)
0.00
M2, av=1.08
speed of the lower roll and a reduced rota-0.25
tional (peripheral) speed of the upper roll.
M1, av=1.10-0.50
Such a method of asymmetric rolling cannot
M2, av=1.10-0.75
be used under the actual conditions of finishM1, av=1.15-1.00
ing mill operation, as the continual overloadM2, av=1.15
ing of the main rolling mill motor driving the-1.25
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
lower roll would result in its overheating (especially during summer months, at relatively
high ambient temperature in the drives hall)Fig. 9. Effect of the relative rolling reduction on the magnitude
and shutting it down.
of rolling moments for a constant strip shape
Therefore, the rolling process asymmetry
factor of h0/D = 0.05
should be introduced alternately by applying
1.50
a higher rotational speed of the lower and theM1=M2,
upper rolls in successive passes, which will
av=1,00
1.25
M1, av=1.01
cause the rolls to be alternately driving anddriven rolls, whereby their excessive over1.00
M2, av=1.01
loading will be prevented.
0.75

M1, av=1.02

0.50

M2, av=1.02
M1, av=1.03

0.25

M2, av=1.03

0.00

M1, av=1.05-0.25

M2, av=1.05-0.50

M1, av=1.08-0.75

M2, av=1.08

-1.00
0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

M1, av=1.10

Fig. 10. Effect of the relative rolling reduction on the magnitudeof rolling moments for a constant strip shapefactor of h0/D = 0.018

4. Summary and conclusions
From the investigation carried out, thefollowing conclusions have been drawn:
by introducing the asymmetric plate
rolling process through differentiating working roll peripheral speeds, depending on theasymmetry factor used, the magnitude of thetotal roll separating force can be reduced and,at the same time, a smaller elastic deflectionof rolling stand elements can be achieved;
thanks to the smaller elastic deflectionof the working rolls, finished plate withsmaller dimensional deviations across its
width and length can be obtained;
the asymmetry of the rolling process
should be introduced alternately by applying

32 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Kawa ek A., Dyja H.

a higher rotational speed of the lower and the upper rollsin successive passes, which will cause the rolls to be alternately driving and driven rolls, whereby their excessive
overloading will be prevented.
References
1.
2.

3.

Dyja H., Sa ganik A. M., Piesin A. M., Kawa ek A. Asymetryczne
walcowanie blach cienkich Teoria, technologia i nowe rozwi zania [M].
Wydawnictwo Politechniki Cz stochowskiej, (Poland), 2008. 345.
Kawa ek A., Dyja H., Knapi ski M. Wp yw asymetrycznego walcowaniana popraw
wska ników techniczno-ekonomicznych procesu
walcowania blach na gor co [J]. Hutnik Wiadomo ci Hutnicze. 2008, 6:
266-270 (in Polish).
Markowski J., Dyja H., Knapi ski M., Kawa ek A. Theoretical analysis of

4.
5.
6.
7.
8.
9.

the asymmetric rolling of sheets on leader and finishing stands [J]. Journalof Materials Processing Technology, 2003, 183-188.
Sinicyn V.G. Nesimmetrichnaja prokatka listov i lent [M]. Metallurgija,
Moskva, 1984, 165 (in Russian).
Kawa ek A. Analiza pól pr dko ci i pr dko ci odkszta cenia w
asymetrycznej kotlinie walcowniczej [J]. Hutnik Wiadomo ci Hutnicze.
2002, 12: 485-488, (in Polish).
Dyja H., Wilk K. Asymetryczne walcowanie blach i ta m [M]. Wydawnictwo
WMiIM Politechniki Cz stochowskiej, (Poland), 1998. 268.
Gorelik V.S., Nalcha G.I., Rudnev A.E., Klimenko I.V., Feofilaktov A.V.
Uluchshenie sluzhebnykh svojstv tolstykh listov putem osvoenija
tekhnologii asimmetrichnoj prokatki [J]. Stal’, 11, 1991, 41-44 (in Russian).
Forge3® Reference Guide Release 6.2, Sophia-Antipolis, 2002.
Kawa ek A. Asymetryczne walcowanie blach grubych w walcarcewyka czaj cej [J]. Hutnik Wiadomo ci Hutnicze, 2006, 6: 266-270, (inPolish).

Chukin M.V., Korchunov A.G., Gun G.S., Polyakova M.A., Koptseva N.V.

NANODIMENTIONAL STRUCTURAL PART FORMATION IN HIGHCARBON STEEL BY THERMAL AND DEFORMATION PROCESSING
Abstract. On the example of high carbon steel of grade 80, updated by boron, the ability of forming nanodimensional structural
constituents has been proved. Special types of thermal and deformation processing are used. The thin- plate pearlite structure, obtained in this way, according to modern material science concept is considered to be a nanomaterial where interlamellar spacing in aferrite-carbide mixture is a nanodimensional element. It is experimentally proved that interlamellar spacing decreasing takes place insteel, being investigated after heat treatment and further cold plastic deformation. The rate of interlamellar spacing, after heat treatment, and cold plastic deformation is 1,66, the rate of billet geometrical dimensions, before and after deformation, is 1,6. The results
obtained are used to achieve desired properties of high-tensile reinforcing bars of 9,6 mm in diameter for the new generation of concrete sleepers.
Keywords: Nanodimensional structural constituents, high carbon steel, pearlite structure, interlamellar spacing, thermal processing, deformation processing

Achievement of high quality and field reliability ofmetallic constructions is possible on the basis ofknowledge-intensive technologies of getting materials
with a new unique property package. Nowadays suchtechnologies are those, which allow obtaining ultrafine
and nanostructures, which considerably affect metal andalloy mechanical properties during the production of
hardware items of different purpose [1]. This investigation actuality is stipulated by searching of an effective
complex of impacts on billet microstructure with major
diameters (more than 10,0 mm) made from high carbon
steel to get the highest strength and ductility.
The aim of this work is to study peculiarities of getting nanodimensional structural constituents in the billet
from high carbon eutectoid steel of grade 80, updated byboron, after special types of thermal and deformation processing. The thin- plate pearlite structure, obtained in thisway, according to modern material science concept is
considered to be a nanomaterial with structural constituents of plate form. Interlamellar spacing in a ferritecarbide mixture is a nanodimensional element of steel
structure.
The subject matter of the chosen thermal processing
lies in heating and isothermal holding in the field of minimal stability of overcooled austenite with further coolingin lead hot melt. The thermal processing task is formed, inmajor diameter billets, steel structure, providing the capability of the highest hardening during the following deformation effect with large total deformation degrees.

The history of steel structural constituent fine crushing is known to be determined mainly by accumulation of
sharing deformation in processing. Considerable steel
structure fine crushing is achieved by large degrees ofplastic deformation close to 1. To provide such processing
conditions, repetitive cold plastic deformation was used.
The differential characteristic of offered deformation effect is that operation modes are appointed in such a way,that each deformation cycle initiates active dislocations
sliding and it provides additional fragmentation of microstructure and the highest hardening of thermally processed steel.
The billet of diameter 16,0 mm from high carbon
steel with carbon content of 0.8 % was used to carry out
the experiments. Thermal processing was realized withthe following parameters: reheat temperature range was
930°C to 970°C; isothermal holding temperature range
was 4700°C to 550°C. Ageing time was chosen that way
to provide finishing diffusional decay of overcooled austenite in the preset temperature. Cold plastic deformation
was carried out with total deformation degree up to 60%.
Herewith the billet diameter decreased from 16,0 mm to
10,0 mm. Scanning electron-microscope analysis of thebars was done on the electron microscope JEOL JSM6490 LV with accelerating voltage 30 kW in modes ofsecondary and temporary reflected electrons in conditionsof Nano Steel Research Studies Institute of Nosov Magnitogorsk State Technical University. Quality and quantity
microanalysis was carried out on the metallographic mi-www.vestnik.magtu.ru. ——————————————————————————————————————————————

33

Nanodimentional structural part formation in high carbon steel by thermal and deformation processing

croscope Meiji Techno using computer system of images
analysis Thixomet Pro.
A steel structure in its initial state represents a ferritecarbide mixture with interlamellar spacing from 0,22 m
to 0,28 m (Fig. 1, a). Small sections of structurally free
ferrite are presented in microstructure (Fig. 1, b).

Previous cold plastic deformation experiments
showed that heat treated steel with interlamellar spacing
in a ferrite-carbide mixture from 0,12 m to 0,16 m
demonstrates the highest treatment and hardening capability [2]. Further decrease of interlamellar spacing in a ferrite-carbide mixture is observed in repetitive deformation
processing for heat-treated steel with such structure parameters (Fig. 3).

a

b

a

b

c

d

e

f

Fig. 1. Steel microstructure in its initial state
After thermal processing the microstructure consistedof a ferrite-carbide mixture and some quantity of structurally free ferrite as small islands on grain junction lines(Fig. 2, a) with interlamellar spacing of ferrite-carbide
mixture from 0,12 m to 0,16 m (Fig. 2, b).

Fig. 3. Heat-treated steel microstructure at different total
degree of cold plastic deformation:a – 21,8 %; b – 34,0 %; c
– 43,3 %; d – 58,8 %; e – 56,3 %; f – 60,9 %abFig. 2. Steel microstructure after thermal processing

In Fig. 4 one can see interlamellar spacing valuechange in a ferrite-carbide mixture depending on total
deformation degree.

Fig. 4. Total deformation degree effect on interlamellar
spacing value in a ferrite-carbide mixture

34 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Chukin M.V., Korchunov A.G., Gun G.S., Polyakova M.A., Koptseva N.V

From the obtained data one can see that decrease ofinterlamellar spacing which is proportional to a diameterdecrease of the billet, being processed, happens in thesteel, being investigated, after heat treatment and further
cold plastic deformation. The rate of interlamellar spacing
after heat treatment and cold plastic deformation is 1,66,
the rate of billet geometrical dimensions before and after
deformation is 1,6. Thickness of cementite and ferrite
plates in cold plastic deformation also decreases.
The results obtained are used in the established manufacturing for obtaining necessary properties for hightensile reinforcing bars of 9,6 mm in diameter for concrete sleepers of new generation [3, 4]. Thermal and deformation processes combine, firstly, the special kind ofthermal treatment of carbon steel, ensured the obtainmentof nanostructured materials, possessed of high strengthand ability to the subsequent deformation with high total
deformation. For the purpose of producing nanostructured
parts in the primary blank structure it intends to use thespecial kind of thermal treatment with mentioned above
heating temperature and further isothermal holding. And
secondly, highly productive constituent deformation process, activating free glide planes in every deformation
cycle is used, which leads to additional fragmentation ofmaterial structure and provides maximal strengthening of
the processed fittings. Deformation treatment modes set toactivate new free glide planes in every deformation cycle
which leads to additional dispersion of ultrafine grained
stricture and fragmentation of ferrite solder pads in pearlite.
In Fig. 5 you can see the structure of quality indices of ahigh-tension reinforcement for armoring concrete sleepers.

maintains sufficiently high ultimate elongation before
rupture (not less than 4 %). Stress relaxation in reinforcement reduces sharply and do not exceeds 2 % at1000 h under 20° and accounts for 75% of tensile
strength. Such complex of consumer attributes for end
production diam. 9,6 mm is a conceptually new kind of
product which cant be obtained by using tradition approaches to manufacture fittings for various applications.
Combination of mentioned treatment methods opens
up high technological possibilities for enhancement ofstrength and special reinforcement properties keeping
their high uniformity without steel alloying. The established high-technology production of high-tensile reinforcement with diameter of 9,6 mm for reinforcing of
concrete sleepers for modern highways possesses thenecessary characteristics of innovation technology. It’s
the first time of complex usage of modern science intensive thermal and deformation processes for influence on
carbon steel structure with forming nanostructured state.
Post graduate students Gulin A., Dolgiy D., Constantinov D., Lysenin A. took part in the presented investigations.
The research corresponds to the realization of complex project for high-technology production development.
This project is performed with participation of Russian
higher education institute (contract 13.G25.31.0061), theprogram of the strategic development of the university
2012–2016 years (the competitive support of The Ministryof Education and Science of the Russian Federation thestrategic development of
SEI HP ) and Grant in
the form of subsidy tosupport scientific researches (agreement
14. 37.21.0068).
References
1.

Chukin M., Koptseva N., Barushnikov M., Efimova Y., Nosov A., Noskov S., Kolomiets B.
Innovative potential of new ware
production technologies fromnanostructured steels. Vestnik
Magnitogorskogo
gosudarstvennogo tehnicheskogo
universiteta im. G.I. Nosova.
[Vestnik of Nosov Magnitogorsk
State Technical University].
2009, no. 2, pp. 64-68.
2. Lebedev V., Chukin M.,
Gun G., Korchunov A., PolyaFig. 5. Structure of quality indices of a high-tension reinforcement
kova M. Prospects of hightensile in manufacturing of large diameter wire rod at «MMK-Metiz» –Magnitigorsk Hardware and Sizing Works / CIS Iron and Steel Review,
Using such thermal and deformation processes in2011. pp. 18-21.
manufacturing of reinforcement for prestressed concrete 3. Chukin M., Gun G., Korchunov A., Polyakova M. Manufacturing prospects
constructions with enhanced apparent elastic limit andof high-tension reinforcement from high carbon steel. Iron and Steel. 2012.
December. pp. 8-15.
conventional yield strength enables to reach these values
S.,. Chukin M., Gun G., Korchunov A., Polyakova M. Highrespectively not less than 80 and 90 % of sorting ultimate 4. Ushakov
tension reinforcement for armoring new age concrete sleepers. The pathstrength minimum. In these conditions reinforcement
and track facilities. 2012. no. 11. P. 25-27.

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35

The development of engineering methods for calculating energy-power parameters of relatively thin strips hot rolling process

Satonin .V., orenko.G., Nastoyashchaya S.S., Perekhodchenko V.A.

THE DEVELOPMENT OF ENGINEERING METHODS FORCALCULATING ENERGY-POWER PARAMETERS OF RELATIVELY
THIN STRIPS HOT ROLLING PROCESS
Abstract. Based on the analytical solutions the engineering mathematical model of the relatively thin strips hot rolling processenergy-power parameters has been and expanded.Criterion evaluation has confirmed a sufficient degree of accuracy of the engineering techniques obtained. It was done on the basis of the skidding lines fields’ method which allows us to take into account twodimensional character of plastic metal forming absolutely.
Keywords: power parameters, relatively thin strips, roll gap, engineering mathematical model.

Further development of ferrous and non- ferrous metcross section area of conjugation lag with the length
allurgy is inextricably linked with the increasing automaof L and timing zone, with the length of L , aretion of relatively thin sheet and strip hot rolling process.
vertical, and parallel to the plane which is passing
Alongside with the numeral solutions some engineering
through the axis of the work rolls rotation;mathematical models of the technological scheme energythe current value of doubled 2Kx shear resistance andpower parameters are also of interest as the ones that arecoefficientof friction of the plastic zone along theable to ensure the rational combination of complexity,
lengthofplastic forming is constant and equal toperformance, and the reliability of the results.
As for engineering methods for calculating the rolling
their average integral estimates 2 and;of relatively thin sheets and strips one of the most freforming surface work rolls in zone plastic metal formquently used technique is the A.I Tselikov’s one, which ising approximated by chords, whereupon the current
based on the analytical description of the external contact
values of the angle x are constant (see Fig. 1);
friction conditions expressed as the Amontons-Coulomb
law. [1]. From the point of view of the conditions of thenormal axial stress x on height cross-section plastic
hot-rolling process realization it is more appropriate toforming zone not changed, and tangent components
use the Siebel’s law as the one providing
condition of non-exceeding tangential
contact stresses x shear resistance ofthe rolled metal
to the entire range ofpossible relative reduction. In this case itis necessary as well to take into accountavailability of an elastic recovery zone,
as well as the influence of the stress deviator tangential components that may
reach sufficiently large relative values.
The purpose of the work is to refine
and expand the engineering power parameters of the mathematical model process of relatively thin strips hot rolling.
Engineering mathematical model ofpower parameters of relatively thin strips
hot rolling process having been developed as similar to the methods of [1, 2]
is based on the following basic assumptions adoption:rolled strips plastic changes are twodimensional and temporally steady;deformation zone (Fig. 1a) includes
the area of plastic forming with thebclength of L and area of the elastic
recovery of the rolled strip with the Fig. 1. Settlement schemes of the deformation integrated center (a), and also
elementary volumes of metal in relation to engineering mathematicallength of L ;the boundaries of plasmodeling of power parameters of relatively thin strips hot rolling process
tic and elastic forming zones, and theallocated in a lag zone ( ) and in an advancing zone ( )36 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Satonin .V., orenko .G., Nastoyashchaya S.S., Perekhodchenko V.A.

stress deviatorchange in law close to linear andxtheir average integral evaluation corresponds to theexpression:

/2=2

/ 2.

(1)

Taking into account character of the accepted assumptions the equation of balance of metal elementaryvolume allocated in a zone of the lag (see fig. 1, a, b),
looks like:h -(+ d )(h x + dh x )+(2)

tg dx- 2 x dx = 0,

where
– are the current values of normal con,tact tension, normal axial and tangent contact tension, andcompression tension is accepted as positive values of tension
and; x , h –are the current quantities ofcontact corners and thickness of the rolled strip corresponding to certain dependences of a kind (we take into
account accepted assumptions):hh1

Proceeding from the law of external contact frictionused and neglecting infinitesimal of the second and moreorders, the expression (2) is transformed into a kind:

d

hx

dhx

(4)

2Kc 2 dhx / (2tq ) 0.

Following a full form of a plasticity condition record [1], the quantity of normal axial tension
can bepresented as:
2

4

4

4

4

2

2

2

k

,

2

1
where k– is the auxiliary variable providing
a form record simplification.
After substitution of the condition (5) in the expression (2), we will receive:

2

k

dhx d

Where

hx 2

dhx

0,

(6)

2 L / h – is the auxiliary quantity

characterizing influence of geometrical parameters and conditions of external contact friction in the deformation center.
Having transformed the differential equation (6) to a
kind:

2

( k

C ,

(8)

h x h02C() ln 0

2

k

0

,

(9)

where 0 – is tension quantity of a rolled strip back tension.
As a result of the substitution (9) in the condition (8)finally for normal contact tension
in a lag zone is
we have the following:

2

(

k

)ln(h0 / hx ) 2

k0. (10)

By analogy with (2) for an advancing zone (see Fig. 1 a,c) the differential equation of a condition of static balance of the allocated elementary volume looks like:

d

)(hx

dhx ) 2

dxtq x(11)

2 x dx 0,

and following that we will get the in accordance withabove mentioned (3)-(8):2( k) ln hx

C ,

(12)

where
– is integrations permanent that is determined
for the zone of passing, and based on the well-known
quantities of normal pin tensions in a section on the plas2 Kc ak
tic form destructing zone exit
1:
h x h1C2()ln 1 2

k

1

.

(13)

2

(5)
2

) ln hx

where C – is the constant of integration defined for alag zone which is preceded from known values of normal
contact tension in section to the deformation center en2 Kc ak
trance0:(3)h( x / L ).

dh

( k

h (

arctg (0,5 h / L );x

2)(dhx / hx ) d,

As a result of its integration we shall receive:(7)

where 1 – is tension quantity of a rolled strip front tension.
Finally in relation to the tension quantities which are
current on the length of advancing zone we have:2()ln(h / h1 ) 2

k

1

.

(14)

On the principle that the value of normal pin tensions
in a neutral section in thick h (see Fig. 1 ) are equivalentboth for the lag zone and for the one of advancing
in accordance with (10) and (14), it is
hx h

hx h

possible to write down:k2)ln(h 0 / h ) 2)ln(h / h ) 2

k

0
k

(15)
1,

From where after some mathematical transformations
the thickness of stripe in a neutral section h , and also extent of advancing zone L (see Fig. 1 ) can be defined as:

www.vestnik.magtu.ru. ——————————————————————————————————————————————

37

The development of engineering methods for calculating energy-power parameters of relatively thin strips hot rolling processhh0 h1 exp
ak ln(h1 / h0 )L

(hand issued from that the quantity of average integrals on
the length of plastic deformation zone of normal pin tensions
may correspond:(16)
1/ 2 Kc0/ 2Kc ) / (2 ) ;h1 ) L / h.

2

(17)

L

n

(1 / L )

as:

L

dx

dx ,

2 2

(18)

2 2

L

0

(21)

Taking into account the well-known values 2 ,,L , of radiuses R of working rollers and widths of therolled stripe the value of rolling total moment can be determined as:

having integrated the distributions of normal pin tensions(10) and(14) it is possible to define the quantity of the tense state coefficient n

n .

RB( L

2L )

RBL [1 2(hh1 ) / h].

(22)

Criterion estimation of authenticity degree of the decisions received (10) and (14) was exeLL
cuted with the use of the fields of skidh1 hx / L11(nak )lndx
akdx
ding lines method, allowing to take into
2Kc
L 0
h1
0
account two-dimensional character ofplastic metal deformation. Construction(19)
LL
h1 hx / Land subsequent analysis of the fields of
0
[(
)]dx
(ak
)dx
ak )ln(descriptions in physical plane and plane
2
h
K
c
0
L
L
of hodograph of speeds (Fig. 2) were produced
numerically in accordance with
As a result of integration (19) with the use of auxiliary
methodologies of works [2, 3].
variables (h1hx / L ) / h1 U1 , (h1 hx / L ) / h0 U2 ,As an example of numeral realization results of soluwe will get finally:tions offered are presented on a Figure 3
the comparisons of calculation distribuh
h
h h1
h h1
1
ak )
ak
n
(
ln
tions of current n values of the metal
h h1
h
h
2Kc
(20) tense state coefficient which were received by analytical decisions using (10),
h0 h
h
h0
h
h
0
0
ak
ak
ln
,
(14) and on basis of the skidding lines
h
h h
h
2 Kc
fields method [2, 3].
from where with an account of (10), (14):

b

L /h

10,0 ;

1,5 ;

0, 4 ;

0, 42 ;

1

/ 2Kc

0,0 ;

0

/ 2Kc

0,175

Fig. 2. he fields of descriptions in the physical plane of XOY(a) and planes of hodograph of speeds X V O'YV (b)as it applies to the process of the hot rolling of relatively thin stripes [2, 3].

38 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Satonin .V., orenko .G., Nastoyashchaya S.S., Perekhodchenko V.A.

quantity of a strip elastic deformation in section at theplastic forming exit zone;
is Poisson's coefficient,and elasticity model of the rolled strip material, whichtake into consideration its temperature.
Proceeding from dependences structure (20), (21),(23) and (24) force value at hot rolling of relatively thin
strips is defined as (and we take into account working
rolls elastic flattening and existence of a elastic restoration zone):

P=( L

Fig. 3 Settlement data, received according to theconsidered technique (1) and on the basis of the skidding
lines fields method of (2) distributions of the metal tension
coefficient current values.
The analysis of these results confirmed the sufficientdegree of reliability of the received engineering calculation procedure.
It should be noted that one of current trends of calculation engineering methods of power parameters development is the accounting of working rolls elastic flattening and existence of a strip elastic restoration zone not
only at cold, but at hot rolling as well [1, 2, 4]. In relation
to working rolls elastic flattening this approach can berealized by iterative determination of plastic forming zone
extent L and the subsequent determination of the elastic
deformed working rolls radius R :L= R h + x 2L + x L ; R = L2 / h,(23)

where x L = 8Rp c (1 - 2 ) / () is the auxiliary variable used for simplification of a form of record [1];is Poisson's coefficient and a model of working,
rolls material elasticity.
The accounting of existence of a rolled strip elastic
restoration zone in sections at the working rolls exit (see.
Fig. 1, a) can be carried out on the basis of algorithmic
sequence of a kind:

=2

1

1

L = R h1 ,

h1 =

(1-

2

)/

;
(24)

where
, 2 1 , h1 is the normal contact tension, doubled value of resistance to rolled metal shift and the+L / 2) ,(25)

Thus, owing to existence of functional interrelations= F(L ) and L = F(p c ) direct determination of
P force can be carried out iteratively using standard approaches [1, 2] at which in the calculations first cycle
working rolls are accepted to be absolutely rigid, normal
contact tension , the value of a plastic forming zone
extent L , are defined and after taking it into accountcalculation is repeated and so on. As convergence criteria assessment of the decision iterative procedure relative
degree of discrepancy of extents L in this and in previous calculation cycles was used.
Conclusions
On the basis of analytical decisions the engineering
mathematical model of hot rolling process power parameters of relatively thin strips is specified and expanded.
This model is distinguished by the correct accounting of
external contact friction conditions and also of tangentscomponents of a tension deviator influence indicators, aswell as accounting of rolled metal elastic restoration zone
existence. The criterion sufficient degree of authenticityof the decision is confirmed by the results of comparison
with the analogical quantitative estimations, which we got
on the basis of method of the skidding lines fields thatallow taking into account two-dimensional character ofplastic form destruction throughout metal at the relatively
thin stripes hot rolling.
References
1.
2.

3.
4.

Celikov A.I., Nikitin G.S., Rokotyan S.E. Teoriya prodol'noj prokatki. [Thetheory of longitudinal rolling]. Moscow : Metallurgiya, 1980, 320 p.
Fedorinov V.A., Satonin A.V., Gribkov E.P. Matematicheskoe modelirovanie napryazhenij, deformacij i osnovnyx pokazatelej kachestva pri prokatke otnositel'no shirokix listov i polos : monografiya. [Mathematical modeling of stresses, strains, and the main indicators of the quality of the rolling sheets and relatively broad bands: monoraph]. Kramatorsk : DGMA,
2010, 243 p.
Potapkin V.F. Metod polej linij skol'zheniya v teorii prokatki shirokix polos :monografiya. [The method of slip-line field theory rolling in broad bands:
Monograph]. Kramatorsk : DGMA, 2005, 316 p.
Kozhevnikova I.A. Garber E.A. Proizvodstvo prokata. Razvitie teorii
tonkolistovoj prokatki dlya povysheniya e'ffektivnosti raboty shirokopolosnyx stanov. [Production of rolled products. The development of the theory of sheet rolling to improve the efficiency of broadband mills]. Moscow :Teplotexnik, 2010, vol. 1, kn. 2, 251 p.

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39

3d model of cutting by rolling cut type shears

Borovik P.V.

3D MODEL OF CUTTING BY ROLLING CUT TYPE SHEARS
Abstract. 3D model of rolling cut process by shears on the base of finite element method is developed and dependence of
maximum cutting force on the knife curve radius is detected. Suggestions directed to increase of productivity of shears arerecommended.
Keywords: shears, rolling cut, curved knife, cutting force.

Separation operations are widely used in rolling production and establish quality and cost price of metal
products. One of such separation operations is thick sheet
cutting using the rolling cut type shears [1, 2].
Rolling cut is used for longitudinal and sectional cutting of sheets. With this type of cutting one can almost
avoid deformation of cutting edge at circulated shear
movement [1, 2].
As experience shows, at rolling cut a dependence of
cutting force on the starting point of the cutter going into
metal has got apparent peak (Fig. 1,b) that can be explained by less value of cutting angle. Because of various
model shears difference between maximum and fixed
cutting force can be about 30…60%. This fact helps inincreasing shears metal content.

Therefore, to give full image of rolling cut process it
is necessary to use modern theoretical approaches andmethods among which finite element method (FEM) has
got a special role [5, 6].
The purpose of this work is to develop 3D model ofrolling cut process on the base of finite element methodand detect factors affecting the cutting force value.
To get to the purpose set theoretical researches havebeen made using ABAQUS software. 3D model has beendeveloped for this describing cutting process of sheetswith curved knife on the shears with rolling cut in Lagrange formula using ALE (Arbitrary Lagrangian Eulerian) mesh adaptation and including gravity.
A model (Fig. 2) is for extremely hard analytical rigid
body – a holder, a Table, upper curved and lower stationary knife, as well as deformable beam as a model of sheet
being cut.
And as an analog to real design of rolling cut typeshears a motion is transmitted to upper curved knife along
the specific trajectory and to the Table in vertical direction while the lower knife and a holder are fixed.
Deformable beam is a mesh of isoparametric an 8-nodelinear brick elements with reduced integration scheme andhourglass control, having the features of entire deformable material. Mesh configuration is irregular getting compacting in the shearing zone (Fig. 3).
Friction between contact surfaces models Coulomb’s
friction law. Herewith, constant of friction is fixed andcharacterizes the relation between contact pressure andequivalent shear stress.
Material fracture was simulated using a method of
elimination of elements from the calculations after theductility resources were over in accordance with ductility
curve [6].

Fig. 1. Scheme for rolling cut (a) and specificdependence of cutting force (b)There are technical decisions known [3, 4] that tend
to reducing the peak loads during rolling cut which ismade by changing the shears design. But such approach has low technical efficiency during manufacturing.
In present days due to advanced computational
tools and progress in theoretical researches simulation
techniques for different pressure treatment technological processes aiming to their thoroughly studying andimprovement are widely used.

Fig. 2. General view of cutting process simulation for sheets
using curved knife on rolling cut type shears

40 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Borovik P.V.

So, further researches have been directed to reveal thepossibilities of reducing such gap.

Fig. 3. Initial mesh configuration
For simulating in cutting processing they used steel
grade St2ps. Sheet depth is 50 mm, width – 2500 mm.
On the first study stage through famous methods[1,2,7] calculations of kinematic operation parameters ofshears have been made. Two-crank shears from NMBW
(Novokramatorsk Machine - Building Works) has beentaken as a model. Fig. 4 shows the calculated trajectory forreference point which afterwards has been put into amodel for simulating the upper knife motion.
In the studied model of rolling cut type shears a radius of curved knife in the initial point is 47m, and a clearance between knives in the initial point is 148 mm. Fig. 5
shows the simulation results.
As you can see from the results presented the maximum cutting force is 1,6 times more than steady cutting.

Fig. 4. Path the reference point of upper knife
In this way they changed the radius of knife curve atconstant clearance between the knives and kinematics ofsystem movement. The results revealed that increasing theknife radius promotes reducing the force in the starting
cutting moment and its simultaneous raise at the end of
cutting (Fig. 6, ). Basing on the results achieved the dependence of maximum cutting force on the knife curve
radius was obtained (Fig. 6, b).

Fig. 5. Simulation results: a – knife position in moving of cams to 99°;b – stress-strained state of sheet in the same position; c – configuration after full separation of the sheet;d –cutting force N × mm dependence on rotation angle of cams
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41

3d model of cutting by rolling cut type shears– applied to the given shears design at cutting the sheets with maximum depth 50 mm
knife curve radius 80…200 meters allows to
obtain more stable force distribution during the
cutting process;– in given conditions maximum cutting
force relatively to curve radius of 47 m reduces
for 25…30 %, that indicates to real opportunity
to increase the range of cut sheets.
The results of the work can be used forpractical application and during research anddevelopment of cutting process for rolling cut
type shears.
References
1.

Korolev A.A. Konstrukcija i raschet mashin i mehanizmov
prokatnyh stanov. [Design and calculation of rolling millmachinery]. Moscow : Metallurgija, 1985. 376 .
2.
vanchenko F.K., Grebenik V.M., Shirja v V. . Rozrahunok
mashin mehan zm v prokatnih ceh v. [Machinery calculating for rolling mills]. Kiev: Vishha shk., 1995. 455 p.
3. Adamovich R.A., Rudel'son L.M., Rogoza A.M., Pal'min
A.D. Nozh dlja listovyh nozhnic s katjashhimsja rezom.
[Knife with rolling cutter for sheet shears]. A.s. USSR, no.
810403, 1981.
Fig. 6. Effect of knife curve radius to cutting force: – specific
4. Adamovich R.A., Rudel'son L.M., Rogoza A.M., Pal'min
dependences of cutting force in increasing knife curve radius; b –A.D. Nozh dlja nozhnic s katjashhimsja rezom. [Knife
dependence of maximum cutting force on knife curve radius
shears with rolling cutter]. A.s. USSR, no. 902989, 1982.
5. Liu G.R., Quek S.S. The Finite Element Method: A Practical Course, 2003, 348 p.
According to the results of the work one can summa- 6. Borovik P.V., Usatjuk D.A. Novye podhody k matematicheskomu modelirovaniju tehnologicheskih processov obrabotki davleniem. [New aprize:
proaches to the mathematical modeling of pressure treatment processing].
– technological opportunities of rolling cut type
Alchevsk : DonGTU, 2011. 299 p.
shears are not always used in full volume due to large 7. Notchenko V.D, Bojdenko A.N., Emchenko E.A., Cherkasov N.D.,
Zozulja E.S., Poslushnjak A.V. Chislennoe matematicheskoe modelirovanie(about 60%) divergence between maximum cutting force
processa rezanija listovogo metalloprokata na nozhnicah s dugoobraznym
and its steady value;
nozhom. [Numerical mathematic process simulation of sheet metal cuttingwith shears with embowed knife]. Udoskonalennja proces v obladnannja– increasing the knife curve radius to certain value proobrobki tiskom v mashinobuduvann metalurg : temat. zb. nauk. pr. [Presvides more even distribution of force during cutting process
sure treatment processing and machinery improving in machine building andand then its visible growth on knife coming out of cut;metallurgy: Col.of Scient. Papers]. Kramators'k, 2001. pp. 454-457.

Gribkov E.P., Danilyuk V.A.

MATHEMATICAL MODELLING OF SRTESS-STRAIN BEHAVOIR IN
ROLLING OF THE COMPOSITIONS INCLUDING POWDER MATERIALS
Abstract. The developed mathematical model of rolling of two-layer powder materials allows to determine the rational technological parameters of process excluding deformation of a substrate and raising an exit of suitable by production of inserts of sliding
bearings. It is established that the less thickness of a metal substrate, the more subjects is deformed, and respectively, powder is lessdeformed. In increasing the layers ratio the force and the rolling moment growing and the increasing of final relative density of powder composition are observed.
Keywords: mathematical model, rolling, powder materials, substrate, relative density, deformation center.

One of the perspective directions in the field of composite hardware production is rolling of compositions
with using the powder materials, allowing to receive wide
assortment of production with simultaneous ensuring specific operational properties and simultaneous economy ofextremely scarce and expensive materials. The mostwidespread ways of rolling of such type production isrolling of compositions powder-powder and powdermonometal.
The mathematical model of rolling single-layer pow-

der materials [1] was taken as a principle of numericalmathematical model of rolling of two-layer powder materials. The settlement scheme of the integrated deformation
center used in this case is submitted in figures 1 and 2.
Splitting of a consolidation zone into a final set of elementary volumes and definition of geometrical characteristics, and also tensions , and p in a final and differential form (Fig. 2) was carried out by analogy to atechnique stated in work [1].

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Gribkov E.P., Danilyuk V.A.

Fig. 1. The settlement scheme of the integrated deformation center in realization of rollingof composition powder (m) – powder (l)Fig. 2. The settlement scheme of allocated i-th of elementary volumeof the deformation center in realization of rolling of composition powder (m) – powder (l)At the same time it should be noted that friction existence between layers alters a condition of static balanceof the allocated elementary volume of the deformation
center, having the following appearance:
for less plastic component:

Fxil

x 2 ilhx 2ilx1il

px 2il f x 22i ) 0.5( p x1il
0.25( p x1il
( h 1ilhx 2 ilp x 2il )
hx1i

hx1i

hx1il

0.5 x ( p x1il f x 21i

px 2il ) xf ci
hx 2i

0.5( px1il

hx 2i / 2) 0;

for more plastic component:(1)

px 2il )Fximhx 2 im x 2 im

( p x1im f x11i
xf ci

h

x1im x1im

0.5 x

p x 2im f x12i ) 0.5( px1im

0.25( p x1im

p x 2 im ) hx1i

hx 2 i

px 2im )(2)0,

where hx1il(m), hx2il(m) are the current thickness less (more)strong components at the entrance and at the exit from theallocated elementary volume, respectively; hx1i, hx2i are thecurrent thickness of all compositions at the entrance and at
the exit from the allocated elementary volume, respectively; x is the extent of the allocated elementary volume ofthe deformation center; fx11(2)i, fx21(2)i are the current values

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43

Mathematical modelling of srtess-strain behavoir in rolling of the compositions including powder materials

of friction coefficients at the entrance and at the exit fromthe allocated elementary volume, respectively; fci is thecurrent value of friction coefficient between composition
layers; px1il(m), px2il(m) are the current values of normal contact tension at the entrance and at the exit from the allocated elementary volume, respectively; x1il(m), x2il(m) are thecurrent values of normal tension at the entrance and at theexit from the allocated elementary volume, respectively.
Substituting in the equation of static balance a condition of plasticity for loose environments [2]:

x

1 2 x
px
1 4 x

1 2 x
1 4 x

px2

2

41 x
31 4 x

1

2
sx

x

, (3)

2 p x 2t1t 2 t 22 t 4

0,

(4)

for less plastic component:

t1

1 2 x 2lhx 2l
1 4 x 2l1
2

t2

0.5 p x1

xf x 21

fc x

t3

2
x 2l

1 ; t44 2 1
x 2l
h x 2l3
1 4 x 2lhh xl

1 2 x2l
1 4 x2lhxl

f x 22 x

2fc x ;x1l

h x1l ;
x 2l

for more plastic component:

t1

1 2
1 4

hx 2m

1
2

h xm

xf x11

x 2m
x 2m

t2

0.5 p x1

t3

h x22 m 1 2

t4

4 2
hx 2 m 1
3

x2m

x2m

h xm

f x12 x

fc x

1 4
1 4

x1m

2
x2m

x2m

x 2m

hx 2 mhx1m hx 2 / hx1 ;

hx1m i 1

hx 0 m ;fc x ;
h x1m ;

1;2
x 2 sm.

2x 2 sl,hx 2l

hx1l i 1hx 2

hx 2l ;

hx 0l .

(5)

Final thickness of the first layer hx2m determined froma condition of equality of normal contact tension between
layers:hx 2imit is possible to determine normal contact tension:

p x22 t12 t3

where ,
are the coefficients characterizing mechanical properties of powder materials of various structure
depending on value of relative density; sx is a limit offluidity of a firm phase of powder composition.
As entry conditions, that is geometrical characteristics
for the first elementary volume, accepted the following:hx 2imAssign px 2im

px 2il,(6)where As is a step of change of the layer thickness, which
size to dependences on extent of approach to initial result
was accepted by a variable; sign{px2im-px2il} is a gradientassessment of the direction of the increment.
As a whole, the considered analytical decisions alongwith iterative procedure of extent deformation center determination, the accounting of elastic flattening of working
rolls surface, procedure of numerical integration of themain indicators of process made full algorithm on numerical one-dimensional mathematical modeling stress-strain
behavior when rolling two-layer powder materials. As an
example of result of numerical realization of the received
mathematical model in figure 3 settlement distributions oflocal and integrated characteristics of process are presented.
Integrated characteristics of process, namely, settlement
distributions of force P and the moment M of rolling, indicators of final relative density 2m, 2l and the relation of
final thickness of layers h2m/h2l of dependence on the size of
relative reduction are submitted in figure 1a. Local characteristics, that are distributions of the current thickness h 2m,
h 2l and relative density of each composition 2l, 2m, aresubmitted in figure 1b. From the analysis of the presented
settlement distributions it is visible that with increase inrelative reduction the intensive growth of the moment androlling force, and also final relative density takes place.

b
Fig. 3. Settlement distributions integrated (a) and local (b) characteristicsof rolling of two-layer powder preparation depending on reduction: m – Cu; l – Fe

44 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Gribkov E.P., Danilyuk V.A.

Besides, results from numerical realization established that increasing in coefficient of external friction of
more intensive deformation are observed from a firmcomponent, growth of normal contact tensions, force andthe total moment of rolling.
In increasing the ratio of thickness of soft component tothickness firm to h1m/h1l=1.75 some decreasing in the total
moment and increasing in force of rolling are observed.
However, in case of further increasing in this ratio there is aboomerang effect. Change of the relation of thickness does
not practically influence on the final relative density.
Comparison of the received settlement distributions
with experimental [3] showed that the error of determination of final relative density was made by about 8%, rolling
forces – about 5%, the rolling moment – about 10%. It confirms sufficient degree of reliability of the received mathematical model and legitimacy of its use for design of themechanical equipment of specialized camps and calculationof technological modes of rolling powder compositions.
The other perspective direction in the field of production of composite hardware is rolling of powder materials
on a metal substrate. Features of this process at halfdevout rolling are a bend of the rolled leaf towards a steel
substrate and the existence of cross cracks in a layer ofthe rolled powder material. These defects are caused
mainly by deformation of a metal substrate, which leads
to different longitudinal deformations of layers of composition, and respectively to above-mentioned defects. Oneof ways of this problem solution is the choice of suchmode of reduction at which powder would be only deformed, that can be possible with using of mathematicalmodel, which would predict substrate deformation.
Considered earlier mathematical model of rolling ofcomposition powder- powder was put in the basis of considered numerical one-dimensional mathematical modelof rolling of two-layer composition powder-monometal.
The problem definition and character of assumptions weresimilar to the previous case.
Full calculation stress-strain behavior for separately
allocated elementary volume is also reduced to definitionof normal 1, 2 and normal contact tensions p on thebasis of the directed search of thickness hx1, hx2 by criterion of section balance at the exit from elementary volume
in the vertical plane:

p 2m

p 2l

p 2,

(7)

where «l» and «m» are indexes determine accessory by atear of monometal and a tear of a powder material, respectively.
Having substituted in the equation (1) condition ofplasticity for continuous environments:x

px

2K x ,(8)

where 2 is a coefficient of the doubled resistance of
deformation of shift which can be determined by [4]:a2 x2 a3 x3 ;2K x 1.155 a0 a1 x

(9)a0, a1, a2, a3 are the coefficients of regression characterizing intensity of deformation hardening of metal.
The normal contact tension operating at the exit fromelementary volume of the deformation center:px 2l

2K x 2l hx 2l

hxl1 x1l

11px1l fc x
px1l hx1l
2
2
hx 2l

1
px1l f x1 x
2
hx 2l

1
1
1
fx2 x
fc x
hx1l
2
2
2

/

(10)

hx 2l

.

The further solution of the task (definition of entry
conditions, conditions transition to the following section,
iterative procedure by definition of the current geometrical characteristics of composition components) is similar
to the previous case, the case of rolling of powder-powder
composition.
As an example of numerical realization of the developed mathematical model of rolling of powder-monometalcomposition in figure 4, settlement distributions of local
characteristics of rolling of powder bronze-graphite(79% Cu; 15% Sn; 4% Pb; 2% C) under following conditions: radius of rolls – R=125 mm; substrate material – steel
DC 01; initial thickness of a powder layer – 5 mm; the initial relative density of a powder material – 0=0.27; final
thickness of all composition – 4 mm; strip width – 100 mm;
initial thickness of a substrate – 4 mm are presented.

bFig. 4. Settlement distributions of local characteristics of rolling of composition the powder M1 – steel DC 01
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45

Mathematical modelling of srtess-strain behavoir in rolling of the compositions including powder materials

From the analysis of the presented settlement distributions it is possible to draw a conclusion that deformation of a metal substrate begins near the neutral line ofrolling. As well as at the time of the beginning of its deformation intensity of growth of normal contact tensions
p sharply decreases, and is observed and with intensity ofgrowth of normal tensions , the difference in the size of
normal tension of a powder material and a metal substrateis also visible.
In figure 5 settlement distributions of integrated characteristics of process depending on a ratio of powder layers and steel are presented. That is at a fixed thickness of

powder – hpo1=4 mm and the variable thickness of a metal
substrate is hpl1=1.2…12 mm. Apparently from the presented settlement distributions than less thickness of ametal substrate of subjects it is more deformed, and powder respectively is less deformed. Also in increasing of aratio of layers growth of force and the rolling moment,
increasing in final relative density of powder composition
is observed.
The developed mathematical model allows to determine the rational technological parameters of processexcluding deformation of a substrate and raising at theexit of suitable by production of bearings sliding inserts.

bFig. 5. Settlement distributions of integrated characteristics of rolling of composition powder-steel
References
1.
2.

Levkin A.N., Gribkov E.P., Vorobyev Yu.A. Mathematical modeling stressstrain behavior and geometrical characteristics at realization of rolling ofbimetallic powder compositions. Kramatorsk, 2000. pp. 360-363.
Volkogon G.M., Dmitriev A.M., Dobryakov E.P. etc. Progressive technological processes of stamping of details of powders and equipment. Mos-

3.
4.

cow : Mechanical engineering. 1991, 320 p.
Tselikov A.I., Nikitin G.S., Rokotyan S.E. Theory of longitudinal rolling.
Moscow : Metallurgy, 1980, 320 p.
Potapkin V.F. Levkin A.N., Satonin A.V., Romanov S.M., Vorobyev Yu.A.,
Gribkov E.P. Stressed state and kinematics in the rolling of powder materials on a metal substrate. Powder Metallurgy and Metal Ceramics, 2000,
vol. 39, no. 1-2, pp. 11–17. ISSN 0032-4795.

Tulupov O.N., Moller A.B., Kinzin D.I., Levandovskiy S.A., Ruchinskaya N.A., Nalivaiko A.V.,
Rychkov S.S., Ishmetyev E.N.

STRUCTURAL-MATRIX MODELS FOR LONG PRODUCT ROLLINGPROCESSES: MODELING PRODUCTION TRACEABILITY
AND FORMING CONSUMER PROPERTIES OF PRODUCTS
Abstract. The development of rolling production processes towards flexible manufacturing schemes in tightening quality
factors makes the search of methods of effective influence on the process, labor management and personnel competence relevant.
To resolve the problems it is expedient to utilise structural matrix of mathematical models based on matrix presentation of longproduct rolling processes, and on a body of structural matrixes. In order to create mathematical apparatus we proposed to assign asophisticated structure matrix consisting of units (cells) to each process operation and operation result. These results are identified
with a rolling phase, while the process operation – with transformation of the product.
Structural matrix description of a process phase includes blocks that contain data of rolling process factors and parameters. To
describe the dynamics of rolling process was presented the relationships between separate process states in a matrix form, e.g. as
matrices of technological transformations.
Keywords: long products, rolling processes, structural-matrix models, computer simulation, consumer properties.

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Tulupov O.N., Moller A.B., Kinzin D.I., Levandovskiy S.A., Ruchinskaya N.A., Nalivaiko A.V., Rychkov S.S., Ishmetyev E.N.

Introduction
The main merit of structural-matrix approach is theability to link various models comprehensively in developing systems to analyze and control long product rolling
processes.
Methodological integration of Ishikawa’s diagram andstructural matrix approach provides science-based solutionsof the following problems using databases and IT:
integrated accounting of the factors that influence
the forming, and the forming influence on the process;adaptability (various complexity levels of shaperolling process description, on various production sites
with no need to change the description structure);
embedding individual models into an integrated
system that links the rolling parameters;
models compliance with up-to-date requirements
for automation systems;
application of simulators to train technical, technological and management personnel of long product mills
and to improve their professional skills.
Examples and results of this approach:roll pass designs (for bars, wires, and structural
shapes), and operation efficiency of rolls considering
wear prediction have been improved;
the amount of non-conforming products has beencut, the equipment workloads has been reduced, and thestrength grades of structural shapes have been increased;
new decisions to form the mechanical properties
have been made;an effective system of corrective and preventive
actions for long product mills has been created;
testing, evaluation and flexible training programson the basis of the above have been developed.
Structural matrix approach and models based on itwith reengineering of long product rolling processes allows to solve main issues of traceability of consumer
properties. The solutions could be rational for modern
challenges of long product rolling technology and quality.
The development of rolling production processes towards flexible manufacturing schemes, while tightening
quality factors, makes the search for methods of effective
influence on the process, labor management and personnel competence relevant. It also includes the flow controlof metal products at the enterprise.
Account should be taken of widespread development
and application of automated process control systems andschemes, which require relatively simple, versatile, fast,
easily expandable and reliable models meeting the requirements of object-oriented mathematical software. The
structure of such models should conform to the principles
of decomposition and hierarchical ordering of preserving
the unity of mathematical apparatus. Often, embedded
systems are highly specialized and do not always agreewith each other, poorly adapted to the changing technological conditions of production process, and they forbid
rapid analysis of alternative technological schemes. Thereis also a lack of unity in math approaches: the descriptionof cross-sectional area [1] and the methodology of quality

management of various long products [2, 3]. That hinders
the monitoring of product quality factors.
Therefore, the relevant scientific and technical challenge: develop and improve comprehensive, integrated
and adaptive long products quality control methods on aunified mathematical basis and unified data representation
principles about quality factors.
The adaptive control problem and product traceability
should be considered in two aspects:
adaptability of models and systems to various technological schemes and changing conditions of production;
adaptability to specific management, engineering andtechnical problems.
The proposed modelling approach is based on a few
concepts which are listed below.
Methods
First, to resolve process tasks of both the analysis
and the control of rolling process patterns for rolled sections of various shapes, a proper mathematical bodyshould be created. Moreover, it should comply with unified concepts of data processing, storage and presentation.
In order to create this mathematical body, it is proposed toassign a complex matrix, consisting of blocks (cells), tied
to each technological process and to each result of thisprocess. The results are identified with a rolling process
phase, while the process itself is identified with technological transformation of the product.
Structural matrix description of a single process
phase [A] includes blocks, containing monotype data ofrolling process factors and parameters.
To describe rolling process in its dynamics, the relationships between single process states should be represented in the matrix form, i.e. as matrices of technologicaltransformations [ ]i = 1…n . Then ‘i’ process phase isdescribed by the following matrix equation:
i -1

×

(1.1)

i

i

Whereas the rolling process itself is described by thefollowing system containing n number of matrix equations:
0

1

1

i-1

i

i

n -1

n

n

(1.2)

,

where [A]o, [A]n are matrices, which describe initial andfinal technological states respectively; [ ]1, [ ]narematrices, which describe the first and the last process
operations respectively;
Such form of process presentation is convenient fordata processing and computer simulation. Matrices oftechnological states transformation description [ ]i, as
well as matrices of technological states [A]i, are complex

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47

Structural-matrix models for long product rolling processes: modeling production traceability and forming consumer properties…

structural matrices consisting of certain finite number ofblocks (cells).
Second, structure and contents of the internal blocks
are determined by the model purpose and by the type of
the problem to be resolved. In general, the following internal blocks are: the block of shape description [ ], theblock of properties description [C] (i.e. block of mechanical properties description), the block of process parameters description [ ]. These blocks can be block matrices
themselves consisting of individual cells.
Data on the shape of rolled section is contained in the
shape description block [ ]i. For this purpose any complex cross-section is subdivided into finite number ofsimple elements k, which can be described according to
the concept of vector description of simple cross-sections.
To render the description coherent and non-ambiguous, amatrix of centres [ ] is introduced. This matrix contains
data on the location of centres of simple elements with respect to the common centre of the description. To determine the connection between local and common centres ofthe description, two values are introduced: distance between the centres, and angle between the vertical line andtheir connection line. The number of significant vectors]i. will depend on the complexity of the cross-section,and the k can be used as an indicator of shape complexity.
Mechanical properties of the feed are contained in theblock of properties description [C]. Each matrix [C]i consists of a set of vectors: Ci = 1…p, determining the location of isometric lines of mechanical properties. The choiceof p (a number of subdivisions of cross-section plane into
isotropic areas of mechanical properties) is determined by
specific conditions of each description task, by the required
accuracy of consideration of mechanical properties distribution across the cross-section. Besides, the value pi depends on complexity of properties transformation process
and can be regarded as an indicator of process sophistication. If average values are sufficient to determine mechanical properties, it is suggested that a block of properties description should be regarded as a degenerated matrix, whilevalues of mechanical properties should be regarded as ,for these particular conditions.
Block of parameters description [ ] can comprise
sub-blocks: [T] is a matrix of temperature conditions;] is a matrix of speeds, [ ] is a matrix of boundary
conditions; [ ] is a matrix of tool conditions (wear,etc.); [ ] is a matrix of tool characteristics. Individual
matrixes of process parameters represent a set of finite
number of elementary blocks. Data presentation is equal
to the one of shape description block, i.e. values of a specific parameter are determined at intersection points ofbasic radius-vectors with cross-section outline and as suchare stored into memory of this parameter to be utilized fordata loading into matrix [ ], [ ], [ ], [V].
When it is necessary to know parameter value in any
point of cross-section in order to resolve a problem (e.g.
temperature field), then data presentation concept in suchblocks (e.g., [T]) is identical to the description block [C].
Third, matrices of technological transformation haveblock structures and block sizes equivalent to those matrices of technological states. Blocks of matrix [ ]i can contain vector-type data (a set of figures ordered according toa certain principle, e.g. matrix of shape deformation –]i), analytical or empirical dependencies (i.e. models).
In any case irrespective of method of data presentation, allcells are included in general matrix model.
Structural matrix of the ‘i’-th process transformation]i includes the blocks []i, [ C]i, [ ]i, change ofsection shape, properties and process parameters respectively: []i = [ ]i / [ ]i-1; [ ]i = [ ]i / [ ]i-1; [ ]i ==[ ]i / [ ]i-1, where i = 1…m.
According to this approach, deformation is describedby means of deformation blocks, representing ratio between the matrices «before» and «after» deformation. Deformation block is a diagonal matrix. Its rank is defined by
the size of shape description block. The advantage of suchinterpretation of deformation is essentially in the possibility
to computer process the roll pass designs.
Fourth, relations between process parameters at eachrolling process phase are logged into the technologicaltransformation matrix (1.3) as lateral components (blocks)of this matrix. These blocks may contain both numericalfactors obtained empirically (e.g. relation of tonnage ofrolled stock per groove to matrix components that describe roll wear), as well as the entire mathematical models that establish a relation between single parameters(e.g. relation of deformation temperature to speed, relation of steel’s tensile strength to spread).

C '1
C '2

1

12

1m

21

2

2m

C1
C2

'm

m1

m2

m

m

(1.3)

where:m] is a matrix that describes initial state of one of
the entity's properties;'m] is a matrix that describes final state of one of
the entity's properties;m] is a matrix of state transformation;
denotes relations between various variation matrices (e.g. «deformation-temperature» relations).
Therefore, this feature presents an important advantage of structural matrix models, since it allows tocomprise and implement the possibilities of other efficientmodels within the frames of common integrated approach.
Thus, the suggested approach to modelling metal
forming processes, and, in particular to modelling shaperolling processes for wire rods, bars, and structural
shapes, ensures the following advantages:
integrated accounting of the factors which have direct impact on the deformation process, and the impact of
shape deformation itself on the rolling process aspects;
versatility (unified method of data interpretation,
suitable for computer processing);
adaptability to metal forming processes (the ability
to describe processes of various complexity, on various
production sites, with no need to change the description
structure);
adaptability to the tasks of rolling patterns analysis
and control to be solved [4, 5, 6];

48 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Tulupov O.N., Moller A.B., Kinzin D.I., Levandovskiy S.A., Ruchinskaya N.A., Nalivaiko A.V., Rychkov S.S., Ishmetyev E.N.

embedding individual models into an integrated cess, we need measurements to ensure the process to be
streamlined and maintained. The extent of regulatory
system that links the rolling parameters;
accordance with the modern approaches to creation of compliance and performance results are usually determined through a comparison of the results to assessment
computer-aided systems of process engineering and control.
criteria. Using the criteria approach to quality manageResults
ment, based on the development of structural matrices, we
Methodological integration of Ishikawa scheme and developed new indicators of profile conformity, characstructural matrix approach using databases and IT pro- terized by a deviation of profile distribution (DPD), exvides science-based and effective solutions of the as- pressed as a single number – the integral profile deviation
signed problems.
(IPD), index of profile match (IPM) of the logical typeThe developed complex of mathematical models and reflecting compliance deviation allowable range. These
descriptions of its practical implementation are listed indicators and a new tool for maintaining quality – model
hereinafter.
cards – are used to develop a method for determining the
To control the quality of rolled stock we improved corrective and preventive actions. Experience in creating«the uneven deformation ratio» – UDR (the criterion that tables of preventive actions revealed stands affecting thehelps evaluate and compare alternative roll pass designs). set up of the mill to the greatest degree and to propose
As a result, the amount of non-conforming products re- criteria that defines their priority. The fewer stands induced along with lower equipment loads and higher
volved in the set up lead to fewer changes of the roll gaps,
strength grade of structural shapes.
decreasing overall value of priority coefficient Cpr.
Instrument was found to form mechanical properties
The ability to solve local problems and skills of sysof rebar by defining the boundaries of the magnetic phasetemanalysis by a group of experts – that is the functionalsensor values variation and to obtain the required meityof
our instruments to manage the quality rolling syschanical properties of wire rod using commercial quality
steel (C 0.06-0.12%, Mn 0.25-0.50%, Si 0.15-0.30%, tem (UDR, Uin, DPD, IPD, IPM, Cpr). Mathematical appaS
0.050%, P
0.040%, Cr
0.30%, Ni
0.30%, ratus created includes new rolling quality indexes andCu
0.30%) instead of expensive alloyed steel technological personnel competence assessment and it has(C 0.20-0.29%, Mn 1.2-1.6%, Si 0.6-0.9%, S 0.045%, the potential to produce a synergetic effect to improve
product quality at the long product mill.
P 0.040%, Cr 0.30%, Ni 0.30%, Cu 0.30%).
The use of such models corresponds with the trends
Previously developed matrix evaluation criteria forsimple shape gauges transformed into the universal crite- of modern management and takes into account a range of
ria for evaluating structural shapes. Besides, we devel- factors: reengineering processes (a), adoption of IT (b),oped adaptive matrix model of complex productibility, product quality control during teaching or retraining the
precision, and stability analysis of forming and energy employees (c) and during production process within theframework of traceability and forming consumer properconsumption during rolling.
The matrix method of describing the forming process ties of products [7, 8].
and the principle of least resistance lead to new formulae
The further development of the matrix approach andthat calculates power parameters and deformation during mathematical models, which were listed above, is thesection rolling.
methodology of the information model formation [9],A new way was introduced to describe the geomet- which will become the basis for an automated tracking
ric parameters of axial segregation during billet defor- system of metal products. We propose to use the followmation – a supplement to the bar rolling process model- ing scheme of information flow that describes the processling using matrix approach and to effectively implement of passing of semi-finished products through long productcomputer modelling of segregation.
mill (see figure).
«LEAN-production» plays an important role in the quality management
strategy. As a part of mathematical apparatus we proposed individual wear index
Uin, and used it to figure out the scheduleof ring rolls and profile changes depending on roll material and diameter (decreased unnecessary supplies, process
steps, and changes of expensive ringrolls). Systematization of acquired
knowledge eases the development andeffective use of section mills, equippedwith three-roll RSB stands. Accumulated
and generalized experience of using carbide ring rolls could be applied on modern wire-rod mills, equipped with expensive durable rolls in their high-speed
finishing blocks.
To assess effectiveness of any proInformation flow scheme at the shape rolling shop of OJSC «MMK»
www.vestnik.magtu.ru. ——————————————————————————————————————————————

49

Structural-matrix models for long product rolling processes: modeling production traceability and forming consumer properties…

Inheritance of technological and organizational
measures of previously passed metallurgical conversions as well as follow-up ones takes part in ensuring
the required level of consumer properties that will let
us predict, monitor and improve the quality of longproducts.
Created adaptive complex comprises: an information
flow scheme (a); new quality indexes of the rolling process (b); methodology to assess and improve the technological competence of personnel (c); methodology ofquality control during design, implementation, long products production and improving.
The considered solution of the information model organization correlates well with object-oriented databasecreation process used in modern automatic process control systems as well as on all CAM systems on all automation levels up to the MES systems and enterprise management systems.
Immutability of the essence of applied mathematical
apparatus and the basic principles of its construction tosolve technical and technological problems and challenges of quality management makes it possible toadapt and use the developed approach in overlapping
technical areas.
References
1.

Tulupov O.N. Structure-matrix models for improving the efficiency of rolling
grades: Monograph. Magnitogorsk: Nosov Magnitogorsk State Technical
University, 2002. 224 p.

2.

3.
4.
5.

6.

7.

8.

9.

Tulupov O.N., Ruchinskaya N.A., Moller A.B., Limarev A.S., Lutsenko
A.N.Quality management of long products by using rational preventive
actions in mill setting Vestnik Magnitogorskogo gosudarstvennogo
tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov
Magnitogorsk State Technical University]. 2007, no 4, pp. 73-80.
Lewandowski S.A. Effectiveness enhancement of section mills by thequality management model improving: PhD Dissertation. Magnitogorsk,
2006.
Alekseev A.M., Loginov V.G., Zaitsev A.A., Tulupov O.N., Moller A.B.,
Rashnikov S.F., Morozov A.A. A method of rod rolling. Patent RUS no.
2148443, 1998.
Tulupov O.N., Moller A.B., Kinzin D.I., Lewandowskiy S.A., Limarev A.S.,
Zavyalov K.A., Richkov S.S., Loginova I.V., Unruh C. J., Nowitskiy R.V.
Resistance increasing of the 370 mill roller by cooling system improving.
Research report («Magnitogorsk Iron and Steel Works»).
Kinzin D.I., Kalugina O.B. Evaluation of values impact of the distortion
structure on widening in rolled section Vestnik Magnitogorskogo
gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova.
[Vestnik of Nosov Magnitogorsk State Technical University]. 2011,
no 4, pp. 21-23.
Nalivayko A.V., Steblov A.B., Tulupov O.N., Rychkov S.S. Issledovaniye
urovnya mekhanicheskikh svoystv armatury klassa A500S s tsel'yu otsenki
vliyaniya osobennostey tekhnologii na pokazateli kachestva. Vestnik
Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I.
Nosova. [Vestnik of Nosov Magnitogorsk State Technical University].
2010, no. 2, pp. 69-73.
Moller A.B., Tulupov O.N., Kinzin D.I., Levandovskiy S.A., Limarev A.S.,
Zav'yalov K.A., Nazarov D.V., Novitskiy R.V., Rychkov S .S., Loginova I.V.
Razrabotka i opytno-promyshlennoye oprobovaniye ekspluatatsii bandazhirovannykh valkov v predchistovoy gruppe kletey stana 170 STS OAO«MMK» [Designing and experiment industrial testing of tire rolls running at
millstand 170 of «MMK»]. Research report («Magnitogorsk Iron and SteelWorks»).
Ruchinskaya N.A., Zaytsev O.YU., Tulupov O.N., Lutsenko A.N. Printsipy
sozdaniya informatsionnykh modeley upravleniya kachestvom sortovogo
prokata. [The principles of creating long products quality management information models]. Proizvodstvo prokata. [Rolling processes]. 2007, no. 8,
pp. 33-41.

Logunova O.S., Matsko I.I., Posochov I.A.

INTEGRATED SYSTEM STRUCTURE OF INTELLIGENTMANAGEMENT SUPPORT OF MULTISTAGE METALLURGICALPROCESSES
Abstract. The necessity to invent a universal technology for creating the intelligent management support of multistage processes,
which is able to interface process variables between local loops at each stage of production is determined. The integrated system
structure of intelligent management support of multistage metallurgical processes and production stage models are suggested. The
improved method of billet macrostructure assessment and block designing technology of intelligent management support of continuous casting billet production are described.
Keywords: control systems, intelligent support, multistage metallurgical processes, continuous cast billet, billet macrostructureassessment.

The actuality of the study
Modern Industries require new systems for multistage
process management. These requirements are due to thenew priority trends in accordance with Russian state policy. One of these trends is the development of informationand telecommunication technologies, which are integrated
in automated control systems (ACS) of large industrial
enterprise production. The use of new ACS modules for
multistage manufacturing processes facilitates unit performance increasing and provides reduced quantity of
low-quality products.
From the management point of view, multistage
technology of steel products is a complicated process.

Such technologies require the system allowing to monitor output product quality in on-line and providing intelligent decision support of process control.
In developing and implementing new modules,
which enlarge already existing ACS, the necessity to use
graphic information obtained during quality estimation
procedure of finished products and semi-finished products emerges.
The effectiveness of using graphic information anddecision-making in ACS production is illustrated by theory and practice.
Methods of image obtaining, processing and segmentation can be found in foreign and Russian scientific pub-

50 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Logunova O.S., Matsko I.I., Posochov I.A.

lications. Mathematical theory development in improving
and graphical information segmentation was defined inscientific papers [1-3]. An overview on the topic of decision-making on basis of tree-type structure was presented
by Quinlan J.R., Janikow C.Z., Hastie T., Tibshirani R.,
Friedman J., Berestneva O.G. and others. The practicalapplication of fuzzy set theory and fuzzy logic refers to
Zadeh L.A., Esposito F., Malebra D., Semeraro G.,
J.J. Dyulichevoy and others.
However, despite the studies carried out and large
number of publications in the field of automated control
systems (ACS) in steel production [4-7], the following
issues are of current interest:– the lack of automated systems permitting to ensuretechnological processes control, based on output productquality information;– the lack of techniques of graphic information collection and processing about the quality of steel products
using low-contrast images with irregular shaped elements;– the lack of application packages for intelligent decision support in automated control systems (ACS) of multistage production, based on adaptable fuzzy trees withdynamic structure, taking into account the values of attributive quality characteristics of products.
In the current circumstances, there is a need to develop a universal technology of creating the intelligent support system of multistage process management, which isable to interface process variables between local loops ateach stage of production.
The structure of research object
Fig. 1 illustrates the diagram of a manufacturing process with N stages. The following notations are displayedin Fig. 1: {Zi} is a task vector for technological parameters values of the i-th process; {Ri} is a decision vector ofparameters values changing of the i-th process; {Mi} is avector of estimation (indicators) of product or semiproduct quality, resulting in redistribution at the N selected stages, Z is a value of final parameters for product assigned position.
A typical example of a multistage manufacturing process is the production of continuous cast billet, with threemain stages: steel melting in alternating-current (AC)electric arc furnace (EAF), steel processing in a ladle furnace unit (LFU) and continuous steel casting in billet continuous casting machines (BCCM).
An illustrative diagram of a multistage production forthe chosen technology, where N = 3, is represented inFig. 2. All input and output parameters, shown in Fig. 2,
become of specific physical and technologic significance(see Table).
Values, which are transmitted between production
stages and determine the operation mode choice of thenext step unit, are highlighted in Table. The presence ofbinding parameters permits to organize the integrated
management of all production stages.

The list of major task vectors for continuous cast billet
production stages
VectorVectorPhysical or technologicalset coordinatessignificance of coordinates{Z1}
charge materials ratiod(crowbar / pig iron), %percentage of chemical elements in{ci}
steel at EAF exit,%
t1
arc time under the current, min
I1current strength, MA
U1current voltage, Velements proportion of non-metallic{li}charge, %{vi1}
flow-rate of solid oxidizer additives kg{gi1}
flow-rate of gas oxygen, m3 / h{fi1}
discharge intensity of ferroalloys, kg / t
T1
metal temperature at EAF exit, °C{Z2}
T1
metal temperature at EAF exit, °C
percentage of chemical elements in{ci}
steel at EAF exit, %t2
arc time under the current, minI2current strength, MA
U2current voltage, MV{gi2}
argon gas flow rate m3 / h{fi2}
discharge intensity of ferroalloys, kg / t
metal temperature in steel teeming
T2ladle at LFU exit, °C{Z3}
metal temperature in steel teeming
T2ladle at LFU exit, °C
metal temperature in tundish ladle at
T3
BCCM exit, °C
percentage of chemical elements in{cie}steel teeming ladle at EAF exit, %vbillet drawing rate, m / minwater flow rate for secondary cooling{Fij}zones BCCM, m3 / h
air flow rate for secondary cooling zones{Dij}
BCCM, m3 / hw
crystallizer oscillation frequency
Fwater flow rate on crystallizer m3 / htask aimed to billet macrostructure{ i}evaluation, grade{Z}task aimed to billet macrostructure{ i}evaluation, grade
percentage of chemical elements in tun{c }dish ladle BCCM, (last test), %Information about template selection{Ii}
for quality evaluation
{ i}
{Oi}
actual results of quality evaluation, grade
Information about template selection{Ii}
for quality evaluationwww.vestnik.magtu.ru. ——————————————————————————————————————————————

51

Inteintegrated system structure of intelligent management support of multistage metallurgical processes

Fig. 1. Diagram of multistage production with integrated system of intelligent management support

Fig. 2. Diagram of multi-stage continuous cast billet production
The structural model of the i-th production stage
The block of each stage (Fig. 1) has a complex structure, which comprises: mathematical process models,visualization module of expected result, current processmonitoring module, decision-making block, systems of
local loops of process variable control (technologic unit or
its field ). The structural diagram of each stage can be
unitized according to the diagram shown in Fig. 3.
The following notations are introduced in Fig. 3:{Ri } is a decision vector leading to the i-th process parameter points changing, as a result of modelling; { Zi }is a correction vector for the task point of process control;{ Zient } is a task vector for the system of local loops ofcontrol object; { Ziex } is a vector of technologic parametervalues transmitting to the control object; { Zi+1} is a vectorof technologic parameters, obtained after the i-th stage production ending and transmitting to the stage i +1 as a task.
Decision-making blocks, which can be implemented
using different technologies, both in automated and automatic modes are represented in Fig. 1 and Fig. 3. Currently, decision-making technologies based on the classification with the help of neural networks, fuzzy logic and treelike structures are the most widespread [4, 8, 9]. A combination of many tree-like structures and fuzzy membershipfunctions about the received quality indicator level is oneof the options, taking into account the information fuzziness and taxonomic criterion of product quality. Taking

into account plenty quality indicators and production process dynamism, an adaptive forest of dynamic structure
fuzzy trees is formed. Each tree adaptability permits to retrain the decision tree in changing the technologic process
running and response to the situations, unspecified in thedecision tree. Dynamism allows to change the relevancelevel of process control variables after a set of tree adaptations towards providing shorter decision branches, reducing
the parameters, requiring correction.
View module (Fig. 3) is designed to exhibit results ofmodelling, and its construction is a separate scientificproblem in the field of information processing. The module is optional and it is not included in many process control systems because of implementation complexity inmapping results in real time.
The block «System of local loops» also has a complex structure and can combine M subsystems, which areresponsible for process variable selection and stabilization. The peculiarity of the suggested solution is the integrated result examination in changing values of many
process parameters not only at the selected i-th stage but
also between stages. Therefore, vector representation of
input and output parameters is shown between the diagram blocks, shown in Fig. 1 and Fig. 3.
Fig. 4 illustrates the example of structural scheme ofcontinuous steel casting stage applicable for arc-furnacesteelmaking plant of OJSC «Magnitogorsk Iron and SteelWorks».

Fig. 3. Structural diagram of the i-th production stage

52 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Logunova O.S., Matsko I.I., Posochov I.A.

From 7 to 215 l/min
yes: 36,76; no: 5,321
To 2,3 m/min
yes: 104,89; no: 23,38

Water flow
on SCZ

More215 to 431 l/min
yes: 62,59; no: 5,43
From 431 to 654 l/min
yes: 5,54; no: 12,62
From 7 to 215
yes: 6,84; no: 6,23

Casting
rate

More 2,3 to 4,m/min
yes: 97,86; no: 57

Water flow
on SCZ

More 215 to 431 l/min
yes: 77,81; no: 5,05
From 431 to 654 l/min
yes: 13,2; no: 45,71
From 7 to 215 l/min
yes: 8,5; no: 16,69

More 4,6 to 7m/min
yes: 42,54; no: 21,31

Water flow
on SCZ

More 215 to 431 l/min
yes: 11,13; no: 2,15
From 431 to 654 l/min
yes: 22,9; no: 2,47

Fig. 4. Structural scheme of continuous steel casting stage
As shown in Fig. 4, a signal of suggested billet quality{R3} is received from the intelligent support block. Binding components of vector {Z3} enter the modeling blockof continuous casting of steel. A system of sub-models isrepresented in this block, including the model of identification of heat transfer coefficient from the billet surface,
the model of the billet thermal state, the model of billet
damage forming, the model of billet quality forecasting,etc. The simulation data {R3m} enter consistently the rendering module, implemented on the SCADA platform, andthe decision-making block. The use of adaptive fuzzy trees
with dynamic structure is one of the ways of decisionmaking block building aimed to adjust the values of process variables. Melting mass; metal temperature after EAF
discharging; metal temperature in pony ladle; oxidation of
metal; steel casting rate; the content of basic chemical elements in steel are defined as the linguistic variables for thedecision making tree of the possible damage origin.
A method of billet macrostructure evaluation
Speaking about steel product quality, firstly macroand microstructures values are noticed, and these values
are foundational for such mechanical properties as
strength, formability, wearability. Discontinuity flaw geometric dimensions, obstacles quantity, density from metal distribution in given volume are the characteristics ofmetal macro- and microstructures. The determination of
the degree of discontinuities flaw extension is generally
defined by the appropriate field and state standards suchas OST 4.14.73 or OST 14-1-235-91. The process of expert knowledge base formation, in order to assess metallurgic product quality, is the most time-consuming. Hitherto, information acquisition and processing are carriedout by traditional methods, based on product visual in-spection results. With modern computing facilities it becomes possible to develop automated system of metal macro- and microstructure assessment. However, the development of a decisive rule base for decision-making is possible
only on the basis of «practical» expert knowledge. Suchknowledge processing leads to the input of membershipfunction of fuzzy sets and rules of their use. Intelligent
support system of billet continuous cast production at arcfurnace plant of the OJSC Magnitogorsk Iron and SteelWorks (MMK) was built based on technology, developedby the authors [9]. Points of the internal macro-damage
extension have been selected as product quality indicators. Macro-damage rating is carried out on crosscut templates and sulphuric marks. The following types of damage such as axial looseness, dotty obstacle and cracks,
perpendicular to the billet edges were examined. Length,
width, strength and ratio of total damage area to templatesize are the characteristics of damages. According to the
OST 14-1-235-91 membership functions for evaluatingeach type of damage were classified in tabulating.
Algorithm S4.5 and algorithm of decision-making
fault reducing in fuzzy tree using were selected as thebasis of classification algorithm. In order to construct a
fuzzy tree forest, which allows to take into account predicable quality classification criteria from the tabulation,
linguistic variables to describe damage parameters such as
width, length, relative length, relative width, area, maximum area, relative area, length-width ratio, width-length
ratio, strength and section attachment have been introduced. Tree type structure building results in order to assess the axial looseness of continuous casting billet are
shown in Fig. 5. Full forest of fuzzy trees contains from
800 to 2,000 leaves. Branches for damage, which has anaverage size, are allocated in Fig. 5 and its part is located inwww.vestnik.magtu.ru. ——————————————————————————————————————————————

53

Inteintegrated system structure of intelligent management support of multistage metallurgical processes

Melting mass; metal temperature after EAF discharging; metal temperature after secondary treatment; metal
temperature in pony ladle; oxidation of metal; steel casting rate; the content of
the basic chemical elements in steel are defined as the linguistic
variables for the decision
making tree of the possible damage origin.
Taking into accountthat the built tree leaves
are presented in Fig. 6,
the decision uses only
two branches marked
with a dotted line. The
solution pertains to theupper branch per 0.14
and to the lower branch
per 0.86. It can be defined for this solutionthat the resulting billet
Fig. 5. A segment of the classification tree of internal macro damages
has 0,357 grade ofof continuous casting billet
membership to a class ofusual quality billets, and that corresponds to 2.5 points
Building block method of intelligent management
according to the OST.
support of continuous cast billet production
The billet is qualitative if the point is less than 2.
In creating the integrated system of intelligent manConsequently,
it is necessary to modify existing solutions.
agement support of multi-stage processes it is necessary
Accordingtothedeveloped algorithm, the control paramto establish cause-and-effect relationships between prodeterchangeisperformed.
It means to reduce fuel cooler
uct quality indexes and process variable values, which
need to be built at the stage of expert knowledge formali- flow from 444 to 438
l / min, in this case billet quality assessment is rezation.
One of the ways to formalize expert knowledge is duced to 2 points, and that is sufficient for its ordinary
quality classification.
adaptive fuzzy tree with dynamic structure (Fig. 6).
section 3. If 10% of damage is in section 3, then templateattachment to target class (qualitative template) is 0.334
that corresponds to 2.5 points according to the OST.

From 7 to 215 l/min
yes: 36,76; no: 5,321
To 2,3 m/min
yes: 104,89; no: 23,38

Water flow
on SCZ

More215 to 431 l/min
yes: 62,59; no: 5,43
From 431 to 654 l/min
yes: 5,54; no: 12,62
From 7 to 215 l/min
yes: 6,84; no: 6,23

Casting
rate

More 2,3 to 4,m/min
yes: 97,86; no: 57

Water flow
on SCZ

More 215 to 431 l/min
yes: 77,81; no: 5,05
From 431 to 654 l/min
yes: 13,2; no: 45,71
From 7 to 215 l/min
yes: 8,5; no: 16,69

More 4,6 to 7m/min
yes: 42,54; no: 21,31

Water flow
on SCZ

More 215 to 431 l/min
yes: 11,13; no: 2,15

Conclusion
Thus, granting modern decisionmaking methods it is possible to develop existing production control systems for their intellectualization. The
use of an integrated system of intelligent management support of multistage metallurgical processes permits
to carry out multiple factor analysis.
Herewith, both well-known deterministic and statistical modelling process
methods and unitized way of decision
making, based on «practical» expert
knowledge, are used in this analysis.
References
1.
2.

From 431 to 654 l/min
yes: 22,9; no: 2,47

3.

Fig. 6. Moving path fraction in decision-making based of fuzzy tree structure
in order to forecast continuous casting billet quality

4.

Shapiro. L., Stockman G. Computer Vision. Moscow: BI-NOM. Knowledge laborator, 2006, 752 p.
Gonzales R.C. and Woods R.E. Tsyfrovaya
obrabotka izobrazheniy [Digital Image Processing], Tekhnosfera, Moscow, Russia, 2005,
1072 p.
Pratt W.K. Digital Image Processing. New York:
Wiley, 1978. Translated under the title Tsifrovaya
obrabotka izobrazhenii, Moscow: Mir, 1982, 312 p.
Ryabchikov M.Y., Parsunkin B.N., Andreev S.M.,
Logunova O.S., Ryabchikova E.S., Golovko N.A., Polko P.G. Achieving maximum perfor-

54 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Logunova O.S., Matsko I.I., Posochov I.A.

5.
6.

mance optimized ore grinding process in utilizing fuzzy extreme control principles. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo
universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State
Technical University]. 2011. no. 2, pp. 5-9.
Tutarova V.D., Logunova O.S. Analysis of the surface temperature ofcontinuosly cast ingot beyond the zones of air cooling. Steel in Translation. 1998. no. 8. pp. 21-23.
Logunova O.S., Matsko I.I., Safonov D.S. Modelling of the thermal state of
the infinitely extended body with the dynamically changing boundary conditions of the third kind. Bulletin of the South Ural State University. Series:

7.
8.
9.

Mathematical modeling and programming. 2012, no. 27, pp. 74-85.
Logunova O.S. Internal-defect formation and the thermal state of continuous-cast billet. Steel in Translation. 2008, vol. 38, no. 10, pp. 849-852.
Golovko N.A., Logunova O.S., Parsunkin B.N., Andreev S.M. Adaptive
system of automatic control of stochastic nonlinear processes. Scientific
Review, 2013, no. 1, pp. 166-170.
Matsko I.I., Logunova O.S., Pavlov V.V.,. Adaptive fuzzy
decision tree with dynamic structure for automatic process control systemof continuous-cast billet production. IOSR Journal of Engineering. 2012,vol. 2, no. 8, pp. 53-55.

Shatokhin I.M., Bigeev V.A., Shaymardanov K.R., Manashev I.R.

INVESTIGATION OF COMBUSTION IN TITANIUM-FERROSILICONSYSTEM
Abstract. Results of self-sustaining combustion process in the titanium-ferrosilicon system investigations are presented. These
data were used for experimental-industrial technology developing of production ferro silico titanium with high titanium content forsteel alloying.
Keywords: titanium, titanium containing steel, ferrotitanium, ferrosilicotitanium, titanium ferrosilicide, self-propagating hightemperature synthesis, combustion rate, combustion temperature.

At present, titanium is actively used for alloying ofwide assortment of steel thanks to its specific properties.
Titanium is used for modern HSLA-steels, pipe-steels,
stainless steels and others. Mainly, the mechanism of its
influence on steel quality is associated with formation oftitanium carbides, nitrides and carbonitrides in steel.
Ferrotitanium is usually used for steel alloying. Depending on the method of production, ferrotitanium canbe with high (~70% Ti) and low ( 40% Ti) titanium content. High-grade ferrotitanium is usually obtained bymelting titanium-containing waste in induction furnaces.
Low-grade ferrotitanium is produced by recovery from
ilmenite in special melting aggregates. Ilmenite concentrate, iron ore, aluminum powder, ferrosilicon and lime
are used as raw materials. Sometimes, when high-purity
steel grades are produced, vacuum-melted ferrotitanium isused. Standard ferrotitanium contains considerable
amount of impurities (such as non-ferrous metals, nitrogen, oxygen, hydrogen, carbon, sulfur, phosphorus),
which come to alloy from raw materials and atmosphere
during production. Moreover, assimilation degree of titanium from ferrotitanium remains low.
That is why, full or partial replacement of ferrotitanium by alternative titanium containing alloys is actual.
This problem can be solved by creating of complex master-alloys, which contain titanium as basic element andhigh-level elements, such as Si, Al, Ca, etc. It is supposed,that these elements will protect titanium against oxidation,
because they are strong deoxidizers. In this way, titanium
assimilation will be higher.
Thus, to be most effective, new alloy should meet thefollowing requirements:
high titanium content;
low impurities content;
the presence of elements with high affinity to oxygen.
This alloy will give high and stable titanium assimilation, will allow to produce steels with narrow titanium

limits and will reduce impurities content in metal. The
most economical alternative to ferrotitanium can be ferro
silico titanium.
Usually ferro silico titanium is obtained by melting titanium, metallic silicon and low-carbon steel in induction
furnace or by recovery from ilmenite ore.
But it is impossible to produce ferro silico titanium
with high titanium content (more than 30% Ti) by furnace
methods, because of high melting point of titanium silicides and strong liquation during crystallization. Moreover, alloy, obtained by furnace methods, has higher concentration of nitrogen, oxygen and hydrogen, penetrating
into the melt from the atmosphere. So, it is important touse fundamentally different method of titanium ferrosilicide obtaining that enables high product recovery with
low impurities content with the lowest electricity costs.
Such method is self-propagating high-temperature synthesis (SHS). When SHS is applied, no traditional furnaces
are used. The process is carried out in special SHSreactors at the atmosphere of inert gas or vacuum. At the
combustion synthesis, as well as at the traditional metallothermic process, energy source is the heat of chemical
reactions. But unlike metallothermy, SHS is slagless.
The Ti-Si system has 5 silicides: TiSi, TiSi2, Ti5Si3,
Ti3Si4
Ti3Si. Ti5Si3 has the highest melting point.
Physical and chemical properties of titanium silicides
are presented in Table 1. The formation of titanium silicides occurs with great heat release, so that adiabatic
combustion temperature is high. Regularities of interaction of titanium and silicon are studied in detail in works[3, 4]. It was shown, that combustion in powder compound of titanium and silicon can be implemented in awide range of parameters changing such as the components ratio, powders dispersion, etc. It can be expected,that heat release during chemical interaction in ternary
system Ti-Si-Fe will be enough to carry out the process
in self-propagating mode.

www.vestnik.magtu.ru. ——————————————————————————————————————————————

55

Investigation of combustion in titanium-ferrosilicon system

Table 1
Physical and chemical properties of titanium silicides [5]Characteristics
Ti5Si3 TiSi TiSi2 Ti3Si4 Ti3Si
Heat formation, kJ/mol
581,2 132,8 136,6 ––Crystallization temperature, °K 2120 1760 1540 1920 1170
Density, g/cm34,3 4,03 4,21 ––Adiabatic combustion tempera–
2500 2000 1800 –ture, °K
It is known, that high exothermicity of raw materials
interaction is the essential condition for all SHS-reactions.
To determine the possibility of self-propagating process,calculation of adiabatic temperature in ternary system
Ti-Si-Fe with iron content of 0 to 90% was carried out
using thermodynamic data and methodology, represented at [5, 6]. During calculation it was assumed, that iron
did not take part in the reaction and titanium silicide
Ti5Si3 and -iron are combustion products:

5Ti 3Si xFe

Ti5 Si3

xFe(1)

Combustion temperature was calculated using the following formula:(1

H TiT 5 Si3

)

) (Q

(1

where LTi 5Si 3 ,T
H Fe
Ti5 Si3(2)

LTi5 Si3 ),The results show, that adiabatic temperature remains
enough high despite heat effect reduction, when iron isadded to (5Ti + 3Si)-compound (more than 2000°K wheniron concentration is changed between 0 and 50%).
Therefore, we can expect, that process can be carried out
in self-propagating mode in wide range of Ti, Si, Fe concentration.
To carry out the researches, a laboratory SHS-reactor
with 20 liters volume was constructed. This plant allows
to carry out researches of SHS-processes in a wide rangeof pressure: from 0,01 to 10 MPa. Ti-Si-Fe-system isqualified as SHS-gas-free system, that is, all raw materials
and products are in condensed state. There is no relationship between combustion parameters and pressure andthis is the distinction of these systems. The relationships
between combustion rate, combustion temperature, raw
components ratio and particle size of titanium powder intitanium-ferrosilicon system were investigated using alaboratory SHS-reactor (Fig. 2).
Porous titanium powder TPP-4 TU 1791-44905785388-99 produced by JSC «VSMPO-AVISMA Corporation» and ferrosilicon powder FeSi75 GOST 1415-93
produced by JCS «Chelyabinsk Electrometallurgical Integrated Plant» are used as raw materials. The temperature
was measured by thermocouple method using tungstenrhenium thermocouples TR-5/TR-20, an analogue transducer RL-16AIF and a signal multiplier RL-4DA200. The
combustion rate was measured by a video camera.

Ti 5Si 3 are the heatand the degree of Ti5Si3 fusion respectively;

H TiT 5Si3 andT
H Fe

are enthalpy change of titanium
silicide formation and iron whentemperature increases from To to
Tad; is the amount of iron in the
combustion products.
The results of calculation arepresented in Fig. 1. It is relationshipcurve between adiabatic temperature of combustion of (5Ti + 3Si)Fe-compound and concentration ofiron in it.

Fig. 2. Laboratory SHS reactor scheme

Calculated com bustion
tem perature, K

3000
2500
2000
1500
1000
500
0
0

10

20

30

40

50

60

70

80

Iron concentration, %Fig. 1. Influence of iron concentration on adiabatic temperatureof combustionof (5Ti + 3Si)-Fe-compound

90

100

Combustion rate and temperatureare basic parameters of a SHS-method.
These parameters determine process
productivity and safety, as well as
equipment requirements. It is known,that modes and possibility of SHS depend on many factors. Most importantfactors, except high exothermicity, areraw components ratio and powder particle size.
In general, combustion synthesis in
Ti-Si-Fe-system can be implemented
using different schemes: Ti + Si + Fe;
Ti + FeSi + Fe; Ti + FeSi; FeTi + Si ++Fe; FeTi + Si and others. In this work

56 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Shatokhin I.M., Bigeev V.A., Shaymardanov K.R., Manashev I.R.

Temperature, K

1800

1750

1700

1650

1600

1550
1,5

1,7

1,9

2,1

2,3

2,5

2,7

2,9

3,1

The ratio of titanium to ferrosilicon, %Fig. 3. Relationship between combustion temperature and components ratio

Com bustion rate, m m /s

4
3
2
1
0
1,5

2

2,5

3

3,5

The ratio of titanium to ferrosilicon, %Fig. 4. Relationship between combustion rate and components ratio
1760
1740
1720
Temperature, K

processing in titanium-ferrosiliconsystem is investigated.
Combustion synthesis in thissystem was carried out in a wide
range of raw components ratio(Fig. 3 and 4). As a result of combustion product with 60-75% Ti
and 18-27% Si is formed. Fig. 3
shows the relationship between
combustion temperature and titanium/ferrosilicon ration in the mixture.
As we can see, combustion
temperature depends weakly on
components ratio and remains almost constant in a wide range ofraw components ratio (1720 ±50°K). We think it happens because the changing of raw components ratio in studied ranges affects
only on the proportion of the liquid
phase in products, but the temperature of forming melted products,that is close to measured temperature, remains constant.
Fig. 4 shows the relationshipbetween combustion rate and component ratio of (5Ti + 3Si)-Fecompound
We can see from the figure,that combustion rate reduces bothwhen titanium concentration increases and when it reduces.
Maximum combustion rate wasobtained on the compound with
72% Ti.
Fig. 5 shows the relationshipbetween combustion temperatureand titanium powder particle size
when component ratio provides
formation of Ti5Si3.
The figure shows that temperature remains at the same level(1720 ± 50°K) and changes weakly
when titanium powder particle size
is varied.
The next figure presents therelationship between combustion
rate and titanium powder particle
size (Fig. 6). This figure demonstrates, that combustion rate changes weakly (2 mm/s ± 0.25 mm/s)
when titanium powder particle size
is varied. Fig. 5 and 6 demonstratethat combustion in this system canbe carried out in wide range oftitanium powder particle size andcombustion temperature with almost constant rate.

1700
1680
1660
1640
1620
1600
0

0,5

1

1,5

2

Avarage particle size, mm

Fig. 5. Relationship between combustion temperature compound and titanium
powder particle size in titanium-ferrosilicon compoundwww.vestnik.magtu.ru. ——————————————————————————————————————————————

57

Investigation of combustion in titanium-ferrosilicon system
1760

Conclusions
The process of obtaining ferro
silico titanium with high titanium
1720
content (to 75%) by self1700
propagating high-temperature synthesis was investigated. The rela1680
tionships between combustion rate,
combustion temperature and initial
1660
components ratio, titanium powder
particle size were obtained. As it
1640
turned out, temperature depends
1620
weakly on initial components ratio
and titanium powder particle size
1600
and remains at the same level
0
0,5
1
1,5
2
(about 1720 ± 50°K). Combustion
rate is also weakly depends on titaAvarage particle size, mm
nium powder particle size, but wecan see, that combustion rate reducFig. 6. Relationship between combustion rate and titanium powder
es when titanium content both inparticle size in titanium-ferrosilicon systemcreases and reduces. Maximum
Thus, these investigations have shown that SHS- combustion rate was obtained on the compound with 72%
technology can be applied to obtain ferro silico titanium titanium. Based on these data, experimental-industrial
with high titanium content. It is possible to obtain alloys technology of obtaining ferro silico titanium by SHSwith various titanium content and various densities by method was developed.
varying of initial mixture and particle size of initial powReferences
ders. Moreover, lack of waste and electricity consumption
will bring low cost and provide high competitiveness of 1. Lyakishev N.P., Pliner, U.L., Lappo S.I. Legiruyuschie splavy i stali s titanom.
[Alloys and alloying steel with titanium]. M.: Metallurgiya, 1985, 230 p.
products. At the same time, producing of new alloy in inert
2. Gasik M.I. Teoriya i tekhnologiya proizvodstva ferrosplavov. [Theory andgas atmosphere will increase the purity of end product.
technology of production of ferroalloys]. Moscow: Metallurgiya, 1988, 340 p.
Investigations results were used for developing the 3. Sarkisyan A.R. and other. Some laws of combustion of mixtures of transition metals with silicon and silicide synthesis. Fizika goreniya i vzryva.
experimental-industrial technology of ferro silico titaof combustion and explosion]. 1977, no. 3, pp. 34-40.
nium production by SHS-method. Specifications for 4. [Physics
Azatyan T.S. Some laws of combustion of titanium with silicon. Fizika gorenioptimal SHS-ferro silico titanium composition are deya i vzryva. [Physics of combustion and explosion]. 1978, no. 1, pp. 44-49.
5. Novikov N.P., Borovinskaya I.P., Merzhanov A.G. Thermodynamic analyveloped (Table 2).
Tem perature, K

1740

Table 2
Chemical composition of SHS-ferro silico titanium
C
S
P
O
N
H
Grade
Ti
Si
max
FST 70 61-74 18-27 0,15 0,005 0,009 0,1 0,05 0,005

6.

sis of self-propagating high-temperature synthesis reactions. Protsessy
goreniya vkhimicheskoy tekhnologii i metallurgii. [Combustion Processes
in Chemical Technology and Metallurgy: Proceedings]. Ed.
A.G. Merzhanov. Chernogolovka, 1975, pp. 174-188.
Bukreev A.E., Manashev I.R., Nikiforov B.A., Bigeev V.A. New nitrogencontaining chrome nitride based alloys, obtained by SHS. Vestnik
Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im.
G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University].
2008, no. 1, pp 49-51.

Parsunkin B.N., Andreev S.M., Akhmetov T.U., Mukhina E.Y.

OPTIMAL ENERGY-EFFICIENT COMBUSTION PROCESS CONTROLIN HEATING FURNACES OF ROLLING MILLS
Abstract. Considering continuous energy price rising, energy- efficient combustion process control is of current interest because
circa 15% of the consumed firing is expended in rolling production for metal heating.
Effective solution of this problem is possible by using the automated systems of optimal control, based on optimizing control algorithms of search type. Such management systems have the ability to provide search and to maintain the maximum value of the
optimized parameters under uncertainty and the lack of accurate quantitative model of the processing.
Keywords: temperature, air volume control, objective variable, extremal control, combustion control.

In iron and steel industry circa 15% of the consumed
firing is expended in rolling production in metal heating.
Therefore, energy-efficient combustion process control isof current interest, especially considering continuous energy price rising.

Optimal energy-efficient combustion process control
is a difficult task in continuous furnaces of modern highperformance hot rolling mills, when their operating ratevaries from 100 up to 1000 t / h, and the initial temperature of continuous cast billets, feeding to heating, ranges

58 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Parsunkin B.N., Andreev S.M., Akhmetov T.U., Mukhina E.Y.

A

VA ( )VF ( ) LO

const ,

where VF ( ) is the current air flow, m3 / h; VF ( ) is thecurrent firing rate, m3 / h;is the current time, s; LO isa coefficient, defining required air quantity for complete
combustion of one unit measure of used fuel.
The combustion process investigation showed that
there is individual dependency of valueon the gas
flow, when the best energy firing conditions are provided
for each type of combustion units (burners) and for eachzone of heating furnace.
For example, rational values
dependency on gas
flow for top zones
1, 3, 5 of a modern highperformance 10-zone continuous furnace 1at Mill 2000
OJSC «MMK» with walking beams, with roof top andside lower natural gas firing, designed for continuous castbillet heating with 250 mm thickness and from 5000 to
12000 mm length is shown in Fig. 1 [1].
Overstated air flow under low gas flow rates is determined by the necessity to maintain the required kinetic
energy of the gas-air jet in order to provide the flow
«sticking» to the flat furnace roof surface. Under high gas
flow rate, less air flow is required in comparison withtheoretically calculated one, since oxygen in intensive
mixing enters gas jet from the workspace by means of
inleakage, where the oxygen content is 5-8%.

Target value A maintaining on required rational value involves constant operator intervention into combustion
process control mode in each gas flow changing. It is physically impossible under non-steady furnace operation behavior. Therefore, overstated A ( ) is set for all flowrates in zones. This reduces the efficiency of fuel combustion process control and increases discharge intensity.
Energy-saving automated system is effectually used
to implement the optimal fuel combustion process control.
This system should independently (without operator intervention) define and maintain that sort ofvalue,
which enables firing to cause maximum thermal effect,with furnace characteristics and external influenceschanging accidentally.
The obligative and necessary functioning condition ofthis optimal fuel combustion process control system is
unimodal (one-extreme without derivative breaking) typeof optimization process steady-state characteristic [1].
The experimental dependencies of top zones workspace temperatures of continuous furnace 1 at the Mill
2000 OJSC «MMK» on value
in each zone are presented in Fig. 2.

Temperature tws ), °C

from 0 to 600°C. Effective solution of this problem ispossible by using optimal control automated systems,
based on the principles of search optimizing algorithms.
Such extreme control systems possess a unique ability toprovide effective control under uncertainty and absence of
accurate quantitative model of the optimizing processing.
In automatic combustion process controlling, underplant conditions, method of volumetric flow rate of firing
and air is frequently used. This method provides target
value stabilization of air flow rate – A in accordancewith the following condition:

Air flow coefficient, m 3/m 3

Air flow coefficient,

a,

m3/m3

Fig.2. Dependency of workspace temperature in the top
welding zones according to zone thermal couple readings
upon air flow rate: 1) zone 3, VTC = 1020m3 / h,and 2) zone 3, VTC = 2600m3 / h, and 3) zone 5,
VTC = 1100m3 / h

Gas flow, ×10 m3/h3

Fig. 1. Dependencies of rational values of air flow rate A
on the gas flow for the upper zones 1, 3, 5 of continuous
furnace 1 at the Mill 2000 OJSC «MMK»

Dependencies analysis obtained proves the ability and
expediency to use optimal fuel combustion process control system in each top zone of fired continuous furnaces.
Long-term practice of automatic optimization systems (AOS) using under real operation conditions showedthat such systems should be two loop circuit [1,7].
The first loop is stabilizing, providing volumetric gas
and air flow proportion, realizes fast but rough firing andair flow ratio. This allows the control system to responsewww.vestnik.magtu.ru. ——————————————————————————————————————————————

59

Optimal energy-efficient combustion process control in heating furnaces of rolling mills

quickly to deep technological indignation, when changing
firing rate and temperature.
The second loop is optimizing, begot on extreme control principles, allows to carry out, within a dedicatedwork area for this circuit, more sensitive optimal condition adjustment of combustion process, but more slowly.
Block diagram of two-loop automatic control systemof optimum combustion process is shown in Fig. 3.
The stabilizing loop, implementing standard PI or
PID controller theory, includes firing rate FS and air rate
AS sensors with rate transmitters VF and V . Functional
generator composes the required air flow rate VA ( ) in
accordance with the expected rational air flow
VF3 ( ) F VF ( ) (see Fig. 1). The value F VF ( ) is
compared in comparison element CE with the current air
flow rate value VA ( ) . The signal VA ( ) is generated
at comparison element output.

V

F V

V

,

where F VF ( ) = VF ( ) LO A ( ) is required current«target» air flow into a zone.
Signal VA ( ) is fed to the input of switch control
unit SCU.
At the same time, signal VA ( ) , which is formed
by a setting device SD and defines target work area of
optimizing loop, is fed to the SCU input.
The switch control unit switches over the control of
the air flow actuating unit AU in accordance with the following condition:( )( ), if VA ( )2 ( ), if VA ( )1

VA ( )VA ( ),

where 1 ( ), 2 ( ) are the switching functions, defining the current travel direction of the actuating unit (AU),that changes the air flow accordingly to stabilizing or optimizing loops in accordance with the following expression:

VA ( )

VAI

i

( )

AU

,

i 1,2 ,

where VAI is the initial value of the air flow;( 1, 1) is the current direction of the air flowi( )rate changing;
AU is constant speed of the actuating
unit (AU), according to technical characteristics.
Optimizing loop involves a heating area temperaturedetector TE, a rate converter RC and an optimizer, begot
on the extreme control principle, providing the detection
and maintenance of optimal combustion conditions within
a set zone VA ( ) in accordance with the extreme type
dependency t°( A ( ) ), (see Fig. 2).
Under normal operating conditions, type of steadystate extreme characteristics and extremum location in thefield «control action – optimizing variable» have not been
defined. Therefore, the using of continuous extreme control system with the remembering of optimized parameter
speed extremum and with actuating unit stop at the moment of maximum speed changing is the most acceptable.
Dynamics of a searching process in such automaticmanagement optimization system (AMOS) of combustion
process is determined by the equations set and logicalconditions [5,6]:

Y X( )

a0 a1 X ( ) a2 X 2 ( ) ... an X n ( )To dZ ( ) / d

Z1 ( ) Y X ( ) ;T dZ ( ) / dZ( )Z1 ( ).

Fig. 3. Block diagram of two-loop system of combustion process control optimization in the workspaceof industrial furnaces

60 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Parsunkin B.N., Andreev S.M., Akhmetov T.U., Mukhina E.Y.

In the case of

search cycle; 3-4 elapsed time of optimizing loop after
AU forced reverse; 4-5 conditioning period before thenext cycle of search, etc.
The time interval C – conditioning before verificatory forced reverse is required for the accumulation of
information about optimizing process current state.
Engineering implementation of two-loop AMOS of
combustion process on the basis of domestic CJSC Mekhanoremontny Komplex (Mechanical Repair Shop) is
examined in detail in [2].
The property of this extremum search method is theabsence of AMOS operation periodic mode and considerably high accuracy in the extremum error less than 5%.

dZ ( )
0d

1, if Z( ) Z ( ) max

Z( )

0;
H

U( )
0, if Z ( ) Z ( ) max

Z( )

0.
H

In the case ofU( )dZ ( )
d1, if Z ( )Z( ) 0Z( )0.
H

If U ( )1 , then 2 ( 1)2( ).
0 , then 2 ( 1) 0 .
If U ( )1 , then 2 ( 1)
2( ) ,
where ( 1) , , ( 1) denote the past, current,

70

18

65

15

posterior time intervals respectively; X ( ) VA ( )is the current value of the control parameter; Z ( ) ,60

the set optimizing parameter point in accordancewith the steady-state characteristic of the optimized
process;obj
L is the equivalent object
0time coefficient, characterizing optimizing process
persistence – obj and lagging – L ; F is thesmoothing filter time coefficient, used for high frequency information signal interference rejection

Z ( ) ; Z ( 1) max is the maximum rate changing
value of the optimized parameter, achieved in theby-past time period;is the optimizing

Z( )
DZ

loop dead zone.
The value Z ( 1) max is formed by a memory
unit in accordance with the following condition:
if Z ( )Z(1) max , then Z (1) maxZ( ) ;

if Z ( ) Z ( 1) max , then Z ( 1) max Z ( 1) max .
The study was made of the automatic optimization
system efficiency on the laboratory setup [1,4], underconditions close to real.
The trajectories of changing Z ( ) , Z ( ) and ( )parameters over time, during search operation mode ofautomatic management optimization system AMOS of
combustion process, in using this extremum search method, are presented in Fig. 4.
The following time intervals are identified in Fig. 4:
0-1 elapsed time of stabilizing loop, 1-2 elapsed time of
optimizing loop; 2-3 conditioning period before the next

50

45

Thermal electromotive force, mV

its change rate over time respectively; Y X ( ) is

55

1

12

9

1 2

3

4

5

6

7

6
2

3

40
Parameter changing
speed, mV/s

Z ( ) are current values of optimizing parameter andAU shaft position, %If U ( )

3

0,3

0
0

150

300

450

600

750

Time, sFig. 4. Change over time Z ( ) , Z ( ) , ( ) in introducing
AMOS of combustion process in the furnace workspace:
1 – relative changing of temperature detector; 2 – air flowchanging, 3 – temperature changing rate
The utilization of the introduced softwareprogrammable optimization technology of control energyintensive process of combustion in industrial furnaces
workspace enables 1.5-2.5% reduction of firing discharge
intensity. That becomes possible due to more effective
and operational control of air flow under heating furnaces
nonsteady behavior.
Moreover, combustion process stabilization will leadto the stabilization of thermal state of heating billets andwill permit to improve calculation accuracy of the strip
thermal state during rolling [8]. Such firing combustion
control systems are applicable for almost all thermal energy consuming units, operating in nonsteady mode, inwhich gaseous firing is used as the source of heat [9].

www.vestnik.magtu.ru. ——————————————————————————————————————————————

61

Optimal energy-efficient combustion process control in heating furnaces of rolling mills
References
1.
2.
3.
4.

5.

Parsunkin B.N., Andreev S.M., Akhmetov U.B. Optimization of processing
control in metallurgy. Magnitogorsk: Nosov Magnitogorsk State Technical
University, 2006. 198 p.
Kazakevitch V.V., Rodov A.B. The automatic optimization systems. Moscow: Energy, 1977, 288 p.
Parsunkin B.N., Andreev S.M. Processing control optimization of fuelcombustion in heating furnaces workspace. Steel. 2000, no. 5, pp. 48-52.
Parsunkin B.N., Andreev S.M., Obukhova T.G. Study of optimum energy
efficient fuel combustion process in metallurgical furnaces workspace.
Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta
im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical
University]. 2005, no. 4, pp. 28-36.
Parsunkin B.N., Bushmanova M.V., Andreev S.M. Calculations ofautomatic systems of processing optimization in metallurgy: Textbooks. Magnitogorsk: Nosov Magnitogorsk State Technical University,
2003, 267 p.

6.

7.

8.

9.

Sayrov A.M. Optimization of thermal management in heating furnace
workspace. Automated technologies and production: Collection of Scientific Papers. Ed. Parsunkin B.N. Magnitogorsk: Nosov Magnitogorsk State
Technical University, 2013. no. 5, pp. 296-301.
Parsunkin B.N., Andreev S.M. Ways to improve the efficiency and noise
immunity of processing control automatic optimization. Automated technologies and production: Collection of Scientific Papers. Ed. Parsunkin B.N. Magnitogorsk: Nosov Magnitogorsk State Technical University, 2013. no. 5, pp. 277-290.
Rumyantsev M.I., Shubin I.G., Nosenko O.U. Model designing to calculate the temperature of low-alloy steels in hot rolling. Vestnik
Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I.
Nosova. [Vestnik of Nosov Magnitogorsk State Technical University].
2007, no. 1, pp. 54-57.
Zadonskaya T.A., Shvetsova E.S., Koptsev V.V. Firing of high-speed
streams of natural gas. Vestnik Magnitogorskogo gosudarstvennogo
tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk
State Technical University]. 2009, no. 3, pp. 67-68.

Antsupov A.V., Antsupov A.V. (jun), Antsupov V.P.

DESIGNED ASSESSMENT OF MACHINE ELEMENT RELIABILITY
DUE TO EFFICIENCY CRITERIA
Abstract. The universal method of reliability assessment of mechanical system loaded elements at the design stage as a sequenceof steps within the procedure of constructing physical and probabilistic models of parametric failure formation based on various
criteria is suggested. The methodology of forecasting durability of parts by kinetic strength is represented and an example of its
implementation is shown.
Keywords: methodology, forecasting, reliability, dependability, durability, failure, damage susceptibility, gamma-percent life.

The main problem of the reliability theory is behavior
prediction of mechanical system parts and components insupposed conditions of external loading, when it becomes
possible to evaluate their reliability and durability in earlystage design. In this case, the assessment of system element behavior and their parameters changing over time infuture running is carried out on the dynamic, physical andprobabilistic models [1].
A single, universal methodological approach to probability forecasting of trouble-free operation and resource
characteristics of loaded elements of mechanical systems
according to various criteria of their performance wasstated in this paper, on basis of mathematical formalization of reliability theory basic concepts of engineering
objects (GOST 27.002-89), and general concept of theirgradual failure formation [2-4].
To describe theoretically the objective formation oftechnical product failures during their damageability (degradation) under external affecting, the suggested approachis stated as a series of rules of their parameter reliability
dynamic models designing.
This approach is presented in a probabilistic form,
and is a combination of the following steps.
I. Selection of object state basic parameter.
Parameter Xt (a random variable) is selected for thetesting product type, according to the standard (GOST20911-89) definition of «object state». Variable changing
over time simulates the parameter behavior (state changing) during the entire operation period under certain external affecting conditions.
II. The equation formulation of object state.
Random function (dependency) elaboration or choosing, that describes parameter Xt increasing (+) or decreas-ing (-) changing over time, and models the product statechanges in aging (degradation) during the operation canbe written as the following:
t

Xt

X0

X t dt ,(I)0where X0 is Xt parameter distribution at time T = t0 characterizing the initial object state; X t dX t / dt denotes
random variable current distribution of object
damageability rate at time T = t;
If a random variable of object damageability rate does
not change over time – X t X const , then the conditions (I) can be written as follows:

Xt

X0

(I. )

X t

Equations (I) simulate object damageability over time.
III. The formulation of object efficiency condition.
In accordance with the standard definition of «object
performance capability», according to GOST 27.002-89,
the condition of its performance is mathematically formulated in the form of one possible inequality:
t

Xt

X0

X t dtxL or

X t dt

xL ,

0
t

Xt

X0

(II)

0

where xL is a limit value of Xt parameter, established in

62 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Antsupov A.V., Antsupov A.V. (jun), Antsupov V.P.

technological standards (TS) or assigned under the operating experience of such objects.
If the random variables in the condition (I) are normally distributed, and X t X const , then performancecapability conditions (II) can be written as the following:

Xt

X0

xL and X t

X t

X0

X t

uL (t ) or Ut

uL ( t ) .

x0

x t

2
x0

2
x

Xt

x0

(II. )

x t

2
x0

2
x

t

uL (t ) .

2

xL

where u L ( t )u L ( t ) or

t2

x0
2
x0

x t
2
x

t2

denotes the current limit

value of SND quantile of a random variable X tx0( x0 max

x0 min ) / 2 ;( x0maxx0

x0min ) / 6

areare numerical characteristics of arandom parameter X .
Equations (II) reflect the range of all possible operable object states.
IV. Elaboration of equations for object reliability
assessment.
Using the basic concepts "distribution function" ofthe probability theory makes possible to formulate thedependencies for estimation of object failure-free operation probability - condition efficiency probability (II) for
any fixed instant of future operation:t

P t

P( X txL )X t dt ) xL ) F ( xL ) or(( X 00

P t

P( X t

xL )

(III)
.

t

1 P(( X 0

X t dt ) xL ) 1 F ( xL )0

If the normal distribution of X t parameter is constantover time ( X t

X

x0
2
x0

P (t )P( X t1( L (t ) ) 1

x t
2
x

or

t2
(III.a)x L ) 1 F (u L ( t ) )
xL

x0
2
x0

x t
2
x

t2

.

Equations (III.a) define the object reliability law indP(t ) / dt ) form, thethe integral (or differential f (t )law of object gradual failure formation in solving the direct task of the reliability theory. According to [2], it isasymmetric and does not obey the normal distribution.
V. The formulation of the object transition equation
to the limit state (the state of parametric failure).
According to GOST 27.002-89 standard definitionsof «object performance capability» and «parametric failure», the conditions of product transition into the parametric failure state in the form of limit value achieved by
Xt parameter are formulated as following:t

stant of time T=t0; x0 max , x0 min are maximum and minimum values of object X0 parameter, defined as the initialxxL( L (t ) )xL ;numerical characteristics (mean and standard) of a random parameter X t X 0 of object state at the initial in-conditions; x

xL ) F (uL (t ) )(II.b)

Expanding the current value of parameter standard
normal distribution quantile (SND), conditions (II.b) canbe written as following:Xt

P(t ) P( X t

Ft ( xL )(uL (t ) ) :or the Laplace function

xL . (II.a)

Centring and normalizing values Xt and xL, inequalities (II.a) can be written, using proper quantiles, as thefollowing:Utbility is denoted using SND function F (uL (t ) )const ), the main indicator of relia-

Xt

X0

X t dt

xL ,

(IV)

0

If the normal distribution of X t parameter is constantover time ( X t
expressed asXt

X

x0 x t
2
x0

Xt

2
x

t2

x0 x t
2
x0

2
x

t2

const ), the models (IV) can beuL(t ) or(IV.a)uL(t ) .

Equations (IV) reflect the range of all possible object
limit states.
VI. Elaboration of equations for object durability
assessment (service life characteristics).
In accordance with GOST 27.002-89 gamma-percent
resource t definition, the dependences are derived for
its assessment by equation (IV) solution concerning
t t for assigned accepted value of failure-free operation probability P (t )and the relevant distribution

quantile [uL( ) ] value owing to the known law of Xt random variable. In general, this dependence can be represented by any function:www.vestnik.magtu.ru. ——————————————————————————————————————————————

63

Designed assessment of machine element reliability due to efficiency criteriaof a large object group – «stationary» triboconjugation, by
their component wear resistance criterion.
Beneath, on basis of suggested approach a reliability
If the normal distribution of X t parameter is constantprediction strategy of different object group - machinein time ( X t X const ), gamma-percent resource is and unit loaded elements, according to kinetic strength
criterion, is formulated.
determined by equation (IV.a) solution concerning t t
Currently, the problem of the strength of solid bodies
during X t xL and uL(t ) [uL( ) ] substitution in the under load is considered from the point of kinetic approach [12-13]. From this point of view, the destruction
form of:process is represented as evolu2
2
2
2
2
2
2
tive process of material structur( x ) xL
( xL x ) ([uL( ) ] x x ) ([uL ( ) ] x 0xL )al damage accumulation in time.
,
(V.a)
t
x 2 [uL ( ) ]2 x2
In reaching material structure defect by current solidity inwhere the value [uL( ) ] is determined by assigned accept- any local volume - its damageability, a limit value, microcrack occurrence takes place, which extends through the, most loaded material volumes and leads to its division
ed value of failure-free operation probability P ( t )and the value xL xL x0 is the assessment of mathe- into parts (destruction).
The degree of local volume structure damage of partmatical expectation of X t limit change of Xt parameter;material at any fixed time point t is estimated quantitaVII. Elaboration of kinetic equation of object dam- tively by density value of potential defect energy
ageability.
u (t ) u t , which is determined by the external loading
On basis of any theory, concept or experimental re- conditions and material properties [13].
searches, a kinetic equation is stacked up to estimate obTaking into account the aforementioned, the methodject damageability rate X t , depending on its geometrical ology steps of loaded part reliability and durability predicand microgeometrical d i , t characteristics, i material tion may be formulated according to (I) - (VI), in a sequence of the following operations.
properties, power and kinematic parameters F, external
At the first stage as part state X t parameter, in which
impact V, time t and other factors.
internal
stresses
emerge, affected by external loading
In general, it can be represented in the form of any
attemperatureT,
wetake the potential energy density of
random function:
defects u t , which characterizes the actual degree of(VI)
X t f ( d i , t , F , V , i , t , ...) .
structure damage of material part local volumes [13].
The represented methodological approach (I)–(VI) Herewith, according to the central limit theorem of probcan be formulated in the form of a separate methodology ability theory, we consider normal the distribution of aof reliability assessment (prediction) of certain groups of random variable X u at any time t, as a parameter,tttechnical objects, using one of the possible criteria such as
depending upon a set of independent random factors [1].
performance conditions (II) [1-4]:
Furthermore, to simplify mathematical expressions we– static or kinetic strength;
will operate with its mean value u t .
– durability;– hardness;
At the second stage, we will formulate the equation of– bearing value;
loaded element states:– heat resistance and others.
t
When selected Xt parameter, the status of a particular
(1)
u
u 0
u t dt .
product (parts, unit) and known data about:0– law of its distribution;– boundary conditions, describing the object loading where u 0 is the average density of material component
diagram, its properties, and the initial state in supposedpart potential energy in the initial state (at t 0 ), which,operating conditions;according to [13], can be defined as a function of hard– its damageability equation (VI) for X t assessment,
ness average value HV according to Vickers:
designated sequence of steps produces a sequence of opera2,4
tions (probabilistic technique) of quantity estimation of fail0,071 HV
;
(1.a)
ue 0
ure-free measure P t P X t x L or P t P X t xL2
6
6,47 10 6 HV 0,12 10 2
and durability t of the investigated object either in its
where u t du e t / dt denotes damageability averagedesigning, or in running.
In particular, in publications [5-11], this approach is velocity (damage accumulation) of element material
implemented as a reliability parametric prediction strategy structure at time t.

tf ( x0 ,

x0

, x,

x

, [uL ( ) ]) .

(V)

64 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Antsupov A.V., Antsupov A.V. (jun), Antsupov V.P.

At the third stage, we will state the condition of loaded component part performance efficiency:
t

u

u 0

u t dtue * ,(2)0

where ue*

u* u denotes the critical density of struc-ture defects energy of material local volumes of loaded
component part [13]; u* is the critical density of materialinternal energy (critical energy intensity), which is equal
to its melting enthalpy in solid H S or liquid H L
T

dT denotes the thermal component ofstate; u0

the material internal energy density of loaded component
part at a given temperature T; ,are density and heat
capacity of the component part material.
At the fourth stage we will write the expression forloaded element reliability evaluation at time t, using as anindicator the reliability safety factor (safety margin), calculated according to the average value u t of state parameter [1]:tu e * / ue tnt

ue * / u 0

u t dt .

where M R2

peak cycle stresses; k

u

u 0

U
0

u t dtue * ,(4)

At the sixth stage, using the expression (5), we formulate the equation, its solution for t t L , will define theaverage limit resource to element failure (damage):tu t dtue * u 0 .

(5)0

At the seventh stage as a damageability kinetic equation for the evaluation of average velocity u t of element
damageability, which is in the loaded state, which is included in the equation (1)–(5) of its failure forming general diagram, one can use V.V. Fedorov dependency, hestacked up in the publication [13] using long-timestrength thermodynamic criterion.
In general, this equation is the following:ue tf ( , T , ue t , t , ...) .

(6)

In carrying out engineering calculations we use oneof the simplified versions of this dependency to determine
the time constant value u
u :
2
R

k2

2

A0 / (6 G

),

(6. )

2

4 is a equivalency coef-

1 6,47 10 6 HV

0,12 10 6

,

h N0

exp

,
R T

,

(6.b)

where h is the Planck constant; N0 is the Avogadro numis activaber; R is the universal gas constant; U ,tion energy of interatomic bond damage process at thegiven voltage
and temperature T:

U

,

U0

U T

2
R

k 2 18

K

2

(6.c)

;

where U 0 is free energy of process activation at T

03
1
is activation energy
0 K
2quantity, determined by the temperature; K E 3 1 2

0;

and

0

1 r

denotes an overstress coefficient of interatomic bonds; G
and are modulus of rigidity and coefficient of internalenergy distribution irregularity over the loaded component part, the value of which is selected referring to [13];
Coefficient A0 of stress tensor ball portion influence
on interatomic bond damage activation energy, is expressed according to [13]:

(3)

t

2

ficient of non-stationary tension state (non-stationary tension state with a coefficient of skewness r
minmaxtransition to the equivalent steady state with voltage); min , max ,are minimum, maximum and0

At the fifth stage we will formulate the equation ofloaded component part transition to the marginal state(parametric failure state):

1 r

U T

is all-round material compression index; 0 ,,arelinear thermal expansion coefficient; the Poisson's ratio
and material elastic modulus.
Complex equations (6.a-c) denote a mathematicalmodel of machine element and construction stationary
damageability process, in which internal static or dynamic
tensions
emerge, affected by external loading and constant temperature T.
For a loaded element stationary damageability process (with constant rate uu , defining by models(6.a-c)), the safety margin average value at any time t isdetermined by the simplified expression (3):ntue * / ue t

u e * / (u 0

u t) .

(3.a)

and the ultimate resource is determined by the simplified
expression solution (5) – u tL
tively to ttL(ue * u 0 ) / respec-t L as:(ue * u 0 ) / u .

(5.a)

The complex of equations (3.a), (5.a)–(6.a-c) denotesa physical probabilistic model of the formation process of

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65

Designed assessment of machine element reliability due to efficiency criteria

gradual failures of machine elements, in which internal
static or dynamic tensions
emerge, affected by external loading and constant temperature T.
The sequence of mathematical operations, based on
this model in order to estimate the expected average resource t L , defines their durability forecasting method andis the academic analogue of S.N. Zhurkov famous experimental equation [12, 13].
The example of the suggested method implementation is shown in figure. A graphical interpretation of theequation solution (5.a), taking into account (6.a-c) for aspindle from 25 steel grade with mechanical properties
230 MPa ,420 MPa and HV 2020 MPa ,exposed to static uniaxial tension at different tempera142,9 MPatures, is represented. In particular, at

40
and temperature
its forecast limit time –average limited endurance under these conditions,comprises t L 3, 7 10 6 s 1, 43 mo (see marked point
ordinate in figure).

Nomograph for loaded element
durability estimation
The suggested approach, in our opinion, allows toforecast different loaded parts durability, taking into account the expected values of maximum tension , temperature T and physical and mechanical material properties, as well as to analyze the possible ways of their life
improving at the design and operational stage.

For example, as can be seen from the nomograph,spindle durability can be greatly prolonged by its temperature reduction, physical and mechanical properties
changing, as well as other parameters, included in theequations (5.a)–(6.a c).
References
1.

Pronikov A.S. Parametricheskaya nadezhnost’ mashyn. [Machine parametric safety]. Moscow: The Bauman University Publishing House
2002, pp. 560.
2. Antsupov A.V., Antsupov A.V. (Jr.), Antsupov V.P. et al. Ocenka
dolgovechnosti nagruzhennyh detalej po kineticheskomu kriteriju
prochnosti. [Evaluation of durability stressed parts on the kinetic
strength criterion]. Materialy 70-j nauchno-tehnicheskoj konferencii:
Sb. dokl. [Proceedings of the 70th Scientific Conference: Sat Reports]. Nosov Magnitogorsk State Technical University, 2012, vol. 1,
pp. 137-141.
3. Antsupov A.V., Antsupov A.V. (Jr.), Antsupov V.P. et al. Metodologija
analiticheskoj ocenki nadezhnosti tehnicheskih ob’ektov [Analytical methodology for evaluating the reliability of technical objects]. Materialy 70-j
nauchno-tehnicheskoj konferencii: Sb. dokl. [Proceedings of the 70th Scientific Conference: Sat Reports]. Nosov Magnitogorsk State Technical
University, 2012, vol. 1, pp. 141-144.
4. Antsupov A.V., Antsupov A.V. (Jr.), Antsupov V.P. and others. The methodology of probabilistic assessment of machine elements according to different criteria. Mehanicheskoe oborudovanie metallurgicheskih zavodov:
Mezhregion. sb. nauch. tr. [Mechanical equipment of metallurgical plants:
Interregional Collection of Scientific Papers]. Ed. Korchunov
A.G. Magnitogorsk, 2012, pp. 29-37.
5. Antsupov A.V., Antsupov A.V. (Jr.), Slobodyanskii M.G. et
al. Reliability prediction and other friction units based on
the thermodynamic analysis of the process of friction.
Vestnik
Magnitogorskogo
gosudarstvennogo
tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of
Nosov Magnitogorsk State Technical University]. 2010, no.
3, pp. 54-60.
6. Antsupov A.V., Antsupov V.P., Antsupov A.V. et al. Prediction reliability friction units by the criterion of wear on thestage of their projection-transformation. Trenie i smazka v
mashinah i mehanizmah. [Friction and lubrication in machinery]. 2010, no. 11, pp. 38-45.
7. Antsupov A.V., Antsupov A.V. (Jr.), Gubin A.S. et al.
Triboconjugation reliability predicting. Materialy 68-jnauchno-tehnicheskoj konferencii: Sb. dokl. [Proceedingsof the 68th Scientific Conference]. Magnitogorsk, 2010,
vol. 1, pp. 262-264.
8. Antsupov A.V. The scientific and methodological basis offorecasting reliability triboconjugation parametric design
stage. Sovremennye metody konstruirovanija i tehnologii
metallurgicheskogo mashinostroenija: Mezhdunarodnyj
sb. nauch. tr. [Modern construction methods and technologies metallurgical engineering: International Collection of
Scientific Papers]. Ed. N.N. Ogarkov. Magnitogorsk: Pabl.
Nosov Magnitogorsk State Technical University, 2011,
pp. 36-39.
9. Antsupov A.V., Antsupov A.V. (Jr.), Gubin A.S. et al. The
methodology of probabilistic forecasting reliability and service life of tribological. Izvestija Samarskogo nauchnogo
centra RAN. [Proceedings of the Samara Scientific Centerof Russian Academy of Sciences]. 2011, vol. 13, no. 4 (3),pp. 947-950.
10. Antsupov A.V., Chukin M.V., Antsupov A.V. (Jr.),
Antsupov V.P. The scientific and methodological basisof forecasting reliability triboconjugation at the design
stage. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo
universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State
Technical University]. 2011, no. 4, pp. 56-61.
11. Antsupov A.V., Antsupov A.V. (Jr.), Antsupov V.P. Methodology for predicting the reliability of tribological. Trenie i smazka v mashinah i mehanizmah. [Friction and lubrication in machinery], 2012, no. 2. pp. 3-9.
12. Regel V.R., Slutsker A.I., Tomaszewski E.E. Kineticheskaja priroda
prochnosti tverdyh tel. [The kinetic nature of the strength of solids].
Moscow, 1974, 560 p.
13. Fedorov V.V. Kinetika povrezhdaemosti i razrushenija tverdyh tel. [Kinetics
of solid damageability and break-down]. Tashkent: Publ. «Fan» UzSSR,
1985, 165 p.

66 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Gun G.S., Rubin G.Sh., Chukin M.V., Gun I.G., Mezin I.U., Korchunov A.G.

Gun G.S., Rubin G. Sh., Chukin M.V., Gun I.G., Mezin I.U., Korchunov A.G.

METALLURGY QUALIMETRY THEORY DESIGNAND DEVELOPMENT
Abstract. The theory of complex quantitative quality assessment (qualimetry) of metalware products and production technologies, based on the same design principle of metalware properties structurization and systematic approach to product quality and technological process assessment has been developed.
The functionally-aimed analysis as the methodological basis of metalware products quality and technologies research has beensuggested.
Keywords: qualimetry, metalware production, effectiveness, reinforced bars for concrete sleepers.

Qualimetry is a scientific theory of the quantitative
qualitydetermination,
firstly
represented
byG.G. Azgaldov [1], who stated the main principles ofgeneral, special and objective qualimetry, being successfully developed in various fields of science, technology
and, as well as in the assessment of social phenomena,
system and state conditions.
For 35 years the authors have been developing thetheory of complex quality assessment – metallurgy
qualimetry [2-24]. During these years a significant number of researches in the field of assessment, prediction andcontrol of metalware product quality and their production
processes have been performed (Fig. 1).
A number of problems (see the Table) of the general
theory of qualimetry have not been solved till the present,
and many research object appendixes are lack of correct
operational methods and algorithms of products and technologies quality assessment.
There are the most significant problem-solving procedures carried out by the authors (Fig. 2):
qualimetry categorical apparatus has been developed on the basis of the following concepts: thefunction of the evaluation object, the consumer
phase of the object, interaction;
structuring principles of object quality using
functional approach have been developed;
new determination methods of the impact level ofseparate structural units and quality hierarchy ongroup and complex assessments have been developed;
methods of quality assessment convolution ingroup assessment, taking into account the synergistic system effect have been developed;
indicators and methods of technological processing complex assessment have been introduced;
methods of operational analysis of technologicalprocessing quality have been developed.
The above mentioned solutions allowed to develop
and implement a strategy of complex quality assessmentof hardware and its production technologies, based on:– a single constructive principle of metalware properties structurization;– a systematic approach to product quality and technological process assessment;– estimation of direct processing parameters, not only
the goods quality.

The functional objective analysis strategy [14, 18] tocontrol metalware production was developed. It is based on:– the determination of definition «function» on thebasis of physical interaction;– the determination of life cycle, which is called a consumer phase, concerning the product assessment period;– the allocation of three stages of a consumer phase,such as transport, mounting and operational.
The basis of the functional-specific analysis comprises the following:– a systematic approach to the integrated quality assessment;– a process approach to the process effectivenessevaluation;– process control methods in order to obtain the desired quality of hardware; improve the efficiency of theprocess.
Qualimetry main issues
Position
Issue
The tree type structure of
The lack of structuring principle
properties
Convolution of estimations,
The lack of an effective method fortaking into account weightiweightiness determining
ness properties
The lack of formulas for the domiConvolution with the help of nant properties convolution taking
into account weightinessmedium and triangularshape formulas
The system properties interaction
isn’t taken into account
Quality is the totality of fea- The period of any object life cycle,tures with a focus on satisfy- where evaluation takes place, ising the definite needs
not definedThus, it was possible to develop general, specific,
and objective qualimetry applied to hardware production (Fig. 2).
The academic staff of Nosov Magnitogorsk State
Technical University together with industrial engineers
managed to solve a number of current challenges for quality assessment, new technologies development and production management at Russian enterprises such as: OJSC
«MMK-Metiz Works», «Avtonormal» Belebeevsk Plant,
Beloretsk Metallurgical Plant, and Cherepovets Steel
Rolling Mill.

www.vestnik.magtu.ru. ——————————————————————————————————————————————

67

Metallurgy qualimetry theory design and development

Fig. 1. Diagram of NMSTU researches in hardware production qualimetry
We developed methods of assessment calculation,technology selection, the first of which were tested on steel
profiles of high accuracy and calibrated metal at Cherepovets Steel Rolling Mill and OJSC «MMK METIZ».
Serious cycles of researches and implements werecarried out on the basis of quality control by the expert
team of «BelZAN» and «Belmag» CJSC NPO whichallowed to introduce new types of fasteners and balljoints and to improve the efficiency of their manufacturing processes.
Along with modern methods of quality assessmentand management, in «MMK METIZ» production, thefollowing high-tech technologies are used:– a special kind of carbon steel heat treatment, thatprovides to obtain material ultra fine grained andnanostructures, having high strength and ability to be influenced by straining with large total strains;– high-performance multiple straining cold plastic
processing using cone shaped surface tools, activating
available glide planes within each straining cycle, whichleads to additional fragmentation of material structure
and provides a maximum hardening of treating reinforcement.
– a special kind of thermal straining processing, consisting in the simultaneous effect of plastic deformation incovering die-rolled section on the rebar surface and thermal effect under strong tension, providing a high set of
special properties of nanostructured reinforcement: coupling with concrete, relaxation resistance, cyclic strengthand corrosion resistance.

68 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Gun G.S., Rubin G.Sh., Chukin M.V., Gun I.G., Mezin I.U., Korchunov A.G.
tive technology choice for high-precision profiles for mechanical engineering]. News of HIGH SCHOOLS. Mechanical engineering. 1981, no. 5, pp. 155-157.
SPECIFIC
10. Rubin G.Sh., Gun G.S., Pudov E.A. and others. KomOBJECTIVE: METALWARE
pleksnaya otsenka kachestva stal'noy kanatnoy provoAND HARDWARE PRODUCTION
loki. [The Complex estimation of steel rope wire quality]. Steel. 1983. no. 1, pp. 56-57.
11. Zakirov D.M., Rubin G.Sh., Salnikov V.V. Apparat
Effectmatematicheskoy logiki dlya kompleksnoy otsenki
effektivnosti tekhnologicheskikh protsessov. [Matheof system
matical logic device for complex evaluation of proAcceleration
Fuzzy control modelinteraction
cessing efficiency]. Rolling. 2006, no. 12, pp. 35-58.
12. Chukin V.V., Rubin G.Sh., Vakhitova F.T. et al. Problema povysheniya kachestva krepezhnykh izdeliy [TheProcessing
Process
Local,
problem of fastener quality improving]. Vestnik
Magnitogorskogo gosudarstvennogo tehnicheskogo
approacheffectivenessGlobaluniversiteta im. G.I. Nosova. [Vestnik of Nosov
Magnitogorsk State Technical University]. 2007, no. 4.
pp. 99-102.
Analysis
Factor
13. Rubin G.Sh., Kamalutdinov I.M. Funktsional'nyy analiz
algorithm
analysis
struktury svoystv geofizicheskogo kabelya [Functional
analysis of the structure of cable geophysical properties].
Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov
ConsumerTransport, wiring,
Magnitogorsk State Technical University]. 2010, no.
phase
operation stages
1(29), pp. 70-71.
14. Rubin G. Sh. Funktsionalno - tselevoy analiz kachestva
izdeliy [Functional-target analysis of products quality].
Fig. 2. Structural and logic diagram of research
Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov
For the first time, in Russia, commercialization ofMagnitogorsk State Technical University]. 2011, no. 2(34), pp. 29-30.
project innovative scientific and practical results allows to 15. Rubin G.Sh., Storozhev S.B., Gun G.S. et al. Vybor ratsionalnoy
tekhnologii pri proizvodstve vysokotochnykh profiley s primeneniem
establish knowledge-intensive rebar production for reinmetodov kolichestvennogo izmereniya kachestva. [Choice of a rational
forcement concrete sleepers of new generation, on basis oftechnology during the manufacturing of high-precision profiles with applicarbon steels thermal straining nanostructuring, that procation of methodology of the quantitative quality measurment]. Pyatiletkekachestva i effektivnosti – trud i poisk molodykh metallurgov. Vsesoyuznavides to achieve nanostructured state of processing material
ya nauchno-tekhnicheskaya konferentsiya. [Labour and search of young
and improve finished product operating performance.
metallurgists for the five year plan of quality and efficiency. All-union scientific and technical conference]. Tula, 1978, pp. 92-93.
Due to the success of the university research team it
G.Sh., Chukin V.V., Zakirov D.M. et al. Vybor effektivnoy tekhnologii
became possible to found a unique Doctoral Council in 16. Rubin
proizvodstva metizov avtomobilnogo naznacheniya. [Choice of efficient
Quality Management in metallurgy at NMSTU (the sole
production technology of metal products for automotive use]. Trudy VII
kongressa prokatchikov. [Proceedings of the VII Congress of rollermen].
Council in Russia). A number of specialties in the field of
Moscow, 2007, vol. 1, pp. 395-399.
certification and production quality management were 17. Mezin
I.Yu., Rubin G.Sh., Zakirov D.M. et al. Metodologiya kompleksnoy
opened; the branch of the Academy of Quality Problems
otsenki protsessov kholodnoy obyemnoy shtampovki. [Methodology of acomplex process evaluation of a cold die forging]. Sovremennye dostiof Russian Federation was organized in Magnitogorsk.
zheniya v teorii i tekhnologii plasticheskoy obrabotki metallov : tretya
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kachestvom metizov. [Functional analysis as a methodological basis of metal[Logical rules of product quality rating]. Magnitogorsk, 1981. 23 p. Deposproducts quality management]. Trudy VIII kongressa prokatchikov. [Proceedited by VINITI 19.09.1981, 4105-81 B.
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proizvodstva avtomobilnogo krepezha : monografiya. °[Quality control estimaInnovatsionnye tekhnologii obrabotki metallov davleniem : sbornik doklation of automobile hardware production : monography]. Magnitogirsk : Nosov
dov mezhdunarodnoy nauchno-tekhnicheskoy konferentsii. [Innovation
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gorsk State Technical University, 2008. 133 p.
the basis of thermal-straining nanostructuring. Ferrous Metallurgy: Bulletin of
8. Rubin G.Sh., Gun I.G., Kireev I.N. et al. Metodika vybora ratsionalnoy tekhnoScientific-Technical Information. Edition 4 (1348), 2012, pp. 100-105.
logicheskoy skhemy proizvodstva profiley kalibrovannogo metalla [Methodolo23. Rubin G.Sh. Qualimetry of hardware production. Magnitogorsk : Nosovgy for the selection of a rational production scheme of calibrated metal profiles.
Magnitogorsk State Technical University, 2012, 167 p.
News of HIGH SCHOOLS. Ferrous Metallurgy. 1980, no. 11, pp 40-42.
24. Korchunov A.G., Chukin M.V., Gun G.S., Polyakova M.A. Product quality
9. Rubin G.Sh., Gun G.S., Pudov E.A. and others. Vybor effektivnoy tekhnologii
management in hardware production technologies. Moscow: Publishing
polucheniya profiley povyshennoy tochnosti dlya mashinostroyeniya. [Effec
House «Ore and Metals», 2012, 164 p.

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69

Technological reserves: reasonable implementation of simple solutions to improve hot rolling technology

Lutsenko A.N., Rumyantsev M.I., Tulupov O.N., Moller A.B., Novitskiy R.V.

TECHNOLOGICAL RESERVES: REASONABLE IMPLEMENTATION OFSIMPLE SOLUTIONS TO IMPROVE HOT ROLLING TECHNOLOGY
Abstract. This article presents results of solving the multifactorial problem of finding and using process-reserves in flat and longproduct rolling.
Keywords: hot rolling technology, mechanical properties, quality, technological reserves.

First. To reduce the number of products with nonconforming mechanical properties we improve thetechnology: realign rolling schedule to minimize thevariation of the properties.
Technology improving in order to reduce the amountof low-quality rolling in terms of mechanical properties
should be done on account of searching for rolling modes
that enable minimum actual variation of product properties. We suggest using properties hereinafter referred to as
conformance aspects to estimate process performance interms of products quality [1]. If the quality is establishedwith maximum tolerable values (top estimate of conformance),
USL

qPU

3s
LSL

qPL

3s

,

to calculate Ppk . Average value (as actual variation centre) and standard deviation (as actual variation property)
for sampling from one lot of products or several lots ofthe same products, but produced from the same melt areused to calculate q pk . Due to such similarity of conformance aspects to process indexes, «excellent», «good» and«satisfactory» process performance estimates that correspond to the following values of aspects (1)-(3): morethan 1.67; 1.33-1.67 and 1.00-1.33 can be used.

(1)

.

(2)

and, if it is established with minimum tolerable value (lowestimate of conformance).
If maximum and minimum tolerable values are established (conformance estimate with regard to average position)q Pk

m in q PU ; q P L .

(3)

In (1)-(2) USL USL x and LSL x LSL aretolerable intervals of quality property variation (Fig. 1),
and 3s is the share of its actual variability, falling withintolerableinterval.
Standard
deviation
n

s

1 n 1

xi
i 1

x

2

n

and sampling mean x 1 n xi
i 1

are used as the property of actual variability and scattering centre appropriate to it, where x i is single measurement result of quality property for a certain product unit
( i 1, , n ).
Conformance aspect q pk is similar to process performance index Ppk , known in SPC [2], as they compare
tolerable variation of quality property with regard to position of centre of actual variation (numerator) and actual
variation (denominator). Though aggregate data presented
in sampling made in the course of production of many lotsof products of certain types from melts with different
chemical compositions for a long period of time are used

Fig. 1. For calculation of conformance aspect at bilateral
restiction of quality property
is tolerance field middle)
As one of the examples of suggested approach application we provide results of estimating quality of hotrolled steel of current production to requirements of
GOST 16523 to mechanical properties of cold rolled steel
of strength groups 270 and
300 . Actual variationof aspects analyzed in comparison with tolerable variation
is demonstrated with data in Table 1. If we compare sampling means x with limits of rated intervals of variation
LSL and USL, estimated hot rolled stripes can bedeemed good to replace cold rolled steel profile in termsof strength group
300 , as well as 270 group (inboth cases LSL x USL ). Though comparison of actual variation of temporary resistance with tolerable variation of group 270 shows that x is shifted towards top
limitof
tolerance,
andaspectrange( 6 s 6 9, 9 59, 4 MPa) makes 42% of tolerable vari-

70 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Lutsenko A.N., Rumyantsev M.I., Tulupov O.N., Moller A.B., Novitskiy R.V.

ation ( USL LSL =410-270=140 MPa). Thus, at excellent low estimate of conformance ( qPL =3.85) top estimate, as well as final differential estimates of temporary
resistance are unsatisfactory ( q pk q PU =0.89).
Table 1
Estimate of conformance of mechanical properties of hotrolled stripes of 2 mm in thickness from steel 08ps torequirements of GOST 16523–97 to cold rolled steel [3]Quality
aspects

Tolerablevariation, MPa 300
25
%

x

s
strength group 270
410 383.8 9,934.38 1.31
strength group 300
480 383.8 9.934.38 1.31

LSL USL, MPa 270
25,%

Actualvariability

Differential
estimates
q pk

qPL

qPU

3.85
2.39

0.89 0.89-

Fig. 2. Influence of rolling end temperature in the field of
non-recrystallizing austenite on conformance aspects foryield strength (1) and ultimate strength (2)

2.83
2.39

3.25 2.83-

The temperature mode improvement of 5,000 heavyduty sheets production of 16-20 mm in thickness on plate
mills for ship-building from steel grade D32 can be used as
example of application of conformance aspects to improve
the technology. Sheets are produced by controlled rolling(CR) technology followed by accelerated cooling. Where
deformation process is divided in two stages – rolling in thefield of recrystallizing austenite (stage I) and rolling in thefield of inhibited recrystallizing (stage II). In this relation,
the following reference properties of temperature mode canbe defined as: t (I) and t (II) is the temperature of stages I
and II rolling beginning; t (I) and t (II) is the temperature ofstages I and II rolling end; t and t is the temperature ofaccelerated cooling beginning and end. The application ofconformances aspects to ensure required mechanical properties of rolled steel at minimum variation is as follows.
The higher q P k the better applied technology ensuresconformance of actual values of product quality to requirements specified in regulatory documentation (i.e. thecloser actual quality values are to the middle of interval oftolerated variation and the smaller their actual variabilityis). Therefore values of references aspects of technology
process that produce maximum values q P k [1] are preferable. Conformance aspect value dependencies for yieldstrength and ultimate strength on temperature at the end ofrolling in the field of non-recrystallizing austenite areshown as an example in Fig. 2. If conformance aspect ismore than 2 for the whole yield strength range t (II), q P k <1 for ultimate strength at t (II) = 825°C and more. It certifies insufficient performance of the process in terms ofultimate strength. To ensure good performance in terms ofultimate strength ( q P k > 1.33), t (II) <820°C should beensured. Similar analysis of performance in terms of otheraspects enabled recommendations given in Table 2.
The specific feature of suggested temperature mode is
the following. For stage I temperature of the rolling beginning should be at least 1050°C, and temperature of therolling end should be at least 1020°C, that is higher thanunder the current technology (1020 and 980°C, respectively). At the same time temperature of the rolling end

If we compare actual variability of properties of hotrolled stripes with requirements for strength group
300 it can be seen that centre of resistance variation
almost coincides with the middle of rated variation range,and scatter does not exceed 33% of rated range value.
Therefore, in this case we see excellent differential estimates of mechanical properties, certifying that these lots
metal can be used for deliveries instead of cold rolled steel.
Based on the obtained results production method of
hot rolled steel to replace cold rolled steel of normal, deepand extremely deep drawing has been developed to include
hot rolling of steel bars with set temperatures of end andreeling, and its difference lies in application of steel containing 0.09…0.11% of carbon and 0.25…0.56% of manganese with carbon equivalent C * C Mn 6 Si 3 == 0.12…0.18, and temperature of rolling end and reelingis set with regard to the following ratios (° ):t
Ar3 300 C * 40 and t
Ar1 100 110 [4].
Whereas temperature values of the beginning ( Ar3 ) andend ( Ar1 ) of phase transformation are calculated withregard to actual chemical composition of a certain melt by
formulas [5]Ar3

913,7 207,13C 46,6 Mn

110,54Cr 108,1N ;Ar1

741,7 7,13C 14,09 Mn

16, 26 Si 11,54Cr 49,69 Ni.

(4)

(5)

Dependencies application (4)-(5) enables promptchanging of temperature t and t for real-scale compensation of natural deviations of steel chemical composition, thus ensuring specified properties of hot rolled
stripes designed to replace cold rolled steel of general
purpose.

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71

Technological reserves: reasonable implementation of simple solutions to improve hot rolling technology

should be reduced at the second stage (810-820°C insteadof 810-850°C under current technology). It has been alsosuggested to set requirements to temperature of accelerated
cooling in the range of 790-800°C (not specified before
testing) and reduce the temperature of accelerated coolingend to 610-620°C instead of 600-650°C currently used.

– to establish a method to improve roll pass design
with reasonable distribution of deformation [9] enablingof rolling at reduced temperature in order to improve operation properties of channel beams;– to improve roll pass design of channel beam at continuous rolling mill.
Availability of a single centre describing proTable 2 file of complex shape (Fig. 3) enables applying
estimates of deformation efficiency with the use of
Recommendations how to improve temperature mode
previous experience of making use of performanceof heavy-duty steel sheets production for ship building from steel
indexes and non-uniform deformation of simple
grade D32 at plate mill 5000 [6]profiles [10, 11].
Temperature, °C
New roll pass design developed within the
Ratingt (I )tt (I )tt ( II ) t ( II )framework of this study covers finishing milling
Current 1,020-1,100 980-1,060 790-830 810-850 Not rated 600-650 group. Shapes of the second and third passes opposite to rolling direction have been changed in sugRecom1,050-1,100 1,020-1,060 820-830 810-820 790-800 600-620 gested calibration. For identification purposes sugmended
gested calibration is called KZ and is compared
Second. Identifying technological reserves in ana- with two current roll pass designs: AVD and DAN.
lyzing the effectiveness of various roll pass designs ofstructural shapes (e.g. channels) through the assessment of valid power parameters.
Matrix approach helps to solve a wide range of technological tasks for various processes of long product rolling [7, 8]. Decision was taken to improve and use it forthe mentioned problem.
The demand for rolled steel with improved performance properties is constantly increasing. It is very difficult to get high mechanical properties of channel beams
using low-alloy steel, in particular channel beams from
09G2S steel grade according to GOST 19281-89, at continuous high-speed mills.
Differentiated cooling of shaped profiles and modification of heating and metal rolling temperatures can beused as possible resources of improving strength properties. Implementation of the cooling idea is related toequipment and associated technology costs. Thus, modification of temperature mode of rolling is a more flexible
and cost-effective tool to achieve required complex ofmechanical properties.
Reduced temperature of billet heating at continuous
mills results in reduced heat loss of metal in roughing millstands. That certifies about reasonable reduction of temperature at heating. Whereas increased power consumption forbillet deformation at roughing stands is greatly compensatedby reduced fuel consumption for billet heating, and totalenergy saving makes at least 15%. Whereas, metal loss infurnace is reduced, i.e. good metal output is increased.
Reduced temperature of metal in the mill will result
in metal yield strength increase and equipment increased
loads. To ensure rolling at reduced temperature energy
reserve is required to be used at rolling with reduced temperature. Such reserve is established on account of deformation distribution that is mainly caused by pass design
scheme at rolling of channel beams. Therefore, search for
the ways of purposeful redistribution of metal deformation at rolling of channel beams is a vital task.
The main tasks of estimating performance of channel
beam pass design in terms of structural-matrix approach
are the following:

Fig. 3. Suggested way of description with one centre
Developed roll pass design enables reducing rolling
force in stands 13, 14 and 15. DAN roll pass design uses
more traditional approach and it thickens the wall during
rolling. As far as such method stipulates wall thickeningfor 2-3 mm for every run, it requires a certain “stock” ofmetal to ensure wall thickness increase, as far as natural
thickening of the wall does not give such growth. Thus,
upstream rolled width is smaller than that of pass width
and the stripe is free at least in one direction to be shiftedin the pass. In other words, the pass is unstable holding
rolled metal. Rolled metal is centered in the pass due toholding wings. Results of roll pass design of rolling force,drawing index and non-uniform deformation index are
given below (Table 3).
The main differences of developed roll pass design
versus existing one:– wall bending radius increased;– wall draft is increased for 4% in 13 cage;– wall draft is reduced for 3% in 14 cage;– changed wall bending radius resulted in reduced
angle between wings. Calibration scheme is closer to traditional one, designed to increase wall;– increased wing height resulted in improved entry ofrolled metal to control pass (in cage with critical load No.14).
Having reached optimum deformation distribution we
can say, that a «reserve» on rolling effort is established.
Thus, we can assume metal temperature reduction, which
will result in increased rolling forces, but such forces will
not be excessive and hazardous due to application of established «reserve».

72 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Lutsenko A.N., Rumyantsev M.I., Tulupov O.N., Moller A.B., Novitskiy R.V.

Table 3Comparative analysis of rated values of rolling aspects forvarious roll pass design options of finishing mill groupTypeof passdesignThird. Identifying technological reserves toimprove roughing process: the influence of squarebillet’s rhomboidity on power parameters andwear in roughing stands.

Stand No.

Billet rhomboidity is a serious problem that influences stability of the rolling process and our ability
to ensure the required geometry and quality of theForce, kN
product.
AVD 1,796.51 1,448.75 1,574.61 1,233.75 881.31 1,020.55
To study specific features of rerolling of continuDAN 2,103.27 1,688.30 1,367.27 1,046.25 1,233.30 920.61
ously cast 150x100 mm billet with rhomboidity up to
30 mm, two boundary conditions of billet feed to theKZ 1,796.51 1,448.75 1,574.61 1,030.01 922.31 961.18
first stand have been considered: locations of big andElongation
small diagonals of billet and diamond pass coincides
AVD
1.51
1.40
1.45
1.29
1.17
1.02
(a), i.e. small diagonal of billet is in vertical plane,
DAN
1.63
1.51
1.35
1.29
1.20
1.15
and big one is in horizontal and do not coincide (b)
KZ
1.51
1.40
1.45
1.23
1.16
1.08
(Fig. 4).
Non-uniformity index
Drafts of continuously cast bloom of 150 mm
with rhomboidity aspect (with increment 0, 1, 2, 3, 4,
AVD
0.221
0.242
0.287
0.195
0.146
0.399
5, 6, 7, 8, 9, 10, 15, 20, 25, 30) for the above ways of
DAN
0.221
0.242
0.287
0.150
0.135
0.171
feeding to the first cage, as well as drafts of the first
KZ
0.200
0.218
0.241
0.168
0.143
0.223
cage of three passes (“old”, modified and with holddown),
applicable/applied at mill 350 of «Severstal»
Such solution to control channel beam rolling quality
OJSC
forrerolling of 150 mm bloom in 100 mm bloom,
was required by lack of possibility to produce rolled
channel beams with uniform conformance of require- have been used to calculate deformation uniformity coefments for specified strength class of 345 N/mm2 of fin- ficient (DUC), breakdown pass performance coefficientished products (channel beams No. 16 from steel 09G2S) (Krp) and rolling forces. Results of rolling DUC calculation are given in Table 5. Calculations of the rest aspects
according to GOST 19281-89.
Temperature in the last stand and temperature of the have been entered to similar tables.
metal rolling beginning can be taken as function of castsections rolling temperature in heating furnace of themill.
Observations for rolling of channel beam No. 16 havebeen provided to estimate influence of rolling temperaturein the last cage on strength properties. Temperature at theend of rolling was recorded.
Yield strength was estimated on 57 sample lots withregard to temperature mode in the last cage (Table 4).
ab
If we connect the temperature at the end of trial samFig. 4. Locations of big and small diagonals of billet
ples rolling with received values of yield strength in aand diamond passlinear equation, we can use it to calculate the required
temperature at the end of rolling to get strength class 345.
Calculation of forces was given for St 3 at heating
Equation of connection is as follows:
temperature 1200° .
Based on comparison of two ways of billet feeding
1,1078 t 1424,6.
into stands and three options of roll pass design has been
To ensure strength class 345 (yield no less than 345 performed and process options have been estimated with
N/mm2) the temperature at the end of rolling not more regard to feeding conditions, rolling forces, contact areas
than 970 is required, thus enabling production of re- between metal and rolls, surface defects and descaling
quality. Dependence diagram of force/rhomboidity aspect
spective strength class and higher operation properties.
of the billet for the first way of stripe feeding to cage(alignment of planes) is progressive,
Table 4 whereas it is decreasing for the second
way of stripe feeding to cage (misaExperimental data on influence of temperature at the end of yield strength
lignment of planes).
rollingin finished rolled steel
Thus, targeted application of new,Temperature after
945 950 955 960 965 970 975 980 985 990 995 1,000 1,010 simple, and effective models and methfinishing stand,ods enables to find and use various
Yield strength of trial
technological reserves in rolling pro375 376 364 363 359 351 341 339 334 325 323 311 311
samples, N/mm2
cesses.
9

11

12

13

14

15

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73

Technological reserves: reasonable implementation of simple solutions to improve hot rolling technology
proizvod-stva. [Technology of plate rolling production]. Moscow: Metallurgy, 1997, 272 p.
5. Rumyantsev M.I., Shubin I.G., Zavalishchin
DUC calculation data
A.N., Tsepkin A.S. and other. Sposob proizvodstva goryachekatanoy tonkolistovoy stali.
DUC
Pass[A method of producing hot-rolled steel
Rhomboidity, mm
sheets]. Pat. RF, no. 2365639, 2009.
design6. Rumyantsev M.I., Denisov S.V., Stekanov
0 1 2 3 4 5 6 7 8 9 10 15 20 25 30
P.A., Kuz'min A.A. Analiz parametrov i rezuAlignment of planes of big and small diagonals of billet and diamond passl'tativnosti prokatki v usloviyakh OAO «MMK»
listov iz stali marki D32 dlya sudostroyeniya.
With
0.123 0.121 0.120 0.118 0.116 0.114 0.113 0.112 0.110 0.109 0.107 0.099 0.091 0.083 0.075[Analysis of rolling parameters and results ofhold-down
steel sheets of D32for shipbuilding at OJSC
«MMK»]. Sovershenstvovaniye tekhno-logii v
0.115 0.114 0.113 0.111 0.109 0.107 0.106 0.104 0.103 0.102 0.100 0.092 0.084 0.076 0.069
Old
OAO «MMK»: sb. nauch. tr. Vyp. 16. [TechModified 0.141 0.139 0.138 0.136 0.134 0.132 0.131 0.129 0.127 0.126 0.124 0.116 0.107 0.099 0.091
nologies Improvement at OJSC «MMK»: Scientific. papers col., Ed.16]. Magnitogorsk,
Misalignment of planes of big and small diagonals of billet and diamond pass«Printing», 2011, pp. 111-120.
With
0.123 0.124 0.125 0.127 0.129 0.131 0.132 0.134 0.135 0.136 0.138 0.146 0.154 0.162 0.169 7. Nalivayko A.V., Ruchinskaya N.A. Povysheniye kachestva i sovershenstvovaniye tekhnohold-downlogii prokatki armatury v usloviyakh metallur0.115 0.117 0.118 0.120 0.122 0.124 0.125 0.126 0.128 0.129 0.131 0.139 0.147 0.155 0.163
Old
gicheskogo mini-zavoda. [Upgrading andtechnology improvement of reinforcement rollModified 0.141 0.143 0.144 0.146 0.148 0.149 0.151 0.152 0.154 0.156 0.157 0.166 0.174 0.182 0.191
ing under a metallurgic mini-works]. Chernaya
metallurgiya. [Iron and steel]. 2012, no. 1347, pp. 59-62.
Conclusion
8. Levandovskiy S.A., Nazarov D.V., Limarev A.S., Moller A.B., Tulupov O.N.
Razra-botka i primeneniye baz dannykh tekhnologicheskikh parametrov s
Targeted application of new, simple, and effective
tsel'yu osvoyeniya i sover-shenstvovaniya sovremennykh sortoprokatnykh
models and methods enables to find and use various techstanov. [The development and application of data bases of process panological reserves in rolling processes.
rameters with the purpose of modern section mills commission and updating]. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical UniReferences
veersity]. 2005, no. 4, pp. 36-40.
1. Rumyantsev M.I., Tsepkin A.S., Oplachko T.V. Unifitsirovannyy podkhod k
9. Kinzin D.I., Rychkov S.S. Ispol'zovaniye programmnogo kompleksa deraschetu differentsial'nykh pokazateley pri kvalimetricheskom otsenivanii
form-3d pri modelirovanii protsessov sortovoy prokatki. [Utilization of dekachestva prokata. [Unified approach to the calculation of differential inform-3d software in bar rolling processes modeling]. Vestnik Magnitogordexes in qualimetry evaluating of the rolled metal quality]. Vestnik Magniskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova.
togorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova.
[Vestnik of Nosov Magnitogorsk State Technical Univeersity]. 2011, no. 2,[Vestnik of Nosov Magnitogorsk State Technical Univeersity]. 2007, no. 3,
pp. 45-48.
pp. 61-64.
10. Tulupov O.N. Strukturno-matrichnyye modeli dlya povysheniya effektivnosti
2. Statisticheskoye upravleniye protsessami. SPC. Perevod s angl. [Statistiprotsessov sortov prokatki: Monografiya. [Structure-matrix models for effical Process Control. SPC. Translated from English]. N. Novgorod: SMC
ciency improving of rolling grades: Monograph]. Magnitogorsk: NosovLtd. «Priority», 2004, 181 p.
Magnitogorsk State Technical University, 2002, 224 p.
3. Rumyantsev M.I., Shubin I.G., Zavalishchin A.N. and other. Razrabotka
11. Lutsenko A.N., Monid V.A., Tulupov O.N., Limarev A.S., Moller A.B.,
tekhnologii proizvodstva goryachekatanogo tonkolistovogo prokata dlya
Trayno A.I., Nazarov D.V. Sovershenstvovaniye tekhnologii prokatki profizameshcheniya kholodnokatanogo analogichnogo naznacheniya.
ley prostoy formy pri ponizhennykh temperaturakh nagreva zagotovki.
[Technology development of hot-rolled sheets production to replace[Technology upgrading of simple form profiles rolling at low temperatures
cold-rolled of the same purpose]. Proizvodstvo prokata. [Rolled producof billet heating]. Trudy sed'mogo kongressa prokatchikov (g. Moskva, 15–tion]. 2009, no. 2, pp. 22-28.
18 oktyabrya 2007 g.). [Proceedings of the Seventh Congress of rollermen
4. Kotsar' S.L., Belyanskiy A.D., Mukhin YU.A. Tekhnologiya listoprokatnogo(Moscow, 15-18 October 2007)]. Moscow, 2007, vol. 1, pp. 208-212.

Table 5

Drobny O.F., Cherchintsev V.D.

DEVELOPMENT AND IMPLEMENTATION OF MEASURESTO IMPROVE ENVIRONMENTAL SITUATION WITHINMAGNITOGORSK INDUSTRIAL HUB
Abstract. The article presents the results of implementation of long-term environmental program at OJSC «Magnitogorsk Iron
and Steel Works», which includes measures aimed at reducing harmful environment impact of metallurgical production thus improving the production efficiency and ecological characteristics.
Keywords: environmental, environmental protection, pollutants, industrial wastes, ecological characteristics.

The program of technological, technical, organizational and socio-economic activities as the basis of environmental policy at OJSC «MMK» (Magnitogorsk Iron
and Steel Works) has been developed and now is being
successfully implemented complying with the RussianFederation state policy in the field of environment protection.
The OJSC «MMK» strategy, aimed at negative environmental impact minimizing, consists in using creativetechnological processes with environmental protection
installations based on the best available technologies andremoving obsolete facilities.
The implementation of the technical revamping program has radically changed not only the manufacturing
structure at OJSC «MMK» but considerably reduced theenvironment impact. In 2012 the overall discharge of pollutants into the atmosphere was reduced by 3.7 and theemissivity by 3.5 times as compared with 1989.

74 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Drobny O.F., Cherchintsev V.D.

Today the environmental complex of OJSC
«MMK» includes 445 gas purification units of different
capacity, 43 local circulating water systems and 32 water purification installations, as well as 6 complexes formetallurgical slag processing. Over the last 10 years
practically all environmental facilities were reconstructed or repaired.
Over the last 5 years capital expenditures for the reconstruction of existing and the construction of new environmental facilities accounted for $250 million. The company annually spends more than $500 million to maintainenvironmental facilities.
The long-term environmental program up to 2015
has been adopted and is being implemented at OJSC
«MMK». The program includes measures aimed at reducing harmful environment impact of metallurgic production, improving production efficiency and ecologicalcharacteristics. This program provides to spend morethan 4 billion dollars for the construction of new and thereconstruction of existing environmental facilities during
the period of 2013-2015.
The problems of planning environmental protection
activities are becoming principal taking into accountthat the implementation of environmental protection
program requires substantial resources. The program
includes a number of factors and faces great difficulties
typical for work organization at any operating enterprise. It is necessary to have a methodology which defines the priorities, considering all factors and characteristics of the enterprise to improve environmental protection efficiency.
Since the atmospheric air pollution control is theprinciple environmental protection activity at OJSC
«MMK», the company has developed and used «Methodsof specifying prevalent pollutants in the air basin and thedevelopment of discharge technique of the dust collection
system at metallurgical enterprises with complete production cycle» [1]. For the effective environment planningand management, the air pollution impact of any enterprise with complete production cycle can be defined bycomparing the indices of environment threat of the production «Jetpj», which are calculated according to the following formula:

J etpj

etpj

,

n

(1)

K etpjj 1

where K is the indicator of the environmental threat of thejth production.
The environment threat index of any production impact can be defined by the following formula:
m

i

Cimax

,

etpj
i 1

(2)

i

where C imax is maximum surface concentration (averag-ing 20 minute interval) of the pollutant «i», being discharged by the production «j» in a set point (located in a
residential area in a close vicinity to the production «j»),
mg/m3; TLV mpi is a maximum threshold limit value ofthe component «i», mg/m3; i is a coefficient, dependingon the class of danger of the component «i».
To determine the value «Ci» in the formula (2), we’ll
use ND-86 recommendations [2].
Surface concentration of the pollutant «i» in a set
point at a given wind speed and direction, discharged by
all production sources is defined by the following formula:
N

C

Cn ,

(3)

n 1

here Cn is the surface concentration of the pollutant
discharged from any pollutant emitter «n» (a compound of the production «j») in a set point at designed
wind speed and direction, mg/m3; N is the number ofpollutant emitters belonging to the production «j»,number of items.
All pollutant emitters at OJSC «MMK» are point, excluded aeration lanterns and outdoor raw material storages. Aeration lanterns and outdoor storages at OJSC
«MMK» are linear sources.
For the calculation of surface concentrations of linear
sources, they are presented as a group of identical equidistant point sources.
Surface concentration of the pollutant from the emitter «n» in a set point at the designed wind speed and direction is calculated by the following formula:Cns 1 s2 r C ,(4)where s1 is a nondimensional coefficient, evaluated according to the distance along the pollution plume axis,
between the pollutant emitter and a set point; s2 is a nondimensional coefficient evaluated according to the vertical distance between a set point and the pollution plumeaxis; r is a nondimensional coefficient evaluated according to the wind speed; Cm is the maximum pollution surface concentration from the pollutant emitter (a compound of the production «j»), mg/m3.
The calculation of the maximum surface concentration of the pollutant from a point source is calculated byconventional methods.
The outskirt of the village «Bruskovy», located in a
residential area, is accepted as the nominal reference
point. Calculation results of the primary production impact on the integral value of the environment threat index
are given in the Table.
Whenever choosing dust collection systems at metallurgical enterprises exposed to full or partial revamping,
the difficulties arise from the lack of free space sufficientfor the installation of large-size dust collection equipmentof high-efficiency, devices and facilities for collected dust
recycling.

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75

Development and implementation of measures to improve environmental situation within Magnitogorsk industrial hub

Calculation of the basik production of JSC «MMK» in the integral index of environmental hazards
Production Impact
Maximum nominal concentration, mg/m3
Level in the Test Point
Production Name
(Designation)
nitrogencarbonsulfurnitrogendust
phenol
K onj
J onj
dioxideoxide
dioxideoxide
Sinter Production
0,31
0,02
1,467
0,9
0,004
2,86
35,6
Coke industry
0,068
0,025
0,838
0,02
0
0,016
2,34
29,2
Blast-Furnace Process
0,464
0,024
0,99
0,068
0,009
1,44
17,9
Electric Steelmaking Plant
0,062
0,019
0,071
0,004
0,005
0,26
–
Oxygen-Converter Plant
0,113
0,005
0,025
0,003
0,002
0,27
–
Total: Steelmaking Industry
0,53
6,6
Thermal Power Station
0,061
0,029
0,003
0,004
0,01
0,30
–
Central Power Station
0
0,043
0,002
0
0,016
0,26
–
Steam-Air Power Station
0
0,015
0,01
0,014
0,006
0,12
–
Total: Power Generation
0,68
8,5
Rolling. (Sheet Rolling Mill-3, Sheet
0
0,013
0,09
0,006
0,005
0,12
–
Rolling Mill-4, Sheet Rolling Mill-5)
Rolling. (Finishing Plant, Sheet
0,001
0,003
0,003
0,002
0,001
0,02
–
Rolling Mill-8)
Sheet Rolling Mill-10
0,001
0,007
0
0
0,002
0,04
–
Total: Rolling
0,18
2,2Maximum threshold limit value (TLV)
0,5
0,2
5
0,5
0,4
0,01
If we take economic efficiency of a dust collection
system as an integral test provided that it achieves maximum permissible emission values MPE as its minimum
limit for the given pollutant emitter, it’s reasonable to use
the following estimating characteristics: efficiency of
selected systems, the technical efficiency of dust collection, capital and maintenance cost, system capability by
the volume of treated gases, specific energy source consumption per unit volume of treated gases, revenue fromsales of the collected dust or the cost of its ground disposal and pay decrease for pollutant discharge into the atmosphere.
In this case, the economic efficiency of the dust collection system
can be calculated by the following
formula [3]:
n

Fr

in

ik

r

i 1

K

qk

Pr

r

,

(5)

where Fr ( in ik) is revenue from sales of utilized materials and pay decrease for pollutant discharge per year; rPr(qk) is full costs for the system maintenance for a year;
is profit reduction in production work per year; r is acoefficient of diverse cost averaging; K is capital expenditures (cost of essential and auxiliary dust collection
equipment, assembling and start-up costs of a dust collection system); in ik are concentrations of the element «i»
per unit of original and treated gas; qk is consumption of
every resource.
At the final stage of evaluation of dust collection alternatives it is reasonable to estimate the efficiency « k»of any of them by the following formula:

n

Ci i

in

ik

i 1

,

m
j

p

q

k k
k 1

(6)

rj

j 1

V

where Ci is specific environmental damage owing to thepollutant «i» discharge into atmosphere; yi is relative
atmospheric pollution threat with the substance «i»; k is
every resource price; rj, j are additional expenditures
per unit of resources used in the production process andtheir cost; V is a volume of gas emission per unit of output.
To make a final choice of the dust collection system itis necessary to take into account the possibility of further
dust reduction of treated gases due to improvement of design and technological parameters of the system equipment,
maintaining its steady operation in changing operationalmode and parameters of the main production process aswell as the possibilities and sufficiency of the system application for recycling and recovery of treated gases. Special
attention should be paid to recovery and recycling of collected dust at steel mills of complete production cycle.
The developed technology makes it possible to evaluate both ecological-and-economic effectiveness of equipment and dust collecting units of gas cleaning systems to
make a proper choice and to estimate ecological-andeconomic effectiveness of environmental measures including recovery and disposal of collected products.
The environmental measures taken over the last 5
years resulted in gross emission reduction by 10800 tons
(by 5%) and totaled 220200 tons in 2012 and specificwastes decreased by 11% (to 18.57 kg per ton of finishedproduct).

76 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Drobny O.F., Cherchintsev V.D.

In Fig. 1 one can see that since 2009 there is a steadytrend to reduction of polluting substances emission into
the environment at OJSC «MMK».

kilogram/tonthousand tons

kilogram/tonthousand tons

allurgical slag doubled over the last 5 years and reached11.5 million tons a year.
Special attention is paid at OJSC
«MMK»
to the complex recycling of in240
50
dustrial
wastesso that they might be used
230,9
45
228,9
in the manufacturing processes as well as
230
40
220,5
to the quarry reclamation of the Magnitna220,9
220,2
35
220
ya Mountain which is proved by the data
30
25,92
given in Fig. 3.
25
210 20,93
21,35
19,96
Actual expenditures on the Ecological
20,44
20Program of the OJSC «MMK» in 2012200
15
reached $38 million (including $34 million
10190
invested in capital development).
5
OJSC «MMK» plans to hold 44 events
0180
in 2013 within the framework of the Eco2008
2009
2010
2011
2012
logical Program.
quantity emissions
generally emissions
Implementation of this program will
provide sustainable development of OJSC
Fig. 1. Emission of polluting substances into the atmosphere«MMK» and create favourable economic
from 2008 to 2012environment for the South Ural in general.
The strategy of water resources protection is aimed at the maximum application of25
180
recycled water for process water supply. The
155,87
share of recycled water supply at OJSC
160
138,88«MMK» has been maintained at the level of20
140
96% for 5 years already.
120
Water-protective measures within the
15
113,82framework of the Ecological Program made it
100
possible to reduce waste water discharge into
14,45
80
65,32
13,42
water bodies by 42050 tons (27%) to 113800
1010,32
60 48,1
tons, specific discharges of polluting substances per 1 ton of finished product de40
7,4
5
creased by 28.6% compared with 2011 and
20 4,36
totaled to 10.32 kg/ton (Fig. 2).
00
OJSC «MMK» pays great attention to in2008
2009
2010
2011
2012
dustrial waste recycling and control. Some 2.9
million tons of wastes were used as raw matequantity discharge
generally discharge
rial in 2012, which is twice as much as in 2008.
Fig. 2. Change of polluting substances discharge into water bodies
The volume of recycled current and dump met14
11,6

12

mikkion tons

10

10,5
9,4

6

10,1

9,1 9,3

8,5

8

11,3

6,9

wastes and slag used for thequarry reclamation of theMagnitnaya Mountain

5,5

4
2

metallurgical slag recycled at
the installations

2,1

2,2

2,3

2,4

industrial wastes used in thesintered ore

1,1

0
2008

2009

2010

2011

2012

Fig. 3. Change of waste utilizationwww.vestnik.magtu.ru. ——————————————————————————————————————————————

77

Development and implementation of measures to improve environmental situation within Magnitogorsk industrial hub
References1.

Drobny O.F., Cherchintsev V.D. The specification of prevalent pollutants inthe air basin at metallurgical enterprises with complete production cycle.Teoriya i tekhnologiya metallurgicheskogo proizvodstva. [Theory andtechnology of metallurgical production. Collected scientific papers]. Magni-

2.
3.

togorsk, 2003, vol. 3, pp. 216-223.
Estimation method of hazardous substances content in the atmosphereresulting from industrial wastes emission. All-Union regulatory document
OND-86. Goskongidromet. Leningrad: Gidrometeoizdat, 1987, 92 p.
Glukhov V.V., Nekrasova T.P. Economical fundamentals of ecology.
S-Petersburg: Special literature, 1997, 304 p.

Kolga M., De Smedt V., Van Nerom L.

PLANNING PRINCIPLES IN METALLURGY
Abstract. Metallurgy is known as one of the most challenging areas for planning. Planning systems for metallurgical production aremeant to solve a wide range of problems: from day-to-day scheduling at the workshop level to the development of the company strategy
for years ahead.
Each level of planning presents specific tasks, degree of abstraction and planning horizon. The modules of the planning system are
responsible to find the optimal solution at each level.
A properly selected, installed and operated planning system helps to improve control over production processes and increase theprofitability of the company.
Keywords: planning system, production plan, planning horizon, scheduling, material flow, bottlenecks management, strategy plan.

Introduction
In terms of industry, planning serves as the bridge between product design, production capacity and the actual
production. Traditionally, planning tasks were performed
manually, based on the experience of the specialists.
Planning systems were designed to integrate, standardize,streamline and improve company planning, reporting andoperational control capabilities.
Although the purposes and principles of the planning
are generally the same, these systems vary from industry
to industry and from company to company. The more
complex the manufacturing, the more sophisticated planning system is required.
Metallurgy is known as one of the most challenging
areas for planning. Such complexity of metallurgical production can largely be attributed to the factors as [2]:wide range of products (thousands of items)
variety of routings (alternative routes betweenlines)
multiple operating modes of the lines
complex rules and constraints at the lines
make-to-stock production and allocation of materials from the stock yard
the capacity required is difficult to predict (since
it depends on the particular mix of products)
work-in-progress inventory is often large
throughput times are generally longcomplex and strict quality requirements
extremely high «cost» of the downtimes
realtime (or «near-realtime») data exchange withthe production leveletc.
The aim of this article is to give an overview of thebasic tasks which planning systems face at different levelsof metallurgical production, and to present successful
approaches to the problem. The latter is best done by way
of example.

PSI Metals GmbH is one of the leading international
companies providing IT solutions for the metals industry[1]. Planning system of PSI Metals presents a group of
products which are meant to solve planning tasks at different levels.
Levels of Planning
Each level of planning varies in purpose, time span,and degree of abstraction.
At the basic workshop level, the aim of planning is
optimal schedules of the production lines. The level ofdetail is very high; the planning horizon lies in the shortterm. Given a big variety of specific rules and constraints,
which are never completely independent, the conflicts areinevitable and a compromise is not easy to find.
Optimization models implemented in PSI Metals
scheduling tools are based on tried-and-tested algorithms,
which use the customer’s priorities to range the goals andensure the most preferable of feasible results.
Depending on the line type, the set of rules can vary
greatly. For example, when talking on the continuous
casting machine, one has to take into account fixed ladlebatch sizes, acceptable steel grade transitions and steel
grade nesting, variable geometry of the output products(slabs or billets), tundish wear and molds changes withthe related stops, as well as many other factors. In case of
the hot strip mill, the focus shifts to the problems likefurnace-charge, width / thickness profile, run up, specificrolling rules («coffin rule»), stops for equipment readjustments and rolls changes, stockpiling, etc.
Thus, each production case requires individual approach; and this means one more challenge for planningsystems – they must be «tailorable». The planning solution of PSI Metals meets this challenge due to the modular structure: a set of line-specific modules delivers the
optimal results to the upper level of planning, where they
are integrated and can be analyzed in the context.
The context of the higher level implies a full scope of
the production lines available. The objective of the planning system is well-balanced load of the equipment with

78 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Kolga M., De Smedt V., Van Nerom L.

respect to delivery dates of the orders. Considering alternative routes and the bottlenecks, the system must establish start and finish dates for each operation required tocomplete the order on time. PSI Metals planning system
also takes care of successive lines synchronization tosolve tasks such as hot charging, which is critical for the
hot rolling. To develop a reliable schedule, the planningalgorithm operates with information on routing, required
and available capacity, competing jobs, and manufacturing lead times at each line involved.
The problem of materials allocation takes place at thesame level. PSI Metals planning solution offers several
task-specific products for assignment of orders to material. Actually this procedure deserves a separate article,
because of its complexity and obvious economic effect itprovides due to minimization of scrap, optimization of
cutting plan, maximization of orders fulfillment, etc.
The next level deals with capacity management andmaterial flow. The planning horizon is usually a few
months; the level of detail is reduced to product groups orfamilies. The objective is to define the target product mix
per period and make the best use of manufacturing resources, while keeping inventory levels down.
The next level of planning deals with capacity
management and material flow. The objective is tomeet delivery dates, to make the best use of manufacturing resources, while keeping inventory levels
down. It involves establishing start and finish
dates for each operation required to complete theorder on time.
In metallurgical production, it is very difficult
to balance the available capacities of the variouslines with the demand for their capacity. As a result, some lines are overloaded and some are underloaded.
The overloaded lines are called bottlenecks. The bottlenecks are critical to the throughput of the whole system
and usually have problems with high work-in-progress
inventory level. Bottlenecks management is one of themost important advantages provided by PSI Metals planning system at this level. To develop a reliable schedule,
the planning algorithm operates with information on routing, required and available capacity, competing jobs, andmanufacturing lead times at each line involved.
The next in the planning hierarchy is sales and demand planning level. The planning horizon for this levelis at most a year, and revised every month or quarter. The
next level in the planning hierarchy deals with the sales
and demand planning. The level of detail is not high; theplanning horizon can be up to several months. The aim of
the planning system is a plan to satisfy market demand
within the resources available to the company, determine
from the demand forecast, that is the best way to accept
orders in order to maximize the throughput of the factoryand EBIT profit of the company, reconcile the commercial demand and technical restriction of the plant. The
plan is devised in terms of product groups or families.
The basic approach of PSI Metals planning solution is
to find a balance between priority and capacity. It is theprivilege of the customer to define the requirements andrank them in order of importance.

The result of this level must, at the same time, agreewith implementing the strategic business plan. The strategic business plan is a statement of the major goals andlong-term objectives of the company and this is the top
level of manufacturing planning.
Strategy planning takes into account the market-,products and pricing strategies of the company, alternatives for the supply chains, and the corresponding procurement strategies.
The plan of this level is the guideline for all further
decisions in planning and execution processes, and thus
must be considered very carefully.
PSI Metals Planning provides the ability to model«what-if» scenarios to see the impact of various factors before making a decision. This helps a company to more thoroughly assess potential risks, more quickly identify opportunities, and more promptly react on the market changes.
Figure summarizes the preceding description of theplanning hierarchy, and establishes a correspondence between the planning levels and existing solutions of PSI
Metals.

Planning Level
Strategy Planning
Capacity & Master Planning
Material Planning & Order Scheduling
Demand & Sales PlanningLine Scheduling
Planning Levels and PSI Metals Planning Products
Advantages of Planning Systems
Depending on the scope of the planning system, thebenefits can be obtained in such operational areas as
manufacturing, sales and marketing, management andothers [3].
In manufacturing: the planning systems provide
faster identification of production process problems andbottlenecks; facilitate more accurate raw materials planning and control; improve inventory control. Besides,
more thorough shop floor planning reduces waste andre-work.
In sales and marketing demand planning, the main
benefits are: improved due date performance, reduced
increased factory throughput and better management of
supply and more flexible delivery times; improved accuracy in sales forecasts; increased accuracy in purchaseorders, etc.

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79

Planning principles in metallurgy

In management: the planning systems help to improve the quality of decisions; faster identify and assess
risks; provide more accurate and timely information. Increased structure and discipline in planning, reporting andforecasting activities improve control over production
processes in general.

and also requires a great deal of expertise and knowledge,
both of which are not easy to model and codify.
A properly selected, installed and operated planningsystem helps to speed up production, reduce costs andincrease the profitability of the company.

Conclusion
The automation of planning activities at metallurgicalenterprises presents many challenges, since it involves a
multitude of conflicting criteria and competing objectives

1.
2.

References3.

www.psimetals.de.
Tony Arnold J.R., Chapman Stephen N., Clive Lloyd M. Introduction tomaterials management. 7th ed. p. cm.
Fawls Tom. A Business Primer for Understanding Integrated Planning,
Reporting and Control Systems. www.SpinningDisc.com.

Polikarpova M.G.

FUZZY-LOGIC-BASED RISK MANAGEMENT OF M&A DEALSOUTCOME: A CASY-STUDY A LARGE RUSSIAN METALLURGICHOLDING
Abstract. The paper researches the application of several fuzzy logic concepts to evaluating risk rating of M&A projects undertaken by a large Russian Metallurgic Holding: maxmin compression, fuzzy relationship of preferences, additive compression. The
way of expert answer treatment is presented for the possibility of further fuzzy logic methods application. 20 M&A projects are usedas the empirical basis for the research. The methods applied show consistency in final estimates proving the ability of their use in
MA deals’ risk outcomes evaluation. The proposed method can be used to evaluate risk consequences for M&A deals.
Keywords: fuzzy logic, fuzzy set, membership functions, rule matrix, risk, M&A, metallurgy

Currently M&A is one of the most solicited ways ofdeveloping an industrial enterprise. Though M&A deals
embed material risks they are efficient to achieve the objectives that are unattainable given other long-term development strategies.
Being highly risky M&A deals often result in losses
for the acquirer. As McKinsey found in 2008 70% of
M&A resulted in business value destruction. Same time
Russian M&A differ in several ways from abroad ones:
no common regulator and no unique pricing procedure exist;
market is rather closed, no unified statistics
available;
there legal blank points enabling raider activity etc.;
legal system drawback in corporate conflicts resolution [2].
Generally the corporate culture to dealing with M&A
deal consequences is not well worked out. As the M&A
deal associated risks need to be dealt with, the paper has
its objective to present the way of evaluating M&A risks
based on fuzzy logic concept.
M&A deal realization passes three stages of its livecycle:
1) project integration (negotiation process);2) company reorganization (sales-and purchaseagreement execution);
3) company integration (incl. corporate cultures) [4].
The majority of M&A deals are subject to UK common law, including deals taking place in off-shore jurisdictions.
When working out methodological principles of
M&A deal risks evaluation for an industrial enterpriseconsidering metallurgic holding as an example industryspecifics should be accounted for:geographic distance of integrated companies andtheir corporate cultures difference;high capital-intensity of metallurgy, demand forhuge initial investments, long period of investment
pay-back;
acquisition of current and developing new plants
is subject to external groups of interest influence.
Dealing with them is of objective necessity;
all large metallurgy plants in Russia provide employment for whole cities implying high social responsibility of M&A projects;
technological similarity needs to be accounted forwhen merging metallurgical companies.
The M&A process complexity is driven by a highnumber of involved parties. Thus different stakeholders’possible actions were analyzed to account for most of the
M&A deal risks.
Figure below presents the worked out process of project gross risk evaluation. The mechanism is self-adaptive
and self-regulative. As risks at each of the stages are difficult to qualify fuzzy logic is used to evaluate gross risk.
The fuzzy logic permits us to treat heterogeneous factors
given lack of sufficient quantitative data [5].
According to the proposed mechanism individual
risks were evaluated based on expert judgments for alternative investment projects.
The research is based on expert judgments for 20
M&A deals of one of the largest Russian metallurgy enterprises. 51 risk criteria have been chosen. Nine topmanagers were questioned to obtain their expert judgments.

80 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Polikarpova M.G.

As expert judgment might are subjective and are reasonably different from manager to manager the Delfi-method isused to iteratively process the filled-in questionnaires.
When ranking alternatives experts tend to provide
different opinions. Therefore it becomes necessary to estimate consistency on expert judgments (the degree ofexpert concordance). Arriving at the quantitative measureof expect non-concordance helps to analyze the reasonsfor differences in opinions.
To measure expert judgments degree of concordance
following measures are often used [7]:spearman rank correlation coefficient;dispersion concordance coefficient (Kendall rankcorrelation coefficient);
entropy concordance coefficient.
Non-parametric module of Statistics software wasused to estimate experts concordance within identified
criteria of M&A deals risks. 2-Pearson criteria for Kendall rank correlation coefficient was used. For all risk
criteria the following holds:

2

2
.

.

(0,05;19) . Thus

the null hypothesis of expert judgments being consistentis not rejected.
Expert competence coefficients were estimated given
ex post data on questionnaire output [6]. Rykov iterativealgorithm was used to obtain competence coefficients.
Let’s take as an example the case of country risk at
the third statge of M&A deal estimation. Firstly take alook at the ranks of all M&A deals for each expert.
Secondly, at zero stage prior expert competence coefficients are estimated:

0
i

1
m

1
. Then9xK

xij . Then adjusted expert

i 1

competence coefficients were obtained given
the below formula:

1

K i1

max x1jj 1, ni 11, m,

,
xij

(1)

0,001.

Coefficient add-ons were based on thevalues of x1j

xij . Additive approach wasused to estimate adjusted competence coefficients:
*

Ki1

Ki0

Ki1 .

(2)

Table 1
1st iteration results for Rykov algorithm are presented

0,196

K11

K 21

0,117

K 21

K 31
K 41
K 51

.

*

K31

0,108

*

K 41

0,105

*

K51

0,120

*

K

1
6

K

1
7

0,142

K 71

K 81

0,153

K81

K 91

0,171

K91

K61

0, 099

*

*

*

K11

0,139

0, 228

K 21

0,103

0, 219

K 31

0,099

0, 216

K 41

0,098

0, 231

K 51

0,105

0, 211

K

1
6

0,095

0,253

K

1
7

0,114

0, 264

K 31

0,119

0, 283

K 91

0,128

As condition (4) does not hold, then 1st iteration steps
are repeated once more. To accomplish the procedure 11
steps were needed. Final output by iteration is presented
in Table 2. Expert competence coefficients on other risks
were estimated similarly.

Generalized rank is obtained accounting for expert
competence based on the ranking of risk sums for all objects (competence coefficients are used as the weights):(3)

Risk k ( j )K i * Riskik ( j ),
i 1

*

K i1
i 1

*

0,307

9

K i1
9

*

K 11

*

K

(4)

Deviation
Expert competence coefficients
Iteraionfrom previNo.
K1
K2
K3
K4
K5
K6
K7
K8
K9
ous iteration
1
0,02768 0,139 0,103 0,099 0,098 0,105 0,095 0,114 0,119 0,128
2
0,01208 0,151 0,099 0,093 0,091 0,102 0,087 0,116 0,124 0,137
30,01294 0,138 0,103 0,099 0,097 0,107 0,096 0,113 0,120 0,126
4
0,01255 0,150 0,100 0,093 0,091 0,103 0,088 0,115 0,124 0,136
5
0,00534 0,156 0,098 0,089 0,087 0,102 0,084 0,116 0,127 0,141
6
0,00235 0,158 0,097 0,087 0,086 0,102 0,082 0,116 0,128 0,143
70,00111 0,159 0,097 0,086 0,085 0,102 0,081 0,116 0,129 0,144
80,00056 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145
90,00027 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145
100,00015 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145
110,00009 0,159 0,096 0,086 0,085 0,102 0,080 0,117 0,130 0,145

As the sum of coefficients needs to equal to unity, theobtained values were normalized using the following
formula (3):1i0,0001 .

i 1, mRykov algorithm application for expert competencecoefficients estimation for country risk

m0i

max Ki1 Ki0

Table 2

average group estimated are calculated:1jFinal estimates are presented in Table 1.
When the 1st iteration is accomplished, the following
condition was checked:

k

.

(5)

1,51, j 1, 20.

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81

Fuzzy-logic-based risk management of m&a deals outcome: a casy-study a large Russian metallurgic holding

Based on the proposed adaptively regulating mechanism of gross risk evaluation next step would be to estimate the M&A deals gross risk.
Fuzzy logic concept is an approach enabling to process information when purely quantitative data in notavailable*. To mention it is possible to proceed from conventional models in theory of probability and expert
judgments to fuzzy sets descriptions. As an example traditional distribution can be substituted by a distribution
with fuzzy parameters. Expert judgments might be interpreted like membership functions that form the fuzzyclassificatory [1].
Consequently membership functions for 51 criteria
were formulated (expert values of [1;9] were mapped tounit interval [0;1]). As the risk criteria was a monotonically increasing function, the following transformation took
place:

x xminxmax xmin

x1( x 1) .
8(6)

As a result risk was scaled to [0;1] values where theminimal ones corresponded to minimum risk and viceversa.
Four methods of fuzzy sets orderings were used in thepaper based on:1) maxmin compression;2) fuzzy relationship of preferences;3) additive compression.
1. Multivariate choice of alternatives based on maxmin compression
Let trace the algorithm for M&A deals ranking basedon fuzzy logic:
1. As the maximum values of membership function
should correspond to the best alternative, it was transformed as follows:
cj.

( ai ) 1

j( ai ).

**

2. Relative importance coefficients(7)jare obtainedon the basis of the first eigenvalue of the rule matrix. Rulematrix is produced with respect to the indicator hierarchy.
The degree of indicator significance is determined according to the principles presented in Table 3.

m 2j ,

j

where

j

(8)

C1 1

C2 2

... Cm m .

D(ai ) min( c j (ai )) j , i 1, n .

(9)*Fuzzy logic was actively applied after Lotfi Zadeh published hisarticle in 1965 (Zadeh, 1965). The motivation for the paper was toprocess complex and difficult-to-formalize real-world problems thatconventional methods of systemic analysis fail to deal with.
**
To mention new membership functions produce the nonriskiness measure.

(10)

j 1, m

4. The best alternative a i* is characterized by thehighest value:D( ai* )

maxD

i 1, n( ai ) .

(11)

5. The values of D ( ai* ) correspond to non-riskinesslevel of M&S deals. Considering our objective of risk
measurement the inverse values should be taken:
FINAL .
D

( a i* )1D( a i* )(12)
Table 3

Table of indicator significance
Degree ofsignificanceDefinition

1

Equal significance357
92,4,6,8

Description

Both indicators equally contribute to the outcome
Immaterial signifiOne of the indicators iscance dominance somewhat more important,of parameter
though it is immaterial
Strong signifiClear evidence is to choose
canceon of the indicators
Very strong signif- Strong evidence exists to
icanceprefer one indicator to another
Absolute signifi- One indicator should be deficancenitely preferred to another
Intermediary values

When i-th indicator is compared to j-th indicator
Inverse to
the above presented values are assigned, whenvalues preon opposite j-th indicator is compared to i-th thesented above
inverse of the above values are assigned
FINAL .

*

Then the higher is D
( ai ) value, the higher isthe risk of deal.
When characteristic equation was solved, first eigenvalue for the rule matrix was 1 63,386 . Solving forthe equation (8) relative importance coefficients j werealso obtained.
Having analyzed the outcome ofis eigenvalue of the first eigenvector.

3. The alternatives ranking rule given different indicator significance is determined as the fuzzy sets intersection:

D

Several approaches can be used to intersect the fuzzy
sets. Nevertheless mostly the minimum is taken:jexpert values

third stage risks as the most important. Inter alia country
risk, risk of the duties not accomplishment, and risk ofcompany goods price decrease were considered to be themost important with the respective values assigned
7,0895 , 50 7,0648 , 49 6,0752 .
46
Finally all projects were ranked based on
FINAL .
(ai* ) . First place corresponds to the highest risk,Dlast – to the minimal. Based on the ranking Pakistan, Canada, Germany, Turkey were the riskiest M&A deals.

82 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

Polikarpova M.G.

2. Multivariate choice of alternatives based on fuzzy
relationship of preferences
When the alternatives are compared with respect topreference relationship, it is logical to assume nondominating alternatives to be preferred. Mathematicallyspeaking the problem converges to tracing out no dominating subset of alternatives within the fuzzy set.
Given R three corresponding fuzzy relationship canbe formulated [3]:fuzzy relationship of indifference:

min 1
Rj

Cj

(a p , ai ) max
min(a p ),1

Cj(ai ) ,

( a p , ai )min

( a p ),

Cj

( ai ) ;(14)

fuzzy relationship of strong preference:Rj( a p , ai )Cj( ai )

0, if

Cj
j

( a p ), if( ai )

Cj( ai )Cj( a p ) . (15)( a p ).

CjAs the obtained alternatives are non-dominated given
the available information, they are considered to be thebest.
Let there is A set and each alternative has several
features j 1, m . Information on pairwise comparison
for all alternatives is presented in Rj relationship. The
rational choice needs to be done given m relationships Rj
on A set.
Matrixes of fuzzy relationships are formulated for all
the fuzzy relationship R1 , R2 ,..., Rm according to formula (15).
1. Fuzzy realtionship Q1 is constructed that symbolizes
the intersection of relationships Q1 R1 R2 ... Rm :Q1

(a p , ai )

min

R1

(a p , ai ),R2(a p , ai ),...,

Rm(a p , ai ) .

(16)

2. Subset of non-dominated alternatives is chosen
A, (Q1 ) for all p and i (i 1, n; p 1, n ) :ND
Q1(a p )

1 sup
ap A

Q1

( a p , ai )Q1

( ai , a p )p , i, pi. (17)

3. Fuzzy relationship Q2 is obtained:m
Q2 ( a p , ai )

j
j 1

Rj

( a p , ai ) .

(a)

ND
Q1

ND
Q2

min( QND
,
1

(18)

ND
Q2

).

(19)

6. The most rational alternative to choose is the one
having the highest degree of non-dominance:a | a A,ND(a) supND(a' ) . (20)'a A

; (13)C j ( a p ), c j ( ai )

Cj

ND

a ND

fuzzy relationship of quasi-equivalence:Rj

4. Subset of non-dominated alternatives is found for
1, n; p 1, n ) .
5. Final subset of non-dominating alternatives is foundas the intersection of subsets A , ( Q1 ) and A, (Q2 ) :A, (Q 2 ) for all p and i (iTo note not only a ND alternatives are the best, sometimes weekly dominated alternatives might be of interest,
i.e. the ones belonging to ND (a ) given the degree ofconfidence is no less then preapproved.
For 20 alternatives’ membership functions 51 matrixes R1,R2,...,R51 of fuzzy relationship were constructed.
Based on formula (16) Q1 fuzzy relationship was obtained
as the intersection Q1 R1 R2 ... Rm . Based on formula (17) subset of non-dominated alternatives was foundA, (Q1 ) . Referring to principle (20) the final set was
obtained.
Similar to maxmin compression four deals were considered as the most risky being assigned respective valuesof riskiness: Canada ( ND ( a 20 ) 0,9593 ), Germany(

ND( a17 ) 0,9335 ), Pakistan (Turkey (ND( a1 )

ND( a4 )

0,8870 ),0, 7915 ).

3. Multivariate choice of alternatives based on additive compression
Current method presents expert judgments as fuzzy
numbers having membership functions of triangular form.
1. To estimate the importance parameters j linguistic variables are used: «not very important», «important»,«very important». Linguistic variables are represented by
the fuzzy numbers from the membership functions of triangular form.
Respectively:
0 1 01) not very important ():;; ;0 0,2 0,4

0 1 0
;
;
;
0,3 0,5 0,72) important ( ):3) very important ():

0 1 0 .
;;
0, 6 0,8 1, 0

2. To estimate criteria Rij linguistic variables are also
used: «very low risk», «low risk», «medium risk», «highrisk», «very high risk».
Respectively:
1 01) very low risk ( ):;;0 0, 2www.vestnik.magtu.ru. ——————————————————————————————————————————————

83

Fuzzy-logic-based risk management of m&a deals outcome: a casy-study a large Russian metallurgic holding

0 1
0
;
;
;
0 0, 2 0, 42) low risk ( ):0 1 0 ;;;
0,2 0,4 0,63) medium risk ( ):

0 1 0
;
;
;
0, 4 0, 6 0,84) high risk ( ):5) very high risk (

):

0 1 0
.
;
;
0,6 0,8 1,0

3. Criteria values for alternatives and their importance parameters are recorded.
4. Weighted estimates Ri are obtained as follows:
m

Ri

j

* Rij , i 1, n, j 1, m.

j 1

5. When weighted estimates Ri are obtained, objects
are compared. For the purpose fuzzy set I is introducedwith values following the below rule:I( ai ) sup minrp ri i 1, nRi( r ).

Currently risk-management becomes an invaluable
resort of strategic planning of Russian industrial enterprises that impacts the company value and might imply
the rise of productivity. The proposed algorithm of M&A
deals gross risk evaluation at OJSC Magnitogorsk Metallurgy Plant has proven its applicability and might be advised for further implementation at industrial enterprises
in order to:
Identify and classify risks mostly impacting M&A
deal outcome;
Provide complex and regular work on riskmanagement when running M&A deal to separate
the duties within the Divisions and Levels ofManagement;
Improve the KPIs of M&A deals by decreasing
the associated risks and optimizing costs to handle
risk minimization;
Increase the efficiency of M&A project management by introducing additional criteria for decision-making and by receiving and analyzing feedback on M&A deals realization;
Support the growth in market capitalization, increase in credit and investment ratings;
Achieve the most beneficial state and to protect
the current market niche.
References

The best alternative is the one having the highest
value. I function values are interpreted as the(
I ai )
alternative level of riskiness.
Similarly to the previous approaches the metallurgy
holding experts would treat the following projects as themost risk: Pakistan( a4 ) 1 , Canada( a20 ) 0,9260 ,

4.

Turkey5.

( a1 )

0,9240 , Germany( a17 )

0, 9200 .

The findings suggest fuzzy logic is a useful tool toevaluating gross risk of M&A projects. The gross risk
estimate obtained enables to forecast the outcome of
M&A deal, adjust the key financials and make the decision on whether to proceed with the deal or not during thefirst stage of M&A process.

1.
2.
3.

6.
7.

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economy. ECO, 2010. no. 2, pp. 75-84 (rus).
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activities of the economic sectors of the Russian Federation. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical Univeersity]. 2010.
no. 3(31), pp. 73-77 (rus).
Rykov A.S. Systemic analysis: models and methos of decision-making andsearch optimization. Moscow: MISiS Publishing House, 2009.
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Shmoilova R.A. Theory of statistics textbook. Moscow: Finance and Statistics Publ., 2003.

84 —————————————————————————— Vestnik of Nosov Magnitogorsk State Technical University 2013. 5.

The information about the authors

TTHHEE IINNFFO
ORRM
MAATTIIO
ONN AABBOOUUTT TTHHEE AAUUTTHHOORRSSAkhmetov Timur Uralovich – serviceman engineer ofLimited Liability Company Scientific and Production Association «Automatica» (Automatics). Phone: 8(3519)29-85-58.
E-mail: pksu035@gmail.com.
Andreev Sergey Mikhailovich – PhD in engineering, Associate Professor, Head of «Industrial cybernetics and control systems» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: 8(3519)29-85-27. E-mail: pk_su@bk.ru.
Antsupov Alexandr Victorovich – PhD in engineering, Associate Professor of «Mechanical Engineering» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone:8(3519)29-85-19. E-mail: ants@mgn.ru
Antsupov Alexei Victorovich – PhD in engineering, Associate Professor of «Steel Works Machinery» Department, «Nosov
Magnitogorsk State Technical University», Russia. Phone:8(3519)29-85-07. E-mail: ants@mgn.ru.
Antsupov Victor Petrovich – Doctor of Technical Sciences(D.Sc.), Professor of «Steel Works Machinery» Department, «Nosov Magnitogorsk State Technical University », Russia. Phone:8(3519)29-85-07. E-mail: ants@mgn.ru.
Bigeev Vahit Abdrashitovich –Doctor of Technical Sciences, Professor, Director of the «Metallurgy, Mechanic Engineering and Materials Processing» Institute, «Nosov Magnitogorsk State Technical University», Russia. Phone: 8(3519)29-8559. E-mail: v.bigeev11@yandex.ru.
Borovik Pavel Vladimirovich – PhD in engineering, Associate Professor, Donbass State Technical University, Alchevsk, doctoral student of Donbass State Engineering Academy, Kramatorsk, Ukraine. E-mail: borovikpv@mail.ru.
Cherchintsev Veacheslav Dmitrievich – Doctor of Technical Sciences, Professor, Head of «Industrial Ecology and Security» Department, «Nosov Magnitogorsk State Technical University». Phone: 8(3519)29-85-15. E-mail: eco_safe@magtu.ru.
Chukin Michail Vital,evich – Doctor of Technical Sciences, Professor, Vice-rector for Scientific and Innovation Work,
Head of «Machine-building and Metallurgical Technologies»
Department, «Nosov Magnitogorsk state technical university»,
Russia. Phone: 8(3519) 29-85-26. E-mail: m.chukin@mail.ru.
Danilyuk Victoria Alexandrovna – postgraduate studentof «Automated Metallurgical Machinery and Equipment» Department, Donbass State Engineering Academy, Kramatorsk,
Ukraine. E-mail: viktoriya1987@yandex.ru.
De Smedt Vivian – PhD in mathematics, Director Planning
at PSI Metals, GmbH, Brussels Area, Belgium. E-mail:vdesmedt@psi.de.
Drobny Oleg Fedorovich – PhD in engineering, chief ofthe department of the environmental protection at the OJSC
«Magnitogorsk Iron and Steel Works», Russia. Phone: 8(3519)2479-83. E-mail: drobny@mmk.ru.
Dyja Henrik – Professor, Doctor of Technical Sciences,
Director of the Institute of Metal Forming and Engineering Security, Czestochowa University of Technology Poland. E-mail:dyja@wip.pcz.pl.
Gorlenko Dmitriy Alexandrovich – assistant of the department of «Materials Science and Thermal Treatment» of«Nosov Magnitogorsk State Technical University», Russia.
E-mail: gorldima@yandex.ru.
Gribkov Eduard Petrovich – PhD. in engineering, Associate Professor, «Automated Metallurgical Machinery andEquipment» Department, Donbass State Engineering Academy,
Kramatorsk, Ukraine. E-mail: amm@dgma.donetsk.ua.
Gun Gennadiy Semenovich – Doctor of Technical Sciences, Professor, «Machine-building and Metallurgical Technolo-gies» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: 8(3519) 29-85-26. E-mail:mgtu@magtu.ru.
Gun Igor Gennadyevich – Doctor of Technical Sciences,
Full Professor, Head of «Technologies, Certification and Vehicles Service» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: 8(3519)29-84-31.
Hamedon Zamzuri – Department of Mechanical Engineering, Toyohashi University of Technology, Aichi, Japan.
Ishmetyev Evgeniy Nikolayevich – KonsOM SKS company, Magnitogorsk, Russia.
Kawa ek Anna – Dr.Sc., Assistant Professor, Czestochowa
University of Technology, Poland. E-mail: kawalek@wip.pcz.pl.
Kinzin Dmitry Ivanovich – PhD in engineering, Associate
Professor, «Metal Forming» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: (3519)
298525. E-mail: kinzin@mail.ru.
Kolga Maria – Research Engineer PSI Metals GmbH,Germany. E-mail: mkolga@psi.de.
Kolokoltsev Valeriy Mikhailovich – Doctor of Technical
Sciences, Professor, Rector of «Nosov Magnitogorsk State
Technical University», Russia. Phone: 8(3519)29-84-02. E-mail:kwm@magtu.ru.
Koptseva Natalya Vasilyevna – Doctor of Technical Sciences, Professor, «Material Science and Metals and Alloys Heat
Treatment» Department, «Nosov Magnitogorsk state technicaluniversity»,
Russia.
Phone:
8(3519)29-85-67.
E-mail: koptsev2002@mail.ru.
Korchunov Alexei Georgievich – Doctor of Technical
Sciences, Professor, Vice-Rector for International Relations,«Nosov Magnitogorsk State Technical University», Russia.
Phone: 8 (3519) 29-84-09. E-mail: international@magtu.ru.
Korenko Marina Georgiyevna – PhD in engineering, Assistant Professor, MT Department, Krivoy Rog Metallurgical
Institute of the State institution of higher education, «National
University of Krivoy Rog», Ukraine. Phone: 75873245. E-mail:marinak 2010@ bk.ru.
Levandovskiy Sergey Anatolievich – PhD in engineering, Associate Professor, «Metal forming» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone:8(3519) 29-85-25. E-mail: levandovskiy@mail.ru.
Logunova Oxana Sergeevna – Doctor of Technical Sciences, Associate Professor, Head of Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: 8(3519)22-0317. E-mail: logunova66@mail.ru
Lutsenko Andrey Nikolaevich – Severstal, Cherepovets,
Russia.
Maeno Tomoyoshi – Department of Mechanical Engineering, Toyohashi University of Technology, Aichi, Japan.
Manashev Ildar Raufovich – PhD in engineering, Limited
Company STIF «Etalon». Phone: 8(3519) 58-01-57.
E-mail: mirney@yandex.ru.
Matsko Igor Igorevich – PhD., engineer, Research and Development Center «Ausferr». E-mail: matskoigor@gmail.com.
Mezin Igor Yurjevitch – Doctor of Technical Sciences,
Professor, Head of «Technologies, Certification and Automobile
Service » Department, «Nosov Magnitogorsk State Technical
University», Russia. Phone: 8(3519)29-84-31. E-mail: meziniy1@mail.ru.
Moller Alexander Borisovich – Doctor of Technical Sciences, Professor «Metal forming» Department, «Nosov Magnitogorsk State Technical University», Russia.Phone:8(3519)29-85-25. E-mail: moller@hotbox.ru.

www.vestnik.magtu.ru. ——————————————————————————————————————————————

85

The information about the authors
Mori Ken-ichiro – Professor, Department of MechanicalEngineering, Toyohashi University of Technology, Aichi, Japan.
Mukhina Elena Yurievna – Assistant Professor, «Industrial
Cybernetics and Control Systems» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: 8(3519)298558.
E-mail: pksu035@gmail.com.
Nalivaiko Alexander Vladimirovich – First Deputy General Director of OJSC «VNIIMETMASH», Moscow.
Phone: 8(495)7304530. E-mail: mail@vniimetmash.ru.
Nastoshchaya Svetlana Sergeyevna – assistant of«Automated Metallurgical Machinery and Equipment»
Department,
Donbass
State
Engineering
Academy,Kramatorsk, Ukraine. Phone: (0626) 41-46-81. E-mail:
amm@dgma.donetsk.Ua
Novitskiy Ruslan Vitalievich – OJSC «Magnitogorsk Iron
and Steel Works», Russia.
Parsunkin Boris Nikolaevich – Doctor of Technical Science (D.Sc.), Professor, «Industrial Cybernetics and Control
Systems» Department, «Nosov Magnitogorsk State Technical
University», Russia. Phone: 8(3519)29-84-32. E-mail:pksu035@gmail.com.
Perekhodchenko Viktor Aleksandrovich –senior engineer, Novokramatorsk Machine Building Plant Public Joint
Stock Company, Kramatorsk, Ukraine. Phone: (0626) 41-46-81.
E-mail: amm@ dgma.donetsk.ua.
Pesin Alexander Moiseevich – Doctor of Technical Sciences, Professor, «Metal Forming» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: 8(3519)29-8525. E-mail: pesin@bk.ru.
Petrochenko Elena Vasilyevna – Doctor of Technical
Sciences, Professor, «Materials Science and Thermal Treatment» Department, «Nosov Magnitogorsk State Technical
University», Russia. E-mail: evp3738@mail.ru.
Pietrzyk Maciej – Professor, «Applied Computer Scienceand Modelling» Departament, AGH Akademia GórniczoHutnicza, Kraków, Poland
Polikarpova Maria Gennadievna – PhD in economics,
Assistant Professor, «Mathematical Methods in Economics»
Department, «Nosov Magnitogorsk State Technical University»,
Russia. E-mail: marjyshka@rambler.ru.
Polyakova Marina Andreevna – PhD in engineering, Associate Professor, «Machine-building and Metallurgical Technologies» Department, «Nosov Magnitogorsk state technical university», Russia. Phone: 8(3519) 29-84-81. E-mail: m.polyakova64@mail.ru.
Posokhov Ivan Alexandrovich – graduate student, «Nosov Magnitogorsk State Technical University». Phone:8(3519)29-85-63. Email: posohoff@bk.ru.

Rubin Gennadiy Shmulyevich – PhD in engineering, Associate Professor, «Technologies, certification and vehicles service» Department, «Nosov Magnitogorsk State Technical University», Russia. Phone: (3519)298563.
Ruchinskaya Natalia Aleksandrovna – PhD in engineering, Associate Professor, «Metal Forming» Department, «Nosov
Magnitogorsk State Technical University», Russia. Phone:8(3519) 29-85-25.
Rumyantsev Mihail Igorevich – PhD in engineering, Professor, «Metal Forming» Department, «Nosov Magnitogorsk State
Technical University», Russia. E-mail: mihigrum@rambler.ru.
Rychkov Sergey Sergeyevich – Open Joint-Stock Company «Magnitogorsk Iron and Steel Works», Russia.
Satonin Alexander Vladimirovich – DSc., Professor, Donbas State Machine-Building Academy, ramatorsk, Ukraine;
Phone: (0626) 41-46-81. E-mail: amm@dgma.donetsk.ua.
Shatohin Igor Mihaylovich – general manager of STIF
Etalon Ltd. Co. Phone: 8(3519) 58-01-55. E-mail: mail@ntpfetalon.ru.
Shaymardanov Kamil Ramilevich – postgraduate student,«Ferrous Metals Metallurgy» Department, «Nosov Magnitogorsk State Technical University», Russia. E-mail: kemlmgn@gmail.com.
Shigorina Anna Yurievna – Master’s program student,«Ferrous Metals Metallurgy» Department, «Nosov Magnitogorsk State Technical University», Russia. E-mail: shigorina89@mail.ru.
Sztangret Mateusz – Departament of Applied Computer
Science and Modelling, AGH Akademia Górniczo-Hutnicza
Kraków, Poland.
Tulupov Oleg Nikolayevich – Doctor of Technical Sciences,
Professor, «Metal Forming» Department, «Nosov Magnitogorsk
State Technical University», Russia. Phone: 8(495)7304999. Email: o.tulupov(@mail.ru.
Van Nerom Luc – Director of Software Architecture,
Methods and Quality PSI Metals GmbH, Germany. E-mail:lvannerom@psi.de.
Vdovin onstantin Nikolaevich – Doctor of Technical
Science, Professor, Head of «Electrometallurgy and Foundry»
Department, «Nosov Magnitogorsk State Technical University»,
Russia. Phone: 8(3519)29-84-19. E-mail: Vdovin@magtu.ru.
YamashitaYuya – Department of Mechanical Engineering,
Toyohashi University of Technology, Aichi, Japan.
Zavalischin Alexander Nicolaevich – Doctor of Technical
Sciences, Professor, «Materials Science and Thermal Treatment»
Department, «Nosov Magnitogorsk State Technical University»,
Russia. Phone: 8(3519)29-85-67. E-mail: zaval1313@mail.ru.

86 ———————————————————————— Vestnik of Nosov Magnitogorsk State Technical University. 2013. 5.