Future-oriented supervision of the cold rolling process in reversing mills (Fosucor).
Date: 2013-12-06
Institutions: Directorate-General for Research and Innovation
Subjects: industrial research, iron and steel-working machinery, production technique, research and development, research report, strip, supplementary budget, testing

European Commission

Research Fund for Coal and Steel

Future-oriented supervision of the cold rolling 
process in reversing mills

(Fosucor)

R. Lathe
VDEh-Betriebsforschungsinstitut GmbH
Sohnstrasse 65, 40237 Düsseldorf, GERMANY

J. Kazmierski
Outokumpu Nirosta GmbH
Oberschlesienstrasse 16, 47807 Krefeld, GERMANY

J. Leven
Swerea MEFOS AB
Arontorpsvägen 1, SE-97 125 Luleå, SWEDEN

Grant Agreement RFSR-CT-2009-00035 
1 July 2009 to 31 December 2012

Final report

Directorate-General for Research and Innovation

2013 

EUR 26171 EN

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Luxembourg: Publications Office of the European Union, 2013 

ISBN 978-92-79-33085-8 
doi:10.2777/41572 

© European Union, 2013 
Reproduction is authorised provided the source is acknowledged. 

Printed in Luxembourg 

Printed on white chlorine-free paper

 
 
 
 
 
 
Table of content 

2.4.4 

2.4.3 

2.4.2 

2.4.1 

2.4.3.1 
2.4.3.2 

2.1 
2.2 
2.3 
2.4 

2.4.2.1 
2.4.2.2 
2.4.2.3 

2.4.1.1 
2.4.1.2 
2.4.1.3 

1 Final Summary ....................................................................................................................................... 5 
Scientific and technical description of results ............................................................... 15 
2 
Introduction ................................................................................................................... 15 
Objectives of the project ................................................................................................ 19 
Comparison of initially planned activities and work accomplished. ............................. 19 
Description of activities and discussion......................................................................... 21 
Provision of the required process and computation data (Work Package 1) ................. 21 
Adaptation and expansion of the long-time database. ................................................... 21 
Establishing an online database for pass schedule calculations. .................................... 21 
Establishing a database for the analysis of process dynamics. ...................................... 21 
Pre-calculation of strip flatness (Work Package 2) ....................................................... 23 
Determination of the factors influencing flatness actuation. ......................................... 23 
Development of a simple flatness model. ...................................................................... 31 
Development of a physical flatness model. ................................................................... 32 
Roll geometry optimization (Work Package 3) ............................................................. 43 
Determining the approach to CVC technology use. ...................................................... 43 
Development of a software programme for optimizing the roll geometry. ................... 46 
Development of a predictive strip defect model (Work Package 4) .............................. 53 
2.4.4.1  Measurement of strip specimens with “heat / pressure stripes”. ................................... 53 
First data-based analysis regarding the surface defect “heat / pressure stripes”. ........... 54 
2.4.4.2 
Test series to avoid the strip defect “heat / pressure stripes”. ........................................ 56 
2.4.4.3 
2.4.4.4 
Second data-based analysis regarding the surface defect “heat / pressure stripes”. ...... 57 
Development of theories about the occurrence of “heat / pressure stripes”. ................. 59 
2.4.4.5 
2.4.4.6  Measurement of strip specimens with diagonal waves (“fishbone effect”). .................. 59 
Data-based analysis regarding the surface defect “diagonal waves”. ............................ 64 
2.4.4.7 
Test series to avoid the strip defect “diagonal waves”. ................................................. 66 
2.4.4.8 
Development of theories about the occurrence of “diagonal waves”. ........................... 67 
2.4.4.9 
Integration of models into pass schedule calculation (Work Package 5) ...................... 69 
Development of an algorithm for strip flatness. ............................................................ 69 
Development of an algorithm for automatic analysis of process dynamic. ................... 73 
Development of an algorithm for calculating the roll force limits. ............................... 74 
Integration into the pass schedule calculation. .............................................................. 75 
Test calculations to validate the new calculation approach. .......................................... 78 
Validation of the system under industrial conditions (Work Package 6) ...................... 81 
Preliminary rolling test to consider the roll force limits. ............................................... 81 
Online validation of the new program. .......................................................................... 81 
Online validation of the roll geometry optimisation. ..................................................... 88 
Conclusions ................................................................................................................... 89 
Exploitation and impact of the research results. ............................................................ 91 
List of Figures. ............................................................................................................... 93 
List of Tables. ................................................................................................................ 95 
List of Symbols, Indices, Acronyms and Abbreviations. .............................................. 95 
List of References .......................................................................................................... 97 
Appendix 1: Additional Figures and Tables. ................................................................. 99 
Appendix 2: Data mining techniques........................................................................... 121 

2.4.5.1 
2.4.5.2 
2.4.5.3 
2.4.5.4 
2.4.5.5 

2.4.6.1 
2.4.6.2 
2.4.6.3 

3 
4 
5 
6 
7 
8 

2.5 
2.6 

2.4.5 

2.4.6 

3 
 
1 Final Summary 

The  project  was  carried  out  at  a  20  high  mills  at  which  stainless  steel  strips  are  produced  in  a  width 
range between 1250 mm and 1550 mm with a typical entry thickness range between 4 mm and 2.5 mm. 
The strips are rolled in reversing manner in several passes down to a typical final thickness between 1 
mm and 0.4 mm. 
The required number of passes and the pass reductions are given by a pass schedule calculation. 
The requirements on a pass schedule are: 
  Considering the Material properties and the Mill parameter (e.g. max. roll force; max. roll torque) 
  High productivity 
  Good flatness in all passes. 
  Achieve of the required surface quality. 
The general layout of a 20 high mill enables a high roll force and the use of small work rolls at the same 
time. This mill type typically has three flatness actuators. These are tilting (e.g. by tilting the mill 
house); a backup roll crown adjustment and axial shiftable taper rolls (Figure 2 page 15). 
Beside the flatness actuators the roll force significantly influences the strip flatness. 
At this point the pass schedule becomes important. As higher the reduction (at a certain pass) as higher 
the roll force will be (example Figure 5 to Figure 9 page 16 ff). The higher roll force in turn does lead to 
longer strip edges. That is no problem as long the flatness actuators have enough remaining adjustment 
range to compensate the flatness deviation. A limitation of increasing the reduction is given when the 
flatness actuators are at their mechanical limitations.  
But the reduction limitation varies in dependence of several parameters. These are: 
• 
Since the interaction of all parameter in conjunction with the strip flatness is very complex the current 
approach to ensure proper flatness is the use of empirical determined reduction limitations. 
Beside  the  strip  flatness  also  the  quality  of  the  final  product  in  terms  of  surface  quality  (e.g.  gloss, 
roughness) needs to be considered. Also for this the current approach is the use of empirical determined 
reduction limitations. 
One major disadvantage of this approach is the fact that one limitation needs to replace two independent 
values (strip flatness and surface quality) what makes it very difficult to find an optimum. Furthermore 
the empirical values typically are not adjusted e.g. to changed products or changed roll geometries. 
Beside the pass schedule the geometry of the rolls have major influence on the productivity of a rolling 
stand. For example, at a 20-high mill the roll force range at which the mill can be operated (considering 
the  strip  flatness)  is  determined  by  the  crown  of  the  intermediate  rolls  and  the  geometry  of  the  taper 
rolls (taper length, taper inclination).  
From experience it can be stated that the suitable roll geometry for a specific rolling mill is always de-
termined empirically. The roll geometry suitable for rolling the range of products is “approximated” by 
trial and error approach. The wider the range of products is, the more difficult this process becomes.  

Strip tension; •  Material strength 

Strip width; • 

Objectives of the project 

Within the framework of this project the intelligent use of existing process data is to replace the use of 
empirical values and to replace the trial and error approach to achieve optimal roll geometries.  
The main objectives of the research project are summarized as follows: 
1.  An Auto-Adaptive Pass schedule calculation taking into consideration pre-calculated strip flatness 
and the pre-calculated probability for the occurrence of fish bones, heat scratches or pressure 
marks. 

2.  Development of a software programme helping the plant operator to optimize the roll geometry. 
3.  Testing of a new procedure suitable for using CVC technology in existing 20-high mills.  

Benefits: 
1.  Elimination of empirically determined limitations, e.g. maximum reduction per pass and maximum 

strip temperature. 
Improved roll geometry for the range of products rolled on the specific mill. 

2. 
3.  Reduction of the number of strips which due to shape or surface defects must be re-commissioned, 

downgraded or even scrapped. 

5 
 
4. 

Increased flexibility of a 20-high mill with a view to the range of products and an increased mill 
performance by using the CVC technology in existing mills.  

5.  These measures are expected to improve the utilization rate of the mill and, as a result, increase 

productivity by at least 5%.  

Description of activities and discussion. 

WP1: Provision of the required process and computation data 

The  main  objective  of  this  work  package  was  the  provision  of  the  required  process  and  computation 
data. For this, databases were created which provide the required functionality and content. 

Adaptation and expansion of the long-time database. 
A  long-time  database  was  basically  already  in  place  at  TKL-NR.  The  database  contains  data  in  com-
pacted form. The database was expanded with the measured flatness, the positions of all flatness actua-
tors,  the  measured  coolant  amount  and  the  work  roll  diameter.  A  connection  to  the  roll  management 
system was established which contains all remaining relevant roll geometry data. 

Establishing an online database for pass schedule calculations. 
For the strip flatness prediction a database was required which provides short retrieval times and covers 
all variants of the product range. To ensure short retrieval times and at the same time to cover all vari-
ants  of  the  product  range  an  algorithm  was  developed  which  analyses  the  database  and  only  deletes 
those older datasets, which are high frequently available. Thus the number of datasets can be limited to 
a relative low level which allows a quick access without loosening the important information of seldom 
type of datasets. The content of the database is similar to the long term database. 

Establishing a database for the analysis of process dynamics. 
This database was intended to be used for the analysis of the dynamics of important process parameters 
such as strip thickness, rolling force and strip flatness. Furthermore this database is useful to investigate 
the influencing effects of the flatness actuators determined by the rolling tests. The database does now 
contain all relevant process data for one week in one second steps. 

WP2: Pre-calculation of strip flatness 

Aim of this task was the development of two different types of flatness models which should be used in 
the  subsequent  stages.  One  simplified  model  with  short  computation  time  which  will  be  used  for  the 
online pass schedule calculation. Secondly a more accurate physical based model for optimizing the roll 
geometry and adapting the computed parameters of the simple flatness model. 

Determination of the factors influencing flatness actuation. 
The major influencing factors of the flatness are the flatness actuators itself, the roll geometry of work 
roll  and  intermediate  rolls,  the  roll  force  and  the  strip  thickness.  To  investigate  the  influence  several 
rolling tests were carried out at two 20 high rolling mills. Since the tests were carried out at different 
passes the thickness influence could be analysed, too. 
The first rolling test were carried out for the flatness actuators backup roll crown adjustment and shift-
ing of the tapered rolls. 
Regarding the backup roll crown adjustment the test results did show that the flatness influence form of 
the roll crown adjustment is almost the same independent of the thickness and is pretty similar for both 
mill types. Here the flatness influence form can be best described as a square function. Furthermore the 
results  did  show  that  flatness  influence  factor  (the  amount  of  flatness  difference  per  unit  adjustment) 
increases for thinner material. 
The  rolling  tests  regarding  the  shifting  of  the  tapered  rolls  were  carried  out  with  three  different  taper 
rolls. The subsequent table gives an overview of the major parameter. The much longer tapered part at 
mill 2 is required because the dimension of mill 2 is related to a max. strip width of 1550 mm. When 
rolling narrow strips (like here) the taper length needs to be accordingly enlarged. 

Mill 1 (Type Sundwig)
Maximum strip width

Mill 1 (Type Sundwig)
1350 mm Maximum strip width

Strip width
Taper length
Taper inclination

1274 mm Strip width
120 mm
3 ‰

Taper length
Taper inclination

Mill 2 (Type Sendzimir)

1350 mm Maximum strip width

1550 mm

1269 mm Strip width
90 mm
5.6 ‰

Taper length
Taper inclination

1290 mm
320 mm
2 ‰

6 
 
 
The test results did confirm that the flatness influence form is very similar independent of the thickness 
and that the flatness influence becomes higher for thinner strip thicknesses.  
As expected the taper with the highest taper inclination (taper 90) led to the highest flatness influence 
for 1 mm taper shifting and taper 320 to the lowest influence. On the other hand the results did show 
that  the  influence  form  is  very  similar  for  all  taper  rolls.  (The  linear  correlation  to  each  other 
was ≈ 0.98). This result led to some further investigations. Instead to calculate the flatness influence for 
1 mm taper roll shifting the flatness influence was calculated to the resulting diameter difference at the 
strip edge which results from the taper shifting. The next figure shall explain this and demonstrates the 
flatness  influence  of  the  different  taper  rolls  recalculated  to  a  diameter  difference  of  100  µm  at  strip 
edge. It can be seen that the flatness influence is almost the same in all cases. This can be explained by 
the  fact  that  the  form  of  the  different  taper  rolls  (within  the  range  covering  the  strip)  correlates  with 
almost 100%.  

Diameter difference 
at strip edge 30 µm

Flatness influence in dependence of 
the diameter difference at strip edge

Taper roll

Work roll

Taper roll
30 mm shifted

Strip

Diameter difference 
at strip edge 100 µm

Taper length which 
covers the strip

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40

20

0

‐20

‐40

‐60

‐80

‐100

‐120

Taper 120 Mill 1
Taper 90 Mill 1
Taper 320 Mill 2
Mean value

‐700

‐500

‐300

‐100

100

300

500

700

Strip Width [mm]

The investigations can be summarized as follows.  
 

If  different  taper  rolls  basically  differs  only  by  the  inclination  the  flatness  influence  mainly  de-
pends on the provoked diameter difference at the strip edge (caused by a taper shifting).  
If the flatness influence of one taper roll is known the flatness influence for a different taper incli-
nation can be extrapolated (within a certain range) with adequate accuracy. 

 

Based  on  the  rolling  test  a  formula  could  be  derived  which  adequate  describes  the  influence  of  strip 
thickness  on  flatness.    The  used  formula  is:  Correlation  =  (c0+c1)  /  (c0+c1*  exit  thickness)  at  which 
c0 = 0.196 and c1 = 0.212 is. 
To  investigate  the  flatness  influence  of  the  roll  force  a  special  phenomenon  observed  in  the  past  was 
used. It was realised that in later passes (pass number > 5) there is a large deviation of the roll force 
which depends on the rolling speed. The roll force difference here can be more than 20%. With the help 
of a newly created program those cases could be selected from the dynamic database and analysed. 
One further rolling test was carried out to investigate the flatness influence of the change of a roll crown 
at which one idle roll was replaced at two certain passes. Beside the flatness influence the test results 
did show that the influence form of the changed roll crown is more or less identical with the influence 
form of the backup roll crown adjustment. This result was helpful since it did show that the used range 
of  the  flatness  actuator  “backup  roll  crown”  basically  can  be  optimized  by  an  adjustment  of  the  roll 
crown of the second intermediate rolls (idle roll or driven rolls). 

Development of a simple flatness model. 
The so far achieved results have been integrated into a simple function with which the individual flat-
ness effects of the flatness actuators and the roll force can be calculated. Ingoing parameter of the func-
tion are the strip width and thickness, the actuator name (respectively roll force) and the actuator ad-
justment  (respectively  roll  force  difference).  The  function  selects  the  influence  function  based  on  the 
actuator name and the strip width, calculates the linear correlation (= factor) based on the thickness and 
finally multiplies the influence function with the factor and the actuator adjustment. 
In several cases it is necessary to calculate the required actuator adjustment(s) or a required roll force 
difference for a given (or wanted) flatness change. For this an inverse flatness model was created. The 
additional  ingoing  parameters  of  this  function  are  the  actuator  range  limits  and  the  wanted  flatness 
change. The result of the function is the required roll force difference or actuator adjustment. The func-
tion is also able to calculate the required adjustments for more than one actuator at the same time. 

7 
 
 
 
 
 
 
 
 
Development of a physical flatness model. 
A previously developed model for simulation and flatness prediction for rolling in cluster mill was fur-
ther developed to fit the needs in this project. The program is rewritten to a callable subroutine with a 
specified interface to suit the other software developed in the project. Specification of the mill, the strip 
and the rolling conditions were transferred in the call and the model returns the flatness response for the 
actual case. 
The model was modified regarding recent findings in behaviour of the strip under plastic deformation. 
FEM calculations are done to study the plastic deformation of the strip and its influence on strains and 
stresses in the strip and in the contact zone between strip and rolls. 
The model is verified by comparison of calculation results and measurements in a production mill. The 
flatness sensitivity of different rolling parameter was investigated. As an example the effect of changed 
roll crowns was investigated. The calculations did confirm that the flatness influence form is very simi-
lar compared to the BUR crown adjustment. With the help of the program furthermore the BUR crown 
adjustment can be calculated which is required to compensate any roll crown change of the intermediate 
rolls.  This  calculation  is  useful  in  frame  of  the  roll geometry  optimisation  to determine  the  estimated 
adjustment of the BUR crown caused by changed roll crowns. The following figure and table exempla-
ry demonstrate some of the calculation results. 

]
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Flatness difference by changed roll crown

Idle roll + 50 µm
Idle roll + 100 µm
Driven roll + 50 µm
Driven roll + 100 µm

175

150

125

100

75

50

25

0

-25

-50

-75

-700

-350

0

350

Width [mm]

WP3: Roll geometry optimization 

Roll crown change

Idle roll + 50 µm
Idle roll + 100 µm
Driven roll + 50 µm
Driven roll + 100 µm

700

BUR crown adjustment
required to compensate
the crown change

‐15%
‐28%
‐43%
‐85%

This work package is divided into two parts. One was to test the use of the CVC technology in existing 
20-high mills by replacing two of the four taper rolls with CVC rolls. The other was the development of 
a software programme which supports the operator in optimizing the roll geometries in a mill stand 

Determining the approach to CVC technology use. 
The idea of this approach was to replace one upper and one lower taper roll by a pair of CVC rolls to 
obtain an additional flatness actuator (see Figure 40). 
If this approach shall work it requires, that it is also possible to roll with a pair of one taper roll com-
bined with one cylindrical roll instead of a pair of taper rolls. 
While  carrying  out  this  rolling  test  a  heavy  strip  break  was  produced  short  after  the  pass  start  while 
accelerating the rolling speed. Within 3 sec. and 20 m strip length at the strip side where the combined 
taper - cylindrical rolls are located the strip becomes extremely long producing a double folding. The 
strip break was that heavy that a fire in the mill was produced. 
At this one needs to know that a strip break (especially caused by a double folding) is extremely seldom 
at the strip thickness (1.2 mm) the strip break occurs. Only reasons for such a strip break can be a large 
lateral movement of the strip (e.g. caused by too much remaining rolling oil on the strip) or a sudden 
breakdown  of  the  coiler  motors  (causing  that  the  tension  suddenly  becomes  zero).  Both  cases  do  not 
appear here. Conversely this means that the combined taper - cylindrical rolls must be the strip break 
source 
A detailed view on the geometric roll gap situation directly at the strip edge does provide some possible 
explanation what provokes the strip break. Caused by the diameter difference between cylindrical and 
taper roll (at the strip edge) the work roll is displaced approximately 0.2 mm towards the rolling direc-
tion. Furthermore it needs to be considered that at the same time the roll gap situation is symmetrical 
where the tapered part ends. The displacement of the upper work roll causes an asymmetry which can 
lead to some shearing tension which decreases the deformation stress. Thereby the local reduction in-
creases what in turn increases the local strip elongation largely (and thus causing the strip break). 

8 
 
 
 
 
Unfortunately the asymmetric rolling conditions would occur in the same way when using a CVC roll 
instead of a cylindrical roll. This means that there was a high risk of strip breaks when carrying out the 
foreseen  CVC  rolling  tests.  In  turn  this  led  to  the conclusion  that  there  is  only  a  low  chance  that  the 
CVC approach would be successful. 
Any heavy strip break in conjunction with a longer production interrupt is very cost intensive. Beside 
this further cost would have been necessary to prepare this rolling test e.g. the revamping of the axial 
shifting control. Considering all facts it was decided to stop the further investigations of the CVC ap-
proach. 

Development of a software program for optimizing the roll geometry 
In a first stage a program was developed which automatically analyses the current state of the flatness 
and the flatness actuator positions periodically. The periodical approach ensures that the resulting da-
tasets are always up to date. 
In a second stage a program was developed with which the operator can view the current as-is state and 
quickly find the optimal roll geometry under consideration of the product range 
Optimising crown of intermediate rolls: 
Since the crown of the intermediate rolls is related in high 
correlation  with  the  flatness  actuator  “backup  roll  crown 
adjustment”  the  optimisation  of  the  roll  crowns  results 
from the current state of this actuator. 
The backup roll actuator is designed in such a way that a 
set of adjustable supporting mounts enables the individual 
adjusting  of  the  backup  rolls.  Since  the  individual  posi-
tions  of  the  support  mounts  are  not  meaningful  they  are 
recalculated to a “crown” value by calculating the square 
part  which  fits  best  to  all  positions  (like  demonstrated  in 
the right figure). 
In the subsequent figure the statistical analysis for one example case is given by the thin lines. The dia-
gram named “backup roll crown” shows the distribution of the BUR crown position in dependence of 
the strip thickness. Here the thin green line represents the mean value while the thin red lines do show 
the actuation range which covers 95% of all measured rolling cases. The y-axis is scaled to the max. 
possible mechanical adjustment range which provides an easier validation of the current state. 
For an easier understanding on the right side a graph is shown, at which the positions of the adjustable 
support mounts are presented for a certain case. (This graph is designed in a similar way the operator 
gets the adjustable support mounts presented at the online flatness control). 
An evaluation of the current state shows clearly that the current crown of the intermediate rolls should 
be modified. For a strip thickness above 3 mm the BUR crown is frequently at the mechanical limita-
tion while only in a few cases the BUR crown becomes slightly negative. The target is to have the BUR 
crown on average centred within the mechanical limits. 
To meet the target at this example one of the roll crowns needs to be increased. By changing one of the 
“new roll crown” values the program calculates the estimated new distribution of the BUR crown dis-
playing the result by the thick green and red lines. At the example the result for the case that the crown 
of the driven rolls is increased from 150 µm to 240 µm (which in addition meets the target). 

9 
 
 
Of course it would be possible to calculate the ideal crown of a selected roll automatically. The “manu-
al”  approach  has  the  advantage  that  the  operator  has  the  possibility  to  configure  the  roll  crowns  very 
flexible to his own requirements. 
Optimising taper length and taper inclination: 
Similar as for the BUR crown the current as-is state of the taper position is displayed in dependence of 
the strip thickness by the thin lines. Also here the y-axis is scaled to the max. possible mechanical ad-
justment range for an easier validation of the current state.  
The operator has the possibility to change either the taper length or the taper inclination. The program 
than calculates the resulting estimated change of the taper positions by the thick lines as demonstrated 
at the following figure. 

Beside the new taper position distribution the new taper form is presented and, in case of an increased 
taper inclination, the new estimated flatness influence. After completion the optimisation the operator 
has the possibility to save the new taper form as an ASCII file for a later use e.g. at the roll grinding 
machine. 

WP4: Development of a predictive strip defect model. 

Aim of this task was the development of a predictive strip defect model. Based on strip specimen meas-
urements and data based analyses the causes and key influencing factors should be determined and, if 
applicable, a statistical prediction model should be developed. 
The investigations were carried out for two high frequent occurring types of defect. One is  named as 
“heat / pressure stripes” and the other as “diagonal waves”. 
Investigations regarding the surface defect “heat / pressure stripes”. 
The defect “heat / pressure stripes” is a surface defect which becomes visible behind the bright anneal-
ing line and only for high gloss strips. Surface measurements did show that the defect is characterised 
by  slight  roughness  differences  between  rolling  direction  and  cross  to  the  rolling  direction  and  by  a 
decreased  surface  isotropy.  The  appearance  of  the  defect  leads  to  the  assumption  that  the  lubrication 
occasional local decreases and with it provokes a higher roughness. Data based analyses do show that 
the frequency of defects clear increases when at the first two passes a certain relative thickness reduc-
tion and within passes 4 to 8 a certain strip temperature is exceeded.  
The investigated limitations are:   Max. thickness reduction at pass 1 ≈ 18 % 

Max. thickness reduction at pass 2 ≈ 17,4 % 
Max. strip temperature ≈ 75° C 

Since in the major number of cases the total number of passes is higher than 8 it also means that a de-
fect, once provoked, cannot be completely removed by the subsequent passes.  
Investigations regarding the surface defect “diagonal waves”. 
The surface defect “diagonal waves” is a form defect occurring at the cold rolling process which pro-
vokes slight beamless and diagonal shadows behind the bright annealing line. Surface measurements on 
annealed specimen did not show differences in roughness between defected and non-defected sections. 
Only measureable cross to the rolling direction was a difference of gloss between the two sections. 

10 
 
 
Samples of rolled strips were measured with regard to flatness in two different measurement devices. 
By eye it could be noted that all samples had edge waves but also low amplitude buckles arranged diag-
onally over the whole sample width.  Both devices showed similar results in  terms of I-units over the 
width.  The  long  edge  observations  were  verified  and  the  low  amplitude  buckles  were  characterized 
regarding amplitude and wavelength 
Analysis did show a correlation for one type of flatness deviation (the centre flatness) and for the rela-
tion neutral point / roll angle. However, a modification of both values did not lead to an indictable de-
crease of the defect frequency. Since no clear correlations were detected no rolling rules or algorithms 
for a pre-calculation could be derived for this type of defect. 

WP5: Integration of models into pass schedule calculation. 

Development of an algorithm for strip flatness. 
One important parameter for the strip flatness is the resulting roll force at one pass. The roll force in 
turn depends directly on the pass reduction. The objective of the algorithm therefore is to select for each 
pass  a  reduction  value  which  achieves  both  good  strip  flatness  and  a  sufficiently  generous  actuation 
range of the flatness actuators for compensating rolling force variations. Thus for each pass an upper 
and lower rolling force limit needs to be determined. Rolling within this range shall ensure that both the 
strip flatness is good and the flatness actuators have a sufficiently generous actuation range. 
For the calculation of the upper and lower roll force limit the knowledge of the actuator variations at a 
typical roll force is required. To determine these values a program was developed which analyses pass 
datasets from the past and stores the calculation result into the online database. 
To calculate the roll force limitations and the “optimal” roll force a further algorithm was developed. 
The “optimal” roll force in this conjunction is defined by this roll force, where the actuators are located 
in the centre of the actuator range and therefor the maximum adjustment range is available. 
The  max.  possible  roll  force  is  given  when  the  flatness  actuators  are  located  at  the  upper  mechanical 
limitation minus the maximum actuator positions (which cover 95% of all cases). To calculate the min. 
possible roll force the lower mechanical limitations and the minimum actuator positions are used. 
Especially for 20 high mills where taper rolls are in use a greater influence of the strip width takes ef-
fect on the roll force limits. Background is the fact that a wider strip typically does enlarge the usable 
adjustment range and in opposite that a narrow strip does reduce the range. The dependency on the strip 
width is calculated.  
To use the calculation result for the pass schedule a user interface was developed with which the opera-
tor can view and evaluate the results. 

Development of an algorithm for automatic analysis of process dynamic. 
As  the  major  process  parameter  (in  conjunction  with  the  flatness)  with  the  greatest  dynamic  the  roll 
force  was  identified.  It  was  observed  that  the  roll  force  deviation  within  one  pass  can  be  more 
than 30%.  Thus  the  roll  force  deviation  need  to  be  considered  when  determining  the  final  roll  force 
limitations valid for a certain pass. 
A program was developed which determines behind each pass the maximum and minimum roll force 
deviation from the major roll force (the roll force from the strip length where the speed is the longest 
time constant) and storing the result into the online database. 
The best correlation regarding the roll force deviation was found for the total reduction which is present 
at a certain pass. Thus a further program was developed which periodically analyses the maximum and 
minimum roll force deviation in dependence of the total reduction. 
With the help of a user interface the operator can view and evaluate the results. 

Development of an algorithm for calculating the roll force limits. 
To determine the roll force limits for the pass schedule calculation the results from the flatness analyses 
and the roll force deviations needs to be brought together. A function was developed which merges the 
results for a certain strip as demonstrated in the subsequent figure. With the help of the user interface 
the operator can view and evaluate the resulting roll force limits for different strip dimensions. 

11 
 
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2000

0

3

Roll force limits indicated by flatness

max. Roll force
best Roll force
min. Roll Force

Roll force deviation

positive Roll Force deviation
negative Roll Force deviation

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Exit thickness [mm]

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Merged Roll force limits

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Total reduction [%]

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max. Roll force
best Roll force
min. Roll Force

2,5

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1,5

1

0,5

Exit thickness [mm]

Integration into the pass schedule calculation. 
Basically the pass schedule calculation is subdivided into two major parts. In part one the required total 
number of passes is calculated by using the max. possible reduction at each pass. Furthermore in part 
one the thickness range (wherein the final pass schedule can be located) for each pass is defined consid-
ering  also  the  min.  possible  reduction.  Here  a  function  was  included  which  iteratively  calculates  the 
maximal  or  minimal  reduction  for  a  certain  pass  considering  the  corresponding  flatness  related  roll 
force limits as well the roll force deviation calculated for the total reduction at this pass. 
Within the second major part the program searches for the thickness distribution which meets a defined 
optimization criterion in a best way. Therefor a new criterion was integrated with the target that the roll 
force at each pass shall be as close as possible to the best roll force. Since this cannot be arrived for all 
passes the algorithm is designed in such a way that the last passes do have priority. 

Test calculations to validate the new calculation approach. 
Several test calculations were carried out to validate the calculation approach and to evaluate the effect 
on performance. Subsequent some of the results are presented. 
Basic data for the calculations:  
Entry thickness 2.6 mm; Target thickness 0.4 mm; Coil weight 20t; Material stainless steel 1.4301 
The first calculation was carried out for a strip width of 1250 mm and a work roll diameter of 100 mm. 
The total rolling time for the resulting pass schedule is calculated with 68 min and the production rate 
with 17.6 t/hour.  
For the case the strip width is 1290 mm and a work roll with a diameter 90 mm is used the required 
number of passes can be reduced by 3 passes. With this the rolling time decreases down to 55 min and 
the production rate increases to 22.9 t/hour (= + 30% compared to the previous case). 

WP6: Validation of the system under industrial conditions. 

Aim of this task was the system test and validation under industrial conditions 

Online validation of the new program. 
The program was installed at the online system. At this also the data communication has been enlarged 
to have all current roll geometries available in front of a calculation. 
The  validation  starts  at  mill  1  by  rolling  several  strips  at  which  the  surface  requirements  were  low 
(beamless surface). It was possible to roll all strips without manual modifications. Typically one or two 
passes could be saved compared to the so far usual pass schedules. However, the available work rolls 
were relative large (diameter ≈ 100 mm) so that the reduction at the first passes was only slight higher 
than usual. 
The  validation  was  continued  with  strips  which  shall  have  high  gloss  surface  behind  annealing.  This 
time thinner work rolls were available (diameter ≈ 80 mm) so that higher reductions could be achieved. 
Especially at the first pass the reduction was clear higher as usual (31.7 %). During rolling this pass it 
could be observed that the roll force becomes much higher than calculated. (Calculated roll force was 

12 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
6750 kN; Measured roll force up to 10400 kN. Usual deviation between  measured and calculated roll 
force is about ± 5%).  
Due to the very high roll force the strip flatness at this pass was almost critical and both flatness actua-
tors need to be adjusted up to their mechanical limits. Furthermore, a visual surface inspection did show 
that the surface became very rough after rolling this pass. Even that the roll force was such higher at 
pass 1 the effect was not present at the subsequent passes. All remaining passes could be rolled without 
any problems. However, a later quantifying of the surface quality did show that this strip had clear pro-
nounced “heat / pressure stripes”. The rolling of one further strip with a similar high reduction did con-
firm the effect. Here at the first pass the roll force was about 35% higher than calculated and a rough 
surface was provoked. 
Consequently the maximum allowed reduction was decreased in a first step to 25%. The analysis of the 
first pass did show that beside the reduction also the rolling speed has an influence. While at a low roll-
ing speed the deviation between measured and calculated roll force was relative low (≈ 6%) at a rolling 
speed of about 390 m/min the deviation did increase up to 34% 
For  the  following  strips  the  maximum  allowed  reduction  was  stepwise  decreased  until  the  maximum 
roll force deviation surly falls below 5% and the influence of rolling speed does not exceed 10%. This 
could be arrived at a limitation of about 20% thickness reduction for the first pass. 
At  this  point it  shall  be  noted  that  such  a  strong  limitation  was  not  expected.  At  a  former  project  [1] 
several parameter were analysed in conjunction with the surface development when rolling a sequence 
of passes. One parameter has been the influence of different reductions on the surface properties. Here 
rolling tests with thickness reductions up to 32% at the first pass were carried out. The final conclusion 
of the rolling tests has been “that different pass reductions do not lead to notable differences in surface 
structure” (at the final strip thickness).  
The validation was continued now at both mills and with the required limitations to avoid the previous-
ly described effect but also to meet the surface requirements. The program worked stable and did pro-
vide improved pass schedules especially in cases outside the usual product range. Such cases are given 
e.g. for high-strength material, for thick and narrow strips and when large work rolls are used. Here in 
the past the thickness reductions often need to be decreased manual to achieve a suitable flatness. 

Online validation of the roll geometry optimization. 
The calculation was validated by comparing the calculation result for a new taper (at which taper length 
and taper inclination was changed) with the resulting distribution present after rolling several strips. 
The average deviation between calculation and resulting value was ≈ 5 mm. Since two parameters were 
changed  at  the  same  time  (length  and  inclination) and  in  relation  to  the  mechanical  adjustment  range 
(200 mm) the calculation result can be rated as quite good. 

Conclusion 

Within the framework of this project the intelligent use of existing process data was intended to replace 
the use of empirical values and to replace the trial and error approach to achieve optimal roll geome-
tries. To replace the empirical values the strip flatness and the pre-calculated probability for the occur-
rence of surface defects should be used at the pass schedule calculation.  
A physical flatness model was recompiled and fitted for use together with other software used. Verifica-
tions  against  mill  measurements  showed  that  the  model  response  to  differential  control  actions  was 
reasonably correct. 
To consider the strip flatness roll force limitations were determined within it is ensured that the flatness 
actuators will be able to achieve the target strip flatness. Example calculations do show that this calcula-
tion approach is reacting much more flexible on different rolling conditions like different strip width, 
different work roll diameter or different material. In case that no other limitations are required the cal-
culations also do demonstrate that a clear increased production rate could be achieved for certain strips. 
A clear further benefit of the calculation approach is the separation of limitations e.g. required to meet 
the  surface  quality  from  the  limitations  concerning  the  strip  flatness.  Through  this  it  becomes  much 
easier for the mill operator to identify the correct reduction limitations where necessary. 
The algorithm was validated successful at two mills. The program worked stable and did provide im-
proved pass schedules especially in cases outside the usual product range. Such cases are given e.g. for 
high-strength material, for thick and narrow strips and when large work rolls are used. 
However,  the  validation  did  also  show  that  strong  limitations  need  to  be  considered  to  avoid  surface 
defects and to achieve the, at this plant, required surface gloss. Thus in the major number of cases the 

13 
 
required number of passes (to roll one strip) could not be decreased so that the primarily expected in-
creased productivity could not be achieved. 
Two  types  of  frequently  occurred  surface  defects  were  analysed.  For  one,  named  “heat  and  pressure 
stripes” rules could be derived to minimize the frequency of defect. In case of the second defect, named 
“diagonal waves”, no clear and confirmed correlations were detected. 
To  replace  the  trial  and  error  approach  to  achieve  optimal  roll  geometries  a  program  was  developed 
with which the mill operator can determine the best suitable roll crown of the intermediate rolls (driven 
or idle rolls) as well to determine the ideal length and inclination of the taper rolls. The program period-
ically and automatically analysis the current as-is state which than can be reviewed with the help of a 
user interface. At this the program furthermore provides the possibility to predict how the change of any 
roll crown or the change of taper length or taper inclination will influence the future used range of the 
flatness  actuators.  Thus  the  mill  operator  has  a  very  helpful  tool  to  investigate  those  roll  geometries 
which fits best to his range of products. The calculation accuracy was successful verified by comparing 
the calculation results with measured data.  
In frame of this project one idea should be tested at which one upper and one lower taper roll should be 
replaced by CVC rolls to obtain an additional flatness actuator and thus to enlarge the flexibility of the 
mill.  The  rolling  test  carried  out  to  test  this  approach  did  show  that  this  does  provoke  an  asymmetry 
close to and direct at the strip edge which than provokes possible shearing tensions at this range. Fol-
lowing this the deformation stress at the strip edge can suddenly decrease causing heavy strip breaks. 
Due to the fact that such an asymmetry cannot be avoided when using one pair of CVC rolls the final 
conclusion must be that this approach is most possible not applicable. 

Exploitation and impact of the research results. 

The consideration of strip flatness for the pass schedule calculation has a clear potential to increase the 
production rate of a mill since this approach accounts the individual rolling conditions and strip parame-
ter  (strip  width,  thickness,  material  strength  etc.)  and  calculates  a  pass  schedule  which  surely  can  be 
rolled in frame of the mill potential. Since the strip flatness no longer has to be considered by simple 
reduction limitations it becomes much easier for the operator to identify other limitations e.g. to achieve 
the required surface quality. 
The  calculation  approach  is  integrated  into  the  BFI  pass  schedule  calculation  program  which  can  be 
used at 20-high mills; 6-high mills as well at 4-mills and for different types of metals. The required data 
for the program has to be transmitted via TCP/IP by defined telegrams.  
Basically the following data is necessary: 
‐  Strip dimension and material information 
‐  Process data like roll force, strip tension, position of all flatness actuators, rolling speed etc.. 
‐  Measured strip flatness 
‐  Roll geometry of all rolls in use. 
The BFI pass schedule calculation program can be used at each standard PC and can be integrated in 
existing Level 2 and Level 3 Systems. 
With the help of the developed roll geometry optimisation program the operator can easily review the 
current as-is state and can quick and easy determine the optimal roll geometry (roll crown of work roll, 
idle and driven rolls; taper length and taper inclination) under consideration of the product range. Im-
proved roll geometry can significantly increase the mill potential regarding strip flatness and in turn the 
roll force range at which the mill can be operated. Thus the program helps to avoid worse geometries 
which  can  lead  to  unnecessary  limitations.  The  program  is  also  integrated  into  the  BFI  ass  schedule 
program.  The  roll geometry  optimisation  basically  requires  the  same  data  as  the  program  part  for  the 
consideration of strip flatness. However, the so far developed program is designed for 20 high mills. A 
transfer to other type of mills is possible but requires some further investigations to account the differ-
ent behaviour of other flatness actuators (like roll bending) 
It is foreseen to publish the results in the technical journal “Stahl und Eisen” and to present it on one of 
the next steel conferences or workshops carried out from the “Stahl Zentrum”. 

14 
 
 
 
2 

Scientific and technical description of results 

2.1 

Introduction 

The  project  was  carried  out  at  a  20  high  mills  at  which  stainless  steel  strips  are  produced  in  a  width 
range between 1250 mm and 1550 mm with a typical entry thickness range between 4 mm and 2.5 mm. 
The strips are rolled in reversing manner in several passes down to a typical final thickness between 1 
mm and 0.4 mm. 

Pass 2

Pass 1

Pass 3

…… etc.

Figure 1:  Layout 20 high mill. 

The required number of passes and the pass reductions are given by a pass schedule calculation pro-
gram. 
The requirements on a pass schedule are: 
  Considering the Material properties and the Mill parameter (e.g. max. roll force; max. roll torque) 
  High productivity 
  Good flatness in all passes. 
  Achieve of the required surface quality. 
The general layout of a 20 high mill enables a high roll force and the use of small work rolls at the same 
time. This mill type typically has three flatness actuators. These are tilting (e.g. by tilting the mill 
house); a backup roll crown adjustment and axial shiftable taper rolls. 

Figure 2:  Layout of roll cluster and flatness actuators of a 20 high mill. 

The flatness actuators do have different types of flatness influence which enables the adjustment of a 
wide range of different flatness deviations. 

15 
 
 
 
Figure 3:  Example flatness influence of BUR crown and taper shifting. 

Beside the flatness actuators the roll force significantly influences the strip flatness. 

Figure 4:  Example flatness influence of Roll force. 

At this point the pass schedule becomes important. Following an example which explains the connec-
tion between pass schedule -> roll force -> strip flatness 
Let say the subsequent figure demonstrates a rolling situation which occurs during rolling. 

Figure 5:  Example rolling situation at a certain pass. 

The same rolling situation with a higher reduction would lead to a higher roll force what in turn would 
lead to longer strip edges. 

16 
 
 
 
 
Figure 6:  Example rolling situation more reduction. 

As long as the flatness actuators have enough remaining adjustment range the resulting flatness devia-
tion can be compensated. 

Figure 7:  Example flatness deviation compensated. 

By adjusting the backup roll crown and moving the taper about 20 mm towards the strip centre the flat-
ness deviation can be compensated completely. 
A limitation of increasing the reduction is given (at this example) at 21%. Here the strip flatness is still 
acceptable but the flatness actuators are at their mechanical limitations. 

17 
 
 
 
Figure 8:  Example rolling situation with max. possible reduction. 

Does any other rolling parameter change the maximal possible reduction can increase or decrease. Let 
say instead of work rolls with a diameter of 80 mm currently only work rolls with a diameter of 90 mm 
are available. This would lead to a higher roll force what in turn would lead to an inacceptable flatness 
deviation. Since the flatness actuators are already at their limitations the only possible solution can be to 
reduce the reduction in this case. The maximum possible reduction in this case would be 18.6 %. 

Figure 9:  Example max. possible reduction larger work rolls. 

Further parameters which influence the maximum possible reduction are: 
 
Strip width 
 
Strip tension 
  Material strength 
Since the interaction of all parameter in conjunction with the strip flatness is very complex the current 
approach to ensure proper flatness is the use of empirical determined reduction limitations. 
Beside  the  strip  flatness  also  the  quality  of  the  final  product  in  terms  of  surface  quality  (e.g.  gloss, 
roughness) needs to be considered. Also for this the current approach is the use of empirical determined 
reduction limitations. 
One major disadvantage of the current approach (the empirical determined reduction limitations) is the 
fact that one limitation needs to replace two independent values (strip flatness and surface quality) what 

18 
 
 
 
makes it very difficult to find an optimum. Furthermore the empirical values typically are not adjusted 
e.g. to changed products or changed roll geometries. 

Beside the pass schedule the geometry of the rolls have major influence on the productivity of a rolling 
stand. For example, at a 20-high mill the roll force range at which the mill can be operated (considering 
the  strip  flatness)  is  determined  by  the  crown  of  the  intermediate  rolls  and  the  geometry  of  the  taper 
rolls (taper length, taper inclination).  
From experience it can be stated that the suitable roll geometry for a specific rolling mill is always de-
termined empirically. The roll geometry suitable for rolling the range of products is “approximated” by 
trial  and  error  approach.  The  wider  the  range  of  products  is,  the  more  difficult  this  process  becomes. 
Whenever the range of products does change this procedure has to be done again. 

2.2  Objectives of the project 

Within the framework of this project the intelligent use of existing process data is to replace the use of 
empirical values and to replace the trial and error approach to achieve optimal roll geometries.  

The main objectives of the research project are summarized as follows: 
1.  An Auto-Adaptive Pass schedule calculation taking into consideration pre-calculated strip flatness 
and the pre-calculated probability for the occurrence of fish bones, heat scratches or pressure 
marks. 

2.  Development of a software programme helping the plant operator to optimize the roll geometry. 
3.  Testing of a new procedure suitable for using CVC technology in existing 20-high mills.  

Benefits: 
1.  Elimination of empirically determined limitations, e.g. maximum reduction per pass and maximum 

strip temperature. 
Improved roll geometry for the range of products rolled on the specific mill. 

2. 
3.  Reduction of the number of strips which due to shape or surface defects must be re-commissioned, 

4. 

downgraded or even scrapped. 
Increased flexibility of a 20-high mill with a view to the range of products and an increased mill 
performance by using the CVC technology in existing mills.  

5.  These measures are expected to improve the utilization rate of the mill and, as a result, increase 

productivity by at least 5%.  

2.3  Comparison of initially planned activities and work accomplished. 

In frame of this project one idea should be tested at which one upper and one lower taper roll should be 
replaced by CVC rolls to obtain an additional flatness actuator and thus to enlarge the flexibility of the 
mill.  The  rolling  test  carried  out  to  test  this  approach  did  show  that  this  does  provoke  an  asymmetry 
close to and direct at the strip edge which than provokes possible shearing tensions at this range. Fol-
lowing this the deformation stress at the strip edge can suddenly decrease causing heavy strip breaks. 
Due to the fact that such an asymmetry cannot be avoided when using one pair of CVC rolls there was a 
high  risk  of  strip  breaks  when  carrying  out  the  foreseen  CVC  rolling  tests.  Any  heavy  strip  break  in 
conjunction  with  a  longer  production  interrupt  is  very  cost  intensive.  Beside  this  further  cost  would 
have been necessary to prepare this rolling test e.g. the revamping of the axial shifting control. Consid-
ering all facts it was decided to stop the further investigations of the CVC approach. Since no other part 
of  the  project  was  depending  on  this  approach  the  failure  here  did  not  jeopardise  the  overall  project 
results or the project progress. 

The following table demonstrates the initially planned activities and work accomplished. 

19 
 
 
PROGRAMME BAR CHART

Work packages’ title

 Provision of the required process and computation data

 Roll geometry optimization

 Pre-calculation of strip flatness

WP 1
Task 1.1 Adaptation and expansion of the long-time database
Task 1.2 Establishing an online database for pass schedule calculations
Task 1.3 Establishing a database for the analysis of process dynamics
WP 2
Task 2.1 Determination of the influence functions of the flatness actuators
Task 2.2 Development of a simple flatness model
Task 2.3 Development of a physical flatness model 
WP 3
Task 3.1 Determining the approach to CVC technology use
Task 3.2 Development of a software programme for optimizing the roll geometry
WP 4
 Development of a predictive strip defect model
Task 4.1 Measurements of strip specimens
Task 4.2 Data-based analysis
Task 4.3 Development of theories about the occurrence of strip defects
Task 4.4 Development of the predictive strip defect model
Task 4.5 Validation of the model
WP 5
Task 5.1 Development of an algorithm for strip flatness
Task 5.2 Integration of the predictive strip defect model
Task 5.3 Development of automatic adaptation of the simple flatness model
Task 5.4 Development of a function for automatic analysis of dynamic process
WP 6
Task 6.1 Installation and commissioning
Task 6.2 Evaluation and Optimization of the system
WP 7
Task 7.1 Coordinating the work
Task 7.2 Reporting

 Integration of models into pass schedule calculation

 Validation of the system under industrial conditions

 Coordinating and reporting

I

X

X
X

X

1st year
II
III

IV I

2nd year
III

II

IV I

3rd year
III

II

4th 
II

IV I

X

X

X

X

X
X

X

X
X

X
X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X
X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

= Original Workplan
X = Work accomplished

X

X

X

X
X

X

X

X

X

X

X

X

X

20 
 
 
 
 
 
2.4  Description of activities and discussion 

2.4.1  Provision of the required process and computation data 

(Work Package 1) 

The  main  objective  of  this  work  package  was  the  provision  of  the  required  process  and  computation 
data. For this, databases were created which provide the required functionality and content. 

2.4.1.1  Adaptation and expansion of the long-time database. 
A  long-time  database  was  basically  already  in  place  at  TKL-NR.  The  database  contains  data  in  com-
pacted form. The database was expanded with the measured flatness, the positions of all flatness actua-
tors,  the  measured  coolant  amount  and  the  work  roll  diameter.  A  connection  to  the  roll  management 
system was established which contains all remaining relevant roll geometry data. A detailed description 
of the database content is given in Annex 1 (Figure 101, Figure 102, Table 16 and Table 17). 
The expansion of the database with computed values has been carried out in a slight different but more 
flexible  way compared  to  the  intended work  plan.  Considering the  target  (e.g. one  defined  surface  or 
form  defect)  the  measured  values  are  taken  form  the  long  term  database  and  the  expected  influence 
values are calculated. The resulting data is stored into a new database which than can be analysed. E.g. 
in case of the so called “fishbone” defect (for description refer to Work package 4) this defect has been 
identified as a form defect. Therefore some flatness indication values and values regarding the work roll 
geometry were calculated and included into a new table. The datasets are already organized in a way 
that the data analyse tool can use the data without any reorganisation required 

2.4.1.2  Establishing an online database for pass schedule calculations. 
For the strip flatness prediction a database was required which provides short retrieval times and covers 
all variants of the product range. 
In a first stage the required process data was defined and the layout of the database was created. The 
database does now contain all important strip parameter like thickness, width and material information. 
Furthermore all relevant process data like roll force, roll torque, speed, tension, measured flatness, the 
positions  of  all  flatness  actuators  etc.  are  included.  The  content  of  the  database  is  similar  to  the  long 
term database. 
To ensure short retrieval times and at the same time to cover all variants of the product range an algo-
rithm was developed which analyses the database and only deletes those older datasets, which are high 
frequently available. Thus the number of datasets can be limited to a relative low level which allows a 
quick access without loosening the important information of seldom type of datasets. A screenshot of 
the program to analyse the database is given in Annex 1 (Figure 103 and Figure 104). 

2.4.1.3  Establishing a database for the analysis of process dynamics. 
This database was intended to be used for the analysis of the dynamics of important process parameters 
such as strip thickness, rolling force and strip flatness. Furthermore this database is useful to investigate 
the influencing effects of the flatness actuators determined by the rolling tests. 
Similar to task 2.4.1.1 in a first stage the required process data was defined and the database created. 
Following this a data acquisition was established via network communication. The database does now 
contain all relevant process data for one week in one second steps. If required the time frame can be 
enlarged  easily.  Compared  to  the  other  databases  this  database  is  stored  in  a  binary  format  which  is 
easier to use within the programming. Some examples of the use of this data can be seen in Figure 10 
and Figure 22 in chapter 0. 

21 
 
 
 
2.4.2  Pre-calculation of strip flatness 

(Work Package 2) 

Aim of this task was the development of two different types of flatness models which should be used in 
the subsequent stages. One simplified model with short computation time which will be used for the 
online pass schedule calculation. Secondly a more accurate physical based model for optimizing the roll 
geometry and adapting the computed parameters of the simple flatness model. 

2.4.2.1  Determination of the factors influencing flatness actuation. 
The major influencing factors of the flatness are the flatness actuators itself, the roll geometry of work 
roll  and  intermediate  rolls,  the  roll  force  and  the  strip  thickness.  To  investigate  the  influence  several 
rolling tests were carried out at two 20 high rolling mills (one mill of type “Sundwig”, the other of type 
“Sendzimir”). 
The first rolling tests were carried out for the flatness actuators backup roll crown adjustment and shift-
ing of the tapered rolls. 
To analyse the tests a program was developed with which the measured data from the rolling tests can 
be fetched from the dynamic database and visualized. The blocks of measured data before and after the 
manual adjustment can be selected and the resulting flatness difference can be viewed. The following 
figures demonstrate an example in case of the backup roll crown adjustment test. 

Figure 10:  Selecting the data where a manual adjustment was done. 

Figure 11:  Measured  flatness  before  and  after  the  adjustment  and  the  resulting  flatness  differ-

ence. 

23 
 
 
 
Since the tests were carried out at different passes the thickness influence could be analysed, too. The 
following tables and figures demonstrate the rolling parameter specifications and the test results. 

Backup roll crown adjustment: 

Mill 1 (Type Sundwig)
Maximum strip width
Strip width 1333 mm
Material
Entry strip thickness
Pass #

X 5 CrNi 189

Entry 
thickness
1,71
1,44
1,05
0,79
0,62

4
5
7
9
11

1350 mm

Exit 
thickness
1,45
1,23
0,90
0,69
0,55

3 mm

roll force 
[kN]

7782
7626
7126
6471
5896

Mill 2 (Type Sendzimir)
Maximum strip width
Strip width 1295 mm
Material
Entry strip thickness
Pass #

X 5 CrNi 189

Entry 
thickness
2,06
1,53
1,09
0,98

2
4
7
8

1550 mm

2,54 mm

Exit 
thickness
1,74
1,36
0,98
0,88

roll force 
[kN]

7223
6792
6107
6150

Table 1:  Rolling parameters of the backup roll crown tests. 

Flatness difference per unit roll crown adjustment

15

10

5

0

-5

-10

pass 4

pass 5

pass 7

pass 9

pass 11

]
2
^
m
m
N

/

[

i

n
o
i
t
a
v
e
d
n
o
s
n
e
T

i

-700

-500

-300

-100

100

300

500

700

Width [mm]

Figure 12:  Flatness influence of the roll crown adjustment Mill 1. 

Flatness difference per unit crown adjustment movement

pass 2
pass 4
pass 7
pass 8

2,0

1,5

1,0

0,5

0,0

-0,5

-1,0

]
2
^
m
m
N

/

[

n
o

i
t

i

a
v
e
d
n
o
s
n
e
T

i

-700

-500

-300

-100

100

300

500

700

Width [mm]

Figure 13:  Flatness influence of the roll crown adjustment Mill 2. 

To compare the results between the mills it needs to be considered the actuator range of the Sundwig 
mill is ± 17,5 while the actuator range of the Sendzimir mill is given in % (with a total range of adjust-
ment of ± 100 %) 

24 
 
 
 
 
 
 
 
 
Beside this the results demonstrate clearly that the flatness influence form of the roll crown adjustment 
is almost the same independent of the thickness and is pretty similar for both mill types. Furthermore it 
can  be  seen  that  flatness  influence  factor  (the  amount  of  flatness  difference  per  unit  adjustment)  in-
creases for thinner material. 

Taper roll shifting: 

X 5 CrNi 189

Mill 1 (Type Sundwig)
Maximum strip width
Strip width
1274 mm
Taper length 120 mm
Material
Entry strip thickness
Entry 
Pass #
thickness
2,00
1,38
1,00

2
4
6

1269 mm

Mill 1 (Type Sundwig)
Maximum strip width
Strip width
Taper length 90 mm
Material
Entry strip thickness
Entry 
Pass #
thickness
1,44
1,05

4
6

X 5 CrNi 189

X 5 CrNi 189

Mill 2 (Type Sendzimir)
Maximum strip width
Strip width
1290 mm
Taper length 320 mm
Material
Entry strip thickness
Entry 
Pass #
thickness
1,84
1,41
1,10

3
5
7

1550 mm

2,54 mm

Exit 
thickness
1,60
1,24
0,98

roll force 
[kN]

7556
7428
7372

1350 mm

2,44 mm

Exit 
thickness
1,66
1,17
0,85

roll force 
[kN]

6867
7220
7000

1350 mm

2,5 mm

Exit 
thickness
1,24
0,90

roll force 
[kN]

6404
6072

Table 2:  Rolling parameters of the taper roll shifting tests. 

Subsequent the different taper forms of the rolling test are demonstrated. 

Taper forms of rolling tests

]

m
m

[
e
c
n
e
r
e
f
f
i
d
r
e
t
e
m
a
D

i

0

-0,1

-0,2

-0,3

-0,4

-0,5

-0,6

-0,7

Taper 120 mill 1

Taper 90 mill 1

Taper 320 mill 2

0

50

100

150

200

250

300

350

Taper length [mm]

Figure 14:  Taper forms used at the rolling tests. 

The much longer tapered part at mill 2 is required because the dimension of mill 2 is related to a max. 
strip width of 1550 mm. When rolling narrow strips (like here) the taper length needs to be accordingly 
enlarged. 
The  subsequent  two  figures  do  show  the  individual  test  results  for  taper  120  (mill  1)  and  taper  320 
(mill 2). 

25 
 
 
 
 
 
Flatness difference per millimetre taper adjustment

2,0

1,0

0,0

-1,0

-2,0

-3,0

-4,0

-5,0

pass 2

pass 4

pass 6

]
2
^
m
m
N

/

[

i

n
o
i
t
a
v
e
d
n
o
s
n
e
T

i

-700

-500

-300

-100

100

300

500

700

Width [mm]

Figure 15:  Flatness influence taper 120 (mill 1). 

Flatness difference per millimetre taper adjustment

]
2
^
m
m
N

/

[

n
o

i
t

i

a
v
e
d
n
o
s
n
e
T

i

2,0

1,0

0,0

-1,0

-2,0

-3,0

-4,0

-5,0

pass 3

pass 5

pass 7

-700

-500

-300

-100

100

300

500

700

Width [mm]

Figure 16:  Flatness influence taper 320 (mill 2). 

The results confirm that the flatness influence form is very similar independent of the thickness. 
The next picture demonstrates the result whereby the individual results were compressed by recalculat-
ing the flatness influence to a strip thickness of 1 mm. (This was done with the help of the investigated 
formula described later in this chapter.) 

Flatness Influence for different Taper Forms

Taper 120 Mill 1
Taper 90 Mill 1
Taper 320 Mill 2

2
1
0
‐1
‐2
‐3
‐4
‐5
‐6
‐7

]
2
^
m
m
/
N

[
n
o
i
t
a
i
v
e
d
n
o
n
s
e
T

i

‐700

‐500

‐300

‐100

100

300

500

700

Strip Width [mm]

Figure 17:  Flatness influence of different taper rolls at 1 mm strip thickness. 

26 
 
 
 
 
 
 
 
 
 
 
 
As expected the taper with the highest taper inclination (taper 90) led to the highest flatness influence 
and taper 320 to the lowest influence (for 1 mm taper shifting). 
On the other hand the figure does show that the influence form seems to be very similar. This can be 
confirmed when calculating the linear correlation. 

Correlation to Taper 120 Mill 1

Taper 90 Mill 1
Factor:
Taper 320 Mill 2
Factor:

0,750

1,476

Correlation Flatness Influence Form:

0,995

Correlation Flatness Influence Form:

0,969

This result led to some further investigations. Instead to calculate the flatness influence for 1 mm taper 
roll shifting the flatness influence was calculated to the resulting diameter difference at the strip edge 
which results from the taper shifting. The subsequent sketch shall explain this. 

Diameter difference at strip edge 30 µm

Taper roll

Work roll

Strip

Taper roll
30 mm shifted

Diameter difference at strip edge 100 µm

Figure 18:  Sketch taper roll shifting and diameter difference. 

Taper length which covers the strip

The  following  figure  shows  the  flatness  influence  at  1  mm  strip  thickness  normalized  to  a  diameter 
difference of 100 µm at strip edge. 

Flatness influence in dependence of 
the diameter difference at strip edge

]
2
^
m
m
/
N

[
n
o
i
t
a
i
v
e
d
n
o
n
s
e
T

i

e
c
n
e
r
e
f
f
i
d
r
e
t
e
m
a
d
m
µ
0
0
1
r
e
p

i

40

20

0

‐20

‐40

‐60

‐80

‐100

‐120

Taper 120 Mill 1
Taper 90 Mill 1
Taper 320 Mill 2
Mean value

‐700

‐500

‐300

‐100

100

300

500

700

Strip Width [mm]

Figure 19:  Flatness influence in dependence of the taper diameter difference at strip edge. 

Compared to the former result (demonstrated in Figure 17) the flatness influence is almost the same in 
all cases. This can be explained by the fact that the form of the different taper rolls (within the range 
covering the strip) correlates with almost 100%. 

27 
 
 
 
 
 
 
 
 
 
 
Taper forms within the range typically covering the strip

0

-0,1

-0,2

-0,3

-0,4

Taper 120 mill 1

Taper 90 mill 1

Taper 320 mill 2

]

m
m

[
e
c
n
e
r
e
f
f
i
d
r
e
t
e
m
a
i
D

0

10

20

30

40

50

60

70

Taper length [mm]

Figure 20:  Taper forms within the range typically covering the strip. 

The investigations can be summarized as follows.  
‐ 

If  different  taper  rolls  basically  differs  only  by  the  inclination  the  flatness  influence  mainly  de-
pends on the provoked diameter difference at the strip edge (caused by a taper shifting).  
If the flatness influence of one taper roll is known the flatness influence for a different taper incli-
nation can be extrapolated (within a certain range) with adequate accuracy. 

‐ 

(Within the range covering the strip the rolling tests here did cover a factor 7 between the smallest and 
the largest taper inclination.) 

Influence of strip thickness on flatness: 

As demonstrated with the individual rolling test the flatness influence increases when the strip becomes 
thinner.  To  investigate  the  influence  of  strip  thickness  on  flatness  the  linear  correlation  between  one 
individual  pass  and  the  pass  where  the  exit  thickness  was  close  to  1  mm  was  calculated.  This  results 
into the subsequent table. 

Mill 1 backup roll crown adjustement

Mill 1 taper shifting adjustment

exit thickness
linear correlation

1,45
0,774

1,23
0,826

0,90
1,000

Mill 2 backup roll crown adjustement

exit thickness
linear correlation
Table 3:  Linear correlation between the passes. 

0,98
1,000

1,74
0,577

1,36
0,859

0,69
1,084

0,88
1,181

0,55
1,197

1,66
0,759

1,17
0,919

0,85
1,000

Mill 2 taper shifting adjustment

1,60
0,740

1,24
0,923

0,98
1,000

Using a known formula the coefficients of this formula could be adapted in such a way that the meas-
ured linear correlations and the calculated correlations match very well (see Figure 21).  
The used formula is: Correlation = (c0+c1) / (c0+c1* exit thickness) 
c0 = coefficient 0 = 0.196 
c1 = coefficient 1 = 0.212 

28 
 
 
 
 
 
Measured
Calculated

l

n
o
i
t
a
e
r
r
o
c

r
a
e
n

i
l

1,8

1,6

1,4

1,2

1,0

0,8

0,6

0,4

0,2

0,0

0

0,5

1

1,5

2

2,5

Strip thickness [mm]

Figure 21:  Linear correlation in dependence of the strip thickness. 

Influence Roll force on flatness: 

To investigate the flatness influence of the roll force primarily it was foreseen to carry out rolling tests. 
At this a change in the rolling force should be provoked by varying the run-out thickness of the strip. In 
practice  this  procedure  was  not  applicable.  The  maximal  allowable  thickness  change  was  limited  in 
such a way that the resulting roll force change was too low.  
Because of this another way was used to investigate the roll force influence. Already in the past it has 
been  realised  that  in  later  passes  (pass  number  >  5)  there  is  a  large  deviation  of  the  roll  force  which 
depends on the rolling speed. The roll force difference here can be more than 20%. (As an example see 
Figure 22).  

Figure 22:  Roll force variation during the last pass (Pass# 10). 

With  the  help  of  a  newly  created  program  those  cases  could  be  selected  from  the  dynamic  database. 
Since not only the roll force does change between two selected points the adjustments of the flatness 
actuators also need to be considered. This was done by recalculating the flatness of the second point to 
the  actuator  position  of  the  first  point.  The  resulting  flatness  difference  between  the  points  does  now 
mainly correlate with the pure roll force flatness influence. Some inaccuracy does remain by this proce-
dure because a possible change of the thickness profile cannot be considered. However, since the inves-

29 
 
 
 
 
tigation was done for a larger amount of rolling cases the final result can be estimated as reliable. Figure 
23 demonstrates one case. 

Figure 23:  Screenshot of the program to investigate the roll force influence on flatness. 

The investigation was carried out for mill 1 and mill 2 for a strip width of approximately 1250 mm re-
spectively 1290 mm. A little bit surprisingly is the fact that the influence form at both mills is almost 
the same (the correlation factor between both curves is 0,997). 

Roll force influence at mill 1 and 2

Mill 1 (Width 1250 mm; Mill type Sundwig)

Mill 2 (Width 1290 mm; Mill type Sendzimir)

e
c
r
o
f

l
l

o
r
N
k
r
e
p
n
o
i
t
a

i
v
e
d
n
o
i
s
n
e
T

]

N
k
/
2
^
m
m
/
N

[
e
c
n
e
r
e
f
f
i
d

0,04

0,02

0,00

‐0,02

‐0,04

‐0,06

‐0,08

‐0,10

0

10

20

30

40

50

60

Figure 24:  Roll force influence on flatness at mill 1 and mill 2. 

Crown of intermediate rolls (idle roll): 

To investigate the flatness influence of the change of a roll crown two tests were carried out at which 
one idle roll was replaced at two certain passes. Each replacement was done within the pass so that the 
resulting flatness change could be clear detected.  
For the first test the lower idle roll was replaced at pass 5 (strip thickness 1.75 mm) by a roll with a 0.2 
mm greater roll crown (related to the diameter) and at pass 6 (thickness 1.53 mm) again replaced with 
the origin. In Figure 25 the resulting flatness change is presented. At this the result is already normal-

30 
 
 
 
 
 
 
 
 
 
 
ized to 1 mm roll crown change and to 1 mm strip thickness. For comparison reasons the flatness influ-
ence of the backup roll crown is included, too. It can be clear seen that the form of both functions are 
almost equal. The result is helpful since it does show that the used range of the flatness actuator “back-
up roll crown” basically can be optimized by an adjustment of the roll crown of the second intermediate 
rolls (idle roll or driven rolls). A second test at the other mill did confirm the result. 

e
g
n
a
h
c
n
w
o
r
c
m
m

r
e
p
n
o
i
t
a

i
v
e
d
n
o
i
s
n
e
T

200

150

100

50

0

‐50

]
2
^
m
m
/
N

[

‐100

‐150

‐200

Flatness influence by one idle crown

Flatness influence idle roll

 Flatness influence backup roll crown

‐800

‐600

‐400

‐200
200
0
Strip width [mm]

400

600

800

n
w
o
r
c

l
l

o
r
p
u
k
c
a
b
e
h
t

f
o
e
c
n
e
u
l
f
n

i

s
s
e
n
t
a
l
F

t
n
e
m
e
t
s
u
d
a

j

0,00

‐0,50

‐1,00

‐1,50

‐2,00

‐2,50

Figure 25:  Flatness influence roll crown change versus backup roll crown. 

2.4.2.2  Development of a simple flatness model. 
The so far achieved results have been integrated into a simple function with which the individual flat-
ness effects of the flatness actuators and the roll force can be calculated. Ingoing parameter of the func-
tion are the strip width and thickness, the actuator name (respectively roll force) and the actuator ad-
justment  (respectively  roll  force  difference).  The  function  selects  the  influence  function  based  on  the 
actuator name and the strip width, calculates the linear correlation (= factor) based on the thickness and 
finally multiplies the influence function with the factor and the actuator adjustment. 

Simple flatness model

width

actuator name

thickness

actuator  adjustment

selecting
influence function

calculating factor

multiply

flatness change

Figure 26:  Layout of the simple flatness model. 

In several cases it is necessary to calculate the required actuator adjustment(s) or a required roll force 
difference for a given (or wanted) flatness change. For this an inverse flatness model was created. The 
additional  ingoing  parameters  of  this  function  are  the  actuator  range  limits  and  the  wanted  flatness 
change. The result of the function is the required roll force difference or actuator adjustment. The func-
tion is also able to calculate the required adjustments for more than one actuator at the same time. The 
layout of the function is given in the next figure. 

31 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
selecting
influence function

calculating factor

Inverse flatness model

least 
square 
coefficient

+

width

actuator name

thickness

flatness change

actuator position

actuator range limits

limit 
adjustment

actuator  adjustment

Iterative inverse flatness model

actuator names

actuator positions

actuator range limits

Inverse flatness 
model

yes

actuator  adjustments

actuator  
adjustments 
< 1%

no

Figure 27:  Layout of the inverse flatness model. 

Of course it would be possible to calculate the least square coefficients at once for all actuator instead 
using an iterative solution. But a calculation in one step would lead to the fact that the individual ad-
justment limitations of the flatness actuators cannot be considered. 

2.4.2.3  Development of a physical flatness model. 
The flatness of the rolled strip is a result of the match between the transverse thickness profile of the 
strip  and  the  by  load  deformed  roll  gap  between  the  rolling  mill  work  rolls.  If  these  profiles  do  not 
match, this will result in a variation of the strip thickness reduction over the strip width. A variation in 
the strip reduction in turn will result in a variation of the strip elongation over the width so that some 
parts of the strip will become longer than others. Rolling is thus an interaction of elastic deformation of 
the mill and plastic deformation of the strip and the result of one has influence on the other.  
Modelling of flatness in cold rolling can be done by a physically correct description of the phenomena 
occurring in the rolling mill during rolling. The literature contains a huge number of references to mod-
els of the rolling process. A model for calculation of flatness in strip rolling can be described as in Fig-
ure 28. As described in the figure a flatness model can be divided into two interacting major parts, the 
mill elastic deformation model (MEDM) and the strip plastic deformation model (SPDM). Those mod-
els interact so that the MEDM results determine the space where the strip deformation takes place and 
the SPDM calculates the forces acting on the mill as a result of the strip deformation. The full model 
has to find the balance between the deformed geometry of the roll gap and the forces generated by the 
strip deformation. 
The theory of continuum mechanics that can be applied to describe these deformations is so complex 
that explicit equations to solve the full rolling case are not available. Some simplifications and approx-
imations have to be done.  

32 
 
 
Figure 28:  Integrated model for flatness prediction. 

Closest to achieve a physically correct description of the reality is the MEDMs. Elasticity and elastic 
deformations of the type of bodies included in a rolling mill are well explored for such load cases that 
occur and deformations can be calculated by explicit formulas. Nevertheless the calculations have to be 
discretized and the deformation is calculated at a number of discrete positions across the mill. Interac-
tions between the discrete points are solved by iteration. Several simple and fast models are reported in 
the literature.  
The plastic deformation of the rolled material handled by the SPDM is more complex to describe since 
relations between forces and deformations are nonlinear and irreversible. By simplifying assumptions it 
has  been  possible  to  describe  the  deformation  process  with  a  reasonable  base  in  the  physics.  One  of 
these is the assumption of plane strain where strains in the width direction are neglected. Since the de-
formation conditions vary over the strip width the equations have to be solved at discrete positions over 
the strip width. Reality has shown that the plane strain assumption is too strict and that strains in the 
width direction occur especially close to the strip edges. The SPDM results have to be modified with 
regard to these strains and their distribution over the strip width.  
Physical flatness modelling with simplifying assumptions. 
The program CLUSTER based on the work by Gunawardene and further developed at Swerea MEFOS 
is based on the method described above. [2, 3] CLUSTER calculates the elastic deformation of the roll 
stack  caused  by  the  forces  generated  by  the  strip  deformation.  It  is  a  static  model  that  is  physically 
based using the beam bending theory and it calculates the elastic deformation of the rolls in the rolling 
mill using the contact forces between the strip and the work rolls during rolling. The model is divided 
into segments in the width direction where data are assumed to be constant within each segment. Calcu-
lations are done for all segments. The elastic deformation gives the roll gap profile which is assumed to 
be the same as the outgoing strip thickness profile. CLUSTER also contains a simple model for calcula-
tion  of  rolling  pressure  distribution  between  rolls  and  strip  and  strip  tension  distribution.[4,  5,  6,  7]. 
From those the strip flatness is calculated. The calculations in CLUSTER follow the flow chart in Fig-
ure 29. 

33 
 
 
Figure 29:  Calculation procedure in CLUSTER. 

One difficulty for calculating the absolute flatness is given by the fact that the thickness profile of the 
strip is unknown (or not known with the required accuracy). However the absolute flatness was of sec-
ondary  importance  in  frame  of  this  project.  The  purpose  here  was  to  calculate  the  flatness  response 
caused by an adjustment of any flatness actuator or caused by other changed rolling parameters (like the 
roll crowns). Thus an algorithm was developed which enables the calculation of the flatness response 
without the knowledge of the strip thickness profile. 
In the first step the aim is to find the incoming strip thickness profile that gives a flat strip after rolling. 
This is necessary because the strip thickness profile is seldom known with required accuracy for flat-
ness calculations. The DLL is called with the current rolling parameters and a reference actuator setting 
and an assumed input strip thickness profile. The input strip thickness profile is then iteratively changed 
for each calculation until the calculated strip shape is regarded as flat. The iteration step size and the 
flatness limit are inputs to the model and can be set by the user. The first step has converged when the 
calculated strip flatness for all the segments across the strip width is below the strip flatness limit. Then 
the incoming strip thickness profile for the reference case has been found. 
In the second step the flatness response of a change in rolling parameters or actuator settings is calculat-
ed in the DLL. One or more of the input parameters are modified and the strip flatness for this new set-
ting is calculated. All other input data from the reference case are used as input data including the input 
strip thickness profile that was calculated in step one. The difference in calculated strip flatness between 

34 
 
 
the reference case in step one and the result from the new calculation in step two is the flatness response 
from the parameter and/or actuator change. 
The parameters or actuators that are possible to change between the first and the second step are 
shifting of the upper and lower taper rolls (separate data for upper and lower rolls) 
rolling force 

 
 
  entry and exit strip tension 
  position of the bearings in the backup rolls 
  crown of the rolls (mainly used for the driven and the non-driven intermediate rolls) 

The model was successful tested with the rolling test data carried out in frame of the determination of 
the  factors  influencing  flatness  (see  chapter  2.4.2.1).  Subsequent  some  of  the  calculation  results  are 
shown for taper roll shifting. 

Shift influence on stress distribution in pass 2

Shift influence on stress distribution in pass 4

Calculated

Measured

Calculated

Measured

)
a
P
M

(

s
s
e
r
t

S

-800

-600

-400

-200

140

120

100

80

60

40

20

0

-20

-40

0

200

400

600

800

Distance from strip centre (mm)

)
a
P
M

(

s
s
e
r
t

S

)
a
P
M

(

s
s
e
r
t

S

250

200

150

100

50

0

-800

-600

-400

-200

0

200

400

600

800

-50

Distance from strip centre (mm)

Shift influence on stress distribution in pass 6

Calculated

Measured

0

200

400

600

800

-800

-600

-400

-200

30

20

10

0

-10

-20

-30

-40

-50

-60

-70

-80

Distance from strip centre (mm)

Figure 30:  Strip tension distribution change as response to taper roll shift in pass 2, 4 and 6. 

To be able to call CLUSTER from another program (in this case LabView), the model was compiled as 
a DLL (dynamic-link library) where all input and output data are transferred to the DLL as parameters 
in  the  call.  The  input  data  are  all  data  needed  for  the  calculation  including  mill  data,  strip  data,  pass 
schedule data and iteration data. Iteration accuracy and convergence parameters are examples of itera-
tion data. Output data is the distribution of flatness change over the strip width, which is specified as a 
table with the position across the strip width and the flatness change at each of these positions. 
Some investigations were carried out to determine the effect of parameters which couldn’t be indicated 
by rolling tests. 
One parameter is the effect of a different work roll diameter on the flatness respond for a taper adjust-
ment (Figure 32). As reference case the rolling test of pass 6 was used. The 1st IMRs were tapered ac-
cording to the next figure. 

35 
 
 
 
 
 
 
]

m
m

[
e
c
n
e
r
e
f
f
i
d
r
e
t
e
m
a
i
D

0

-0,1

-0,2

-0,3

-0,4

-0,5

-0,6

-0,7

1300

1400

1500
Roll body length [mm]

1600

1700

Figure 31:  Shape of the taper on the 1st IMRs. 

Flatness difference taper adjustment

]
2
^
m
m
N

/

[

i

n
o
i
t
a
v
e
d
n
o
s
n
e
T

i

50

0

-50

-100

-150

-200

Work roll diameter 100 mm
Work roll diameter 80 mm
Work roll diameter 60 mm
Work roll diameter 140 mm

-700

-350

0

350

700

Width [mm]

Figure 32:  Influence of work roll diameter on flatness respond of taper adjustment. 

It can be noted that moving the taper rolls has a much larger effect on the strip flatness when the work 
roll radius is smaller. However, within the frame the mill is operating (Diameter 80 mm to 100 mm) the 
effect is relative low so that the rolling test results can be used for the further investigations. 
Regarding the BUR crown all calculations carried out did show that a different work roll diameter does 
not change the flatness respond of this actuator. 
One further parameter was the influence of the taper location which cannot be tested by rolling test due 
to the fact that large adjustments would lead to strip breaks. 

Flatness difference taper adjustment

]

2
^
m
m
N

/

[

i

n
o
i
t
a
v
e
d
n
o
s
n
e
T

i

50

25

0

-25

-50

-75

-100

-125

-150

adjustment 40 mm to 80 mm

adjustment 120 mm to 160 mm

adjustment 1 (simple model)

adjustment 2 (simple model)

-700

-350

0

350

700

Width [mm]

Figure 33:  Influence of taper location on flatness respond of taper adjustment. 

A positive taper adjustment does mean that the taper is moved towards the strip edge. Thus the “active” 
taper length (the tapered part which is covered by the strip) becomes smaller (case adjustment 120 mm 

36 
 
   
 
 
 
 
 
 
 
 
to  160 mm).  Within  the  first  50  mm  of  the  tapered  part  the  taper  inclination  is  relative  small  which 
causes  the  clear  smaller  flatness  influence.  A  similar  result  can  be  achieved  with  the  simple  flatness 
model  when  using  the  taper  influence  function  in  dependence  on the  diameter  difference  (description 
see page 27 Figure 19). 
A further investigation was carried out to analyse the effect of changed roll crowns. The calculations 
did  confirm  that  the  flatness  influence  form  is  very  similar  compared  to  the  BUR  crown  adjustment. 
The subsequent figure demonstrates some of the calculation results.  

]
2
^
m
m
N

/

[

i

n
o
i
t
a
v
e
d
n
o
s
n
e
T

i

Flatness difference by changed roll crown

Idle roll + 50 µm
Idle roll + 100 µm
Driven roll + 50 µm
Driven roll + 100 µm

175

150

125

100

75

50

25

0

-25

-50

-75

-700

-350

0

350

700

Width [mm]

Figure 34:  Flatness influence of different roll crowns. 

With  the  help  of  the  program  furthermore  the  BUR  crown  adjustment  can  be  calculated  which  is  re-
quired to compensate any roll crown change of the intermediate rolls. The following table exemplary 
shows the values for the previously demonstrated calculation results. 

Roll crown change

BUR crown adjustment required
to compensate the crown change
‐15%
‐28%
‐43%
‐85%

Idle roll + 50 µm
Idle roll + 100 µm
Driven roll + 50 µm
Driven roll + 100 µm
Table 4:  BUR crown adjustment required to compensate crown change. 

This calculation is useful in frame of the roll geometry optimisation to determine the estimated adjust-
ment of the BUR crown caused by changed roll crowns. 
Physical flatness modelling using advanced calculation methods. 
The  Finite  Element  Method  (FEM)  is  the  modelling  method  that  comes  closest  to  a  perfect  physical 
representation of the rolling process in today’s knowledge. The full three-dimensional geometry of the 
mill  and  the  strip  is  divided  into  finite  elements.  Within  each  element  the  variation  of  stresses  and 
strains are approximated by low order polynomial but the total system is guarded by the fundamental 
equations describing the behaviour of the included components. To limit the errors from the polynomial 
approximations the size of the finite elements and the time steps of the calculations have to be small.  
A full FEM model of a cluster mill would contain too many elements to be able to handle with the lim-
ited computer resources available at research institutions in this research field. The calculations would 
take too long time to be useful. FEM can be used in few cases to verify simplified models.  
Some efforts are spent on calculations to study the plastic deformation of the strip. 
The purpose is to investigate the flatness result and the material flow that occurs in the strip when it is 
rolled.  The  analysis  has  started  with  making  a  strip  rolling  model  in  the  finite  element  program  LS-
DYNA. During the development a small model was created so that the calculation time when running 
simulations  was  rather  short.  Symmetry  conditions  are  assumed  in  the  width  and  the  thickness  direc-
tions so that only one quarter of the roll and the strip had to be modelled. This is done to reduce the 
calculation time. The strip width is 1000 mm and the strip thickness 1.5 mm. 

37 
 
 
 
 
 
Several different parameters were changed and tested to get a model where the results were accurate. 
The simulation results seem reasonable. In Figure 35 the strip is seen from above, the rolling direction 
is to the right and the middle part of the strip is at the bottom. The figure to the left shows the displace-
ment in the width direction of the strip and here the whole strip has just been rolled. The large red are at 
the right is an end effect at the front end of the strip.  
The left figure shows that there is a displacement in the width direction over the whole strip width for 
the steady state part, but near the strip edge, at the top of the figure the displacements become larger. 
The  displacement  curves  are  equidistant  over  most  of  the  strip  width  but  near  the  edge  the  displace-
ments become larger. The total strip width change in this case is about 1.8 mm.  
The figure to the right shows the longitudinal stress and here the strip is still under rolling. The position 
of the roll can be seen as a vertical stripe. The stresses are low for the main part of the strip but at the 
edge there is sharp increase. 

Figure 35:  FEM simulation of strip rolling with lateral flow to the left (legend in mm) and longi-

tudinal stress to the right (legend in MPa). 

If the calculation is representative for real rolling the assumption of plane strain mentioned above has to 
be modified. Strains in the width direction occur to some extent over the whole strip width but they are 
larger close to the strip edge.  
When plane strain is assumed all thickness strain is converted to longitudinal strain. A variation of the 
thickness strain (reduction) over the width will in this case lead to a resembling variation in the longitu-
dinal strain over the width. Those parts that are reduced more than mean reduction become longer and 
parts with less reduction than mean become shorter and this will result in inner stresses or bad flatness.  
The FEM calculation above does show that plane strain is a too rigid assumption and that we have to 
assume that only a fraction of the differential thickness strain is resulting in a variation of the differen-
tial longitudinal strain. 
The size of this fraction has been named ξ (ksi) at Swerea MEFOS. By experiments it has been found 
that ξ  is related to the geometry of the actual rolling pass. The fraction becomes lower if the strip is 
thick and narrow and higher for wide and thin strips. An increased roll diameter gives a smaller value of 
ξ. Previous experiments and the FEM calculations described above have also shown that the value of ξ 
also varies over the strip width so that it becomes smaller towards the strip edge. This can be explained 
by the fact that the friction between the strip and the roll prohibits strain in the width direction at the 
centre part of the strip. Closer to the edge the strip material is more free to flow in the width direction.  
Using this experience flatness is calculated according to the following equation: 


 

y
)(

y
)(

RC



 
y

where:  

y 
λ 
ξ 
ΔRC 
The parameter ξ is found in the literature [7]. 

transverse position 
flatness 
flatness correction parameter 
change in relative profile 





1



a
1

1



a

2

2




where 



3
HD

2
2
DW


3
2

0

and:  

a1,a2 
D 
H 
W 

constants 
work roll diameter 
strip exit thickness 
strip width 

38 
 
 
 
 
  
 
D0 

constant reference diameter 

The parameter is initially used and fitted for hot rolling of plate and strip. For such applications it has 
been widely used in modelling at Swerea MEFOS with reasonable results. It is also used for cold rolling 
applications in the lack of better theories. Some efforts are spent to verify or improve the description 
with the help of FEM calculations but computer limitations have caused limited success in these efforts. 
For  the  cases  reported  below  the  formula  gives  ξ-values  close  to  1.  Comparisons  with  measurements 
however indicate that 0.1 would be a more suitable value. This may be caused by differences in friction 
or other influences. 
In CLUSTER strains in the width direction is regarded by modification of the differential longitudinal 
strain over the width using the parameter ξ. In the original version of CLUSTER ξ has been regarded to 
be constant over the whole strip width. From calculations with other programs and also indicated in the 
literature the experience has been that it is reasonable to assume that ξ shall drop towards zero close to 
the strip edge as indicated by the FEM calculations and the reasoning above. This is included in CLUS-
TER and applied when σ2(y) is calculated with results as follows. Figure 36 shows how the calculated 
exit stress distribution is influenced by different values of ξ and when ξ drops to zero toward the strip 
edges (mod).  

Figure 36:  Calculated and measured strip tension distribution at the exit of pass 4 with different 

values of ξ. 

It can be noted that the calculated result that is closest to the measured values is the one where ξ=0.1 
and ξ drops to zero at the strip edges (ksi=0.1 mod). 
The diagrams in Figure 37 show the calculated absolute flatness with constant ξ (= Calc orig) compared 
with the calculation results with the modified ξ function (= Calc mod) and the measured flatness at the 
certain passes.  

39 
 
 
 
 
Figure 37:  Calculated and measured strip tension distribution at the exit of pass 2, 4 and 6. 

It can be noted that the agreement between the measured results and the calculations with the modified 
version is closer compared to the original calculations. There is however potential for further enhance-
ments. 
The results above indicate that assumptions regarding the stress and strain conditions close to the strip 
edges  have  a  large  impact  on  the  modelling  results. A  FEM  study  is  done  to  study  strip  deformation 
behaviour close to the strip edges. The calculations are done for narrow strips, 60, 90 or 120 mm wide. 
This is done to save computational time. This has to be considered when conclusions are drawn from 
the results.  
The aim of the simulation is to understand the effect of various parameters on cold rolling process. 
ε

Local broadening computer using 
gives an indication of the broadening along the 
roll
width of the strip. The width of the strip measured after the finish of the rolling pass gives the measure 
of the total broadening. The force profile over the width of the strip and also the plastic strain in rolling 
and thickness directions give more insights into the process. 

ε=

local

thick

ε

The factors are listed in the subsequent table with their high and low values. The strip thickness is var-
ied between 2mm and 4mm whereas the width between 60mm and 120mm. The Diameter of the rolls is 
varied between 100mm and 200mm. The thickness of the strip is reduced by 30% for high and 15% for 
low. A tensile load is applied on the strip varying from 10% to 20% of the virgin yield limit. The in-
coming crown of the strip is varied between -5% and +5%.  

#  Name 

Factors 

1  Strip Thickness 

2  Strip Width 

3  Roll Diameter 

4  Thickness Reduction 

5 

6 

Stretching Load 

Crown 

A 

B 

C 

D 

E 

F 

Low(-) 

2mm 

60mm 

100mm 

15% 

High(+) 

4mm 

120mm 

200mm 

30% 

0.1σy (45.7MPa) 

0.2 σy (91.4MPa) 

-5.0% 

+5.0% 

Required Number of Simulations = 16; Resolution = 4   
The schematic diagram of the problem and the Finite element model of the roll and strip are shown in 
the next Figure. 

Figure 38:  Schematic Diagram and Isometric-View of the model. 

40 
 
 
 
 
 
Response

Defining Relation 

The  fractional  factorial  design  matrix  is  given  in  Table  5.  Main  effects  are  aliased  with  three-factor 
interactions and no main effects are confounded with any 2 factor interactions. The run order is same as 
the standard order. The 17th run denotes the mean values of all the factors. 
Basic Design
C
B  
-
- 
-
- 
-
+ 
-
+ 
+
- 
+
- 
+
+ 
+
+ 
-
- 
-
- 
-
+ 
-
+ 
+
- 
+
- 
+
+ 
+
+ 
/
/ 

F=BCD 
- 
- 
+ 
+ 
+ 
+ 
- 
- 
+ 
+ 
- 
- 
- 
- 
+ 
+ 
/ 

E=ABC
-
+
+
-
+
-
-
+
-
+
+
-
+
-
-
+
/

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 

A 
- 
+ 
- 
+ 
- 
+ 
- 
+ 
- 
+ 
- 
+ 
- 
+ 
- 
+ 
/ 

D
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
/

Table 5:  Fractional Factorial Design. 

Work piece is a strip with thickness of 2mm or 4mm. This is meshed with linear solid elements with 6 
elements across the thickness. The element dimensions in width and rolling directions are 1mm. 
The crown of the strip is modelled by using a parabolic equation. 
The roll is modelled as rigid and has a radius of 100 or 200 mm. This is meshed by 1000 elements along 
the  circumference  and  one  element  across  the  width.  The  roll  dimension  in  width  exceeds  the  strip 
width by a small distance to ensure complete contact during the simulation.  
The strip is rolled at the room temperature with practically no heating during deformation and therefore 
the  thermal  physics  is  ignored.  The  strip  is  pulled  through  the  rolls  until  complete  contact  is  attained 
and thereafter driven by friction. After the rolling is finished, the strip and rolls are removed from con-
tact. During release, necessary boundary conditions are provided to avoid rigid body motion. 
A power law model with Von-Misses yield criteria is used for modelling plasticity. The parameters for 
power law model are, 

(cid:2026) (cid:3404) (cid:1827) ∙ (cid:2013)(cid:3040) (cid:3397) (cid:1828) 

where  

A = 392.24MPa 
B = 0 
m = 0.076 

Hexahedral 8-noded solid elements (7) are used to model the strip and quadrilateral 4-noded shell ele-
ments  (85)  are  used  to  model  the  tool. In  order  to  avoid problems  with  shear  locking  and volumetric 
locking of the solid elements, two modified integration schemes, assumed strain and constant dilatation 
is used. Assumed strain formulation is a hybrid element with additional degrees of freedom which will 
reduce the shear locking. Constant dilatation is a selective reduced integration which will cure volumet-
ric locking. 
Contact is modelled by using rigid and deformable bodies. The roll is modelled by rigid shell elements 
and strip is modelled by solid elements. Rigid bodies will not deform and they don't detect contact with 
each other.  
During  the  incremental  procedure,  each  node  is  checked  for  its  nearness  to  a  contact  segment,  which 
can be a rigid body or a deformable body node itself. This process of search is optimized by using a 
bounding box algorithm. Also a contact tolerance is allowed in order to avoid numerical difficulties to 
obtain a zero contact condition. This tolerance is divided between the inside (penetration) and outside of 
the surfaces by using a bias. A tolerance of 0.01mm and a bias of 0.95 are used in this simulation. The 
motion of the roll is modelled by prescribing the velocity of rotation to 10rad/s. 
At the start of the analysis, the strip is pulled under the rolls with zero friction. This is to ensure that the 
simulation  proceeds  during  the  initial  stage  because  the  contact  normal  forces  are  absent.  However, 

41 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
contact detection during the first increment requires much iteration because of numerical problems gen-
erated from the low contact reaction forces.  
Friction is modelled by using Coulomb friction model. Arctangent model is used to model the friction 
force  which  gives  a  continuous  function  in  terms  of  relative  sliding  velocity.  The  relative  velocity 
threshold used in this simulation is 0.01 with a friction coefficient of 0.5. 
The node which is in contact with a surface or another node, during the subsequent iterations or incre-
ments, might fall off contact. This is modelled by applying a minimum relative separation stress value 
which is equal to 0.1 in this simulation. The release of the tool is modelled by applying stiff springs to 
the nodes in contact replacing the contact condition and gradually reducing their stiffness values. This 
will avoid the sudden reorientation of forces and the numerical problems due to the rigid body motions 
associated with it. 
The problem is solved using a large strain Updated Lagrangian procedure with no follower force. The 
solver  is  a  multi-frontal  sparse  solver  working  on  6 processors  (16GB  RAM)  and  took  8-10  hours  to 
solve on a 3GHz machine. 
The whole simulation is solved using a mix of constant and adaptive time stepping procedures.  
The local width strain of the strip calculated as the difference of the plastic strain in thickness and roll-
ing directions and the force profile along the width of the strip are given in Figure 39. The legend also 
shows, within parenthesis, the final width of the strip after the rolling process keeping in mind that only 
half the strip is modelled.  

Figure 39:  : Local width strain and force distribution along the nominal width. 

As can be seen in the left part the width strain is close to zero at the strip centre for all cases. Width 
strain can be both positive and negative depending on the local rolling conditions. If the strip edge is 
reduced more than the rest of the strip the width strain is positive and if reduction at the edge is less the 
strain is negative. The conclusion is that width strain for these cases is significant to a distance between 
30-60 mm from the strip edge and that there is an increasing width strain towards the strip edge. This 
means that the assumption of plane strain in simplified models has to be modified at least close to the 
strip edges. Further investigations are necessary to see the mechanisms of this. 
In the right part of the figure it can be noted that the rolling force falls rapidly towards zero at the strip 
edge for all cases. This is important since the contact force has a direct influence on the elastic bending 
and  flattening  of  the  rolls  in  the  mill.  The  rolling  force  distribution  calculations  in  simplified  models 
have to be modified to take regard of this. Also for this further investigations are necessary to see the 
mechanisms of this for different rolling cases. 

42 
 
 
 
 
 
2.4.3  Roll geometry optimization 

(Work Package 3) 

This work package is divided into two parts. 
One was to test the use of the CVC technology in existing 20-high mills by replacing two of the four 
taper rolls with CVC rolls. 
The other was the development of a software programme which supports the operator in optimizing the 
roll geometries in a mill stand 

2.4.3.1  Determining the approach to CVC technology use. 
The idea of this approach was to replace one upper and one lower taper roll by a pair of CVC rolls (and 
adjusting each roll individual) to obtain an additional flatness actuator (see next Figure 40 and Figure 
41). 

Figure 40:  Approach to use CVC technology in 20 high mills. 

Top View on upper pair

Almost cylindrical part of CVC roll

Top View on bottom pair

Taper roll

CVC roll

Taper roll

CVC roll

Figure 41:  Top view on upper and bottom pair -Taper rolls / CVC Rolls-. 

43 
 
 
 
 
With the help of the sketch it becomes visible, that at the end of the roll barrel the CVC roll is almost 
cylindrical. 
Following this a precondition of this type of CVC use is that it must be possible, also to roll with one 
upper and one lower taper roll replaced by a cylindrical roll (Figure 42). 

Figure 42:  Layout one upper and one lower taper roll replaced by a cylindrical roll. 

The advantage of this layout was that rolling tests could be carried out without any mill revamping (the 
change of the current pairwise taper roll control to individual roll control) and that a successful rolling 
test would provide the information that this kind of CVC roll use most possible will be applicable. 
However, to obtain additional information’s at the rolling tests it was decided to carry out the tests only 
with one cylindrical roll. (Layout see Figure 43 and Figure 44) 
The advantage of this kind of test is that the behaviour of the combined taper roll / cylindrical roll can 
be tested and at the same time the flatness results can be compared with the mill side where the normal 
combination of two taper rolls is present. 

Figure 43:  Test constellation with one cylindrical roll. 

44 
 
 
 
 
Top View on upper pair

Taper roll

Cylindrical roll

Mill side with 
combined taper and 
cylindrical roll

Top View on bottom pair

Taper roll

Taper roll

Mill side with 
normal behavior

Figure 44:  Top view on upper and bottom pair -Taper rolls / one cylindrical Roll-. 

For a first test the remaining taper rolls had the same taper length and inclination as usual (taper length 
120 mm; mean inclination 3 ‰). One strip was rolled in 9 passes with this roll constellation. At pass 7 a 
manual taper adjustment was carried out to analyse the flatness influence of the pair of taper and cylin-
drical roll and to compare this with the taper rolls pair. In Figure 45 the resulting flatness difference per 
unit taper adjustment is demonstrated. Analysing this result do show that the effect of the combination 
taper roll and cylindrical roll is about 80% compared to two taper rolls. 

Flatness difference per unit taper adjustment

]
2
^
m
m
N

/

[
e
c
n
e
r
e
f
f
i
d
s
s
e
n
t
a
F

l

2,00

1,00

0,00

-1,00

-2,00

-3,00

-4,00

-5,00

-6,00

upper taper (with cylindrical combined)

lower taper

300

400

500

600

700

Width [mm]

Figure 45:  First test result with one cylindrical roll. 

Based on the analysis the test was repeated at which the inclination of one taper roll (the one which was 
combined with the cylindrical roll) was increased by 25 % to compensate the lower flatness effect.  
While rolling the first 3 passes it was observed that there seems to be an effect caused by the rolling 
direction. After each pass  change a larger adjustment of the combined taper -  cylindrical roll was re-
quired to compensate the flatness deviation. Compared to this the other taper roll pair on the opposite 
mill side remains more or less at the same position.  
While rolling pass 4 and accelerating the rolling speed a heavy strip break was produced. Within 3 sec. 
and 20 m strip length at the strip side where the combined taper - cylindrical rolls are located becomes 
extremely long producing a double folding. The strip break was that heavy that a fire in the mill was 

45 
 
 
 
 
 
 
produced. (Figure 105 in Appendix 1 does show screenshots of the flatness evolution of the last 3 sec-
onds before the strip break) 
At this one needs to know that a strip break (especially caused by a double folding) is extremely seldom 
at this strip thickness (1.2 mm). Only reasons for such a strip break can be a large lateral movement of 
the strip (e.g. caused by too much remaining rolling oil on the strip) or a sudden breakdown of the coiler 
motors  (causing  that  the  tension  suddenly  becomes  zero).  Both  cases  do  not  appear  here.  Conversely 
this means that the combined taper - cylindrical rolls must be the strip break source. 
A detailed view on the geometric roll gap situation directly at the strip edge does provide some possible 
explanation what provokes the strip break. Caused by the diameter difference between cylindrical and 
taper roll (at the strip edge) the work roll is displaced approximately 0.2 mm towards the rolling direc-
tion. Furthermore it needs to be considered that at the same time the roll gap situation is symmetrical 
where the tapered part ends. (The subsequent sketches shall demonstrate the roll gap situation.) 

Cylindrical roll

Taper roll

Work roll
(viewed 
from top)

Strip thickness: 1.45 mm

0.216 mm

Strip thickness : 1.22 mm

Δh = 0.23mm
Contact length: ≈ 3.8 mm

Taper rolls

Figure 46:  Geometric roll gap situation with combined taper - cylindrical rolls. 

The displacement of the upper work roll causes an asymmetry which can lead to some shearing tension 
which decreases the deformation stress. Thereby the local reduction increases what in turn increases the 
local strip elongation largely (and thus causing the strip break).  
What is not clear so far is the fact that this effect is not stable and that a sudden strip break can occur. 
The strip break occurs while accelerating the rolling speed and at the same time the combined taper - 
cylindrical rolls were slightly adjusted (4 mm towards the strip edge) by the flatness control. Both nor-
mally is uncritical for the rolling process, but might be a reason that a certain critical point was passed 
for the asymmetrical rolling conditions at the strip edge. 
Unfortunately the asymmetric rolling conditions would occur in the same way when using a CVC roll 
instead of a cylindrical roll. This means that there is a high risk of strip breaks (and following this sev-
eral hours production interrupt) when carrying out the foreseen CVC rolling tests. In turn this leads to 
the conclusion that there is only a low chance that the CVC approach would be successful.  
Any heavy strip break in conjunction with a longer production interrupt is very cost intensive. Beside 
this further cost would have been necessary to prepare this rolling test e.g. the revamping of the axial 
shifting control.  
Considering all facts it was decided to stop the further investigations of the CVC approach. 

2.4.3.2  Development of a software programme for optimizing the roll geometry. 
In a first stage a program was developed which automatically analyses the current state of the flatness 
and the flatness actuator positions periodically (every 6 hours). The periodical approach ensures that the 
resulting datasets are always up to date.  

46 
 
 
The procedure is carried out for a given set of thickness ranges and for the different types of taper rolls. 
The  thickness  ranges  are  fixed  and  distributed  in  such  a  way  that  the  thickness  increment  becomes 
smaller when the strip becomes thinner. 
The subsequent Figure 47 demonstrates the calculation sequence. A screenshot of the program is given 
in Appendix 1 Figure 107 and Figure 108. 
Since the calculation was intended to run automatically a lot of effort was carried out to develop algo-
rithm  to  remove  invalid  data  and  as  well  to  remove  outliers  and  to  calculate  the  statistical  values.  In 
several cases the data is randomly distributed as e.g. the crown of the rolls. Furthermore the number of 
available  datasets  can  be  very  low.  Thus  statistical  standard  algorithms  were  not  applicable  here.  A 
function was created using the histogram approach either to remove outliers (even independent of the 
distribution) or  to  define a  range  of  values  which  covers  e.g.  95%  of  the  values  (A  screenshot  of  the 
program is given in Appendix 1 Figure 106). The function was tested for  several cases regarding the 
value distribution and the amount of data to ensure a proper working. 

Loop over thickness 
ranges.

1.

2.

3.

4.

5.

Fetch datasets for the selected thickness range.
(for one taper length OR one width range)

Removing invalid datasets.
Removing outliers regarding crown of all rolls, strip 
width and roll force.

Calculating the difference between individual flatness 
and mean flatness. 
(= “wanted” flatness change for the inverse flatness model) 
Re‐calculating the individual flatness actuator 
positions to the mean flatness.

Calculating the statistical values for all flatness 
actuators as well for width distribution. 

Saving the result into the online database. 

Figure 47:  Calculation sequence for defining the basic statistical values. 

A program was developed with which the mill operator has the possibility to view the statistical values 
as  well  to  optimise  the  roll  geometry  (roll  crown of work  roll,  idle  and  driven rolls;  taper  length  and 
taper inclination). 
To demonstrate the functionality subsequent an example for a Sendzimir mill is given. 
The dimension of the mill is related to a max. strip width of 1550 mm. The main product range rolled at 
this mill is divided into two major width ranges (≈ 1220 to 1350 mm; ≈ 1450 to 1550 mm) with a thick-
ness range ≈ 6 to 0.5 mm. To cover the different width ranges two types of taper rolls are in use.  
After the program start first the statistical values will be loaded from the online database and displayed 
at an overview page (a screenshot of the first page is given at Annex 1 Figure 109). Beside the current 
state of the flatness actuators additional information is displayed (e.g. the width distribution). 
First  the  operator  has  to  select  for  which  taper  the  further  investigations  shall  be  carried  out.  For  the 
example the taper with a taper length of 320 mm is selected. This taper is destined for the first width 
range. 

Optimising crown of intermediate rolls: 

The crown of the intermediate rolls is related in high correlation with the flatness actuator “backup roll 
crown adjustment” (see also the rolling test results in chapter 2.4.2.1). Therefor the optimisation of the 
roll crowns results from the current state of this actuator. 

47 
 
 
The backup roll actuator is designed in such a way that a set of adjustable supporting mounts enables 
the individual adjusting of the backup rolls. The two subsequent sketches demonstrate the adjustment 
for the max. possible BUR crown (at which the centred BUR is moved max. towards the mill centre) 
and the min. possible BUR crown. 

Backup 
roll 

Max. Position

…….

adjustable support mounts 

Min. Position

Figure 48:  Layout of the backup roll crown adjustment. 

Since  the  individual  positions  of  the  support  mounts  are  not  meaningful  they  are  recalculated  to  a 
“crown” value by calculating the square part which fits best to all positions (like demonstrated in the 
subsequent figure). 

Figure 49:  Determining the backup roll crown. 

The BUR crown is calculated for each rolling case and the (previously described) statistical analysis is 
carried out for the different thickness ranges. 
With the help of the developed program the operator can view the current state of the BUR crown as 
demonstrated in the next Figure 50. 

48 
 
 
 
Figure 50:  Program part to view the current state of the BUR crown. 

The diagram  named “backup roll crown” demonstrates the distribution of the BUR crown  position in 
dependence of the strip thickness (x-axis). At this the axis is scaled form thick to thin strip.  
The y-axis is scaled to the  maximal possible  mechanical adjustment range. This provides a improved 
validation of the current state. 
For the current state three lines are presented. The green line represents the mean value while the red 
lines do show the actuation range which covers 95% of all measured rolling cases. 
For an easier understanding on the right side a graph is shown, at which the positions of the adjustable 
support mounts are presented for a certain case. (This graph is designed in a similar way the operator 
gets the adjustable support mounts (BUR) presented at the online flatness control). To select a certain 
case the operator can move the cursor (the black vertical line) within the thickness range. Furthermore 
he can switch between mean, maximum and minimum position (with the help of the “view” button). 
An evaluation of the current state shows clearly that the current crown of the intermediate rolls should 
be modified. For a strip thickness above 3 mm the BUR crown is frequently at the mechanical limita-
tion while only in a few cases the BUR crown becomes slightly negative. The target is to have the BUR 
crown on average centred within the mechanical limits. 
To meet the target at this example one of the roll crowns needs to be increased. By changing one of the 
“new roll crown” values the program calculates the estimated new distribution of the BUR crown. Fig-
ure 51 presents as an example the result for the case that the crown of the driven rolls is increased from 
150 µm to 240 µm (which in addition meets the target). The same result would be arrived when the roll 
crown of the idle roll is increased from 350 µm to 570 µm. 
Of course it would be possible to calculate the ideal crown of a selected roll automatically. The “manu-
al”  approach  has  the  advantage  that  the  operator  has  the  possibility  to  configure  the  roll  crowns  very 
flexible to his own requirements. E.g. at this example (considering that the mill is used for two major 
width  ranges)  it  makes  sense  to  define  one  common  roll  crown  of  the  driven  roll  which  covers  both 
width ranges and then to find the ideal roll crown of the idle roll for each width range. Thus only the 
idle roll has to be replaced when skipping from one width range to the other. The subsequent table shall 
demonstrate the ideal combination for this mill. 

Width range
1250 ‐ 1350
1450 ‐ 1550

Driven roll crown
200 µm
200 µm

Idle roll crown
450 µm
50 µm

49 
 
 
 
Figure 51:  New BUR crown distribution caused by an increased roll crown. 

To calculate the new BUR crown distribution first the flatness change caused by the different roll crown 
is calculated (with the help of the rolling test results or taken from the physical flatness model calcula-
tions). 
Following  this  the  required  adjustment  of  the  BUR  crown  is  calculated  to  compensate  the  flatness 
change. The resulting value then is added to the current values of the BUR crown distribution. 

Optimising taper length and taper inclination: 

With the help of the program the operator also can view the current state of the taper rolls as demon-
strated in Figure 52 
The diagram named “Taper roll” demonstrates the distribution of the taper roll position in dependence 
of the strip thickness (x-axis). At this the axis is scaled form thick to thin strip. Also here the y-axis is 
scaled to the max. possible mechanical adjustment range for an easier validation. 
For the current state three lines are presented. The green line represents the mean value while the red 
lines do show the actuation range which covers 95% of all measured rolling cases. 
On the right side two further graphs are shown. The upper one presents the current taper form. Beside 
the taper form the location of the strip edge is given e.g. for the average width and for the case that the 
taper is located at the centre position within the mechanical adjustment range.  
The  lower  graph  displays  the  flatness  influence  of  the  current  taper  for  the  average  width  and  a  strip 
thickness of 1mm. 

50 
 
 
Figure 52:  Program part to view the current state of the taper rolls. 

Similar  as  for  the  BUR  crown  the  target  is  to  have  the  average  taper  position  centred  within  the  me-
chanical limits. An evaluation of the current state does show that there is a certain potential to optimise 
the taper form. For a strip thickness above 3 mm the taper roll is frequently located at the mechanical 
limitation. On the other hand for a strip thickness below 1 mm the remaining adjustment range is only 
about 15 mm. Thus the pure change of the taper length will not improve the situation significantly.  
This improves clearly when the taper inclination is increased instead. Due to the fact that the taper in-
fluence increases, too, the required actuation range (to cover 95% of all rolling cases) does decrease in 
average by 15 mm. The result of the inclination change on the distribution of the taper position is given 
in Figure 53. 

Figure 53:  New taper roll distribution caused by an increased taper inclination. 

51 
 
 
 
The calculation of the new taper roll distribution based on an observation figured out during the project 
process. At both mills 4 different taper rolls with different taper lengths and taper inclinations are used 
or were tested for a longer period. When analysing the mean taper position and calculating the diameter 
difference at the strip edge (for these positions) it becomes visible that this value differs only slightly 
for the different taper rolls. (Under the precondition that the strip thickness is the same and the strip is 
flat). 
Conversely  this  means  that  a  change  of  the  taper  inclination  will  provoke  an  adjustment  of  the  taper 
position in such a way that the diameter difference at the strip edge becomes the same as it is for the 
current position. 
Following this an algorithm was developed at which for each thickness as well for the mean, maximum 
and  minimum taper position the current diameter difference is calculated and based on the new taper 
form the estimated new taper position (a screenshot of the program is given in Annex 1 Figure 110). 
Beside the new distribution of the taper positions the new estimated flatness influence is calculated and 
displayed. The calculation based on the investigated result that the flatness influence is very similar for 
different taper inclinations when the flatness influence is correlated with the taper diameter difference at 
the  strip  edge  (see  also  Figure  19  chapter  2.4.2.1).  Therefor  the  new  flatness  influence  can  be  easily 
calculated considering the new inclination. 
Together with the flatness influence a recommended flatness influence is given (by the maximum value 
given  with  the  blue  line).  One  would  say  that  the  flatness  influence  (and  thus  the  taper  inclination) 
should as large as possible to decrease the required actuation range of the taper rolls. But on the other 
hand a too large influence can cause problems at thin strips. During rolling it is possible that the strip 
width varies over the strip length or, what happens more often, that the strip moves lateral some milli-
metre. If, e.g. the strip moves lateral it provokes a flatness change at both strip edges as demonstrated in 
Figure 54. The amount of flatness change for a certain movement at this depends from the taper inclina-
tion and the strip thickness. Thus there is a risk of  strip breaks if the selected taper inclination is too 
large. 

Figure 54:  Flatness change caused by a lateral strip movement. 

The recommended flatness influence is taken from experience from one mill at which the taper layout 
leads to well flatness results for the whole production range without causing problems at thin strips. 
To recalculate the recommended flatness influence for the current mill the thinnest strip thickness found 
at the database is used. Beside this the operator has the possibility to change this value for the case that 
the current available data does not cover the full production range (e.g. for newly installed mills). 
Finally the operator has the possibility to save the new taper form as an ASCII file for a later use e.g. at 
the roll grinding machine.  

52 
 
 
 
2.4.4  Development of a predictive strip defect model 

(Work Package 4) 

Aim of this task was the development of a predictive strip defect model. Based on strip specimen meas-
urements and data based analyses the causes and key influencing factors should be determined and, if 
applicable, a statistical prediction model should be developed. 
The investigations were carried out for two high frequent occurring types of defect. One is  named as 
“heat / pressure stripes” and the other as “diagonal waves”. 

2.4.4.1  Measurement of strip specimens with “heat / pressure stripes”. 
A test specimen with high pronounced defects was shipped to BFI. The specimen was taken behind the 
bright annealing line. The defect is only visible at strips with high surface requirements and which are 
bright annealed. A visual inspection indicates clear that this type of defect is a surface defect. Often it 
appears for several 100 m strip length and disappears again. The location over the width can vary. 
At  the  specimen  two  sections  were  selected  for  the  surface  measurement,  one  section  with  and  one 
without the defect. The measurement was carried out with a confocal microscope which can provide a 
two- and a three dimensional result. 
The following figure demonstrates the result of the three dimensional measuring. 

µm
1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7

-0.8

-0.9

-1

µm
1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7

-0.8

-0.9

-1

defect free section 

section with heat / pressure stripes 

Figure 55:  Surface topography of the defect free and the heat stripe section. 

There  are  no  significant  differences  between  the  two  sections  identifiable  and the  surface  topography 
seems to be the same. 
Clearer differences were detected when the isotropy and the roughness between the sections were com-
pared. The value for the isotropy decreases form 65% to 35% at the heat / pressure stripes. This means 
that the topography is more directional at this section. The comparison of the roughness in rolling direc-
tion and cross to the rolling direction does provide also some directional differences (see Figure 56).  

Ra(λc = 0.08 mm)

Ra (in rolling direction)

Ra (cross to rolling direction)

0,040

0,030

0,020

0,010

0,000

]

m
µ
[
a
R

1

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6

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h

Figure 56:  Roughness of the defect free and the heat stripe section. 

53 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
In both directions the roughness increases for the heat stripe section; however the increase cross to the 
rolling direction is approximately 50% higher.  
The results leads to the estimation that some type of “grooves” were caused by the rolling process e.g. 
by a localized decreased lubrication. 

2.4.4.2  First data-based analysis regarding the surface defect “heat / pressure stripes”. 
To have the data for the data mining system in an applicable form available, in a first stage a program 
was created which re-organizes the data from a pass by pass towards a coil by coil manner. Beside this, 
additional values were calculated which are not present as measured values. Also only those coils with 
high surface requirements and which were bright annealed were selected for the analyzing. 
First all values were removed which had been identified as not significant or which were high correlat-
ed with other values. For the further investigation the focus was on all values which are in connection 
with  the  strip  temperature,  the  roll  force  and  the  roll  gap  geometry.  At  this  each  dataset  contains  the 
data of passes 2, 3, 4 (respectively 2 to 6 for the roll gap temperature) and for the last three passes. Thus 
only coils where selected where the total number of pass was equal or greater than 9. (Table 18 in An-
nex 1 gives an overview of the selected measured and calculated values.) 
First the most significant parameter needs to be identified. For that the following methods were used: 

  Discriminatory analysis  
  Decision tree (C4.5) 
  Self-Organising Map (SOM) 

(A short description of the methods is given in Appendix 2: Data mining techniques) 
Even that the methods are using a different approach the results can be compared by the priority list of 
variables.  If  the  application  of  all  methods  leads  to  the  same  (or  nearly  the  same)  list  of  influencing 
variables, the relationship can be seen as strong. (The subsequent tables demonstrate the results.) 

Discriminatory analysis backward 

Discriminatory analysis forward 

Fitness (-1…+1): 0.37102 
Fitness (-1…+1): 0.41616 
Table 6:  Discriminatory analysis of the heat / pressure stripe defect 

Decision tree 

Self-Organising Map 

Table 7:  Decision tree and SOM result of the heat / pressure stripe defect 

54 
 
 
 
 
 
 
   
 
Legende: 
F_ = Roll force  
relation_NP_RA_ = Relation roll angle to neutral point 
Indexing last passes (e.g. _m0) = index 0 = last pass, index 1 = last pass -1 etc. 
Indexing first passes (e.g. _2) = Index 1 = first pass, index 2 = second pass etc. 

It can be seen that a clear relationship is not present for a single or a set of values. What can be noted is 
the fact that the roll gap temperature and values, which are direct connected to the temperature, mostly 
have a high priority. 
To get some additional information (and this for each variable separate) a special type of categorized 
histograms were created. The data of one variable is categorized and each category is set into relation to 
the quotient of the defect occurrence. (At this only the datasets were used which either have no defect or 
a high pronounced defect because this analyse is only applicable for two groups). For each category the 
occupancy is given as a value and also by the intensity of the bar colour. The more dark a bar is the 
higher the number of values are within this category. In addition a best-fit line is given which considers 
by a weighting the occupancy of the categories (blue line). The small red line in the graphs marks the 
total defect frequency. The advantage of these histograms is that it is easily identifiable if a correlation 
is covered by a meaningful occupancy and if the variation of the values is large enough. 
The clearest relationship was found for the roll gap temperature while other parameters were removed 
due to the low variation or worse occupancy. Subsequent some of the histograms are demonstrated. 

]

%

[

y
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t
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D

f

Figure 57:  Histogram max. strip temperature versus heat / pressure stripe defect (all passes). 

In the major number of cases (93%) the max. temperature does occur within passes 4 to 8. However, the 
pass, at which the maximum temperature occurs, has no influence on the defect frequency. 

55 
 
 
 
 
 
]

%

[

y
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Figure 58:  Histogram strip temperature versus heat / pressure stripe defect (Pass 6). 

The results for the other passes were similar except for the last three passes. 
The fact that the correlation of the temperature with the defect at the passes 2 to 6 is always similar can 
be explained by the fact, that if already e.g. in pass 2 the temperature is high it is most possible that the 
temperature in the subsequent passes will also higher than usual.  
Some similar correlations like the temperature were found for the rolling speed in the first passes. Since 
the rolling speed is strong related to the temperature this fact was assumed as the reason for this. 

2.4.4.3  Test series to avoid the strip defect “heat / pressure stripes”. 
Based on the carried out measurements and analyses it was estimated that the major factor in provoking 
“heat stripes” is the exceedance of a certain strip temperature. Thus a test series was carried out for one 
month at which the strip temperature was limited and where the pass schedule calculation provides the 
required coolant amount and maximal allowed rolling speed. 
The defect frequency decreases clear during the test series. The strange point is the fact that the defect 
frequency remains on the lower lever in the following month (see Figure 59) even that the strip temper-
ature for the major part of strips was on the same level as usual. Also in the subsequent months the de-
fect frequency haphazardly increases and decreases again (see Figure 60). 

56 
 
 
 
 
 
]

%

[

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Figure 59:  Defect frequency heat /pressure stripes during test series and one month later. 

Defect frequency heat / pressure stripes

Test series

y
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100
90
80
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60
50
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0

04
2011

05
2011

06
2011

07
2011

08
2011

09
2011
Month

10
2011

11
2011

12
2011

01
2012

02
2012

Figure 60:  Defect frequency heat /pressure stripes during one year. 

Due to the results it becomes clear that additional factors do influence the defect frequency. 

2.4.4.4  Second data-based analysis regarding the surface defect “heat / pressure stripes”. 
While carrying out the rolling test regarding the use of roll force limitations for the pass schedule calcu-
lation some effects were observed which did show that a high relative thickness reduction at the first 
pass  can  cause  a  significant  increased  friction  and  thus  a  strong  increased  roughness  (see  chapter 
2.4.6.2).  
Therefore a further analyse was carried out to investigate required reduction limitations to minimize this 
type of surface defect.  

57 
 
 
 
 
 
 
 
The subsequent figures demonstrate the correlation of the first two passes. 

]

%

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Figure 61:  Histogram relative reduction versus heat / pressure stripe defect (Pass 1). 

While the relative thickness reduction at the first pass is normally distributed the reduction at the second 
pass has two core areas (see Figure 62). Thus two classes were defined and compared which each other. 
Class 1 is defined by the value range 0.17 -> 0.174 and class 2 by the range 0.177 -> 0.180. As it can be 
seen in Figure 63 the frequency of defected strips decreases clearly when the relative reduction is below 
0.174. 

Figure 62:  Histogram relative thickness reduction at pass 2. 

58 
 
 
 
 
 
 
Class 1

Class 2

y
c
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f

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

no defect

heat / pressure stripes

Figure 63:  Relative reduction versus heat / pressure stripe defect (Pass 2). 

A analyze of the subsequent passes was not meaningful since here only one core part were present and 
only a low variation within this part were given. 
From the analysis some rules can be derived to minimize the frequency of heat and pressure stripes. 
These are:   Max. thickness reduction at pass 1 ≈ 18 % 

Max. thickness reduction at pass 2 ≈ 17,4 % 
Max. strip temperature ≈ 75° C 

When selecting those strips which cover all restrictions at the same time the number of defected strips 
becomes zero. (However, only 15 strips do meet all restrictions so that a good statistical validation is 
not given here.) 
Since the second data base analyse was carried out close to the end of the project a verification of this 
limits by a long term test series couldn’t be carried out. 

2.4.4.5  Development of theories about the occurrence of “heat / pressure stripes”. 
The surface measurement did show that the defect “heat stripes” is a surface defect at which the direc-
tionality is toward the rolling direction. Together with the appearance it leads to the assumption that the 
lubrication occasional local decreases and with it provokes a higher roughness. Based on the results of 
the database analyses furthermore it can be estimated that this case more often occurs when a certain 
relative thickness reduction and / or a certain strip temperature is exceeded. Since these cases are pre-
sent either in the first two passes (for the reduction)  or within passes 4 to 8 (for the temperature) the 
conclusion must be that a defect, once provoked, cannot be removed by the subsequent passes. At this 
point it needs to be considered that the surface is high glossy (behind the bright annealing line) and that 
even  a  very  slight  beamless  becomes  visible.  Thus  already  small  differences  in  roughness  lead  to  an 
indication of a surface defect. 
To  minimise  the  defect  frequency  strong  restrictions  are  required  which  also  restricts  the  production 
rate. On the other hand, lower surface requirements or the use of a different lubrication may result in 
lessen restrictions. Nevertheless, the required limitations need to be determined than again. 

2.4.4.6  Measurement of strip specimens with diagonal waves (“fishbone effect”). 
Test  specimens  with  high  pronounced  defects  were  shipped  to  Mefos  and  BFI.  The  specimens  were 
taken direct after the cold rolling process and some behind the bright annealing line. A visual inspection 
of  the  specimens  taken  after  the  cold  rolling  process  indicates  clear  that  this  type  of  defect  is  a  form 
defect. The appearance of the defect can be described as diagonal waves which either appears in one 
direction almost over the whole width or in two directions like fish bones. The defect is almost not to 
identify direct at the cold rolling mill (and not to measure with the flatness measurement roll) but very 
good to see at the entry of the bright annealing line. Behind the annealing line (which is a combined 
annealing and temper rolling line) the form defect is no longer present. Instead of the waves some kind 
of  slight  beamless  and  diagonal  shadows  do  appear  which  can  be  good  observed  as  long  the  strip 
moves. The diagonal shadows correlates clear with the diagonal waves at the annealing line entry here. 
When  the  movement  stops  or  at  a  single  specimen  it  becomes  very  difficult  to  recognize  these  slight 
shadows. 

59 
 
 
At the annealed specimen four sections were selected for the surface measurement, two sections with 
and two without the defect. All sections were measured with the confocal microscope. 

Ra(λc = 0.08 mm)

Ra (in rolling direction)

Ra (cross to rolling direction)

0,040

0,030

0,020

0,010

0,000

]

m
µ
[

a
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Figure 64:  Roughness of the defect free and the beamless shadow section. 

It can be seen that there is almost no difference in roughness present. A more clear difference is given 
when  measuring  the  gloss  of  the  sections.  The  gloss  decreases  by  about  7%  for  the  shadow  section, 
independent of the measurement direction. However, that is much less than the difference of the results 
between the measurement in rolling direction and cross to the rolling direction itself. Here the differ-
ence is approximately 13%. The subsequent figure demonstrates the measurement results. 

Cross to rolling direction

In rolling direction

]
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°
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e
f
e
d

2

e
e
r
f

t
c
e
f
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d

1
w
o
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a
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2
w
o
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1

e
e
r
f

t
c
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2

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1
w
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2
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a
h
s

Figure 65:  Gloss of the defect free and the beamless shadow section. 

Four strip specimens were shipped to Swerea MEFOS for characterisation of flatness defects. The spec-
imen dimensions are given in the next table. 
Specimen No 
1 
2 
3 
4 

Thickness (mm) 
0.38 
0.38 
0.39 
0.39 

Length (mm) 
2590 
2562 
2514 
2585 

Width (mm) 
1273 
1275 
1277 
1278 

Notation 
Flat 
Flat 
Non-flat 
Non-flat 

60 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Looking at the plates with the eye none of the plates can be regarded as perfectly flat. (Figure 111 at 
Annex 1 does show the photographs of the four plates) 
Close  eye  examinations  reveal  small  amplitude  buckles  over  the  whole  strip  width  on  all  four  speci-
mens. The buckles have an extension of 50 to 100 mm and are oriented diagonally over the plates. The 
amplitude is very small but clearly visible on the reflective material as shown in the next figure. 

Figure 66:  Low amplitude buckles. 

Eye examination also reveals edge waves on all four specimens. 
The manifest flatness of the specimens is measured using laser triangulation. The specimens are placed 
on a flat surface situated on a wagon moving in the specimen´s longitudinal direction. The specimen is 
thus oscillating under the laser triangulation device and for each passage the laser is moved 10 mm in 
the specimen width direction. The top surface elevation is thus measured over the whole specimen sur-
face and used to calculate the flatness. 
The measurements on the four specimens gave results as shown in Figure 67. 

61 
 
 
 
  
Figure 67:  Elongation distribution for strip specimens. 

The first two specimens have a narrow region (30-40 mm) of long edges. The shortest region is within a 
distance of 50 – 250 mm from the edges and then there is a longer region ±40mm from the specimen 
centres. The last two specimens have a wider region (300-350 mm) of long edges and are shortest in a 
region around the specimen centres. 
Swerea MEFOS also did reference measurements with commercial shape measurement equipment de-
livered  by  the  Swedish  company  Shapeline  AB.  The  system  is  laser  based  and  is  using  triangulation 
with  three  red  line  lasers  and  three  2D-cameras  covering  the  whole  strip  width.  The  specimens  were 
placed on a thick flat plate and moved under the measurement systems on a roller table. Plots from the 
measurements are shown in Figure 68 and Figure 69. 

Figure 68:  Topography plots of strip specimens, Shapeline system. 

Figure 69:  Elongation distribution for strip specimens, Shapeline system. 

There is a strong similarity between the measurements with the Swerea MEFOS point laser system and 
the Shapeline system. The elongation distribution (=flatness) from specimen 1 and 2 differs clear com-
pared to specimen 3 and 4.  
The specimens 1 and 2 have long parts close to the edges, then 200 mm wide short parts around 150 
mm from the edges and a 500 mm wide long part around the strip centre.  
The specimens 3 and 4 have a more or less parabolic distribution of the flatness with long edges and a 
short strip centre.  
Since  the  low  amplitude  diagonal  waves  were  present  on  all  specimens  it  is  not  possible  from  these 
specimens to find a flatness case where no low amplitude waves occur. The Shapeline can be used to 
plot  the  specimen  surface  height  over  a  line  across  the  strip.  Figure  70  shows  such  plots  for  all  four 
specimens. 

62 
 
 
 
 
 
 
 
 
 
 
 
Figure 70:  Specimen surface height across the width, Shapeline system. 

The plots show the waves caused by the long edges and overlaid low amplitude waviness. The low am-
plitude waves have a wavelength of about 100 mm and amplitude of 0.1-0.2 mm. The waviness can be 
seen on all specimens but it is not possible to see a quantitative difference in size of the waviness be-
tween the specimens. Thus it is not possible to formulate any relation between the flatness profile and 
the occurrence of the low amplitude diagonal waves. More tests have to be done to formulate a theory 
about occurrence of the diagonal waves.  
Just before report deadline the specimens were measured with a system developed by SwereaMEFOS in 
another project. Also this system is based on laser triangulation but with only one camera and one line 
laser and measurements were done on the same location as the Shapeline system. Figure 72 shows a 3D 
topography view of the upper surface of the specimens. 

Figure 71:  Topography plots of strip specimens, Swerea MEFOS laser line system. 

A comparison of these topography’s with those in Figure 43a shows strong similarities. Since no ten-
sion  is  applied  the  long  edges  causes  the  whole  specimens  to  buckle  so  the  low  amplitude  “diagonal 
waves” drown in large amplitude waves. In some more flat parts the pattern can however be discernible. 
This  system  also  can  plot  the  I-curve  as  a  rolling  value  over  the  length  of  the  specimen.  The  rolling 
value  is  calculated  over  a  one  meter  length  of  the  specimens.  The  value  is  calculated  over  shorter 
lengths in the beginning of the specimen so there accuracy is lower. A plot for specimen 1 is shown in 
Figure 72. 

Figure 72:  Topography  plots  of  rolling  I-values  for  specimen  1,  Swerea  MEFOS  laser  line  sys-

tem. 

The plot verifies the I-curve for specimen 1 measured by the Shapeline system and also shows that the 
curve form is quite stationary along the specimen length. I-value curves for the whole length of all four 
specimens are shown in Figure 73. 

63 
 
 
 
 
 
 
 
Figure 73:  Elongation distribution for strip specimens, Swerea MEFOS laser line system. 

The curves above verify the  measurements with the two systems  mentioned above. All three systems 
give very similar information regarding the flatness of the four specimens so the measurements of the 
manifest flatness of the specimens can be trusted. The first measurement was done two years before the 
two last ones so flatness has not changed much while the specimens were stored. 

2.4.4.7  Data-based analysis regarding the surface defect “diagonal waves”. 
Similar to the procedure to analyse the heat / pressure stripes the data was re-organized from a pass by 
pass towards a coil by coil manner and additional values were included. Also here only those coils with 
high surface requirements and which are bright annealed were selected for the analysing. 
Since the defect is identified as a form defect and furthermore it was known that the defect does only 
appear when rolling thinner material the analyses was carried out for the last three passes. 
Even that the specimens do not show a correlation between flatness and diagonal waves a few number 
of meaningful values were included which are able to describe the flatness deviation. 
The analysis was carried out with some intermediate steps where additional values were included and 
low influencing values were removed. (Table 19 in Annex 1 gives an overview of the selected measured 
and calculated values.) 
Three indicators were used to describe the major flatness deviation forms. These are: 

a)  The flatness deviation direct at the strip edge. 
b)  The amplitude of the so called “quarter buckles”. This type of flatness deviation is located be-
ginning near the strip edge with a width of approximately ¼ strip width towards the strip centre. 

c)  The flatness deviation of the strip centre 

For a) the slope of the linear part of the flatness was calculated, for b) and c) the square part. The fol-
lowing sketch (Figure 74) shall clarify the values meaning. 

64 
 
 
 
Strip centre line

Square part of 
the centre

Square part of 
the “quarter buckle”

Slope of the linear part
of the edge flatness

Measured flatness

200 mm

≈ 600 mm

50 mm

Figure 74:  Sketch for description the flatness indicator values. 

A priority list was generated with the help of the different data mining technics. At this only the datasets 
were used which either have no defect or a high pronounced defect. A high priority was found for the 
total reduction and for the last pass the -relation of neutral point to the roll angle- and one of the flatness 
indicators. 
Discriminatory analysis backward 

Discriminatory analysis forward 

Fitness: 0.21 
Table 8:  Discriminatory analysis of the diagonal waves defect. 

Fitness: 0.19 

Self-Organising Map 

Categorized histogram 

Table 9: 

SOM and categorized histogram of the diagonal waves defect. 

Legende: 
F_ = Roll force 
VW_ = Rolling speed 
R_WR_ = Radius of the work roll 
crown_ = Actuator position of the backup roll crown adjustment. 
relation_NP_RA_ = Relation roll angle to neutral point 
flat_centre = Flatness deviation of the strip centre 
quarter_flatt_ = Amplitude of the so called “quarter buckles”. 
Indexing last passes (e.g. _m0) = index 0 = last pass, index 1 = last pass -1 etc. 

Furthermore weighted histograms were created. At this the clearest relationship was found for the total 
reduction and the relation of neutral point to the roll angle at the last pass. (Since the total reduction is a 
given value this parameter was not further investigated.) The flatness deviation of the strip centre could 
be  also  interpreted  as  a  higher  influence  factor  while  the  influence  of  the  so  called  “quarter  buckles” 
was not as clear. The following figures demonstrate the results. 

65 
 
 
  
 
 
 
]

%

[

y
c
n
e
u
q
e
r
f

t
c
e
f
e
D

Figure 75:  Histogram -relation neutral point / roll angle- versus diagonal waves defect. 

]

%

[

y
c
n
e
u
q
e
r
f

t
c
e
e
D

f

(positive value = strip centre is longer than strip edge) 
Figure 76:  Histogram centre flatness versus diagonal waves defect. 

It can be noted that the -relation neutral point to roll angle- has the clearest relation. On the other hand 
the distribution of the data for the different sections is not very well here. In some cases the occupancy 
of a section is critical low.  
An adequate occupancy for the centre flatness is only given for a small range. But within this range the 
relation to the defect is relative low so that the result is not really confirmed. 

2.4.4.8  Test series to avoid the strip defect “diagonal waves”. 
From the detected values which seems to influence the diagonal waves two can be used to reduce the 
frequency of defects. The total reduction is a given value and cannot be changed, but the –relation neu-
tral point to roll angle- can be changed by the strip tension and the centre flatness by a modified target 
flatness.  

66 
 
 
 
 
 
 
 
 
 
The  –relation  neutral  point  to  roll  angle-  depends  significantly  from  the  pass  reduction  and  the  strip 
tension relation between entry and exit side. An increasing of the exit strip tension leads to an increased 
relation of the neutral point to the roll angle here.  
A test series was carried out for one month at which the strip tension was modified in such a way that 
the  –relation  neutral  point  to  roll  angle-  improves.  Furthermore  the  target  flatness  was  changed  to 
achieve a improved flatness in account with the results of the data analyses. However, the changes did 
not provide an indictable decrease of the defect frequency so that it needs to be stated that this test was 
not successful. 
A further test was carried out which based on older observations. The assumption was that the number 
of diagonal waves decreases when a taper with a large taper inclination was used. Thus, a taper with a 
taper length of 90 mm and a mean inclination of 5.6 ‰ was grinded and used at about 60 strips. The 
analysis  of  these  strips  didn’t  show  any  effect  on  the  development  of  diagonal  waves  and  could  not 
confirm the assumption. 

2.4.4.9  Development of theories about the occurrence of “diagonal waves”. 
A  theory  about  what  provokes  the  diagonal  waves  cannot  be  given.  So  far  it’s  not  understood  what 
causes the diagonal waves during rolling and why the waves seem to cause the glossy shadows during 
annealing. 
Since no other correlations were detected the key factors provoking this defect must be located outside 
the currently available process data. 

67 
 
 
 
2.4.5 

Integration of models into pass schedule calculation 
(Work Package 5) 

Aim of this task is to avoid empirical limitation values used for the pass schedule calculation. As far as 
possible so far used limitations of reduction per pass, the maximum strip temperature and simple rules 
for determining strip tension values shall be replaced by calculated values. 

2.4.5.1  Development of an algorithm for strip flatness. 
One important parameter for the strip flatness is the resulting roll force at one pass. The roll force in 
turn depends directly on the pass reduction. The objective of the algorithm therefore is to select for each 
pass  a  reduction  value  which  achieves  both  good  strip  flatness  and  a  sufficiently  generous  actuation 
range of the flatness actuators for compensating rolling force variations. Thus for each pass an upper 
and lower rolling force limit needs to be determined. Rolling within this range shall ensure that both the 
strip flatness is good and the flatness actuators have a sufficiently generous actuation range. 
In a first stage the actual state was analysed using the data of the long term database. Here the measured 
flatness,  the  roll  force  and  the  flatness  actuator  positions  where  pass  wise  averaged  and  the  double 
standard deviation calculated. The results do show that there is only a small deviation of the flatness at 
one pass while the variation of actuator positions is larger. Thus it can be stated: If the flatness actuators 
are within their adjustment range the flatness control system or the operator typically can meet the tar-
get flatness. (This rule is only than not valid when the given roll geometry is in such a manner that un-
der no circumstances the target flatness can be arrived) 
Therefor it follows that for the calculation of the upper and lower roll force limit the knowledge of the 
actuator variations at a typical roll force is required. To determine these values a program was devel-
oped which analyses pass datasets from the past and stores the calculation result into the online data-
base. This is done for a sequence of thickness ranges. The thickness ranges are fixed and distributed in 
such a way that the thickness increment becomes smaller when the strip becomes thinner. 
Target of the procedure is to calculate all individual datasets toward one mean point regarding flatness 
and roll force. The sequence of the procedure is demonstrated in Figure 77. (A screenshot of the pro-
gram is given in Appendix 1 Figure 107 and Figure 108.) The procedure runs periodically so that an 
automatic update of the statistical values is given. 
Since the calculation was intended to run automatically a lot of effort was carried out to develop algo-
rithm  to  remove  invalid  data  and  as  well  to  remove  outliers  and  to  calculate  the  statistical  values.  In 
several cases the data is randomly distributed as e.g. the crown of the rolls. Furthermore the number of 
available  datasets  can  be  very  low.  Thus  statistical  standard  algorithms  were  not  applicable  here.  A 
function was created using the histogram approach either to remove outliers (even independent of the 
distribution) or to define a range of values which covers e.g. 95% of the values. 
To consider the width variation within the datasets for one taper length (or one width range) the specific 
roll force (per mm strip width) is used instead the total roll force. By selecting these datasets where the 
specific  roll  force  is  close  to  the  mean  value  the  calculation  error  of  the  subsequent  re-calculation 
(step 4) can be hold as low as possible. 
The statistical values calculated for each flatness actuator are: 

  Centre position. 
  Maximum position. 
  Minimum position. 

at which the range between maximum and minimum position covers 95% of all cases. This information 
is required for the later determination of the upper and lower roll force limit. 
Figure 78 and Figure 79 are presenting the result for mill 1 and the taper with a length of 120 mm. (At 
this the BUR crown is calculated as described in chapter 2.4.3.2) 

69 
 
Loop over thickness 
ranges.

1.

2.

3.

4.

5.

6.

7.

Fetch datasets for the selected thickness range.
(for one taper length OR one width range)

Removing invalid datasets and outliers.

Calculating the mean specific roll force.
Selecting datasets where the specific roll force is close 
to mean value.
Calculating the mean flatness.

Re‐calculating the individual flatness to the mean 
specific roll force.

Calculating the difference between individual flatness 
and mean flatness. 
(= “wanted” flatness change for the inverse flatness model) 
Re‐calculating the individual flatness actuator 
positions to the mean flatness.

Calculating the statistical values for all flatness 
actuators. 

Saving the result into the online database. 

Figure 77:  Sequence to calculate the statistical values for all actuators. 

]
2
^
m
m
/
N

[
n
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t
a
i
v
e
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s
n
e
T

800

600

400

200

0

‐200

‐400

‐600

‐800

‐700

‐350

0
Strip width [mm]

350

700

exit 
thicknes
2,83

2,41

2,09

1,75

1,51

1,33

1,14

0,95

0,79

0,67

0,57

0,49

0,43

0,38

]

m
m
/
N

i

[
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r
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r
o
F
l
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o
R

8000

7000

6000

5000

4000

3000

2000

1000

0

3,00

mean Roll Force per milimeter width

2,00
1,00
Strip thickness [mm]

0,00

Figure 78:  Mean flatness and mean roll force in dependence of the thickness. 

70 
 
 
 
 
 
 
 
 
 
 
max taper
mean taper position
min taper

200

180

160

140

120

100

80

60

40

20

0

]

m
m

[
n
o
i
t
i
s
o
P
r
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p
a
T

max. BUR crown
mean BUR crown position
min. BUR crown

‐17,50

‐12,50

n
o
i
t
i
s
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P
n
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l
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a
B

‐7,50

‐2,50

2,50

7,50

12,50

17,50

3,00

2,50

1,50
2,00
1,00
Strip thickness [mm]

0,50

0,00

3,00

2,00

1,00

Strip thickness [mm]

0,00

Figure 79:  Corresponding statistical values for the taper and the backup roll crown. 

The  figures  demonstrate  that  the  flatness  is  very  similar  independent  from  the  thickness.  The  current 
state regarding the roll force shows that it is decrementing towards the thinner material. Corresponding 
to this the taper position becomes higher (which means at this mill that the taper is moved more towards 
the strip edge) and the backup roll crown becomes lower. (Please note that the scaling of the strip thick-
ness is reversed. This is done for improved comparison with later figures). 
To calculate the roll force limitations and the “optimal” roll force a further algorithm was developed. 
The “optimal” roll force in this conjunction is defined by this roll force, where the actuators are located 
in the centre of the actuator range and therefor the maximum adjustment range is available. The sche-
matic diagram of the algorithm is given in Figure 80. 

mean actuator positions

min. and max. positions

actuator range limits

current strip width

mean flatness

mean specific roll force

Roll force prediction model

Determine the 
centre, max. or min. 
actuator position

Calculating the 
flatness which would 
occur at the new 
actuator position.

‐

Calculating the mean 
specific roll force which is 
required to meet again 
the mean flatness. 

“optimal”, max. or
min. specific roll force

Figure 80:  Schematic diagram of the roll force prediction model. 

The  max.  specific  roll  force  is  given  when  the  flatness  actuators  are  located  at  the  upper  mechanical 
limitation minus the maximum actuator positions (which cover 95% of all cases). To calculate the min. 
specific roll force the lower mechanical limitations and the minimum actuator positions are used. 
However, one special limitation needs to be considered for the taper roll adjustment. When the distance 
between the taper edge and the strip edge becomes too small (or even zero or negative) there is no fur-
ther flatness influence possible. Thus a minimum distance between taper edge and strip edge must be 
kept as shown in Figure 81. 
Based on the current strip width the maximum position of the taper roll can be calculated. With the help 
of Figure 81 it becomes also clear that the possible actuator range becomes smaller when the strip be-
comes narrow. The current minimum distance is set to 10 mm. 

71 
 
 
 
 
 
 
 
 
 
mechanical limited
max. taper roll position

upper taper roll

work roll

minimum distance 
taper edge to strip edge

strip

Figure 81:  Demonstration of the required minimum distance of taper edge to strip edge. 

To use the calculation result for the pass schedule a user interface was developed with which the opera-
tor can view and evaluate the results and with which functions can be defined which e.g. describes the 
correlations between strip thickness and roll force limits. (A screenshot of the complete user interface is 
given in Appendix 1 Figure 112). 
There are two reasons which led to the decision to include this step. 
The analysis for different mills and different taper rolls did show that in some few cases the calculation 
results seem to be not consistent (e.g. the lower roll force limit is close to the upper roll force limit). 
Thus the valuation of an expert does avoid the use of invalid datasets. 
Depending on the product range rolled at one mill the available range of data might be relative small. 
(This  also  can  occur  when  the  system  is  newly  installed  and  the  total  number  of  datasets  is  low).  To 
ensure that the calculation results can be used outside the analysed range a function can be used to ex-
trapolate the limitation values. Furthermore a function provides fast calculation capability for the later 
use  at  the  pass  schedule  calculation.  On  the  other  hand  the  extrapolation  with  a  function  (especially 
polynomial functions) can result in invalid values so that the review of an expert is required here, too. 
The user interface consists of three sections at which the user can analyse the flatness results (described 
here), the roll force deviation and to check the resulting behaviour. 
The analysis of the flatness results firstly describes the correlation between strip (exit) thickness and the 
roll force per mm strip width. (See Figure 82 as an example). The displayed result at this is given for 
the average width. Currently there are two types of functions selectable (linear and square) which shall 
describe the correlation. (These two functions are defined so far based and the analyses carried out for 
the different mill types.) 

Figure 82:  Roll force limits in dependence of the strip thickness. 

Especially for 20 high mills where taper rolls are in use a greater influence of the strip width takes ef-
fect on the roll force limits. Background is the fact that a wider strip typically does enlarge the usable 
adjustment range and in opposite that a narrow strip does reduce the range. 

72 
 
 
 
The dependency on the strip width is calculated and displayed at the second graph. (See Figure 83 as an 
example). Also here the user can select either a linear or a square function to describe the correlation. 

Figure 83:  Influence of strip width on the roll force limits. 

2.4.5.2  Development of an algorithm for automatic analysis of process dynamic. 
As  the  major  process  parameter  (in  conjunction  with  the  flatness)  with  the  greatest  dynamic  the  roll 
force  was  identified.  It  was  observed  that  the  roll  force  deviation  within  one  pass  can  be  more 
than 30%.  
To analyse the roll force dynamic within one pass a program was created which calculates and stores 
some statistical values immediately after rolling one pass. The procedure starts with analysing the roll-
ing  speed  distribution.  This  part  of  the  strip  length  where  the  speed  was  the  longest  time  constant  is 
defined as uniform. (From experience it is known that this part has a very low variation in roll force, 
thickness and flatness actuator adjustment). The roll force of the uniform part is averaged and presents 
the “Major Roll Force”. Beside this for the whole strip length the  minimum and  maximum  roll force 
(and their location) is determined. (A screenshot of the program is given in Annex 1 Figure 113.) 
Based on the data of all passes the statistical roll force difference between the major roll force and the 
minimum and maximum roll force is calculated. The calculation is carried out pass wise but stored to-
gether with the mean total reduction of the corresponding pass. The analysis is done for a set of thick-
ness ranges. Instead of the individual thickness of each pass the so called hot strip thickness is used for 
the selection. (A screenshot of the program is given in Annex 1 Figure 114. The consent of the achieved 
data is given in Annex 1 Table 20.) 
With  the  help  of  the  second  section  of  the  user  interface  (Figure  112)  the  results  can  be  viewed  and 
functions can be defined.  
In  Figure  84  the  positive  roll  force  deviation  for  one  mill  is  presented.  At  this  the  positive  roll  force 
deviation is defined by the difference between the maximum roll force at one pass minus the “centre” 
roll force (where rolling speed is constant and a low variation of the thickness is given). The result al-
ready considers 95% of all cases. For the positive roll force deviation currently the user can select be-
tween three types of functions (Exponential; Linear; Square) to describe the correlation. 
The  following  Figure  (Figure  85)  demonstrates  the  negative  roll  force  deviation  (=”centre”  roll  force 
minus minimum roll force). Due to the distribution of the indicated deviations a classic function was not 
applicable here. Up to a certain total reduction the negative roll force deviation becomes smaller in a 
more  or  less  linear  manner.  Behind  this  reduction  the  deviation  remains  almost  steady.  Therefor  two 
connected linear functions were selected to describe the correlation. The program automatically calcu-
lates the point where the two functions are connected. 

73 
 
 
Figure 84:  Positive roll force deviation in dependence of the total reduction. 

Figure 85:  Negative roll force deviation in dependence of the total reduction. 

2.4.5.3  Development of an algorithm for calculating the roll force limits. 
To determine the roll force limits for the pass schedule calculation the results from the flatness analyses 
and  the  roll  force  variation  needs  to  be  brought  together  (see  Figure  86).  A  function  was  developed 
which merges the results for a certain strip using the defined functions (a screenshot of the programs 
source code is given in Appendix 1 Figure 115).  

i

h
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8000

6000

4000

2000

0

3

Roll force limits indicated by flatness

max. Roll force
best Roll force
min. Roll Force

Roll force deviation

positive Roll Force deviation
negative Roll Force deviation

i

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2000
1500
1000
500
0
‐500
‐1000
‐1500

2
1
Exit thickness [mm]

0

0

20

Merged Roll force limits

40

60

Total reduction [%]

80

100

i

h
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7000

6000

5000

4000

3000

2000

1000

0

max. Roll force
best Roll force
min. Roll Force

2,5

2

1,5

1

0,5

Exit thickness [mm]

Figure 86:  Merging roll force limits. 

74 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The user can view and evaluate the resulting roll force limits for different strip dimensions at the third 
section of the user interface (see Figure 87 as an example). Here the user also has the possibility to de-
fine some damping to soften the max. roll force. This option can become necessary since otherwise in 
many  cases  pass  schedules  would  be  calculated,  where  in  all  passes  a  roll  force  is  required  which  is 
equal  or  close  to  the  un-damped  max.  roll  force  to  meet  the  final  thickness.  But  especially  when  the 
strip becomes thinner it can be beneficial to have the roll force more close to the best roll force. This 
ensures  a  safer  rolling  and  (known  from  experience)  increases  the  acceptations  by  the  mill  operators. 
(However, to damp the maximum roll force is just an option and can remain unused if wanted.)  
After the evaluation and definition of all functions the data can be stored into a file for the later use at 
the pass schedule calculation. Together with the functions several additional values of the analysis are 
stored.  Basically  these  are  the  taper  roll  information’s  (where  applicable),  the  strip  width  and  strip 
thickness ranges and the crown values of all rolls. 

Figure 87:  Resulting roll force limits for a certain strip. 

Integration into the pass schedule calculation. 

2.4.5.4 
The  current  pass  schedule  program  provides  the  possibility  to  define  several  calculation  parameters 
which are considered at the pass schedule calculation. For a better handling the mill operator can store 
this parameters into a file with should have a meaningful filename (in this example the calculation pa-
rameter for the material Austenite). The number of parameter files which can be defined is (in principle) 
unlimited. (Other parameter like mill data and parameter of the coolant device are defined once during 
setup of the program for one mill.) 

Figure 88:  Current handling of pass schedule calculation parameters. 

In front of rolling a new coil (and a new pass schedule is required) the operator can select one of the 
previously created calculation parameter files and subsequent start the pass schedule calculation (Figure 
89).  

75 
 
 
 
For the next to roll coil the operator can (if required) a different parameter file (e.g. if a different mate-
rial is to roll). 

Figure 89:  Screenshot of the pass schedule calculation program. 

To use the (previously) investigated roll force limitations for the pass schedule calculation the existing 
file  management  of  the  current  calculation  parameters  was  enlarged  as  shown  in  Figure  90.  Here  the 
user can select an existing roll force limitation file (in this case “taper 120.rfli”) and define if the roll 
force limits shall be used and under which conditions. When this step is completed it means, that this 
roll force limitations are linked to the current active parameter file (in this case “Austenit.calc”) and that 
the next time a pass schedule calculation is carried out, the roll force limitations are considered. (Up to 
six different files can be managed e.g. for different strip width ranges or taper roll types.) 

76 
 
 
 
Figure 90:  Screenshot of the user interface to manage the roll force limit files. 

The roll force limitations which are stored at the file (here in file “taper 120.rfli”) remain active unless 
the content of this file may change e.g. by a subsequent analyse (as described in the previous chapter). 
This means that the mill operator periodically needs to become active to have the roll force limitations 
up  to  date.  While  the  analysis  of  measured  process  data  runs  automatically  (as  described  in  chapter 
2.4.5.1 and chapter 2.4.5.2) a manual step (as described in chapter 2.4.5.3) is included to validate and 
confirm  the  results.  (This  procedure  shall  ensure  that  unexpected  fails  of  the  program  do  not  lead  to 
strange pass schedules.) 
Unless the roll geometry of the intermediate rolls (roll crown, taper form) remain steady it is adequate 
to carry out the analysis every 6 month. 
Following any roll geometry change (e.g. caused by findings given by the roll geometry optimisation) 
an analysis should be done after 2 month, 6 month and then again every 6 month. 
In some cases it can become necessary to modify the roll force limitations (e.g. for the setup of a new 
system where no process data is present and parameter files from a similar mill are used). In this case 
the user has optional the possibility to view and edit the selected roll force limitations. A screenshot of 
this user interface is presented in Appendix 1 Figure 116. 

The next step was the modification of the pass schedule calculation to consider the new roll force limits 
and the indicated best roll force. First the matching roll force limit parameters are selected based on the 
current  strip  width  and  roll  geometry  data  (roll  crowns  and  taper  type).  Than  the  roll  force  limits  are 
calculated for the current strip using the same function as already used for the evaluation of the result 
(see previous chapter). 
Basically the pass schedule calculation is subdivided into two major parts. In part one the required total 
number of passes is calculated by using the max. possible reduction at each pass. Furthermore in part 
one the thickness range (wherein the final pass schedule can be located) for each pass is defined consid-
ering  also  the  min.  possible  reduction.  Here  a  function  was  included  which  iteratively  calculates  the 
maximal  or  minimal  reduction  for  a  certain  pass  considering  the  corresponding  roll  force  limits  (A 
screenshot of this program part is presented in Appendix 1 Figure 117). In Figure 91 an example for the 
resulting thickness ranges is demonstrated. 
Within the second major part the program searches for the thickness distribution which meets a defined 
optimization criterion in a best way. Therefor a new criterion was integrated with the target that the roll 
force at each pass shall be as close as possible to the best roll force. Since this cannot be arrived for all 
passes the algorithm is designed in such a way that the last passes do have priority. The red curve in 
Figure 91 gives an example for the final thickness distribution. 

77 
 
 
Figure 91:  Thickness ranges (white curves) and final thickness distribution (red curve). 

2.4.5.5  Test calculations to validate the new calculation approach. 
Several test calculations were carried out to validate the calculation approach and to evaluate the effect 
on performance. Subsequent some of the results are presented. 
Basic data for the calculations:  
Entry thickness 2.6 mm; Target thickness 0.4 mm; Coil weight 20t; Material stainless steel 1.4301 
The first calculation was carried out for a strip width of 1250 mm and a work roll diameter of 100 mm 

Figure 92:  Example pass schedule strip width 1250 mm and work roll diameter 100 mm. 

The  total  rolling  time  for  this  pass  schedule  is  calculated  with  68  min  and  the  production  rate  with 
17.6 t/hour. 
The next figure demonstrates the calculation result for the case that the strip width is 1290 mm and the 
work roll diameter is 90 mm. The required number of passes is reduced by 3 passes, but also the rolling 
time decreases down to 55 min and the production rate increases to 22.9 t/hour (= + 30% compared to 
the previous case). 

78 
 
 
 
Figure 93:  Example pass schedule strip width 1290 mm and work roll diameter 90 mm. 

But even that the reductions at the passes are clear higher the roll force limits are not exceeded and the 
roll force level at the last passes is close to the best roll force (see also the subsequent Figure 94). Back-
ground  is  that  the  smaller  work  roll  diameter  leads  to  clear  lower  roll  forces.  Furthermore  the  wider 
strip allows a higher roll force level. 

Figure 94:  Roll force distribution of the pass schedule. 

The example calculations basically do show that this calculation approach is reacting more flexible on 
different rolling conditions but also demonstrate the possible potential regarding the mill productivity if 
no other limitations are present. 

79 
 
 
 
 
 
2.4.6  Validation of the system under industrial conditions 

(Work Package 6) 

Aim of this task was the system test and validation under industrial conditions. 

2.4.6.1  Preliminary rolling test to consider the roll force limits. 
To analyse the new way of calculation a rolling test was carried out at which the pass schedule calcula-
tion was done “offline” on a separate computer. For the test a strip was selected which usually is rolled 
in 12 passes. The strip dimensions have been: Strip width 1296 mm; Entry thickness 2.5 mm; Target 
thickness 0.39 mm; Material 1.4301. To achieve higher reductions as usual also work rolls with a diam-
eter of 90 mm were used.  
The strip was rolled in 9 passes accordant to the calculated pass schedule (shown in Figure 24). At no 
pass  any  correction  from  the  mill  operator  was  necessary  and  the  achieved  flatness  at  all  passes  was 
good. 

Figure 95:  Pass schedule of the first test rolling. 

2.4.6.2  Online validation of the new program. 
The program was installed at the online system. At this also the data communication has been enlarged 
to have all current roll geometries available in front of a calculation. 
The  validation  starts  at  mill  1  by  rolling  several  strips  at  which  the  surface  requirements  were  low 
(beamless surface). It was possible to roll all strips without manual modifications. Typically one or two 
passes could be saved compared to the so far usual pass schedules. However, the available work rolls 
were relative large (diameter ≈ 100 mm) so that the reduction at the first passes was not as high as at the 
first rolling test. 
The  validation  was  continued  with  strips  which  shall  have  high  gloss  surface  behind  annealing.  This 
time thinner work rolls were available (diameter ≈ 80 mm) so that higher reductions could be achieved. 
Subsequent the pass schedule is shown for the first strip. 

Material
14301

Width
1295

Workroll diameter
82

Pass

1

Entry thickness 2,520
Exit thickness 1,720
31,7

Reduction

2
1,720
1,402
18,5

3
1,402
1,159
17,3

4
1,159
0,960
17,2

5
0,960
0,794
17,3

6
0,794
0,657
17,3

7
0,657
0,551
16,1

8
0,551
0,467
15,2

9

0,467 mm
0,400 mm
14,3 %

81 
 
 
 
Especially at the first pass the reduction was clear higher as usual. During rolling this pass it could be 
observed that the roll force becomes much higher than calculated (see Figure 96). At this the deviation 
between calculated and measured roll force was temporary up to 55%. (Usual is a range of about ± 5%).  

Roll Force at 31% thickness reduction

]

N
k
[
e
c
r
o
F
l
l

o
R

12000

10000

8000

6000

4000

2000

0

Measured Roll Force

Calculated Roll Force

Rolling Speed

800

700

600

500

400

300

200

100

0

]
i

m
/
m

[
d
e
e
p
S
g
n

i
l
l

o
R

Figure 96:  Calculated versus measured roll force at 31% thickness reduction. 

Due to the very high roll force the strip flatness at this pass was almost critical and both flatness actua-
tors (BUR crown and taper rolls) need to be adjusted up to their mechanical limits. Furthermore, a visu-
al surface inspection did show that the surface became very rough after rolling this pass. Even that the 
roll force was such higher at pass 1 the effect was not present at the subsequent passes. All remaining 
passes could be rolled without any problems. However, a later quantifying of the surface quality (be-
hind the bright annealing line) did show that this strip had clear pronounced “heat / pressure stripes”. 
It needs to be stated that also at the first rolling test some higher roll force at the first pass was observed. 
However, here the effect was not such pronounced and therefore not detailed analysed. 
The rolling of one further strip with a similar high reduction did confirm the effect. Here at the first pass 
the roll force was about 35% higher than calculated.  
The only explanation for the rough surface and the increased roll force can be seen in a strong increased 
friction caused by the high reduction. In turn this means that the lubrication film becomes instable when 
a certain reduction is exceeded. 
Consequently the maximum allowed reduction was decreased in a first step to 25%. The analysis of the 
first pass does show that beside the reduction also the rolling speed has an influence. While at a low 
rolling speed the deviation between measured and calculated roll force is relative low (≈ 6%) at a roll-
ing speed of about 390 m/min the deviation increases up to 34%. Reviewing roll force and rolling speed 
at this pass does show a clear correlation between both values (Figure 97). 

82 
 
 
 
 
 
 
]

N
k
[
e
c
r
o
F
l
l

o
R

8000

7500

7000

6500

6000

5500

5000

4500

4000

3500

3000

Roll Force at 25% thickness reduction

Measured Roll Force

Calculated Roll Force

Rolling Speed

800

700

600

500

400

300

200

100

0

]
i

m
/
m

[
d
e
e
p
S
g
n

i
l
l

o
R

Figure 97:  Calculated versus measured roll force at 25% thickness reduction. 

Even that the roll force was temporary 7500 kN this roll force was not critical in conjunction with the 
strip flatness. But the deviation of 34% indicates that most possible the lubrication film becomes more 
or less instable and thus a high risk of increased surface defects is given. 
For  the  following  strips  the  maximum  allowed  reduction  was  stepwise  decreased  until  the  maximum 
roll force deviation surly falls below 5% and the influence of rolling speed does not exceed 10%. This 
could be arrived at a limitation of about 20% thickness reduction for the first pass. 
At  this  point it  shall  be  noted  that  such  a  strong  limitation  was  not  expected.  At  a  former  project  [1] 
several parameter were analysed in conjunction with the surface development when rolling a sequence 
of passes. One parameter has been the influence of different reductions on the surface properties. Here 
rolling tests with thickness reductions up to 32% at the first pass were carried out. The final conclusion 
of the rolling tests has been “that different pass reductions do not lead to notable differences in surface 
structure” (at the final strip thickness).  
The validation was continued now at both mills and with the required limitations to avoid the previous-
ly described effect but also to meet the surface requirements. The program worked stable and did pro-
vide improved pass schedules especially in cases outside the usual product range. Such cases are given 
e.g. for high-strength material, for thick and narrow strips and when large work rolls are used. Here in 
the past the thickness reductions often need to be decreased manual to achieve a suitable flatness. 
The following example (Table 10) should demonstrate such a seldom but nevertheless possible constel-
lation  and  the  effect  on  the  new  pass  schedule  calculation.  The  maximum  roll  force  at  this  example 
(given in the first row) is calculated with the help of the roll force limitations under consideration of the 
current strip width (refer also to Figure 81 and Figure 83 in chapter 2.4.5.1). Especially at the first pass-
es the maximum roll force would be clear exceeded when the roll force limitations are not taken into 
account. Under the given conditions three additional passes would be required to ensure that at no pass 
the limitations are passed. 

83 
 
 
 
 
 
 
Material

14310

Width

1250

Workroll diameter

100

Max. Roll Force

8676

8502

8363

8237

8118

8002

7889

7775

7664 kN

Pass schedule without considering the roll force limitation

Pass

1

Entry thickness

4,000

Exit thickness

3,312

Reduction

17,20

2

3,312

2,884

12,92

3

2,884

2,597

9,95

Roll Force

9696

10066

9711

New Pass schedule

Pass

1

Entry thickness

4,000

Exit thickness

3,446

Reduction

13,85

2

3,446

3,109

9,78

3

3,109

2,877

7,46

Roll Force

8449

8307

8113

4

2,597

2,372

8,66

9233

4

2,877

2,689

6,53

7997

5

2,372

2,176

8,26

6

2,176

2,000

8,09

8893

8610

mm

mm

%

kN

5

2,689

2,525

6,10

6

2,525

2,378

5,82

7

2,378

2,243

5,68

8

2,243

2,117

5,62

9

2,117 mm

2,000 mm

5,53 %

7879

7709

7537

7385

7224 kN

Table 10:  Comparison old and new pass schedule 

The situation changes clear for a wider strip and when the used work roll is thinner (Table 11). Consid-
ering the new strip width the maximum possible roll force increases significantly while at the same time 
the roll force at each pass becomes lower due to the thinner work roll. Thus, three passes can be saved 
in this case. 

Material

14310

Width

1330

Workroll diameter

80

Max. Roll Force

9754

9523

9318

9127

8942

8758

Pass

1

Entry thickness

4,000

Exit thickness

3,291

Reduction

17,73

Roll Force

9214

2

3,291

2,909

11,61

9009

3

2,909

2,622

9,87

8962

4

2,622

2,388

8,92

8683

5

2,388

2,184

8,54

6

2,184

2,000

8,42

8371

8115

Table 11:  Pass schedule for strip width 1330 mm 

7

8

9

kN

mm

mm

%

kN

The example demonstrates the clear benefit of the program since it reacts in a clear more flexible way 
on the different rolling conditions. 
One further benefit is the separation of limitations e.g. required to meet the surface quality (like in this 
case) and the limitations concerning the strip flatness. Through this it becomes much easier for the mill 
operator to identify the correct reduction limitations where necessary. 
However, the major part of the product range at this plant requires a very high surface quality. This, in 
turn, requires strict reduction limitations so that in the major number of cases the required number of 
passes (to roll one strip) could not be decreased. Therefore the primarily expected increased productivi-
ty could not be achieved at this plant. 
The new calculation approach is still in use. Subsequent some examples shall be demonstrated, how the 
pass  schedule  was  designed  in  past  compared  with  the  way  how  the  operator  did  roll  these  types  of 
strips (data taken from the long term database) and how the strips are rolled based on the new pass cal-
culation approach. 
The examples are given for two types of materials which clearly differ from each other. Subsequent the 
adapted  stress  strain  curve  for  both  materials  is  demonstrated.  (Adapted  means  that  the  stress  strain 
curve is tuned in such a way that measured and calculated roll force fit together). 

84 
 
 
 
]
2
^
m
m
/
N

[
h
t
g
n
e
r
t
s
d
e
Y

i

l

Stress strain curve (adapted to measured roll force)

1800

1350

900

450

0

0

14310

14301

20

40

60

80

100

Total reduction  [%]

Figure 98:  Stress strain curves of material 1.4310 and material 1.4301. 

The examples are given for two mills. 

Mill 1 Mill type: Sundwig 20 high mill

Max. Roll Force:
12000 kN Width range: 800 ‐> 1350 mm
Max. Power:
5200 kW
Thickness range: 5 ‐> 0.15 mm
50 kNm
Max. Torque:
Max. Tensile Coiler: 400 kN

The subsequent tables demonstrate first the old pass schedule calculation result, following this the way 
the operator did roll these strips in the past and finally the way the strips are currently rolled based on 
the  new  pass  schedule  calculation  approach.  At  the  last  row  the  max.  roll  force  concerning  the  strip 
flatness is given. 

Material

14301

Width

1295

Workroll diameter

92,4

Calculated pass schedule using empirical determined limitations (=max. reduction)

Pass

1

2

3

4

5

6

7

8

9

10

11

12

Entry thickness 2,520

2,066

1,710

1,429

1,210

1,030

0,878

0,750

0,644

0,556

0,490

0,439 mm

Exit thickness 2,066

1,710

1,429

1,210

1,030

0,878

0,750

0,644

0,556

0,490

0,439

0,400 mm

Reduction 18,02

17,23

16,43

15,33

14,88

14,76

14,58

14,13

13,66

11,87

10,41

8,88 %

Roll Force 5028

6282

6722

6510

6322

6328

6268

6215

6232

6056

5941

5812 kN

Max. reduction

18,0

17,2

16,4

15,3

14,8

14,7

14,5

14,2

14,0

12,0

11,0

10,0 %

That way (typically) rolled by the operator

Pass

1

2

3

4

5

6

7

8

9

10

11

12

Entry thickness 2,520

2,057

1,702

1,421

1,203

1,025

0,869

0,743

0,642

0,561

0,496

0,442 mm

Exit thickness 2,057

1,702

1,421

1,203

1,025

0,869

0,743

0,642

0,561

0,496

0,442

0,398 mm

Reduction 18,36

17,29

16,47

15,34

14,84

15,23

14,44

13,60

12,60

11,62

10,83

9,92 %

Roll Force 5155

6301

6639

6325

6092

5974

5776

5477

5171

4967

4739

4390 kN

That way rolled based on the new pass schedule calculation

Pass

1

2

3

4

5

6

7

8

9

10

11

12

Entry thickness 2,520

2,078

1,720

1,443

1,222

1,039

0,886

0,758

0,652

0,566

0,498

0,444 mm

Exit thickness 2,078

1,720

1,443

1,222

1,039

0,886

0,758

0,652

0,566

0,498

0,444

0,400 mm

Reduction 17,54

17,23

16,11

15,32

14,98

14,71

14,43

13,97

13,17

11,99

11,02

9,91 %

Roll Force 5155

Max.Roll force 7834

6301

8093

6639

8158

6325

8080

6092

7860

5974

7770

5776

7511

5477

7381

5171

7252

4967

7122

4739

6993

4390 kN

6798 kN

Table 12:  Comparison of pass schedules for material 14301 (mill 1) 

85 
 
 
 
 
 
 
 
 
It can be seen that for this type of strips the pass schedules are very similar. Since this material and strip 
dimension covers a large part of the product range the empirical limitations do meet the requirements 
very well. 

Material

14310

Width

1280

Workroll diameter

94,5

Calculated pass schedule using empirical determined limitations (=max. reduction)

Pass

1

Entry thickness

2,930

Exit thickness

2,389

Reduction

18,46

Roll Force

6232

Max. reduction

18,5

2

2,389

1,969

17,58

7946

17,5

3

1,969

1,644

16,51

8697

16,5

That way (typically) rolled by the operator

Pass

1

Entry thickness

2,930

Exit thickness

2,383

Reduction

18,66

Roll Force

6424

2

2,383

2,025

15,02

7206

3

2,025

1,758

13,18

7449

4

1,644

1,380

16,06

8771

16,0

4

1,758

1,489

15,34

7362

5

1,380

1,178

14,66

8517

15,6

5

1,489

1,309

12,05

7066

That way rolled based on the new pass schedule calculation

Pass

1

Entry thickness

2,930

Exit thickness

2,387

Reduction

18,53

Roll Force

Max. Roll Force

6095

7404

2

2,387

1,992

16,55

7516

7706

3

1,992

1,744

12,45

7481

7872

4

1,744

1,541

11,64

7473

7955

5

1,541

1,363

11,55

7485

7834

6

1,178

1,043

11,45

8055

14,8

6

1,309

1,173

10,44

6974

6

1,363

1,208

11,37

7512

7718

7

1,043

0,946

9,29

7744

13,3

7

1,173

1,057

9,88

6807

7

1,208

1,074

11,09

7663

7687

8

0,946

0,872

7,81

7485

12,5

8

1,057

0,961

9,10

6705

8

1,074

0,969

9,78

7571

7642

9

0,872

0,812

6,90

7320

12,0

9

0,961

0,879

8,49

6553

9

0,969

0,885

8,67

7440

7552

Table 13:  Comparison of pass schedules for material 14310 (mill 1) 

mm

mm

%

kN

%

10

0,879 mm

0,812 mm

7,61 %

6589

kN

10

0,885 mm

0,812 mm

8,25 %

7405

7462

kN
kN

Here  it  can  be  seen  that  for  the  more  seldom  rolled  material  1.4310  the  empirical  limitations  do  not 
meet the requirements. Since the operator do know (from experience) that especially at the passes 2 to 5 
the roll force will become too high (considering the strip flatness) they typically add one pass and did 
reduce the reduction at these passes. What also becomes visible is that the consideration of the flatness 
based roll force limitations does provide a pass schedule which is very close to the way the operator did 
(manual) design the pas schedule in the past so that the strip can be rolled without manual modifica-
tions. 
The next examples demonstrate the results for mill 2. 

Mill 2 Mill type: Sendzimir 20 high mill

14000 kN Width range: 800 ‐> 1550 mm
Max. Roll Force:
6740 kW
Thickness range: 5 ‐> 0.15 mm
Max. Power:
Max. Torque:
75 kNm
Max. Tensile Coiler: 450 kN

Material

14301

Width

1290

Workroll diameter

90,5

Calculated pass schedule using empirical determined limitations (=max. reduction)

Pass

1

Entry thickness

4,420

Exit thickness

3,710

Reduction

16,06

Roll Force

6147

Max. reduction

17,0

2

3,710

3,143

15,28

6987

15,6

3

3,143

2,786

11,36

6515

14,8

4

2,786

2,502

10,19

6167

14,0

5

2,502

2,259

9,71

5902

12,9

6

2,259

2,049

9,30

5644

12,0

7

2,049

1,866

8,93

5432

10,0

8

1,866

1,707

8,52

5270

9,5

mm

mm

%

kN

%

86 
 
 
 
 
 
 
That way (typically) rolled by the operator

Pass

1

Entry thickness

4,420

Exit thickness

3,737

Reduction

15,46

Roll Force

6022

2

3,737

3,239

13,33

6495

3

3,239

2,854

11,89

6624

4

2,854

2,544

10,86

6351

5

2,544

2,285

10,18

6038

That way rolled based on the new pass schedule calculation

Pass

1

Entry thickness

4,420

Exit thickness

3,686

Reduction

16,61

Roll Force

Max. Roll Force

6285

6642

2

3,686

3,226

12,48

6382

6596

3

3,226

2,889

10,45

6273

6550

4

2,889

2,596

10,15

6158

6458

5

2,596

2,334

10,10

6018

6366

6

2,285

2,064

9,68

5751

6

2,334

2,099

10,05

5902

6319

7

2,064

1,873

9,24

5511

7

2,099

1,888

10,05

5780

6273

8

1,873

1,707

8,84

5347

8

1,888

1,707

9,60

5498

6227

Table 14:  Comparison of pass schedules for material 14301 (mill 2) 

mm

mm

%

kN

mm

mm

%

kN
kN

Here the pass schedules are quite similar except pass 2 of the old pass schedule. For pass 2 the operator 
typically reduced the reduction. The reason becomes clear when the max. possible roll force regarding 
the strip flatness (last row) is considered. 

Material

14310

Width

1290

Workroll diameter

93

Calculated pass schedule using empirical determined limitations (=max. reduction)

Pass

1

Entry thickness

2,710

Exit thickness

2,195

Reduction

19,00

Roll Force

6641

Max. reduction

19,0

2

2,195

1,852

15,63

7105

15,6

3

1,852

1,585

14,42

7382

14,8

That way (typically) rolled by the operator

Pass

1

Entry thickness

2,710

Exit thickness

2,201

Reduction

18,79

Roll Force

6594

2

2,201

1,868

15,10

6965

3

1,868

1,623

13,14

7059

4

1,585

1,375

13,25

7152

14,0

4

1,623

1,432

11,74

6766

5

1,375

1,210

12,00

6877

12,9

5

1,432

1,277

10,86

6537

That way rolled based on the new pass schedule calculation

Pass

1

Entry thickness

2,710

Exit thickness

2,195

Reduction

19,00

Roll Force

Max. Roll Force

6641

7125

2

2,195

1,855

15,49

7073

7100

3

1,855

1,626

12,35

6865

6965

4

1,626

1,444

11,19

6622

6946

5

1,444

1,290

10,67

6488

6896

6

1,210

1,078

10,91

6680

12,0

6

1,277

1,148

10,06

6388

6

1,290

1,161

10,00

6374

6827

7

1,078

0,970

10,02

6506

12,0

7

1,148

1,041

9,34

6255

7

1,161

1,051

9,48

6298

6777

8

0,970

0,880

9,28

6355

11,0

8

1,041

0,949

8,83

6160

8

1,051

0,957

8,94

6199

6698

9

0,880

0,802

8,86

6216

9,5

9

0,949

0,870

8,33

6038

9

0,957

0,875

8,57

6118

6628

Table 15:  Comparison of pass schedules for material 14310 (mill 2) 

mm

mm

%

kN

%

10

0,870 mm

0,802 mm

7,86 %

5896

kN

10

0,875 mm

0,802 mm

8,34 %

6054

6529

kN
kN

Also here it becomes visible that for the more seldom rolled material 1.4310 the empirical determined 
limitations do not meet the requirements. As at the other mill the operator did add one pass to ensure 
that the resulting roll force is at a level which results on proper flatness. The new pass schedule calcula-
tion meets these requirements here, too. 
The examples demonstrate that the consideration of the strip flatness by the use of flatness based roll 
force  limitations  do  work  and  that  with  it  pass  schedules  are  calculated  which  can  be  rolled  without 
manual modifications. 

87 
 
 
 
 
 
 
2.4.6.3  Online validation of the roll geometry optimisation. 
At mill 1 no modifications of the intermediate roll crowns or the taper geometry were required. But in 
frame to avoid the surface defect “diagonal waves” one taper roll was tested at which the taper had a 
taper length of 90 mm and a taper inclination of ≈ 5,6 ‰ (see also chapter 2.4.4.8). Therefor the results 
of these rolling tests can also be used to verify the accuracy of the roll geometry calculation. By taking 
the  data  of  the  usual  used  taper  the  estimated  new  actuator  position  distribution  can  be  calculated  as 
demonstrated in Figure 99. (The estimated new distribution is marked by the thick lines). 

Figure 99:  Calculated actuator distribution for the test taper. 

By comparing the calculation result with the resulting distribution of taper “90” the calculation accura-
cy can be quantified. In the subsequent Figure 100 both distributions of the mean positions are given. 

]

m
m

[
n
o
i
t
i
s
o
p
r
e
p
a
T

Estimated new mean Position

Resulting new mean Position

200

180

160

140

120

100

80

60

40

20

0

2,4

1,9

1,4

0,9

0,4

Exit thickness [mm]

Figure 100: Calculated versus measured position distribution for the test taper. 

The average deviation between calculation and resulting value is ≈ 5 mm. Since two parameters were 
changed  at  the  same  time  (length  and  inclination) and  in  relation  to  the  mechanical  adjustment  range 
(200 mm) the calculation result can be rated as quite good. 

88 
 
 
 
 
 
 
 
2.5  Conclusions 

Within the framework of this project the intelligent use of existing process data was intended to replace 
the use of empirical values and to replace the trial and error approach to achieve optimal roll geome-
tries. 

To replace the empirical values the strip flatness and the pre-calculated probability for the occurrence of 
surface defects should be used at the pass schedule calculation.  

A physical flatness model was recompiled and fitted for use together with other software used. Verifica-
tions  against  mill  measurements  showed  that  the  model  response  to  differential  control  actions  was 
reasonably correct. In absolute terms however the model predictions were differing from measurements. 
By  physically  explainable  corrections  to  the  simplified  model  calculations  it  is  however  possible  to 
significantly improve predictions also in absolute terms.  

The elastic deformation of the mill cluster is quite well modelled. Much more difficult is the modelling 
of the deformation strains and stresses in the rolled material. The constitutive laws of deformation and 
interface friction models have still to be improved to give trustworthy results. Calculation speed of ad-
vanced modelling methods as FEM still have to be increased by one or two orders of magnitude to be 
fast enough to be useful for cold rolling. Single calculations can be done to study specific cases. 

An  important  difficulty  is  that  the  strip  thickness  profile  is  seldom  known  with  sufficient  accuracy. 
Since flatness is directly coupled to how the mill through its settings tries to change this profile this is 
an important issue. If the strip profile would be accurately known it should be much easier to find the 
optimal pre-setting of the mill. 

To consider the strip flatness roll force limitations were determined within it is ensured that the flatness 
actuators will be able to achieve the target strip flatness. Example calculations do show that this calcula-
tion approach is reacting much more flexible on different rolling conditions like different strip width, 
different work roll diameter or different material. In case that no other limitations are required the cal-
culations also do demonstrate that a clear increased production rate could be achieved for certain strips. 
A clear further benefit of the calculation approach is the separation of limitations e.g. required to meet 
the  surface  quality  from  the  limitations  concerning  the  strip  flatness.  Through  this  it  becomes  much 
easier for the mill operator to identify the correct reduction limitations where necessary. 
The algorithm was validated successful at two mills. The program worked stable and did provide im-
proved pass schedules especially in cases outside the usual product range. Such cases are given e.g. for 
high-strength material, for thick and narrow strips and when large work rolls are used. 
However,  the  validation  did  also  show  that  strong  limitations  need  to  be  considered  to  avoid  surface 
defects and to achieve the, at this plant, required surface gloss. Thus in the major number of cases the 
required number of passes (to roll one strip) could not be decreased so that the primarily expected in-
creased productivity could not be achieved. 

Two types of frequently occurred surface defects were analysed. One named as “heat / pressure stripes” 
and one named “diagonal waves” (fishbone effect).  
The defect “heat / pressure stripes” is a surface defect which becomes visible behind the bright anneal-
ing line and only for high gloss strips. The defect is characterised by slight roughness differences be-
tween rolling direction and cross to the rolling direction and by a decreased surface isotropy. The ap-
pearance of the defect leads to the assumption that the lubrication occasional local decreases and with it 
provokes a higher roughness. Data based analyses do show that the frequency of defects clear increases 
when at the first two passes a certain relative thickness reduction and within passes 4 to 8 a certain strip 
temperature is exceeded. Since in the major number of cases the total number of passes is higher than 8 
it  also  means  that  a  defect,  once  provoked,  cannot  be  completely  removed  by  the  subsequent  passes. 
With  the  help  of  the  analysis  some  rolling  rules  were  derived  to  minimize  the  frequency  of  heat  and 
pressure stripes. However, when lower surface requirements are given or e.g. a different lubrication is 
present the required limitations need to be determined again. 
The surface defect “diagonal waves” is a form defect occurring at the cold rolling process which pro-
vokes slight beamless and diagonal shadows behind the bright annealing line. Surface measurements on 
annealed specimen did not show differences in roughness between defected and non-defected sections. 
Only measureable cross to the rolling direction was a difference of gloss between the two sections. 

89 
 
Measurements on four samples that all had “diagonal waves” showed that they also had long edges. For 
two of them the long parts were concentrated to a narrow region close to the edges but the two others 
had  a  more  or  less  parabolic  distribution  of  the  length  over  the  width.  The  only  conclusion  from  the 
measurements is that rolling with loose edges and short centre might be risky for the occurrence of “di-
agonal waves”. Analysis did show a correlation for one type of flatness deviation (the centre flatness) 
and for the relation neutral point / roll angle. However, a modification of both values did not lead to an 
indictable decrease of the defect frequency. Since no clear correlations were detected no rolling rules or 
algorithms for a pre-calculation could be derived for this type of defect. 

To  replace  the  trial  and  error  approach  to  achieve  optimal  roll  geometries  a  program  was  developed 
with which the mill operator can determine the best suitable roll crown of the intermediate rolls (driven 
or idle rolls) as well to determine the ideal length and inclination of the taper rolls. The program period-
ically and automatically analysis the current as-is state which than can be reviewed with the help of a 
user interface. At this the program furthermore provides the possibility to predict how the change of any 
roll crown or the change of taper length or taper inclination will influence the future used range of the 
flatness  actuators.  Thus  the  mill  operator  has  a  very  helpful  tool  to  investigate  those  roll  geometries 
which fits best to his range of products. The calculation accuracy was successful verified by comparing 
the calculation results with measured data.  

In frame of this project one idea should be tested at which one upper and one lower taper roll should be 
replaced by CVC rolls to obtain an additional flatness actuator and thus to enlarge the flexibility of the 
mill.  The  rolling  test  carried  out  to  test  this  approach  did  show  that  this  does  provoke  an  asymmetry 
close to and direct at the strip edge which than provokes possible shearing tensions at this range. Fol-
lowing this the deformation stress at the strip edge can suddenly decrease causing heavy strip breaks. 
Due to the fact that such an asymmetry cannot be avoided when using one pair of CVC rolls the final 
conclusion must be that this approach is most possible not applicable. 
A comparison of the initial objectives with the achieved objectives and benefits can be summarized as 
follows. 
A  calculation  approach  was  developed  to  consider  the  pre-calculated  strip  flatness  by  the  automatic 
determination of flatness based roll force limitations and the program was successful integrated into the 
existing  pass  schedule  calculation  program.  A  manual  step  is  included  to  validate  and  confirm  these 
limitations (to ensure that unexpected fails of the program cannot lead to strange pass schedules). The 
manual step is supported by a program with a GUI which enables a fast and easy result analyse. How-
ever, due to this manual step the program is not full auto-adaptive. In periods of e.g. 6 month the opera-
tor needs to carry out the manual step. 
Some findings regarding the surface defects could be obtained. However, a model or clear rules which 
could be transferred to other mills / operator couldn’t be achieved. Furthermore a clear reduction of the 
defect frequency was not achieved. On the other hand the (already existing) reduction limitations were 
confirmed  to  avoid  an  increase  of  the  defect  frequency.  Caused  by  these  limitations  the  expected  in-
crease of productivity couldn’t be achieved at this mill operator. 
The  development  of  a  software  programme  to  optimize  the  roll  geometry  was  carried  out  successful. 
The program supports the operator to analyse the as-is state and to indicate the optimal roll geometry 
which fits best to his product range. A GUI provides an easy to understand handling. 
The carried out rolling tests did lead to the conclusion that the use of the CVC technology (in the fore-
seen way) is most possible not applicable. 

90 
 
 
 
2.6  Exploitation and impact of the research results. 

The consideration of strip flatness for the pass schedule calculation has a clear potential to increase the 
production rate of a mill since this approach accounts the individual rolling conditions and strip parame-
ter  (strip  width,  thickness,  material  strength  etc.)  and  calculates  a  pass  schedule  which  surely  can  be 
rolled in frame of the mill potential. Since the strip flatness no longer has to be considered by simple 
reduction limitations it becomes much easier for the operator to identify other limitations e.g. to achieve 
the required surface quality. 
The  calculation  approach  is  integrated  into  the  BFI  pass  schedule  calculation  program  which  can  be 
used at 20-high mills; 6-high mills as well at 4-mills and for different types of metals. The required data 
for  the  program  has  to  be  transmitted  via  TCP/IP  by  defined  telegrams.  (The  required  content  of  the 
telegrams can be indicated at Table 16Table 1 and Table 17). 
Basically the following data is necessary: 
‐  Strip dimension and material information 
‐  Process data like roll force, strip tension, position of all flatness actuators, rolling speed etc.. 
‐  Measured strip flatness 
‐  Roll geometry of all rolls in use. 
The BFI pass schedule calculation program can be used at each standard PC and can be integrated in 
existing Level 2 and Level 3 Systems. 

With the help of the developed roll geometry optimisation program the operator can easily review the 
current as-is state and can quick and easy determine the optimal roll geometry (roll crown of work roll, 
idle and driven rolls; taper length and taper inclination) under consideration of the product range. Im-
proved roll geometry can significantly increase the mill potential regarding strip flatness and in turn the 
roll force range at which the mill can be operated. Thus the program helps to avoid worse geometries 
which can lead to unnecessary limitations.  
The program is also integrated into the BFI ass schedule program. The roll geometry optimisation basi-
cally requires the same data as the program part for the consideration of strip flatness. However, the so 
far  developed  program  is  designed  for 20  high  mills.  A  transfer  to  other  type of  mills  is  possible  but 
requires some further investigations to account the different behaviour of other flatness actuators (like 
roll bending). 

It is foreseen to publish the results in the technical journal “Stahl und Eisen” and to present it on one of 
the next steel conferences or workshops carried out from the “Stahl Zentrum”. 

91 
 
3  List of Figures. 

Figure 1: 
Figure 2: 
Figure 3: 
Figure 4: 
Figure 5: 
Figure 6: 
Figure 7: 
Figure 8: 
Figure 9: 
Figure 10: 
Figure 11: 
Figure 12: 
Figure 13: 
Figure 14: 
Figure 15: 
Figure 16: 
Figure 17: 
Figure 18: 
Figure 19: 
Figure 20: 
Figure 21: 
Figure 22: 
Figure 23: 
Figure 24: 
Figure 25: 
Figure 26: 
Figure 27: 
Figure 28: 
Figure 29: 
Figure 30: 
Figure 31: 
Figure 32: 
Figure 33: 
Figure 34: 
Figure 35: 

Figure 36: 

15 
Layout 20 high mill. 
15 
Layout of roll cluster and flatness actuators of a 20 high mill. 
16 
Example flatness influence of BUR crown and taper shifting. 
16 
Example flatness influence of Roll force. 
16 
Example rolling situation at a certain pass. 
17 
Example rolling situation more reduction. 
17 
Example flatness deviation compensated. 
18 
Example rolling situation with max. possible reduction. 
18 
Example max. possible reduction larger work rolls. 
23 
Selecting the data where a manual adjustment was done. 
Measured flatness before and after the adjustment and the resulting flatness difference.  23 
24 
Flatness influence of the roll crown adjustment Mill 1. 
24 
Flatness influence of the roll crown adjustment Mill 2. 
25 
Taper forms used at the rolling tests. 
26 
Flatness influence taper 120 (mill 1). 
26 
Flatness influence taper 320 (mill 2). 
26 
Flatness influence of different taper rolls at 1 mm strip thickness. 
27 
Sketch taper roll shifting and diameter difference. 
27 
Flatness influence in dependence of the taper diameter difference at strip edge. 
28 
Taper forms within the range typically covering the strip. 
29 
Linear correlation in dependence of the strip thickness. 
29 
Roll force variation during the last pass (Pass# 10). 
30 
Screenshot of the program to investigate the roll force influence on flatness. 
30 
Roll force influence on flatness at mill 1 and mill 2. 
31 
Flatness influence roll crown change versus backup roll crown. 
31 
Layout of the simple flatness model. 
32 
Layout of the inverse flatness model. 
33 
Integrated model for flatness prediction. 
34 
Calculation procedure in CLUSTER. 
35 
Strip tension distribution change as response to taper roll shift in pass 2, 4 and 6. 
Shape of the taper on the 1st IMRs. 
36 
36 
Influence of work roll diameter on flatness respond of taper adjustment. 
36 
Influence of taper location on flatness respond of taper adjustment. 
37 
Flatness influence of different roll crowns. 
FEM  simulation  of  strip  rolling  with  lateral  flow  to  the  left  (legend  in  mm)  and 
38 
Calculated  and  measured  strip  tension  distribution  at  the  exit  of  pass  4  with  different 

longitudinal stress to the right (legend in MPa). 

values of ξ. 39 

Figure 37: 
Figure 38: 
Figure 39: 
Figure 40: 
Figure 41: 
Figure 42: 
Figure 43: 
Figure 44: 
Figure 45: 
Figure 46: 
Figure 47: 
Figure 48: 
Figure 49: 
Figure 50: 
Figure 51: 
Figure 52: 
Figure 53: 
Figure 54: 
Figure 55: 
Figure 56: 
Figure 57: 
Figure 58: 

Calculated and measured strip tension distribution at the exit of pass 2, 4 and 6. 
Schematic Diagram and Isometric-View of the model. 
: Local width strain and force distribution along the nominal width. 
Approach to use CVC technology in 20 high mills. 
Top view on upper and bottom pair -Taper rolls / CVC Rolls-. 
Layout one upper and one lower taper roll replaced by a cylindrical roll. 
Test constellation with one cylindrical roll. 
Top view on upper and bottom pair -Taper rolls / one cylindrical Roll-. 
First test result with one cylindrical roll. 
Geometric roll gap situation with combined taper - cylindrical rolls. 
Calculation sequence for defining the basic statistical values. 
Layout of the backup roll crown adjustment. 
Determining the backup roll crown. 
Program part to view the current state of the BUR crown. 
New BUR crown distribution caused by an increased roll crown. 
Program part to view the current state of the taper rolls. 
New taper roll distribution caused by an increased taper inclination. 
Flatness change caused by a lateral strip movement. 
Surface topography of the defect free and the heat stripe section. 
Roughness of the defect free and the heat stripe section. 
Histogram max. strip temperature versus heat / pressure stripe defect (all passes). 
Histogram strip temperature versus heat / pressure stripe defect (Pass 6). 

40 
40 
42 
43 
43 
44 
44 
45 
45 
46 
47 
48 
48 
49 
50 
51 
51 
52 
53 
53 
55 
56 

93 
 
Figure 59: 
Figure 60: 
Figure 61: 
Figure 62: 
Figure 63: 
Figure 64: 
Figure 65: 
Figure 66: 
Figure 67: 
Figure 68: 
Figure 69: 
Figure 70: 
Figure 71: 
Figure 72: 
Figure 73: 
Figure 74: 
Figure 75: 
Figure 76: 
Figure 77: 
Figure 78: 
Figure 79: 
Figure 80: 
Figure 81: 
Figure 82: 
Figure 83: 
Figure 84: 
Figure 85: 
Figure 86: 
Figure 87: 
Figure 88: 
Figure 89: 
Figure 90: 
Figure 91: 
Figure 92: 
Figure 93: 
Figure 94: 
Figure 95: 
Figure 96: 
Figure 97: 
Figure 98: 
Figure 99: 
Figure 100: 
Figure 101: 
Figure 102: 
Figure 103: 
Figure 104: 
Figure 105: 
Figure 106: 
Figure 107: 
Figure 108: 
Figure 109: 
Figure 110: 
Figure 111: 
Figure 112: 
Figure 113: 
Figure 114: 
Figure 115: 
Figure 116: 
Figure 117: 

57 
Defect frequency heat /pressure stripes during test series and one month later. 
57 
Defect frequency heat /pressure stripes during one year. 
58 
Histogram relative reduction versus heat / pressure stripe defect (Pass 1). 
58 
Histogram relative thickness reduction at pass 2. 
59 
Relative reduction versus heat / pressure stripe defect (Pass 2). 
60 
Roughness of the defect free and the beamless shadow section. 
60 
Gloss of the defect free and the beamless shadow section. 
61 
Low amplitude buckles. 
62 
Elongation distribution for strip specimens. 
62 
Topography plots of strip specimens, Shapeline system. 
62 
Elongation distribution for strip specimens, Shapeline system. 
63 
Specimen surface height across the width, Shapeline system. 
63 
Topography plots of strip specimens, Swerea MEFOS laser line system. 
Topography plots of rolling I-values for specimen 1, Swerea MEFOS laser line system.  63 
64 
Elongation distribution for strip specimens, Swerea MEFOS laser line system. 
65 
Sketch for description the flatness indicator values. 
66 
Histogram -relation neutral point / roll angle- versus diagonal waves defect. 
66 
Histogram centre flatness versus diagonal waves defect. 
70 
Sequence to calculate the statistical values for all actuators. 
70 
Mean flatness and mean roll force in dependence of the thickness. 
71 
Corresponding statistical values for the taper and the backup roll crown. 
71 
Schematic diagram of the roll force prediction model. 
72 
Demonstration of the required minimum distance of taper edge to strip edge. 
72 
Roll force limits in dependence of the strip thickness. 
73 
Influence of strip width on the roll force limits. 
74 
Positive roll force deviation in dependence of the total reduction. 
74 
Negative roll force deviation in dependence of the total reduction. 
74 
Merging roll force limits. 
75 
Resulting roll force limits for a certain strip. 
75 
Current handling of pass schedule calculation parameters. 
76 
Screenshot of the pass schedule calculation program. 
77 
Screenshot of the user interface to manage the roll force limit files. 
78 
Thickness ranges (white curves) and final thickness distribution (red curve). 
78 
Example pass schedule strip width 1250 mm and work roll diameter 100 mm. 
79 
Example pass schedule strip width 1290 mm and work roll diameter 90 mm. 
79 
Roll force distribution of the pass schedule. 
81 
Pass schedule of the first test rolling. 
82 
Calculated versus measured roll force at 31% thickness reduction. 
83 
Calculated versus measured roll force at 25% thickness reduction. 
85 
Stress strain curves of material 1.4310 and material 1.4301. 
88 
Calculated actuator distribution for the test taper. 
88 
Calculated versus measured position distribution for the test taper. 
99 
Screenshot of the used database. 
102 
Roll numbering for the upper cluster. 
103 
Screenshot of the program (part 1) to analyse the online database. 
104 
Screenshot of the program (part 2) to analyse the online database. 
106 
Flatness evolution of the last 3 sec. before strip break. 
107 
Screenshot of the program to remove outlier or to define a major range. 
Screenshot of the program to calculate the statistic values (Part Roll Force limitation).  108 
109 
Screenshot of the program to calculate the statistic values (Part Roll Geometry). 
110 
Overview page of the program to optimize the roll geometry. 
111 
Screenshot of the program to calculate the new taper position. 
114 
Strip specimen photographs. 
115 
Screenshot of the user interface program to evaluate and define the roll force limits. 
116 
Screenshot of the program to determine the statistical Roll Force data for one pass. 
117 
Screenshot of the program to calculate the statistical Roll Force deviation. 
118 
Screenshot of the program to evaluate the roll force limits for a certain strip. 
119 
Screenshot of the user interface to view and edit the roll force limitation parameter. 
120 
Program part which calculates the max. or min. reduction by the roll force limits. 

94 
 
 
4  List of Tables. 

Table 1: 
Table 2: 
Table 3: 
Table 4: 
Table 5: 
Table 6: 
Table 7: 
Table 8: 
Table 9: 
Table 10: 
Table 11: 
Table 12: 
Table 13: 
Table 14: 
Table 15: 
Table 16: 
Table 17: 
Table 18: 
Table 19: 
Table 20: 

Rolling parameters of the backup roll crown tests. 
Rolling parameters of the taper roll shifting tests. 
Linear correlation between the passes. 
BUR crown adjustment required to compensate crown change. 
Fractional Factorial Design. 
Discriminatory analysis of the heat / pressure stripe defect 
Decision tree and SOM result of the heat / pressure stripe defect 
Discriminatory analysis of the diagonal waves defect. 
SOM and categorized histogram of the diagonal waves defect. 
Comparison old and new pass schedule 
Pass schedule for strip width 1330 mm 
Comparison of pass schedules for material 14301 (mill 1) 
Comparison of pass schedules for material 14310 (mill 1) 
Comparison of pass schedules for material 14301 (mill 2) 
Comparison of pass schedules for material 14310 (mill 2) 
Content of the long-term database (amount: ≈ 50,000 datasets) 
Content of the roll geometry database (amount: ≈ 40,000 datasets) 
Content of the database to analyse the heat / pressure stripe defect 
Content of the database to analyse the diagonal wave defect 
Content of the statistical Roll Force deviation results. 

5  List of Symbols, Indices, Acronyms and Abbreviations. 

24 
25 
28 
37 
41 
54 
54 
65 
65 
84 
84 
85 
86 
87 
87 
101 
101 
112 
113 
118 

Symbols 

Indices 

0 = before roll gap 
1 = after roll gap 

Acronyms 

h = thickness 
h hot = thickness after last hot treatment e.g. after the last annealing 
RF =roll force 

Abbreviations 

OS = Operator side of the mill 
DS = Drive side of the mill 
CVC = Continuously Variable Crown 
BUR = Backup roll 
MEDM = Mill Elastic Deformation Model 
SPDM = Strip Plastic Deformation Model 

95 
 
 
 
 
 
6  List of References 

[1]  Wicklund O., Norberg V., Lathe R.: „ Optimisation of the Rolling Process (Pass Scheduling) to 

Avoid Roll Spalling and Surface Defects “, RFCS Final Report (2006), EUR 22054 EN 

[2]  G.W.D.M. Gunawardene.: "Static model for the Sendzimir 1-2-3-4 cold rolling mill", Meikle 

Ardo House, Cairnoirre, Methlick, Aberdeenshire, June 1990 

[3]  O. Wiklund : "Program development for cluster mills – Final report", MEFOS-report BTF94032, 

1994 (in Swedish) 

[4]  Orowan E. : “The calculation of roll pressure in hot and cold flat rolling”, Proc. Inst. Mech. 

Eng., vol 150, 1943 

[5]  Bland D.R., Ford H. : “The calculation of roll force and torque in cold strip rolling with ten-

sions”, Proc. Inst. Mech. Eng., vol 159, 1948 

[6]  Bryant G.F. : “Derivation and assessment of roll force models from ‘Automation of tandem 

mills’”, Iron and Steel Inst., London, 1973 

[7]  Nakajima K. : “Research on crown control for hot strip mills”, Nippon Steel technical report, No 

15, June 1980 

97 
 
 
 
 
 
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120 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
8  Appendix 2: Data mining techniques 

Allows visualizing data clusters, including non-supervised classification. 

This annex presents a description of the modelling techniques which have been used for the develop-
ment as well as its strengths and weaknesses. 
Self-Organizing Maps (SOM) 
The Self-Organizing Map (SOM) was introduced by Teuvo Kohonen in 1982. The SOM (also known as 
the Kohonen feature map) algorithm is one of the best known artificial neural network algorithms. In 
contrast to many other neural networks using supervised learning, the SOM is based on unsupervised 
learning. 
The SOM is quite a unique kind of neural network in the sense that it constructs a topology preserving 
mapping from the high-dimensional space onto map units in such a way that relative distances between 
data  points  are  preserved.  The  map  units,  or  neurons,  usually  form  a  two-dimensional  regular  lattice 
where the location of a map unit carries semantic information. The SOM can thus serve as a clustering 
tool of high-dimensional data. Because of its typical two-dimensional shape, it is also easy to visualize. 
Another important feature of the SOM is its capability to generalize. In other words, it can interpolate 
between previously encountered inputs. 
Strengths 
- 
Weaknesses 
- 

Does not guarantee faithful approximation to probability density of data samples, although there 
are ways to correct it. 
Sensitive to noise in data (irrelevant features). 

Decision trees represent rules which are legible and simple; therefore the interpretation of re-

- 
Decision Trees 
Decision  trees  are  an  easy  representation  method,  frequently  used  in  supervised  learning  systems,  to 
classify examples from a finite number of classes. They are based on the partitioning of the example set 
according to certain conditions applied to the features values. 
Decision trees are composed by nodes. There are terminal nodes (belong to last level), a root node (ini-
tial) and several intermediate nodes or non-terminals. Relationships between them are also established, 
so the ancestor of one node is called father and any node dependant on any other is called descendent. 
Each node has an associated rule, so the path followed on each node is a function of the answer to the 
rule, arriving to a terminal node, where classification is really carried out. 
Strengths 
- 
sults is direct and intuitive. 
- 
Weaknesses 
- 

It needs rather large sample sizes to work effectively as with small sample sizes the respondent 
groups can quickly become too small for reliable analysis. 
Possible complexity of the resulting model. 
Generalization behaviour. 
Rules are quite sensitive to data instability 

- 
- 
- 
Categorised histograms: 
Categorized histograms are a simple statistic method to detect one-dimensional dependencies between 
input parameters  and  class  information.  By  dividing the  input data  into  groups  by  means  of  the  class 
information (category) and the following comparison of the frequency distributions inside these groups 
one will derive information about the relationship between the selected input and the class parameter. If 
the frequency distributions of the categories are similar, the input parameter hasn't a significant relation 
to  the  class  parameter.  But  if  there  are  obvious  differences  between  the  frequency  distributions,  this 
input has  a  relation  to  the  class  parameter.  By  calculation  of  a  similarity  index  a  list  of  the  input  pa-
rameters can be generated showing the "level of relationship" between this input and the class parame-
ter. 

Computationally fast. 

121 
 
European Commission

EUR 26171 —  Future-oriented supervision of the cold rolling process in reversing mills (Fosucor)

Luxembourg: Publications Office of the European Union

2013 — 121 pp. — 21 × 29.7 cm

ISBN 978-92-79-33085-8
doi:10.2777/41572

123