# Mechanical Characterization and Machinability Behavior of Annealed AISI D6 Cold Working Steel

Authors: Manoj Nayak; Rakesh Sehgal; Rajiv Kumar Sharma
Journal: Indian Journal of Materials Science
 (2015)

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## Abstract

Tool steels in metal forming industry are exposed to complex and aggressive conditions due to multiple effects (mechanical, thermal, or tribological loading) and require defined mechanical properties. Also machining of tool steel with poor machinability like AISI D6 to manufacture form tools is an extremely difficult task. This paper investigates the microstructural, mechanical, and machining behavior of AISI D6 steel in annealed and hardened conditions. Various mechanical tests indicated good hardenability, improved surface hardness, and phenomenal improvement  in tensile strength but extremely poor resistance to impact in both annealed and hardened condition for this steel.  The machining characteristics of AISI D6 steel were evaluated using a 2k unreplicated  full factorial design approach and statistical techniques have been used to assess and identify the significant factors, namely, cutting speed, feed, depth of cut, and approach angle, in minimizing surface roughness and main cutting force while machining this steel with a carbide tool. It was found that the depth of cut, feed, and approach angle are the most significant factors affecting the surface roughness and  depth of cut and feed affect the main cutting force. Cutting speed has no effect on surface roughness and main cutting force in machining of the steel in annealed condition.


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## Body

## 1. Introduction

Tool steels for drawing dies, cold extrusion dies, broaches, mandrels, tooling for compaction of steel powder, thread rolls, burnishing rolls, and forming rolls should have good mechanical properties, exhibit minimal distortion on hardening, and provide good machinability. Metal forming processes such as cold forging, cold deep drawing, thread rolling, or any form of rolling are performed using high strength tool steels. Apart from high resistance to wear, dynamic loading, thermal shocks, and fracture, these steels own a high tensile and compression yield strength to resist plastic deformations at localized stress concentration points in the tooling. Hence well-defined mechanical and tribological properties of the material are required to limit the high cost of wear to metal forming industry incurred due to the complex and demanding phenomenon [1].Tool steel for cold work includes three classes of steel with AISI designation O, A, and D. Each of these classes has high carbon content for high hardness and high wear resistance in cold working applications but differs in alloy content, which affects the hardenability and the carbide distributions incorporated in the hardened microstructure. AISI D6 is high carbon high chromium steel containing carbon 2.00–2.50%. It is further modified to obtain better machinability and less brittleness by lowering the carbon content to 1.00–1.50% and is commercially available as AISI D1, D2, D3, D4, and D5 steel. Good steel machinability is defined as a combination of low power consumption, low tool wear, and good surface finish [2]. These steels should be easily machinable in annealed condition. Steel mills provide the tool steel in the annealed condition so that the machinist can readily machine the tool steel into a premachined tool providing machining allowances. Poor surface finish, high cutting force, and high tool wear are also observed during machining of tool steels. Surface quality generated and machining performance of the tool steels are determined by cutting parameters, types of coolants, types of tool material, and tool coating used during machining.Podgornik et al. [1] in their experimental study found that cryogenic treatment to tool steels improves dimensional stability, abrasive, fatigue, and wear resistance and increases strength and hardness of the material. Amini et al. [3] studied the effects of cryogenic treatment on the wear behavior of AISI D6 tool steel using a pin-on-disk wear tester. The material demonstrated improved wear resistance and hardness due to more homogenized carbide distribution as well as the elimination of the retained austenite compared with the shallow cryogenic treatment. Further improvement in wear resistance and hardness was achieved by keeping the samples for a period of one week at room temperature after quenching (stabilization) as more retained austenite was transformed into martensite. Naravade et al. [4] studied the wear behaviors of AISI D6 tool steel after cryogenic treatment, which showed decreased retained austenite and thereby improvement in wear resistance and hardness. Bressan et al. [5] carried out an experiment to evaluate the mechanical properties of AISI D6 steel in heat treated and in annealed condition. Their results showed an increase in yield stress by 40% and decrease in toughness by 50% after heat treatment.Davim and Figueira [6] experimentally investigated the machinability of AISI D2 tool steel to find the significant factors. The feed rate and cutting time, which, respectively, showed contribution of 29.6% and 32% using statistical techniques, were the most significant factors. Cakir et al. [7] developed mathematical models for predicting the surface roughness of AISI P20 cold work tool steel in annealed condition using two types of inserts. They suggested that, among the cutting parameters, feed rate has the greatest significance and depth of cut the least and observed poor surface finish with higher feed rate and good surface finish with high cutting speed. Fnides et al. [8] in an experimental study developed statistical models for cutting forces in hard turning of AISI H11 hot work tool steel showing depth of cut as the dominant factor instead of feed rate. Bouacha et al. [9] used statistical analysis to find the most significant factors during machining of hardened AISI 52100 material using CBN tools. They found that the surface roughness is influenced by feed rate and cutting speed, main cutting forces are influenced by depth of cut, and thrust forces are sensitive to workpiece hardness and negative rake angle. Lima et al. [10] in an experimental study observed good surface finish while turning a softer steel AISI 4340 steel using low feed rates and depths of cut and improved surface finish at high cutting speed. Lalwani et al. [11] investigated the influence of cutting conditions like cutting speed, feed rate, and depth of cut on cutting forces and surface roughness during hard turning of MDN250 steel using coated ceramic tool and showed that when cutting speed and depth of cut are at high level and feed is at low level, good surface finish is achieved. Ebrahimi and Moshksar [12] observed poor machinability during machining of microalloyed steel (30MnVS6) and quenched tempered (QT) steels (AISI 1045 and AISI 5140), at different cutting conditions (depth of cut was kept constant, feed rate was in range of 0.11, 0.22, and 0.44 mm/rev., cutting speed was 10–250 m/min, and hardness was of 245 and 330 BHN). These studies suggest that machining characteristics of hardened and annealed steel are different and have different significant factors influencing different quality characteristics.The cost of wear to metal forming industry due to complex and demanding mechanical, thermal, chemical, or tribological loading is so high that it requires well-defined mechanical and tribological properties along with continuing development in the field of advanced materials. The concern is of good uniform machinability of tool steels as the cost of machining accounts for a large amount of total cost of tools, moulds, and dies. Otherwise grinding equipment and practices used for tool steels with CBN wheel for the best performance become costlier. Literature survey reveals that only a few studies have been done in evaluating the mechanical and machining behaviour of AISI D6 tool and hence the present study focuses on mechanical and machinability aspects of the tool steel.


## 2. Material and Methods

### 2.1. Metallurgical Test

The material was subjected to metallurgical test according to ASTM E 415 [13] on an Emission Spectrometer, Make: LECO, USA, Model GDS500A. The chemical composition of test material is C 2.130%; Si 0.238%; Mn 0.240%; Cr 11.10%; Ni 0.090%; Mo 0.032%; V 0.130%; Cu 0.030%; Al 0.06%; S 0.02%; P 0.010%; Co 0.025%; W 0.620%; Fe 85.267%. The test material conforms to ASTM A 681 standard of ASM Handbook (Vol. 1) [14]. The carbon content of the steel influences the martensitic hardening and 2.130% of carbon present in this steel is an advantage. Traces of other alloying elements are seen apart from the prominent presence of chromium and tungsten because on austenitizing some of the carbide dissolves in the austenite, thus supplying the matrix with alloying elements necessary for high hardenability and as quenched hardness. The steel is alloyed with Cr, W to get hard and abrasive resistance carbides in the steel. The hard carbides in steel reduce the machinability by giving a high wear on the cutting tool. The presence of tungsten in this steel produces very high densities of stable carbides. The presence of high chromium content enables this steel to resist staining particularly form tools when the steel is hardened and polished. The presence of vanadium benefits the effects of mechanical properties and refines austenite grain size.


### 2.2. Hardness Measurement

The hardness of the steel measured according to BIS, IS: 1586-2000 [15], in annealed condition was 96.8 HRB and 58 HRC after hardening and tempering. On each specimen several measurements were performed across the surface in order to obtain representative average hardness value.


### 2.3. Microhardness Measurement

A Vickers hardness testing machine capable of applying a predetermined force with the required range of test forces, an indenter and measuring device, was used to measure the surface hardness of the test piece. The test piece of Ø 42 × 12 mm cylindrical work pieces was faced on the flat face with CBN tool (cutting condition 775 rpm; DOC = 0.1 mm; feed 0.1 mm/rev.) to generate a surface. The Rockwell hardness measured on the surface of the steel according to BIS, IS: 1586-2000 [15], was 59.7 HRC. The Vickers hardness test was conducted in accordance to BIS, IS: 1501-2002 [16], and the test forces along with the results are shown in Table 1. The approximate hardness ranges between 63 and 64 HRC which only suggests the increase of hardness on the surface as a result of metallurgical alteration due to the cutting forces and temperature. This hardened surface further improves the wear and abrasion resistance of the tool surface and prevents any hard particles usually leaving deep scratches and causing damage to the form rolls.Table 1
Microhardness of the steel.
Serial  number
9807 Nfor 15 sec
4903 Nfor 15 sec
2942 Nfor 15 sec
1
788.6
828.6
798.2
2
796.7
843.3
806.3
3
785.1
815.1
802.5
4
791.0
844.7
797.7
Average
790 HV1
833HV0.5
801HV0.3


### 2.4. Hardenability Test

The hardness measured on the surface after hardening and tempering of the steel according to IS: 1586-2000 was 60.3 HRC [15]. To measure the hardness of the steel at the core, step turning procedure was adopted. The hardness values were taken in each step turned at 5 mm below the surfaces generated. It was found that there was hardly any major variation of hardness at the surface of Ø 42 mm and at Ø 15 mm core of the cylinder. The hardness varied from 59.3 HRC at the surface to 57.8 HRC at the core. This only suggests that the material is very much susceptible to through hardening and possesses good hardenability property.


### 2.5. Optical Microscopic Test

Optical microscopic test was done using an inverted optical microscope as per ASME standard. The two test samples, one before heat treatment and one after heat treatment, were sectioned from two lengths (one length each from hardened and nonhardened lengths) with an abrasive cutter and then polished successfully with emery paper with fine grit meshes 120, 320, 400, 600, and 2000 followed by polishing with velvet cloth using diamond paste and diamond fluid until mirror like surface was obtained. The samples were then cleaned using lab detergent and immediately rinsed using running water and then dried using hot air immediately followed by etching to prevent surface oxidation using 3% nital solution (3 mL of HNO3 and 97% methanol) and the observation was done under the optical microscope.The microstructure observed in the annealed steel is of massive and spheroidal carbides in ferrite matrix as shown in Figure1 and long granular carbides in tempered martensite as shown in Figure 2. The presence of chromium carbides in the ferrite matrix is clearly noted. Dispersion of small and large particles is seen in both of the conditions. The only disadvantage of the steel is that the long granular carbide dendrites as seen in the hardened steel are brittle and if found on the machined surface of the dies and rolls are prone to chipping and fracture.Figure 1
Micrographs in annealed state.Figure 2
Micrographs after heat treatment.


### 2.6. Tensile Test

Tensile test was performed according to BIS, IS: 1608-2005 [17], on a 40-tonne UTM. Tool steel bars were machined to a smooth gage section in the center and a larger shoulder on each end for tensile tests. For each test condition two samples were tested and average value was reported as given in Table 2. The tensile strength of tool steel is directly related to its hardness. The hardness of the tensile specimen was measured to be 57 HRC. The tensile strength of the hardened steel improved phenomenally from 687.90 to 1855.03 N/mm2 and the ductility decreased from 7.40 to 1.16% (Table 2). Although compressive yield strength is of more importance but tensile strength and ductility are important properties in tooling area as in some situations a preexisting crack in tools starts developing due to tension. No yielding phenomenon was observed in the hardened specimen and fracture occurred without any prior yield. The yield strength of the annealed steel was 445.69 N/mm2 and brittle cleavage was observed on all of the fractured surfaces.Table 2
Tensile test data.
Parameter
Specimen 1 (annealed)
Specimen 2 (hardened and double tempered)
Hardness measured
98.6 HRB
58 HRC
Diameter (mm)
10.00
10.02
Area (mm2)
78.50
81.67
Gauge length (mm)
50.00
50.00
Breaking load (N)
54000
151500
Yield load (N)
35000
No yield
Elongated length (mm)
53.70
50.58
Tensile strength (mm)
687.90
1855.03
Yield stress (N/mm2)
445.86
NA
Elongation %
7.40
1.16


### 2.7. Charpy (V-Notch) Test

Characterization of the toughness is done by this test. This test specifies the Charpy impact (V-notch) method for determining impact strength of the tested steel and was conducted as per BIS, IS: 1757-1988 [18]. Nine standard steel specimens or three sets (three specimens in each set) for this experiment were machined from annealed steel bar. Two sets of the steel specimens were hardened and one set was tempered twice and another set was tempered thrice and the average Rockwell hardness was measured to be 55±2 HRC and then subjected to Charpy impact test.The test piece was made to lay squarely against the supports, with the plane on symmetry of the notch within 0.5 mm of the plane midway between them. It was made to strike by the striker in the plane of the symmetry of the notch and on the side opposite the notch. The results are shown in Table3. The results indicate that the material has a very poor resistance to impact in both annealed and hardened condition. Brittleness is characterized by fracturing with low energy under impact. Characteristics of cleavage and brittleness were observed with fine grained fracture surface.Table 3
Charpy (V-notch) impact test data.
Serial number
Absorbed energy for annealed specimen in KV
Absorbed energy for hardened specimen in KV with double tempering
1
4 J
3 J
2
4 J
3 J
3
4 J
3 J
Average
4 J
3 J


### 2.8. Machinability Test

#### 2.8.1. Work and Tool Material

Annealed cold working tool steel AISI D6 with 96.8 HRB was selected for this machinability study using cemented carbide inserts. CVD coated (multiphase Al2O3) carbide inserts bearing ISO code CCMT 09T308N-SU with 80° rhombus shape, having cutting geometry 6° rake angle, 7° relief angle, and 0.793 mm nose radius, were used.


#### 2.8.2. Machine and Equipment Used

The experiments were carried out on an all geared DRO Lathe (Model: Bajaj-Pioneer-175 Geared Headed), 8-spindle cutting speed (8–1200 rpm), and 24 numbers of feeds as shown in Figure3. A dynamometer (Make TELC Germany) with quick approach/feed angle adjustment 45°, 60°, 75°, and 90° CCMT09 tool seat in the tool holder with XKM 2000 software was used for cutting force and temperature measurements. A surface roughness tester (SJ-301 Mitutoyo, Japan), x-axis (drive units), with measuring range of 12.5 μm was used to measure the surface roughness (Ra) during the experiments.Figure 3
Cutting force measurement.


#### 2.8.3. Experimental Procedure

The samples of both the annealed and hardened workpiece were machined by removing 0.5 mm thickness of the top cylindrical surface to Ø 41 × 150 mm, in order to eliminate any surface defects and wobbling and then centered and faced. Tests were performed to identify the main effects of machining parameters on surface roughness and cutting forces. The independent variables are cutting speed, feed, depth of cut, and approach angles for annealed workpiece and the independent variables are cutting speed, feed, depth of cut, and workpiece hardness for hardened steel. Corresponding cutting speeds were equalized at different workpiece diameters to the extent that rotational speed ratios permit. Short duration tests were performed (machined length of 20 mm) without coolant. Each test was realized with fresh cutting edge.Surface roughness was measured offline with the profilometer by taking the measurements across the lay. Three measurements (λc = 0.8 mm; N=5) were taken along the feed length for each sample length machined and measurements were made about 120° apart and the average value was used in the analysis. The cutting force and its components generated on the tool point in the turning operation were measured using a lathe tool dynamometer (Make DKM 2010 of TELC Germany) with software XKM 2000 as shown in Figure 3. In the present work, the machining process of the annealed steel was studied under DOE with full factorial unreplicated design (24) giving all combinations of factors at two levels as shown in Table 4 and sixteen experimental runs were taken and 50% of the experiments were repeated to minimize the experimental error. The two levels of these parameters have been decided on the basis of literature review, machine capabilities, and shop floor practice and the experiments were conducted randomly and measurements are shown in Table 5.Table 4
Experimental factors and factor levels for annealed steel.
Code
Process parameters
Low level
High level
A
Cutting speed (V)
39.6
97.5
B
Feed (f)
0.1
0.27
C
Depth of cut (d)
0.2
1.0
D
Approach angle (Ae)
45
90Table 5
Matrix design and experimental data.
Std.
Run
V (m/min)
“f”(mm)
“d”(mm)
A
e (degree)
R
a (μm)
F
c (N)
3
1
39.6
0.27
0.2
45
2.78
349
2
2
97.5
0.10
0.2
45
0.76
164
13
3
39.6
0.10
1.0
90
4.18
461
11
4
39.6
0.27
0.2
90
3.35
170
4
5
97.5
0.27
0.2
45
3.22
298
6
6
97.5
0.10
1.0
45
2.76
412
1
7
39.6
0.10
0.2
45
0.96
188
15
8
39.6
0.27
1.0
90
4.09
871
10
9
97.5
0.10
0.2
90
0.71
108
14
10
97.5
0.10
1.0
90
4.91
408
7
11
39.6
0.27
1.0
45
3.08
614
12
12
97.5
0.27
0.2
90
2.90
189
5
13
39.6
0.10
1.0
45
3.28
307
8
14
97.5
0.27
1.0
45
1.07
722
9
15
39.6
0.10
0.2
90
1.06
132
16
16
97.5
0.27
1.0
90
3.11
747


## 2.1. Metallurgical Test

The material was subjected to metallurgical test according to ASTM E 415 [13] on an Emission Spectrometer, Make: LECO, USA, Model GDS500A. The chemical composition of test material is C 2.130%; Si 0.238%; Mn 0.240%; Cr 11.10%; Ni 0.090%; Mo 0.032%; V 0.130%; Cu 0.030%; Al 0.06%; S 0.02%; P 0.010%; Co 0.025%; W 0.620%; Fe 85.267%. The test material conforms to ASTM A 681 standard of ASM Handbook (Vol. 1) [14]. The carbon content of the steel influences the martensitic hardening and 2.130% of carbon present in this steel is an advantage. Traces of other alloying elements are seen apart from the prominent presence of chromium and tungsten because on austenitizing some of the carbide dissolves in the austenite, thus supplying the matrix with alloying elements necessary for high hardenability and as quenched hardness. The steel is alloyed with Cr, W to get hard and abrasive resistance carbides in the steel. The hard carbides in steel reduce the machinability by giving a high wear on the cutting tool. The presence of tungsten in this steel produces very high densities of stable carbides. The presence of high chromium content enables this steel to resist staining particularly form tools when the steel is hardened and polished. The presence of vanadium benefits the effects of mechanical properties and refines austenite grain size.


## 2.2. Hardness Measurement

The hardness of the steel measured according to BIS, IS: 1586-2000 [15], in annealed condition was 96.8 HRB and 58 HRC after hardening and tempering. On each specimen several measurements were performed across the surface in order to obtain representative average hardness value.


## 2.3. Microhardness Measurement

A Vickers hardness testing machine capable of applying a predetermined force with the required range of test forces, an indenter and measuring device, was used to measure the surface hardness of the test piece. The test piece of Ø 42 × 12 mm cylindrical work pieces was faced on the flat face with CBN tool (cutting condition 775 rpm; DOC = 0.1 mm; feed 0.1 mm/rev.) to generate a surface. The Rockwell hardness measured on the surface of the steel according to BIS, IS: 1586-2000 [15], was 59.7 HRC. The Vickers hardness test was conducted in accordance to BIS, IS: 1501-2002 [16], and the test forces along with the results are shown in Table 1. The approximate hardness ranges between 63 and 64 HRC which only suggests the increase of hardness on the surface as a result of metallurgical alteration due to the cutting forces and temperature. This hardened surface further improves the wear and abrasion resistance of the tool surface and prevents any hard particles usually leaving deep scratches and causing damage to the form rolls.Table 1
Microhardness of the steel.
Serial  number
9807 Nfor 15 sec
4903 Nfor 15 sec
2942 Nfor 15 sec
1
788.6
828.6
798.2
2
796.7
843.3
806.3
3
785.1
815.1
802.5
4
791.0
844.7
797.7
Average
790 HV1
833HV0.5
801HV0.3


## 2.4. Hardenability Test

The hardness measured on the surface after hardening and tempering of the steel according to IS: 1586-2000 was 60.3 HRC [15]. To measure the hardness of the steel at the core, step turning procedure was adopted. The hardness values were taken in each step turned at 5 mm below the surfaces generated. It was found that there was hardly any major variation of hardness at the surface of Ø 42 mm and at Ø 15 mm core of the cylinder. The hardness varied from 59.3 HRC at the surface to 57.8 HRC at the core. This only suggests that the material is very much susceptible to through hardening and possesses good hardenability property.


## 2.5. Optical Microscopic Test

Optical microscopic test was done using an inverted optical microscope as per ASME standard. The two test samples, one before heat treatment and one after heat treatment, were sectioned from two lengths (one length each from hardened and nonhardened lengths) with an abrasive cutter and then polished successfully with emery paper with fine grit meshes 120, 320, 400, 600, and 2000 followed by polishing with velvet cloth using diamond paste and diamond fluid until mirror like surface was obtained. The samples were then cleaned using lab detergent and immediately rinsed using running water and then dried using hot air immediately followed by etching to prevent surface oxidation using 3% nital solution (3 mL of HNO3 and 97% methanol) and the observation was done under the optical microscope.The microstructure observed in the annealed steel is of massive and spheroidal carbides in ferrite matrix as shown in Figure1 and long granular carbides in tempered martensite as shown in Figure 2. The presence of chromium carbides in the ferrite matrix is clearly noted. Dispersion of small and large particles is seen in both of the conditions. The only disadvantage of the steel is that the long granular carbide dendrites as seen in the hardened steel are brittle and if found on the machined surface of the dies and rolls are prone to chipping and fracture.Figure 1
Micrographs in annealed state.Figure 2
Micrographs after heat treatment.


## 2.6. Tensile Test

Tensile test was performed according to BIS, IS: 1608-2005 [17], on a 40-tonne UTM. Tool steel bars were machined to a smooth gage section in the center and a larger shoulder on each end for tensile tests. For each test condition two samples were tested and average value was reported as given in Table 2. The tensile strength of tool steel is directly related to its hardness. The hardness of the tensile specimen was measured to be 57 HRC. The tensile strength of the hardened steel improved phenomenally from 687.90 to 1855.03 N/mm2 and the ductility decreased from 7.40 to 1.16% (Table 2). Although compressive yield strength is of more importance but tensile strength and ductility are important properties in tooling area as in some situations a preexisting crack in tools starts developing due to tension. No yielding phenomenon was observed in the hardened specimen and fracture occurred without any prior yield. The yield strength of the annealed steel was 445.69 N/mm2 and brittle cleavage was observed on all of the fractured surfaces.Table 2
Tensile test data.
Parameter
Specimen 1 (annealed)
Specimen 2 (hardened and double tempered)
Hardness measured
98.6 HRB
58 HRC
Diameter (mm)
10.00
10.02
Area (mm2)
78.50
81.67
Gauge length (mm)
50.00
50.00
Breaking load (N)
54000
151500
Yield load (N)
35000
No yield
Elongated length (mm)
53.70
50.58
Tensile strength (mm)
687.90
1855.03
Yield stress (N/mm2)
445.86
NA
Elongation %
7.40
1.16


## 2.7. Charpy (V-Notch) Test

Characterization of the toughness is done by this test. This test specifies the Charpy impact (V-notch) method for determining impact strength of the tested steel and was conducted as per BIS, IS: 1757-1988 [18]. Nine standard steel specimens or three sets (three specimens in each set) for this experiment were machined from annealed steel bar. Two sets of the steel specimens were hardened and one set was tempered twice and another set was tempered thrice and the average Rockwell hardness was measured to be 55±2 HRC and then subjected to Charpy impact test.The test piece was made to lay squarely against the supports, with the plane on symmetry of the notch within 0.5 mm of the plane midway between them. It was made to strike by the striker in the plane of the symmetry of the notch and on the side opposite the notch. The results are shown in Table3. The results indicate that the material has a very poor resistance to impact in both annealed and hardened condition. Brittleness is characterized by fracturing with low energy under impact. Characteristics of cleavage and brittleness were observed with fine grained fracture surface.Table 3
Charpy (V-notch) impact test data.
Serial number
Absorbed energy for annealed specimen in KV
Absorbed energy for hardened specimen in KV with double tempering
1
4 J
3 J
2
4 J
3 J
3
4 J
3 J
Average
4 J
3 J


## 2.8. Machinability Test

### 2.8.1. Work and Tool Material

Annealed cold working tool steel AISI D6 with 96.8 HRB was selected for this machinability study using cemented carbide inserts. CVD coated (multiphase Al2O3) carbide inserts bearing ISO code CCMT 09T308N-SU with 80° rhombus shape, having cutting geometry 6° rake angle, 7° relief angle, and 0.793 mm nose radius, were used.


### 2.8.2. Machine and Equipment Used

The experiments were carried out on an all geared DRO Lathe (Model: Bajaj-Pioneer-175 Geared Headed), 8-spindle cutting speed (8–1200 rpm), and 24 numbers of feeds as shown in Figure3. A dynamometer (Make TELC Germany) with quick approach/feed angle adjustment 45°, 60°, 75°, and 90° CCMT09 tool seat in the tool holder with XKM 2000 software was used for cutting force and temperature measurements. A surface roughness tester (SJ-301 Mitutoyo, Japan), x-axis (drive units), with measuring range of 12.5 μm was used to measure the surface roughness (Ra) during the experiments.Figure 3
Cutting force measurement.


### 2.8.3. Experimental Procedure

The samples of both the annealed and hardened workpiece were machined by removing 0.5 mm thickness of the top cylindrical surface to Ø 41 × 150 mm, in order to eliminate any surface defects and wobbling and then centered and faced. Tests were performed to identify the main effects of machining parameters on surface roughness and cutting forces. The independent variables are cutting speed, feed, depth of cut, and approach angles for annealed workpiece and the independent variables are cutting speed, feed, depth of cut, and workpiece hardness for hardened steel. Corresponding cutting speeds were equalized at different workpiece diameters to the extent that rotational speed ratios permit. Short duration tests were performed (machined length of 20 mm) without coolant. Each test was realized with fresh cutting edge.Surface roughness was measured offline with the profilometer by taking the measurements across the lay. Three measurements (λc = 0.8 mm; N=5) were taken along the feed length for each sample length machined and measurements were made about 120° apart and the average value was used in the analysis. The cutting force and its components generated on the tool point in the turning operation were measured using a lathe tool dynamometer (Make DKM 2010 of TELC Germany) with software XKM 2000 as shown in Figure 3. In the present work, the machining process of the annealed steel was studied under DOE with full factorial unreplicated design (24) giving all combinations of factors at two levels as shown in Table 4 and sixteen experimental runs were taken and 50% of the experiments were repeated to minimize the experimental error. The two levels of these parameters have been decided on the basis of literature review, machine capabilities, and shop floor practice and the experiments were conducted randomly and measurements are shown in Table 5.Table 4
Experimental factors and factor levels for annealed steel.
Code
Process parameters
Low level
High level
A
Cutting speed (V)
39.6
97.5
B
Feed (f)
0.1
0.27
C
Depth of cut (d)
0.2
1.0
D
Approach angle (Ae)
45
90Table 5
Matrix design and experimental data.
Std.
Run
V (m/min)
“f”(mm)
“d”(mm)
A
e (degree)
R
a (μm)
F
c (N)
3
1
39.6
0.27
0.2
45
2.78
349
2
2
97.5
0.10
0.2
45
0.76
164
13
3
39.6
0.10
1.0
90
4.18
461
11
4
39.6
0.27
0.2
90
3.35
170
4
5
97.5
0.27
0.2
45
3.22
298
6
6
97.5
0.10
1.0
45
2.76
412
1
7
39.6
0.10
0.2
45
0.96
188
15
8
39.6
0.27
1.0
90
4.09
871
10
9
97.5
0.10
0.2
90
0.71
108
14
10
97.5
0.10
1.0
90
4.91
408
7
11
39.6
0.27
1.0
45
3.08
614
12
12
97.5
0.27
0.2
90
2.90
189
5
13
39.6
0.10
1.0
45
3.28
307
8
14
97.5
0.27
1.0
45
1.07
722
9
15
39.6
0.10
0.2
90
1.06
132
16
16
97.5
0.27
1.0
90
3.11
747


## 2.8.1. Work and Tool Material

Annealed cold working tool steel AISI D6 with 96.8 HRB was selected for this machinability study using cemented carbide inserts. CVD coated (multiphase Al2O3) carbide inserts bearing ISO code CCMT 09T308N-SU with 80° rhombus shape, having cutting geometry 6° rake angle, 7° relief angle, and 0.793 mm nose radius, were used.


## 2.8.2. Machine and Equipment Used

The experiments were carried out on an all geared DRO Lathe (Model: Bajaj-Pioneer-175 Geared Headed), 8-spindle cutting speed (8–1200 rpm), and 24 numbers of feeds as shown in Figure3. A dynamometer (Make TELC Germany) with quick approach/feed angle adjustment 45°, 60°, 75°, and 90° CCMT09 tool seat in the tool holder with XKM 2000 software was used for cutting force and temperature measurements. A surface roughness tester (SJ-301 Mitutoyo, Japan), x-axis (drive units), with measuring range of 12.5 μm was used to measure the surface roughness (Ra) during the experiments.Figure 3
Cutting force measurement.


## 2.8.3. Experimental Procedure

The samples of both the annealed and hardened workpiece were machined by removing 0.5 mm thickness of the top cylindrical surface to Ø 41 × 150 mm, in order to eliminate any surface defects and wobbling and then centered and faced. Tests were performed to identify the main effects of machining parameters on surface roughness and cutting forces. The independent variables are cutting speed, feed, depth of cut, and approach angles for annealed workpiece and the independent variables are cutting speed, feed, depth of cut, and workpiece hardness for hardened steel. Corresponding cutting speeds were equalized at different workpiece diameters to the extent that rotational speed ratios permit. Short duration tests were performed (machined length of 20 mm) without coolant. Each test was realized with fresh cutting edge.Surface roughness was measured offline with the profilometer by taking the measurements across the lay. Three measurements (λc = 0.8 mm; N=5) were taken along the feed length for each sample length machined and measurements were made about 120° apart and the average value was used in the analysis. The cutting force and its components generated on the tool point in the turning operation were measured using a lathe tool dynamometer (Make DKM 2010 of TELC Germany) with software XKM 2000 as shown in Figure 3. In the present work, the machining process of the annealed steel was studied under DOE with full factorial unreplicated design (24) giving all combinations of factors at two levels as shown in Table 4 and sixteen experimental runs were taken and 50% of the experiments were repeated to minimize the experimental error. The two levels of these parameters have been decided on the basis of literature review, machine capabilities, and shop floor practice and the experiments were conducted randomly and measurements are shown in Table 5.Table 4
Experimental factors and factor levels for annealed steel.
Code
Process parameters
Low level
High level
A
Cutting speed (V)
39.6
97.5
B
Feed (f)
0.1
0.27
C
Depth of cut (d)
0.2
1.0
D
Approach angle (Ae)
45
90Table 5
Matrix design and experimental data.
Std.
Run
V (m/min)
“f”(mm)
“d”(mm)
A
e (degree)
R
a (μm)
F
c (N)
3
1
39.6
0.27
0.2
45
2.78
349
2
2
97.5
0.10
0.2
45
0.76
164
13
3
39.6
0.10
1.0
90
4.18
461
11
4
39.6
0.27
0.2
90
3.35
170
4
5
97.5
0.27
0.2
45
3.22
298
6
6
97.5
0.10
1.0
45
2.76
412
1
7
39.6
0.10
0.2
45
0.96
188
15
8
39.6
0.27
1.0
90
4.09
871
10
9
97.5
0.10
0.2
90
0.71
108
14
10
97.5
0.10
1.0
90
4.91
408
7
11
39.6
0.27
1.0
45
3.08
614
12
12
97.5
0.27
0.2
90
2.90
189
5
13
39.6
0.10
1.0
45
3.28
307
8
14
97.5
0.27
1.0
45
1.07
722
9
15
39.6
0.10
0.2
90
1.06
132
16
16
97.5
0.27
1.0
90
3.11
747


## 3. Results and Discussion

The results and discussion for determining the significant factors using statistical analysis during machining of the steel in annealed condition are presented in the following subsections.


### 3.1. Statistical Analysis

The two-level statistical design for four independent variables consists of sixteen factorial points (24 = 16) where each variable is fixed at two levels. The surface roughness and main cutting force are assumed to be linearly dependent on the level of each independent factor. The effect of each experimental factor can be defined as the change in the response when the factor changes from one level to another level such as from high to low. An interaction is the variation among the differences between means for different levels of one factor over different levels of the other. MINITAB-15 is used in this analysis process, with an approach to the statistical analysis of the 2k design as discussed by Montogomery [19].


#### 3.1.1. Estimating the Factor Effects

In a single replicate of2k there is no internal estimate of error. The approach to the analysis of an unreplicated factorial is to assume that certain high order interactions are negligible and combine their mean squares to estimate the error. A simple method of analysis suggested is to examine a normal probability plot of the estimates of the effects. This is a plot of the absolute value of the effect estimates against their normal probability. Here the effects which are active and real will have nonzero mean and will fall off the straight line, whereas the inactive and insignificant effects that are normally distributed, with zero mean and variance σ2, will fall along the straight line. The graphs in Figures 4 and 5 suggest that the assumption of normal distribution is fairly reasonable; factors f, d and interaction of f×d, d×Ae are statistically significant for main cutting force; factors dandAe and interaction of f×d, are statistically significant for surface finish. Since f×d lie on the left hand side of the line, their contribution has negative effect on the model. The reverse is true for the rest of the significant effects lying on right hand side. The estimated effect and coefficient for surface roughness and main cutting force are shown in Tables 6 and 7. Analysis of variance (ANOVA) is carried out to test the null hypothesis that the main effect and the interactions are equal to zero. The small p values (<0.05) mean that all the main effects and interactions are zero at the 5% significance level. In other words, there is reasonably strong evidence that at least some of the main effects and interactions are not equal to zero.Table 6
Estimated effects and coefficients for surface roughness (coded units).
Term
Effect
Coef.
SE coef.
T
p
Constant
2.6387
0.1432
18.43
0.000
V
−0.4175
−0.2087
0.1432
−1.46
0.205
f
0.6225
0.3113
0.1432
2.17
0.082
d
1.3425
0.6713
0.1432
4.69
0.005
A
e
0.8000
0.4000
0.1432
2.79
0.038
V
×
f
−0.3325
−0.1662
0.1432
−1.16
0.298
V
×
d
−0.2775
−0.1388
0.1432
−0.97
0.377
V
×
A
e
0.1550
0.0775
0.1432
0.54
0.612
f
×
d
−1.5675
−0.7838
0.1432
−5.47
0.003
f
×
A
e
0.0250
0.0125
0.1432
0.09
0.934
d
×
A
e
0.7250
0.3625
0.1432
2.53
0.052
S
=
0.572735, PRESS = 16.7949, and R-Sq = 93.80%.
R-Sq (pred.) = 36.47%, R-Sq (adj.) = 81.39%.Table 7
Estimated effects and coefficients for main cutting force (coded units).
Term
Effect
Coef.
SE coef.
T
p
Constant
384.25
15.78
24.35
0.000
V
−6.50
−3.25
15.78
−0.21
0.845
f
223.50
111.75
15.78
7.08
0.001
d
367.00
183.50
15.78
11.63
0.000
A
e
5.00
2.50
15.78
0.16
0.880
V
×
f
−7.50
−3.75
15.78
−0.24
0.822
V
×
d
15.50
7.75
15.78
0.49
0.644
V
×
A
e
−41.00
−20.50
15.78
−1.30
0.251
f
×
d
118.00
59.00
15.78
3.74
0.013
f
×
A
e
−4.50
−2.25
15.78
−0.14
0.892
d
×
A
e
103.00
51.50
15.78
3.26
0.022
S = 63.1189; PRESS = 203981.
R-Sq = 97.70%, R-Sq (pred.) = 76.42%, and R-Sq (adj.) = 93.09%.Figure 4
Normal plot of the standardized effects (Fc).Figure 5
Normal plot of the standardized effects (Ra).


#### 3.1.2. Initial Model

Surface Roughness. The regression model equation for surface roughness is represented by(1)Ra=2.639-0.21x1+0.311x2+0.671x3+0.4x4-1.66x1x2-0.139x1x3+0.0.077x1x4-0.784x2x3+0.012x2x4+0.3625x3x4+⋯+ε,where factors A, B, C, and D are represented by x1, x2, x3, and x4.Main Cutting Force. The regression model equation for main cutting force is represented by(2)Fc=384.25-3.25x1+111.75x2+183.5x3+2.50x4-3.75x1x2+7.75x1x3-20.50x1x4+59.00x2x3-2.25x2x4+51.50x3x4+⋯+ε.


#### 3.1.3. Statistical Testing

The main effects are highly significant (those having smallp value); p value indicates that the two main factors “d” and “Ae” and the interaction f×d have statistically significant effect on the surface roughness. The ANOVA for main cutting force shows the main effects which are highly significant (all having small p value); p value indicates that the two main factors “f” and “d” and their interactions have statistically significant effect on the response. The ANOVA in Tables 8 and 9 indicates the specific effects and interaction, which are statistically significant or insignificant.Table 8
ANOVA for surface roughness.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
p
V
1
0.6972
0.6972
0.6972
2.13
0.205
f
1
1.5500
1.5500
1.5500
4.73
0.082
d
1
7.2092
7.2092
7.2092
21.98
0.005
A
e
1
2.5600
2.5600
2.5600
7.80
0.038
V
×
f
1
0.4422
0.4422
0.4422
1.35
0.298
V
×
d
1
0.3080
0.3080
0.3080
0.94
0.377
V
×
A
e
1
0.0961
0.0961
0.0961
0.29
0.612
f
×
d
1
9.8282
9.8282
9.8282
29.96
0.003
f
×
A
e
1
0.0025
0.0025
0.0025
0.01
0.934
d
×
A
e
1
2.1025
2.1025
2.1025
6.41
0.052
Error
5
1.6401
1.6401
0.3280
Total
15
26.4362
S = 0.572735, R-Sq = 93.80%, and R-Sq (adj.) = 81.39%.Table 9
ANOVA for main cutting force.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
p
V
1
169
169
169
0.04
0.845
f
1
199809
199809
199809
50.15
0.001
d
1
538756
538756
538756
135.23
0.000
A
e
1
100
100
100
0.03
0.880
V
×
f
1
225
225
225
0.06
0.822
V
×
d
1
961
961
961
0.24
0.644
V
×
A
e
1
6724
6724
6724
1.69
0.251
f
×
d
1
55696
55696
55696
13.98
0.013
f
×
A
e
1
81
81
81
0.02
0.892
d
×
A
e
1
42436
42436
42436
10.65
0.022
Error
5
19920
19920
3984
Total
15
864877
S =63.1189, R-Sq = 97.70%, and R-Sq (adj.) = 93.09%.


#### 3.1.4. Refining of Model

Refining the model usually consists of removing of any nonsignificant variables from the full model. Thus the final regression model for surface finish is represented by(3)Ra=2.639+0.671x3+0.4x4-0.784x2x3.The final regression model for main cutting force is represented by(4)Fc=384.25-111.75x2+183.5x3+59.00x2x3+51.50x3x4.


#### 3.1.5. Residual Analysis

Regression modeling is done to obtain the predicted or fitted value of the response surface finish (Ra) only. Similar analysis can be done for main cutting force. Violation of the basic assumptions and model adequacy can be easily investigated by the examination of residuals. Residual plots are frequently used to diagnose inequality of variance. These are discussed in the following subsections.(i) Normal Probability Plot. Normal probability plot of the raw data is used to check the assumption of normality when using the t-test. The equal variance and normality assumptions are easy to check using a normal probability plot. It indicates whether the data are normally distributed, other variables are influencing the response, or outlier exists in the data. It can be seen from Figure 6 that the residual appears to follow a straight line. No evidence of nonnormality or skewness unidentified variable or no potential outlier is located in the normal probability plot.Figure 6
Normal probability plot of residual values.(ii) Residual versus Fitted Values. If the model is correct and if the assumptions are satisfied, the residual should be structureless; that is, they should be unrelated to any variable including the predicted response or fitted values. It indicates whether the variance is constant, a nonlinear relationship exists, or any outliers exist in the data. This plot should not reveal any unusual pattern. Based on this plot, Figure 7, there is no unusual structure apparently, that is, no obvious pattern. The residual appears to be randomly scattered about the zero line. There is no evidence of nonconstant variance, missing terms, outliers, or any influential points.Figure 7
Residual values versus fitted values for surface roughness.(iii) Standardized Residual versus the Variables. A rough check for outliers is made by examining the standardized residuals. The standardized residuals should be approximately normal with zero mean and unit variance. Thus about 68% of the standardized residuals should fall within the limits ±1, about 95% should fall within ±2, and all of them should fall within ±3. A residual bigger than 3 or 4 standard deviation from zero is a potential outlier. Figures 8, 9, 10, and 11 show the residual versus variables, that is, cutting speed, feed, depth of cut, and approach angle.Figure 8
Residual versus cutting speed (m/min).Figure 9
Residual versus feed (mm/rev.).Figure 10
Residual versus depth of cut (mm).Figure 11
Residual versus approach angle (degree).(iv) Residual versus Observation Order. This plot is useful when the order of the observations may influence the results, which can occur when the data are collected in a time sequence or in some other sequence. This plot indicates whether there is any correlation between error terms that are near each other. Correlation among residuals may be signified by ascending or descending trends in the residuals and rapid change in sign of the adjacent residuals. Figure 12 almost indicates a fairly satisfactory result.Figure 12
Residual versus observation order.(v) Interpretation of Plots. The main effect plot for surface roughness is shown in Figure 13; the slopes for feed, DOC, and approach angle are upward (positive); this graph plots the mean of the high and low of each factor. From this graph, it is seen that if the feed, depth of cut, and approach angle increase the surface roughness increases whereas the cutting speed has negligible effect on surface roughness. The main effect plot for main cutting force is shown in Figure 14. From this graph, it is seen that if the feed and depth of cut are increased, the main cutting force also increases whereas cutting speed and approach angle have no effect on main cutting force. Results of interaction plots for surface roughness values are shown in Figure 15. In the plots, the x-axis indicates the value of each parameter at two levels and y-axis the response value. The lines that are nearly parallel, that is, approach angle and feed, cutting speed and approach angle, and so forth, have no interaction whereas there is clear interaction between feed and DOC. Results of interaction plots for main cutting force values are presented in Figure 16. The lines that are nearly parallel indicate that there is no interaction, for example, feed and cutting speed, cutting speed and DOC, approach angle and feed, and cutting speed and approach angle.Figure 13
Main effect plot (surface roughness).Figure 14
Main effect plot (main cutting force).Figure 15
Interaction plots (surface roughness).Figure 16
Interaction plots (main cutting force).With increase in feed the surface roughness increases as expected. It is a well-known theory that, for a given tool nose radius, the theoretical surface roughnessRa≅f2/(32×noseradius) is mainly a function of feed. Increase in feed increases the helicoid furrows generated due to the resultant nose shape helicoid tool-work-piece movement. Deeper and broader furrows are formed due to increase in feed resulting in poor Ra values. Also with the increase in feed the contact area between the cutting tool and work material increases and hence the main cutting force increases due to increase in chip load. As the depth of cut increases, the material removal rate increases and therefore there is an increase in main cutting force. On the other hand increase in depth of cut causes increase in the ploughing action of the annealed steel during machining, thereby decreasing the surface roughness. The approach angle along with the nose radius of the tool affects the chip formation in a way that the chip cross section changes. The chip thickness is reduced and the width increases with smaller angle; that is, at larger approach angle the chip thickness increases, which then has a negative influence on the machining process, and the surface roughness deteriorates.


### 3.2. Confirmation Experiments

In order to verify the accuracy of the model developed representing (3) and (4), three confirmation run experiments were performed (Table 10). The test conditions for the confirmation test were so chosen that they are within the range of the levels defined previously [20]. The predicted values and the associated experimental values were compared. The error percentage is within the permissible limits. So, the response equation for the surface roughness and main cutting forces predicted through this model can be used to successfully predict the surface roughness and main cutting force for any combination of the cutting speed, feed, depth of cut, and approach angle within the range of the experimentation performed.Table 10
Confirmation test.
Serial number
“V”(m/min)
“f”(mm/rev.)
“d”(mm)
A
e (degree)
Exp.(Ra)
Pred.(Ra)
Error (%)
Exp.(Fc)
Pred.(Fc)
Error (%)
1
58.4
0.13
0.4
45
2.97
3.18
7.07
496
462
6.8
2
72.7
0.18
0.6
75
3.23
3.48
7.7
492
519
5.4
3
97.5
0.21
0.8
90
3.53
3.67
3.6
544
582
6.9Table10 presents the results between experimental run and predicted data for surface roughness and main cutting force. It is found that the difference between the experimental value and predicted model is very small. The difference in terms of error is less than 7.7% for surface roughness and less than 6.9% for main cutting force. It proves that the model and equation generated give a fair reading indicating a reasonable model as per the previous study by Lazoglu et al. [21]. The results obtained also validated the reliability of the model.


## 3.1. Statistical Analysis

The two-level statistical design for four independent variables consists of sixteen factorial points (24 = 16) where each variable is fixed at two levels. The surface roughness and main cutting force are assumed to be linearly dependent on the level of each independent factor. The effect of each experimental factor can be defined as the change in the response when the factor changes from one level to another level such as from high to low. An interaction is the variation among the differences between means for different levels of one factor over different levels of the other. MINITAB-15 is used in this analysis process, with an approach to the statistical analysis of the 2k design as discussed by Montogomery [19].


### 3.1.1. Estimating the Factor Effects

In a single replicate of2k there is no internal estimate of error. The approach to the analysis of an unreplicated factorial is to assume that certain high order interactions are negligible and combine their mean squares to estimate the error. A simple method of analysis suggested is to examine a normal probability plot of the estimates of the effects. This is a plot of the absolute value of the effect estimates against their normal probability. Here the effects which are active and real will have nonzero mean and will fall off the straight line, whereas the inactive and insignificant effects that are normally distributed, with zero mean and variance σ2, will fall along the straight line. The graphs in Figures 4 and 5 suggest that the assumption of normal distribution is fairly reasonable; factors f, d and interaction of f×d, d×Ae are statistically significant for main cutting force; factors dandAe and interaction of f×d, are statistically significant for surface finish. Since f×d lie on the left hand side of the line, their contribution has negative effect on the model. The reverse is true for the rest of the significant effects lying on right hand side. The estimated effect and coefficient for surface roughness and main cutting force are shown in Tables 6 and 7. Analysis of variance (ANOVA) is carried out to test the null hypothesis that the main effect and the interactions are equal to zero. The small p values (<0.05) mean that all the main effects and interactions are zero at the 5% significance level. In other words, there is reasonably strong evidence that at least some of the main effects and interactions are not equal to zero.Table 6
Estimated effects and coefficients for surface roughness (coded units).
Term
Effect
Coef.
SE coef.
T
p
Constant
2.6387
0.1432
18.43
0.000
V
−0.4175
−0.2087
0.1432
−1.46
0.205
f
0.6225
0.3113
0.1432
2.17
0.082
d
1.3425
0.6713
0.1432
4.69
0.005
A
e
0.8000
0.4000
0.1432
2.79
0.038
V
×
f
−0.3325
−0.1662
0.1432
−1.16
0.298
V
×
d
−0.2775
−0.1388
0.1432
−0.97
0.377
V
×
A
e
0.1550
0.0775
0.1432
0.54
0.612
f
×
d
−1.5675
−0.7838
0.1432
−5.47
0.003
f
×
A
e
0.0250
0.0125
0.1432
0.09
0.934
d
×
A
e
0.7250
0.3625
0.1432
2.53
0.052
S
=
0.572735, PRESS = 16.7949, and R-Sq = 93.80%.
R-Sq (pred.) = 36.47%, R-Sq (adj.) = 81.39%.Table 7
Estimated effects and coefficients for main cutting force (coded units).
Term
Effect
Coef.
SE coef.
T
p
Constant
384.25
15.78
24.35
0.000
V
−6.50
−3.25
15.78
−0.21
0.845
f
223.50
111.75
15.78
7.08
0.001
d
367.00
183.50
15.78
11.63
0.000
A
e
5.00
2.50
15.78
0.16
0.880
V
×
f
−7.50
−3.75
15.78
−0.24
0.822
V
×
d
15.50
7.75
15.78
0.49
0.644
V
×
A
e
−41.00
−20.50
15.78
−1.30
0.251
f
×
d
118.00
59.00
15.78
3.74
0.013
f
×
A
e
−4.50
−2.25
15.78
−0.14
0.892
d
×
A
e
103.00
51.50
15.78
3.26
0.022
S = 63.1189; PRESS = 203981.
R-Sq = 97.70%, R-Sq (pred.) = 76.42%, and R-Sq (adj.) = 93.09%.Figure 4
Normal plot of the standardized effects (Fc).Figure 5
Normal plot of the standardized effects (Ra).


### 3.1.2. Initial Model

Surface Roughness. The regression model equation for surface roughness is represented by(1)Ra=2.639-0.21x1+0.311x2+0.671x3+0.4x4-1.66x1x2-0.139x1x3+0.0.077x1x4-0.784x2x3+0.012x2x4+0.3625x3x4+⋯+ε,where factors A, B, C, and D are represented by x1, x2, x3, and x4.Main Cutting Force. The regression model equation for main cutting force is represented by(2)Fc=384.25-3.25x1+111.75x2+183.5x3+2.50x4-3.75x1x2+7.75x1x3-20.50x1x4+59.00x2x3-2.25x2x4+51.50x3x4+⋯+ε.


### 3.1.3. Statistical Testing

The main effects are highly significant (those having smallp value); p value indicates that the two main factors “d” and “Ae” and the interaction f×d have statistically significant effect on the surface roughness. The ANOVA for main cutting force shows the main effects which are highly significant (all having small p value); p value indicates that the two main factors “f” and “d” and their interactions have statistically significant effect on the response. The ANOVA in Tables 8 and 9 indicates the specific effects and interaction, which are statistically significant or insignificant.Table 8
ANOVA for surface roughness.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
p
V
1
0.6972
0.6972
0.6972
2.13
0.205
f
1
1.5500
1.5500
1.5500
4.73
0.082
d
1
7.2092
7.2092
7.2092
21.98
0.005
A
e
1
2.5600
2.5600
2.5600
7.80
0.038
V
×
f
1
0.4422
0.4422
0.4422
1.35
0.298
V
×
d
1
0.3080
0.3080
0.3080
0.94
0.377
V
×
A
e
1
0.0961
0.0961
0.0961
0.29
0.612
f
×
d
1
9.8282
9.8282
9.8282
29.96
0.003
f
×
A
e
1
0.0025
0.0025
0.0025
0.01
0.934
d
×
A
e
1
2.1025
2.1025
2.1025
6.41
0.052
Error
5
1.6401
1.6401
0.3280
Total
15
26.4362
S = 0.572735, R-Sq = 93.80%, and R-Sq (adj.) = 81.39%.Table 9
ANOVA for main cutting force.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
p
V
1
169
169
169
0.04
0.845
f
1
199809
199809
199809
50.15
0.001
d
1
538756
538756
538756
135.23
0.000
A
e
1
100
100
100
0.03
0.880
V
×
f
1
225
225
225
0.06
0.822
V
×
d
1
961
961
961
0.24
0.644
V
×
A
e
1
6724
6724
6724
1.69
0.251
f
×
d
1
55696
55696
55696
13.98
0.013
f
×
A
e
1
81
81
81
0.02
0.892
d
×
A
e
1
42436
42436
42436
10.65
0.022
Error
5
19920
19920
3984
Total
15
864877
S =63.1189, R-Sq = 97.70%, and R-Sq (adj.) = 93.09%.


### 3.1.4. Refining of Model

Refining the model usually consists of removing of any nonsignificant variables from the full model. Thus the final regression model for surface finish is represented by(3)Ra=2.639+0.671x3+0.4x4-0.784x2x3.The final regression model for main cutting force is represented by(4)Fc=384.25-111.75x2+183.5x3+59.00x2x3+51.50x3x4.


### 3.1.5. Residual Analysis

Regression modeling is done to obtain the predicted or fitted value of the response surface finish (Ra) only. Similar analysis can be done for main cutting force. Violation of the basic assumptions and model adequacy can be easily investigated by the examination of residuals. Residual plots are frequently used to diagnose inequality of variance. These are discussed in the following subsections.(i) Normal Probability Plot. Normal probability plot of the raw data is used to check the assumption of normality when using the t-test. The equal variance and normality assumptions are easy to check using a normal probability plot. It indicates whether the data are normally distributed, other variables are influencing the response, or outlier exists in the data. It can be seen from Figure 6 that the residual appears to follow a straight line. No evidence of nonnormality or skewness unidentified variable or no potential outlier is located in the normal probability plot.Figure 6
Normal probability plot of residual values.(ii) Residual versus Fitted Values. If the model is correct and if the assumptions are satisfied, the residual should be structureless; that is, they should be unrelated to any variable including the predicted response or fitted values. It indicates whether the variance is constant, a nonlinear relationship exists, or any outliers exist in the data. This plot should not reveal any unusual pattern. Based on this plot, Figure 7, there is no unusual structure apparently, that is, no obvious pattern. The residual appears to be randomly scattered about the zero line. There is no evidence of nonconstant variance, missing terms, outliers, or any influential points.Figure 7
Residual values versus fitted values for surface roughness.(iii) Standardized Residual versus the Variables. A rough check for outliers is made by examining the standardized residuals. The standardized residuals should be approximately normal with zero mean and unit variance. Thus about 68% of the standardized residuals should fall within the limits ±1, about 95% should fall within ±2, and all of them should fall within ±3. A residual bigger than 3 or 4 standard deviation from zero is a potential outlier. Figures 8, 9, 10, and 11 show the residual versus variables, that is, cutting speed, feed, depth of cut, and approach angle.Figure 8
Residual versus cutting speed (m/min).Figure 9
Residual versus feed (mm/rev.).Figure 10
Residual versus depth of cut (mm).Figure 11
Residual versus approach angle (degree).(iv) Residual versus Observation Order. This plot is useful when the order of the observations may influence the results, which can occur when the data are collected in a time sequence or in some other sequence. This plot indicates whether there is any correlation between error terms that are near each other. Correlation among residuals may be signified by ascending or descending trends in the residuals and rapid change in sign of the adjacent residuals. Figure 12 almost indicates a fairly satisfactory result.Figure 12
Residual versus observation order.(v) Interpretation of Plots. The main effect plot for surface roughness is shown in Figure 13; the slopes for feed, DOC, and approach angle are upward (positive); this graph plots the mean of the high and low of each factor. From this graph, it is seen that if the feed, depth of cut, and approach angle increase the surface roughness increases whereas the cutting speed has negligible effect on surface roughness. The main effect plot for main cutting force is shown in Figure 14. From this graph, it is seen that if the feed and depth of cut are increased, the main cutting force also increases whereas cutting speed and approach angle have no effect on main cutting force. Results of interaction plots for surface roughness values are shown in Figure 15. In the plots, the x-axis indicates the value of each parameter at two levels and y-axis the response value. The lines that are nearly parallel, that is, approach angle and feed, cutting speed and approach angle, and so forth, have no interaction whereas there is clear interaction between feed and DOC. Results of interaction plots for main cutting force values are presented in Figure 16. The lines that are nearly parallel indicate that there is no interaction, for example, feed and cutting speed, cutting speed and DOC, approach angle and feed, and cutting speed and approach angle.Figure 13
Main effect plot (surface roughness).Figure 14
Main effect plot (main cutting force).Figure 15
Interaction plots (surface roughness).Figure 16
Interaction plots (main cutting force).With increase in feed the surface roughness increases as expected. It is a well-known theory that, for a given tool nose radius, the theoretical surface roughnessRa≅f2/(32×noseradius) is mainly a function of feed. Increase in feed increases the helicoid furrows generated due to the resultant nose shape helicoid tool-work-piece movement. Deeper and broader furrows are formed due to increase in feed resulting in poor Ra values. Also with the increase in feed the contact area between the cutting tool and work material increases and hence the main cutting force increases due to increase in chip load. As the depth of cut increases, the material removal rate increases and therefore there is an increase in main cutting force. On the other hand increase in depth of cut causes increase in the ploughing action of the annealed steel during machining, thereby decreasing the surface roughness. The approach angle along with the nose radius of the tool affects the chip formation in a way that the chip cross section changes. The chip thickness is reduced and the width increases with smaller angle; that is, at larger approach angle the chip thickness increases, which then has a negative influence on the machining process, and the surface roughness deteriorates.


## 3.1.1. Estimating the Factor Effects

In a single replicate of2k there is no internal estimate of error. The approach to the analysis of an unreplicated factorial is to assume that certain high order interactions are negligible and combine their mean squares to estimate the error. A simple method of analysis suggested is to examine a normal probability plot of the estimates of the effects. This is a plot of the absolute value of the effect estimates against their normal probability. Here the effects which are active and real will have nonzero mean and will fall off the straight line, whereas the inactive and insignificant effects that are normally distributed, with zero mean and variance σ2, will fall along the straight line. The graphs in Figures 4 and 5 suggest that the assumption of normal distribution is fairly reasonable; factors f, d and interaction of f×d, d×Ae are statistically significant for main cutting force; factors dandAe and interaction of f×d, are statistically significant for surface finish. Since f×d lie on the left hand side of the line, their contribution has negative effect on the model. The reverse is true for the rest of the significant effects lying on right hand side. The estimated effect and coefficient for surface roughness and main cutting force are shown in Tables 6 and 7. Analysis of variance (ANOVA) is carried out to test the null hypothesis that the main effect and the interactions are equal to zero. The small p values (<0.05) mean that all the main effects and interactions are zero at the 5% significance level. In other words, there is reasonably strong evidence that at least some of the main effects and interactions are not equal to zero.Table 6
Estimated effects and coefficients for surface roughness (coded units).
Term
Effect
Coef.
SE coef.
T
p
Constant
2.6387
0.1432
18.43
0.000
V
−0.4175
−0.2087
0.1432
−1.46
0.205
f
0.6225
0.3113
0.1432
2.17
0.082
d
1.3425
0.6713
0.1432
4.69
0.005
A
e
0.8000
0.4000
0.1432
2.79
0.038
V
×
f
−0.3325
−0.1662
0.1432
−1.16
0.298
V
×
d
−0.2775
−0.1388
0.1432
−0.97
0.377
V
×
A
e
0.1550
0.0775
0.1432
0.54
0.612
f
×
d
−1.5675
−0.7838
0.1432
−5.47
0.003
f
×
A
e
0.0250
0.0125
0.1432
0.09
0.934
d
×
A
e
0.7250
0.3625
0.1432
2.53
0.052
S
=
0.572735, PRESS = 16.7949, and R-Sq = 93.80%.
R-Sq (pred.) = 36.47%, R-Sq (adj.) = 81.39%.Table 7
Estimated effects and coefficients for main cutting force (coded units).
Term
Effect
Coef.
SE coef.
T
p
Constant
384.25
15.78
24.35
0.000
V
−6.50
−3.25
15.78
−0.21
0.845
f
223.50
111.75
15.78
7.08
0.001
d
367.00
183.50
15.78
11.63
0.000
A
e
5.00
2.50
15.78
0.16
0.880
V
×
f
−7.50
−3.75
15.78
−0.24
0.822
V
×
d
15.50
7.75
15.78
0.49
0.644
V
×
A
e
−41.00
−20.50
15.78
−1.30
0.251
f
×
d
118.00
59.00
15.78
3.74
0.013
f
×
A
e
−4.50
−2.25
15.78
−0.14
0.892
d
×
A
e
103.00
51.50
15.78
3.26
0.022
S = 63.1189; PRESS = 203981.
R-Sq = 97.70%, R-Sq (pred.) = 76.42%, and R-Sq (adj.) = 93.09%.Figure 4
Normal plot of the standardized effects (Fc).Figure 5
Normal plot of the standardized effects (Ra).


## 3.1.2. Initial Model

Surface Roughness. The regression model equation for surface roughness is represented by(1)Ra=2.639-0.21x1+0.311x2+0.671x3+0.4x4-1.66x1x2-0.139x1x3+0.0.077x1x4-0.784x2x3+0.012x2x4+0.3625x3x4+⋯+ε,where factors A, B, C, and D are represented by x1, x2, x3, and x4.Main Cutting Force. The regression model equation for main cutting force is represented by(2)Fc=384.25-3.25x1+111.75x2+183.5x3+2.50x4-3.75x1x2+7.75x1x3-20.50x1x4+59.00x2x3-2.25x2x4+51.50x3x4+⋯+ε.


## 3.1.3. Statistical Testing

The main effects are highly significant (those having smallp value); p value indicates that the two main factors “d” and “Ae” and the interaction f×d have statistically significant effect on the surface roughness. The ANOVA for main cutting force shows the main effects which are highly significant (all having small p value); p value indicates that the two main factors “f” and “d” and their interactions have statistically significant effect on the response. The ANOVA in Tables 8 and 9 indicates the specific effects and interaction, which are statistically significant or insignificant.Table 8
ANOVA for surface roughness.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
p
V
1
0.6972
0.6972
0.6972
2.13
0.205
f
1
1.5500
1.5500
1.5500
4.73
0.082
d
1
7.2092
7.2092
7.2092
21.98
0.005
A
e
1
2.5600
2.5600
2.5600
7.80
0.038
V
×
f
1
0.4422
0.4422
0.4422
1.35
0.298
V
×
d
1
0.3080
0.3080
0.3080
0.94
0.377
V
×
A
e
1
0.0961
0.0961
0.0961
0.29
0.612
f
×
d
1
9.8282
9.8282
9.8282
29.96
0.003
f
×
A
e
1
0.0025
0.0025
0.0025
0.01
0.934
d
×
A
e
1
2.1025
2.1025
2.1025
6.41
0.052
Error
5
1.6401
1.6401
0.3280
Total
15
26.4362
S = 0.572735, R-Sq = 93.80%, and R-Sq (adj.) = 81.39%.Table 9
ANOVA for main cutting force.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
p
V
1
169
169
169
0.04
0.845
f
1
199809
199809
199809
50.15
0.001
d
1
538756
538756
538756
135.23
0.000
A
e
1
100
100
100
0.03
0.880
V
×
f
1
225
225
225
0.06
0.822
V
×
d
1
961
961
961
0.24
0.644
V
×
A
e
1
6724
6724
6724
1.69
0.251
f
×
d
1
55696
55696
55696
13.98
0.013
f
×
A
e
1
81
81
81
0.02
0.892
d
×
A
e
1
42436
42436
42436
10.65
0.022
Error
5
19920
19920
3984
Total
15
864877
S =63.1189, R-Sq = 97.70%, and R-Sq (adj.) = 93.09%.


## 3.1.4. Refining of Model

Refining the model usually consists of removing of any nonsignificant variables from the full model. Thus the final regression model for surface finish is represented by(3)Ra=2.639+0.671x3+0.4x4-0.784x2x3.The final regression model for main cutting force is represented by(4)Fc=384.25-111.75x2+183.5x3+59.00x2x3+51.50x3x4.


## 3.1.5. Residual Analysis

Regression modeling is done to obtain the predicted or fitted value of the response surface finish (Ra) only. Similar analysis can be done for main cutting force. Violation of the basic assumptions and model adequacy can be easily investigated by the examination of residuals. Residual plots are frequently used to diagnose inequality of variance. These are discussed in the following subsections.(i) Normal Probability Plot. Normal probability plot of the raw data is used to check the assumption of normality when using the t-test. The equal variance and normality assumptions are easy to check using a normal probability plot. It indicates whether the data are normally distributed, other variables are influencing the response, or outlier exists in the data. It can be seen from Figure 6 that the residual appears to follow a straight line. No evidence of nonnormality or skewness unidentified variable or no potential outlier is located in the normal probability plot.Figure 6
Normal probability plot of residual values.(ii) Residual versus Fitted Values. If the model is correct and if the assumptions are satisfied, the residual should be structureless; that is, they should be unrelated to any variable including the predicted response or fitted values. It indicates whether the variance is constant, a nonlinear relationship exists, or any outliers exist in the data. This plot should not reveal any unusual pattern. Based on this plot, Figure 7, there is no unusual structure apparently, that is, no obvious pattern. The residual appears to be randomly scattered about the zero line. There is no evidence of nonconstant variance, missing terms, outliers, or any influential points.Figure 7
Residual values versus fitted values for surface roughness.(iii) Standardized Residual versus the Variables. A rough check for outliers is made by examining the standardized residuals. The standardized residuals should be approximately normal with zero mean and unit variance. Thus about 68% of the standardized residuals should fall within the limits ±1, about 95% should fall within ±2, and all of them should fall within ±3. A residual bigger than 3 or 4 standard deviation from zero is a potential outlier. Figures 8, 9, 10, and 11 show the residual versus variables, that is, cutting speed, feed, depth of cut, and approach angle.Figure 8
Residual versus cutting speed (m/min).Figure 9
Residual versus feed (mm/rev.).Figure 10
Residual versus depth of cut (mm).Figure 11
Residual versus approach angle (degree).(iv) Residual versus Observation Order. This plot is useful when the order of the observations may influence the results, which can occur when the data are collected in a time sequence or in some other sequence. This plot indicates whether there is any correlation between error terms that are near each other. Correlation among residuals may be signified by ascending or descending trends in the residuals and rapid change in sign of the adjacent residuals. Figure 12 almost indicates a fairly satisfactory result.Figure 12
Residual versus observation order.(v) Interpretation of Plots. The main effect plot for surface roughness is shown in Figure 13; the slopes for feed, DOC, and approach angle are upward (positive); this graph plots the mean of the high and low of each factor. From this graph, it is seen that if the feed, depth of cut, and approach angle increase the surface roughness increases whereas the cutting speed has negligible effect on surface roughness. The main effect plot for main cutting force is shown in Figure 14. From this graph, it is seen that if the feed and depth of cut are increased, the main cutting force also increases whereas cutting speed and approach angle have no effect on main cutting force. Results of interaction plots for surface roughness values are shown in Figure 15. In the plots, the x-axis indicates the value of each parameter at two levels and y-axis the response value. The lines that are nearly parallel, that is, approach angle and feed, cutting speed and approach angle, and so forth, have no interaction whereas there is clear interaction between feed and DOC. Results of interaction plots for main cutting force values are presented in Figure 16. The lines that are nearly parallel indicate that there is no interaction, for example, feed and cutting speed, cutting speed and DOC, approach angle and feed, and cutting speed and approach angle.Figure 13
Main effect plot (surface roughness).Figure 14
Main effect plot (main cutting force).Figure 15
Interaction plots (surface roughness).Figure 16
Interaction plots (main cutting force).With increase in feed the surface roughness increases as expected. It is a well-known theory that, for a given tool nose radius, the theoretical surface roughnessRa≅f2/(32×noseradius) is mainly a function of feed. Increase in feed increases the helicoid furrows generated due to the resultant nose shape helicoid tool-work-piece movement. Deeper and broader furrows are formed due to increase in feed resulting in poor Ra values. Also with the increase in feed the contact area between the cutting tool and work material increases and hence the main cutting force increases due to increase in chip load. As the depth of cut increases, the material removal rate increases and therefore there is an increase in main cutting force. On the other hand increase in depth of cut causes increase in the ploughing action of the annealed steel during machining, thereby decreasing the surface roughness. The approach angle along with the nose radius of the tool affects the chip formation in a way that the chip cross section changes. The chip thickness is reduced and the width increases with smaller angle; that is, at larger approach angle the chip thickness increases, which then has a negative influence on the machining process, and the surface roughness deteriorates.


## 3.2. Confirmation Experiments

In order to verify the accuracy of the model developed representing (3) and (4), three confirmation run experiments were performed (Table 10). The test conditions for the confirmation test were so chosen that they are within the range of the levels defined previously [20]. The predicted values and the associated experimental values were compared. The error percentage is within the permissible limits. So, the response equation for the surface roughness and main cutting forces predicted through this model can be used to successfully predict the surface roughness and main cutting force for any combination of the cutting speed, feed, depth of cut, and approach angle within the range of the experimentation performed.Table 10
Confirmation test.
Serial number
“V”(m/min)
“f”(mm/rev.)
“d”(mm)
A
e (degree)
Exp.(Ra)
Pred.(Ra)
Error (%)
Exp.(Fc)
Pred.(Fc)
Error (%)
1
58.4
0.13
0.4
45
2.97
3.18
7.07
496
462
6.8
2
72.7
0.18
0.6
75
3.23
3.48
7.7
492
519
5.4
3
97.5
0.21
0.8
90
3.53
3.67
3.6
544
582
6.9Table10 presents the results between experimental run and predicted data for surface roughness and main cutting force. It is found that the difference between the experimental value and predicted model is very small. The difference in terms of error is less than 7.7% for surface roughness and less than 6.9% for main cutting force. It proves that the model and equation generated give a fair reading indicating a reasonable model as per the previous study by Lazoglu et al. [21]. The results obtained also validated the reliability of the model.


## 4. Conclusion

The commercial value of a material is due to its properties. AISI D6 tool steel can be commercially exploited and used in several industrial applications because of the following reasons:(1)
2.130% of carbon presence along with other alloying elements in this steel is an added advantage but the long granular carbides formed after heat treatment, if found on the machined surface, are prone to cracks on sudden loads. Therefore, this steel can be used for industrial dies and tools like form rolls, thread rolls, and gauges which are not subjected to any sudden impact loads.(2)
The tensile strength of the hardened steel improved phenomenally from 687.90 to 1855.03 N/mm2 and the ductility decreased from 7.40 to 1.16%. Although compressive yield strength is of more importance, tensile strength and ductility are important properties in tooling area as in some situations a preexisting crack in tools starts developing due to tension. No yielding phenomenon was observed in the hardened specimen and fracture occurred without any prior yield. The yield strength of the annealed steel was 445.69 N/mm2.(3)
The material has a very poor resistance to impact in both annealed and hardened condition. The puzzling observation is no change in toughness after hardening and tempering suggesting that the toughness of the steel in annealed state is terribly low and hence has limited applications as compared to other direct hardening tool steels. Therefore, in certain industrial applications like thread rolls, which are not subjected to heavy impacts, gradual loads are applied on the blank, and the tool steel can be used as thread rolls. Hence an appropriate toughness is sufficient if handled with care. Due to its favourable property profile, the tool steel is capable of performing as thread rolls for threading low strength threaded components (mild steel) in an economical manner. Similar tools like extrusion dies for tube forming or gauges for measurements can be manufactured with the help of this tool steel.(4)
Linear regression model is a good fit for both main cutting force and surface roughness measured during machining of annealed steel. The DOC is the most significant factor followed by feed for main cutting force and surface roughness. If the feed, depth of cut, and approach angle increase, the surface roughness increases whereas the cutting speed has negligible effect on surface roughness. If the feed and depth of cut are increased, the main cutting force also increases whereas cutting speed and approach angle have no effect on main cutting force.(5)
Verification experiments carried out show that the empirical models developed can be used for turning of annealed AISI D6 steel within the error of 8%.



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*Source: 196178-2015-09-17.xml*