Analysis of Surface Roughness and Cutting Forces in Hard Turning of 42CrMo4 Steel using Taguchi and RSM Method

In this study, effects of cutting speed (V), feed rate (f), depth of cut (a) and tool tip radius (R) on  surface roughness (Ra, Rz, and Rt) and cutting forces (radial force (Fx), tangential force (Fy), and feed force (Fz)) in hard finish turning processes of hardened 42CrMo4 (52 HRC) material was investigated experimentally. Taguchi’s mixed level parameter design (L18) is used for the experimental design (2x1,3x3). The signal-to-noise ratio (S/N) was used in the evaluation of test results.  By using Taguchi method, cutting parameters giving optimum surface roughness and cutting forces were determined. Regression analyses are applied to predict surface roughness and cutting forces. Analysis of variance (ANOVA) is used to determine the effects of the machining parameters on surface roughness and cutting forces. According to ANOVA analysis, the most important cutting parameters were found to be feed rate for surface roughness and depth of cut among cutting forces.  By conducting validation experiments, optimization was seen to be applied successfully.


Introduction
42CrMo4 steel is alloy structural steels which are suitable for hardening in terms of carbon content and show high toughness under certain loads at the end of the tempering process. Therefore, machining is more difficult compared to alloy steels. The most important feature is that it can form a rigid martensitic structure after quenching due to Cr and Mo alloy elements it contains and it allows having mechanical properties such as strength, ductility and toughness, simultaneously. For all these reasons, 42CrMo4 steel is alloy structural steels that are always widely used. Among its main usage areas, they are used in the automobile and aircraft construction and the manufacturing of parts and gear wheels with high ductility such as crankshaft, axle shaft and housing, grooved shaft and etc. [1][2][3].
When examining the studies in literature, many studies are found. In their study, Özel et al., examined experimentally the impacts of cutting-edge geometry, workpiece hardness, feed rate and cutting speed on surface roughness and cutting forces in the finish hard turning of AISI H13 steel [7]. Panzera et al., investigated the effect of cutting parameters on cutting force in dry turning of AISI 4340 steel by using coated carbide tips. In addition, the effects of cutting parameters on cutting force were investigated with the results of Variance (ANOVA) analysis [8]. Singh and Rao investigated the surface roughness behaviour of tool geometry and cutting conditions in finish hard turning process for AISI 52100 (58 HRC) material. They used ANOVA in the analysis [9]. Jayant and Kumar used hardened steel AISI 4140 carbide as the test material. They found the most appropriate cutting parameters by evaluating the data with the help of ANOVA and Taguchi Method [10]. Derakhshan and Akbari investigated the effect of workpiece hardness and cutting speed of AISI 4140 material on surface roughness in the process of machining with CBN tool in hard turning process [11]. Chavoshi and Tajdari observed the change of Ra value by machining AISI 4140 steel with hard turning process with CBN cutting edge with hardness and cutting speed variables [12]. Yallese et al., determined the statistical models of cutting forces in dry turning process of AISI H11 hot working tool steel (50 HRC). They formed the mathematical models with multiple linear regression and Response Surface Methodology (RSM) and determined the most effective cutting parameters on cutting forces [13]. Suresh et al. in-vestigate the effect of cutting parameters (cutting speed, feed rate, depth of cut and cutting time) in turning of AISI 4340 hardened steel on cutting forces, tool wear and surface roughness by using RSM [14]. Abou-El-Hosseinb et al., conducted an experimental study for the estimation of forces occurring during the machining of AISI P20 tool steel. They evaluated the effects of four input parameters on cutting force by using RSM [15]. Yang et al., investigated the test results obtained by using cutting parameters such as cutting speed, feed rate, and depth of cut for finish turning of Titanium alloy (TC 11) material with RSM [16]. Asiltürk and Akkuş investigated the effect of cutting parameters on surface roughness (Ra and Rz) in hard turning processes by using Taguchi method [17]. Günay and Yücel conducted the optimization of surface roughness values obtained in machining of high alloy casting materials (50 HRC and 62 HRC) under cutting conditions (cutting speed, feed rate and depth of cut). Optimal conditions were determined using S/N ratio [18]. Bouacha et al., conducted a study on the statistically analysis of surface roughness and cutting forces using RSM in hard turning of AISI 52100 bearing steel. The effect of cutting forces and cutting parameters affecting surface roughness was analysed by ANOVA [19]. Lalwani et al., conducted an experimental study on the effect of cutting parameters (cutting speed, feed rate and depth of cut) on cutting forces and surface roughness in finish hard turning of MDN250 steel [20]. In their study, Agrawal et al., studies the estimation of surface roughness during hard turning of AISI 4340 steel [21].
In this study, the effect of cutting parameters on surface roughness and cutting forces were investigated during the machining of high hardness 42CrMo4 alloy structural steel with ceramic insert having different tip radiuses. During the experiments, the interactions between the cutting parameters and the effects of the parameters on cutting force (Fx, Fy and Fz) and surface roughness (Ra, Rz and Rt) were focused. In this research, optimization of cutting parameters (cutting speed, feedrate, cutting depth and tool radius) was made by using Taguchi L18 composite orthogonal array. Using Taguchi method, optimum surface roughness and cutting forces values were determined and the relationship between the parameters was investigated. In addition, the effects of control factors on surface roughness and cutting forces were determined by ANOVA. Finally, the validity of the optimization was tested by validation tests and the results of the experiments were evaluated.

Material and method
For the hard finish turning processes of hardened 42CrMo4 (52 HRC) material in CNC lathe machine, three cutting speeds (200, 250 and 300 m/min), three feed rates (0.05, 0.1, and 0.15 mm/rev), three depths of chip (0.1, 0.25 and 0.4 mm), and two tool tip radii (0.8 and 1.2 mm) were used. An experimental study was conducted to investigate the effect of machining parameters on surface roughness Ra, Rz and Rt and cutting forces Fx, Fy and Fz. Hard finish turning tests were carried out on GOODWAY GS-260/Y brand CNC turning lathe with maximum speed of 4500 rpm. In the machining tests, 42CrMo4 (52 HRC) material hardened to the core in the dimensions of Ø80x560 mm was used. Table 1 shows the chemical composition of the test material used. In the study, Kennanetal TNGA 160408 and TNGA 160412 KY1615 type uncoated ceramic tips were preferred. Cutting tool catalogue was used to determine the cutting parameters of the tools. Prior to the experiment, cuttings were made in the catalogue values so that a preliminary assessment opportunity was obtained. Coolant was not used in the study. Fig. 1 The system used in turning tests. Taguchi method is an effective analysis method used to optimize the machining parameters affecting the production process. With the experimental design made by using this method, the number of experiments is significantly reduced and the time losses are minimized. In the study, the experimental design was made with Taguchi method and surface roughness Ra, Rz and Rt and cutting forces Fx, Fy and Fz were taken as a basis for quality features. Control factors were determined as cutting speed (m/min), feed rate (mm/rev), depth of cut (mm) and tool tip radius (mm). As control factors, Taquchi L18 (2x1, 3x3) mixed orthogonal array was used. Table 2 shows control factors and their levels. Since conducting a total of 27x2=54 experiments with full factorial design would cause loss in terms of cost and time, L18 (2x1, 3x3) mixed orthogonal array was made with Taguchi method in order to eliminate these problems. When the time and material costs of these tests are evaluated, the method developed by Taguchi responds to the need by reducing the number of experiments [22].
In the study, Taguchi method was used as experimental design and analysis method. A statistical performance measure known as the S/N ratio is used to analyse the test results. The results obtained from the tests are evaluated by converting them to the signal to noise ratio (S/N). In S/N ratio, S and N refer to the signal factor and noise factor, respectively. The signal factor refers to the real value taken from the system and the noise factor refer to the factors that cannot be included in the test design but affect the test results. In the calculation of S/N ratios, the methods of "the nominal is the best", "the larger is better", and "the smaller is better" are used depending on the characteristic type.
Since surface roughness value was desired to be the smallest in the determination of S/N values in this study, the formula corresponding to the principle of "the smaller is better" given in Eq.(1) was used [23][24][25].
In order to determine the effect of control factors on cutting forces and surface roughness values, ANOVA analysis was applied to the test results at confidence interval of 95%. Taguchi method and ANOVA analysis were performed using Minitab16 program. The experimental design was made by using Taguchi L18 mixed orthogonal array with main machining parameters in Table 3. Table 3 shows the Taguchi L18 experiment design prepared with Minitab 16 software.
The average surface roughness Ra, Rz and Rt values were measured using the Mahr MarSurf PS10 brand and model surface roughness measuring device in accordance with ISO 4287 standard. In the measurement of cutting forces generated during the machining of 42CrMo4 material, a KİSTLER 9129AA-Kistler TYPE 5070 piezoelectric-based dynamometer which can simultaneously measure three force components Fx, Fy, Fz was used. After the measurements, surface roughness and cutting force values were obtained by taking arithmetic mean of the values.

Results and analysis
In Taguchi mixed orthogonal array, S/N ratios are used to determine the optimum levels of control factors. Table 3 and Table 4 show the surface roughness and cutting force values obtained during the machining of 42CrMo4 material on the CNC turning lathe and S/N ratios obtained with the function of "the smaller is better", respectively.
The S/N response table is used to analyse the effect of each control factor on surface roughness. Table 3 shows the S/N response table obtained as a result of the analysis. It shows the optimum levels of control factors for optimum surface roughness values determined by using Taguchi technique. The best level for control factors was found based on the highest S/N ratio in all levels of those control factors. Accordingly, the levels and S/N ratios of the factors giving the best Ra value were determined as factor V (Level 3, S/N=9.488), factor f (Level 1, S/N=13.124), factor a (Level 1, S/N=8.167), and factor R (Level 2, S/N=9.395). In other words, the optimum Ra value was obtained with 300 m/min cutting speed (V3), 0.05 mm/rev feed rate (f1), 0.1 mm depth of cut (a1) and 1.2 mm tool tip radius (R2) (Fig. 2, a). When Table 5 is examined, the most effective control factors on Ra were determined in significance order as feed rate, tool tip radius, cutting speed, and depth of cut.    Table 6 Response  Table 7 Response   Table 9 Response  Table 10 Response The effect of the control parameters on Rz and Rt was determined according to the S/N ratios. Tables 6 and 7 show the effect level of each factor on Rz and Rt. (Fig. 2, b) and (Fig. 2, c) show that 3 rd level of cutting speed, 1 st level of feed rate, 2 nd level of depth of cut and tool tip radius are effective on Rz and Rt. When the effectiveness factors of the control factors on Rz and Rt were examined, it was determined that the most effective factor was feed rate, which was followed by tool tip radius, cutting speed and depth of cut, respectively.  3 shows the surface graphs showing the effects of the machining parameters f, R, a and V on surface roughness. By increasing f, the most effective parameter on surface roughness, the amount of chips that need to be removed by the cutter in one cycle increases. Thus, the surface quality deteriorates. In order to obtain low surface roughness in finishing processes, the most effective method is to reduce f [26,27]. In this context, the increase in Ra, Rz and Rt values on the surface with the increase of f is an expected result (Figs. 3, ac). Therefore, it was determined that there was a direct correlation between surface roughness and f. This result supports the evaluation made according to S/N ratios and is in parallel with the theoretical formula Ra=0.321f 2 /R pointing out that the surface roughness value will increase proportionally with the square of "f".
It is seen that Ra, Rz and Rt tend to decrease with the increasing tool radius R (Figs. 3, ac). This result can be explained by chip formation depending on uncut chip thickness decreasing with the increase of R. Based on the increase in cutting tool radius, it was emphasized that the uncut chip thickness would decrease along the cutting edge due to the increase in cutting tool radius [26]. It was determined that the cutting speed was not as effective as feed rate and tool tip radius on surface roughness. (Figs. 3, df) show that there was a decrease in surface roughness values with the decreased depth of cut. The effects of control factors on cutting forces Fx, Fy, and Fz were determined with S/N ratios in Table 4. Table 8 and Table 10 show the individual effects of the levels of these control factors on cutting forces. When examining Table 8 and Table 10, it was determined that 3 rd level of cutting force V3, 2 nd level of tool tip radius R2, and 1 st level of the feeding rate f1 and depth of cut a1 were effective on Fx and Fz forces V3-R2-f1-a1. 3 rd level of cutting speed and 1 st level of feeding rate, depth of cut and tool tip radius factors were found to be effective on Fy force V3-f1-a1-R1 (Table 9).
When S/N values giving the effect of Fx average by factors in (Fig. 4, a) were examined, the most effective parameter on Fx was found to be depth of cut. Changes in other factors (from big to small) are listed as feeding rate, cutting speed, and tool tip radius. When (Fig. 4, b) and (Fig. 4, c) were examined, it was determined that feeding rate was the most effective on Fy and Fz forces and the impact level of the other parameters were listed from big to small as feeding rate, tool tip radius and cutting speed. When (Fig. 4) was examined, depth of cut and feeding rate were determined to be the most effective factors on Fx, Fy, and Fz.
ANOVA was used to determine the effects of cutting parameters on cutting forces Fx, Fy and Fz used in the experimental design. Table 11 shows the results of ANOVA performed at confidence interval of 95 % for Fx, Fy, and Fz. When Table 11 was examined, it was determined that a and f factors were significant and R and V were insignificant on Fx and Fy according to the significance value of p<0.05. It was determined that a, f, and R were significant and V was not significant on Fz. It was determined that a, the most effective factor on Fx, Fy and Fz, gave contributions of 53.48%, 56.63%, and 63.47%, respectively. The second most effective factor f affected Fx by 33.21%, Fy by 36.18%, and Fz by 14.22%. The effect of the third most effective control factor R on Fx, Fy and Fz was determined as 3.88%, 1.52 % and 12.40%, respectively. Lastly, parameter V which had the least effect among the control factors affected Fx by 2.28%, Fy by 1.21% and lastly Fz by 0.45%. When examining (Fig. 5), it was seen that the low effect of V and R on Fx, Fy and Fz confirmed the ANOVA tables.
ANOVA was used to determine the effects of control factors on Ra, Rz and Rt. Table 12 shows the results of ANOVA performed at the confidence interval of 95% for Ra, Rz and Rt. When examining Table 12, it was seen that while the parameters V and a were not effective on surface roughness in terms of significance value of p<0.05, f, R and R*f interaction was significant. The contribution rates in Table 11 show the significance level of control parameters on Ra, Rz, and Rt. It was determined that f was the most effective factor on Ra, Rz and Rt with the contribution rates of 62.36%, 55.33% and 50.36%, respectively. It was determined that R which is the second most effective control factor contributed to Ra by 12.58%, Rz by 19.16% and Rt by 18.58%. The changes in other factors were listed as V and a (from big to small). While the contribution rates of V on Ra, Rz and Rt were 5.25%, 5.04% and 7.02%, respectively, the factor a which had the lowest effect affected Ra by 1.83%, Rz by 2.52%, and Rt by 3.64%. The contribution rates of R*f interaction on Ra, Rz, and Rt were determined as 8 Fig. 7 show the comparative graphs of the simulation Ra, Rz and Rt results and the Fx, Fy and Fz test results obtained by experimental and RSM. When the figures were examined, it was observed that the experimental and simulation results were compatible with each other. Fig. 5 shows the Fx, Fy, and Fz values increased with the increased feed rate and depth of cut. Along with the increasing feed rate, the increase of cutting force required for the chip formation due to increasing chip cross section and indirectly the increase of Fx, Fy and Fz are an expected result (Fig. 5, a, Fig. 5, b and Fig. 5, c). On the other hand, there was no significant increase in Fx, Fy and Fz values as tool tip radius increased. This result refers to the entering angle decreasing with the increase of the R, which is in parallel with the knowledge that the increase in R will mainly affect the Fx [28,29]. In addition, it was observed that Fx, Fy and Fz did not tend to increase with the increase of cutting tool radius. The reason for this can be shows as the difference of cutting speed in the experiments carried out for the same feed rate. Furthermore, Table 8-Table 10  The relationship between the surface roughness and machining parameters such as cutting speed V, feed f, depth of cut a and tool nose radius R for second order response surface model has been developed using RSM from the observed data in uncoded units as follows. The predicted actual uncoded factors, i.e., Ra, Rz and Rt was calculat-ed using Eqs. (2) -(4) and cutting forces of Eqs. (5) -(7).
Optimal results of Ra, Rz, and Rt and Fx, Fy and Fz values were obtained in the experimental study conducted by using Taguchi optimization method and the percentage distribution of the parameters affecting the result was determined with ANOVA analysis. The final step of the optimization process is the conduction of the validation tests and testing the validity of the optimization process. As a result of the Taguchi optimization, the parameter group giving the optimal Ra, Rz, and Rt and Fx, Fy and Fz could sometimes be any of the current tests; whereas, it may sometimes be an experiment other than the tests. In the study, the validation tests were repeated 3 times other than the current tests with the cutting parameters of V2-f2-a2-R2 (V=250 m/min, f=0.1 mm/rev, a=0.25 mm and R=1.2 mm) for Ra, Rz, Rt and V1-f2-a1-R1(V=200 m/min, f=0.1 mm/rev, a=0.05 mm and R=0.8 mm) for Fx, Fy, and Fz and the arithmetic means were collected. As a result of validation tests, Table 13 shows that high convergence values were obtained in the experimental results with the estimated results. In this context, it was noteworthy that the difference between the validation test results and those obtained from Taguchi approach was negligible.

Conclusions
In this study, the effects of different cutting speed, feed rate, depth of cut and tool tip radius on Ra, Rz and Rt and Fx, Fy and Fz in the turning of hardened 42CrMo4 steel were investigated. The following results were obtained as a result of the study where Taguchi method was used in the optimization of machining parameters.  According to the results of variance analysis of S/N ratios, the significance rank of the variables that were effective on Ra, Rz and Rt was determined as f, R, V and ap. In the optimization made with the help of S/N analysis, it was observed that the optimum machining parameters giving the lowest Ra, Rz and Rt value (Ra=0.184 µm, Rz=1.273 µm and Rt=1.397 µm) were V3-f3-a2-R1 for Ra; whereas, they were V3-f1-a1-R2 for Rz and Rt.  When ANOVA results were examined, it was determined that f was the most effective parameter on Ra, Rz and Rt with the rates of 62.37%, 55.33% and 50.96% and then R contributed to Ra by 12.85%, Rz by 19.16% and Rt by 18.58%. When the effect of cutting parameters on surface roughness was examined in terms of P significance value (p<0.05), it was determined that while V and a were not significant, f and R were significant.
 In cutting tests, the surface roughness values increased with the increasing f, whereas, it decreased as R increased. It was found that there was a direct correlation between the feed rate and the surface roughness.  When S/N ratios of cutting parameters on Fx, Fy and Fz were examined, it was determined that the most effective parameter was a, the second one was f followed by V and R. Optimum machining parameters were V3-f1-a1-R2 for Fx and Fz cutting forces and V3-f1-a1-R1 for Fy.  It was determined that as f and a increased, Fx, Fy and Fz increased, they tended to decreased with the increase of V but they did not show any change with the increase of R.  As a result of ANOVA analysis, it was determined that a and f contributed by 53. 48%