Application of Response Surface Methodology for Determining Cutting Forces in Hard Turning Using Castrol Coolant

The present paper investigates the effect of different cutting parameters (cutting speed, feed rate, and depth of cut) on cutting force components using Castrol cooling condition in hard turning of alloy steel AISI 52100 . Mathematical models for cutting force components were developed using the response surface methodology (RSM). Experiment designs completed with a statistical analysis of variance (ANOVA) were performed. These models would be helpful in selecting optimum values of cutting parameters when turning hardened steels using coated carbide cutting tools. Results show that the cutting force components are influenced principally by the depth of cut, while feed rate and cutting speed have small effect on the cutting force components


Introduction
Hard turning is a technique that can be used to substitute grinding in the finishing operations for hardened steel (HRC 45 and above).Turning of hard steel using advanced tool materials such as coated carbide has more advantages than grinding or polishing, such as short cycle time, fewer process steps, where provides high flexibility and ability to cut complex geometries, so that the need of grinding parts for finishing can be eliminated [1][2][3][4][5][6][7].Cutting force is the important technological parameter to control in machining process.There have been considerable amounts of researches on cutting forces during turning hardened steels.TulioHallak Panzera et al. [8] studied the effect of the cutting parameters (cutting speed, feed rate and depth of cut) on the cutting force components.The results indicated that the three components of the turning force decrease slightly as cutting speed was elevated and increase linearly with feed rate and depth of cut.Furthermore, the analysis of variance indicated that the three components are not significantly affected by cutting speed; however, they are significantly affected by feed rate and depth of cut..Benedikt Sieben et al. [9] presented experimental study to investigate the turning of hardened AISI 6150 heat treatable steel using polycrystalline boron nitride (PCBN) tools to study the effects of the parameters cutting speed, feed and depth of cut on the cutting forces.The force components showed no corresponding effect for the selected ranges of depth of cut.Thus, the reason of the effect stays unclear.A. I. Fernándezet al. [10] studied the behaviour of austenitic stainless steel when machining at very high cutting speeds in dry turning.The results pointed out that the material undergoes a significant change in its behaviour when machining at cutting speeds above 450 m/min that favors the machining operation.The main component of cutting forces reaches a minimum value at this cutting speed.P Vamsi Krishna [11] presented a specific study of the application of solid lubricants in turning of AISI 1040 steel with carbide tool.It was observed from the experimental results that the cutting forces are significantly less in all the solid lubricant conditions compared to dry and coolant machining.HE Xinfeng et al. [12] analyzed a model for predicting cutting forces in hard turning of 51CrV4 steel for validation, cutting forces predicted by the model were compared with experimental measurements, and most of the results agree quite well.
In this paper, an experimental contribution that focuses on prediction and optimization of response (cutting force components) during hard turning of AISI 52100 alloy steel which it offers high hardness and excellent resistance to wear and deformation.Therefore, it is widely used in the automotive, gear, bearing and die industry [13][14][15][16].The ANOVA study involves the effect of cutting parameters (cutting speed, feed rate and depth of cut) on these responses.

Experimental procedure
Coolant turning tests carried out on CNC lathe machine using Castrol coolant.The workpiece material used is AISI 52100 hardened alloy steel which has chemical composition as shown in Table 1.The cutting parameters that have been used in turning are showed in Table 2.The cutting tool used is coated carbide insert mounted on a tool holder, which is held in a Kistler threecomponent piezoelectric dynamometer for measuring cutting force components as illustrated in Fig. 1

Experimental design:
The response surface methodology (RSM) is a procedure able to determine a relationship between independent input process parameters and output data (process response).This design method has more advantages than other design methods.The effect of various design parameters and the analysis with consideration of correlation between factors were studied through this design.Therefore, it has performed in hard turning in the recent researches [17][18][19][20][21][22][23][24].In this work a sequential set of experimental runs was established using a Central Composite Design (CCD) built according to the design is reported in Table 3to study the influence of three factors (cutting speed, feed rate, and depth of cut) on the cutting forces during coolant turning.

Thrust force
The results of analysis of variance (ANOVA) for thrust force (Fx) in turning using Castrol coolant are shown in Table 4.It is clear from the results of ANOVA that cutting speed (A), feed rate (B), depth of cut (C), the quadratic value for depth of cut (C 2 ),the interaction between speed and depth of cut (AC), and the interaction between feed rate and depth of cut (BC) are the most significant factors affecting thrust force (Fx).While the quadratic value for (B 2 )has less significant effect on (Fx).The quadratic value for feed rate (A 2 ) and the interaction (AB) are not significant.It is clear from the table that the "Pred R-Squared" of 0.9958 is in reasonable agreement with the "Adj R-Squared" of 0.9990."Adeq Precision" measures the signal to noise ratio.A ratio greater than 4 is desirable.our ratio of 164.779 indicates an adequate signal.This model can be used to navigate the design space.
Final Equation in Terms of Actual Factors for the thrust force model (Fx) is given by Eq.1: Fig. 2 presents the normal probability plot of the residuuals for (Fx).This plot revealeds that the residuals fall on a straight line implying that the errors are distributed normally.Fig. 3 shows the standardized residuals with respect to the predicted values for thrust force (Fx).The residuals do not show any obvious pattren and are distributed in both positive and negative directions.This implies that the model is adequate and there is no reason to suspect any violation of the independence or constant variance assumption.Fig. 4 illustrates the main effects of varying the two factors cutting speed (A) and feed rate (B) parameters on thrust force (Fx) and keeping the depth of cut (C) at 0.6 mm at constant level.The lower cutting speed and lower feed rate resulted in lower thrust force.Fig. 5 illustrates the main effects of varying the two factors cutting speed (A) and depth of cut (C) parameters on thrust force with constant level of feed rate at 0.16 mm/rev.According to the previous analysis, Table 4 indicates that the effect of this interaction is not statistically significant and it can be seen from Fig. 4 that lower cutting speed and lower depth of cut resulted in lower thrust force (Fx).The influence of varying the two factors feed rate (B) and depth of cut (C) parameters on thrust force and keeping cutting speed at 175 m/min at constant is depicted in Fig. 6.The previous analyses have shown that the interaction of feed rate and depth of cut are statistically significant and it is concluded that lower feed rate and lower depth of cut resulted lower thrust force.

Feed force
The results of analysis of variance (ANOVA) for feed force (Fz) with using Castrol coolant are shown in Table 5.It can be seen that (B), (C), quadratic for feed rate (B 2 ), quadratic for depth of cut (C 2 ), and the interaction (BC) have significant effect on feed force (Fz).The cutting speed (A), quadratic (A 2 ), the interaction (AB), and the interaction (AC) do not have significant effect.It is showed noise ratio "Adeq Precision" of 201.318 greater than 4 this indicates an adequate signal.This model can be used to navigate the design space.The "Pred R-Squared" of 0.9974 is in reasonable agreement with the "Adj R-Squared" of 0.9995.Fig. 7 presents the normal probability plots of the residuuals.This plots appear satisfactory where the points on these plots lie reasonably close to astraight line.Fig8 shows that there are normaly and independantly distribution for values of feed forces.Fig.9 is constructed to illustrate the main effects of varying the two factors cutting speed (A) and feed rate (B) parameters on feed force (Fz) and keeping depth of cut at 0.6 mm at constant level.Based on the above analysis (Table ), the interaction has no significance.Similarly in the Fig. 10, it has been noticed the effect of interaction cutting speed (A) and depth of cut (C) on feed force (Fz) with constant level of feed rate at 0.16 mm/rev doesn't have significance.Fig. 11 shows the effect of feed rate (B) and depth of cut (C) on feed force with constant level of cutting speed at 175 m/min is significant.Where lower feed rate and lower depth of cut resulted lower thrust force.

Resultant force
Table 6 presents the results of analysis of variance (ANOVA) for resultant force (R).It is clear from the results of ANOVA that B, C, B 2 , C 2 , AC, BC have significant effect on the response resultant force (R). the cutting speed (A), the quadratic (A 2 ), and the interaction (AB) are't significant.It is clear that the noise ratio "Adeq Precision" of 456.807 greater than 4 this indicates an dequate signal.This model can be used to navigate the design space.The "Pred R-Squared" of 0.9997 is in reasonable agreement with the "Adj R-Squared" of 0.9999.12 is the normal probability plot of the residuals.The points on these plots lie reasonably close to astraight line, leading support to our conclusion that the underlying assumptions of the analysis are satisfied.Fig13 shows the standardized residuals with respect to the predicted values for rasultant force.The residuals do not show any obvious patren and are distributed in both positive and negative directions.This implies that the model is adequate.It can be seen in Fig. 14 the effect of cutting speed and feed rate on resultant force isn't statistically significant.Fig. 15 reveals the effect of cutting speed and depth of cut on resultant force (R) with constant level of feed rate at 0.16 mm/rev.It can be seen lower cutting speed and lower depth of cut resulted in lower resultant force (R).The influence of feed rate and depth of cut on resultant force is depicted Fig. 16.It is concluded that the lower feed rate and the lower depth of cut resulted in lower resultant cutting force (R).

Optimization
The objective of the optimization was to find cutting parameters within the cutting speed range of 100 m/min to 250 m/min; the feed rate range 0.1 mm/rev to 0.22 mm/rev, and a depth of cut range from 0.2 mm to 1 mm.Cutting parameters all should be carried out so that the cutting forces are minimized.Fig. 17 shows the optimum value for cutting parameters to obtain minimum values of cutting forces.When cutting speed, feed rate, and depth of cut were 100m/min, 0.1mm/rev, and 0.2mm respevtivly the optimum valus of cutting forces (Fx,Fz, and R) were 82.886, 26.689, and 127.393N respectivly.The numerical optimization finds apoint that maximizes the desirability fuction.The disirability value is 0.996 corresponded to the minimum values of cutting forces.

Conclusions
In this paper the effect of the cutting parameters (cutting speed, feed rate, and depth of cut) on cutting force components during coolants turning of high hard alloy steel with coated carbide insert was investigated.Optimum values of machining parameters have been studied and computed by application of RSM.The following conclusions can be drawn from these experimental investigations: The depth of cut has the most significant statistical effect on cutting force components during.It can be deduced from ANOVA table the contribution percent for (Fx), (Fz), and (R) (76.06%), (98.14%), and (86.47%) respectively.
The feed rate has small effect on the cutting force components where can be deduced the contribution percentages are (12.95%),(1.05%), and (10.39%) respectively.The cutting speed has a very small effect on the cutting forces where the contribution percentages are 1.06%, 0.01%, and 0.002%.

Fig. 5
Fig.5 Effect of cutting speed and depth of cut on Fx

Fig. 9
Fig.9 Effect of cutting speed and feed rate on Fz

Fig.17Ramp fuction
Fig.17Ramp fuction gragh for cutting conditions in hard turning and cutting forces.

Table 2 : Cutting parameters are used in turning tests Factor Symbol Unit Level 1 Level 2
.

Table 3 :
Experimental results for cutting force components using Castrol coolant Table4 :Response: Results of ANOVA for thrust force Fx (Response Surface Quadratic Model)

Table 5 :
Response: Results of ANOVA for feed force Fz (Response Surface Quadratic Model)

Table 6Response :
Results of ANOVA for resultant force R ( Response Surface Quadratic Model)