Comparison between mixed ceramic and reinforced ceramic tools in terms of cutting force components modelling and optimization when machining hardened steel AISI 4140 (60 HRC)

– This paper describes a comparison between mixed ceramic [Al 2 O 3 (70%) + TiC (30%)] and reinforced ceramic [Al2O 3 (75%) + SiC (25%)] tools in terms of cutting force components when machining in dry hard turning AISI 4140 steel, hardened to 60 HRC. The response surface methodology (RSM) and the analysis of variance (ANOVA) are applied to investigate eﬀects of cutting speed, feed rate and depth of cut on cutting force components in order to model and optimize these technological parameters. Results of this study indicate that the machining with the mixed ceramic insert generates lower values of cutting force components than reinforced ceramic insert. Consequently, the mixed ceramic CC650 is the most powerful tool. The developed models can be used in the metal machining industries and would be helpful in selecting cutting variables for optimization of hard cutting process.


Introduction
Hard turning is a turning operation which is applied on high resistance alloy steels (45 < HRC < 70) to obtain surface roughness values that are close to those obtained in grinding (Ra ≈ 0.1 μm). The workpiece materials involved include various hardened alloy steels, tool steels, case-hardened steels, super alloys, nitride irons and hard-chrome-coated steels, and heat-treated powder metallurgical parts. Although this production method is a new subject, there are quite a few studies by several researchers in the literature. These studies mostly concern the turning of AISI 52100 bearing steel, H11-H13 hot work tool steel, and AISI 4130-4340 low alloy steel using CBN, ceramic, and coated carbide tools [1][2][3][4].
Alumina (Al 2 O 3 ) based ceramics are considered to be one of the most suitable tool materials for machining hardened steels because of their high hot hardness, wear resistance and chemical inertness. However, the ceramic tools possess a high degree of brittleness and low thermal shock resistance which may result in excessive a Corresponding author: fbrahim@yahoo.fr chipping or fracture thereby reducing tool life. In order to improve their toughness, alumina (Al 2 O 3 ) based ceramics are usually reinforced with TiC, TiN, Ti(C, N), SiC, or TiB 2 additions. Alumina reinforced with SiC whiskers is the toughest and most resistant to thermal shock of the Al 2 O 3 -based ceramics. This whisker reinforcement improves the notch resistance of the insert. The end result is a ceramic insert that can run at speeds five to six times that of conventional carbide insert in nickel-based materials. As an added benefit, the toughness of the SiC whiskers also makes this category of ceramic available for machining harder materials with interruptions [5].
The productivity in terms of volume chip carved of six cutting tools was investigated for two different cutting conditions in straight hard turning of X38CrMoV5-1 (50 HRC). The authors found that for the first cutting regime (V c = 120 m.min −1 , ap = 0.15 mm, and f = 0.08 mm.rev −1 ), the productivity of the uncoated cermets CT5015, the coated cermets GC1525, the uncoated carbide H13A, the reinforced ceramic CC670, the coated carbide GC3015 and the mixed ceramic CC650 are 2160; 1440; 6480; 11 520; 23 040 and 70 560 mm

Investigators
Major factors Materials studied Tools Methodology C. Fetecau and F. Stan [15] cutting speed, feed AISI1045 Coated Taguchi method rate and side cutting steel carbide edge angle (SCEA) insert K. Bouacha et al. [16] cutting speed, feed AISI 52100 CBN Response surface methodology rate and depth of cut bearing steel R. Suresh et al. [17] cutting speed, AISI 4340 Coated Taguchi method and ANOVA feed rate and depth of cut steel carbide insert M.W. Azizi et al. [18] cutting speed, feed AISI 52100 coated Taguchi method and ANOVA rate, depth of cut and steel mixed workpiece hardness ceramic H. Aouici et al. [19] cutting speed, feed AISI CBN7020 Response surface methodology rate and depth of cut H11steel insert A.K. Sahoo and B. Sahoo [20] cutting speed, feed AISI 4340 coated carbide / rate, depth of cut and steel inserts machining time M.H. Cetin et al. [21] cutting speed, feed AISI 304L carbide insert Taguchi method rate, depth of cut and steel Type of cutting fluid S.R. Das et al. [22] cutting speed, feed AISI 4140 coated Taguchi method, RSM rate and depth of cut steel mixed ceramic and ANOVA respectively. The productivity of these three selected tools, i.e., mixed ceramic CC650, reinforced ceramic CC670, and coated carbide GC3015, for the second cutting regime (f = 0.08 mm.rev −1 , ap = 0.15 mm and V c = 90 m.min −1 ) are 85 860; 12 960 and 30 780 mm 3 , respectively. Their results prove that the mixed ceramic Al 2 O 3 + TiC (CC650) is more efficient than other tools used in terms of productivity [6]. The response surface methodology (RSM) is a family of statistical techniques for the design, empirical modelling and optimization of processes, where the responses of interest are influenced by several process variables (termed factors) [7,8]. RSM comprises the following three major components: (i) experimental design to determine the process factors' values based on which the experiments are conducted and data are collected; (ii) empirical modelling to approximate the relationship (i.e. the response surface) between responses and factor; (iii) optimization to find the best response value based on the empirical model. In addition, the above three stage procedure is typically operated in an iterative manner, where the information attained from previous iterations is utilized to guide the search for better response variables.
Dureja et al. applied the response surface methodology (RSM) to investigate the effect of cutting parameters on flank wear and surface roughness in hard turning of AISI H11 steel with a coated-mixed ceramic tool. The study indicated that the flank wear is influenced principally by feed rate, depth of cut and workpiece hardness [9]. Neseli et al. [10] applied response surface methodology (RSM) to optimize the effect of tool geometry parameters on surface roughness in hard turning of AISI 1040 with P25 tool. Aouici et al. [11] applied response surface methodology (RSM) to investigate the effect of cutting parameters on surface roughness in hard turning of AISI H11 with CBN tool. Recently, Aouici et al. [7] have applied response surface methodology (RSM) to optimize the effect of cutting parameters at the different levels of hardness workpiece on surface roughness in the case of the hard turning of AISI H11 with CBN tool. Elbah et al. [12] applied response surface methodology (RSM) and ANOVA to investigate the machinability of hardened AISI 4140 cold work tool steel using a range of cutting tools. The results indicated that surface roughness of 4140 steel was improved as cutting speed was elevated and deteriorated with feed rate. However, the surface quality obtained with the wiper ceramic insert allowed a surface finish as good when compared with conventional ceramic insert is 2.5. Lalwani et al. [13] studied the effect of cutting parameters in turning on cutting forces and surface roughness. To this end, a number of experiments based on RSM have been carried out and linear and quadratic models have been formed to explain the relation between the parameters.
Lima et al. [14] published the results of an investigation concerning the effect of cutting speed, feed rate and depth of cut on cutting forces in hardened AISI 4340 high strength low alloy steel and AISI D2 cold work tool steel materials.
Cutting force components influence the deformation of the machined workpiece, its dimensional accuracy, the formation of chip and the tool nose. Previously published studies show the tendency to seek effect of cutting conditions (like cutting speed, feed rate and depth of cut) on cutting force components (Tab. 1).

Experimental procedure
Turning experiments were performed in dry conditions using an universal lathe type SN 40C with 6.6 kW spindle    1). Its nose radius is r ε = 0.8 mm. These inserts were mounted on commercial toolholders of designation PSBNR2525M12 and CSBNR2525M12 with the geometry of active part characterized by the following angles:major cutting edge angle χ = 75 • ; clearance angle α = 6 • ; rake angle γ = −6 • ; inclination angle λ = −6 • . Short duration tests were performed (machining length is 18 mm). Each test is realized three times with a new cutting edge. In order to carry out this experimental study, these measurements were repeated three times and the considered result is an average of the three values given by the three trials. The three components of the cutting force; feed force or axial force (Fx:Fa), thrust force or radial force (Fy:Fr ) and tangential force (Fz:Ft ), schematically shown in Fig  Since there are a large number of variables controlling the cutting process, some mathematical models are required to represent this process. However, these models have to be developed using only the significant parameters influencing the process rather than including all the parameters.
In order to achieve this, statistical analysis of the experimental results will have to be processed using the analysis of variance (ANOVA). The latter is a computational technique that enables the estimation of the relative contributions of each of the control factors to the overall measured response. In this work, only the significant parameters will be used to develop mathematical models using response surface methodology (RSM). RSM is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which response of interest is influenced by several variables and the objective is to optimize the response [7,8].
Two levels were defined for each cutting variable as given in Table 2. The variable levels were chosen within the intervals recommended by the cutting tool manufacturer. Three cutting variables at two levels led to a total of 8 tests.

Evolution of the cutting force components
3.1.1 Influence of the cutting parameters on the feed force (axial force Fx:Fa) It can be seen in Figure 3 that all components of the feed force (axial force Fa) increased as the feed rate was increased, for both ceramic tools CC650 and CC670. For the reason that as the feed rate increases, the chip cross-sectional area increases. In this case, more plastic deformation energy is required for chip formation which leads to increase in main cutting force. However, the insert CC650 provides lower values than the CC670 ceramic tool. As seen in Figure 3 ceramic tools CC650 and CC670. Increasing the cutting parameters increases the thrust force and the depth of cut seems to be the most influential parameter. This can be attributed to the increase in chip cross-sectional area with increasing depth of cut, as mentioned by Aouici et al. [7] and proved by Bouacha et al. [16]. In general the CC650 tool gives lower values than CC670.In fact, an increase of depth of cut from 0.25 to 0.50 mm causes a drop mean of the tow thrust forces (F r CC650 and F r rCC670 ) at 83.3% and 54% for CC650 and CC670 tools, respectively.

3.1.3
Influence of the cutting parameters on the tangential force (Fz:Ft) Figure 5 shows the evolution of the tangential force F t as a function of the feed rate, for several depths of cut and several cutting speeds values for both ceramic tools CC650 and CC670. According to the graph, it can be seen that Ft increases with feed rate and mostly with depth of cut. The evolution of F t with cutting speed is not clear for this range of cutting conditions. In general, the lower cutting forces were registered at the higher cutting speeds. This can be related to the temperature increase in cutting zone and leads to the drop of the workpiece yield strength and chip thickness. These results are similar to those mentioned by the authors [23,24].

Response surface methodology (RSM)
RSM is a statistical technique based on simple multiple regressions. With this technique, the effect of two or more factors on quality criteria can be investigated and optimum values are obtained [7]. In RSM design, there should be at least two levels for each factor. In this way, the factor values that are not actually tested using fewer experimental combinations and the combinations themselves can be estimated [25,26]. Table 3 presents experimental results of cutting force components (Fx, Fy and Fz ) for various combinations of cutting regime parameters (cutting speed, feed rate and depth of cut) according to 2 3 (8) full factorial design.
The results of analysis of variance for cutting force components (Fx, Fy and F z) are shown in Tables 4-6. These tables also show the degrees of freedom (DF), sum of squares (SS), mean square (MS), F-values (F-value) and probability (Prob.) of each factor and different interactions. A low P-value indicates statistical significance for the source on the corresponding response. Table 4 shows the results of analysis of variance (ANOVA) for feed force of CC650 and CC670 tools. This analysis was carried out for a 5 per cent significance level, i.e. for a 95 per cent confidence level. The last column of the table shows the percentage of each factor contribution (Cont.%) on the total variation, thus indicating the  The other important coefficient R 2 in the resulting ANOVA table is defined as the ratio of the explained variation to the total variation and is a measure of the degree of fit. When R 2 approaches to unity, the better response model fits the actual data. The values of R 2 calculated in Table 3 for these models are over 0.95 and reasonably close to unity, which are acceptable. It denotes that about 95% of the variability in the data is explained by these models. It also confirms that these models provide an excellent explanation of the relationship between the independent factors and the response.
From Table 5, feed rate had the main statistical influence on thrust force F y (54.02 and 51.07)% for CC650 and CC670 tools, respectively. The next largest factor influencing on Fy is cutting speed with (26.27 and 39.11)% contribution. The depth of cut with (2.75 and 1.14)% contribution, has a very weak significance effect.
The R 2 value is high, close to 1, which is desirable. The "R-Squared" of (0.9998 and 0.9807) are in reasonable agreement with the "AdjR-Squared" of (0.9984 and 0.8651) for CC650 and CC670 tools, respectively. The adjusted R 2 value is particularly useful when comparing models with different number of terms. "Adequate Precision" measures the signal to noise ratio. A ratio greater than 4 is desirable. Our ratio of (77.265 and 7.804) for CC650 and CC670 tools respectively, indicates an adequate signal. So, these models can be used to navigate the design space.
According to Table 6, it can be seen that the cutting speed (47.72 and 54.72)% followed by feed rate (39.86 and 39.58)% had the greatest influence on Fz for both cutting tools (CC650 and CC670), respectively. The depth of cut The R 2 value is high, close to 1, which is desirable. The "R-Squared" of (0.9992 and 0.9840) are in reasonable agreement with the "AdjR-Squared" of (0.9941 and 0.8883) for CC650 and CC670 tools, respectively. The adjusted R 2 value is particularly useful when comparing models with different number of terms. "Adequate Precision" measures the signal to noise ratio. A ratio greater than 4 is desirable. Our ratio of (40.087 and 8.741) for CC650 and CC670 tools respectively, indicates an adequate signal. So, these models can be used to navigate the design space.

Regression equations
The relationship between the factors and the performance measures were modeled by polynomial regression. The regression equations obtained were as follows.
The feed force (Fx CC650 ) model is given below in Equation (1). Its coefficient of determination (R 2 ) is 99.88%.
The feed force (Fx CC670 ) model is given below in Equation (2). Its coefficient of determination (R 2 ) is 96.48%.   Figure 6a presents the influences of cutting speed (Vc) and feed rate (f ) on the cutting force components (Fa:Fx, Fr:Fy and Ft:Fz ) for both ceramic tools CC650 and CC670, while the depth of cut (ap) is kept at the middle level. The effects of the cutting speed (Vc) and depth of cut (ap) on the cutting force components for both ceramic tools CC650 and CC670 are shown in Figure 6b, while the feed rate (f ) is kept at the middle level. Figure 6c shows the estimated response surface in relation to the feed rate (f ) and depth of cut (ap), while cutting speed (Vc) is kept at the middle level. Mixed ceramic cutting tool CC650 has the lower values compared with reinforced ceramic cutting tools CC670, in particular the feed force.

Responses surface analysis
In general, the insert CC650 generates lower values of cutting force components than the CC670 ceramic reinforced tool. For example: F x CC670 ≈ 1.07F x CC650 , F y CC670 ≈ 1.4F y CC650 and Fz CC670 ≈ 1.05F z CC650 .This is due to the chemical composition of CC650 insert (percentage of TiC). TiC guarantees low thermal conductivity, toughness and ensures high chemical inertness. The properties of TiC slow triggering process of the different mechanisms of wear.

Optimization of cutting conditions
The optimal manufacturing conditions for hard turning of AISI 4140 with the constraints of cutting parametric range is that corresponding to lower values of feed force (Fa:Fx ), thrust force (Fr:Fy) and tangential force (Ft:Fz ) during the dry turning process. The constraints used during the optimization process are summarized in Table 7 Whereas the optimal solutions are reported in Table 8 in a decreasing desirability level order. This same Table shows the RSM optimization results for feed force, thrust force and tangential force. The optimum cutting parameters were obtained in Table 8 with cutting speed of (90 to 92.42) m.min −1 , feed rate of 0.08 mm.rev −1 and depth of cut (0.25 to 0.31) for CC650 and CC670 tools respectively The optimization was based on the Least Squares Method, i.e. the derived variables according to the minimum. The statistical software called Design-Expert 8 was used.
Desirability function approach has been used for multiple response factors (Fx:Fa, Fy:Fr and Fz:Ft ) optimization. The optimization module searches for a combination of factor levels that simultaneously satisfies the requirements placed on each of the responses and factors in an attempt to establish the appropriate model. During the optimization process the aim was to find the optimal values of machining parameters in order to produce the lowest values of cutting force components. To resolve this type of parameter design problem, an objective function, F (x), is defined as follows: where d i is the desirability defined for the ith targeted output and w i is the weighting of d i . For various goals of each targeted output, the desirability, d i , is defined in different forms. If a goal is to reach a specific value of T i , the desirability d i is: For a goal to find a maximum, the desirability is shown as follows: For a goal to search for a minimum, the desirability can be defined by the following formulas: where the Yi is the found value of the ith output during optimization processes; the Low i and the High i are, respectively, the minimum and the maximum values of the experimental data for the ith output. In Equation (7), w i is set to one since the d i is equally important in this study. The DF is a combined desirability function, and the objective is to choose an optimal setting that maximizes a combined desirability function DF, i.e., minimizes F (x).

Conclusions
The research work presents the application of RSM models which influences the machining variables of feed force, thrust force and tangential force. The relationship between the factors and the performance measures were modeled by polynomial regression. Three process parameters (cutting speed, feed rate and depth of cut) are considered for the development of the models. The developed RSM models are tested through ANOVA and found to be adequate at 95% confidence interval. The following conclusions are drawn from the present investigation.