Roughness modeling and optimization in CNC end milling using response surface method: effect of workpiece material variation

Transcription

1 Int J Adv Manuf Technol (2009) 40: DOI /s ORIGINAL ARTICLE Roughness modeling and optimization in CNC end milling using response surface method: effect of workpiece material variation B. C. Routara & A. Bandyopadhyay & P. Sahoo Received: 2 March 2007 / Accepted: 12 February 2008 / Published online: 15 March 2008 # Springer-Verlag London Limited 2008 Abstract Influence of machining parameters, viz., spindle speed, depth of cut and feed rate, on the quality of surface produced in CNC end milling is investigated. In the present study, experiments are conducted for three different workpiece materials to see the effect of workpiece material variation in this respect. Five roughness parameters, viz., centre line average roughness, root mean square roughness, skewness, kurtosis and mean line peak spacing have been considered. The second-order mathematical models, in terms of the machining parameters, have been developed for each of these five roughness parameters prediction using response surface method on the basis of experimental results. The roughness models as well as the significance of the machining parameters have been validated with analysis of variance. It is found that the response surface models for different roughness parameters are specific to workpiece materials. An attempt has also been made to obtain optimum cutting conditions with respect to each of the five roughness parameters considered in the present study with the help of response optimization technique. Keywords Roughness parameters. CNC milling. Response surface method. Optimization 1 Introduction Surface roughness is an important measure of product quality since it greatly influences the performance of mechanical parts as well as production cost. Surface roughness has an impact on the mechanical properties like B. C. Routara : A. Bandyopadhyay : P. Sahoo (*) Department of Mechanical Engineering, Jadavpur University, Calcutta , India [email protected] fatigue behavior, corrosion resistance, creep life, etc. It also affects other functional attributes of parts like friction, wear, light reflection, heat transmission, lubrication, electrical conductivity, etc. Sometimes, various catastrophic failures causing high costs have been attributed to the surface finish of the components in question. As a result, there have been a great many research developments in modeling surface roughness and optimization of the controlling parameters to obtain a surface finish of desired level since only proper selection of cutting parameters can produce a better surface finish. But such studies are far from complete since it is very difficult to consider all the parameters that control the surface roughness for a particular manufacturing process. Figure 1 shows the fishbone diagram with the parameters that affect surface roughness [1]. In the manufacturing industries, various machining processes are adopted for removing the material from the workpiece for a better product. Out of these, end milling process is one of the most vital and common metal cutting operations used for machining parts because of its ability to remove materials faster with a reasonably good surface quality. In recent times, computer numerically controlled (CNC) machine tools have been implemented to realize full automation in milling since they provide greater improvements in productivity, increase the quality of the machined parts and require less operator input. It is in general observed that surface roughness in turning operations has traditionally received considerable research attention while the same for multipoint cutting like end milling process has received only limited attention. A brief review of literature on roughness modeling in milling is presented here. Kline et al. [2] investigated the effect of vibration, deflection and chatter of the tool-workpiece system on roughness in end milling. Alauddin et al. [3] developed the mathematical model of surface roughness for the end milling of 190 BHN steel considering only the

2 Int J Adv Manuf Technol (2009) 40: Fig. 1 Fishbone diagram showing parameters affecting surface roughness [1] centre line average (CLA) roughness parameter (R a ) in terms of cutting speed, feed rate and depth of cut using response surface method (RSM). Fuh and Wu [4] studied using RSM the influence of tool geometries (nose radius and flank width) and cutting parameters (cutting speed, depth of cut, feed) on surface roughness (R a ) in end milling of Al alloy. Chen and his co-workers [5 7] studied the effect of spindle speed, feed rate and depth of cut on R a in end milling of Al workpiece. They have used in process surface roughness recognition and a neural fuzzy system to predict the roughness [6]. Mansour and Abdalla [8] studied the roughness (R a ) in end milling of EN 32 steel in terms of machining parameters using RSM. Ertekin et al. [10] considered three different materials, viz., 6061 Al, 7075 Al and ANSI 4140 steel for roughness (R a ) study in CNC milling. Benardos and Vosniakos [9] used Taguchi design to consider prediction of R a in CNC face milling of Al alloy. Dweiri et al. [11] considered neuro-fuzzy approach for roughness (R a ) modeling in CNC down milling of Alumic-79. Ghani et al. [12] considered Taguchi method for optimization of surface roughness (R a ) in end milling of hardened steel in terms of cutting parameters. Brezocnik et al. [13] used genetic programming for prediction of R a in CNC end milling of 6061 Al in terms of machining parameters as well as vibrations. Wang and Chang [14] investigated surface roughness (R a ) in slot end milling of Al. Oktem and co-workers [15, 16] analyzed the optimum cutting condition leading to a minimum roughness (R a )in end milling by combining RSM with neural network and genetic algorithm for Al and plastic mold parts. Wang et al. [17] investigated the influence of micro-end-milling cutting conditions on roughness (R a ) of a brass surface using RSM. Reddy and Rao [18] developed a mathematical model for surface roughness considering the cutting parameters and tool geometry during end milling of medium carbon steel using RSM. Recently, Ozcelik and Bayramoglu [19] have modelled R a in high speed flat end milling of steel including total tool operating time along with other machining variables such as spindle speed, feed rate, depth of cut and step over. Ryu et al. [20] incorporated the effect of cutting edge angle on roughness and texture generation on end milled steel surfaces. They have used RMS deviation, skewness and kurtosis for evaluating the generated surface texture characteristics. Bagci and Aykut [21] used the Taguchi optimization method for low surface roughness value (R a ) in terms of cutting parameters in CNC face milling of Cobalt based alloy. More recently, Chang and Lu [22] have presented the optimization of cutting parameters for side milling of medium carbon steel with multiple roughness characteristics, viz., feeding direction roughness, axial direction roughness and waviness using grey relational Taguchi approach. The review of literature on roughness modeling of milled surfaces reveals the fact that the centre line average roughness (R a ) has mostly been investigated. However, a surface generated by machining is composed of a large number of length scales of superimposed roughness [23] and generally characterized by three different types of parameters, viz., amplitude parameters, spacing parameters and hybrid parameters. Amplitude parameters are measures of the vertical characteristics of the surface deviations and examples of such parameters are centre line average roughness, root mean square roughness, skewness, kurtosis, peak-to-valley height, etc. Spacing parameters are the measures of the horizontal characteristics of the surface deviations and examples of such parameters are mean line peak spacing, high spot count, peak count, etc. On the other hand, hybrid parameters are a combination of both the vertical and horizontal characteristics of surface deviations and example of such parameters are root mean square slope of profile, root mean square wavelength, core roughness depth, reduced peak height, valley depth, peak area, valley area, etc. Thus consideration of only one parameter like centre line average roughness is not sufficient to describe the surface quality though it is the most commonly used roughness parameter. The present study aims at consideration of five different roughness parameters, viz., centre line average roughness (R a ), root mean square roughness (R q ), skewness (R sk ), kurtosis (R ku ) and mean line peak spacing (R sm ) for the surface texture generated in CNC end milling of three different materials, viz., brass, aluminum and mild steel. Direct as well as interactive effect of process parameters on surface roughness parameters have been examined quantitatively by the analysis of variance (ANOVA). Statistical models have been developed using response surface methodology based on experimental results. Thus the present study incorporates two new considerations; it develops roughness models for five different roughness

3 1168 Int J Adv Manuf Technol (2009) 40: Table 1 Variable levels used in the experimentation Levels Aluminium Brass Mild steel d (mm) N (rpm) f (mm/min) d (mm) N (rpm) f (mm/min) d (mm) N (rpm) f (mm/min) parameters as well as it considers the effect of workpiece material variation using three different materials. For each of the three materials, the roughness model is developed using response surface method for each of the five parameters considering the cutting parameters, viz., spindle speed (N, rpm), depth of cut (d, mm) and feed rate (f, mm/min)as independent variables. Finally an attempt has been made to obtain optimum cutting conditions with respect to each of the roughness parameters considered in the present study with the help of response optimization technique. 2 Response surface method Response surface method (RSM) adopts both mathematical and statistical techniques which are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize the response [24]. In most of the RSM problems, the form of the relationship between the response and the independent variables is unknown. Thus the first step in RSM is to find a suitable approximation for the true functional relationship between response of interest y and a set of controllable variables {x 1, x 2,...x n }. Usually when the response function is not known or non-linear, a second-order model is utilized [24] in the form: y ¼ b 0 þ Xn i¼1 b i x i þ Xn i¼1 b ii x 2 i þ XX b ij x i x j þ " i<j ð1þ where, ɛ represents the noise or error observed in the response y such that the expected response is (y -ɛ) and b s are the regression coefficients to be estimated. The least square technique is being used to fit a model equation containing the input variables by minimizing the residual error measured by the sum of square deviations between the actual and estimated responses. The calculated coefficients or the model equations, however, need to be tested for statistical significance. Analysis of variance (ANOVA) is used to check the adequacy of the model for the responses in the experimentation. ANOVA calculates the F-ratio, which is the ratio between the regression mean square and the mean square error. If the calculated value of F-ratio is higher than the tabulated value of F-ratio for roughness, then the model is adequate at desired significance level α to represent the relationship between machining response and the machining parameters. For testing the significance of individual model coefficients, the model is optimized by adding or deleting coefficients through backward elimination, forward addition or stepwise elimination or addition. It involves the determination of P- value or probability of significance that relates the risk of falsely rejecting a given hypothesis. If the P-value is less or equal to the selected α-level, then the effect of the variable is significant. If the P-value is greater than the selected α-value, then it is considered that the variable is not significant. Sometimes the individual variables may not be significant. If the effect of interaction terms is significant, then the effect of each factor is different at different levels of the other factors. In the present study, ANOVA for different response variables is carried out using commercial software Minitab [25] with confidence level set at 95%, i.e., the α-level is set at Table 2 Composition and mechanical properties of workpiece materials Work material Chemical composition (%Wt) Mechanical property Aluminium (6061-T4) Brass (UNS C34000) Mild steel (AISI 1040) 0.2% Cr, 0.3%Cu, 0.85%Mg, 0.04% Mn, 0.5%Si, 0.04%Ti, 0.25% Zn, 0.5% Fe and balance Al 0.095%Fe, 0.9%Pb, 34%Zn and balance Cu 0.42%C, 0.48%Mn, 0.17%Si, 0.02%P, 0.018%S, 0.1%Cu, 0.09%Ni, 0.07%Cr and balance Fe Hardness-65 BHN, density-2.7 g/cc, tensile Strength-241 Mpa Hardness 68 HRF, density-8.47 g/cc, tensile strength-340 Mpa Hardness-201 BHN, density-7.85 g/cc, tensile strength-620 Mpa

4 Int J Adv Manuf Technol (2009) 40: Table 3 Complete experimental results for milling of aluminium Std. order Run order d N f R a (μm) R q (μm) R sk R ku R sm (mm)

5 1170 Int J Adv Manuf Technol (2009) 40: Table 3 (continued) Std. order Run order d N f R a (μm) R q (μm) R sk R ku R sm (mm)

6 Int J Adv Manuf Technol (2009) 40: Table 3 (continued) Std. order Run order d N f R a (μm) R q (μm) R sk R ku R sm (mm) To have an assessment of pure error and model fitting error, some of the experimental trials are replicated. The adequacy of the models is also investigated by the examination of residuals [24]. The residuals, which are the difference between the respective observed responses and the predicted responses are examined using the normal probability plots of the residuals and the plots of the residuals versus the predicted response. If the model is adequate, the points on the normal probability plots of the residuals should form a straight line. On the other hand, the plots of the residuals versus the predicted response should be structureless, i.e., they should contain no obvious pattern. 3 Experimental details 3.1 Design of experiment The design of experiments technique is a very powerful tool, which permits us to carry out the modeling and analysis of the influence of process variables on the response variables. The response variable is an unknown function of the process variables, which are known as design factors. There are a large number of factors that can be considered for machining of a particular material in end milling. However, the review of literature shows that the following three machining parameters are the most widespread among the researchers and machinists to control the milling process [5, 7]: depth of cut (d, mm), spindle speed (N, rpm) and feed rate (f, mm/min). In the present study these are selected as design factors while other parameters have been assumed to be constant over the experimental domain. A full factorial design [24] is used with five levels of each of the three design factors so that all the interactions between the independent variables can be investigated though it was required to conduct large number of experiments. Thus the design chosen is five level-three factor (5 3 ) full factorial design consisting of 125 sets of coded combinations for each workpiece material. The upper and lower limits of a factor are coded as +1 and -1, respectively, the coded value being calculated from the following relationships: ½ x i ¼ 2x ð x max þ x min ÞŠ ðx max x min Þ where x i is the required coded value of a variable x. The process variables/design factors with their values on different levels are listed in Table 1 for three different workpiece materials. The selection of the levels of the variables is limited by the capacity of the machine used in the experimentation as well as the recommended specifications for different workpiece tool material combinations [26]. Table 4 ANOVA for secondorder model for R a in CNC milling of aluminium Source Degrees of freedom Sum of squares Mean squares F calculated F 0.05 P Regression Residual error Total

7 1172 Int J Adv Manuf Technol (2009) 40: Table 5 ANOVA for model coefficients for R a in CNC milling of aluminium Source Degrees of freedom Sum of squares Mean squares F calculated F 0.05 P d N f d*n d*f N*f Error Total Response variables selected Literature review shows that the centre line average roughness (R a ) has received maximum attention from the researchers. However, in the present study, the following five different roughness parameters [27] have been selected as the response variables: centre line average roughness (R a, μm), root mean square roughness (R q,μm), skewness (R sk ), kurtosis (R ku ) and mean line peak spacing (R sm, mm). 3.3 Equipment used The machine used for the milling tests is a DYNA V4.5 CNC end milling machine having the control system SINUMERIK 802 D with a vertical milling head and equipped with maximum spindle speed of 9000 rpm, feed rate 10 m/min and 10 kw driver motor. For generating the milled surfaces, CNC part programs for tool paths were created with specific commands. 3.4 Cutting tools used Coated carbide tools are known to perform better than uncoated carbide tools. Thus commercially available CVD coated carbide tools were used in this investigation. The tools used were flat end mill cutters (8 mm diameter, 30 helix angle, TiAlN coated solid carbide, parallel shank, four flutes) produced by WIDIA (EM-TiAlN). The tools were coated with TiAlN coating having hardness, density and Table 6 Summary of ANOVA for roughness parameters in aluminium milling d N f d*n d*f N*f R a # # # # R q # # # R sk # R ku # # R sm # # # Significant parameters transverse rupture strength as 1570 HV, 14.5 g/cc and 3800 N/mm 2. The compressed coolant servo-cut was used as cutting environment. For each material a new cutter of same specification was used. 3.5 Workpiece materials The present study was carried out with three different materials, viz., 6061-T4 aluminium, AISI 1040 steel and medium leaded brass UNS C The chemical composition and mechanical properties of the workpiece materials are shown in Table 2. All the specimens were in the form of 100 mm 75 mm 25 mm blocks. 3.6 Roughness measurement Roughness measurement was done using a portable stylustype profilometer, Talysurf (Taylor Hobson, Surtronic 3+). The profilometer was set to a cut-off length of 0.8 mm, filter 2CR, traverse speed 1 mm/sec and 4 mm evaluation length. Roughness measurements, in the transverse direction, on the workpieces were repeated four times and average of four measurements of surface roughness parameter values was recorded. The measured profile was digitized and processed through the dedicated advanced surface finish analysis software Talyprofile for evaluation of the roughness parameters. 4 Results and discussion The influences of the cutting parameters (d, N and f) on the response variables selected have been assessed for three different materials by conducting experiments as outlined in Sect. 3. The results are put into the Minitab software for further analysis following the steps outlined in Sect. 2. The second-order model was postulated in obtaining the relationship between the surface roughness parameters and the machining variables. The analysis of variance (ANOVA) was used to check the adequacy of the second-

8 Int J Adv Manuf Technol (2009) 40: order model. The results for the three different materials are presented one by one. 4.1 Results and analysis for aluminium The complete results from the 125 machining trials for aluminium performed as per the experimental plan are shown in Table 3 along with the run order selected at random. The second-order response surface equations have been fitted using Minitab software for all the five response variables (R a, R q, R sk, R ku and R sm ). The equations can be given in terms of the coded values of the independent variables as the following: R sk ¼ 0:157 þ 0:0503d 0:1120N 0:0018f 0:0275dN 0:0450df þ 0:0582Nf þ 0:0096d 2 þ 0:1240N 2 0:0258f 2 R ku ¼ 2:72 þ 0:2090d 0:109N 0:0306f 0:155dN 0:0574df 0:0818Nf 0:0870d 2 þ 0:2890N 2 0:1070f 2 R sm ¼ 0:134 0:0005d 0:0026N þ 0:0057f ð4þ ð5þ R a ¼ 0:613 0:0609d 0:0257N þ 0:0291f þ 0:0420 dnþ 0:0047 df þ 0:0157Nf þ 0:0661d 2 0:0446N 2 þ 0:0041f 2 R q ¼ 0:741 0:0637d 0:0330N þ 0:0336f þ 0:0395dN þ 0:0020df þ 0:0156Nf þ 0:0733d 2 0:0324N 2 0:0024f 2 ð2þ ð3þ þ 0:0024dN þ 0:0051df 0:0035Nf þ 0:0076d 2 0:0090N 2 0:0074f 2 ð6þ The ANOVA and the F-ratio test have been performed to check the adequacy of the models as well as the significance of the individual model coefficients. For brevity, the ANOVA table for only R a is presented here. Table 4 presents the ANOVA table for the second-order model proposed for R a given in Eq. (2). It can be appreciated that the P-value is less than 0.05 which means that the model is significant at 95% confidence level. Also the calculated value of the Fig. 2 Main effect plots for roughness parameters in aluminium milling: (a) R a (μm), (b) R q (μm), (c) R sk (d) R ku (e) R sm (mm) [units for d, N and f are mm, rpm and mm/min, respectively]

9 1174 Int J Adv Manuf Technol (2009) 40: Fig. 2 (continued) F-ratio is more than the standard value of the F-ratio for R a. It means the model is adequate at 95% confidence level to represent the relationship between the machining response and the machining parameters of the CNC end milling process. Table 5 represents the ANOVA table for individual model coefficients where it can be seen that there are three effects with a P-value less than 0.05 which means that they are significant at 95% confidence level. These significant effects are depth of cut, spindle speed and the interaction between spindle speed and feed rate. P-value for feed rate is very close to 0.05, thus it may be concluded that feed rate is also significant. Similarly, analysis of variance is carried out for all the response models as given in Eq. (3 6). Table 6 presents the summary of ANOVA for all the roughness parameters in CNC milling of Al showing the significant effects. Figure 2 depicts the main effects plot for the roughness parameters and the design factors considered in the present study. From this figure also, the significant effects can be identified. Though the experiments were conducted using full factorial design, replication of the experiments with each combination could not be carried out due to limitation of

10 Int J Adv Manuf Technol (2009) 40: Table 7 Replication results for R a on aluminium Exp. No. d N f R a (replication 1) R a (replication 2) experimental resources. To have an assessment of pure error and model fitting error, 20% of the experiments, i.e., 25 experiments are chosen at random for replication. Table 7 shows the results for R a for the replication trials. ANOVA (Table 8) performed on these replication trials shows that lack-of-fit error is insignificant indicating that the fitted model is accurate enough to predict the response. Fig. 3 Normal probability plot of residuals for R a (μm) data in aluminium milling The normal probability plot of the residuals and the plot of residuals versus the predicted response for R a are shown in Figs. 3 and 4. A check on the plot in Fig. 3 reveals that the residuals generally fall on a straight line implying that the errors are distributed normally. Also Fig. 4 reveals that there is no obvious pattern and unusual structure. This implies that the model proposed is adequate and there is no reason to suspect any violation of the independence or constant variance assumption. Similar residual analysis has also been carried out for other parameters. However, plots have been omitted for brevity. Finally, since optimization of machining parameters increases the utility for machining economics as well as the product quality, to a great extent, an effort has been made to estimate the optimum machining conditions to produce the best possible surface quality within the experimental constraints. In this context, a response surface optimization is attempted using Minitab software for individual roughness parameters in CNC milling of Al. The objective function for optimization is set as minimization of R a, R q and R sm while R sk and R ku are targeted at 0 and 3, respectively. Table 9 shows the RSM optimization Table 8 ANOVA for replication experiments for R a of aluminium Source Degrees of freedom Seq. sum of squares Adj mean squares F calculated F 0.05 P Regression Linear Square Interaction Residual error Lack-of-fit Pure error Total

11 1176 Int J Adv Manuf Technol (2009) 40: roughness parameters. The second-order response surface equations for the roughness parameters in brass milling are obtained in terms of coded values of design factors as: R a ¼ 1:02 0:1530d 0:2230N þ 0:0707f þ 0:0217dN þ 0:0390df þ 0:0561Nf þ 0:0168d 2 þ 0:1430N 2 0:0030f 2 ð7þ Fig. 4 Plot of residuals versus fitted value for R a (μm) in aluminium milling R q ¼ 1:23 0:1670d 0:2620N þ 0:0881f þ 0:0056dN þ 0:0395df þ 0:0558Nf results for the roughness parameters in Al milling. It also includes the results from confirmation experiments conducted with the optimum conditions. It is found that the error in prediction of the optimum conditions for different roughness parameters is about 6 to12%. Thus the response optimization predicts the optimum conditions fairly well. Figure 5(a) shows the SEM micrograph of surface texture of aluminium workpiece before machining while Fig. 5(b) shows the surface texture observed on the milled aluminium workpiece machined with the optimum cutting conditions for roughness parameter R a. The brightness difference seen the micrographs is due to surface roughness effects. A decrease in roughness after milling is clearly visible in these micrographs. þ 0:0266d 2 þ 0:1670N 2 þ 0:0102f 2 R sk ¼ 0:285 0:1010d þ 0:0294N 0:0805f 0:0429dN 0:0309df 0:0186Nf 0:0470d 2 0:0271N 2 þ 0:0009f 2 R ku ¼ 2:49 þ 0:2050d þ 0:0550N 0:0078f 0:0759dN 0:1040df 0:1910Nf þ 0:0754d 2 þ 0:0047N 2 þ 0:1080f 2 R sm ¼ 0:163 0:0024d 0:0319N þ 0:0104f ð8þ ð9þ ð10þ 4.2 Results and analysis for brass For brass, 125 machining trials are performed as per the experimental plan to evaluate the roughness parameters and the second-order response surface models are fitted for the roughness parameters. The detailed results are omitted here for brevity. Similar to earlier case for aluminium, replication experiments are carried out for 20% cases to check pure error and model fitting error. Residual analysis is also performed to check the adequacy of the models of the 0:0016dN þ 0:0030df þ 0:0049Nf þ 0:0062d 2 þ 0:0194N 2 0:0162f 2 ð11þ These model equations as well as the individual coefficients are checked for adequacy by ANOVA and F-test. However, the detailed ANOVA results and plots are omitted here for brevity. Table 10 shows the summary of ANOVA for all the roughness parameters in milling of brass and it presents the significant parameters for individual roughness responses. Response optimization is also carried out in this case and Table 9 RSM optimization for roughness parameters in aluminium milling Parameters Objective function Optimum combination Predicted response Confirmation Expt. Error% d N f R a Minimum R q Minimum R sk Target R ku Target R sm Minimum

12 Int J Adv Manuf Technol (2009) 40: Figure 6(a) shows the SEM micrograph of surface texture of brass workpiece before machining while Fig. 6(b) shows the surface texture observed on the milled brass workpiece machined with the optimum cutting conditions for roughness parameter R a. A definite pattern of milling marks is clearly visible in the micrograph of milled surface. 4.3 Results and analysis for mild steel For mild steel also, 125 machining trials are performed as per the experimental plan to evaluate the roughness parameters and the second-order response surface models are fitted for the roughness parameters. Replication experiments are carried out for 20% cases to check pure error and model fitting error. Residual analysis is also performed to check the adequacy of the models of the roughness parameters. The detailed results are omitted here for brevity. The second-order response surface equations for the roughness parameters in CNC milling of mild steel are also obtained in terms of coded values of design factors as: R a ¼ 0:594 þ 0:1430d þ 0:0049N þ 0:0200f 0:0289dN 0:0028df 0:0387Nf þ 0:0049d 2 þ 0:0659N 2 þ 0:0130f 2 ð12þ Fig. 5 SEM micrograph of surface texture of aluminium workpiece: (a) before machining, (b) after machining Table 11 shows the RSM optimization results for the roughness parameters in brass milling. It also includes the results from confirmation experiments conducted with the optimum conditions. It is found that the error in prediction of the optimum conditions for different roughness parameters is about 7 to15%. Thus the response optimization predicts the optimum conditions fairly well. Table 10 Summary of ANOVA for roughness parameters in brass milling d N f d*n d*f N*f R q ¼ 0:822 þ 0:1780d þ 0:0052N þ 0:0299f 0:0397dN 0:0046df 0:0473Nf þ 0:0052d 2 þ 0:0659N 2 þ 0:0080f 2 R sk ¼ 2:13 þ 0:2080d 0:0653N 0:0214f þ 0:0131dN 0:0001df þ 0:0713Nf þ 0:2240d 2 þ 0:3590N 2 þ 0:0949f 2 R ku ¼ 10:6 1:280d þ 0:2840N 0:4430f þ 0:1350dN þ 0:1550df 0:1060Nf 0:6830d 2 2:0200N 2 0:6850f 2 R sm ¼ 0:0937 0:0120d 0:0014N 0:0061f ð13þ ð14þ ð15þ R a # # # # # R q # # # # # R sk # # # R ku # # # # R sm # # # # # Significant parameters þ 0:0068dN þ 0:0018df þ 0:0020Nf þ 0:0067d 2 0:0150N 2 þ 0:0014f 2 ð16þ These model equations as well as the individual coefficients are also checked for adequacy by ANOVA and F-test. However, the detailed ANOVA results and plots are omitted

13 1178 Int J Adv Manuf Technol (2009) 40: Table 11 RSM optimization for roughness parameters in brass milling Parameters Objective function Optimum combination Predicted response Confirmation Expt. Error% d N f R a Minimum R q Minimum R sk Target R ku Target R sm Minimum here. Table 12 shows the summary of ANOVA for all the roughness parameters in milling of mild steel and it presents the significant parameters for individual roughness responses. Response optimization is also carried out in this case, and Table 13 shows the RSM optimization results for the roughness parameters in milling of mild steel. It also includes the results from confirmation experiments conducted with the optimum conditions. It is found that the error in prediction of the optimum conditions for different roughness parameters is from about 4% to13%. Thus the response optimization predicts the optimum conditions fairly well. Figure 7(a) shows the SEM micrograph of surface texture of mild steel workpiece before machining while Fig. 7(b) shows the surface texture observed on the milled mild steel workpiece machined with the optimum cutting conditions for roughness parameter R a. Clearly an improvement of surface texture is visible in the micrograph of milled surface. A comparison of the response surface models for roughness parameters in different materials reveals the fact that these models are material specific or in other words, the tool workpiece material combination plays a vital role in surface roughness modeling. Also the effect of the cutting parameters on roughness parameters is different for different materials. Accordingly, optimum machining parameter combinations for different roughness parameters depend greatly on the workpiece material within the experimental domain. However, it can be concluded that it is possible to select a combination of spindle speed, depth of cut and feed rate for achieving the best possible surface finish expressed in terms of a specific roughness parameter of choice within the constraints of the available machine. The application of the present approach to obtain optimal machining conditions may be quite useful in computeraided process planning. Thus with the known boundaries of desired surface roughness parameter and machining param- Table 12 Summary of ANOVA for roughness parameters in milling of mild steel d N f d*n d*f N*f Fig. 6 SEM micrograph of surface texture of brass workpiece: (a) Before machining, (b) After machining R a # # # # # # R q # # # # R sk # # R ku # # # R sm # # # # # # Significant parameters

14 Int J Adv Manuf Technol (2009) 40: Table 13 RSM optimization for roughness parameters in milling of mild steel Parameters Objective function Optimum combination Predicted response Confirmation Expt. Error% d N f R a Minimum R q Minimum R sk Target R ku Target R sm Minimum eters, machining can be performed with a relatively high rate of success. Establishment of efficient machining parameters has been a problem that has confronted manufacturing industries for years. Obtaining optimum machining parameters is of great concern in manufacturing industries, where the economy of machining operation plays a vital role in the competition to survive in the market. In material removal processes like milling, etc., an improper selection of cutting conditions causes surfaces with high roughness and dimensional errors. In view of the significant role that the milling operation plays in today s manufacturing world, it is very essential to optimize the machining parameters for the operation for different workpiece materials. The practical value of the foregoing predicted models for different roughness parameters is that they can be robust tools for identification of the machining parameters ranges to achieve a desired value of a surface roughness parameter. One of the new incorporations of this work is the selected surface roughness parameters. Different machine elements require specific ranges of particular roughness parameter for functional requirements. Thus in the present work, five important roughness parameters are studied. These results could become a reference to machine manufacturers especially when the similar workpiece tool combination is used. It would be possible to manufacture parts with certain surface roughness requirements using the results instead of trial and error. Therefore, the manufacturing time will be reduced. It is believed that this approach is quite advantageous in order to have the range of the surface roughness values and their corresponding optimum machining conditions for a certain range of input parameters depending on the capacity of the machine used for the purpose. Thus this would be helpful for a manufacturing engineer to select the machining conditions for the desired machining performance of the product. workpiece materials using response surface method. The second-order response models have been validated with analysis of variance. It is found that all the three cutting parameters (spindle speed, depth of cut and feed rate) and their interactions have significant effect on roughness parameters considered in the present study though the influences vary with the nature of workpiece material. Thus response surface models are specific with respect to the 5 Conclusions The present study develops roughness models for five different roughness parameters and for three different Fig. 7 SEM micrograph of surface texture of mild steel workpiece: (a) Before machining, (b) After machining

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