Proceedings of 1st International Conference on Mechanical Engineering: Emerging Trends for Sustainability Edited by: C.M. Krishna, A.R. Siddiqui and M.K. Pradhan Copyright 2014© MANIT, Bhopal
Modeling and Optimization of Machining Parameters in Milling Al-SiCp Metal Matrix Composites using Taguchi Method and Regression based GA M. Chandrasekaran, S. Tamang, Manish Sharma and Sumit Kumar Mechanical Engineering, North Eastern Regional Institute of Science and Technology, Arunachal Pradesh, INDIA
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Abstract In this paper an experimental investigation and optimization process parameters is performed in milling Al-SiCp metal matrix composites (MMC) using carbide tool. The experiments were carried out to investigate the surface quality of the machined component. The spindle speed (N), feed (f), depth of cut (d) and SiCp percentage (SiC) are considered as four independent variables on which the surface roughness (Ra) depends. Experimental design based on L9 (43) orthogonal array is employed. The optimal level of the process parameters was determined through the analysis of means (ANOM). The ANOVA results indicated that the most significant process parameter is feed followed by spindle speed and depth of cut that affect the response characteristics. Multiple linear regression model is developed to establish the relationship between the response characteristics (i.e., surface roughness) and the machining factors. The model prediction is compared with experimental result and average prediction error is found as 9.06 %. Parameters optimization using Genetic Algorithm (GA) provide improved result showing signal-to-noise (S/N) ratio improvement in comparision with Taguchi optimization. Keywords: GA, Milling, MMC, Regression, Taguchi, Surface roughness
1. Introduction The surface roughness is one the important measure of product quality of the machined component. Optimum machining parameter selection for obtaining (i) the minimum surface roughness or (ii) the desired value of surface roughness is very essential for the economic aspects of machining process. The conventional approaches that optimizes the process include Taguchi method and multiple regression/response surface methodology (RSM) techniques [Mukherjee and Ray, 2006]. Apart from conventional approaches recently researchers use soft computing approaches such as genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO) and ant colony optimization (ACO) [Zain et al., 2010]. Among various conventional machining processes milling is widely used for shaping and removing high rate of metal for manufacturing prismatic components. Milled surfaces are largely used to mate with other parts in die, particularly in automotive and aerospace industries. The selection of cutting parameters during finishing machining process is one of the important factors in achieving the high cutting performance as well as minimum surface roughness. Most of the researchers performed the machinability study on particulate reinforced MMCs in turning, milling, and grinding, drilling and other non conventional machining processes for estimation of different performance measures [Davim, 2003; Tamang et al., 2013]. Survey of previous research on modeling and optimization of milling and other machining process was carried out by [Chandrasekaran et al., 2010]. Researchers have attempted to model the surface
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roughness prediction using multiple regression, mathematical modeling based on physics of the process, fuzzy logic and artificial neural network. These methods are expensive in terms of time and material consumption. Taguchi method of parametric optimization using the Design of Experiment (DoE) is used by the number of researchers [Taguchi, 1990]. It offers a simple and systematic approach to optimize, design for performance, quality and cost. It optimizes the performance characteristic through the setting design parameter and reduces the sensitivity of the system performance due to variation of sources [Ghani et al., 2004]. Lou and Chen (1999) studied the effect of spindle speed, feed rate and depth of cut on the surface roughness of end milling processes employing in-process surface roughness recognition (ISRR) and a neural fuzzy system to predict the work piece surface roughness. Zain et al. (2010) also used neural network model for predicting surface roughness in the milling process. In this work an experimental investigation is carried out in an end milling of LM 25 aluminium alloy matrix with silicon carbide particulate reinforced MMC using carbide tool. Three machining parameters viz. spindle speed, N (rpm), feed rate, f (mm/min) and depth of cut, d (mm) along with one more variable i.e., silicon carbide content on the work material, SiC (%) are considered for investigation of surface roughness. Taguchi L9 (with four factors with three levels) orthogonal array of experimental design is followed and analysis are performed using MINITAB 15 statistical software. The contribution of different parameters was analyzed with ANOVA. Alternatively a mathematical model based on multiple linear regression is developed. Statistical regression model for predicting the surface roughness was developed. The process variables are optimized to minimize the surface roughness using GA. 2. Taguchi approach of experimental design and optimization Taguchi methodology is a simple and robust technique for design of experiments and optimizing the process parameters that involves reduced process variation. The classical experimental design methods are too complex and need large number of experiments if the number of variable are more. Taguchi has suggested an orthogonal array based (DoE) in a tabular form for the selection of input parameters design for experimentation. The method allows controlling the variations caused by the uncontrollable factors which are not considered in conventional experimental design [Zhang et al., 2007]. The methodology saves time and money in performing experiments. In optimizing the paramters Taguchi converts the response to signal-to-noise (S/N) ratios. S/N ratio is the logithmic function of desired response. It is defined as the desired signal ratio for the undesired random noise value and it shows the quality characteristics of the experimental data [Ross, 1996]. Three different equations namely (i)‘the-smaller-the-better’, (ii)‘the-larger-the-better’ and (iii)‘thenominal-the-best’ are employed depending upon the response to minimize, maximize, or nominalize respectively. The S/N ratio is used as the measure of the response characteristics and the significant process parameters through analysis of variance. The optimal parametric setting is obtained through analysis of means (ANOM). It is the process of estimating the main effects of each parameter [Phadke, 1989]. The effect of a parameter level is the deviation that it causes from the overall mean response (m) and is given by Eq. 1 1 k m = ∑η k , k k =1
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(1)
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where η is the S/N ratio, k is the number of experimental trials. The effect of process parameter of level i for the parameter j is obtained as ( m )i , j =
1 l ∑ (ηi ) j . l i =1
(2)
Finally, the best combination of parameter is selected based on the level of the process parameter that gives the highest S/N ratio.
3.
Experimental procedure
The machining experiments were carried out on milling machine (Batliboi model) and machining is performed at machine shop in NERIST, Arunachalpradesh (INDIA). The carbide end mill cutter of 10 mm diameter is held on the spindle of the machine and rotates in vertical axis. The MMC work piece is clamped on vice mounted on the table of the machine. The spindle speed (N), feed rate (f), depth of cut (d) and silicon carbide percentage (SiC) of the workpiece were considered as input parameters on which the surface roughness depends. The selected factors are varied through three levels within the range of parameters available in the machine. Higher range of spindle speed and lower range of feed rate that leads to better surface finish was considered. Table 1 shows the factors and different levels of the end milling process. Table 1. Assignments of levels to the factors Code
Factor
Level 1
Level 2
Level 3
A
Spindle speed (N) rpm
710
1000
1400
B
Feed (f) mm/min
20
28
40
C
Depth of cut (d) mm
0.5
1.0
1.5
D
Silicon carbide percentage (SiC) %
10
20
30
The OA selection is based on the limitation of minimum number of experiments (Expmin) needed for the particular number of factors and levels. It is calculated using Eq. 3. Expmin = k (l − 1) + 1,
(3)
where k and l are number of factors and number of levels respectively. For 4 factors with 3 levels the minimum number of experiments needed is 9 and Taguchi’s L9 (43) OA is selected. Nine experimental trials were performed. Fig.1 demonstrate the conduct of milling experiments for the analyse of surface roughness of the component The experimental set up with work-tool motion of the machining process is shown in Fig.1(a). Each experiment was carried out for the designed combination of machining parameter on the work material having particular percentage of SiC. The cutting is performed for the machining length of 100 mm. The measurement of performance there are various measure of surface roughness
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amplitude parameters are used in manufacturing industries. This includes centre line average values of surface roughness (Ra), root-mean square (rms) value of roughness (Rq) and maximum peak-to-valley reoughness (R max of R y) measurement [Yang and Chen, 2001]. In this study CLA surface roughness (Ra) which is arithmetic average deviation from the mean line, is used. It is defied as the integral of the absolute value of the roughness profile height over the evaluation length and is given as
Ra =
1 L Y ( x) dx, L ∫0
(4)
where L is the the evaluation length and Y(x) is the ordinate of the profile curve. The evaluation length was taken as 2.4 mm. The Ra is measured at 3 different locations along the length, repeated twice at each points and average values are recorded. The Pocket Surf (Mahr, GmbH) was used to measure surface roughness. The measuring range is between 0.03–6.35 µm. Table 2 shows the experimental result of each run. Table 2. Experimental result of Ra
Fig 1: Experimental set up 3.1 Taguchi optimization The experimental data are analysed using Taguchi method. The most essential criterion is signal-tonoise ratio. S/N ratio is used instead of mean value to interpret the experimental results into a value for the evaluation characteristic in the optimum setting analysis [Phadke, 1989]. In this study, smaller-thebetter S/N ratio is used and is defined by the Eq. 5 1 n 2 ∑ Rai , n i =1
(5)
η = −10 log10
where η is the S/N ratio, n is the number of data sets and Ra is CLA surface roughness. Analysis of interaction effects of parameters on performance characteristics is performed to study the various effects on the performance characteristic with change of parameters. The plots of two factor interaction effects on S/N ratio of output characteristics are generated using MINITAB16 statistical software. The study shows combination of lower value of feed rate and higher value of spindle speed provide better S/N ratio and the surface finish will improve. It is to be noted that better surface finish
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means lower value of surface roughness and higher value of surface finish, but as the value of feed rate increases and reach up to its maximum level then S/N ratio decreases comparatively even with increase of spindle speed. Also, we can clearly observe that a combination of maximum spindle speed and medium Silicon carbide percentage gives higher value S/N ratio. From Fig. 2 it can be seen from the main effect graph that the maximum and minimum values of S/N ratio obtains significant effect of the factors on surface roughness. The feed rate has highest difference of 1.35 followed by spindle speed of 0.78. Thus, it can be concluded that increasing the feed rate will increase the Ra significantly and also the spindle speed. The main effects of each factor that influence on response characteristics is evaluated using analysis of means (ANOM). S/N ratio of the Ra is used to determine the optimum levels of each variables. The analysis of means determine the optimal process parametric settings and it is the Figure 2 Mean S/N ratio plot for surface roughness process of estimating the main effects of each parameter. The effect of a parameter level is the deviation it causes from the overall mean response. The overall mean of η associated with nine trials is computed by using Eq. 1. From Fig. 2 S/N ratio is higher for the third level of A factor (spindle speed), the first level of B factor (feed), the third level of C factor (depth of cut) and the second level of factor D (SiCp percentage). Thus optimum cutting parameters setting for the investigation of surface roughness is A3, B1, C3 and D2. The best combination values for achieving minimum surface roughness are at the spindle speed of 1400 rpm, feed rate of 20 mm/min, depth of cut of 1.5 mm and silicon carbide percentage of 20%. The value of surface roughness for above combination of input parameters is 1.53 µm. 3.2 Analysis of varience Analysis of varience is perfomed to estimate the relative significance of each factor in terms of percent contribution on the overall response. The factor with higher percentage contribution are ranked higher in terms of importance in the experiment and also have significant effects in controlling the overall response. The analysis was carried out for a level of confidence of 95% (i.e., level of significance os 5%). The result shows that the feed rate has major contribution (78.12%) followed by spindle speed (19.20%). However, depth of cut and SiC percentage has minor effect on response.
4. Regression and GA based parameter optimization Apart from Taguchi optimization the conventional method of modeling multiple parameters employe different statistical tools such as multiple regression analysis and response surface methodology (RSM) being widely used for the development of mathematical models. The correlation between the factors and the measured surface roughness were obtained by statistical regression. The functional relationship between output and input variables of the process is useful for manufacturing process data description, parameter estimation and control.
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4.1 Development of mathematical model In this work the functional relationship between surface roughness and four machining factors viz., speed, feed, depth of cut and silicon carbide percentage is established using regression analysis. The linear functional relationship between surface roughness and different process factors under investigation is postulated by Eq. 6 Ra = a0 + a1 N + a2 f + a3 d + a4 SiC ,
(6)
where Ra = surface roughness (µm), N = spindle speed (rpm), f = feed (mm/rev) d = depth of cut (mm), and SiC = Silicon carbide content (%). The a0 is a constant and a1, a2, a3 and a4 are coefficients. The regression model is predicted from the MINITAB 15 statistical software using the experimental data. The multiple linear regression equation for surface roughness (Ra) is obtained as: Ra = 1.76 – 0.00109N + 0.0641 f – 0.047d + 0.0088 SiC
(7)
Fig 3: Comparison of result (Avg. error %= 9.06) The predictive performance of the developed model obtain an average error percentage of 9.06. The comparision of model performance is given in Table 3 an Fig. 3. 4.2 Optimization with conventional GA The objective of the GA optimization is to determine the optimal cutting parameters that obtain minimum value of Ra. The problem is formulated with the objection function being the multiple linear regression obtained from statistical modeling. The minimization function is subjected to variable bounds of the factors. The range of the level of each factor decides the upper and lower bounds of the variables. The formulation of the problem is written as follows: Minimize _ Ra ( N , f , d , SiC ) = 1.76 − 0.00109 N + 0.0641 f − 0.0047d + 0.0088SiC
Subjected to 710 ≤ N ≤ 1400 20 ≤ f ≤ 40 0.5 ≤ d ≤ 1.5 10 ≤ SiC ≤ 30
(8)
(9)
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The problem is solved in GA using MATLAB tool box. The parametric study shows that the GA parameters that yield the best results are (i) crossover probability, pc = 0.90, (ii) mutation probability, pm = 0.001, (iii) population size = 100, (iv) maximum number of generations G = 50000. The minimum value of fitness (i.e., Ra=1.50 µm) is obtained at 59 the generation. The minimum surface roughness is obtained at (N, f, d, SiC: 1379 rpm, 20 mm/min, 1.5 mm, 11.4 %) found as optimum factors. 4.3 Comparision of result The comparision of result is made between Taguchi and regression based GA optimization. The optimal parameters obtained by Taguchi (A3B1C3D2) correceonds to 1400 rpm, 20 mm/min, 1.5 mm and 20% predicts 1.53µm and also confirms the experimental result. The improvement of S/N ratio from the initially selected factors to the optimal factors is found as 6.75 dB. The optimal factors Table 4. Result of comparision obtained by regression based GA optimization correspondes to only variation in SiC % content. The optimal factors are N at 1400 rpm, f at 20 mm/min, d at 1.5 mm and SiC at 10% predicting surface roughness 1.50µm. The experimental confirmation is 1.48 µm that gives increased improvement in S/N ratio compared to Taguchi. The improvement of the S/N ratio of individual performace is shown in Table 4.
5. Conclusion In this study, Taguchi’s method of signal-to-noise (S/N) ratio and anlysis of variance (ANOVA) are applied to evaluate the effects of different factors on average surface roughness of the milled component. Experiments are conducted using L9 orthogonal array. Spindle speed, feed, axial depth of cut and silicon carbide percentage are considered for the present investigation of surface roughness.The optimal variable levels are obtained for producting minimum surface roughness in end milling of Al-SiCp MMC composites using carbide tool. The multiple linear regression model for the prediction of Ra has been developed. The developed mathematical model is used optimize the process factors employing conventional GA. The results obtained in this study are presented here. 1.
The experimental design based on Taguchi L9 (with four factors with three levels) orthogonal array minimize the experimental effort and time instead of the full factorial of 81 experiments.
2.
Taguchi parameteric optimization provides a simple, systematic and efficient method. optimal level of the factors was determined through the analysis of means (ANOM). The best combination values for achieving minimum surface roughness as (A3B1C3D1) were found as spindle speed of 1400 rpm, feed rate of 20 mm/min, axial depth of cut of 1.5 mm and silicon carbine percentage of 20 %. The resulting surface roughness is 1.53 µm.
3.
Based on ANOVA anlysis the influencing parameters for the surface roughness was determined. Feed rate is found as the main factor that has the most importance on the surface roughness and
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this factor is about 3 times more important than the next ranking factor (i.e., spindle speed). The other factors does not seem to have much of influence on the response. 4.
The multiple linear regression model developed for prediction of surface soughness showed that the deviations between the experimental and predicted values have good correlation and have average percentage of error of 9.06.
5.
Both the method provides nearly same optimum parameters except the change in SiC %. Regression based GA provide increased improvement in S/N ratio of 7.10 dB compare with the selection of initial factors. The corresponding optimum factors are N at 1380 rpm, f at 20 mm/min, d at 1.5 mm and SiCp % at 10. The experimental confirmation in milling produce 1.48 µm while GA prediction is 1.5 µm.
References Mukherjee, I. and P.K. Ray, P.K. (2006) A Review of Optimization Techniques in Metal Cutting Processes. Comput. Ind. Eng., 50, 15–34. Zain, A.M., Haron, H. and Sharif, S. (2010) Application of GA to Optimize Cutting Conditions for Minimizing Surface Roughness in End Milling Machining Process. Expert Syst. Appl., 37, 4650–4659. Davim, J. P (2003) Design of optimization of cutting parameters for turning metal matrix based on the orthogonal arrays. Journal of Material Processing Technology, 132,340–344. Tamang, S., Chandrasekaran, M. and Samanta, S. (2013) Application of computational methods in modeling optimization of composite machining processes: a literature review. 3rd International Conference on RAMPT’13,Tamlnadu, India. Chandrasekaran, M., Muralidhar, M., Murali Krishna, C. and Dixit, U. S. (2010) Application of soft computing techniques in machining performance prediction and optimization: a literature review. International Journal Advance Manufacturing Technology,46,445–464. Taguchi, G. (1990) Introduction to Quality Engineering, Asian Productivity Organization, Tokyo. Ghani, J.A., Choudhury, I.A. and Hassan, H.H. (2004) Application of Taguchi method in the optimization of end milling parameters. Journal of Material Processing Technology,145,84-92. Lou, S.J. and Chen, J.C. (1999) In-process surface roughness recognition (ISRR) system in endmilling operation. International Journal of Advance Manufacturing Technology,15, 200–209. Zhang, J.Z., Chen, J.C. and Kirby, E.D. (2007) Surface roughness optimization in an end-milling operation using the Taguchi design method. J. Mater. Process. Technol., 184 , 233–239. Ross, P.J.(1996) Taguchi Techniques for Quality Engineering. McGraw-Hill International Book Company, OH. Phadke, M.S. (1989) Quality Engineering Using Robust Design. Prentice Hall, New Jersey.
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Yang, J.L and Chen, J.C.(2001) A systematic approach for identifying optimum surface roughness performance in end-milling operations. J Indus Technology, 17(2 ),1–8.
Biographies AuthorName1: M.Chandrasekaran currently working as Associate Professor in the department of Mechanical Engg., NERIST, Arunachal Pradesh, India. He has 17 years of teaching experiences. He has obtained M.Tech in Production Engg.Systems Technology (PEST) in the year 1996. Currently he is pursuing PhD in the Mechanical Engg. Deptt, Indian Institute of Technology, Guwahati, India. He has published 7 research papers in the referred International Journals, 6 papers in National Journals and 23 papers in International/national conferences. He guided 6 PG and 14 UG projects. He is Life member of ISTE, MIE, and WSI. His area of research interest includes Machining optimization, Automated manufacturing, Soft computing techniques, and Fluid power control system. AuthorName2: S. Tamang currently working as Guest Faculty in department of Mechanical Engg., NERIST, Arunachal Pradesh, India. He has obtained M.Tech in Computer Integrated Manufacturing and Automation (CIMA) in the 2013.He has published 1 research paper in Indian Journal and few paper in International and National conference. His area of research interest includes Machining optimization,and Soft computing techniques. AuthorName3: Manish Sharma grauated B.Tech in Mechanical engineering from NERIST. His area of research interest is Taguchi optimization and modeling. AuthorName4: Sumit Kumar grauated B.Tech in Mechanical engineering from NERIST. His area of research interest is Taguchi optimization and modeling.
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