National Institute of Technology (NIT), Rourkela, Orissa , India

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1 Prncpal Component Analyss n Grey Based Taguch Method for Optmzaton of Multple Surface Qualty Characterstcs of 661-T4 Alumnum n CNC End Mllng Saurav Datta a, Bharat Chandra Routara b, Assh Bandyopadhyay c and Sba Sankar Mahapatra d a, d Department of Mechancal Engneerng, Natonal Insttute of Technology (NIT), Rourkela, Orssa-7698, Inda Emal: sdattaju@gmal.com, mahapatrass23@gmal.com b Department of Mechancal Engneerng, KIIT Unversty, Bhubaneswar, Orssa, Inda Emal: routray_bharat@redffmal.com c Department of Mechancal Engneerng, Jadavpur Unversty, Raja S. C. Mallk Road, Kolkata- 732, West Bengal, Inda Emal: asshbanerjee@yahoo.com Abstract. The present study hghlghts a mult-objectve optmzaton problem by applyng Prncpal Component Analyss (PCA) coupled wth grey based Taguch method through a case study n CNC end mllng of 661-T4 Alumnum. The study amed at evaluatng the best process envronment whch could smultaneously satsfy multple requrements of surface qualty. In vew of the fact, that tradtonal Taguch method cannot solve a mult-objectve optmzaton problem; to overcome ths lmtaton, grey relaton theory has been coupled wth Taguch method. Furthermore, to follow the basc assumpton of Taguch method.e. qualty attrbutes should be uncorrelated or ndependent; whch s not always satsfed n practcal stuaton. To overcome ths shortcomng the study appled Prncpal Component analyss to elmnate response correlaton and to evaluate ndependent or uncorrelated qualty ndces called Prncpal Components whch were aggregated to compute an overall qualty ndex denoted as overall grey relatonal grade whch was optmzed (mnmzed) fnally. The study combned PCA and grey based Taguch method for predctng optmal settng. Optmal result was verfed through confrmatory test. Keywords: Prncpal Component Analyss (PCA); grey Taguch method; CNC end mllng PACS: 89 INTRODUCTION AND PRIOR STATE OF ART In recent tmes, computer numercally controlled (CNC) machne tools have been mplemented to realze full automaton n machnng. CNC machne tools provde greater mprovements n productvty, and ncrease the qualty of the machned parts

2 and requre less operator nput. Mllng s a common metal removal operaton n ndustry because of ts ablty to remove materal faster wth a reasonably good surface qualty. It s wdely used n a varety of manufacturng ndustres ncludng aerospace and automotve sectors, where qualty s an mportant factor n the producton of slots, pockets, precson moulds and des. Lterature [Ghan et al. (24), Yang and Chen (21), Chang and Lu (27)) depcts that work have been done for optmzng the process parameters and mprovng the performance measures of CNC end mllng process. However, all these studes whether expermental or analytcal mostly concentrate on the centre lne average roughness Ra value for surface qualty. But surface generated by machnng s composed of a large number of length scales of supermposed roughness, [Sahoo, (25)] that are generally characterzed by three dfferent types of parameters, vz., ampltude parameters, spacng parameters and hybrd parameters. Thus consderaton of centre lne average roughness alone s not suffcent to descrbe surface qualty. The other roughness parameters lke root mean square roughness (R q ), kurtoss (R ku ) and mean lne peak spacng (R sm ) need to be addressed. Optmzaton of varous producton processes hghlghted n lterature assumed that ndvdual qualty ndces are ndependent to each other.e. they are not correlated. But n practce the assumpton may not be vald always. Therefore, hybrd Taguch based optmzaton approaches lke grey based Taguch [Datta el al. (28)], desrablty functon based Taguch [Datta el al. (26)], utlty concept [Wala et al. (26)] based Taguch methods those do not account response correlaton may lead to erroneous results. To overcome ths lmtaton the study proposes applcaton of Prncpal Component Analyss (PCA) to elmnate response correlaton and to convert correlated responses nto uncorrelated qualty ndces called prncpal components. These prncpal components have been aggregated further to calculate the Mult-response performance ndex (MPI) called overall grey relatonal grade [Datta et al. (21)]. Ths serves as the sngle objectve functon for optmzaton wth the am to maxmze t. Thus, the mult-objectve optmzaton problem has been converted nto an equvalent sngle objectve optmzaton stuaton whch has been solved by Taguch method by analyzng dsperson statstcs of the response data. EXPERIMENTATION In the present study; depth of cut, spndle speed and feed rate have been consdered as machnng parameters whle the followng four roughness parameters have been selected as the response varables: centre lne average roughness (R a ); root mean square roughness (R q ); and mean lne peak spacng (R sm ). The work pece materal was 661-T4 alumnum. Commercally avalable CVD coated carbde tools have been used n ths nvestgaton. Apart from depth of cut (d, mm), spndle speed (N, rpm) and feed rate (f, mm/mn) have been selected as desgn factors whle other parameters have been assumed to be constant over the expermental doman (Table 1). L 25 Orthogonal Array (OA) has been consdered for expermentaton. Interacton effect of process parameters has been assumed neglgble. The machne used for the mllng tests s a DYNA V4.5 CNC end mllng machne havng the control system SINUMERIK 82

3 D wth a vertcal mllng head. The surface roughness parameters have been measured usng the stylus-type proflometer, Talysurf (Taylor Hobson, Surtronc 3+). The measured roughness parameters along wth desgn matrx have been shown n Table 2. Table 1. Process parameters and doman of experments Levels Alumnum d (mm) N (rpm) f (mm/mn) Table 2. Expermental results along wth desgn matrx Sl. No. L 25 Orthogonal Array Response parameters d N f R a µm R q µm R sm mm EVALUATION OF OPTIMAL RESULT Detaled methodology for optmzaton has been descrbed n the paper by Datta et al. (21). In ths nvestgaton, expermental data have been normalzed usng (Lowerthe-Better) LB crtera. A check has been made to verfy whether the responses are correlated or not. It has been observed that, all responses are correlated to each other (Table 3). In order to elmnate response correlatons, Prncpal Component Analyss (PCA) has been appled to derve three ndependent qualty ndexes called prncpal components Z1, Z2 and Z3 (Table 4). The analyss of correlaton matrx has been

4 made to calculate the values of three ndependent prncpal components n all expermental runs (Table 5). Qualty loss of three ndvdual components (compared to the deal) has been converted nto ndvdual grey relatonal coeffcents; whch have been aggregated further to compute the overall grey relatonal grade (Table 6). Thus, the mult-crtera optmzaton problem has been transformed nto a sngle objectve optmzaton problem usng the combnaton of Taguch approach and grey relatonal analyses. Hgher s the value of grey relatonal grade, the correspondng factor combnaton s sad to be close to the optmal. The S/N rato plot for the overall grey relatonal grade s represented graphcally n Fgure 1. The S/N rato for overall grey relatonal grade has been calculated usng HB (Hgher-the-Better) crteron. Wth the help of the Fgure 1, optmal parametrc combnaton has been determned. The optmal factor settng becomes d() N(-1) f(-1). [Number ndcates level of factors] whch been verfed by the satsfactory result of confrmatory experment. CONCLUSIONS 1. Applcaton of PCA has been recommended to elmnate response correlaton by convertng correlated responses nto uncorrelated qualty ndces called prncpal components whch have been as treated as ndependent response varables for optmzaton. 2. Grey relaton theory can combne ndvdual prncpal components nto a sngle mult-response performance ndex MPI (overall grey relatonal grade) to be taken under consderaton for optmzaton. Ths s really helpful n stuatons where large number of responses have to be optmzed smultaneously. 3. The sad approach can be recommended for contnuous qualty mprovement and off-lne qualty control of a process/product. Sl. No. 1 a 3 a 5 q Table 3. Check for correlaton Pearson s Comment Correlaton between correlaton coeffcent R and R.996 Both are correlated q R and R.114 Both are correlated sm R and R.112 Both are correlated sm Table 4. (Analyss of correlaton matrx) Egenvalues, egenvectors, accountablty proporton (AP) and cumulatve accountablty proporton (CAP) computed for the three ndvdual prncpal components Z1 Z2 Z3 Egenvalues Egenvector AP CAP

5 Table 5. Indvdual Prncpal Components Sl. No. Indvdual Prncpal Components Z1 Z2 Z3 Ideal Stuaton Table 6. Calculaton of ndvdual grey relatonal coeffcents Sl. No. (1 ) st PC (2 ) nd PC (3 ) rd PC Γ,

6 Table 6 (contnued) Sl. No. (1 ) st PC (2 ) nd PC (3 ) rd PC Γ, = Qualty of prncpal component (w. r. t the deal) n th expermental run Γ, =Overall grey relatonal grade n th expermental run FIGURE 1. Evaluaton of optmal settng REFERENCES 1. J.A. Ghan, I.A. Choudhury and H.H. Hassn, Journal of Materals Processng Technology, 145, (24). 1. J.L. Yang and J.C. Chen, Journal of Industral Technology, 17(2), 1-8(21). 2. C.K. Chang and H.S. Lu, Internatonal Journal of Advanced Manufacturng Technology, 32, 18-26(27). 3. P. Sahoo, Engneerng Trbology, Prentce Hall of Inda, New Delh (25). 4. S. Datta, A. Bandyopadhyay and P.K. Pal, Internatonal Journal of Advanced Manufacturng Technology, 39, (28). 5. S. Datta, A. Bandyopadhyay and P. K. Pal, Internatonal Journal of Manufacturng Scence and Producton, 7(2), (26). 6. R. S. Wala, H. S. Shan, and P. Kumar, Materals and Manufacturng Processes, 21, (26). 7. S. Datta, S. S. Mahapatra, A. Bandyopadhyay, Elmnaton of mult-response correlaton for applyng Taguch phlosophy n optmzaton of submerged arc weld, proceedngs of the Natonal Semnar on Jonng Processes: Challenges for Qualty, Desgn and Development, organzed by Mechancal and Producton Engneerng Department, held durng March 5-6, 21 at Natonal Insttute of Technology, Agartala, Trpura (West), Inda.