International Journal of Industrial Engineering Computations
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1 Internatonal Journal of Industral Engneerng Computatons 4 (2013) Contents lsts avalable at GrowngScence Internatonal Journal of Industral Engneerng Computatons homepage: Optmzaton of machnng parameters of turnng operatons based on mult performance crtera Abhjt Saha a* and N.K.Mandal b* a M. Tech.Student, Natonal Insttute of Techncal Teachers Tranng & Research, Kolkata ,Inda b Assocate Professor, Natonal Insttute of Techncal Teachers Tranng & Research, Kolkata, Inda C H R O N I C L E A B S T R A C T Artcle hstory: Receved August Receved n revsed format November Accepted November Avalable onlne 21 November 2012 Keywords: Turnng Power consumpton Surface roughness Grey relatonal analyss Frequency of tool vbraton The selecton of optmum machnng parameters plays a sgnfcant role to ensure qualty of product, to reduce the manufacturng cost and to ncrease productvty n computer controlled manufacturng process. For many years, mult-objectve optmzaton of turnng based on nherent complexty of process s a compettve engneerng ssue. Ths study nvestgates multresponse optmzaton of turnng process for an optmal parametrc combnaton to yeld the mnmum power consumpton, surface roughness and frequency of tool vbraton usng a combnaton of a Grey relatonal analyss (GRA). Confrmaton test s conducted for the optmal machnng parameters to valdate the test result. Varous turnng parameters, such as spndle speed, feed and depth of cut are consdered. Experments are desgned and conducted based on full factoral desgn of experment Growng Scence Ltd. All rghts reserved 1. Introducton Turnng s one of the most basc machnng processes n ndustral producton systems. Turnng process can produce varous shapes of materals such as straght, concal, curved, or grooved work peces. In general, turnng uses smple sngle-pont cuttng tools. Many researchers have studed the effects of optmal selecton of machnng parameters n turnng. Tzeng and Chen (2006) used grey relatonal analyss to optmze the process parameters n turnng of tool steels. They performed Taguch experments wth eght ndependent varables ncludng cuttng speed, feed, and depth of cut, coatng type, type of nsert, chp breaker geometry, coolant, and band nose radus. The optmum turnng parameters were determned based on grey relatonal grade, whch maxmzes the accuracy and mnmzes the surface roughness and dmensonal precson. Smlarly, the researchers have appled grey relatonal analyss (GRA) to dfferent machnng processes, whch nclude electrc dscharge machnng Ln et al. (2002), determnng tool condton n turnng (Lo, 2002), chemcal mechancal polshng (Ln & Ho, 2003), sde mllng (Chang & Lu, 2007), * Correspondng author. Tel: E-mal: alfa.nta2010@gmal.com (A. Saha) 2013 Growng Scence Ltd. All rghts reserved. do: /j.jec
2 52 and flank mllng (Kopac & Krajnk, 2007) to compare the performance of damond tool carbde nserts n dry turnng (Arumugam et al., 2006), and optmzaton of drllng parameters to mnmze surface roughness and burr heght (Tosun, 2006). Ln (2004) mplemented grey relatonal analyss to optmze turnng operatons wth multple performance characterstcs. He analyzed tool lfe, cuttng force, and surface roughness n turnng operatons. Tosun (2006) reported the use of grey relatonal analyss for optmzng the drllng process parameters for the work pece surface roughness and the burr heght s ntroduced. Ths study ndcated that grey relatonal analyss approach can be appled successfully to other operatons n whch performance s determned by many parameters at multple qualty requests. Al-Refae et al. (2010) used Taguch method grey analyss (TMGA) to determne the optmal combnaton of control parameters n mllng, the measures of machnng performance beng the MRR and SR. Based on the ANOVA; t was found that the feed rate s mportant control factor for both machnng responses. If there are multple response varables for the same set of ndependent varables, the methodology provdes a dfferent set of optmum operatng condtons for each response varable. The grey system theory ntated by Deng (1982) has been proven to be useful for dealng wth poor, ncomplete, and uncertan nformaton. The grey relatonal based on the grey system theory can be used to solve the complcated nterrelatonshps among the multple performance characterstcs effectvely (Wang et al., 1996). Therefore, the purpose of the present work s to ntroduce the use of grey relatonal analyss n selectng optmum turnng condtons on mult-performance characterstcs, namely the surface roughness, power consumpton and frequency of tool vbraton. In addton, the most effectve factor and the order of mportance of the controllable factors to the mult-performance characterstcs n the turnng process were determned. 2. Expermentaton procedure and test results The cuttng experments were carred out on an expermental lathe setup usng a HSS MIRANDA S- 400 (AISI T 42) cuttng tool for the machnng of the IS: 2062, Gr. B Mld Steel bar, whch s 24 mm n dameter. The percent composton of the work pece materal s lsted n Table 1. Mar Surf PS1 surface roughness tester was used to measure the Surface roughness R a (µm) of the machned samples and Lathe tool dynamometer was used to measure the cuttng forces and measurng cuttng tool vbraton usng Pco Scope 2202 Table 1 Chemcal composton of IS: 2062, Gr. B. mld steel Materal Composton C Mn S S P Weght Percentage (%) In the present expermental study, spndle speed, feed and depth of cut have been consdered as machnng parameters. The machnng parameters wth ther unts and ther levels as consdered for expermentaton are lsted n Table 2. Table 2 Machnng parameters and ther lmts Symbol Machnng Parameter Unt Level 1 Level 2 Level 3 A Spndle Speed RPM B Feed rate mm/rev C Depth of cut mm
3 A. Saha and N. K. Mandal / Internatonal Journal of Industral Engneerng Computatons 4 (2013) 53 Table 3 Expermental condtons, cuttng force and calculated power Exp. No Spndle Speed N (RPM) Feed rate F (mm/rev) Depth of cut d cut (mm) Response man force Fc (N) Cuttng speed V c (m mn 1 ) Power calculated P c (W = N * V c ) Watt Table 4 Expermental desgn and collected response data Parameter Exp No. Spndle Speed N(RPM) Feed rate f(mm/rev) Depth of cut d cut (mm) Power consumpton P(W) Response features Surface roughness R a (µm) Frequency of tool vbraton f (Hz)
4 54 3. Methodologes 3.1 Grey relatonal analyss Orgnal Taguch method has been desgned to optmze a sngle performance characterstc. The Grey relatonal analyss based on the Grey system theory can be used to solve complcated multple performance parameters effectvely. As a result, optmzaton of the complcated outputs can be converted nto optmzaton of a sngle Grey relatonal grade. Grey relaton analyss s used to fnd out whether there s consstency between the changng trends of two factors or not, and to fnd out the possble mathematcal relatonshp among the factors or n the factors themselves Data preprocessng Data preprocessng s normally requred snce the range and unt n one data sequence may dffer from the others. Data preprocessng s also necessary when the sequence scatter range s too large or when the drectons of the target n the sequences are dfferent. Data preprocessng s a means of transferrng the orgnal sequence to a comparable sequence. Dependng on the characterstcs of a data sequence, there are varous methodologes of data preprocessng avalable for the gray relatonal analyss. If the target value of the orgnal sequence s nfnte, then t has a characterstc of the hgher s better. The orgnal sequence can be normalzed as follows: * x ( k) mn x ( k) x ( k) =. max x ( k) mn x ( k) (1) When the lower s better s a characterstc of the orgnal sequence, then the orgnal sequence should be normalzed as follows: * x ( k) =. max x ( k) mn x ( k) max x ( k) x ( k) (2) However, f there s a defnte target value (desred value) to be acheved, the orgnal sequence wll be normalzed n from: x ( k) x * x ( k) = 1 max x ( k ) mn x. Alternatvely, the orgnal sequence can be smply normalzed by the most basc methodology,.e., let the value of the orgnal sequence be dvded by the frst value of the sequence: * x ( k) x ( k) =, x (1) 0 0 where =1,.,m; k =1,, n. m s the number of expermental data tems, and n s the number of parameters. x o (k)denotes the orgnal sequence, x * (k) the sequence after the data preprocessng, max. x o (k) the largest value of x o (k), mn. x o (k) the smallest value of x o (k), and x o s the desred value of x o (k) Gray relatonal coeffcent and gray relatonal grade In gray relatonal analyss, the measure of the relevancy between two systems or two sequences s defned as the gray relatonal grade. When only one sequence, x o (k), s avalable as the reference sequence, and all other sequences serve as comparson sequences called a local gray relaton (3) (4)
5 A. Saha and N. K. Mandal / Internatonal Journal of Industral Engneerng Computatons 4 (2013) 55 measurement. After data preprocessng s carred out, the gray relaton coeffcent ξ (k) for the k th performance characterstcs n the th experment can be expressed as follows, ξ (k)=., (5) ( ). where, ( ) = ( ) ( ) and = 1.00, =0.00 and Δ o (k) s the devaton sequence of the reference sequence x o * (k)and the comparablty sequence x * (k). s the dstngushng or dentfcaton coeffcent defned n the range 0 ξ 1 (the value may be adjusted based on the practcal needs of the system). A value of s the smaller, and the dstngushed ablty s the larger. The purpose of defnng ths coeffcent s to show the relatonal degree between the reference sequence x o * (k) and the comparablty sequence x * (k). = 0.5 s generally used.after the grey relatonal coeffcent s derved, t s usual to take the average value of the grey relatonal coeffcents as the grey relatonal grade. The grey relatonal grade s defned as follows: = 1 ( ). However, n a real engneerng system, the relatve mportance of varous factors vares. In the real condton of unequal weght beng carred by the varous factors, the grey relatonal grade n Eq. (1) was extended and defned as recommended by Deng (1982). = 1 ( ), where = 1 and w k denotes the normalzed weght of factor k. Here, the grey relatonal grade γ represents the level of correlaton between the reference sequence and the comparablty sequence. If the two sequences are dentcal by concdence, then the value of grey relatonal grade s equal to 1. The grey relatonal grade also ndcates the degree of nfluence that the comparablty sequence could exert over the reference sequence. Therefore, f a partcular comparablty sequence s more mportant than the other comparablty sequences to the reference sequence, then the grey relatonal grade for that comparablty sequence and reference sequence wll be hgher than other grey relatonal grade. Grey relatonal analyss s actually a measurement of absolute value of data dfference between sequences, and t could be used to measure approxmaton correlaton between sequences. 4. Results and dscusson 4.1 Optmal parameter combnaton We know from the analyss of machnng process that the lower power consumpton and surface roughness as well as lower value of frequency of tool vbraton provdes better qualty of the machned surface. Thus, the data sequences power consumpton, surface roughness and frequency of tool vbraton both have smaller-the-better characterstcs. Table 5 lsts all of the sequences followng data pre-processng of power consumpton, surface roughness and frequency of tool vbraton by usng Eq. (2). Then, the devaton sequences, ( ) = ( ) ( ) has been determned and are shown n Table 6. Grey relatonal coeffcent and Grey relatonal grade values of each experment of the full factoral desgn were calculated by applyng equaton 5 and 6 and Table 7 and table 8 shows the Grey relatonal coeffcent and grey relatonal grade for each experment usng full factoral desgn. (6) (7)
6 56 Table 5 Grey relatonal generaton of each performance characterstcs Exp. No. Power consumpton P(W) Surface roughness R a (µm) Frequency of tool vbraton f (Hz) Ideal sequence The mult- response optmzaton problem has been transformed nto a sngle equvalent objectve functon optmzaton problem usng ths approach. The hgher grey relatonal grade s sad to be close to the optmal. Accordng to performed experment desgn, t s clearly observed that experment no. 16 has the hghest Grey relaton grade. Thus, the sxteenth experment gves the best mult-performance characterstcs of the turnng process among the 27 experments. Table 6 Evaluaton of devaton sequence o (k) for each of the responses Exp. No. Power consumpton P(W) Surface roughness R a (µm) Frequency of tool vbraton f (Hz) Ideal sequence
7 A. Saha and N. K. Mandal / Internatonal Journal of Industral Engneerng Computatons 4 (2013) 57 Table 7 Grey relatonal coeffcents of each performance characterstcs for 27 comparablty sequences Expt. No. Power consumpton P(W) Surface roughness R a (µm) Frequency of tool vbraton f (Hz) Table 8 Evaluated grey relatonal grades for 27 groups Expt. No. Grey relatonal grade Rank Table 9 shows the response table and graph of grey relatonal grade for each turnng parameter at dfferent levels, respectvely. As shown n Table 9, the mportant rank n sequence for varous turnng parameters n machnng of mld steel. The order of mportance of the controllable factors to the multperformance characterstcs n the turnng process, n sequence can be lsted as: factor B (Feed rate), A
8 58 (Spndle speed), C (Depth of cut). Factor B (Feed rate) was the most effectve factor to the performance. Ths ndcates that the turnng performance was strongly affected by the feed rate Table 9 Response of grey relatonal grade Grey relatonal grade Symbol Turnng parameters Level I Level II Level III Max - Mn Rank A Spndle speed 0.698* B Feed rate 0.801* C Depth of cut 0.688* * optmal turnng parameters Total mean Grey relatonal grade = Optmum set of parameters are A n frst level, B n frst level and C n frst level respectvely (A 1 B 1 C 1 ). 1.0 S catterplot of G rey relatonal grade vs Expt. N o. 0.9 Grey relatonal grade Expt. No Fg. 1. Grey relaton grades for the power consumpton, surface roughness and frequency of tool vbraton 4.2 Confrmaton Test After obtanng the optmal level of the machnng parameters, the next step s to verfy the mprovement of the performance characterstcs usng ths optmal combnaton. The estmated grey relatonal grade usng the optmum level of the `parameter s the total mean of the grey relatonal grade s the mean of the grey relatonal grade at the optmum level and o s the number of machnng parameters that sgnfcantly affects the multple performance characterstcs. = +, where s the total mean of the grey relatonal grade, s the mean of the grey relatonal grade at the optmum level and o s the number of machnng parameters that sgnfcantly affects the multple performance characterstcs. Based on equaton 8 the estmated grey relatonal grade usng the optmal machnng parameters can then be obtaned. Table 10 shows the results of the confrmaton experment usng the optmal machnng parameters The Power consumpton P s greatly reduced from 9.65 to 6.63 W, Surface roughness R a s mproved from 1.97to 1.88 μm and the frequency of tool vbraton f s greatly reduced from to 260 Hz. It s clearly shown that multple performance characterstcs n turnng process are greatly mproved through ths study. (8)
9 A. Saha and N. K. Mandal / Internatonal Journal of Industral Engneerng Computatons 4 (2013) 59 Table 10 Results of machnng performance usng ntal and optmal machnng parameters Intal machnng parameters Optmal machnng parameters Predcton Experment Settng Level A 1 B 1 C 2 A 1 B 1 C 1 Power consumpton P(W) Surface roughness A 1 B 1 C 1 R a (µm) Frequency of tool vbraton f(hz) Grey relatonal grade Improvement n grey relatonal grade = 0.05 Therefore, a comparson of the predcted values of the power consumpton, surface roughness and frequency of tool vbraton wth that of the actual parameters by usng the optmal machnng condtons s shown n the above table. An mprovement of 5.00% s observed n the grey relatonal grade. A good agreement between the two has been observed. Ths ensures the usefulness of grey relatonal approach n relaton to product/process optmzaton, where multple qualty crtera have to be fulflled smultaneously. 5. Concluson Experments are desgned and conducted on lathe machne wth Hgh speed steel MIRANDA S-400 (AISI T 42) and IS: 2062, Gr. B Mld Steel bar as work materal to optmze the turnng parameters. Power consumpton, surface roughness and frequency of tool vbraton are the responses. Full factoral desgn of experments and Grey relatonal analyss s constructve n optmzng the mult responses. Based on the results of the present study, the followng conclusons are drawn: The optmum combnaton of turnng parameters and ther levels for the optmum multperformance characterstcs of turnng process are A 1 B 1 C 1 (.e. Speed 180 RPM, Feed rate 0.08 mm/rev and Depth-of-cut 0.1 mm). Confrmaton test results prove that the determned optmum condton of turnng parameters satsfy the real requrements. References Al-Refae, A., Al-Durgham, L., & Bata, N. (2010).Optmal Parameter Desgn by Regresson Technque and Grey Relatonal Analyss. The World Congress on Engneerng, WCE Arumugam, P. U., & Malshe, A. P., & Batzer, S. A. (2006). Dry machnng of alumnum slcon alloy usng polshed CVD damond-coated cuttng tools nserts. Surface Coatng Technology, 200, Chang, C.K., & Lu, H.S. (2007). Desgn optmzaton of cuttng parameters for sde mllng operatons wth multple performance characterstcs. Internatonal Journal of Advanced Manufacturng Technology, 32, Deng, J. (1982). Control problems of grey systems. System Control, 5, Kopac, J., & Krajnk, P. (2007). Robust desgn of flank mllng parameters based on grey-taguch method. Internatonal Journal of Advanced Manufacturng Technology, 191, Ln, C, L., & Ln, J.L., & Ko, T.C. (2002). Optmzaton of the EDM process based on the orthogonal array wth fuzzy logc and grey relatonal analyss method. Internatonal Journal of Advanced Manufacturng Technology, 19,
10 60 Ln, Z.C., & Ho, C.Y. (2003). Analyss and applcaton of grey relaton and ANOVA n chemcalmechancal polshng process parameters. Internatonal Journal of Advanced Manufacturng Technology, 21, Ln, C.L. (2004). Use of the Taguch method and grey relatonal analyss to optmze turnng operatons wth multple performance characterstcs. Materal Manufacturng Process, 19, Lo, S.P. (2002). The applcaton of ANFIS and grey system method n turnng tool-falure detecton. Internatonal Journal of Advanced Manufacturng Technology, 19, Tosun, N. (2006). Determnaton of optmum parameters for multperformance characterstcs n drllng by usng grey relatonal analyss. Internatonal Journal of Advanced Manufacturng Technology, 28, Tosun, N. (2006). Determnaton of optmum parameters for mult-performance characterstcs n drllng usng grey relatonal analyss. Internatonal Journal of Advanced Manufacturng Technology, 28, Tzeng, Y.F., & Chen, F.C. (2006). Mult-objectve process optmzaton for turnng of tool steels. Internatonal Journal of Machnng and Machnablty of Materals, 1(1), Wang, Z.L., & Zhu, J, H., & WU. (1996). Grey relatonal analyss of correlaton of errors n measurement. Journal Grey System, 8(1),
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