OPTIMIZATION OF MACHINING PARAMETERS FOR TURNING OPERATION WITH MULTIPLE QUALITY CHARACTERISTICS USING GREY RELATIONAL ANALYSIS

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1 F. Puh dr. Optmzacja parametara obrade tokarenja s vše krterja kvaltete uporabom Grey relacjske analze ISSN (Prnt) ISSN (Onlne) DOI: /TV OPTIMIZATION OF MACHINING PARAMETERS FOR TURNING OPERATION WITH MULTIPLE QUALITY CHARACTERISTICS USING GREY RELATIONAL ANALYSIS Franko Puh Zoran Jurkovc Mladen Pernc Mran Brezocnk Stpo Buljan Orgnal scentfc paper Optmzaton of machnng processes s essental for achevng of hgher productvty and hgh qualty products n order to reman compettve. Ths study nvestgates mult-objectve optmzaton of turnng process for an optmal parametrc combnaton to provde the mnmum surface roughness (Ra) wth the maxmum materal-removal rate (MRR) usng the Grey Based Taguch method. Turnng parameters consdered are cuttng speed feed rate and depth of cut. Nne expermental runs based on Taguch s L 9 (3 4 ) orthogonal array were performed followed by the Grey relatonal analyss to solve the multresponse optmzaton problem. Based on the Grey relatonal grade value optmum levels of parameters have been dentfed. The sgnfcance of parameters on overall qualty characterstcs of the cuttng process has been evaluated by the analyss of varance (ANOVA). The optmal parameter values obtaned durng the study have been valdated by confrmaton experment. Keywords: ANOVA; Grey relatonal analyss; mult-objectve optmzaton; Taguch method; turnng Optmzacja parametara obrade tokarenja s vše krterja kvaltete uporabom Grey relacjske analze Izvorn znanstven članak Optmzacja procesa obrade je neophodna za postzanje veće produktvnost vsoke kvaltete prozvoda kako b ostal tržšno konkurentn. Ovaj rad stražuje vše-krterjsku optmzacju procesa tokarenja s optmalnom kombnacjom parametara obrade koj osguravaju mnmalnu hrapavost površne (Ra) s maksmalnm učnkom uklanjanja materjala (MRR) uporabom Grey based Taguch metode. Razmatran parametr obrade tokarenjem su brzna rezanja posmak dubna rezanja. Prmjenom Taguchjevog L 9 (3 4 ) ortogonalnog plana provedeno je devet ekspermenata te je korštena Grey relacjska analza kako b se rješo všekrterjsk problem optmzacje. Temeljem vrjednost Grey relacjskog stupnja utvrđene su optmalne razne parametara. Sgnfkantnost parametara na sveukupne krterje kvaltete procesa tokarenja ocjenjena je analzom varjance (ANOVA). Optmalne vrjednost parametara dobvene tjekom stražvanja potvrđene su verfkacjskm ekspermentom. Ključne rječ: ANOVA; Grey relacjska analza; Taguchjeva metoda; tokarenje; všekrterjska optmzacja 1 Introducton Determnaton of optmal machnng parameters s contnuous engneerng task whose goals are to reduce the producton costs and to acheve the desred product qualty. In turnng process surface qualty s one of the most mportant performance measures. Surface roughness (Ra) s a wdely used ndex of product qualty and n most cases a techncal requrement for mechancal products. Achevng the desred surface qualty s of great mportance for the functonal behavor of a part. At the same tme hgher materal removal rate (MRR) s consdered as the factor that drectly affects the producton cost and the machnng hour rate. In a turnng operaton t s an mportant task to select cuttng parameters to acheve hgh cuttng performance for a partcular machne and envronment. Hence multple qualty optmzaton method based on a combnaton of Grey relatonal analyss (GRA) and the Taguch method was used n ths paper to determne the optmal values of cuttng parameters n order to obtan better surface roughness and ncreased materal removal rate n the fnsh turnng operaton. To search for the optmal process condton through a lmted number of expermental runs Taguch s L 9 orthogonal array consstng of three factors and three levels was appled to optmze the multple qualty characterstcs of the fnsh turnng process. The three controllng factors ncludng the cuttng speed (V) the depth of cut (d) and feed rate (f) were selected. Grey relatonal grade s used to convert mult objectve problem nto a sngle objectve. To dentfy the optmal combnaton of process parameters that concurrently mnmze the surface roughness (Ra) and maxmze the materal removal rate (MRR) Grey relatonal analyss was employed. Grey relatonal analyss (GRA) utlzes a specfc concept of nformaton. It defnes stuatons wth no nformaton as black and those wth perfect nformaton as whte [1]. Addtonally an analyss of varance (ANOVA) was also utlzed to examne the most sgnfcant nfluental factors for the Ra and MRR n the turnng process. Confrmaton test was conducted usng the optmum cuttng parameters determned by the Taguch optmzaton method. Based on ths analyss valuable remarks about presented optmzaton approach are ponted out n the concluson of ths study. Many researchers have studed the effects of optmal selecton of machnng parameters n turnng. Tzeng and Chen [2] used grey relatonal analyss to optmze the process parameters n turnng of tool steels. They performed Taguch experments wth eght ndependent varables the optmum turnng parameters were determned based on grey relatonal grade whch maxmzes the accuracy and mnmzes the surface roughness and dmensonal precson. Sahoo et al. [3] have used Grey relatonal analyss to perform mult-objectve optmzaton of surface roughness and MRR n turnng of AA 1040 steel and determned that cuttng speed s the most nfluencng parameter affectng combned Grey relatonal grade followed by depth of cut and feed rate. Tzeng et al. [4] have used Grey relatonal analyss to perform optmzaton of turnng operatons wth multple performance characterstcs such as roughness average roughness maxmum and roundness. The depth of cut was dentfed to be the most nfluencng parameter Tehnčk vjesnk 23 2(2016)

2 Optmzaton of machnng parameters for turnng operaton wth multple qualty characterstcs usng Grey relatonal analyss F. Puh et al. affectng the Grey relatonal grade followed by cuttng speed and feed rate. Smlarly the researchers have appled the Grey relatonal analyss (GRA) to dfferent processes wth multple performance characterstcs and greatly mproved through ths approach. Tosun [5] nvestgated optmzaton of drllng parameters to mnmze surface roughness and burr heght Chang and Lu [6] nvestgated optmzaton of cuttng parameters for sde mllng operatons Datta et al. [7] nvestgated optmzaton of bead geometry n submerged arc weldng process Chakradhar and Gopal [8] nvestgated optmzaton of electrochemcal machnng of EN31 steel etc. In the recent tmes researchers have also tred to optmze the machnng parameters usng varous methods lke Genetc Algorthm Partcle swarm optmzaton ANN Smulated annealng method Mult-Objectve Evolutonary Algorthm etc. [9 12]. 2 Expermental procedure 2.1 Machnng condtons Expermental research was performed on lathe machne "Georg Fsher NDM-16". Test samples were carbon steel bars DIN Ck45 wth 100 mm n dameter and 380 mm n length. Chemcal composton and mechancal propertes of DIN Ck45 steel are gven n Tab. 1 and Tab. 2. Experments were carred out by the external machnng turnng tool wth the holder mark DDJNL 3225P15 and the coated nserts type DNMG PM4025 under dry cuttng condtons. The tool geometry was: rake angle 17 clearance angle 5 man cuttng edge 93 wth nose radus 08 mm. Before each cut the nsert was changed to elmnate the effect of toolwear. Surface roughness measurements were performed wth SurftestMtutoyo SJ-201P. The surface roughness measured n the paper s the arthmetc mean devaton of surface roughness of profle Ra [13 15].The materal removal rate of the work pece s the volume of the materal removed per mnute. It can be calculated usng the followng equaton: MRR = Vfd (1) where three man cuttng parameters are cuttng speed V (m/mn) feed rate f (mm/r) and depth of cut d (mm). Table 1 Chemcal composton of carbon steel Ck45 (wt%) Element C S Mn P S N Mo Content Table 2 Mechancal propertes of carbon steel Ck45 Tensle Yeld % of Hardness Materal strength strength Elongaton (HB) (MPa) (MPa) Ck Desgn of experments The Taguch method uses a specal desgn of orthogonal arrays to study the entre parameter space wth a lmted number of experments [16]. The experments have been carred out by usng the standardzed Taguchbased expermental desgn a L 9 (3 4 ) orthogonal arrays wth three levels (coded by: 1; 2 and 3) of three man cuttng parameters namely cuttng speed V feed rate f and depth of cut d (shown n Tab. 3). Table 3 Cuttng parameters and ther lmts Parameters Levels Symbol Codng orthogonal array A X 1 = V (m/mn) B X 2 = f (mm/rev.) C X 3 = d (mm) The necessary number of test runs s nne. The last column (for the fourth factor) n the L 9 (3 4 ) orthogonal array s left empty for ths specfc study. The expermental results and the Taguch L 9 (3 4 ) orthogonal array are shown n Tab. 4. Table 4 Orthogonal array L9(3 4 ) of the expermental runs and results Exp. A B C MRR No. R a (µm) V f d (cm 3 /mn) Results and dscussons 3.1 Grey relatonal analyss Grey relatonal analyss was proposed by Deng n 1989 [17] and t s wdely used for measurng the degree of relatonshp between sequences by Grey relatonal grade [18]. By employng Grey relatonal analyss assocated wth the Taguch method optmzaton of the complcated mult-response characterstcs can be converted nto optmzaton of a sngle response characterstc wth Grey relatonal grade as an objectve functon. In the present work the objectves are to mnmze the surface roughness and maxmze the MRR of fnsh turnng process. Thus surface roughness and materal removal rate as the mult-responses are combned by Grey relatonal grade usng Grey relatonal analyss. 3.2 Grey relatonal generaton In Grey relatonal analyss the frst step s to perform the Grey relatonal generaton n whch the results of the experments are normalzed n the range between 0 and 1 due to dfferent measurement unts. Data pre-processng converts the orgnal sequences to a set of comparable sequences. Normalzng the expermental data for each qualty characterstc s done accordng to the type of performance response. Thus the normalzed data processng for Ra correspondng to smaller-the-better crteron can be expressed as: 378 Techncal Gazette 23 2(2016)

3 F. Puh dr. Optmzacja parametara obrade tokarenja s vše krterja kvaltete uporabom Grey relacjske analze x ( k) y( k) y( k) ( ) mn ( ) max = max y k y k The normalzed data processng for MRR correspondng to larger-the-better crteron can be expressed as: x ( k) ( ) mn ( ) y ( k) mn y ( k) y k y k = max where = m m s the number of expermental runs n Taguch orthogonal array n the present work L 9 orthogonal array s selected then m = 9. k = n n s the number of qualty characterstcs or process responses n the present work surface roughness and materal removal rate are selected then n = 2. Mn y (k) s the smallest value of y (k) for the k th response. Max y (k) s the largest value of y (k) for the k th response. x (k) s the value after Grey relatonal generaton. The normalzed values of surface roughness and materal removal rate calculated by Eq. (2) and (3) are shown n Tab. 5. (2) (3) 3.3 Grey relatonal coeffcent and Grey relatonal grade The second step s to calculate the Grey relatonal coeffcent based on the normalzed expermental data to represent the correlaton between the desred and actual expermental data. The overall Grey relatonal grade s then computed by averagng the Grey relatonal coeffcent correspondng to each performance characterstc. As a result optmal combnaton of process parameters s evaluated consderng the hghest Grey relatonal grade by usng the Taguch method. Based on the normalzed expermental data the Grey relaton coeffcent can be calculated usng the followng equatons: x mn max ( k ) 0 ( k ) ς max 0( k) x0 ( k) x( k) x ( k) x ( k) + ς = (4) + = (5) = max max (6) max 0 j k mn 0 j k ( ) ( ) = mn mn x k x k (7) where Δ o = x 0 (k) x (k) s dfference of the absolute value between x 0 (k) and x (k) x 0 (k) s the reference sequence of the k th qualty characterstcs. Δ mn and Δ max are respectvely the mnmum and maxmum values of the absolute dfferences (Δ o ) of all comparng sequences. ζ s a dstngushng coeffcent 0 ζ 1 the purpose of whch s to weaken the effect of Δ max when t gets too bg and thus enlarges the dfference sgnfcance of the relatonal coeffcent. In the present case ζ = 05 s used due to the moderate dstngushng effects and good stablty of outcomes. The Grey relaton coeffcent of each performance characterstc s shown n Tab. 6. After averagng the Grey relatonal coeffcents the Grey relatonal grade γ can be calculated as follows: n 1 γ = ξ( k ) (8) n k= 1 where = (L 9 orthogonal array s selected) ξ (k) s the Grey relatonal coeffcent of k th response n th experment and n s the number of responses. The optmum level of the process parameters s the level wth the hghest Grey relatonal grade. The hgher value of the Grey relatonal grade corresponds to an ntense relatonal degree between the reference sequence x 0 (k) and the gven sequence x (k). The Grey relatonal coeffcents and Grey relatonal grade are presented n Tab. 6 calculated by Eq. (4) and (8) respectvely. The hghest Grey relatonal grade s the rank of 1. Therefore the experment number 5 s the best combnaton of turnng parameters for surface roughness and materal removal rate among the nne experments. Exp. No. Table 6 Grey relatonal coeffcent Grey relatonal grade and correspondng S/N ratos Grey relatonal S/N Rato coeffcent Ra MRR Grey relatonal grade Rank Table 5 Normalzed values and devaton sequences of responses Normalzed values of Devaton sequences Δ responses 0 (k) Exp. Ra MRR No. Smallerthe-bettebetter Larger-the- Ra MRR Larger-thebetter The mult-objectve optmzaton problem has been transformed nto a sngle equvalent objectve functon optmzaton problem usng Grey relatonal analyss. Accordngly optmal combnaton of process parameters s evaluated consderng the hghest Grey relatonal grade by usng the Taguch method. 3.4 Analyss of S/N ratos Taguch method recommends the use of the S/N rato to measure the qualty characterstcs devatng from the desred values [19]. The sgnal-to-nose (S/N) rato s a Tehnčk vjesnk 23 2(2016)

4 Optmzaton of machnng parameters for turnng operaton wth multple qualty characterstcs usng Grey relatonal analyss F. Puh et al. measure of the magntude of a data set relatve to the standard devaton. In the Taguch method sgnal to-nose S/N rato s used to represent a performance characterstc and the largest value of S/N rato means the optmal level of the turnng parameters. There are three types of S/N rato: the larger-thebetter the nomnal-the better and the smaller-the-better. Tab. 6 shows the S/N rato based on the larger-the-better crteron for the overall Grey relatonal grade calculated usng Eq. (9): 1 n 1 S / N = 10 log 2 n = 1 y (9) where n s the number of measurements and y s the measured characterstc value. The mean response for the Grey relatonal grade wth ts grand mean and the man effect plot of the Grey relatonal grade are very mportant because the optmal process condton can be evaluated from ths plot (shown n Fg. 1. and 2.). The dashed lne s the value of the total mean of the S/N rato and mean effect plot. As ndcated n Fg. 1. and 2. the optmal parameter condton for turnng of the C45 carbon steel regardng surface roughness and materal removal rate multple performance characterstcs are levels: A-level 1 B-level 1 C-level 3. Namely cuttng speed of V = 400 m/mn feed rate of f = 01 mm/rev and depth of cut d = 12 mm. 3.5 Analyss of varance (ANOVA) The purpose of the analyss of the varance (ANOVA) s to nvestgate whch turnng parameters sgnfcantly affect the qualty characterstc. By usng the Grey relatonal grade value ANOVA s ndcated for dentfyng the sgnfcant factors. In addton to degree of freedom (DF) mean of squares (MS) sum of squares (SS) F-rato and contrbuton (C) assocated wth each factor was presented. The hgher the percentage contrbuton was the more mportant the factor was for affectng the performance characterstcs. The results of ANOVA for the Grey grade values are represented n Tab. 8. The results of the ANOVA ndcate that the percentage contrbuton of cuttng speed (V) feed rate ( f ) and the depth of cut (d) nfluencng the multple performance characterstcs were 1263 % 841 % and 3462 % respectvely. From the percentage contrbuton of the ANOVA the cuttng speed and depth of cut were two parameters sgnfcantly nfluencng the Grey relatonal grade. And the depth of cut was the most effectve factor on the performance. 3.6 Confrmaton experment Fgure 1 Mean plot for the Grey relatonal grade After the optmal level of turnng parameters has been dentfed a verfcaton test needs to be carred out n order to check the accuracy of analyss. The estmated Grey relatonal grade γγ s used to predct the mprovement of the performance characterstc by usng optmum combnaton of turnng parameters. The estmated Grey relatonal grade γγ can be calculated as: o ˆ γ = γ + γ γ ( ) (10) m m = 1 Fgure 2 S/N plot for the Grey relatonal grade The means of the Grey relatonal grade for each level of turnng parameters were calculated from Tab. 6 and summarzed n Tab. 7. The larger the Grey relatonal grade the better the multple qualty characterstcs. Table 7 Response table for the mean Grey relatonal grade Parameter Grey relatonal grade Level 1 Level 2 Level 3 Delta A (V) B (f) C (d) Total mean value of the Grey relatonal grade = here γ m s the total mean Grey relatonal grade γγ s the mean Grey relatonal grade at the optmal level and o s the number of the machnng parameters sgnfcantly affect the multple performance characterstcs. The A1B1C3 was an optmal combnaton of turnng parameters by the Grey relatonal analyss. Therefore the A1B1C3 optmal combnaton parameters were regarded as the confrmaton test. Tab. 9 shows the comparson of the estmated Grey relatonal grade wth the actual Grey relatonal grade obtaned n verfcaton experment usng the optmal cuttng parameters. Namely surface roughness Ra was mproved from 201 μμm to 111 μμm and the materal removal rate MRR was also mproved from 36 cm 3 /mn to 48 cm 3 /mn consderng ntal cuttng condtons. In concluson t s clearly shown that the multple performance characterstcs n turnng C45 carbon steel were sgnfcantly mproved by ncrease n Grey relatonal grade of Techncal Gazette 23 2(2016)

5 F. Puh dr. Optmzacja parametara obrade tokarenja s vše krterja kvaltete uporabom Grey relacjske analze Table 8 ANOVA results of turnng process parameters Man control factors Symbol Degree of freedom Sum of squares Mean of squares Contrbuton F-rato DF (SS) (MS) C (%) Cuttng speed V A Feed rate f B Depth of cut d C Error Total Table 9 Results of confrmaton test Intal factor settngs Optmal process condton Predcton Experment Factor levels A2B3C1 A1B1C3 A1B1C3 Ra (μm) MRR (cm 3 /mn) S/N rato of overall Grey relatonal grade Overall Grey relatonal grade Improvement n Grey relatonal grade = Conclusons In ths study the Grey-based Taguch method was appled for the multple performance characterstcs of turnng operatons. Mult-response optmzaton of turnng process has been used to obtan optmal parametrc combnaton that provdes the mnmum surface roughness (Ra) wth the maxmum materal-removal rate (MRR). The applcaton of the Grey relatonal analyss based on the Taguch method drectly ntegrates the multple qualty characterstcs nto a sngle performance characterstc called Grey relatonal grade. Optmal combnaton of process parameters s evaluated consderng the hghest Grey relatonal grade by usng the Taguch method. By applyng the Taguch method the number of experments s drastcally reduced. A L 9 (3 4 ) Taguch orthogonal array the sgnal to nose (S/N) rato and the analyss of varance (ANOVA) were used for the optmzaton of cuttng parameters consderng Grey relatonal grade. Accordng to the analyss the optmal parameter combnaton for turnng of the C45 carbon steel regardng surface roughness and materal removal rate multple performance characterstcs were levels: A-level 1 B-level 1 and C-level 3. Namely cuttng speed of V = 400 m/mn feed rate of f = 01 mm/rev and depth of cut d = 12 mm. The results of the ANOVA ndcate that the percentage contrbuton of cuttng speed feed rate and the depth of cut nfluencng the multple performance characterstcs were 1263 % 841 % and 3462 % respectvely. From the percentage contrbuton of the ANOVA the cuttng speed and depth of cut were two parameters sgnfcantly nfluencng the Grey relatonal grade. And the depth of cut was the most effectve factor on the performance. Effectveness of ths method was verfed by the test experment. The Grey relatonal grade of the multple performance characterstcs was sgnfcantly mproved by through ths method. Namely surface roughness Ra was mproved from 201 μμm to 111 μμm and the materal removal rate MRR was mproved from 36 cm 3 /mn to 48 cm 3 /mn consderng ntal cuttng condtons. Therefore the optmzaton of the complcated multple performance characterstcs of the processes can be greatly smplfed by usng the Grey-based Taguch method. The performance characterstcs of the turnng operatons such as the materal removal rate and the surface roughness are greatly enhanced by usng ths method. 5 Acknowledgments The work was supported by the Federal Mnstry of Educaton and Scence of Bosna and Herzegovna through grant No /13 and by the Unversty of Rjeka through grant No References [1] Chan J. W. K.; Tong T. K. L. Mult-crtera materal selectons and end-of-lfe product strategy: Grey relatonal analyss approach. // Materals & Desgn. 28 5(2007) pp DOI: /j.matdes [2] Tzeng Y. F.; Chen F. C. Multobjectve process optmsaton for turnng of tool steels. // Internatonal Journal of Machnng and Machnablty of Materals. 1 1(2006) pp DOI: /IJMMM [3] Sahoo A. K.; Baral A. N.; Rout A. K.; Routra B. C. Mult-objectve optmzaton and predctve modellng of surface roughness and materal removal rate n turnng usng Grey Relatonal and Regresson Analyss. // Proceda Engneerng. 38 (2012) pp DOI: /j.proeng [4] Tzeng C. J.; Ln Y. H.; Yang Y. K.; Jeng M. C. Optmzaton of turnng operatons wth multple performance characterstcs usng the Taguch method and Grey relatonal analyss. // Journal of Materals Processng Technology (2009) pp DOI: /j.jmatprotec [5] Tosun N. Determnaton of optmum parameters for multperformance characterstcs n drllng by usng grey relatonal analyss. // Internatonal Journal of Advanced Manufacturng Technology (2006) pp DOI: /s y [6] Chang C. K.; Lu H. S. Desgn optmzaton of cuttng parameters for sde mllng operatons wth multple performance characterstcs. // Internatonal Journal of Advanced Manufacturng Technology (2007) pp DOI: /s Tehnčk vjesnk 23 2(2016)

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