APPLICATION OF VIKOR BASED TAGUCHI METHOD FOR MULTI-RESPONSE OPTIMIZATION: A CASE STUDY IN SUBMERGED ARC WELDING (SAW)

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1 Proceedgs of the Iteratoal Coferece o Mechacal Egeerg 009 (ICME009) 6-8 December 009, Dhaka, Bagladesh ICME09- APPLICATION OF VIKOR BASED TAGUCHI METHOD FOR MULTI-RESPONSE OPTIMIZATION: A CASE STUDY IN SUBMERGED ARC WELDING (SAW) S. Aay Bswas, Saurav Datta, Swapa Bhaumk, Gautam Maumdar 3 Departmet of Mechacal Egeerg,Natoal Isttute of Techology (NIT), Barala, Trpura (W) Departmet of Mechacal Egeerg, Natoal Isttute of Techology (NIT), Rourkela 3 Departmet of Mechacal Egeerg, Jadavpur Uversty, Kolkata ABSTRACT The term optmzato s tesvely related to the feld of qualty egeerg. The product qualty depeds o dfferet qualty dces (called attrbutes) whch should reach expected target level order to meet customer s satsfacto. Devato from the target results severe qualty loss whch may ot be accepted by the cosumers. Therefore, every maufacturg or producto ut should have better cocer for both qualty as well as productvty. Hgh qualty ca be acheved by optmzg varous qualty attrbutes or by selectg a optmal process evromet effcet eough to fetch desred requremets of qualty. To address ths ssue several methodologes were recommeded lterature but most of the research carred out earler seeks for optmzg a sgle obectve fucto. I ths cotext, Taguch s desg of expermet (Orthogoal Array) ad Sgal-to-Nose (S/N) rato cocept were foud to be the most effcet havg worldwde applcato varous felds. Ths method was proved robust ad largely recommeded for cotuous qualty mprovemet ad off-le qualty cotrol. However, tradtoal Taguch method caot solve a mult-obectve optmzato problem. To overcome ths shortcomg several hybrd Taguch techques were developed. But these methods are based o qualty loss of dvdual attrbutes from ther deal codto. They fal to cosder varatos of relatve qualty loss of multple attrbutes. It may so happe that the qualty loss assocated wth some resposes s small; but the qualty loss assocated wth rest of the resposes s very large, eve though the overall average qualty loss s small. Such stuato may ot be accepted by the customers. I cosderato of the above, the preset study explores applcato of Taguch based VIKOR method adapted from Mult-Crtera-Decso Makg (MCDM) order to solve mult-respose optmzato problem through a case study SAW. A attempt has bee made to evaluate the best process evromet (process codto) for achevg desred mult-qualty features of the weldmet. Keywords: Taguch Based Vkor Method, Mult-Crtera-Decso Makg (Mcdm), Saw. INTRODUCTION It s well kow that several process cotrol parameters fluece weld bead geometry, bead qualty ad ot performace Submerged Arc Weldg. These parameters should be selected a udcous maer to reach the desred target or obectve whch s dctated by the area of applcato of the weldmet. Ths ca be acheved by optmzato of weldg pheomea. Lterature depcts that the commo approaches to tackle smulato modelg ad optmzato problem weldg clude multple regresso aalyss, Respose Surface Methodology (RSM), Artfcal Neural Network (ANN) modelg ad Taguch method, [Ual, R. ad Dea, Edw B., (99), Rowlads, H., et al. 000, Atoy, J. ad Atoy, F., (00), Maghsoodloo, S. et al. (004)]. I most of the cases the optmzato has bee performed usg sgle obectve fucto. For a mult-respose process, whle applyg the optmal settg of cotrol factors, t ca be observed that, a crease/mprovemet of oe respose may cause chage aother respose, beyod the acceptable lmt. Thus for solvg mult-crtera optmzato problem, t s coveet to covert all the obectves to a equvalet sgle obectve fucto. Ths equvalet obectve fucto, whch s the represetatve of all the qualty characterstcs of the product, s to be optmzed (maxmzed). Optmzato usg desrablty fucto (DF) approach s very helpful ths cotext [Asabapour, B. et al. (004), Ful-Chag, Wu. (005)]. Smlarly Taguch s phlosophy has also bee recommeded as a effcet tool for the desg of hgh qualty maufacturg system. However, tradtoal Taguch method caot solve mult-obectve optmzato problem Jeyapaul, R. et al. (005). Therefore, Taguch method coupled wth grey relatoal aalyss s the ICME009

2 approprate opto. Targ, Y. S. et al. (00) appled grey-based Taguch methods for optmzato of Submerged Arc Weldg process parameters hardfacg. Apart from desrablty fucto ad grey-based Taguch approach, Geetc Algorthm (GA) ad Fuzzy Logc are also foud to be useful techques to solve optmzato problem the feld of weldg [Al-Aomar, Red (00)]. Apart from Geetc Algorthm, fuzzy logc also comes to the scearo of solvg optmzato problems materal processg techology [Wag, Je-Tg ad Jea, Mg-Der (006)]. Xue, Y. et al. (005) reported the possbltes of the fuzzy regresso method modelg ad optmzato of the bead wdth the robotc arc-weldg process. Desrablty Fucto (DF) approach coupled wth Taguch method has bee used by some researchers to vestgate codtos leadg to process optmzato. I ths cotext, applcato of other hybrd techques deserves meto. These techques are: - () Taguch method coupled wth fuzzy logc, () Geetc Algorthm ad fuzzy logc, () desrablty fucto approach coupled wth fuzzy logc, (v) Geetc Algorthm combato wth Respose Surface Methodology, ad (v) Taguch-Geetc Algorthm [Tsa, J-Tsog (August 004)]. Targ, Y. S. et al. (July 000) appled fuzzy logc the Taguch method to optmze the submerged arc weldg process wth multple performace characterstcs. Aother approach for optmzato s the Cotrolled Radom Search Algorthm (CRS), developed by Prce, W. L. (977). It has bee observed that Taguch based hybrd methods are based o qualty loss of dvdual qualty attrbutes from ther deal (desred) codto. They fal to cosder varatos of relatve qualty loss of multple attrbutes. The stuato may arse that the qualty loss assocated wth some resposes s small; but the qualty loss assocated wth rest of the resposes s very large, eve though the overall average qualty loss s small. Such stuato may ot be accepted by the cosumers. I order to overcome aforesad shortcomg, the preset study proposes VIKOR method adapted from Mult-Crtera Decso Makg (MCDM) hybrdzed wth Taguch method for solvg mult-crtera optmzato problem of submerged arc weldg. Wth relevat llustratos, the robustess ad applcato feasblty of the proposed method has bee verfed through a case study, dscussed the paper.. VIKOR METHOD The MCDM method s very popular techque wdely appled for determg the best soluto amog several alteratves havg multple attrbutes or alteratves. A MCDM problem ca be represeted by a decso matrx as follows: Cx Cx.... Cx A x x.... x A x x.... x D () Am xm xm.... x m Here, A represets th alteratve,,,..., m ; Cx represets the th crtero,,,..., ; ad x s the dvdual performace of a alteratve. The procedures for evaluatg the best soluto to a MCDM problem clude computg the utltes of alteratves ad rakg these alteratves. The alteratve soluto wth the hghest utlty s cosdered to be the optmal soluto. The followg steps are volved VIKOR method [Oprcovc, S. ad Tzeg, G.-H., 007]: Step : Represetato of ormalzed decso matrx The ormalzed decso matrx ca be expressed as follows: F f () Here, f m x m x,,,..., m; ad x s the performace of alteratve A wth respect to the th crtero. Step : Determato of deal ad egatve-deal solutos: The deal soluto A ad the egatve deal soluto A are determed as follows: / (max f J ) or (m f JK ), A,,..., m (3) f, f,..., f A { } { f, f,..., f } (m f J ) or (max f,,..., m J ), Here, J,,..., f, f desred resposesl arg e / (4) { } {,,...,, } ' J f f desred resposes small ICME009

3 Step 3: Calculato of utlty measure ad regret measure The utlty measure ad the regret measure for each alteratve are gve as ( f f) ( ) ( f f) ( ) S w f f (5) R Maxw (6) f f where, S ad R, represet the utlty measure ad the regret measure, respectvely, ad w s the weght of the th crtero. Step 4: Computato of VIKOR dex The VIKOR dex ca be expressed as follows: S S R R Q υ ( υ + ) (7) S S R R Here, Q, represets the th alteratve VIKOR value,,,..., m; S M( S ); S Max( S ) ; R R M ( R ) ; Max ( R ) ad υ s the weght of the maxmum group utlty (usually t s to be set to 0.5). The alteratve havg smallest VIKOR value s determed to be the best soluto. 3. OPTIMIZATION PROCEDURE ADOPTED Step : Estmato of qualty loss Taguch defed qualty loss estmates for resposes usg Lower-the-better (LB) ad Hgher-the-better (HB) crtero are gve bellow. (a) For a lower-the-better (LB) respose: r r k L k y (8) k (b) For a lower-the-better (LB) respose: r L k (9) r k yk Here, L s the qualty loss assocated wth the th respose the th expermetal ru; y k s the observed kth repetto datum for the th respose the th expermetal ru; r s the umber of repettos for each expermetal ru. k, k are qualty loss coeffcets,,,..., m ;,,..., ; k,,..., r. Step : Calculato of ormalzed qualty loss (NQL) for dvdual resposes each expermetal ru. The NQL ca be obtaed as follows: L f,,,..., m;,,...,. (0) m L Here f represets the NQL of the th respose the th expermetal ru. Step 3: Evaluato of deal ad egatve-deal solutos. { m,,..., } {,,...,,..., } A f m f f f f { max,,..., } {,,...,,..., } A f m f f f f () () A smaller NQL s preferred, so the deal ad egatve-deal solutos whch represet the mmum ad maxmum NQL of all expermetal rus are as follows: Step 4: Calculato of the utlty ad regret measures for each respose each expermetal ru usg equato (5) ad (6) respectvely. Step 5: Calculato of VIKOR dex of the th expermetal ru. Substtutg S ad R to equato (7) yelds the VIKOR dex of theth expermetal ru as follows. A smaller VIKOR dex produces better mult-respose performace. Step 6: Determato of optmal parametrc combato The mult-respose qualty scores for each expermetal ru ca be determed from the VIKOR dex obtaed step 5, ad the effects of the factors ca be estmated from the calculated VIKOR values. The optmal combato of factor-level called optmal parametrc combato s fally determed, vew of the fact that a smaller VIKOR value dcates a better qualty. Taguch method s to be appled fally to evaluate ths optmal settg (by mmzg the VIKOR dex). Optmal result s to be verfed through cofrmatory tests. 4. CASE STUDY 4. Expermets ad Data Collecto Bead-o-plate submerged arc weldg o mld steel plates (thckess 0 mm) has bee carred out as per Taguch s L 5 OA desg, wth 5 combatos of voltage (OCV), wre feed rate, traverse speed ad electrode stck-out. Copper coated electrode wre of dameter 3.6 mm (AWS A/S 5.7:EH4) has bee used durg the expermets. Weldg has bee performed wth flux (AWS A5.7/SFA 5.7) wth gra sze 0. to.6 mm wth bascty dex.6 (Al O 3 +MO 35%, CaO+MgO 5% ad SO +TO 0% ad CaF 5%). The expermets have bee performed o Submerged Arc Weldg Mache- INDARC AUTOWELD MAJOR (Maker: IOL Ltd., Ida). Weld beg made, the specmes have bee prepared for metallographc test. Features of bead geometry: bead wdth, peetrato depth, reforcemet ad %dluto have bee observed Optcal Trocular Metallurgcal Mcroscope (Make: Leca, GERMANY, Model No. DMLM, S6D & DFC30 ad Q w Software). The doma of expermetato s show Table. The desg of expermet, based o ICME009 3

4 Taguch s L 5 OA, ad the collected expermetal data, related to dvdual qualty dcators of bead geometry have bee lsted Table ad Table 3 respectvely. 4. Data Aalyss Qualty loss estmates for dvdual resposes have bee calculated usg equatos (8 ad 9). For peetrato depth, %dluto (HB) ad for reforcemet ad bead wdth (LB) crtero have bee selected. Normalzed qualty loss estmates have bee determed usg equato (0). Whle calculatg utlty measure of dvdual resposes (crtero) t has bee assumed that all resposes are equalty mportat. Therefore, 5% weghtage has bee assged to each respose. Utlty ad regret measure for each alteratve have bee calculated ext. VIKOR INDEX of each alteratve has bee evaluated fally. The optmal parametrc codto dcates smallest VIKOR INDEX. Ths has bee acheved by optmzg (mmzg) the VIKOR INDEX by Taguch method. The S/N rato of VIKOR INDEX has bee calculated usg LB (Lower-the-Better) crtera. Optmal parametrc settg has bee evaluated from Fgure. The predcted optmal settg becomes: V F5 S4 N4. Mea respose table for (VIKOR INDEX) dcates that the most sgfcat factor s wre feed, ext traverse speed the voltage. Stck-out showed eglgble effect. After predctg the optmal settg, t has bee verfed through coducto of cofrmatory test. It showed satsfactory result. Table 4 represets the result of cofrmatory test. 5. CONCLUSIONS I the preset work, mult-respose optmzato problem has bee solved by searchg a optmal parametrc combato, capable of producg desred qualty weld. Four bead geometry features: depth of peetrato, reforcemet, bead wdth ad dluto has bee optmzed usg VIKOR based Taguch method. The study demostrates the effectveess of VIKOR s mult-attrbute decso makg techque hybrdzed wth Taguch method relato to parametrc optmzato of SAW process Table 3: Respose data (dvdual qualty attrbutes related to bead geometry) Respose data (qualty attrbutes) Sl. Bead No. Reforcemet Peetrato %Dluto wdth Table : Doma of expermetato Parameters Uts Notato Voltage (OCV) Volts V Wre feed cm/s F Traverse speed cm/s S Stck-out mm N Table : Taguch s L5 OA desg Sl. No. Levels of factors (Factoral combatos) V F S N Fg. S/N rato plot for VIKOR INDEX Table 4: Results of cofrmatory test Optmal settg Predcto Expermet Level of factors V F5 S4 N4 V F5 S4 N4 S/N rato of VIKOR INDEX ICME009 4

5 6. REFERENCES. Atoy, J. ad Atoy, F., 00, Teachg the Taguch Method to Idustral Egeers, Work Study, Volume 50, Number 4, pp Al-Aomar, Red, 00, A Robust Smulato-Based Multcrtera Optmzato Methodology, Proceedgs of the 00, Wter Smulato Coferece. 3. Asabapour, B., Palmer, K. ad Khoshevs, B., 004, A Expermetal Study of Surface Qualty ad Dmesoal Accuracy for Selectve Ihbto of Sterg, Rapd Prototypg Joural, Volume 0, Number 3, pp Ful-Chag, Wu, 005, Optmzato of Correlated Multple Qualty Characterstcs Usg Desrablty Fucto, Qualty Egeerg, Volume 7, Issue, pp Jeyapaul, R., Shahabudee, P. ad Krshaah, K., 005, Qualty Maagemet Research by Cosderg Mult-Respose Problems the Taguch Method-A Revew, Iteratoal Joural of Advaced Maufacturg Techology, Volume 6, pp Maghsoodloo, S., Ozdemr, G., Jorda, V. ad Huag, C-H., 004, Stregths ad Lmtatos of Taguch s Cotrbutos to Qualty, Maufacturg, ad Process Egeerg, Joural of Maufacturg Systems, Volume 3, Number, pp Prce, W. L., 977, A Cotrolled Radom Search Procedure for Global Optmzato, The Computer Joural, Volume 0, Number 4, pp Rowlads, H., Atoy, J. ad Kowles, G., 000, A Applcato of Expermetal Desg For Process Optmzato, The TQM Magaze, Volume, Number, pp Targ, Y. S., Yag, W. H. ad Juag, S. C., July 000, The Use of Fuzzy Logc the Taguch Method for the Optmzato of the Submerged Arc Weldg Process, Iteratoal Joural of Advaced Maufacturg Techology, Volume 6, pp Targ, Y. S., Juag, S. C., Chag, C. H., 00, The Use of Grey-Based Taguch Methods to Determe Submerged Arc Weldg Process Parameters Hardfacg, Joural of Materals Processg Techology, Volume 8, pp Tsa, J-Tsog, Lu, Tug-Kua ad Chou, Jyh-Horg, 004, Hybrd Taguch-Geetc Algorthm for Global Numercal Optmzato, Evolutoary Computato, IEEE Trasactos, Volume 8, Issue 4, pp Ual, R., ad Dea, Edw B., 99, Taguch Approach to Desg Optmzato for Qualty ad Cost: A Overvew, Preseted at the Aual Coferece of the Iteratoal Socety of Parametrc Aalyss. 3. Wag, Je-Tg ad Jea, Mg-Der, 006, Optmzato of Cobalt-Based Hardfacg Carbo Steel usg the Fuzzy Aalyss for the Robust Desg, Iteratoal Joural of Advaced Maufacturg Techology, Volume 8, pp Xue, Y., Km, I. S., So, J. S., Park, C. E., Km, H. H., Sug, B. S., Km, I. J., Km, H. J. ad Kag, B. Y., 005, Fuzzy Regresso Method for Predcto ad Cotrol the Bead Wdth the Robotc Arc-Weldg Process, Joural of Materals Processg Techology, Volume 64-65, pp Oprcovc, S. ad Tzeg, G.-H., 007, Exteded VIKOR Method Comparso wth Outrakg Methods, Europea Joural of Operatos Research, Volume 78, pp MAILING ADDRESS Dr. Saurav Datta Departmet of Mechacal Egeerg Natoal Isttute of Techology (NIT), Rourkela E-mal: s_bppmt@yahoo.com ICME009 5