OPTIMIZATION OF PROCESS PARAMETERS USING AHP AND TOPSIS WHEN TURNING AISI 1040 STEEL WITH COATED TOOLS

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1 Internatonal Journal of Mechancal Engneerng and Technology (IJMET) Volume 7, Issue 6, November December 2016, pp , Artcle ID: IJMET_07_06_047 Avalable onlne at ISSN Prnt: and ISSN Onlne: IAEME Publcaton OPTIMIZATION OF PROCESS PARAMETERS USING AHP AND TOPSIS WHEN TURNING AISI 1040 STEEL WITH COATED TOOLS D Bhanu Prakash Research Scholar (PP M.E 020), Rayalaseema Unversty, Kurnool, AP, Inda Dr. G Krshnaah Professor, SV Unversty, Trupath, AP, Inda N V S Shankar Assocate Professor, Department of Mechancal Engneerng, Swarnandhra College of Engneerng and Technology, Seetharampuram, AP, Inda ABSTRACT In our prevous work, optmal machnng parameter selecton durng turnng of AISI 1040 steel usng coated tools s dscussed. Durng ths process Taguch analyss has been used for selecton of parameters. Durng ths process, optmum parameter selecton ndvdually for surface Roughness, Power Consumpton and Materal Removal Rate are determned. Interacton plots are dscussed but based on the plots, sngle combnaton has been selected whch gves optmum values for the three varables. In the current work, nvestgatons have been performed nto the use of MCDM technque, AHP wth TOPSIS, for optmum parameter selecton, values of Speed, Feed and Depth of cut, s done such that all the three varables, namely Surface Roughness (Ra), Power Consumpton (PC) and Materal Removal Rate (MRR) are optmzed. Key words: AHP, TOPSIS, Fuzzy lngustc varables, PVD Tool, CVD Tool, Optmzaton, Turnng. Cte ths Artcle: D Bhanu Prakash, Dr. G Krshnaah and N V S Shankar, Optmzaton of Process Parameters Usng AHP and TOPSIS When Turnng AISI 1040 Steel wth Coated Tools. Internatonal Journal of Mechancal Engneerng and Technology, 7(6), 2016, pp INTRODUCTION Saaty [1]defned APH (Analytcal Herarchy Process) as a MCDM technque whch calculates the prorty scales based on judgement by experts. It s these scales, whch can further be used to measure the physcally unmeasurable parameters and non-commensurable nformaton. Fgure 1.1 shows varous steps n mplementng AHP as mentoned by hm

2 D Bhanu Prakash, Dr. G Krshnaah and N V S Shankar Fgure 1 AHP Process Saaty gave a detaled mathematcal formulaton of AHP n [2].Examples for AHP are presented n[3]. Analytcal Network Process (ANP) s also explaned. Alexander explaned how AHP can be used to determne prortes and thus determne optmze soluton, wth an example, usng SAS/IML [4] and JMP scrptng [5]. Bunruamkaew [6] detaled the step wse procedure to solve MCDM problems usng AHP n Excel. The use of Trangular Fuzzy Technques for AHP s explaned by NagoorGan [7]. The use of AHP for selecton of optmum values usng non-quantfable factors s gven n [8]. Balasubramanyan & Selvaraj [9] used AHP for optmzng machnng parameters of EN-25 steel. All the steps followed by them, were explaned n detal. Torf [10]explaned the mplementaton of Fuzzy TOPSIS for solvng MCDM technques. The expressons and methodologes descrbed n ths publcaton are used n the current artcle. In our current work, t s amed at mplementng Fuzzy AHP& Fuzzy TOPSIS technques for optmzng machnng parameters (Speed, Feed and Depth of Cut) for mnmzng Surface Roughness and Power Consumpton whle maxmzng Materal Removal Rate,.e. a Mult Crtera Decson Makng (MCDM) problem. 2. OBJECTIVE In author s prevous work [11], nvestgatons were performed to nvestgatee the effect of each factors (Speed, Feed, Depth of Cut) on varous parameters (Surface Roughness, Materal Removal Rate and Power Consumpton). For ths, optmum factor values are calculated usng Taguch technques for each parameter and combned effect s studed usng nteracton plots. But no concrete decson has been reached by usng DOE. Thus t s amed at determnng optmum factor values consderng ther combned effect on the three target parameters. To acheve ths objectve, MCDM technque AHP wth TOPSIS s used. 3. METHODOLOGY The orthogonal array descrbed n our prevous work [11] s beng used n the current work. The data s gven n table 1 (for CVD tool) and table 2 (for PVD tool). Durng ths optmzaton process, the factor to be optmzed are Speed (rpm), Feed (mm/rev) and Depth of Cut (mm), the parameters that are beng measured are Surface Roughness (µm), Power Consumpton (W) and Materal Removal Rate (m3/mn). Durng the analyss, only the target parameters are analyzed

3 Optmzaton of Process Parameters Usng AHP and TOPSIS When Turnng AISI 1040 Steel wth Coated Tools Table 1 L27 orthogonal array wth process parameters and target parameters for CVD Tool No Speed Feed Depth of Cut Surface Roughness Ra (μm) Materal Removal Rates (mm^3/mn) Power Consumpton (kw)

4 D Bhanu Prakash, Dr. G Krshnaah and N V S Shankar Table 2 L27 orthogonal array wth process parameters and target parameters for PVD Tool Expt. No Speed (rpm) Feed, f (mm/rev) Depth of cut, (mm) Surface Roughness Ra (µm) Materal removal rate (mm3/mn) Power Consumed (kw) In ths paper, AHP and TOPSIS appled to data of CVD tool s only dscussed. The same procedure s appled for data of PVD tool and thus that procedure s not presented here. Rather fnal result s presented all the benefcary parameters, namely Surface Roughness, Power Consumpton and Materal Removal Rate are tabulated separately. The objectves are: Mnmze surface Roughness Mnmze Power Consumpton Maxmze Materal Removal Rate Normalzaton s then performed on the table. The equaton (1) s used for Normalzaton process dependng on the target acton. The resultng normalzed values are shown n table

5 Optmzaton of Process Parameters Usng AHP and TOPSIS When Turnng AISI 1040 Steel wth Coated Tools max y( k) y( k) For mnmzaton crteron X ( k) = max y( k) mn y( k) y( k) mn y( k) For maxmzaton crteron X ( k) = max y( k) mn y( k) (1) Table 3 Normalzed Parameter Values Normalzed Ra Normalzed PC Normalzed MRR Weghts are now derved based on Fuzzy lngustc varables that are defned based on the outcome of Taguch Analyss. The fuzzy lngustc varables are defned are gven n table 4 and are shown graphcally n fgure 1. The par wse comparson matrx for responses s shown n table 5. The same matrx n terms of Trangular fuzzy numbers s shown n table

6 D Bhanu Prakash, Dr. G Krshnaah and N V S Shankar Table 4 Fuzzy Lngustc Varables Lngustc Varables Trangular Fuzzy Numbers Extremely Low (EL) (0, 0, 0.1) Very Low (VL) (0, 0.1, 0.3) Low (L) (0.1, 0.3, 0.5) Medum (M) (0.3, 0.5, 0.7) Hgh (H) (0.5, 0.7, 0.9) Very Hgh (VH) (0.7, 0.9, 1) Extremely Hgh (EH) (0.9, 1, 1) Fgure 1 Fuzzy Trangular Membershp Functons Table 5 Parwse Comparson matrx for Responses n terms of Lngustc Varables Prortes MRR Ra PC MRR 1 VH EH Ra 1/VH 1 H PC 1/EH 1/H 1 Table 6 Parwse Comparson Matrx n Terms of Trangular Fuzzy numbers Prortes MRR MRR (1, 1, 1) Ra (0.7, 0.9, 1) PC (0.9, 1, 1) Ra (1, , 1.429) (1, 1, 1) (0.5, 0.7, 0.9) PC (1, 1, 1.111) (1.111, 1.429, 0.2) (1, 1, 1) Geometrc aggregaton s then carred out on table 6. Equaton 2 s used for geometrc aggregaton. Table 7 shows the aggregated values for varous propertes. Best non-fuzzy Performance (BNP) value s then calculated usng (3). Weght for each th parameter s then computed usng expresson (4). Calculated BNP values and weghts of varous parameters are gven n table 8. k k k GA = ( lj = j = 1 lj, mj = j= 1 mj, uj = j= 1 uj ) where = 1... n (2) [( c a) + b a] BNP = + a (3)

7 Optmzaton of Process Parameters Usng AHP and TOPSIS When Turnng AISI 1040 Steel wth Coated Tools w BNP BNP = (4) Table 7 GA values of varous propertes Prortes GA Values MRR Ra PC Table 8 GA values of varous propertes Crtera BNP values Weght MRR Ra PC Usng the weghts calculated, weghted normalzed parameters are computed. Weghted normalzed parameter value s the product of weght of the parameter and parameter value. Table 9 shows the weghted normalzed values. Table 9 Weghted Normalzed Values Weghted Normalzed Ra Weghted Normalzed PC Weghted Normalzed MRR

8 D Bhanu Prakash, Dr. G Krshnaah and N V S Shankar Fuzzy TOPSIS method s now used to select the optmal value from ths weghted normalzed matrx as mentoned n [10]. Postve-Ideal soluton ( A + ) and Negatve-Ideal soluton ( A ) for each parameter of the weghted normalzed matrx n table 8 are calculated usng the expressons (5) & (6). A { v% 1 v% 2 v% 3 v% n} {( j m j n) } { v% 1 v% 2 v% 3 v% n} = {( j = m j = n) },,,..., = max v = 1.., = 1.. for Maxmzaton =,,,..., mn v 1.., 1.. for Mnmzaton (5) A { v% 1 v% 2 v% 3 v% n} {( j m j n) } { v% 1 v% 2 v% 3 v% n} = {( j = m j = n) },,,..., = max v = 1.., = 1.. for Mnmzaton =,,,..., mn v 1.., 1.. for Mnmzaton (6) The obtaned values are shown n Table 10. Now the dstance of each alternatve s calculated from both A + & A usng expresson (7). S = v v, = 1.. n (7) Dstance from A +, + ( + ) 2 m j j= 1 S = v v, = 1.. n (8) Dstance from A, ( ) 2 m j j= 1 Table 10 A + & A computed for the three parameters Postve Ideal Soluton ( A + ) Negatve Ideal Soluton ( A ) Surface Roughness Ra (µm) Power Consumpton (KW) Materal removal rate (mm3/mn) Once the dstances are calculated, the smlartes or Closeness Coeffcent ( CC ) to deal soluton s computed usng expresson (9). The alternatves are then ranked n descendng order of these smlarty rato. The soluton havng the rank 1 s the optmal soluton n TOPSIS [10]. The calculated data s summarzed n table 11 S CC = (9) + S + S 490

9 Optmzaton of Process Parameters Usng AHP and TOPSIS When Turnng AISI 1040 Steel wth Coated Tools Table 11 TOPSIS appled on Weghted Averaged Matrx Closeness Experment Dstance from Number Dstance from A + Coeffcent ( A CC ) Rank L L L L L L L L L L L L L L L L L L L L L L L L L L L From the above data, t can be observed that 2 nd experment s the optmal soluton. The factors of L27 experment are 740 rpm speed, 0.09 mm/rev feed and 0.1 mm depth of cut yeldng µm Surface Roughness, W of power consumpton and mm 3 /mn materal removal rate. Ths soluton s for CVD coated tools. The same procedure s appled for PVD coated tool and t s found that experment 27 th experment, values lsted n table 2, s the optmal soluton 5. CONCLUSION Use of AHP and Fuzzy TOPSIS n optmzng parameters durng turnng AISI 1040 steel usng coated tools has been presented. A detaled dscusson gvng the calculatons for CVD tools are presented n ths paper. Based on the analyss, t was found that 2nd experment s the optmal soluton for turnng wth CVD tool. The same procedure when appled to data for PVD tool gave 27th experment as optmal value

10 D Bhanu Prakash, Dr. G Krshnaah and N V S Shankar REFERENCE [1] T. L. Saaty, Decson makng wth the analytc herarchy process, Int. J. Serv. Sc., vol. 1, no. 1, p. 83, [2] T. L. Saaty, A scalng method for prortes n herarchcal structures, J. Math. Psychol., vol. 15, no. 3, pp , [3] R. W. Saaty, Decson Makng n the Comples Envronments: The Analytc Herarchy Process (AHP) for Decson Makng The Analytc Network Process (ANP) Dependence and Feedback, pp , [4] M. Alexander, Decson-Makng usng the Analytc Herarchy Process (AHP) and SAS/ IML, Unted States Soc. Secur. Adm. Balt., pp. 1 12, [5] M. Alexander, Decson-Makng Usng the Analytc Herarchy Process ( AHP ) and JMP Scrptng Language. [6] K. Bunruamkaew, How to do AHP analyss n Excel, pp. 1 21, [7] A. N. Gan and S. N. M. Assarudeen, A new operaton on trangular fuzzy number for solvng fuzzy lnear programmng problem, Appl. Math. Sc., vol. 6, no. 11, pp , [8] Wkpeda_contrbutors, Analytc herarchy process leader example, Wkpeda, The Free Encyclopeda. [Onlne]. Avalable: _leader_example. [9] B. Sngaravel and T. Selvaraj, Optmzaton of machnng parameters n turnng operaton usng combned TOPSIS and AHP method, Teh. Vjesn. - Tech. Gaz., vol. 22, no. 6, pp , [10] F. Torf, R. Z. Farahan, and S. Rezapour, Fuzzy AHP to determne the relatve weghts of evaluaton crtera and Fuzzy TOPSIS to rank the alternatves, Appl. Soft Comput. J., vol. 10, no. 2, pp , [11] D. B. Prakash, G. Krshnaah, and N. V. S. Shankar, Optmzaton of Process Parameters Usng Taguch Technques When Turnng AISI 1040 Steel Usng Coated Tools, Int. J. Mech. Eng. Technol., vol. 7, no. 6, pp , [12] Krankumar Ramakantrao Jagtap, S.B.Ubale and Dr.M.S.Kadam. Optmzaton of Cylndrcal Grndng Process Parameters for AISI 1040 Steel Usng Taguch Method. Internatonal Journal of Mechancal Engneerng and Technology (IJMET), 3(1), 2012, pp [13] G Venkata Kshore and F Anand Raju. Selecton of Optmum Parameters for MRR & SR Smultaneously n AWJM of Inconel-625 Alloy Usng TOPSIS Method. Internatonal Journal of Mechancal Engneerng and Technology (IJMET), 6(9), 2015, pp