Use of GRA-Fuzzy and TOPSIS for Multi-Response Optimization in CNC End Milling

Transcription

1 Use of GRA-Fuzzy and TOPSIS for Mult-Response Optmzaton n CNC End Mllng Thess submtted n partal fulfllment of the requrements for the Degree of Bachelor of Technology (B. Tech.) In Mechancal Engneerng By BIKASH MOHANTY Roll No. 108ME010 Under the Gudance of Prof. SAURAV DATTA NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA , INDIA

2 NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA , INDIA Certfcate of Approval Ths s to certfy that the thess enttled USE OF GRA-FUZZY AND TOPSIS FOR MULTI-RESPONSE OPTIMIZATION IN CNC END MILLING submtted by Sr Bkash Mohanty has been carred out under my supervson n partal fulfllment of the requrements for the Degree of Bachelor of Technology n Mechancal Engneerng at Natonal Insttute of Technology, Rourkela, and ths work has not been submtted elsewhere before for any other academc degree/dploma. Rourkela Date: Dr. Saurav Datta Assstant Professor Department of Mechancal Engneerng Natonal Insttute of Technology, Rourkela 2

3 Acknowledgement I have taken efforts n ths project. However, t would not have been possble wthout the knd support and help of many ndvduals and the department. I would lke to extend my sncere thanks to all of them. I am hghly ndebted to Department of Mechancal Engneerng for provdng necessary nformaton and gudance regardng the project and also for ther support n completng the project. I would lke to express my grattude towards my co-project members for ther knd cooperaton whch helped me n completon of ths project. I would lke to express my specal grattude and thanks to my project gude Dr. Saurav Datta, Assstant Professor, Department of Mechancal Engneerng, NIT Rourkela, for all the cooperaton and tme. I would also lke to thank Mr. Kunal Nayak, Mr. Kumar Abhshek, Mr. Chtrasen Samantra and others for gvng me such attenton and tme. My thanks and apprecatons also go to the machne operators and people who have wllngly helped me out wth ther abltes to understand varous operatons and machnes. Last but not the least I would lke to thank NIT Rourkela for gvng me ths wonderful opportunty. BIKASH MOHANTY 3

4 Abstract In producton/manufacturng context, mult-response optmzaton of machnng processes s one of the most mportant areas of research to fnd out the best process envronment for any machnng operaton. Lterature s seemed rch n addressng multresponse optmzaton problems usng varous technques. It has been vewed that these methods are not effcent enough due to so many assumptons and lmtatons mposed upon t. Therefore, researchers are concentratng n hybrdzng varous methods to empower advantageous aspects thereby avodng/overcomng nherent lmtatons of aforesad ndvdual methodologes. The present study amed to develop such a hybrd method whch could effcently be appled for contnuous qualty mprovement for a process/product and to facltate n off-lne qualty control of any manufacturng process. In the present work, two optmzaton phlosophes () TOPSIS based Taguch method and () Grey relaton analyss (GRA) followed by Fuzzy logc and Taguch method has been proposed here to optmze machnng parameters n CNC end mllng operaton towards mprovng qualty as well as productvty smultaneously. 4

5 Index Item Page No. Ttle Page 01 Certfcate 02 Acknowledgement 03 Abstract 04 Index Introducton: Overvew of CNC Machnng State of Art Understandng and Problem Formulaton Outlne of Taguch Method TOPSIS Method Grey Relatonal Analyss Fuzzy Inference System (FIS) Expermentaton Data Analyss: GRA-Fuzzy Combned wth Taguch Method Data Analyss: TOPSIS based Taguch Method Conclusons Bblography 31 Communcaton 32 5

6 1. Introducton: Overvew of CNC Machnng As far as machnng processes are concerned CNC has evolved over the conventonal machne tools. Some of the advantages of CNC machne tool over conventonal machne tool are lsted below: 1) Consstency of work peces produced- Snce a CNC machne executes a program, and t wll do so n exactly the same fashon tme and tme agan, the consstency of work peces produced s much better than work peces run on conventonal machne tools. 2) Faster work pece machnng- Snce current model CNC machne tools are guarded (splash guards, wndows, etc.) n a much better manner than most conventonal machne tools, users can apply the most effcent cuttng condtons to attan the best cycle tmes. Manual machnsts tend to nurse-along ther machnng operatons to mnmze the chps and coolant s constantly thrown from the work area. 3) Lowered skll level of machnst- Though there are some msconceptons n ths area (some people beleve that anyone can run CNC machnes wthout tranng), the level of skll requred to run (but not program) a CNC machne s much lower than that requred to run a conventonal machne tool - especally n a producton envronment when the same work pece s run over and over agan. 4) Complexty of work peces to be machned- CNC machnes can generate very complex motons, makng t possble to machne shapes that cannot be generated (or are extremely dffcult to generate) on conventonal machne tools. 6

7 5) Flexblty, faster turn-around, and smaller lots- Because they're programmable, a gven CNC machne can be used to machne a large varety of dfferent work peces. Most are also desgned to mnmze downtme between producton runs (setup tme). Some conventonal machnes they're replacng (screw machnes and transfer lnes, for example) are extremely dffcult to setup, makng them feasble only for larger lot szes. In CNC end mllng, whch s the area of focus n the present work, the varous process parameters are nvolved lsted as follows: 1) Cuttng speed (also called surface speed or smply speed) s the speed dfference (relatve velocty) between the cuttng tool and the surface of the work pece t s operatng on. It s expressed n unts of dstance along the work pece surface per tme, typcally surface feet per mnute (sfm) or meters per mnute (m/mn). 2) Feed rate (feed) s the relatve velocty at whch the cutter s advanced along the work pece; ts vector s perpendcular to the vector of cuttng speed. Feed rate unts depend on the moton of the tool and work pece; n rotatng systems (e.g., turnng and borng), the unts are almost always dstance per spndle revoluton (nches per revoluton [n/rev or pr] or mllmeters per revoluton [mm/rev]). 3) Depth of cut - The depth of cut (DOC) s the dstance that a tool penetrates nto the work pece. It s generally measured n mm. The output responses of the CNC mllng process can be measured n terms of varous surface roughness characterstcs of statstcal mportance (of the CNC end mlled surface), Materal Removal Rate (MRR), dmensonal accuracy, tool (cutter) lfe-tool wear, extent of chatter and vbraton and many others. Approprate selecton as well as 7

8 precse control of process parameters can yeld desred level of product qualty wth ncreased productvty. 2. State of Art Understandng and Problem Formulaton Ghan et al. (2004) outlned the Taguch optmzaton methodology, whch was appled to optmze cuttng parameters n end mllng when machnng hardened steel AISI H13 wth TN coated P10 carbde nsert tool under sem-fnshng and fnshng condtons of hgh speed cuttng. The mllng parameters evaluated was cuttng speed, feed rate and depth of cut. An orthogonal array, sgnal-to-nose (S/N) rato and Pareto analyss of varance (ANOVA) were employed to analyze the effect of these mllng parameters. Wattanutcharya and Pntasee (2006) attempted to optmze the metallc mllng parameters for surface fnshng. The two controlled parameters were spndle speed and feed rate. Three materals: alumnum, brass and cast ron were tested. The research methodology concerned the Response Surface Methodology (RSM) by Central Composte Desgn (CCD). Then, the Al 2072, brass wth 10% znc and cast ron (A287) were tested n order to nvestgate the relatonshp between the controlled parameters. Gopalsamy (2009) appled Taguch method to fnd optmal process parameters for end mllng whle hard machnng of hardened steel. An orthogonal array, sgnal-to-nose rato and ANOVA were appled to study performance characterstcs of machnng parameters (cuttng speed, feed, depth of cut and wdth of cut) wth consderaton of surface fnsh and tool lfe. Chppng and adheson were observed to be the man causes of wear. Multple regresson equatons were formulated for estmatng predcted values of surface roughness and tool wear. 8

9 Gnta et al. (2009) focused on developng an effectve methodology to determne the performance of uncoated WC-Co nserts n predctng mnmum surface roughness n end mllng of ttanum alloys T-6Al-4V under dry condtons. Central composte desgn of response surface methodology was employed to create an effcent analytcal model for surface roughness n terms of cuttng parameters: cuttng speed, axal depth of cut, and feed per tooth. Ab. Rashd et al. (2009) presented the development of mathematcal model for surface roughness predcton before mllng process n order to evaluate the ftness of machnng parameters; spndle speed, feed rate and depth of cut. Multple regresson method was used to determne the correlaton between a crteron varable and a combnaton of predctor varables. It was establshed that the surface roughness was most nfluenced by the feed rate. Alw (2010) studed the optmum of surface roughness by usng response surface method. The experments were carred out usng CNC mllng machne. All the data was analyzed by usng Response Surface Method (RSM) and Neural Network (NN). The result showed that the feed gave the more affect on the both predcton value of Ra compare to the cuttng speed and depth of cut. Routara et al. (2010) hghlghted a mult-objectve optmzaton problem by applyng utlty concept coupled wth Taguch method through a case study n CNC end mllng of UNS C34000 medum leaded brass. Patwar et al. (2011) descrbed mathematcally the effect of cuttng parameters on surface roughness n end mllng of Medum Carbon Steel. The mathematcal model for the surface roughness was developed, n terms of cuttng speed, feed rate, and axal depth 9

10 of cut. The effect of these cuttng parameters on the surface roughness was carred out usng desgn of experments and response surface methodology (RSM). In order to solve a mult-objectve optmzaton problem, t s recommended to convert multple objectves nto a sngle representatve objectve functon. Ths s to be optmzed (maxmzed/mnmzed) fnally usng any optmzaton algorthm/phlosophy. In product/process optmzaton Taguch method s very popular as t selects optmal soluton (parameter settng) n dscrete ponts n the parameter doman. But ths approach fals to solve mult-response optmzaton problem. In ths context, applcaton of TOPSIS adapted from Mult-Crtera Decson Makng (MCDM) and GRA-Fuzzy deserves menton. Aforesad methodologes help to convert mult response parameters nto sngle response. The study exhbts that applcaton of grey-fuzzy has been found more advantageous over TOPSIS method. In fuzzy-based approach prorty weghts of ndvdual responses need not to be assgned by decson-makers. Fuzzy nference engne can tackle ths aspect n ts nternal herarchy. Ths s the man advantage of usng fuzzy expert system over conventonal optmzaton tools. 3. Outlne of Taguch Method Taguch s phlosophy s an effcent tool for the desgn of hgh qualty manufacturng system. Dr. Gench Taguch, a Japanese qualty management consultant, developed a method based on Orthogonal Array (OA) of experments, whch provded much-reduced varance for the experment wth optmum settng of process control parameters. Thus the ntegraton of Desgn Of Experments (DOE) wth parametrc optmzaton of process s acheved n the Taguch Method, whch would yeld desred results. Orthogonal Array 10

11 (OA) provdes a set of well-balanced experments (wth less number of expermental runs), and Taguch s sgnal-to-nose ratos (S/N), whch are logarthmc functons of desred output; serve as objectve functons n the optmzaton process. Ths technque helps n data analyss and predcton of optmum results. In order to evaluate optmal parameter settngs, Taguch Method uses a statstcal measure of performance called sgnal-to-nose rato. The S/N rato takes both the mean and the varablty nto account. The S/N rato s the rato of the mean (Sgnal) to the standard devaton (Nose). The rato depends on the qualty characterstcs of the product/process to be optmzed. The standard S/N ratos generally used are as follows: - Nomnal s Best (NB), Lower the Better (LB) and Hgher the Better (HB). The optmal settng s the parameter combnaton, whch has the hghest S/N rato. The steps nvolved n Taguch Method are as follows: Step 1: Formulaton of the problem: the success of an experment depends on complete understandng of the nature of the problem. Identfcaton of the performance characterstc of the process output s most mportant n connecton wth applcaton of Taguch method. Step 2: Identfcaton of control factors, nose factors and sgnal factors: A controlled factor s a characterstc that can be controlled n the product or process subjected to desgnng. Nose factors are those that cannot be easly controlled n the manufacture or use of a product. In the expermental settng, the levels of nose factors are to be controlled for smulatng the sources of varaton the product wll be subjected to n actual use. The goal of robust parameter desgn s to fnd levels of the control factors that wll mnmze the senstvty of the product to changes n the nose factors. A sgnal 11

12 factor s an nput to the expermental system that s supposed to affect the output. Taguch s dynamc experment measures the response varable at dfferent levels of a sgnal factor. Step 3: Selecton of factor levels, possble nteractons and degrees of freedom assocated wth each factor and the nteracton effects: Expermental doman has to be selected frst wth dfferent levels of factors. Man/drect effects as well as nteracton effects of the factors are to be selected to ncorporate n expermental desgn accordngly. Step 4: Desgn of an approprate Orthogonal Array (OA): Taguch s orthogonal arrays are expermental desgns that usually requre only a fracton of the full factoral combnatons. The arrays are desgned to handle as many factors as possble n a certan number of runs as that dctated by full factoral desgn. The columns of the arrays are balanced and orthogonal. Ths means that n each par of columns, all factor combnatons appear the same number of tmes. Orthogonal desgns allow estmatng the effect of each factor on the response ndependently of all other factors. Step 5: Expermentaton and data collecton: Experments are to be conducted and collected data are to be utlzed for analyss of the process towards process optmzaton. Step 6: Statstcal analyss and nterpretaton of expermental results: Evaluaton of statstcal sgnfcance of the factors on the selected response varable s done n ths step and nterpretaton s made based on ths evaluaton. Step 7: Conductng confrmatory test: Taguch s predcted optmal result can be verfed by ths test. 12

13 4. TOPSIS Method TOPSIS (technque for order preference by smlarty to deal soluton) method was frstly proposed by (Hwang and Yoon, 1981). The basc concept of ths method s that the chosen alternatve (approprate alternatve) should have the shortest dstance from the postve deal soluton and the farthest dstance from negatve deal soluton. Postve deal soluton s a soluton that maxmzes the beneft crtera and mnmzes adverse crtera, whereas the negatve deal soluton maxmzes the adverse crtera and mnmzes the beneft crtera. The steps nvolved for calculatng the TOPSIS values are as follows: Step 1: Ths step nvolves the development of matrx format. The row of ths matrx s allocated to one alternatve and each column to one attrbute. The decson makng matrx can be expressed as: A x x. x j x n A x x. x j x n D = (1) A x 1 x2. xj Am xm 1 xm2. xmj xmn Here, A ( ( = 1, 2,..., m) represents the possble alternatves; ( j 1, 2, n) x j =..., represents the attrbutes relatng to alternatve performance, j = 1, 2,...., n and x j s the performance of A wth respect to attrbute X j. Step 2: Obtan the normalzed decson matrx r j.ths can be represented as: r j = x m j = 1 x 2 j (2) 13

14 Here, r j represents the normalzed performance of Step 3: obtan the weghted normalzed decson matrx, = [ ] A wth respect to attrbute X j. V can be found as: v j V = w j r j (3) Here, n w j j= 1 = 1 Step 4: Determne the deal (best) and negatve deal (worst) solutons n ths step. The deal and negatve deal soluton can be expressed as: a) The deal soluton: A + = ' {( max vj j J ), ( mn vj j J = 1,2,..., m) } { v + v +,..., v + + j,... v } = 1, 2 n b) The negatve deal soluton: A = ' {( mn vj j J ), ( max vj j J = 1, 2,..., m) } { v v,..., v j,... v } = 1, 2 n (4) (5) Here, J = { j = 1,2,..., n j}: Assocated wth the benefcal attrbutes ' J = { j = 1,2,..., n j}: Assocated wth non benefcal adverse attrbutes Step 5: Determne the dstance measures. The separaton of each alternatve from the deal soluton s gven by n-dmensonal Eucldean dstance from the followng equatons: S + = n + ( vj v j ) j= 1 2, = 1, 2,..., m (6) 14

15 S = n ( vj v j ) j= 1 2, = 1, 2,..., m (7) Step 6: Calculate the relatve closeness to the deal soluton: + S + C =, = 1,2,..., m;0 C 1 + (8) S + S Step 7: Rank the preference order. The alternatve wth the largest relatve closeness s the best choce. In the present study + C for each product has been termed as Mult-Performance Characterstc Index (MPCI) whch has been optmzed by Taguch method. 5. Grey Relatonal Analyss In grey relatonal analyss, expermental data.e. measured features of qualty characterstcs are frst normalzed rangng from zero to one. Ths process s known as grey relatonal generaton. Next, based on normalzed expermental data, grey relatonal coeffcent s calculated to represent the correlaton between the desred and actual expermental data. Then overall grey relatonal grade s determned by averagng the grey relatonal coeffcent correspondng to selected responses. The overall performance characterstc of the multple response process depends on the calculated grey relatonal grade. Ths approach converts a multple- response- process optmzaton problem nto a sngle response optmzaton stuaton, wth the objectve functon s overall grey relatonal grade. The optmal parametrc combnaton s then evaluated whch would result hghest grey relatonal grade. The optmal factor settng for maxmzng overall grey relatonal grade can be performed by Taguch method. 15

16 In grey relatonal generaton, the normalzed bead wdth, renforcement and HAZ wdth, correspondng to lower-the-better (LB) crteron can be expressed as: max y ( k) y ( k) x ( k) = (9) max y ( k) mn y ( k) Bead penetraton and %Dluton should follow larger-the-better crteron, whch can be expressed as: y ( k) mn y ( k) x ( k) = (10) max y ( k) mn y ( k) Here x (k) s the value after the grey relatonal generaton, mn ( k) y s the smallest value of y (k) for the kth response, and max y ( k) s the largest value of (k) for the kth response. An deal sequence s x ( k) ( k 1, 2,3...,9) for the responses. The 0 = defnton of grey relatonal grade n the course of grey relatonal analyss s to reveal the degrees of relaton between the sequences say, [ x 0 ( k) and x ( k), = 1, 2,3...,9]. The grey relatonal coeffcent ξ (k) can be calculated as: y ξ ( k) = + ψ mn max (11) 0 ( k) + ψ max Here = x k) x ( ) = dfference of the absolute value x ( ) and (k) ; ψ s the 0 0 ( k 0 k x mn mn dstngushng coeffcent 0 ψ 1; mn = j k x0( k) xj( k) = the smallest value of max max 0 ; and max = j k x0( k) xj( k) = largest value of 0. After averagng the grey relatonal coeffcents, the grey relatonal grade γ can be computed as: 16

17 n 1 γ = ξ ( k) n 1 k = (12) Here n = number of process responses. The hgher value of grey relatonal grade corresponds to ntense relatonal degree between the reference sequence x ( ) and the gven sequence x (k). The reference sequence x ( ) represents the best process sequence. Therefore, hgher grey relatonal grade means that the correspondng parameter combnaton s closer to the optmal. The mean response for the grey relatonal grade wth ts grand mean and the man effect plot of grey relatonal grade are very mportant because optmal process condton can be evaluated from ths plot. 0 k 0 k 6. Fuzzy Inference System (FIS) Fuzzy logc s a superset of conventonal (boolean) logc that has been extended to handle the concept of partal truth, where the truth value may range between completely true and completely false. A fuzzy nference system (FIS) defnes a nonlnear mappng of the nput data vector nto a scalar output, usng fuzzy rules. A fuzzy rule based system conssts of four parts: 1. knowledge base, 2. fuzzfer, 3. nference engne and 4. defuzzfer. Fuzzfer: The real world nput to the fuzzy system s appled to the fuzzfer. In fuzzy lterature, ths nput s called crsp nput snce t contans precse and specfc nformaton 17

18 about the parameter. The fuzzfer convert ths precse quantty to the form of mprecse quantty lke large, medum, hgh etc. wth a degree of belongngness to t. Typcally the value ranges from 0 to 1. Knowledge base: The man part of the fuzzy system s the knowledge base n whch both rule base and database are jontly referred. The database defnes the membershp functons of the fuzzy sets used n the fuzzy rules whereas the rule base contans a number of fuzzy IF THEN rules. Inference engne: The nference system or the decson makng nput perform the nference operatons on the rules. It handles the way n whch the rules are combned. Defuzzfer: The output generated by the nference block s always fuzzy n nature. A real world system wll always requre the output of the fuzzy system to the crsp or n the form of real world nput. The job of the defuzzfer s to receve the fuzzy nput and provde real world output. In operaton, t works opposte to the nput block. The frst step n system modelng was the dentfcaton of nput and output varables called the system varables. In the selecton procedure, the nputs and the outputs are taken n the form of lngustc format. A lngustc varable s a varable whose values are words or sentences n natural or man-made languages. Lngustc values are expressed n the form of fuzzy sets. A fuzzy set s usually defned by ts membershp functons. In general, trangular or trapezodal membershp functons are used to the crsp nputs because of ther smplcty and hgh computatonal effcency. In the present study, a fuzzy set A ~ s represented by trangular fuzzy number whch s defned by the trplet ( a, b, c). Membershp functon ( x) x, a, b, c R µ s defned as: A ~ 18

19 x a c x µ ~ ( x) = 0, f x < a else A, f a x b else, f b x c else 0, f x > c b a c b Usng a defuzzfcaton method, fuzzy values can be obtaned nto one sngle crsp output value. The centre of gravty, one of the most popular methods for defuzzfyng fuzzy output functons, s employed n the study. The formula to fnd the centrod of the combned outputs: y = y µ µ c ( y ) ( y ) c dy dy (13) Fg. 1: Elements of Fuzzy Inference System (FIS) 19

20 7. Expermentaton Samples of copper bars (Ø25x10mm) have been used as work materal. Taguch s L 9 orthogonal array has been used here (Table 1). Table 2 ndcates selected process control parameters and ther lmts. Three machnng parameters: cuttng speed, feed rate and depth of cut has been vared nto three dfferent levels have been used to optmze the machnng condtons. HSS tool (C00662D, 12 HSS, TYPE A & N) has been used durng experments. Mllng has been performed n CNC MAXMILL set up. Correspondng to each expermental run MRR and average surface roughness values (R a ) have been computed (Table 3). The surface roughness has been measured by the Talysurf (Taylor Hobson, Surtronc 3+). 8. Data Analyss: GRA-Fuzzy combned wth Taguch Method The methodology used for the optmzaton s grey relatonal analyss (GRA) coupled wth fuzzy nference system. Grey relatonal analyss has been utlzed to compute grey relaton coeffcents for ndvdual responses. These have been fed to a Fuzzy Inference System (FIS) as nputs; whose output has been defned as Mult-Performance Characterstc Index (MPCI). MPCI has been optmzed fnally by Taguch method. Taguch method has been used to fnd an optmal soluton at some dscrete ponts at the expermental doman whch can be easly adjusted n CNC machne. It s based on two prncple namely quadratc qualty loss functon and Sgnal-to-Nose (S/N) rato. The loss functon has been used to measure the process response devatng from the desred value and the value of the loss functon has been further transformed nto an S/N rato. 20

21 Data analyss has been carred out by the procedural herarchy as shown below. 1. Expermental data (Table 3) have been normalzed frst (Table 4) whch s known as grey relatonal generaton. 2. Computaton of grey relatonal coeffcents for ndvdual responses n all expermental run (Table 6) by consderng qualty loss estmates of ndvdual responses (Table 5). For calculatng grey relatonal coeffcents of MRR, a Hgherthe-Better (HB) crteron and for R a, a Lower-the-Better (LB) crteron has been selected. 3. These grey relatonal coeffcents correspondng to ndvdual responses have been fed as nputs to a Fuzzy Inference System (FIS) (Fg. 1). For each of the nput parameters seven trangular type membershp functons (MFs) have been chosen as: Very Low (VL), Low (L), Farly Low (FL), Medum (M), Farly Hgh (FH), Hgh (H) and Very Hgh (VH) (Fg. 2-3). Based on fuzzy assocaton rule mappng (Table 7) FIS combned multple nputs nto a sngle output termed as Mult-Performance Characterstc Index (MPCI). The lngustc valuaton of MPCI has been represented by seven trangular type membershp functons (MFs) have been chosen as: Very Low (VL), Low (L), Farly Low (FL), Medum (M), Farly Hgh (FH), Hgh (H) and Very Hgh (VH) (Fg. 4). These lngustc values haven transformed nto crsp values by defuzzfcaton method. 4. The crsp values of MPCI (Table 8) have been optmzed by usng Taguch phlosophy. The predcted optmal settng has been evaluated from Mean (S/N rato) Response Plot of MPCIs (Fg. 5) and t became A3 B3 C2 D1. 5. Optmal settng has been verfed by confrmatory test. 21

22 6. Mean response table of S/N ratos of MPCIs has been found n Table Data Analyss: TOPSIS based Taguch Method In TOPSIS based Taguch approach, expermental data have been normalzed frst. The normalzed data have been furnshed n Table 10. Elements of normalzed decsonmakng matrx have been multpled wth correspondng response weghts to obtan weghted normalzed decson-makng matrx shown n Table 11. Computed Ideal and Negatve-Ideal solutons have been furnshed n Table 12. Computed dstance measures: S + and S - have been tabulated n Table 13. Closeness Coeffcent (CC) aganst each expermental run has been calculated and shown n Table 14. CC has been optmzed (maxmzed) fnally usng Taguch method. Fg. 6 reveals S/N rato plot of closeness coeffcent values. Predcted optmal parameter combnaton has been verfed by confrmatory test. Rankng of factors accordng to ther nfluence on CC has been shown n Table 15 (mean response table for S/N rato of CCs). 10. Conclusons Ths paper outlnes applcaton of TOPSIS and grey based fuzzy nference system coupled wth Taguch method to optmze qualty and productvty measurements n CNC mllng operaton. The optmzaton of machnng parameters has been carred out wth mnmum number of test condtons by usng orthogonal array. Based on expermental results and data analyss, the followng conclusons are summarzed below: 22

23 (1) Maxmzaton the MRR and mnmzaton the surface roughness has been found possble smultaneously under ths aforesad optmal parameter combnaton. (2) Multple objectves can be optmzed n an effectve logcal effcent manner. (3) Ths method can effcently be appled n any manufacturng/ producton envronment to determne the optmal envronment capable of producng desred yeld ether n the process or n the product. Table 1: Desgn of experment Sl. No. Factoral combnaton (Coded form) N f d Table 2: Doman of experments Factors Unt Leve Level Leve l 1 2 l 3 Cuttng Speed, N RPM Feed Rate, f mm/mn Depth of Cut, d mm

24 Table 3: Expermental data Sl. No. Expermental Data MRR (mm 3 /mn) R a (µm) Table 4: Normalzed data for MRR and R a (grey relaton generaton) Sl. No. Normalzed data MRR R a Table 5: Qualty loss estmates ( ) of ndvdual responses Sl. No. o o for MRR o for R a

25 Table 6: Grey relatonal coeffcent [ ( k) ] ξ of ndvdual responses [Dstngushng coeffcent (ψ ) value taken as 0.5] Sl. No. ξ ( k) of MRR ( k) ξ of Ra Fg. 1 Proposed Fuzzy Inference System (FIS) Fg. 2 Membershp Functons (MFs) for MRR 25

26 Fg. 3 Membershp Functons (MFs) for R a Fg. 4 Membershp Functons for MPCI Table 7: Fuzzy rule matrx MPCI R a MRR VL L FL M FH H VH VL VL VL L L FL FL M L VL VL L FL FL M M FL L L FL FL M M FH M L L FL M M FH H FH L FL FL M FH H H H L FL M FH FH H VH VH FL FL M FH H H VH 26

27 Table 8: Computed MPCI values Sl. No. MPCI Fg. 5 S/N rato plot for MPCIs (Evaluaton of optmal settng) A1 B3 C3/ N1 f3 d3 Table 9: Response Table for Sgnal to Nose Ratos Level A B C Delta Rank

28 Sl. No. Table 10: Normalzed decson-makng matrx Normalzed Response Data R a MRR Sl. No. Table 11: Weghted normalzed decson-makng matrx Weghted Normalzed Response Data R a MRR Table 12: Computed Ideal and Negatve-Ideal solutons Sl. No. Ideal Negatve-Ideal

29 Table 13: Computed dstance measures Sl. No. S + S Table 14: Calculaton of Closeness Coeffcent (CC) aganst each expermental run Sl. No. C + S/N Rato

30 Fg. 6 S/N rato plot for CC (Evaluaton of optmal settng) N2 f1 d1 Table 15: Mean-Response (S/N ratos of CC) table Level N f d Delta Rank

31 11. Bblography 1. Hwang, C. L. and Yoon, K. (1981) Multple Attrbute Decson Makng Methods and Applcatons, A State-of-the-Art Survey, Sprnger Verlag, New York. 2. Ghan J.A., Choudhury I.A. and Hassan H.H. (2004) Applcaton of Taguch method n the optmzaton of end mllng parameters, Journal of Materals Processng Technology, Vol. 145, No. 1, pp Wattanutcharya W. and Pntasee B. (2006) Optmzaton of metallc mllng parameters for surface fnshng, Proceedngs of the 7th Asa Pacfc Industral Engneerng and Management Systems Conference 2006, December 2006, Bangkok, Thaland. 4. Gopalsamy B.M., Mondal B. and Ghosh S. (2009) Taguch method and ANOVA: An approach for process parameters optmzaton of hard machnng whle machnng hardened steel, Journal of Scentfc and Industral Research, Vol. 68, pp Gnta T., Amn A.K.M. Nurul, Radz H.C.D. M. and Lajs M.A. (2009) Development of surface roughness models n end mllng Ttanum Alloy T-6Al-4V usng uncoated Tungsten carbde nserts, European Journal of Scentfc Research, Vol. 28, No. 4, pp Ab. Rashd M.F.F., Gan S.Y. and Muhammad N.Y. (2009) Mathematcal modelng to predct surface roughness n CNC mllng, World Academy of Scence, Engneerng and Technology, Vol. 53, pp Alw Mohd A.B.M. (2010) Optmzaton of surface roughness n mllng by usng response surface method (RSM), Thess of Bachelor of Mechancal wth 31

32 Manufacturng Engneerng, Faculty of Mechancal Engneerng, Unversty Malaysa Pahang. 8. Routara B.C., Mohanty S.D., Datta S., Bandyopadhyay A. and Mahapatra S.S. (2010) Optmzaton n CNC end mllng of UNS C34000 medum leaded brass wth multple surface roughness characterstcs, Sadhana, Indan Academy of Scences, Vol. 35, No. 5, pp Patwar Md. A.U., Amn A. K. M. Nurul and Arf M.D. (2011) Optmzaton of surface roughness n end mllng of medum carbon steel by coupled statstcal approach wth genetc algorthm, The Frst Internatonal Conference on Interdscplnary Research and Development, 31 May - 1 June 2011, Thaland Communcaton 1. Bkash Mohanty, Kumar Abhshek, Chtrasen Samantra, Saurav Datta, Sba Sankar Mahapatra, Use of GRA-Fuzzy towards Mult-Response Optmzaton n CNC End Mllng, The 3rd Asan Symposum on Materals & Processng, ASMP2012, wll be held from August 30 to 31, 2012 n IIT Chenna, Inda. (Abstract Submtted) 32