Application of Taguchi-grey multi responses optimization on process parameters in electro erosion

Measurement 58 (2014) 495–502<br /> <br /> Contents lists available at ScienceDirect<br /> <br /> Measurement<br /> journal homepage: www.elsevier.com/locate/measurement<br /> <br /> Application of Taguchi-grey multi responses optimization<br /> on process parameters in electro erosion<br /> T. Muthuramalingam a,⇑, B. Mohan b<br /> a<br /> b<br /> <br /> Department of Mechatronics Engineering, SRM University, Kattankulathur, India<br /> Department of Mechanical Engineering, Anna University, Chennai, India<br /> <br /> a r t i c l e<br /> <br /> i n f o<br /> <br /> Article history:<br /> Received 3 April 2014<br /> Received in revised form 4 September 2014<br /> Accepted 11 September 2014<br /> Available online 19 September 2014<br /> Keywords:<br /> Current<br /> Duration<br /> EDM<br /> Optimization<br /> Spark<br /> Taguchi<br /> <br /> a b s t r a c t<br /> Convention Taguchi method deals with only single response optimization problems. Since<br /> the electrical discharge machining process involved with many response parameters,<br /> Taguchi method alone cannot help to obtain optimal process parameters in such process.<br /> In the present work, an endeavor has been made to derive optimal combination of electrical process parameters in electro erosion process using grey relational analysis with<br /> Taguchi method. This multi response optimization of the electrical discharge machining<br /> process has been conducted with AISI 202 stainless steel with different tool electrodes such<br /> as copper, brass and tungsten carbide. Gap voltage, discharge current and duty factor have<br /> been used as electrical excitation parameters with different process levels. Taguchi L27<br /> orthogonal table has been assigned for conducting experiments with the consideration<br /> of interactions among the input electrical process parameters. Material removal rate,<br /> electrode wear rate and surface roughness have been selected as response parameters.<br /> From the experimental results, it has been found that the electrical conductivity of the tool<br /> electrode has the most influencing nature on the machining characteristics in EDM process.<br /> The optimal combination of the input process parameters has been obtained using<br /> Taguchi-grey relational analysis.<br /> Ó 2014 Elsevier Ltd. All rights reserved.<br /> <br /> 1. Introduction<br /> 1.1. Electro erosion process<br /> Electro erosion process or electrical discharge machining (EDM) is removing material from the work piece by<br /> thermal erosion owing to the spark energy happened<br /> between two conductors. The ionization of dielectric<br /> medium has the important role in such process. Ho and<br /> Newman narrated about the mechanism involved in thermal erosion process [1]. This process can create crater in<br /> any conducting material by thermal energy irrespective<br /> ⇑ Corresponding author. Tel.: +91 44 22516155.<br /> E-mail addresses: muthu1060@gmail.com (T. Muthuramalingam),<br /> mohan@mitindia.edu (B. Mohan).<br /> http://dx.doi.org/10.1016/j.measurement.2014.09.029<br /> 0263-2241/Ó 2014 Elsevier Ltd. All rights reserved.<br /> <br /> of hardness of the material. This causes less tool wear than<br /> the conventional manufacturing processes. In this process,<br /> two conductors i.e. tool and workpiece are separated by an<br /> isolating region called the dielectric medium. With the<br /> presence of the dielectric medium, the material is removed<br /> by producing precisely controlled electrical discharges<br /> occurring between the tool and the work piece. The tool<br /> electrode does not make contact with the work piece and<br /> it is separated by the distance required for electrical discharge sparking, known as ‘spark gap’. The number of<br /> sparks depends on the DC pulse frequency [2]. The air<br /> gap is filled by the dielectric medium. Whenever the spark<br /> gap is sufficient to ionize the dielectric medium, there is an<br /> electricity flow in a closest point between tool and work<br /> piece. The electrically conductive tool materials such as<br /> graphite, copper, brass, tungsten carbide and copper<br /> <br /> 496<br /> <br /> T. Muthuramalingam, B. Mohan / Measurement 58 (2014) 495–502<br /> <br /> Table 1<br /> Chemical composition of AISI 202 stainless steel.<br /> Elements<br /> <br /> C<br /> <br /> Si<br /> <br /> Cu<br /> <br /> Mn<br /> <br /> P<br /> <br /> S<br /> <br /> Mo<br /> <br /> Cr<br /> <br /> Sn<br /> <br /> Ni<br /> <br /> W<br /> <br /> Al<br /> <br /> Ti<br /> <br /> Fe<br /> <br /> % Composition<br /> <br /> 0.05<br /> <br /> 0.35<br /> <br /> 1.93<br /> <br /> 8.76<br /> <br /> 0.03<br /> <br /> 0.011<br /> <br /> 0.22<br /> <br /> 16.04<br /> <br /> 0.09<br /> <br /> 1.56<br /> <br /> 0.17<br /> <br /> 0.07<br /> <br /> 0.011<br /> <br /> Remain<br /> <br /> tungsten can be utilized as the tool electrodes in electrical<br /> discharge machining process [3]. A controlled DC pulse<br /> (30–100 V) is applied between tool and workpiece separated by small air gap (0.002–2 mm) with high frequency<br /> (100 kHz–10 MHz) [4]. When the dielectric medium<br /> reaches its breakdown voltage, the ionization effect occurs<br /> in the air gap. This ionization produces a initiation of spark<br /> between tool and workpiece. It leads to dissipation of<br /> higher amount of heat in terms of 8000–12000 °C. Because<br /> of this higher thermal energy, the material is melted and<br /> vaporized. The melted material in the air gap can be<br /> removed by the flushing process.<br /> 1.2. Importance of multi response optimization in electro<br /> erosion process<br /> Due to the random nature of such machining process, it<br /> is very essential to optimize the process parameters in<br /> EDM process. Conventional Taguchi method deals with<br /> single response optimization only. It may give different<br /> set of optimal combinations for multiple responses. It is<br /> needed to introduce multi response optimization technique in the process. In this approach, the multiple<br /> responses can be converted into single normalized<br /> response. Then it is easy to obtain the optimal set of<br /> process parameters. Lin et al. discussed about need of optimizing non linear machining process [5]. Lin et al.<br /> <br /> explained about the methodology for finding influencing<br /> process parameters with Taguchi method while machining<br /> high speed steel [6]. Panda proposed the innovative<br /> modeling of electro erosion process [7]. Mukherjee and<br /> Chakraborty depicted the biogeography based optimization algorithm for selecting thermal erosion process<br /> parameters [8]. Chakravorty et al. discussed about need<br /> of optimizing the electrical process parameters involved<br /> in EDM process [9]. Panda and Yadava explained about<br /> the multi response optimization in chemical spark erosion<br /> process using genetic algorithm [10]. Jailani et al. obtained<br /> the optimal set of sintering parameters in grinding process<br /> using Taguchi method with grey technique [11]. Patel et al.<br /> applied the response surface methodology technique in<br /> machining process for optimization purpose [12]. Meena<br /> and Azad discussed about grey relational analysis in thermal erosion process [13]. Somashekhar et al. described<br /> about the optimization technique in EDM process using<br /> artificial intelligence and genetic techniques [14].<br /> From the above literatures, it is clearly understood that<br /> only multi response optimization technique can give better<br /> optimal set of process parameters [15]. It is very clear that<br /> only few researches have been carried out in EDM process<br /> for optimizing electrical process parameters. While<br /> reviewing the literatures, it has been also found that<br /> interactions have not been taken into account, in case of<br /> electrical parameters optimization in EDM process. Since<br /> <br /> Table 2<br /> Orthogonal table L27 for responses.<br /> Trial no.<br /> <br /> Voltage (V)<br /> <br /> Current (A)<br /> <br /> Duty factor<br /> <br /> Tool<br /> <br /> MRR (mm3/min)<br /> <br /> SR (lm)<br /> <br /> EWR (mm3/min)<br /> <br /> 1.<br /> 2.<br /> 3.<br /> 4.<br /> 5.<br /> 6.<br /> 7.<br /> 8.<br /> 9.<br /> 10.<br /> 11.<br /> 12.<br /> 13.<br /> 14.<br /> 15.<br /> 16.<br /> 17.<br /> 18.<br /> 19.<br /> 20.<br /> 21.<br /> 22.<br /> 23.<br /> 24.<br /> 25.<br /> 26.<br /> 27.<br /> <br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 60<br /> 60<br /> 60<br /> 60<br /> 60<br /> 60<br /> 60<br /> 60<br /> 60<br /> 70<br /> 70<br /> 70<br /> 70<br /> 70<br /> 70<br /> 70<br /> 70<br /> 70<br /> <br /> 9<br /> 9<br /> 9<br /> 12<br /> 12<br /> 12<br /> 15<br /> 15<br /> 15<br /> 9<br /> 9<br /> 9<br /> 12<br /> 12<br /> 12<br /> 15<br /> 15<br /> 15<br /> 9<br /> 9<br /> 9<br /> 12<br /> 12<br /> 12<br /> 15<br /> 15<br /> 15<br /> <br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> 0.4<br /> 0.6<br /> 0.8<br /> <br /> WC<br /> Br<br /> Cu<br /> Br<br /> Cu<br /> WC<br /> Cu<br /> WC<br /> Br<br /> Br<br /> Cu<br /> WC<br /> Cu<br /> WC<br /> Br<br /> WC<br /> Br<br /> Cu<br /> Cu<br /> WC<br /> Br<br /> WC<br /> Br<br /> Cu<br /> Br<br /> Cu<br /> WC<br /> <br /> 0.783<br /> 4.896<br /> 8.097<br /> 4.673<br /> 8.811<br /> 0.971<br /> 7.142<br /> 0.982<br /> 6.562<br /> 4.328<br /> 8.323<br /> 1.157<br /> 7.566<br /> 1.128<br /> 8.862<br /> 0.973<br /> 7.769<br /> 15.485<br /> 9.363<br /> 1.111<br /> 10.647<br /> 1.135<br /> 8.453<br /> 16.621<br /> 7.865<br /> 13.803<br /> 1.568<br /> <br /> 0.326<br /> 3.724<br /> 5.286<br /> 5.523<br /> 5.604<br /> 0.725<br /> 5.124<br /> 0.731<br /> 12.458<br /> 3.789<br /> 4.464<br /> 0.618<br /> 3.592<br /> 0.674<br /> 10.235<br /> 0.595<br /> 10.357<br /> 10.562<br /> 3.125<br /> 0.595<br /> 8.934<br /> 0.484<br /> 8.128<br /> 8.159<br /> 7.653<br /> 8.364<br /> 0.905<br /> <br /> 0.0157<br /> 1.3219<br /> 0.9716<br /> 1.2617<br /> 1.0573<br /> 0.0194<br /> 0.857<br /> 0.0196<br /> 1.7717<br /> 1.1686<br /> 0.9988<br /> 0.0231<br /> 0.9079<br /> 0.226<br /> 2.3927<br /> 0.0195<br /> 2.0976<br /> 1.85282<br /> 1.1236<br /> 0.0222<br /> 2.8747<br /> 0.0227<br /> 2.2823<br /> 1.9945<br /> 2.1236<br /> 1.6564<br /> 0.0314<br /> <br /> T. Muthuramalingam, B. Mohan / Measurement 58 (2014) 495–502<br /> <br /> the electrical parameters have relations between them, it is<br /> important to consider the interactions effect among those<br /> parameters. In this present paper, interactions effects<br /> between the process parameters have been taken into<br /> account for designing orthogonal table. L27 orthogonal<br /> table based Taguchi design of experiment with grey relational analysis methodology has been utilized to perform<br /> multi response optimization in thermal erosion process.<br /> In the aerospace engineering and auto motive engineering<br /> field, surface quality with high material rate is the<br /> favorable one. This multi response optimization can be<br /> adopted for such situations. The main aim of this work<br /> on machinability of AISI 202 stainless steel in EDM process<br /> with different process parameters are as follows:<br /> 1. To analyze the effect of process parameters on machining characteristics.<br /> 2. To find the optimal combination of input process<br /> parameters for obtaining better multiple response<br /> parameters.<br /> 3. To identify the most influencing electrical process<br /> parameter in thermal erosion process.<br /> 2. Experiments and methods<br /> In this present study, AISI 202 stainless steel has been<br /> used as the work material. It is widely used in automobile<br /> industries and railway tracks. The stainless steel with<br /> complicated shapes can be easily machined using EDM<br /> process. The chemical composition of that material is<br /> shown in Table 1. Copper, brass and tungsten carbide have<br /> been selected as the tool electrodes due to their various<br /> electrical conductivity. Owing to the uniform energy distribution, the iso current pulse generator has been used for<br /> applying pulses between tool and work piece. Kerosene<br /> has been used as dielectric medium in EDM process. It<br /> has been utilized for insulating purpose and flushing process. Since the discharge energy depends on gap voltage,<br /> duty factor and discharge current, they have been selected<br /> as electrical input process parameters with different types<br /> of tool electrode [2]. Material removal rate (MRR), electrode wear rate (EWR) and surface roughness (Ra) have<br /> <br /> 497<br /> <br /> been selected as the response parameters. 40 V, 60 V and<br /> 70 V have been selected as gap voltage ranges. Discharge<br /> current has been chosen as 9 A, 12 A and 15 A with duty<br /> factor of 0.4, 0.6 and 0.8. Material removal rate and electrode wear has been calculated on weight difference of<br /> the material during the machining process. The average<br /> surface roughness has been computed by SE1200 surfcoder<br /> surface roughness tester with cutoff length of 0.8 mm.<br /> 3. Taguchi method<br /> 3.1. Design of experiments<br /> Due to its simplicity and easy adaptability, Taguchi<br /> method can be adopted for optimizing the process<br /> variables. This method provides the desired information<br /> from the minimum number of trials with different number<br /> of levels. The least number of trials can be calculated as per<br /> following equation<br /> <br /> DOF ¼ ðP À 1Þ ðFÞ þ ðP À 1Þ ðP À 1Þ ðQ Þ<br /> þ 1 for the average<br /> <br /> ð1Þ<br /> <br /> where DOF is degree of freedom, F is number of independent variables, p is their levels, and Q is number of interactions. The number of trials should be larger than or equal to<br /> DOF for conducting experiments in any process. Since four<br /> input factors have been selected with three interfaces in<br /> the present study, L27 orthogonal table has been chosen<br /> as per the Taguchi design of experiments. Table 2 shows<br /> the L27 orthogonal table with input parameter levels and<br /> response values in EDM process.<br /> 3.2. Selection of quality characteristics level<br /> The response in the each trial has to be transformed<br /> into S/N ratio to determine quality characteristics. Since<br /> the MRR has to be maximized, it is chosen as superior<br /> the better type of quality characteristics. Hence the S/N<br /> ratio for this response has been computed from the following equation.<br /> <br /> S=N ratio ¼ À10 à logð1=xÞRð1=Y 2 Þ<br /> nj<br /> <br /> ð2Þ<br /> <br /> Surface roughness and TWR are smaller the better type<br /> and their S/N ratios have been computed from the<br /> following equation.<br /> <br /> S=N ratio ¼ À10 à logð1=xÞRY 2<br /> nj<br /> <br /> ð3Þ<br /> <br /> where x is number of experimental replication and Ynj is<br /> response of nth trial of jth dependent level.<br /> 4. Grey relational optimization<br /> Grey relational technique is used for solving interrelationships among the multiple responses. This analysis<br /> consists of following rules.<br /> <br /> Fig. 1. SEM micro structure image of crater in EDM process.<br /> <br /> Step 1: Transform the responses into the S/N ratio Ynj<br /> using the appropriate equations depending on the<br /> quality characteristics.<br /> <br /> 498<br /> <br /> T. Muthuramalingam, B. Mohan / Measurement 58 (2014) 495–502<br /> Table 3<br /> Signal to noise ratio with their normalized value for various response parameters.<br /> <br /> 1.<br /> 2.<br /> 3.<br /> 4.<br /> 5.<br /> 6.<br /> 7.<br /> 8.<br /> 9.<br /> 10.<br /> 11.<br /> 12.<br /> 13.<br /> 14.<br /> 15.<br /> 16.<br /> 17.<br /> 18.<br /> 19.<br /> 20.<br /> 21.<br /> 22.<br /> 23.<br /> 24.<br /> 25.<br /> 26.<br /> 27.<br /> <br /> Material removal rate (mm3/min)<br /> <br /> Surface roughness (lm)<br /> <br /> S/N ratio<br /> <br /> Trial no.<br /> <br /> Electrode wear rate (mm3/min)<br /> <br /> Normalized S/N ratio<br /> <br /> S/N ratio<br /> <br /> Normalized S/N ratio<br /> <br /> S/N ratio<br /> <br /> Normalized S/N ratio<br /> <br /> À2.124765<br /> 13.796828<br /> 18.166483<br /> 13.391916<br /> 18.900504<br /> À0.255615<br /> 17.076397<br /> À0.15777<br /> 16.340725<br /> 12.725745<br /> 18.405598<br /> 1.2666672<br /> 17.577327<br /> 1.046182<br /> 18.950635<br /> À0.237743<br /> 17.807302<br /> 23.798224<br /> 19.4283<br /> 0.9142812<br /> 20.544545<br /> 1.0999172<br /> 18.540217<br /> 24.413143<br /> 17.913975<br /> 22.79947<br /> 3.9069212<br /> <br /> 0<br /> 0.599956605<br /> 0.764613691<br /> 0.584698712<br /> 0.792273039<br /> 0.070433193<br /> 0.723537135<br /> 0.074120189<br /> 0.695815568<br /> 0.559596108<br /> 0.773624013<br /> 0.127795762<br /> 0.742413145<br /> 0.119487451<br /> 0.794162069<br /> 0.071106653<br /> 0.751079076<br /> 0.976828663<br /> 0.812161436<br /> 0.114517172<br /> 0.854223704<br /> 0.1215123<br /> 0.778696737<br /> 1<br /> 0.755098689<br /> 0.939193653<br /> 0.227285669<br /> <br /> 9.735648<br /> À11.4202<br /> À14.4625<br /> À14.8435<br /> À14.97<br /> 2.79324<br /> À14.1922<br /> 2.721652<br /> À21.909<br /> À11.5705<br /> À12.9945<br /> 4.18023<br /> À11.1067<br /> 3.426802<br /> À20.2018<br /> 4.509661<br /> À20.3047<br /> À20.4749<br /> À9.897<br /> 4.509661<br /> À19.0209<br /> 6.303093<br /> À18.1997<br /> À18.2327<br /> À17.6766<br /> À18.4483<br /> 0.867028<br /> <br /> 0<br /> 0.66854406<br /> 0.764685111<br /> 0.776723725<br /> 0.78072003<br /> 0.219386486<br /> 0.756141463<br /> 0.221648714<br /> 1<br /> 0.673293636<br /> 0.718293081<br /> 0.175556306<br /> 0.658638218<br /> 0.199365338<br /> 0.946049548<br /> 0.165146009<br /> 0.949301996<br /> 0.954681855<br /> 0.620409759<br /> 0.165146009<br /> 0.908733981<br /> 0.108471904<br /> 0.882781881<br /> 0.883826758<br /> 0.866253348<br /> 0.890638078<br /> 0.280256541<br /> <br /> 36.08201<br /> À2.42397<br /> 0.25025<br /> À2.01912<br /> À0.48396<br /> 34.24397<br /> 1.340384<br /> 34.15488<br /> À4.9678<br /> À1.35332<br /> 0.010429<br /> 32.72776<br /> 0.83924<br /> 12.91783<br /> À7.57776<br /> 34.19931<br /> À6.43445<br /> À5.35666<br /> À1.01223<br /> 33.07294<br /> À9.17185<br /> 32.87948<br /> À7.16745<br /> À5.99668<br /> À6.54145<br /> À4.3833<br /> 30.06141<br /> <br /> 0<br /> 0.850888345<br /> 0.791794559<br /> 0.841942147<br /> 0.80801891<br /> 0.040616305<br /> 0.767705262<br /> 0.042584907<br /> 0.907100824<br /> 0.827229492<br /> 0.797094009<br /> 0.07412074<br /> 0.77877932<br /> 0.511871889<br /> 0.964774607<br /> 0.04160313<br /> 0.939510209<br /> 0.915693702<br /> 0.819692389<br /> 0.066493101<br /> 1<br /> 0.070768044<br /> 0.955707747<br /> 0.9298365<br /> 0.941874667<br /> 0.894184815<br /> 0.13304065<br /> <br /> Table 4<br /> Grey relational co-efficient with their grade and rank.<br /> Trial<br /> no.<br /> 1.<br /> 2.<br /> 3.<br /> 4.<br /> 5.<br /> 6.<br /> 7.<br /> 8.<br /> 9.<br /> 10.<br /> 11.<br /> 12.<br /> 13.<br /> 14.<br /> 15.<br /> 16.<br /> 17.<br /> 18.<br /> 19.<br /> 20.<br /> 21.<br /> 22.<br /> 23.<br /> 24.<br /> 25.<br /> 26.<br /> 27.<br /> <br /> Grey relational coefficient<br /> MRR<br /> <br /> SR<br /> <br /> EWR<br /> <br /> 0.3333<br /> 0.5555<br /> 0.6799<br /> 0.5462<br /> 0.7064<br /> 0.3497<br /> 0.6439<br /> 0.3506<br /> 0.6217<br /> 0.5316<br /> 0.6883<br /> 0.3643<br /> 0.6599<br /> 0.3621<br /> 0.7083<br /> 0.3499<br /> 0.6676<br /> 0.9557<br /> 0.7269<br /> 0.3608<br /> 0.7742<br /> 0.3627<br /> 0.6931<br /> 1<br /> 0.6712<br /> 0.8915<br /> 0.3928<br /> <br /> 0.3333<br /> 0.6013<br /> 0.6799<br /> 0.6912<br /> 0.6951<br /> 0.3904<br /> 0.6721<br /> 0.3911<br /> 1<br /> 0.6048<br /> 0.6396<br /> 0.3775<br /> 0.5942<br /> 0.3844<br /> 0.9026<br /> 0.3745<br /> 0.9079<br /> 0.9168<br /> 0.5684<br /> 0.3745<br /> 0.8456<br /> 0.3593<br /> 0.8100<br /> 0.8114<br /> 0.7889<br /> 0.8205<br /> 0.4099<br /> <br /> 0.3333<br /> 0.7702<br /> 0.7060<br /> 0.7598<br /> 0.7225<br /> 0.3426<br /> 0.6827<br /> 0.3430<br /> 0.8433<br /> 0.7431<br /> 0.7113<br /> 0.3506<br /> 0.6932<br /> 0.5060<br /> 0.9341<br /> 0.3428<br /> 0.8920<br /> 0.8557<br /> 0.7349<br /> 0.3487<br /> 1<br /> 0.3498<br /> 0.9186<br /> 0.8769<br /> 0.8958<br /> 0.8253<br /> 0.3657<br /> <br /> Grey<br /> relational<br /> grade<br /> <br /> Rank<br /> <br /> 0.3333<br /> 0.6424<br /> 0.6886<br /> 0.6658<br /> 0.7081<br /> 0.3609<br /> 0.6663<br /> 0.3616<br /> 0.8217<br /> 0.6266<br /> 0.6798<br /> 0.3642<br /> 0.6492<br /> 0.4175<br /> 0.8484<br /> 0.3558<br /> 0.8225<br /> 0.9094<br /> 0.6768<br /> 0.3614<br /> 0.8733<br /> 0.3573<br /> 0.8073<br /> 0.8961<br /> 0.7853<br /> 0.8458<br /> 0.3895<br /> <br /> 27<br /> 17<br /> 11<br /> 15<br /> 10<br /> 24<br /> 14<br /> 22<br /> 7<br /> 18<br /> 12<br /> 21<br /> 16<br /> 19<br /> 4<br /> 26<br /> 6<br /> 1<br /> 13<br /> 23<br /> 3<br /> 25<br /> 8<br /> 2<br /> 9<br /> 5<br /> 20<br /> <br /> Table 5<br /> Average grey relational grade for each input parameters.<br /> Factor<br /> Control factor<br /> notation<br /> <br /> Average grey relational<br /> grade<br /> Level 1<br /> <br /> V<br /> I<br /> DF<br /> Tool<br /> <br /> Gap voltage (V)<br /> Discharge<br /> current (A)<br /> Duty factor<br /> Tool material<br /> <br /> Level 2<br /> <br /> Level 3<br /> <br /> 0.5832<br /> 0.5829<br /> <br /> 0.6304<br /> 0.6345<br /> <br /> 0.6659<br /> 0.6620<br /> <br /> 0.0827<br /> 0.0791<br /> <br /> 0.5685<br /> 0.7663<br /> <br /> 0.6836<br /> 0.3668<br /> <br /> 0.6270<br /> 0.7467<br /> <br /> 0.1151<br /> 0.3995<br /> <br /> Total mean grey relational grade = 0.6265.<br /> <br /> Z nj ¼ ðY nj À min Y nj Þ=ðmax Y nj À min Y nj Þ<br /> ½for larger the better caseŠ<br /> <br /> ð4Þ<br /> <br /> Z nj ¼ ðmax Y nj À Y nj Þ=ðmax Y nj À min Y nj Þ<br /> ½for smaller the better caseŠ<br /> <br /> ð5Þ<br /> <br /> where Znj is the normalized value of nth trial for jth dependent response.<br /> Step 3: Compute the grey co-efficient (GC) for the<br /> normalized S/N ratio values as per following equation<br /> <br /> GCnj ¼ ðWmin þ dWmax Þ=ðWnj þ dWmax Þ<br /> Step 2: Normalize the S/N ratio to distribute the data<br /> evenly and scale it into acceptable range for further<br /> analysis by following equations.<br /> <br /> Max–min<br /> <br /> ð6Þ<br /> <br /> where GC is the grey co-efficient for nth trial of jth dependent response, d is the quality loss and W is the distinctive<br /> co efficient which has value from 0 to 1.<br /> <br /> T. Muthuramalingam, B. Mohan / Measurement 58 (2014) 495–502<br /> <br /> 499<br /> <br /> 5. Results and discussion<br /> 5.1. Computation of S/N ratio and grey relational grade<br /> <br /> Fig. 2. Response graph of average grey relational grade.<br /> <br /> Step 4: Compute grey relation grade by following equation<br /> <br /> Gn ¼ ð1=Q ÞRGCnj<br /> <br /> ð7Þ<br /> <br /> Step 5: Utilize response graph method to select optimal<br /> levels of the input factors based on maximum average<br /> Gn value.<br /> <br /> Fig. 1 shows the surface topography of machined<br /> workpiece using EDM process which has been taken by<br /> scanning electron microscope (SEM) with the input parameter settings of trail number 27. Owing to the higher discharge energy dissipation, larger crater has been<br /> observed [3]. Table 3 depicts the signal to noise ratio with<br /> their normalized value for various response parameters.<br /> MRR has been assumed as higher the best quality whereas<br /> EWR and Ra have been considered as smaller the better<br /> quality characteristics. Since this study has been contained<br /> with both the quality characteristics, the distinguishing<br /> co-efficient value has been taken as 0.5 [11].<br /> The values of grey relational components with their<br /> rank of all the experiments are furnished in Table 4. The<br /> higher value of grey relational grade indicates the better<br /> multi response characteristics during the machining process. Therefore, it has been observed that experiment trial<br /> number 18 has the optimal parameters setting among the<br /> <br /> Fig. 3. Effects of process parameters on material removal rate (MRR).<br /> <br />