Study of surface integrity and dimensional accuracy in EDM using Fuzzy TOPSIS and sensitivity analysis

Measurement 63 (2015) 364–376<br /> <br /> Contents lists available at ScienceDirect<br /> <br /> Measurement<br /> journal homepage: www.elsevier.com/locate/measurement<br /> <br /> Study of surface integrity and dimensional accuracy in EDM<br /> using Fuzzy TOPSIS and sensitivity analysis<br /> S. Dewangan a, S. Gangopadhyay a,⇑, C.K. Biswas a,b<br /> a<br /> b<br /> <br /> AISI P20 tool steel<br /> <br /> Department of Mechanical Engineering, National Institute of Technology, Rourkela-769008, India<br /> Department of Petroleum Engineering, Universiti Teknologi Petronas, Ipoh, Malaysia<br /> <br /> a r t i c l e<br /> <br /> i n f o<br /> <br /> Article history:<br /> Received 28 November 2013<br /> Received in revised form 26 September 2014<br /> Accepted 27 November 2014<br /> Available online 8 December 2014<br /> Keywords:<br /> Electrical Discharge Machining (EDM)<br /> AISI P20 tool steel<br /> Fuzzy-TOPSIS<br /> Sensitivity analysis<br /> <br /> a b s t r a c t<br /> Surface integrity and dimensional accuracy remain critical concern in Electrical Discharge<br /> Machining (EDM). The current research work aims at investigating the influence of various<br /> EDM process parameters like pulse current (Ip), pulse-on time (Ton), tool work time (Tw)<br /> and tool lift time (Tup) on various aspects of surface integrity like white layer thickness<br /> (WLT), surface crack density (SCD) and surface roughness (SR). The dimensional accuracy,<br /> characterized by over cut (OC), has also been studied in the similar way. A response surface<br /> methodology (RSM) – based design of experiment has been considered for this purpose.<br /> The present study also recommends an optimal setting of EDM process parameters with<br /> an aim to improve surface integrity aspects after EDM of AISI P20 tool steel. This has been<br /> achieved by simultaneous optimization of multiple attributes (i.e. WLT, SCD, SR and OC)<br /> using Fuzzy-TOPSIS-based multi-criteria decision making (MCDM) approach. The optimal<br /> solution was obtained based on five decision makers’ preferences on the four responses<br /> (i.e. WLT, SCD, SR, and OC). From this analysis, an optimal condition of process parameters<br /> of Ip = 1 A, Ton = 10 ls, Tw = 0.2 s, and Tup = 1.5 s has been determined. Furthermore, sensitivity analysis was also carried out to study the sensitivity or robustness of five decision<br /> makers’ preference of optimal machining parameters. Form this study, decision makers’<br /> preference for surface crack density has been found to be the most sensitive response<br /> and therefore should be chosen first and analyzed very carefully.<br /> Ó 2014 Elsevier Ltd. All rights reserved.<br /> <br /> 1. Introduction<br /> Electrical Discharge Machining (EDM) is an erosion process, whereby rapidly recurring spark is generated<br /> between the tool and the workpiece in order to remove<br /> the materials form the later. EDM is the one of the most<br /> versatile non-conventional machining processes since the<br /> effectiveness of EDM process is absolutely independent of<br /> mechanical properties of the workpiece material. Therefore, very hard and difficult-to-cut materials can be effectively machined into desired complex shape, if the work<br /> ⇑ Corresponding author. Tel.: +91 9439096336; fax: +91 661 2472926.<br /> E-mail address: soumya.mech@gmail.com (S. Gangopadhyay).<br /> http://dx.doi.org/10.1016/j.measurement.2014.11.025<br /> 0263-2241/Ó 2014 Elsevier Ltd. All rights reserved.<br /> <br /> piece materials are electrically conductive. During the process of EDM, material removal takes place due to melting<br /> and vaporization from the localized zone of the workpiece.<br /> Thermal energy liberated during EDM due to generation of<br /> spark leads to formation of thermally affected layers on the<br /> machined surface. The properties of such layers are different from parent workpiece material [1]. Therefore, surface<br /> integrity in EDM is an issue which requires considerable<br /> research attention. Surface integrity in EDM is usually<br /> characterized by surface roughness, formation of recast<br /> layer or white layer and surface cracks, residual stress<br /> and metallurgical modification of parent material [2].<br /> Therefore, if the surface integrity is not adequately<br /> addressed, the EDMed component would be more prone<br /> <br /> 365<br /> <br /> S. Dewangan et al. / Measurement 63 (2015) 364–376<br /> Table 2<br /> Linguistic variable for the important weight of each output.<br /> Fuzzy subset<br /> <br /> Fig. 1. Experimental setup.<br /> <br /> Table 1<br /> Machining parameters and their levels.<br /> Parameters<br /> <br /> Symbol<br /> <br /> Level<br /> <br /> Unit<br /> <br /> 1<br /> <br /> 2<br /> <br /> 3<br /> <br /> 3<br /> 80<br /> 0.6<br /> 0.75<br /> <br /> 5<br /> 150<br /> 1.0<br /> 1.5<br /> <br /> Control parameters<br /> Pulse current<br /> Pulse on Time<br /> Tool work time<br /> Tool lift time<br /> <br /> Ip<br /> Ton<br /> Tw<br /> Tup<br /> <br /> 1<br /> 10<br /> 0.2<br /> 0.0<br /> <br /> Fixed parameters<br /> Duty cycle<br /> Voltage<br /> Flashing pressure<br /> Sensitivity<br /> Inter electrode gap<br /> <br /> f<br /> V<br /> Fp<br /> SEN<br /> IEG<br /> <br /> 70<br /> 45<br /> 0.3<br /> 6<br /> 90<br /> <br /> A<br /> <br /> ls<br /> s<br /> s<br /> %<br /> V<br /> Kg f/cm2<br /> <br /> lm<br /> <br /> to failure during its intended application. Surface finish in<br /> EDM attracted significant research interest. Different<br /> mathematical models have been developed to correlate<br /> surface roughness with various EDM parameters like discharge current (Ip), pulse-on time (Ton), pulse-off time<br /> (Toff), duty cycle (Tau), polarity, input power, and thermal<br /> physical and electrical properties of workpiece and tool<br /> [3,4]. It has been found that process parameters like Ip<br /> and Ton played a major role in influencing EDMed surface<br /> roughness. For better surface finish, Ip and Ton should preferably be low [5,6]. Effect of EDM parameters on white<br /> layer and surface crack formation for D2 and H13 tool steel<br /> was studied by Lee and Tai [7]. It was observed that white<br /> <br /> Respected fuzzy weight<br /> <br /> Tiny (T)<br /> Very Small (VS)<br /> Small (S)<br /> Medium (M)<br /> Large (L)<br /> Very Large (VL)<br /> Huge (H)<br /> <br /> (0.000, 0.000, 0.0769, 0.1538)<br /> (0.0769, 0.1538, 0.2307, 0.3076)<br /> (0.2307, 0.3076, 0.3845, 0.4612)<br /> (0.3845, 0.4614, 0.5383, 0.6152)<br /> (0.5383, 0.6152, 0.6921, 0.7690)<br /> (0.6921, 0.7690, 0.8459, 0.9228)<br /> (0.8459, 0.9228, 1.000, 1.000)<br /> <br /> layer thickness (WLT) and induced residual stress<br /> appeared to increase at higher value of Ip and Ton. Cracks<br /> found on the transverse plane of machined component<br /> was quantified it terms of surface crack density (SCD)<br /> which increased at lower Ip and decreased as Ton was<br /> increased. Similar observation was also made on AISI<br /> 1045 steel [8] and AISI D2 tool steel [1]. Pradhan [9] determined optimal setting of EDM parameters using RSM combined with grey relation analysis (GRA) as multi-objective<br /> optimization technique with an aim to achieve improved<br /> surface integrity during EDM of AISI D2 tool steel.<br /> Another issue of concern during EDM is overcut phenomenon due to sparking from lateral surface or corner<br /> of bottom surface of the tool electrode. This leads to<br /> dimensional inaccuracy of EDMed component. Pulse current and pulse-on time have been found to be major<br /> parameters in influencing overcut. Increase in both Ip and<br /> Ton resulted in rise in overcut [10–12] owing to higher<br /> amount of discharge energy associated with them. However, inverse relationship between Ip and overcut has also<br /> been reported during micro-EDM of Ti–6Al–4V alloy [13].<br /> It is evident that EDM is always characterized by multiple output responses. Therefore, multi-objective optimization has become one of the major areas of research in EDM<br /> for determining optimal process condition. In the recent<br /> years, fuzzy logic-based multi-criteria decision making<br /> approaches have become very popular in optimization of<br /> different manufacturing processes. Sivapirakasam et al.<br /> [14] applied Fuzzy-TOPSIS technique to optimize various<br /> responses like process time, relative electrode wear rate,<br /> process energy and consumption of dielectric fluid during<br /> EDM of tool steel. Grey-fuzzy logic-based optimization<br /> technique was utilized to optimize MRR, TWR and SR during EDM of SKD11 alloy steel [15]. Puhan et al. [16] integrated principal component analysis (PCA) and fuzzy<br /> inference system coupled with Taguchi method to find<br /> out optimal condition of EDM parameters.<br /> <br /> Fig. 2. Membership function of responses.<br /> <br /> 366<br /> <br /> S. Dewangan et al. / Measurement 63 (2015) 364–376<br /> <br /> Table 3<br /> Decision maker for responses with aggregated fuzzy weight.<br /> Responses<br /> <br /> Decision Maker (DM)<br /> <br /> Aggregated fuzzy weight<br /> <br /> DM-1<br /> <br /> DM-3<br /> <br /> DM-4<br /> <br /> DM-5<br /> <br /> VS<br /> S<br /> S<br /> M<br /> <br /> WLT<br /> SCD<br /> SR<br /> OC<br /> <br /> DM-2<br /> S<br /> VS<br /> M<br /> S<br /> <br /> S<br /> VS<br /> S<br /> S<br /> <br /> T<br /> S<br /> M<br /> VS<br /> <br /> S<br /> T<br /> M<br /> S<br /> <br /> (0.1538,<br /> (0.1230,<br /> (0.3230,<br /> (0.2307,<br /> <br /> 0.2153,<br /> 0.1846,<br /> 0.3999,<br /> 0.3076,<br /> <br /> 0.2922,<br /> 0.2615,<br /> 0.4768,<br /> 0.3845,<br /> <br /> 0.3691)<br /> 0.3348)<br /> 0.5537)<br /> 0.4612)<br /> <br /> Table 4<br /> Design matrix and the normalized response value.<br /> Run no.<br /> <br /> Pt type<br /> <br /> Ip<br /> <br /> Ton<br /> <br /> Tw<br /> <br /> Tup<br /> <br /> WLT (lm)<br /> <br /> SCD (lm/lm2)<br /> <br /> SR (lm)<br /> <br /> OC (mm)<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 /> 28<br /> 29<br /> 30<br /> <br /> 0<br /> 1<br /> 1<br /> 1<br /> 1<br /> 0<br /> 1<br /> 1<br /> 1<br /> 1<br /> À1<br /> À1<br /> À1<br /> À1<br /> 0<br /> À1<br /> À1<br /> 0<br /> À1<br /> À1<br /> 1<br /> 1<br /> 1<br /> 0<br /> 1<br /> 0<br /> 1<br /> 1<br /> 1<br /> 1<br /> <br /> 2<br /> 3<br /> 1<br /> 1<br /> 3<br /> 2<br /> 3<br /> 1<br /> 3<br /> 1<br /> 2<br /> 2<br /> 2<br /> 3<br /> 2<br /> 2<br /> 1<br /> 2<br /> 2<br /> 2<br /> 1<br /> 3<br /> 3<br /> 2<br /> 1<br /> 2<br /> 1<br /> 3<br /> 3<br /> 1<br /> <br /> 2<br /> 3<br /> 1<br /> 3<br /> 1<br /> 2<br /> 3<br /> 3<br /> 1<br /> 1<br /> 2<br /> 2<br /> 1<br /> 2<br /> 2<br /> 3<br /> 2<br /> 2<br /> 2<br /> 2<br /> 3<br /> 3<br /> 1<br /> 2<br /> 1<br /> 2<br /> 3<br /> 3<br /> 1<br /> 1<br /> <br /> 2<br /> 3<br /> 3<br /> 3<br /> 3<br /> 2<br /> 1<br /> 1<br /> 1<br /> 1<br /> 2<br /> 1<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 3<br /> 3<br /> 3<br /> 3<br /> 2<br /> 3<br /> 2<br /> 1<br /> 1<br /> 1<br /> 1<br /> <br /> 2<br /> 3<br /> 3<br /> 1<br /> 1<br /> 2<br /> 1<br /> 3<br /> 3<br /> 1<br /> 1<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 3<br /> 2<br /> 3<br /> 1<br /> 3<br /> 2<br /> 1<br /> 2<br /> 1<br /> 3<br /> 1<br /> 3<br /> <br /> 12.452<br /> 28.379<br /> 3.755<br /> 7.479<br /> 15.633<br /> 15.209<br /> 26.882<br /> 10.271<br /> 17.469<br /> 6.954<br /> 18.243<br /> 13.717<br /> 7.299<br /> 23.166<br /> 14.66<br /> 17.302<br /> 4.972<br /> 17.993<br /> 16.305<br /> 13.001<br /> 9.595<br /> 29.842<br /> 16.553<br /> 16.435<br /> 3.146<br /> 18.275<br /> 9.267<br /> 24.615<br /> 19.594<br /> 6.684<br /> <br /> 0.0210<br /> 0.0078<br /> 0.0662<br /> 0.0703<br /> 0.0210<br /> 0.0066<br /> 0.0066<br /> 0.0605<br /> 0.0004<br /> 0.0202<br /> 0.0093<br /> 0.0110<br /> 0.0011<br /> 0.0009<br /> 0.0096<br /> 0.0186<br /> 0.0637<br /> 0.0134<br /> 0.0031<br /> 0.0156<br /> 0.0690<br /> 0.0092<br /> 0.0370<br /> 0.0027<br /> 0.0730<br /> 0.0071<br /> 0.0650<br /> 0.0069<br /> 0.0010<br /> 0.0230<br /> <br /> 4.86<br /> 7.13<br /> 1.73<br /> 1.73<br /> 3.40<br /> 5.20<br /> 5.86<br /> 2.00<br /> 3.66<br /> 2.06<br /> 4.66<br /> 5.26<br /> 3.20<br /> 6.06<br /> 5.06<br /> 5.06<br /> 2.89<br /> 5.40<br /> 4.66<br /> 4.80<br /> 1.73<br /> 5.53<br /> 3.26<br /> 4.80<br /> 1.66<br /> 4.96<br /> 1.86<br /> 6.60<br /> 3.00<br /> 1.82<br /> <br /> 0.1775<br /> 0.1950<br /> 0.0067<br /> 0.2100<br /> 0.0935<br /> 0.1684<br /> 0.1934<br /> 0.0180<br /> 0.2667<br /> 0.1017<br /> 0.1650<br /> 0.1450<br /> 0.1885<br /> 0.1650<br /> 0.1734<br /> 0.1955<br /> 0.0267<br /> 0.1409<br /> 0.1850<br /> 0.1217<br /> 0.1267<br /> 0.1934<br /> 0.1550<br /> 0.1617<br /> 0.1134<br /> 0.1610<br /> 0.1246<br /> 0.1950<br /> 0.1734<br /> 0.0417<br /> <br /> Rij<br /> WLT<br /> <br /> From the study of past literature, it is evident that some<br /> research work has been carried out to examine the influence of EDM parameters on surface integrity aspects and<br /> overcut phenomenon separately. However, it is also very<br /> essential to determine optimal parametric combination in<br /> order to achieve maximum dimensional accuracy (i.e. minimum overcut) as well as improved surface integrity.<br /> Although AISI P20 tool steel has wide industrial applications in the manufacturing of plastic molds, frames for<br /> plastic pressure dies, hydro forming tools and many more,<br /> surface integrity and dimensional accuracy during EDM of<br /> AISI P20 tool steel has hardly been reported so far.<br /> Therefore, the current study aims at investigating the<br /> influence of different EDM process parameters on different<br /> surface integrity aspects like surface roughness (SR), white<br /> layer thickness (WLT) and surface crack density (SCD) and<br /> dimensional accuracy in terms of overcut (OC) phenomenon. The second major objective of the current study is<br /> to determine optimal setting of EDM parameters using<br /> <br /> SCD<br /> <br /> SR<br /> <br /> OC<br /> <br /> 0.138<br /> 0.316<br /> 0.042<br /> 0.083<br /> 0.174<br /> 0.169<br /> 0.299<br /> 0.114<br /> 0.194<br /> 0.077<br /> 0.203<br /> 0.153<br /> 0.081<br /> 0.258<br /> 0.163<br /> 0.192<br /> 0.055<br /> 0.200<br /> 0.181<br /> 0.145<br /> 0.107<br /> 0.332<br /> 0.184<br /> 0.183<br /> 0.035<br /> 0.203<br /> 0.103<br /> 0.274<br /> 0.218<br /> 0.074<br /> <br /> 0.111<br /> 0.041<br /> 0.349<br /> 0.371<br /> 0.111<br /> 0.035<br /> 0.035<br /> 0.319<br /> 0.002<br /> 0.107<br /> 0.049<br /> 0.058<br /> 0.006<br /> 0.005<br /> 0.051<br /> 0.098<br /> 0.336<br /> 0.071<br /> 0.016<br /> 0.082<br /> 0.364<br /> 0.049<br /> 0.195<br /> 0.014<br /> 0.385<br /> 0.037<br /> 0.343<br /> 0.036<br /> 0.005<br /> 0.121<br /> <br /> 0.206<br /> 0.302<br /> 0.073<br /> 0.073<br /> 0.144<br /> 0.220<br /> 0.248<br /> 0.085<br /> 0.155<br /> 0.087<br /> 0.197<br /> 0.223<br /> 0.135<br /> 0.256<br /> 0.214<br /> 0.214<br /> 0.122<br /> 0.228<br /> 0.197<br /> 0.203<br /> 0.073<br /> 0.234<br /> 0.138<br /> 0.203<br /> 0.070<br /> 0.210<br /> 0.079<br /> 0.279<br /> 0.127<br /> 0.077<br /> <br /> 0.205<br /> 0.226<br /> 0.008<br /> 0.243<br /> 0.108<br /> 0.195<br /> 0.224<br /> 0.021<br /> 0.309<br /> 0.118<br /> 0.191<br /> 0.168<br /> 0.218<br /> 0.191<br /> 0.201<br /> 0.226<br /> 0.031<br /> 0.163<br /> 0.214<br /> 0.141<br /> 0.147<br /> 0.224<br /> 0.179<br /> 0.187<br /> 0.131<br /> 0.186<br /> 0.144<br /> 0.226<br /> 0.201<br /> 0.048<br /> <br /> Fuzzy-TOPSIS-based multi criteria decision making<br /> (MCDM) approach by simultaneously considering surface<br /> integrity and dimensional accuracy aspects. Sensitivity<br /> analysis would also be carried out to study the sensitivity<br /> or robustness of five decision makers’ preference on optimal machining parameters.<br /> 2. Experimental details<br /> 2.1. Equipment, machining process and workpiece material<br /> The experiments were conducted on Electronica Electraplus PS 50ZNC die sinking EDM equipment. Commercial<br /> grade EDM oil (with specific gravity of 0.763 and flash<br /> point of 94 °C) is used as dielectric fluid. The selected<br /> EDM parameters for the current research work include<br /> pulse current (Ip), pulse-on time (Ton), tool work time<br /> (Tw) and tool lift time (Tup). The sparking cycle consists of<br /> Tw and Tup. Tw is made up of multiple sparks each of which<br /> <br /> S. Dewangan et al. / Measurement 63 (2015) 364–376<br /> <br /> tempered for better toughness. A commercially pure<br /> (99.9% purity) and cylindrical shaped copper with 12 mm<br /> diameter was used as tool electrode. The workpiece<br /> (+ve polarity) and tool (Àve polarity) are shown in Fig. 1.<br /> <br /> Table 5<br /> Positive and negative ideal value.<br /> Sj+ and SjÀ<br /> WLT<br /> SÀ<br /> 1<br /> S+<br /> 1<br /> SCD<br /> SÀ<br /> 2<br /> S+<br /> 2<br /> SR<br /> À<br /> S3<br /> S+<br /> 3<br /> OC<br /> SÀ<br /> 4<br /> S+<br /> 4<br /> <br /> 367<br /> <br /> (0.0510, 0.0714, 0.0970, 0.1225)<br /> (0.0054, 0.0075, 0.0102, 0.0129)<br /> (0.0473, 0.0711, 0.1007, 0.1303)<br /> (0.0003, 0.0004, 0.0006, 0.0007)<br /> (0.0974, 0.1206, 0.1438, 0.1670)<br /> (0.0227, 0.0281, 0.0335, 0.0389)<br /> (0.0712, 0.0949, 0.1187, 0.1423)<br /> (0.0018, 0.0024, 0.0030, 0.0035)<br /> <br /> Table 6<br /> Closeness coefficient.<br /> Run no.<br /> <br /> diÀ<br /> <br /> d+<br /> i<br /> <br /> CCi<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 /> 28<br /> 29<br /> 30<br /> <br /> 0.3821<br /> 0.2268<br /> 0.5684<br /> 0.3755<br /> 0.4825<br /> 0.3968<br /> 0.2854<br /> 0.5260<br /> 0.3765<br /> 0.5767<br /> 0.3945<br /> 0.4109<br /> 0.5123<br /> 0.3364<br /> 0.3936<br /> 0.3384<br /> 0.5101<br /> 0.3783<br /> 0.4053<br /> 0.4387<br /> 0.4324<br /> 0.2735<br /> 0.3939<br /> 0.4190<br /> 0.4731<br /> 0.3922<br /> 0.4412<br /> 0.2699<br /> 0.4601<br /> 0.6275<br /> <br /> 0.3554<br /> 0.5107<br /> 0.1692<br /> 0.3620<br /> 0.2550<br /> 0.3407<br /> 0.4521<br /> 0.2116<br /> 0.3611<br /> 0.1608<br /> 0.3430<br /> 0.3266<br /> 0.2252<br /> 0.4011<br /> 0.3439<br /> 0.3991<br /> 0.2274<br /> 0.3592<br /> 0.3322<br /> 0.2988<br /> 0.3051<br /> 0.4640<br /> 0.3437<br /> 0.3185<br /> 0.2644<br /> 0.3453<br /> 0.2963<br /> 0.4676<br /> 0.2774<br /> 0.1100<br /> <br /> 0.5181<br /> 0.3075<br /> 0.7707<br /> 0.5092<br /> 0.6543<br /> 0.5380<br /> 0.3869<br /> 0.7132<br /> 0.5104<br /> 0.7819<br /> 0.5349<br /> 0.5572<br /> 0.6946<br /> 0.4561<br /> 0.5337<br /> 0.4588<br /> 0.6916<br /> 0.5130<br /> 0.5495<br /> 0.5948<br /> 0.5864<br /> 0.3709<br /> 0.5340<br /> 0.5681<br /> 0.6415<br /> 0.5317<br /> 0.5983<br /> 0.3660<br /> 0.6239<br /> 0.8508<br /> <br /> is associated with pulse-on time (Ton) and pulse-off time<br /> (Toff). Tw is followed by Tup i.e. duration for which the tool<br /> will be lifted up to facilitate effective flushing of dielectric<br /> fluid across the spark gap. Obviously, there is no sparking<br /> during the period of Tup. Flushing was intermittent and carried out through a solenoid valve that is synchronized with<br /> the lifting of tool. The values of control parameters along<br /> with their levels and those of fixed parameters are provided in Table 1. The work piece material is AISI P20 tool<br /> steel with semi-circular shape (100 mm diameter and<br /> 10 mm thickness). The composition of AISI P20 tool steel<br /> is 0.4% C, 1% Mn, 0.4% Si, 1.2% Cr, 0.35% Mo, 0.25% Cu,<br /> 0.03% P, 0.03% S. The work piece is first heated to the temperature range of 843–898 °C in a controlled furnace and<br /> held for half an hour. Then, it is oil quenched and later<br /> <br /> 2.2. Measurement of responses<br /> In the current study, surface integrity was characterized<br /> by machined surface roughness, formation of white layer<br /> and surface cracks. While formation of white layer was<br /> investigated in the form of white layer thickness (WLT),<br /> surface cracks were quantified by means of surface crack<br /> density (SCD). Dimensional accuracy was characterized<br /> by overcut (OC) phenomenon. The measurement techniques for these output responses have been described<br /> briefly in the following section.<br /> 2.2.1. White layer thickness<br /> For the measurement of recast or white layer, each<br /> specimen was sectioned vertically followed by polishing<br /> of each specimen with different grades of polishing papers<br /> with deceasing grit size. The polished surface was then<br /> etched with Nital solution to reveal microstructure along<br /> with white layer. Images were then captured on five different locations of each specimen using optical microscope<br /> (with model: SCD313 BPD and make: Radical Instrument)<br /> with a magnification of 400X. These images were then<br /> used to determine white layer thickness (WLT). Recast area<br /> was measured using software (PDF X-change viewer) and<br /> then the area was divided by total length of optical microscopic images to get the average height of white layer (i.e.<br /> WLT).<br /> 2.2.2. Surface crack density<br /> In order to measure density of surface cracks, the top<br /> surface morphology of the EDMed surface was studied<br /> using scanning electron microscopy (SEM) at a magnification of 1000X. Randomly five sample areas were selected<br /> on each specimen and the length of cracks was measured<br /> using same software. The average crack length on each<br /> specimen was divided by area of each micrograph<br /> (10649.072 lm2) to measure the SCD. Similar measurement of SCD has been reported elsewhere [1,16].<br /> 2.2.3. Surface roughness<br /> The measurement of surface roughness (Ra value) of the<br /> EDMed surface was made with portable style type profilometer, Talysurf (Model: Taylor Hobson, Surtronic 3+),<br /> with cut-off length (Lc) of 0.8 mm, sample length (Ln) of<br /> 4 mm, and filter CR ISO.<br /> 2.2.4. Overcut<br /> The over cut which is a measure of dimensional accuracy is calculated by half the difference between the sizes<br /> of the cavity and the diameter of the tool after EDM process. The OC was measured on a tool makers microscope<br /> (Make: Carl Zeiss) with an accuracy of 0.001 mm using following equation.<br /> <br /> OC ¼<br /> <br /> Djt À Dt<br /> 2<br /> <br /> ð1Þ<br /> <br /> 368<br /> <br /> S. Dewangan et al. / Measurement 63 (2015) 364–376<br /> <br /> Fig. 3. Main effect plots for WLT.<br /> <br /> where Dj is the diameter of hole produced in the workpiece<br /> and Dt is the diameter of tool.<br /> 3. Analysis methods<br /> 3.1. Experimental design using RSM<br /> Response surface methodology (RSM) consists of mathematical and statistical techniques that can be utilized for<br /> modeling and analysis of problems. This methodology is of<br /> particular interest when output is influenced by several<br /> variables and the goal is to determine relationship<br /> between the output and the input variables [17,18]. Moreover, RSM helps to extract significant amount of information from small number of experimental runs. Since EDM<br /> involves a large number of process variables, in the current<br /> study, experiment has been designed using RSM using<br /> face-centered central composite design (CCD) with four<br /> variables (Ip, Ton, Tw and Tup). This scheme of design yields<br /> a total of 30 runs (as shown in Table 4) in three blocks,<br /> where the cardinal points used are sixteen cube points,<br /> eight axial points and six center points [19]. RSM-based<br /> design of experiment helps to conveniently study the influence of different process parameters on output responses<br /> (i.e. SR, WLT, SCD and OC) in the form of mean effect of<br /> plot.<br /> 3.2. Fuzzy TOPSIS<br /> After studying the influence of different machining<br /> parameters on surface integrity and dimensional accuracy<br /> aspects, further attempt would be made to determine an<br /> optimal setting of EDM parameters using technique for<br /> order of preference by similarity to ideal solution (TOPSIS)<br /> method. TOPSIS method for multiple attribute optimization was proposed by [20]. This method was used in fuzzy<br /> environments [21] and fits human thinking under actual<br /> <br /> environment. Fuzzy numbers such as triangular and trapezoidal are primarily used for modeling the uncertainty<br /> under multiple engineering environments. While triangular fuzzy numbers have been widely studied, trapezoidal<br /> numbers are sometimes preferred due to its computational<br /> simplicity [22]. The advantage is that trapezoidal fuzzy<br /> number of the form (a, b, c, d) presents most fundamental<br /> class of fuzzy numbers with linear membership function<br /> over the triangular fuzzy number (a, b, c) [22–24]. Therefore, this technique can be utilized for modeling linear<br /> uncertainty in various engineering applications [24–26].<br /> The fuzzy linguistic variable is designated using trapezoidal fuzzy number that is shown in Fig. 2. According to this<br /> figure, the value of fuzzy weight numbers are denoted by<br /> linguistic values that are shown in Table 2. The similar type<br /> of calculation in triangular fuzzy number is described by<br /> Sivapirakasam et al. [14]. The five decision makers give<br /> their decisions of responses for each attribute weight in<br /> linguistic term that are shown in Table 3. The average<br /> fuzzy weight of the decision makers for each response<br /> parameter is shown in same table. The experimental<br /> design matrix along with normalized response (Rij) is<br /> shown in Table 4. Rij is the normalized value and this normalized matrix can be calculated by Eq. (2).<br /> <br /> xij<br /> Rij ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi<br /> P30 2<br /> i¼1 xij<br /> <br /> ð2Þ<br /> <br /> where xij is the experimental value of the ith attribute of<br /> the jth experimental run.<br /> In the next step, all attributes of normalized matrix<br /> (Rij’s) are multiplied by fuzzy weights. Then resultant<br /> matrix is called weighted performance matrix which is<br /> denoted by Sij (for ith experimental run and jth response).<br /> Similar methodology was adopted by different researchers<br /> [14,27,28]. Now positive ideal solution (S+) and negative<br /> ideal solution are expressed by the following equations<br /> and their values are provided in Table 5.<br /> <br />