Electrical discharge machining (EDM) is important unconvetnional machining method for making the manufacturing tools and mould (Park et al., 1997; Jeon et al., 2006). Many technological solutions have been introduced to improve the machining process such as optimizing process parameters (Kwon et al., 2012), introducing powders into dielectric fluid (Talla et al., 2016), incorporating the vibration in EDM (Son, 2005; Je et al., 2011). Powder mixed EDM (PMEDM) provides the promising solution to improve productivity and quality in EDM (Vinod et al., 2016; Himadri et al., 2017). Since the number of parameters in PMEDM is high with non-linear nature, the optimization of the technology requires different methods and techniques, especially multi-objective optimization problems.

Taguchi method is well suit and commonly used for experimental design in PMEDM (Mohapatra et al., 2017). This has contributed to the reduction of experimental costs and increased experimental efficiency in the PMEDM. However, Taguchi method has dealt single-response problem only. Several multi criteria making methods were proposed for solving the optimal multi-objective in EDM (Nayak et al., 2017). Vijay et al. (2017) used the Taguchi - Grey Relational Analysis (GRA) to optimize MRR, electrode wear rate (TWR) and overcut (OC) in μ - EDM for machining Titanium alloy. The results show that the use of GRA for multi-objective optimization is appropriate. Durairaj et al. (2013); Rajesh et al. (2017) and Pawan et al. (2018) applied the multi – objective optimization in EDM and WEDM processes tp obtain better quality characteristics such as MRR, SR, wire wear ratio (WWR) and kerf width. The optimal result should provide the high accuracy, fit consistent between theory and experiment. Mahapatra and Sahoo (2018) performed a multi-objective optimization of the process parameters in gear processing by Wire EDM for Inconel 718 using Taguchi - TOPSIS method. The optimal results have shown that the quality of the gears at optimum conditions is better. The comparison of the results of Taguchi-GRA with Taguchi-TOPSIS in multi- objective optimization in EDM (Dastagiri et al., 2017; Gadakh, 2016) and PMEDM (Tripathy et al., 2016) were researched. It has observed that Taguchi-TOPSIS method could be better than Taguchi-GRA method. Sivapirakasam et al. (2011), Tiwary et al. (2014) and Dewangan et al. (2015) also incorporated Taguchi - TOPSIS based multi-objective optimization in EDM process parameter. “Triangular fuzzy” was used to determine the weighted values of the 5 output norms. The combination was also used to optimize three quality indicators simultaneously (SR, MRR and Fractal dimension) in die sinking - EDM by Prabhu et al. (2016). However, the weights of quality indicators are determined by the Analytic Hierarchy Process (AHP). The best quality parameters have been identified with the optimal set of parameters and weighted values have been calculated on a scientific basis even though the method is difficult. Rajesh et al. (2016) simultaneously optimized MRR, TWR, ROC and SR in EDM for Al-18Wt% SiCp MMC by the VIKOR method. The weighted values of indicators can be determined by the method of Entropy weighted measurement. It has been confirmed that this method was suitable for other types of process. Nevertheless the determined the weighting method is quite complex. The literatures proposed the need of multi-objective optimization problem in EDM and PMEDM. In recent times, Dušan et al. (2017) introduced the Performance Selection Index (PSI) methodology for multi-objective optimization in processing methods. The optimization problem is much simpler, since it does not require weighted values of indicators.

From the literature survey, it has been observed that the multi-objective optimization of process parameter in EDM and PMEDM by PSI method had not been researched in a considerable level. Hence, Taguchi - PSI method has been used to enhance the titanium powder mixed EDM process in the present study.

With target of enhancing the productivity and surface quality, the performance measures have been selected as higher MRR and lower SR. The experimental results of two examined criteriaaccording to Taguchi’s L27 matrix as shown in Table 2. MRR is standardized according to the Eq. (2) and SR is standardized according to the Eq. (3) as shown in Table 3. The computation results have been calculated according to the steps involved in PSI method as shown in Table 4. The priority index of problem with S/N analysis has been also determined as shown in Table 5.

It has been observed that the 17th experiment has provided larger index as shown in Fig. 2. Hence the respective experiment was chosen as the optimal process parameters as SKD11 (WM), Gr (tool), + (polarity), 5 μs (t_on), 57 μm (t_off), 8 A (I_p) and 10 g/l (PC).

Fig. 2 
Compare to PSI, TOPSIS, MOORA and GRA results with graph

It has observed from experimental analysis that,17th experiment has also provided the maximum value of S/N. The ANOVA analysis of S/N ratio has shown that electrode material and powder concentration could provide strong influence on performance measures owing to their importance on determining spark energy. The polarity of electrode has provided lower influence on determining machining characteristics in PMEDM process. The pulse- on time and current has also given considerable contribution in the machining process. The interactions of the factors could provide significant influence than individual factors on determining the optimal results in PMEDM process as shown in Table 6. The accuracy of the optimum conditions has been evaluated by the Eq. (10) as shown in Table 7. The results have shown that the deviation of the computed values and the empirical values have been lower values only. The PSI method can effectively increase the optimal values as approximately 7.82%. It has proved that PSI based optimization could be completely suitable for PMEDM process with titanium powder. The quality of optimal surface layer was analyzed by Phan et. al., 2018. The analytical results showed that surface layer is good and it contributes advancing the working ability of the steel surface molding.

Evaluate the relevance of the PSI method: The results of multi-objective optimization in PMEDM using titanium powder by PSI method are compared with those of TOPSIS, GRA and MOORA methods, Table 5 and Fig. 2. The results showed that the PSI, TOPSIS and MOORA results were the same. The optimal result by GRA method is obtained at the 6th experiment. In this study, TOPSIS, MOORA and PSI methods are more effective than MOORA method. Compared to PSI method, TOPSIS, MOORA and GRA are more complex methods in solving multi-objective optimization problem because the number of steps to be implemented is more. In addition, It is necessary to determine the priority weights of quality indicators in TOPSIS, MOORA and GRA. And this is often very difficult for new products and machining methods are unclear, and PMEDM is such a machining method. All these have shown that PSI is the simplest and most suitable method in the methods surveyed for PMEDM’s multi-objective optimization using titanium powder.

Fig. 3 
Main effects plot for S/N of θ_j

Fig. 4 
Interaction plot for S/N of θ_j

An endeavor was attempted to optimize the process parameters in titanium based PMEDM for machining die steels using Taguchi-PSI. From the trials and investigation, the following decisions were made:

PSI, TOPSIS and MOORA are better than GRA in multi-objective optimization in PMEDM using titanium powder. And PSI is the most suitable method.

PSI method can provide better effective solution to overcome the limitations of TOPSIS, MOORA and GRA methods in PMEDM process.

The optimal values have been found as SKD11 (workpiece), Gr (tool), + (polarity), 5 μs (t_on), 57 μm (t_off), 8 A (I_p) and 10 g/l (PC) with high accuracy of 7.82%.

The electrode material and powder concentration could provide strong influence on performance measures owing to their importance on determining spark energy.