Keywords

1 Introduction

Electrical discharge machining (EDM) is a non-traditional machining process employed to remove material from any electrically conductive difficult-to-machine materials by the use of thermal energy. It can create any intricate shape irrespective of hardness of the materials. A sequence of spark generated between the tool and work helps in removing material. Simultaneous optimizations of vital performance measures like material removal rate (MRR), tool wear rate (TWR), and surface roughness (Ra) are extremely important to make the machined parts suitable for desired applications. One of the major objectives of a manufacturing engineer is to decrease the cost of tooling and time for product development for any manufacturing operation. In order to achieve both the objectives in EDM process, rapid prototyping (RP) technology may be explored to manufacture tool electrode. Arthur et al. [1] have employed thin metal coating on stereolithography (SL) models to machine-hardened tool steel. Those electrodes found to be useful in both semi-roughing and finishing operations in EDM. Rennie et al. [2] have manufactured EDM electrodes of complex geometry by employing electroforming on a die built through rapid prototyping process and found its performance comparable with the conventional copper electrode. Durr et al. [3] have manufactured simple cylindrical metal electrodes using nickel, bronze, and copper phosphite metal powder by direct metal laser sintering. Excessive tool wear and poor surface quality were observed in comparison with conventional electrodes. Dimla et al. [4] produced complex components having sloped surfaces and deep slots by electroplating on DMLS electrodes. Czyzewski et al. [5] have prepared EDM electrodes by 3-dimentional printing technology. Amorim et al. [6] have used tools made by selective laser sintering (SLS) using different powder materials. Czelusniak et al. [7] have focused on the choice of suitable materials to manufacture EDM electrode using selective laser sintering. Mohanty et al. [8] have carried out experiments using electrodes made of DirectMetal20 prepared by DMLS. Reddy et al. [9] have produced electroless-coated EDM electrodes by coating materials prepared earlier by fused deposition modeling. Padhi et al. [10] found the suitability of electroplated ABS plastic electrode for semi-finishing and roughing operation. Singh and Pandey [11] prepared EDM electrode by utilizing 3D printing in combination with pressure-less sintering. Singh et al. [12] have employed loose powder sintering on polymer part prepared by 3D printing to prepare copper electrode for machining of D2 steel. Peak current is observed to be the most significant parameter on the responses like MRR, TWR, and cavity dimensional deviation.

In the present study, direct metal laser sintering is employed to prepare the electrode which has been chosen along with conventional electrode like copper and brass to assess the feasibility of substituting these conventional electrodes by the RP electrode considering different machining responses like MRR, TWR, and surface roughness (Ra).

The main objective of the present work is the multi-objective optimization of die-sinking EDM process of D2 steel using DMLS electrode. Under the materials and methods section, the materials for work piece and electrodes and the optimization method of various process parameters have been discussed. D2 steel has been selected as work piece, while brass, copper, and DMLS electrodes have been taken as tools. Utility concept-based Taguchi method has been used for optimizing various process parameters. Under the results and discussion section, DOE has been used to determine utility values of different quality attributes from the experimental results conforming L27 orthogonal array. Then, a confirmatory test has been performed to validate the experiment results. Also, a comparative study has been presented to assess the response using different electrodes. The conclusions section discusses the best response by optimizing various process parameters and recommendation for further work.

2 Materials and Methods

2.1 Materials

D2 steel has been chosen as work piece due to its widespread applications. Three cylindrical tools (20 × 20 mm) selected were brass electrode, copper electrode, and DMLS electrode using DirectMetal20. The selected process parameters (inputs) are peak current represented by Ip, on time represented by Ton, off time represented by Toff, flushing pressure represented by Fp, and tool electrode represented by TE. TWR, MRR, and Ra have been taken as response variables (outputs). Different process parameters along their levels while carrying out EDM are given in Table 1.

Table 1 Process parameters along with their levels
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2.2 Methods

Taguchi Method. Taguchi method is an innovative method to solve single-objective optimization problems with less number of experimentation. It uses signal-to-noise (S/N) ratio [13] as a degree of performance. S/N ratio is the ratio between signal (mean) and noise (standard deviation). The S/N ratios for greater-the-better and lesser-the-better are presented by Eqs. (1–2). The best setting corresponds to the maximum S/N ratio.

$${\text{For greater - the - better }}\left( {{\text{GB}}} \right), \, {S \mathord{\left/ {\vphantom {S N}} \right. \kern-\nulldelimiterspace} N}{\text{ ratio }} = - 10\,\log_{10} \left( {\frac{1}{n}\sum\limits_{i = 1}^{n} {\frac{1}{{y_{i}^{2} }}} } \right)$$
(1)
$${\text{For lesser - the - better }}\left( {{\text{LB}}} \right), \, {S \mathord{\left/ {\vphantom {S N}} \right. \kern-\nulldelimiterspace} N}{\text{ ratio }} = - 10\,\log_{10} \left( {\frac{1}{n}\sum\limits_{i = 1}^{n} {y_{i}^{2} } } \right)$$
(2)

In both the cases, n represents number of repetitions and \(y_{i}\) represents output.

Utility Concept-Based Taguchi Method. As per the utility theory [14, 15], if \(Z_{i}\) represents degree of usefulness of a quality characteristic i and n, number of attributes are involved in assessing the result; then, the combined utility function is represented as:

$$U(Z_{1} ,Z_{2} , \ldots ,Z_{n} ) = f(U_{1} (Z_{1} )U_{2} (Z_{2} ) \ldots U_{n} (Z_{n} ))$$
(3)

Here, \(U_{i} (Z_{i} )\) is the utility corresponding to the ith attribute.

The overall utility function is the summation of different utilities by considering the attributes (qualities) to be independent of each other and is presented as follows:

$$U(Z_{1} ,Z_{2} , \ldots ,Z_{n} ) = \sum\limits_{i = 1}^{n} {U_{i} } (Z_{i} )$$
(4)

The attributes (qualities) may be given weightages on the basic of their significances. The overall utility function can be represented as:

$$U(Z_{1} ,Z_{2} , \ldots ,Z_{n} ) = \sum\limits_{i = 1}^{n} {W_{i} U_{i} } (Z_{i} )$$
(5)

Here, Wi represents the weightage allotted to the attribute i.

The summation of the weightages for all the attributes considered should be 1,

$${\text{i}}.{\text{e}}.,\sum\limits_{i = 1}^{n} {W_{i} } = 1$$
(6)

A scale is essential to fix the utility value of each characteristic. Two numbers 0 and 9 (chosen arbitrarily) represent just satisfactory and the finest possible value of the quality attribute, respectively. Now, Pi can be represented as follows:

$$P_{i} = A \times \ln \left( {\frac{{Z_{i} }}{{Z^{\prime}_{i} }}} \right)$$
(7)

\(Z_{i}\) represents the value of any quality i represents \(Z^{\prime}_{i}\) represents just acceptable value of quality i; A is a constant that can be calculated by the circumstance.

If \(Z_{i} = Z^{ * }\) (\(Z^{ * }\) being the best value), then Pi = 9. Hence,

$$A = \frac{9}{{\ln \frac{{Z^{ * } }}{{Z^{\prime}_{i} }}}}$$
(8)

The overall utility index (OUI) can be presented as follows:

$$U = \sum\limits_{i = 1}^{n} {W_{i} P_{i} }$$
(9)

where Wi is the weightage given to attribute i.

As the utility function is greater-the-better category, by maximizing this, the quality attributes chosen for its evaluation will be optimized. OUI is the mean of the utility values of individual responses as equal weightage has been given to all the responses. Then, the OUI is optimized using Taguchi method.

DMLS Tool Preparation. DMLS is an advanced sintering procedure, which forms 3-dimentional geometries on layer-by-layer basis. The chosen material for preparation of tool is DirectMetal20. The machine employed for the purpose is EOSINT 250 extended machine.

3 Results and Discussion

Experimental results conforming to L27 orthogonal array, DOE (presented in Table 2), have been used to determine utility values of different quality attributes by using Eqs. (7)–(8). Lesser-the-better (LB) principle has been used for TWR and Ra, and greater-the-better principle has been used for MRR.

Table 2 Experimental results
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The utility values of the individual objectives have been calculated using Eqs. (7) and (8) and are presented in Table 3. Then, OUIs for each setting are calculated using Eq. 9 and are presented in the fifth column of Table 3. While calculating the OUI, equal weightage has been given to all the three responses (attributes). S/N ratios corresponding to the OUIs for all the 27 setting have been calculated and are presented in the last column of Table 3. The OUI has then been optimized using Taguchi’s HB (Higher-the-better) criterion given by Eq. (1). Ideal setting has been found to be \((I_{p1} \,T_{{{\text{on3}}}} \,T_{{{\text{off3}}}} \,F_{p1} \,TE_{1} )\) from Fig. 1. The process model for responses obtained through regression analysis is given by;

$$\begin{aligned} {\text{OUI}} & = 7.45052 - 0.687056I_{p} + 0.0379444T_{{{\text{on}}}} + 0.516T_{{{\text{off}}}} + 0.0400556F_{p} \\ & \quad - 1.09428TE({\text{Coded}}\,\,{\text{units}}) \\ \end{aligned}$$
Table 3 Utility values of different responses, OUI and SN ratio
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Fig. 1
figure 1

Estimation of best setting

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The predicted value for OUI is found to be 7.371. Finally, a confirmatory test was conducted to validate the experiment.

The TWR, MRR, and Ra for the setting \((I_{p1} \,T_{{{\text{on3}}}} \,T_{{{\text{off3}}}} \,F_{p1} \,TE_{1} )\) have been found to be 5.275 mm3/min, 12.862 mm3/min, and 2.14 μm, respectively, and the calculated OUI is 7.394 which is greater than the predicted value of 7.371. So, the quality has improved.

The ANOVA for OUI is shown in Table 4. R2 value of 94.50% indicates the effectiveness of carrying out the experiments. \(I\) is found to be the most significant factor as found from Table 4. OUI is decreasing significantly with increase in I. OUI is in decreasing order for brass, copper, and DMLS electrodes.

Table 4 ANOVA for OUI
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4 Conclusions and Future Work

Tool electrode and peak current have been found to be the most significant factors affecting the responses which are on the expected lines and prove the efficacy of conducting the experiments. Ideal setting for best performance has been found to be \((I_{p1} \,T_{{{\text{on3}}}} \,T_{{{\text{off3}}}} \,F_{p1} \,TE_{1} )\) which has been verified by a confirmatory test. The performance of the copper electrode is found to be better than the performance of brass electrode whose performance is again found to be better than the DMLS electrode. Comparatively poor performance of DMLS electrode is owing to the higher porosity level and comparatively lower composition of copper. The future researchers should reduce porosity levels of the DMLS electrode as well as increase in the copper composition in the powder mixture (which in turn would significantly improve the electrical conductivity) to make it possible to replace conventional electrodes. Thus, DMLS tool may be recommended for semi-finishing job.