Keywords

1 Introduction

In today’s fastest development of machine-driven industry, the demands for alloy materials and other type of steel material they have good hardness and impact resistance are increasing. Nevertheless, some materials are challenging to be machined by conventional methods. Hence, non-conventional machining methods including ECM, electrical discharging machine and abrasive jet machining are applied to machine such as difficult-to-machine tools and materials. Moreover, it has been used in wide applications such as railways, bridges and suspension system [1,2,3,4].

However, wire EDM is a continuous process in which electrode they can be made of thin brass or tungsten and copper with diameter 0.05–0.35 mm, which is capable of machining for very small corner radii [2]. The wire undergoes tension using a device so reducing the trend of producing inaccurate parts. During the process of wire EDM, the material is eroded from wire zone, and there is no contact between the tool (wire) and workpiece; it can be controlled by servo controller eliminating the mechanical stresses during machining.

Durairaj et al. [3] have described the multi-optimization techniques by grey relational analysis and optimized the machining parameters in wire EDM for SS304 material. The main objective is to optimize the kerf width and the best surface quality. Sreenivasa et al. [4] established the influence of various process parameters of wire EDM such as pulse-on time, pulse-off time, peak voltage, pulse current, wire speed and wire tension on the responses are material removal rate (MRR), surface roughness (Ra), width of cut, wire wear ratio and surface integrity factors. Saravanan et al. [5] used Titanium Grade 2 alloy for machining of wire EDM and also optimized the machining parameters with the help of Taguchi strategy. Ishfaq et al. [6] used stainless-clad steel for machining of wire EDM and also optimized machining parameters setting. Other researchers did wire EDM and EDM process for optimization of different machining parameters [7, 8].

In the available literature, a number of gaps have been perceived in machining of wire EDM. Most of the scholars have investigated influence of process parameters on the different response measures of wire EDM. Literature review exposes that the researchers have carried out most of the work on wire EDM developments, observing and controlling but partial work has been reported on optimization of process variables with multi-objective optimization. The effect of machining parameters on AISI P20 tool steel has not been fully explored using wire EDM with copper wire as electrode.

2 Experimentation

The present work conducted an Electronica MAXICUT 734 Wire Electric Discharge Machine, with the workpiece dimension of 10 mm × 1 mm square block, and copper wire tool material individual was used having 0.25 mm diameter. Distilled water is used as dielectric fluid to accomplish the experiment. Side flushing system is used for the sparking zone.

The total three machining parameters are selected as variables, and other factors are kept constant (such as dielectric fluid pressure, cutting speed, servo voltage, servo feed, wire speed, wire tension and cutting length). The factors have three levels along L9 orthogonal array have been selected with Taguchi design that are presented in Table 1.

Table 1 Input parameters and their levels
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The calculation of material removal rate has been done by weight loss method with the help of electronic balance weight machine. This electronic balance weight machine has maximum capacity of 300 g, and accurateness is 0.1 mg. Overcut was measured by using Toolmaker microscope. The design of experiment with observed MRR and overcut value is shown in Table 2 (Fig. 1).

Table 2 Experimental observed value
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Fig. 1
figure 1

Wire electric discharge machining with tool and workpiece

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3 Results and Discussion

In this section, the impact of process parameters on the responses like material removal rate and overcut of AISI P20 tool steel was described. And also discussed which parameters are most influencing factors for increasing the quality and productivity in the form of overcut and material removal rate.

3.1 Impact of Process Parameters of MRR and Overcut

The histogram plot for MRR versus input factors such as pulse-on time, wire feed and pulse-off time is shown in Fig. 2. According to this graph, pulse-on time has better impact on MRR as compared to pulse-off time and wire feed, in which MRR increases with increases on Ton. MRR representing the Ton is the most significant factor during machining of AISI P20 tool steel.

Fig. 2
figure 2

Impact of process parameter versus MRR

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Figure 3 indicates the overcut (OC) against pulse-on time, wire feed and pulse-off time, respectively. When the Toff increases OC when Ton increases OC decreases, when F increases OC has slightly increases similarly, when Toff increases, OC increasing. This analysis clearly indicates that the factors Toff are directly proportional to OC and the value of Ton is maximum influencing of OC, and also wire feed of copper wire tool is significant effect.

Fig. 3
figure 3

Impact of process parameters versus OC

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3.2 Multi-objective Optimization Using PCA-Based GRA Analysis

All the experimental values (Table 2) have been converted to the optimal quality performance index (OQPI). The OQPI value is obtained using hybrid multi objective optimization techniques that is PCA based grey relation analysis. Calculation of PCA-based GRA analysis the following stages is given below.

  • Converting the MRR and OC to S/N ratio.

  • Converted SN ratio of MRR and OC is to find principal component scores (PCS).

  • Normalized principal component scores.

  • After normalized data finding GRC using principal component score.

  • Calculating optimal quality performance index (OQPI).

All experimental run to finding MRR and Overcut is higher-the-better and lower-the-better conditions has been chosen. The maximum value of MRR is 8.8865 mm3/min, and minimum value of overcut is 0.030 mm. In order to avoid complexity, in computing S/N ratio. The S/N ratio for MRR and OC is represented in Eqs. (1) and (2) correspondingly.

$$\eta_{ij} = - 10 \log \left[ {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} y_{i}^{ - 2} } \right]$$
(1)
$$\eta_{ij} = - 10 \log \left[ {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} y_{i}^{2} } \right]$$
(2)

whereas \(\eta_{ij}\) represents the S/N ratios \(i\)th experiment and \(j\)th result (MRR and OC), and yi is observe resulted value of MRR and OC. In this calculation for all nine experiments, n is kept as one because there is no repeated number of experiments. After calculating the S/N ratio, the second step is computing principal component score by using Eq. (3).

$${\text{PCS}}_{il} = a_{l1} \eta_{i1} + a_{l2} \eta_{i2} + \cdots + a_{lj} \eta_{ij}$$
(3)

whereas \(a^{2}_{l1} + a^{2}_{l2} + \cdots + a^{2}_{lj} = 1.\) The \(a_{l1} ,a_{l2} \ldots a_{lj}\) are the elements of eigenvector. The calculated eigenvalue with respective eigenvector is represented in Table 3. Then the next step to normalizing all PCS data in this equation:

Table 3 Eigenvalue and their correspondence matrix
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$$X_{il} = \frac{{{\text{PCS}}_{il} - {\text{PCS}}_{il}^{\hbox{min} } }}{{{\text{PCS}}_{il}^{\hbox{max} } - {\text{PCS}}_{il}^{\hbox{min} } }}$$
(4)

whereas \(X_{il}\) is the normalized data with \(i\)th experiment expending \(l\)th principal component score. And \({\text{PCS}}_{il}\) are normalized data. Eigenvalue and their correspondence matrix are given in Table 3.

After normalizing, then calculate the grey relational coefficient of normalized PCS data with the help of Eq. (5).

$${\text{GRC}}_{ij} = \frac{{\Delta_{\hbox{min} } + \zeta \Delta_{\hbox{max} } }}{{\Delta_{ij} + \zeta \Delta_{\hbox{max} } }}$$
(5)

whereas \(\Delta_{ij} = \left| {1 - X_{il} } \right|\); in this equation GRCij of \(i\)th experiment using \(j\)th result (MRR and OC), ∆max and ∆min are the global maximum and global minimum values for corresponding values, correspondingly. The distinguishing coefficient (ζ) range is 0–1; this is clearly designated by Dewangan and Biswas [9]. In computing grey relation coefficient value for both response, then finding the optimal quality performance index by using Eq. (6).

$${\text{OQPI}} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} W_{l} \zeta_{ij}$$
(6)

whereas wl is the proportion of variance that is associated with Table 3. The magnitude of OQPI replicates that optimal quality performance index value. That value is higher-the-better quality characteristics. In all the nine experimental runs the OQPI was calculated and is presented in Table 4.

Table 4 Design of optimal quality performance index
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4 Exploration of OQPI

Optimal quality performance index value is higher-the-better quality characteristics means high value of OQPI (run no 7, value 0.9006) which represent better quality and productivity for this machining parameters setting. According to the graph (Fig. 4) of influence plot for OQPI to knowing the optimal setting of machining parameters that is Ton is 124 µs, F is 6 mm/min and Toff is 20 µs. which would simultaneously ensure better quality in terms of minimum value of overcut and better productivity in terms of maximum value for MRR.

Fig. 4
figure 4

Influence plots for OQPI

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5 Conclusions

Based on the above experimental examination, MRR representing the Ton is the essential factor during machining of AISI P20 tool steel, whereas the factor Toff is directly proportional to OC and the value of Ton is maximum influencing of OC.

The modern research work develops hybrid multi-response optimization technique using PCA-based grey relational analysis for simultaneously optimizing the MRR and OC in wire EDM. The optimal wire EDM parameter setting was found to be as follows: Ton is 124 µs, F is 6 mm/min, and Toff is 20 µs, which would simultaneously ensure better quality in terms of minimum value of overcut and better productivity in terms of maximum value for MRR.