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Investigation of machining characterization of solar material on WEDM process through response surface methodology

  • Anish Kumar EMAIL logo , Raminder Singh and Renu Sharma
Published/Copyright: July 19, 2023

Abstract

The photovoltaic sector needs a high-throughput slicing method that produces minimal waste to meet rising demand. Wire electric discharge machining (WEDM) has emerged as an alternative slicing method in recent research efforts. Polycrystalline silicon is sliced using the WEDM process with a zinc-coated electrode of Ø0.25 mm in diameter. Experiments were planned and conducted according to Box Behnken’s design of experiments. As inputs, seven different process parameters were used: pulse on time (PONT), pulse off time (POFFT), peak current (PC), spark gap voltage (SGV), wire feed (WF), wire tension (WT), and water pressure (WP). Response parameters measured were cutting speed (CS), surface roughness (SR), and kerf width (KW). Various process parameters have also been analyzed with ANOVA methods for predictive modeling. Based on experimental data, this study determines the appropriate optimal solutions via desirability functions. During the WEDM process, the PONT, POFFT, PC, and SGV significantly influence the discharge energy on the sliced surface. As a result of this study, CS of 0.78 mm2/min, SR of 2.87 μm, and KW of 0.70 mm were observed at the optimal settings of PONT of 119 μs, POFFT of 42 μs, PC of 38A, SGV of 36V, WF of 3 mm/min, WT of 2 kg and WP of 6 kg/cm2. Surface morphology was determined using scanning electron microscope and Energy dispersive X-ray to investigate the surface characteristics.

1 Introduction

Silicon products have a wide range of applications in industry, including computers, electronics, textiles, vehicles, and architecture. The semiconductor business and its applications in electronics, microelectronics, computer systems, and the photovoltaic (PV) industry have grown rapidly in the last several decades. Hence the slicing of silicon ingots by increasing cutting speed and minimizing of kerf loss is of much significance. Luque and Hegendus [1] the typical wafer thickness in the industry varies between 250 and 350 μm, the kerf size was obtained with a wire saw when cutting a WC–Co composite. Muthuraman and Ramakrishan [2] used the wire electric discharge machining (WEDM) process when machining a composite material to obtain the surface roughness (SR). Luo et al. [3] employed the WEDM process for the first time to cut silicon ingots in 1992. Uno et al. [4] examined the WEDM process as a novel approach for slicing mono-crystalline silicon ingots, concluding that the new method of slicing silicon ingots reduced contamination caused by wire electrode material adhesion and diffusion to the machined surface, as well as producing a lower value of SR. Sreejith and Udupa [5] did research on various machining methods available for silicon processing and concluded that processing of silicon wafers from silicon ingots was done as required by industrial applications using WEDM. Peng and Liao [6] determined that WEDM slices medium and heavily doped silicon ingots. They were able to do this with no complications by cutting silicon wafers that were 1 mm thick without breaking the wires and using kerosene as the dielectric fluid. Takion et al. [7] experimented with WEDM to shape polished single crystal silicon plates and studied the results. This project’s goal is to learn how to slice PV-grade silicon ingots using WEDM. Shah et al. [8] investigated the impact on WEDM process optimization of varying machining settings and material thicknesses in terms of material removal rate and SR. The modeling strategy used led to the conclusion that the rate of material removal and the degree of SR were both considerably impacted by the thickness of the work material. Yu et al. [9] looked at how adjusting the WEDM parameters might affect the machining process. An investigation into the feasibility of using WEDM on polycrystalline silicon with a resistivity of 2–3 revealed that the open voltage was a crucial parameter for breaking the insulation of polycrystalline silicon. Singh et al. [10] studied the effects of changing the pulse on time (PONT), pulse off time (POFFT), peak current (PC), servo voltage, and wire feed (WF) on WEDM machining of AISI D2 steel. Luo et al. [3] showed that the surface potential barrier of semiconductor had a substantial influence on the cutting speed and machining parameters. Rakhwal and Bamberg [11] investigated fabricating germanium wafers from gallium-doped ingots. The completed wafers were inspected using scanning electron microscopy (SEM) and surface profilers. Singh and Garg [12] used the WEDM process to optimize the dimensional deviation, surface roughness and material removal rate. Dongre and Singh [13] presented the WEDM as a method for slicing polycrystalline silicon that might maximize cutting speed while minimizing kerf loss and SR. Joshi and Sharma [14] reported that WEDM is the best approach for slicing Si ingots with little kerf loss and a crack-free surface. Punturat and Tangwarodomnukun [15] investigated the effect of varying process settings on the sliced surface’s characteristics and the degree of damage. Chuang and Mai [16] studied the machining of 156 mm square ingots of polycrystalline silicon and concluded that higher machining rates (343 mm3/min) were achieved. Murugan and Kumar [17] studied the effect of WEDM parameters on ceramic composites by adjusting input factors including pulse current, on time, and off time. This observation led us to integrate experimental findings with parameters to investigate a wide variety of inputs. Verma and Singh [18] examined the material removal rate, SR, and slicing speed when slicing mono crystalline silicon under various conditions, including different values of open voltage, PONT, servo voltage, POFFT, and WT. Tosun and Cogun [19] used a regression analysis model to look at how different machining factors affected WEDM outcomes including wire wear, crater size, and SR. These parameters included pulse duration, wire speed, open circuit voltage, and dielectric cleaning pressure. The machining of silicon ingots by wire EDM is discussed in this work, and the cutting qualities are examined. This study shows that wafers can be cut from silicon ingots using WEDM by detailing the experimental setup used to make this cut. Wire cut electric discharge machining is a kind of machining that makes use of an electrical discharge to cut material. Dielectric fluid is sent via a series of small tubes to the work area, where it fills the gap between the machined surface and the wire. Using a WEDM, polycrystalline silicon was sliced, and the impact of various machining parameters on the rate of cutting was studied. The best parameters for cutting the materials are determined using response surface methodology. The effects of WEDM parameters such as PTON, POFFT, PC, spark gap voltage (SGV), WF, wire tension (WT), and water pressure (WP) were investigated.

Furthermore, past research has not explored deeply the WEDM method of cutting and surface characterization of polycrystalline material. Moreover, parametric optimization is required for better results. To analyze cutting speed (CS), surface roughness (SR), and kerf width (KW) in the present study, the seven parameters are taken into consideration based on past research, pilot experiments, and machine limitations as shown in Table 1. According to the literature, not much work has been done on the cutting of polycrystalline silicon material.

Table 1

Parameters and their levels (coded and actual)

Factors Parameters/variables Units Actual low level Actual high level Coded low Coded high
A PONT µs 110 125 −1 +1
B POFFT µs 40 55 −1 +1
C PC A 25 45 −1 +1
D SGV V 35 55 −1 +1
E WF mm/min 2 6 −1 +1
F WT kg 2 6 −1 +1
G WP kg/cm2 6 10 −1 +1

2 Materials and methods

In order to conduct this experiment, polycrystalline silicon was selected (Table 2), and a 4-axis computer numerical control-type WEDM (Electronica India Sprintcut, 734 Model) was used (Figure 1). During the slicing process, CS, SR, and KW were analyzed using parameters such as PONT, POFFT, PC, SGV, WF, WT, and WP. The design matrix for the major experiment and its outputs is shown in Table 3. The zinc (Zn)-coated brass wire with a diameter of Ø0.25 mm was used during the WEDM process. For analysis, the sample was sliced into a square form with dimensions of 125 mm × 125 mm × 10 mm. Mitutoyo’s SURFTEST was used to determine the SR of the machined surface (Model: SJ-301). Table 1 shows the factors and levels (coded and actual). An ingot of polycrystalline silicon was purchased by Tianjin Yucai Photoelectric Technology Co. Ltd, China. In conjunction with Energy dispersive X-ray spectroscopy (EDX), SEM (Model: JEOL, Japan, JSM-6610LV) was used to analyze surface morphology.

Table 2

Composition of polycrystalline material

Material Chemical composition
Polycrystalline silicon C Si P S
1.0% 1.31% 0.31% 0.042%
Figure 1 
               Slicing mechanism in WEDM process. (a) Workpiece in a square plate form (125 mm × 125 mm), (b) Wafer Sample, (c) WEDM Machine set-up, (d) WEDM Slicing Process.
Figure 1

Slicing mechanism in WEDM process. (a) Workpiece in a square plate form (125 mm × 125 mm), (b) Wafer Sample, (c) WEDM Machine set-up, (d) WEDM Slicing Process.

Table 3

Experimental design plan with output observations

Run A: PONT (µs) B: POFFT (µs) C: PC (A) D: SGV (V) E: WF (mm/min) F: WT (kg) G: WP (kg/cm2) CS (mm2/min) SR (µm) KW (mm)
1 118 48 45 35 4 4 10 0.51 2.49 0.639
2 118 48 35 55 6 2 8 0.54 2.46 0.641
3 110 48 25 45 2 4 8 0.49 2.23 0.442
4 118 48 35 45 4 4 8 0.51 2.71 0.655
5 110 40 35 35 4 4 8 0.65 2.51 0.489
6 125 55 35 35 4 4 8 0.75 2.92 0.949
7 118 40 25 45 4 6 8 0.59 2.66 0.649
8 118 55 35 45 6 4 6 0.47 2.49 0.647
9 118 40 35 45 2 4 10 0.62 2.62 0.659
10 125 48 25 45 2 4 8 0.72 3.25 0.943
11 118 48 35 45 4 4 8 0.54 2.62 0.651
12 118 48 25 35 4 4 6 0.54 2.46 0.635
13 118 48 35 35 2 6 8 0.51 2.55 0.651
14 118 48 35 55 6 6 8 0.49 2.46 0.642
15 118 55 35 45 2 4 6 0.51 2.49 0.647
16 118 40 35 45 2 4 6 0.67 2.89 0.651
17 110 48 35 45 4 6 6 0.52 2.29 0.455
18 118 48 35 45 4 4 8 0.52 2.55 0.658
19 118 55 45 45 4 2 8 0.57 2.61 0.639
20 110 48 45 45 2 4 8 0.49 2.26 0.435
21 110 55 35 35 4 4 8 0.48 2.33 0.449
22 118 48 25 55 4 4 10 0.46 2.31 0.631
23 118 48 35 35 6 6 8 0.52 2.52 0.646
24 118 55 35 45 6 4 10 0.49 2.46 0.641
25 110 40 35 55 4 4 8 0.52 2.48 0.476
26 118 40 45 45 4 2 8 0.68 2.75 0.654
27 125 48 35 45 4 2 10 0.75 3.21 0.954
28 118 48 45 55 4 4 10 0.49 2.49 0.639
29 125 40 35 55 4 4 8 0.78 3.18 0.958
30 118 55 45 45 4 6 8 0.57 2.45 0.635
31 118 55 35 45 2 4 10 0.54 2.49 0.648
32 118 48 45 55 4 4 6 0.56 2.49 0.643
33 110 48 45 45 6 4 8 0.49 2.29 0.436
34 118 48 35 55 2 6 8 0.54 2.46 0.639
35 110 55 35 55 4 4 8 0.48 2.19 0.439
36 125 48 45 45 2 4 8 0.79 3.31 0.965
37 118 48 35 35 6 2 8 0.66 2.59 0.652
38 118 48 35 45 4 4 8 0.55 2.75 0.662
39 118 55 25 45 4 6 8 0.51 2.49 0.645
40 118 40 35 45 6 4 10 0.55 2.68 0.654
41 125 40 35 35 4 4 8 0.85 3.55 0.964
42 125 48 35 45 4 2 6 0.83 3.38 0.974
43 110 48 25 45 6 4 8 0.46 2.21 0.437
44 118 48 25 55 4 4 6 0.43 2.32 0.636
45 118 55 25 45 4 2 8 0.57 2.41 0.636
46 118 48 45 35 4 4 6 0.58 2.53 0.646
47 118 48 35 45 4 4 8 0.54 2.65 0.663
48 125 48 25 45 6 4 8 0.71 3.21 0.945
49 125 55 35 55 4 4 8 0.71 2.85 0.955
50 125 48 35 45 4 6 10 0.72 3.35 0.977
51 110 48 35 45 4 2 10 0.54 2.38 0.475
52 118 40 45 45 4 6 8 0.71 2.72 0.655
53 110 48 35 45 4 2 6 0.51 2.39 0.488
54 110 48 35 45 4 6 10 0.58 2.39 0.469
55 118 40 25 45 4 2 8 0.61 2.51 0.643
56 118 48 35 55 2 2 8 0.55 2.46 0.636
57 118 48 35 35 2 2 8 0.64 2.51 0.649
58 118 48 35 45 4 4 8 0.54 2.54 0.657
59 118 48 25 35 4 4 10 0.62 2.41 0.631
60 118 40 35 45 6 4 6 0.66 2.74 0.661
61 125 48 45 45 6 4 8 0.72 3.11 0.979
62 125 48 35 45 4 6 6 0.79 3.19 0.975

3 Measurement of responses using empirical models

3.1 Empirical modeling for responses through ANOVA

The objective of WEDM is to find optimal input variables with the least amount of noise, but this is a very challenging task. In this case, response surface methodology (RSM) can be used to evaluate the mathematical relationship between the inputs and outputs. It uses the statistical technique of Analysis of Variance (ANOVA) to analyze the data.

3.2 ANOVA and mathematical model for CS

ANOVA uses different test procedures to determine the importance of significant differences among the factors. Tables 46 present the results of ANOVA for CS, SR, and KW. By using the backward elimination rule, influential parameters are examined. Figure 2 illustrates the residual error and error deviation between predicted and actual values for CS. Furthermore, a reasonable agreement between actual and predicted values indicates that the ANOVA model meets the criteria for CS. The ANOVA for CS shows a significant F-value of 64.21. A p-value less than 0.05 indicates that the model terms are acceptable. A, B, C, D, E, F, and G are effective model terms in this model, along with AF, AG, BC, BD, BG, CD, CG, and degree of freedom (DF). With a value of 0.1412, the lack of fit (LOF) is not significant compared to the pure error. As a result of noise, it is 64.21% likely that the F-value will be larger when the LOF exists. The predicted R 2 (PR 2) of 0.9218 is within a feasible covenant with the adjusted R 2 (AR 2) of 0.9491, indicating that variation is below 0.2. As a result of the 34.931 signal-to-noise ratios, there is a signal that must be present in order to predict the CS.

Table 4

ANOVA for CS (reduced quadratic after backward elimination)

Source Sum of squares (SS) DF Mean square (MS) F-value p-value Remarks
Model 0.6382 18 0.0355 64.21 <0.0001 Significant
A: PONT 0.3528 1 0.3528 638.92 <0.0001 Significant
B: POFFT 0.0641 1 0.0641 116.01 <0.0001 Significant
C: PC 0.0084 1 0.0084 15.28 0.0003 Significant
D: SGV 0.0241 1 0.0241 43.58 <0.0001 Significant
E: WF 0.0040 1 0.0040 7.25 0.0101 Significant
F: WT 0.0067 1 0.0067 12.07 0.0012 Significant
G: WP 0.0017 1 0.0017 3.02 0.0895 Significant
AF 0.0018 1 0.0018 3.26 0.0780 Significant
AG 0.0072 1 0.0072 13.04 0.0008 Significant
BC 0.0021 1 0.0021 3.83 0.0570 Significant
BD 0.0032 1 0.0032 5.79 0.0204 Significant
BG 0.0055 1 0.0055 9.98 0.0029 Significant
CD 0.0066 1 0.0066 11.97 0.0012 Significant
0.1134 1 0.1134 205.40 <0.0001 Significant
0.0222 1 0.0222 40.22 <0.0001 Significant
0.0195 1 0.0195 35.25 <0.0001 Significant
LOF 0.0226 38 0.0006 2.63 0.1413 Not significant
R 2 0.9641
AR 2 0.9491
PR 2 0.9218
Table 5

ANOVA for SR (reduced quadratic after backward elimination)

Source SS DF MS F-value p-value Remarks
Model 6.17 12 0.5146 86.31 <0.0001 Significant
A: PONT 4.65 1 4.65 779.35 <0.0001 Significant
B: POFFT 0.4030 1 0.4030 67.60 <0.0001 Significant
C: PC 0.0442 1 0.0442 7.41 0.0089 Significant
D: SGV 0.0620 1 0.0620 10.40 0.0022 Significant
F: WT 0.0007 1 0.0007 0.1181 0.7326
G: WP 0.0060 1 0.0060 1.01 0.3200
AB 0.0300 1 0.0300 5.03 0.0294 Significant
CF 0.0221 1 0.0221 3.70 0.0603 Significant
FG 0.0242 1 0.0242 4.06 0.0494 Significant
0.6173 1 0.6173 103.55 <0.0001 Significant
0.0792 1 0.0792 13.29 0.0006 Significant
0.1509 1 0.1509 25.31 <0.0001 Significant
LOF 0.2566 44 0.0058 0.8206 0.6836 Not significant
R 2 0.9548
AR 2 0.9438
PR 2 0.9205
Table 6

ANOVA for KW (reduced quadratic after backward elimination)

Source SS DF MS F-value p-value Remarks
Model 1.59 15 0.1060 2465.09 <0.0001 Significant
A: PONT 1.52 1 1.52 35444.17 <0.0001 Significant
B: POFFT 0.0014 1 0.0014 32.45 <0.0001 Significant
C: PC 0.0004 1 0.0004 8.20 0.0063 Significant
D: SGV 0.0002 1 0.0002 4.09 0.0489 Significant
E: WF 0.0000 1 0.0000 0.2481 0.6208
F: WT 3.750 × 10−7 1 3.750 × 10−7 0.0087 0.9260
G: WP 0.0001 1 0.0001 1.63 0.2083
AB 0.0004 1 0.0004 10.12 0.0026 Significant
AC 0.0005 1 0.0005 11.91 0.0012 Significant
AF 0.0005 1 0.0005 11.54 0.0014 Significant
FG 0.0003 1 0.0003 6.98 0.0112 Significant
0.0523 1 0.0523 1217.01 <0.0001 Significant
0.0028 1 0.0028 64.03 <0.0001 Significant
0.0009 1 0.0009 20.30 <0.0001 Significant
0.0007 1 0.0007 16.89 0.0002 Significant
LOF 0.0019 41 0.0000 2.31 0.1775 Not significant
R 2 0.9988
AR 2 0.9984
AR 2 0.9973
Figure 2 
                  Graph for CS: (a) normal plot for residual and (b) predicted vs actual.
Figure 2

Graph for CS: (a) normal plot for residual and (b) predicted vs actual.

3.3 ANOVA and mathematical model for SR

The output of quadratic model suggested by Design-Expert software 12 is shown in Table 5 for ANOVA for SR and conformity. For SR, Figure 3 shows a reasonable agreement between actual and predicted values that satisfies ANOVA’s desire criteria. Backward elimination is used to eliminate parameters that fit Table 7. An F-value of 86.31 indicates that the model is significant. Noise is extremely likely to change the F-value, with a possibility of 0.01%. Therefore, there is a 68.36% chance that a LOF F-value may happen due to noise. A, B, C, D, AB, FG, A2, C2, and D2 are significant model terms. Model terms with values greater than 0.1000 are not significant. When there are many insignificant model terms (excluding those required for supporting the hierarchy), model reduction may improve the model. Each factor contributes 71.8, 6.22, 0.68, and 0.95% respectively. The other factors have contributed very less significantly to SR. As a result of coefficient estimation, the SR is expected to change with a single factor while keeping all other remaining factors constant. The PR 2 of 0.9205 is close to the AR 2 of 0.9438, that is, there is a difference of less than 0.2 closer to the model. Therefore, the model is used to predict SR, taking maximum and minimum factors into account.

Figure 3 
                  Graph for SR: (a) normal plot for residual and (b) predicted vs actual.
Figure 3

Graph for SR: (a) normal plot for residual and (b) predicted vs actual.

Table 7

Optimal solution obtained through desirability approach

S. no. PTON POFFT PC SGV WF WT WP CS SR KW Desirability
1 119 42 38 36 3 2 6 0.78 2.87 0.707 1.000
2 119 41 45 38 2 3 6 0.78 2.87 0.707 1.000
3 119 41 37 35 6 2 6 0.78 2.87 0.707 1.000
4 119 40 41 36 5 3 7 0.78 2.87 0.707 1.000
5 119 40 45 37 3 3 7 0.78 2.87 0.710 0.999
6 119 40 37 37 4 2 7 0.78 2.88 0.707 0.999
7 119 40 43 37 6 2 7 0.78 2.89 0.707 0.998
8 119 40 36 35 6 2 7 0.78 2.87 0.719 0.998
9 119 41 36 39 2 2 6 0.78 2.90 0.707 0.998
10 119 40 45 51 4 2 6 0.77 2.89 0.707 0.997
11 119 40 45 43 2 4 6 0.77 2.87 0.707 0.997
12 119 41 45 40 5 2 7 0.78 2.91 0.707 0.997
13 119 40 39 40 3 2 6 0.78 2.91 0.707 0.997
14 120 40 44 35 6 4 6 0.78 2.87 0.725 0.996
15 119 42 40 40 2 2 6 0.78 2.92 0.707 0.996
16 119 40 30 38 3 2 6 0.78 2.87 0.725 0.996
17 120 40 31 37 2 2 7 0.78 2.87 0.727 0.996
18 119 43 45 38 3 2 7 0.76 2.87 0.707 0.995
19 120 40 45 41 2 5 6 0.78 2.87 0.731 0.995
20 119 40 45 45 5 3 6 0.77 2.90 0.707 0.994

3.4 ANOVA and mathematical model for KW

As shown in Table 6, the ANOVA for KW and the conformity of the quadratic model was suggested by Design-Expert software 12. Figure 4 shows that there are reasonable agreements between actual values and predicted values that meet the ANOVA model’s desire criteria. Parameters were examined by the backward elimination rule. The model for KW, with an F-value of 2465.09, showed that the model implied significance. The 0.01% chance of noise altering the F-value is extremely high. The F-value for LOF may be 17.75% due to noise, so A, B, C, D, AB, AC, AF, FG, A2, C2, D2, and E2 are significant model terms. The model terms having values greater than 0.1000 are suggested to be not significant. Model reduction may be useful when there are many insignificant model terms (excluding those required to support the hierarchy). PONT is responsible for 95.59% of the KW. As long as all other remaining factors remain constant, coefficient estimation describes the expected change in KW with a single factor. KW is predicted using the model with maximum and minimum factors taken into account, as shown by the PR 2 of 0.9973, which is within 0.2 of the AR 2 of 0.9984.

Figure 4 
                  Graph for KW: (a) normal plot for residual and (b) predicted vs actual.
Figure 4

Graph for KW: (a) normal plot for residual and (b) predicted vs actual.

3.5 Modeling equation for quadratic responses

For each input variable’s specified value, the quadratic modeling equations established in the present study can predict the response variable. For the reduced quadratic model, the significance level = 0.05 at 95% confidence interval. The following expressions are second-order quadratic polynomial regression equations for CS, SR, and KW:

(1) CS = 21.3544 + 0.333833 × PONT + 0.0914911 × POFFT + 0.0117292 × PC + 0.0311458 × SGV + 0.00645833 × WF + 0.0232735 × WT + 0.202396 × WP + 0.001 × PONT × WT + 0.002 × PONT × WP + 0.000216667 × POFFT × PC + 0.000266667 × POFFT × SGV + 0.00175 × POFFT × WP + 0.0002875 × PC × SGV + 0.0015625 × PC × WP + 0.0013125 × SGV × WT + 0.00157447 × PONT 2 + 0.00069669 × POFFT 2 + 0.00917221 × WT 2 ,

(2) SR = 38.4325 + 0.752778 × PONT + 0.110667 × POFFT + 0.0666028 × PC + 0.0868435 × SGV + 0.0208333 × WT + 0.0629167 × WP + 0.00108889 × PONT × POFFT + 0.002625 × PC × WT + 0.01375 × WT × WP + 0.00367305 × PONT 2 + 0.00074016 × PC 2 + 0.00102141 × SGV 2 ,

(3) KW = 12.7219 + 0.23121 × PONT + 0.0164222 × POFFT + 0.00243646 × PC + 0.00676176 × SGV + 0.0145863 × WF + 0.074 × WT + 0.00697917 × WP + 0.000131111 × PONT × POFFT + 0.000106667 × PONT × PC + 0.000525 × PONT × WT + 0.00153125 × WT × WP + 0.00107553 × PONT 2 + 0.000138765 × PC 2 + 7.81399 × 10 5 × SGV 2 + 0.00178162 × WF 2 .

A comparative influence of factors can also be detected by equating factor coefficients. To amalgamate the dimensions of each element, the ratio is scaled. Eqs. (1)–(3) give the quadratic equations of the proposed model for CS, SR, and KW.

4 Results and discussion

An analysis of the responses has been demonstrated using a three-dimensional plot and a perturbation graph. Each machining parameter, along with its dielectric and parametric interactions, is analyzed in detail in the following subsection. Three-dimensional response surface graphs reveal how input variables affect response measures. In the graph, the 3D surface represents the main as well as interaction effects of two input variables at the same time, while other variables remain constant at their mid-levels. An illustration of a 3D surface’s reflection is depicted by contour lines at the base of the graph. Colored contour lines show the range of response values.

4.1 Analysis of the effect of machining parameters on CS

The research work illustrates how machine control factors affect the CS on polycrystalline material through WEDM process. In Design-Expert 12.0, the midpoint of all factors serves as a reference point. All significant parameters like A, B, C, and D have steep slopes. This indicates that CS is highly sensitive to these parameters, while E, F, and G have lower sensitivity. As a function of discharge energy, gas explosion, ion generation, and bridging effect mostly affect CS. In Table 4, the significant interactions between input variables such as AF, AG, BD, BG, CD, and CG are shown. Figure 5a–f illustrates that the surface plots of interactions lie at the middle point between two parameters. According to Figure 5a, CS increases sharply with an increase in PONT (A) and WP (G). Because of the higher WP (G), the debris particle is removed from the gap over a longer period due to the higher discharge energy produced by the higher PONT (A). Figure 5b and c also demonstrate an interaction between BD and BG effects. The effect of these interactions indicates that the CS increases from 0.515 to 0.664 mm2/min simultaneously. Due to the constant effect of WP (G), these interactions exhibited minimal effect. Based on the interaction effect, as shown in Figure 5d–f, the CS increases from 0.546 to 0.581 mm2/min. As a result, WT (F) and WP (G) show a constant and less significant effect for CS. Due to this, a late explosion occurs and expands the spark gap in the plasma channel. Sparks are produced less often, resulting in a lower CS. This process is dependent on the weightage value of the PONT (A). As a result, low pulse settings improve production efficiency at a lower cost. The frequency of sparks is reduced when POFFT (B) is reduced, thus reducing gas eruptions. Furthermore, higher POFFT (B) allows sufficient time for debris to be removed from the gap zone, triggering the next batch of spark discharges.

Figure 5 
                  (a–f) 3D interaction surface plots for CS.
Figure 5

(a–f) 3D interaction surface plots for CS.

4.2 Analysis of the effect of machining parameters on SR

In Table 5, the parameters that have the greatest impact are listed. Figure 6a–c illustrates the surface plot for these parameter interactions. From Figure 6a, it can be seen that SR sharply raises (3.44 μm) and then decreases (2.65–2.63 μm) as shown in Figure 6b and c. As a consequence, WT (F) and WP (G) show less significant effects on SR. The reason for this is that WT (F) and WP (G) have a constant and less significant effect on SR. As a result of PC, the dielectric strength decreases, and discrete sparks are avoided, and as a result of parameter B, debris from the gap zone is removed over some time. Therefore, the machining process becomes more stable, and machining performance improves. Contrary to other parameter settings, certain POFFT (B) and PC (C) parameters have lower sensitivity. PONT and PC control the generation and discharge of ions. To achieve the best surface finish, fewer craters, voids, and micro-cracks are visible, which are mostly caused by POFFT and PC. The significant interactions between the input variables are AB, CF, and FG, according to ANOVA Table 5.

Figure 6 
                  (a–c) 3D interaction surface plots for SR.
Figure 6

(a–c) 3D interaction surface plots for SR.

4.3 Analysis of the effect of machining parameters on KW

With changes in machining parameters, KW can increase or decrease as a result of the cutting process. As shown in Table 6, the most influential parameters are those that have the greatest impact. An analysis of the change in KW due to variation in the interaction between parameters is displayed in Figure 7a–d. Figure 7a illustrates how KW (0.967 mm) of polycrystalline material increases with concurrent decreases in POFFT (B) and increases in PONT (A). On the other hand, PONT has a significant effect on KW. By increasing PONT, more energy can be discharged for melting and vaporizing the work material. Low POFFT values allow work material to be removed easily, while higher POFFT values cause the substrate metal to melt when discharged intensely. Figure 7b indicates that KW is 0.967mm at higher values of PONT (125 μs) and PC (45A). The amplitude of wire vibration increases when PC is high, resulting in a reduction in dielectric fluid flow around the wire, thus resulting in the inefficient removal of debris and reinforced particles from the discharge gap. In addition, the debris particles that adhered to the wire also produced high KWs. The 3D surface graph (Figure 7c) illustrates that KW increases as tension in the wire increases (0.972 mm). When the wire is at a low WT, the wire amplitude is relatively high, resulting in a wider kerf. A 3D surface plot of WT and WP in Figure 7d indicates that the KW decreases (0.662 mm). In Figure 7d, the effect was much less significant.

Figure 7 
                  (a–d) 3D interaction surface plots for SR.
Figure 7

(a–d) 3D interaction surface plots for SR.

5 Surface morphology of work material after the WEDM process

As shown in Figures 8 and 9, SEM has been used to analyze the surface morphology of machined specimens. Samples machined with Zn-coated wire exhibit micro-voids, globules, small and shallow craters, and debris particles adhered to the surface of the sample. As a result of its superior electrical conductivity, Zn-coated wire performs exceptionally well because its enlarged discharge channel prevents the melted material from re-solidifying on the work surface and makes flushing easy. The surface of the workpiece is dramatically altered during metal removal as a result of rapid heating, melting, and vaporization in the sparking zone, followed by rapid cooling. Several studies have examined the surface integrity of popular steel alloys, and composites, particularly tool and die steels, using the WEDM process. WEDM has not been adequately documented in terms of how it alters the surface properties of polycrystalline silicon. Specifically, there is not a lot of literature on polycrystalline silicon machining. Due to the uneven distribution of spherical and non-spherical agglomerates, WEDM surfaces are often rough cut. The workpiece composition was analyzed with an EDX and metals other than the base metal were found. During WEDM, metal particles are transported from the Zn coated wire to the workpiece and the dielectric is broken down. A substantial amount of electrode material is brought to the surface of the workpiece during WEDM because not all particles can be flushed out of the spark gap. Figure 10a and b illustrates images of machined surfaces taken with 3 KV EDX. We can infer that a substantial amount of electrode material is brought to the surface of the workpiece during WEDM. Quantitative EDX was used to analyze the workpiece and electrodes’ surface chemistry. According to EDX measurements, carbon (C), copper (Cu), oxygen (O2), Fe, silicon (Si), and Zn migrated to the surface of the workpiece. During machining, the Zn wire electrode melted, evaporated, and re-solidified, leaving Cu and Zn residues. The transfer of Cu and Zn elements occurs during sparking, which were deposited on the machined workpiece surface in addition to C and Fe. Shock impulses cause the welding of the detached elements on the workpiece. The electrode boils off the Zn, which is flushed with dielectric fluid during machining. The major content of oxygen and carbon was due to decomposition of dielectric, oxidation and mixing of debris at high temperature involved in the process. The perturbation plot in Figure 11 shows four parameters, A, B, C, and D, for CS, SR, and KW of a sliced polycrystalline WEDM surface. The steep slope, which includes the most significant parameters such as A, B, and C, indicates that SR responds very strongly to these parameters. When POFFT is shorter, the number of discharges within a given period becomes more which may result in more number of cracks. High PC and low POFFT increases the amount of debris in the spark gap which leads to abnormal arcing. At higher PC, the impact of discharge energy on the surface of workpiece becomes greater, and thus, resulting in the increase in the number of cracks.

Figure 8 
               (a) (Run nos. 1 and 35), (b) small craters, (c) Shallow and wide deep craters, (d) Micro voids on the sub-surface.
Figure 8

(a) (Run nos. 1 and 35), (b) small craters, (c) Shallow and wide deep craters, (d) Micro voids on the sub-surface.

Figure 9 
               (a) (Run nos. 14 and 25), (b) Wavy pattern, micro-cracks, wider-deep craters, and globules of debris have appeared on sub-surfaces.
Figure 9

(a) (Run nos. 14 and 25), (b) Wavy pattern, micro-cracks, wider-deep craters, and globules of debris have appeared on sub-surfaces.

Figure 10 
               (a and b) EDX analysis of machined samples.
Figure 10

(a and b) EDX analysis of machined samples.

Figure 11 
               Perturbation plots for (a) CS, (b) SR and (c) KW.
Figure 11

Perturbation plots for (a) CS, (b) SR and (c) KW.

6 Multi-response optimization with a desirability approach

Desirability is an objective function that increases from zero to one at the target. It is possible to transform the goal’s characteristics by modifying its weight or importance. High desirability values indicate how much closer the lower and upper limits are to the best value (desirability value of 1.0) as shown in Table 7. An optimization problem with a single objective and multiple responses can be solved using the desirability approach. The desirability function for multi-responses and factors is derived from combining all goals. CS, SR, and KW are shown in Figures 12 and 13 with a ramp function diagram and bar graph, respectively, in the numerical optimization ramps view. As a result, the point on the ramp view graph represents the estimation value for the machining parameter and response measure, making it desirable. As shown in the bar graph, the value is closer to 1, indicating satisfactory constraints. For the combined case, performance measures are considered, and their satisfactory constraint is closer to the desired value for both input and output variables.

Figure 12 
                Ramp plot for CS, SR, and KW showing the optimal parameters solution.
Figure 12

Ramp plot for CS, SR, and KW showing the optimal parameters solution.

Figure 13 
               Bar graph for CS, SR, and KW showing the combined and individual desirability.
Figure 13

Bar graph for CS, SR, and KW showing the combined and individual desirability.

7 Conclusion

This study presents an experimental and statistical analysis of wafer slicing of polycrystalline silicon with WEDM at different levels of process parameters using Box Behnken’s Design to measure the CS, SR, and KW. Following are the conclusions derived from the results:

  1. With RSM technique, we can analyze and optimize the stochastic nature and process behavior of WEDM process.

  2. Based on the results of ANOVA of CS, SR, and KW, it was found that the PONT, POFFT, PC, and SGV are the four most significant variables. In addition, a reasonable agreement between actual and predicted values indicates that the ANOVA model meets the criteria.

  3. As a result, WT (F) and WP (G) show a constant and less significant effect for CS. Due to this, a late explosion occurs and expands the spark gap in the plasma channel. Sparks are produced less often, resulting in a lower CS. This process is dependent on the weightage value of the PONT (A).

  4. To obtain the maximum CS (0.779 mm2/min) and minimum SR (2.87 μm) and KW (0.707 mm), the parameters for WEDM should be set at PTON = 119 µs, POFFT = 42 μs, PC = 38 A, SGV = 36 V, WT = 3 kg, WF = 2 mm/min, and WP = 6 kg/cm2.

  5. As a result of PC, the dielectric strength decreases, and discrete sparks are avoided, and as a result of parameter B, debris from the gap zone is removed over some time. Therefore, the machining process becomes more stable, and machining performance improves. Contrary to other parameter settings, certain POFFT (B) and PC (C) parameters have lower sensitivity.

  6. On the other hand, PONT has a significant effect on KW. By increasing PONT, more energy can be discharged for melting and vaporizing the work material. Low POFFT values allow work material to be removed easily, while higher POFFT values cause the substrate metal to melt when discharged intensely.

  7. Samples machined with Zn-coated wire exhibit micro-voids, globules, small and shallow craters, and debris particles adhered to the surface of the sample. As a result of its superior electrical conductivity, Zn-coated wire performs exceptionally well because its enlarged discharge channel prevents the melted material from re-solidifying on the work surface and makes flushing easy

  8. The experiment results indicated that increasing the PTON and PC values increases the kerf width of machined samples.

  9. Quantitative EDX was used to analyze the workpiece and electrodes’ surface chemistry. According to EDX measurements, carbon, Cu, O2, Si, and Zn migrated to the surface of the workpiece. During machining, the Zn wire electrode melted, evaporated, and re-solidified, leaving Cu and Zn residues.

Abbreviations

AR 2

adjusted R 2

ANOVA

analysis of variance

EDX

energy dispersive X-ray spectroscopy

LOF

lack of fit

MS

mean square

PONT

pulse on time

POFFT

pulse off time

PC

peak current

PR 2

predicted R 2

RSM:

response surface methodology

SR

surface roughness

SEM

scanning electron microscope

SGV

spark gap voltage

SS

sum of squares

WEDM

wire electric discharge machining

WP

water pressure

WS

wire speed

WT

wire tension

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2022-12-20
Revised: 2023-04-24
Accepted: 2023-05-29
Published Online: 2023-07-19

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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