Optimisation of wire-cut EDM process parameter by Grey-based response surface methodology
Abstract
Wire electric discharge machining (WEDM) is one of the advanced machining processes. Response surface methodology coupled with Grey relation analysis method has been proposed and used to optimise the machining parameters of WEDM. A face centred cubic design is used for conducting experiments on high speed steel (HSS) M2 grade workpiece material. The regression model of significant factors such as pulse-on time, pulse-off time, peak current, and wire feed is considered for optimising the responses variables material removal rate (MRR), surface roughness and Kerf width. The optimal condition of the machining parameter was obtained using the Grey relation grade. ANOVA is applied to determine significance of the input parameters for optimising the Grey relation grade.
Keywords
Wire-cut EDM Response surface methodology Grey relation analysis WEDMNomenclature
- AE
Angular error
- ANOVA
Analysis of variance
- CCD
Central composite design
- EDM
Electric discharge machining
- GC
Gap current
- GRA
Grey relational analysis
- MRR
Material removal rate
- MRSN
Multiple response signal-to noise ratio
- MS
Machining speed
- RSM
Response surface methodology
- S/N
Signal-to-noise ratio
- SG
Spark gap
- SO
Single objective
- SR
Surface roughness
- WEDM
Wire electric discharge machining
- WSN
Weighted signal-to-noise ratio
- T_{m}
Machining time (min)
- T_{off}
Pulse-off time (μs)
- T_{on}
Pulse-on time (μs)
- \(\hbox{max}\,x_{i}^{(o)} (k)\)
Maximum of \(x_{i}^{(o)} (k)\)
- \(\hbox{min}\,x_{i}^{(o)} (k)\)
Minimum of \(x_{i}^{(o)} (k)\)
- W_{i}
Initial weight of workpiece material (g)
- W_{f}
Final weight of workpiece material (g)
- \(\in_{i} (k)\)
Grey relational coefficient of the ith experiment for the kth response
- \(y_{i}^{*} (k)\)
Normalised data
- \(\varGamma_{i}\)
Grey related grade
Introduction
Wire electric discharge machining (WEDM) process has opened a new swing in the manufacturing sector. Non-traditional machining processes changed the whole scenario of manufacturing industries. Traditional machining processes are rapidly replaced by non-traditional methods for achieving better production rates and quality. One of the successful methods is WEDM, which is based on the conventional electric discharge machining (EDM). The principle remains the same for WEDM as in conventional EDM, a thermo-electrical process. WEDM process involves the erosion effect by rapid repetitive and discrete spark discharges between the wire tool electrode and work piece in a liquid dielectric medium. Manufacturing the parts of high quality at high production efficiency is the main objective of WEDM process. Selecting the appropriate machining parameter for high quality product is very difficult. Much research is not found in the field of WEDM to find the optimum parameter; in the present research, GRA is used to find the response variable of WEDM. An attempt is made by Majhi et al. (2013) for the determination of the optimal process parameters material removal rate, surface roughness and tool wear rate for EDM process. Modelling and optimisation of WEDM were given by Kumar and Kumar (2013). To find the optimum surface roughness, they used to input parameters such as Time On, Time Off, Wire Speed and Wire Feed. Taguchi techniques have been used for optimisation of minimizing the SR. Due to multiple variables, an extremely trained operator with a modern WEDM is rarely to achieve the optimal performance. Pasam et al. (2010) conducted research to solve this problem to determine the relation among the responses and its parameter. The most important responses in WEDM are metal removal rate, workpiece’s surface finish, and kerf width. Discharge current, pulse duration, pulse frequency, wire speed, wire tension, and dielectric flow rate are some of the machining parameters which affect the responses. The gap between the wire and work piece is also an important in wire EDM and it usually ranges from 0.02 to 0.075 mm given by Mahapatra and Patnaik (2007). Taguchi-based Grey relational analysis, to find the optimal process parameter setting for multi-matrix composite using molybdenum wire of 0.18 mm diameter, as electrode is applied by Lal et al. (2015). Similar technique for optimisation was used by Shivade and Shinde (2014) for D3 tool steel material. Nayak and Mahapatra (2016) applied an artificial neural network (ANN) model to determine the relationship between input parameters and performance characteristics for taper cutting of deep cryo-treated Inconel 718 with cryo-treated coated Bronco cut-W. In wire electrical discharge machining process 0.2 mm diameter wire electrode was used. Jaganathan et al. (2012) optimised the wire EDM parameter and responses MRR and surface finish for EN31 is done by Taguchi L27 orthogonal array (OA). Singha and Pradhan (2014) conducted experiment through Taguchi method and response surface methodology is applied to estimate the optimum machining condition within the experimental constraints. Varun and Venkaiah (2014) used an optimisation strategy by coupling Grey relational analysis (GRA) with genetic algorithm (GA) to optimise the response parameters. Experiments were conducted on EN-353 work material to study the effects of input parameters. Zinc-coated copper wire with 0.25 mm diameter is used as an electrode. The response parameter such as material removal rate (MRR), the surface roughness (SR), and kerf width is observed. Saha and Mondal (2016) applied an optimisation technique combining Grey relational analysis with principal component analysis to identify the optimal combination of process parameters in WEDM for machining nanostructured hard facing materials. Sinha et al. (2015) used Taguchi method for single objective optimisation and then the signal-to-noise (S/N) ratios obtained from Taguchi method have been further used in principal component analysis (PCA) for multi-objective optimisation. Huang and Liao (2003) applied Grey relational analyses with L18 mixed orthogonal array to determine the optimal selection of machining parameters for the wire electrical discharge machining process. Baig and Vankaiah (2001) applied Taguchi and Grey relation analysis to find the optimal parameter settings for WEDM for a nickel-based alloy.
This work investigates and optimizes the potential process parameters influencing the MRR, SR and kerf width while machining HSS M2 alloys using WEDM process. This work involves study of the relation between the various input process parameters like pulse-on time (T_{on}), pulse-off time (T_{off}), pulse peak current (IP), and wire feed. The RSM method, a powerful experimental design tool, uses a simple, effective, and systematic approach for deriving the optimal machining parameters. Further, this approach requires minimum experimental cost and efficiently reduces the effect of the source of variation. An inexpensive and easy to operate methodology must be evolved to modify the machined surfaces as well as to maintain accuracy. RSM methodology by face centred design is used for conducting the design of experiments to optimise the experimental values for machining HSS M2 alloys by WEDM. A Grey relation approach is used to combine all the response in single response for optimisation to achieve single operating optimal condition for all the response MRR, SR and Kerf width.
Experimentation detail
Chemical composition of the material HSS-M2
Constituent | C | Mn | Si | S | P | Cr | V | Mo | W | Co | Cu |
---|---|---|---|---|---|---|---|---|---|---|---|
% composition | 0.92 | 0.23 | 0.18 | 0.016 | 0.018 | 3.85 | 2.19 | 4.80 | 6.40 | 0.90 | 0.18 |
Process parameters and their levels
Variable | Unit | Level | ||
---|---|---|---|---|
− 1 | 0 | 1 | ||
Pulse-on time, T_{on} (A) | µs | 20 | 30 | 40 |
Pulse-off time, T_{off} (B) | µs | 5 | 10 | 15 |
Current, IP (C) | A | 1 | 2 | 3 |
Wire feed, W_{f} (D) | mm/s | 30 | 40 | 50 |
Measurement of responses
Material removal rate
Surface roughness
Kerf width
Experimental results for four parameters in uncoded units
Run order | Process parameter | Responses | |||||
---|---|---|---|---|---|---|---|
A (T_{on}), µs | B (T_{off}), µs | C (IP), A | D (W_{f}), mm/s | MRR (g/min) | Surface roughness (µm) | Kerf width (mm) | |
1 | 40 | 15 | 3 | 30 | 0.0349 | 3.77 | 0.22 |
2 | 30 | 10 | 3 | 40 | 0.0314 | 4.48 | 0.22 |
3 | 40 | 15 | 3 | 50 | 0.0263 | 3.66 | 0.23 |
4 | 40 | 10 | 2 | 40 | 0.0357 | 4.85 | 0.25 |
5 | 20 | 5 | 3 | 50 | 0.0253 | 3.96 | 0.215 |
6 | 30 | 10 | 2 | 50 | 0.0268 | 4.23 | 0.2 |
7 | 40 | 15 | 1 | 30 | 0.0095 | 3.55 | 0.24 |
8 | 30 | 10 | 2 | 30 | 0.0383 | 4.5 | 0.225 |
9 | 30 | 5 | 2 | 40 | 0.0298 | 5.5 | 0.23 |
10 | 40 | 5 | 1 | 50 | 0.0163 | 5.82 | 0.225 |
11 | 20 | 5 | 1 | 50 | 0.019 | 4.19 | 0.19 |
12 | 20 | 15 | 3 | 30 | 0.0277 | 2.94 | 0.199 |
13 | 20 | 5 | 3 | 30 | 0.028 | 4.4 | 0.22 |
14 | 20 | 10 | 2 | 40 | 0.0276 | 3.04 | 0.19 |
15 | 20 | 15 | 3 | 50 | 0.0208 | 2.32 | 0.19 |
16 | 20 | 15 | 1 | 50 | 0.0088 | 2.61 | 0.19 |
17 | 30 | 10 | 2 | 40 | 0.0309 | 4.42 | 0.21 |
18 | 40 | 15 | 1 | 50 | 0.0141 | 3.3 | 0.21 |
19 | 40 | 5 | 3 | 30 | 0.0529 | 6.55 | 0.24 |
20 | 30 | 10 | 1 | 40 | 0.0201 | 4.35 | 0.205 |
21 | 30 | 10 | 2 | 40 | 0.0304 | 4.38 | 0.2 |
22 | 20 | 15 | 1 | 30 | 0.0073 | 2.78 | 0.195 |
23 | 40 | 5 | 3 | 50 | 0.0283 | 6.38 | 0.225 |
24 | 40 | 5 | 1 | 30 | 0.0101 | 5.9 | 0.24 |
25 | 30 | 15 | 2 | 40 | 0.0278 | 3.27 | 0.19 |
26 | 20 | 5 | 1 | 30 | 0.0064 | 4.21 | 0.22 |
Grey relation analysis
GRA is a decision-making method based on Grey system theory firstly technologically advanced by Deng (1982). In Grey theory, black means a system with insufficient information, while a white system represents complete information. However, the Grey relation is relative to partial information and is used to characterise the degree of relationship between the sequences so that the distance of two factors can be measured individually. When experiments are uncertain or if the experimental method cannot be performed accurately, Grey analysis contributes to compensating for the lack of statistical regression. Therefore, Grey relation analysis is an effective means of analysing the relationship between less-than-data sequences and can analyse many factors that can overcome the drawback of the statistical method by Pradhan (2013). In the Grey relational analysis, experimental data, that is the measured quality characteristics, are normally normalised in the range from 0 to 1. This process is called Grey relational generation. Based on these data, the Grey relational coefficients are calculated to represent the correlation between the (best) ideal and the actual normalised experimental data. The overall Grey relational grade is determined by averaging the Grey relational coefficients corresponding to the selected responses. The overall quality characteristics of the multiple response process depend on the calculated grey relational grade.
Grey relational generation
Grey relational coefficient
Grey relation grade
Multi-response optimisation by Grey analysis
Grey relation coefficient
Experiment no. | MRR | SR | Kerf width | Grey relation coefficient | ||
---|---|---|---|---|---|---|
\(MRR \in_{i} (1)\) | \(SR \in_{i} (2)\) | \({\text{Kerf }}\;{\text{width}} \in_{i} (3)\) | ||||
1 | 0.0349 | 3.77 | 0.22 | 0.5636 | 0.5933 | 0.5 |
2 | 0.0314 | 4.48 | 0.22 | 0.5196 | 0.4947 | 0.5 |
3 | 0.0263 | 3.66 | 0.23 | 0.4664 | 0.6122 | 0.4286 |
4 | 0.0357 | 4.85 | 0.25 | 0.5748 | 0.4553 | 0.3333 |
5 | 0.0253 | 3.96 | 0.215 | 0.4572 | 0.5632 | 0.5455 |
6 | 0.0268 | 4.23 | 0.2 | 0.4711 | 0.5255 | 0.75 |
7 | 0.0095 | 3.55 | 0.24 | 0.3488 | 0.6323 | 0.375 |
8 | 0.0383 | 4.5 | 0.225 | 0.6143 | 0.4924 | 0.4615 |
9 | 0.0298 | 5.5 | 0.23 | 0.5016 | 0.3994 | 0.4286 |
10 | 0.0163 | 5.82 | 0.225 | 0.3885 | 0.3767 | 0.4615 |
11 | 0.019 | 4.19 | 0.19 | 0.4068 | 0.5307 | 1 |
12 | 0.0277 | 2.94 | 0.199 | 0.4799 | 0.7733 | 0.7692 |
13 | 0.028 | 4.4 | 0.22 | 0.4829 | 0.5042 | 0.5 |
14 | 0.0276 | 3.04 | 0.19 | 0.4789 | 0.746 | 1 |
15 | 0.0208 | 2.32 | 0.19 | 0.4201 | 1 | 1 |
16 | 0.0088 | 2.61 | 0.19 | 0.3452 | 0.8794 | 1 |
17 | 0.0309 | 4.42 | 0.21 | 0.5138 | 0.5018 | 0.6 |
18 | 0.0141 | 3.3 | 0.21 | 0.3747 | 0.6834 | 0.6 |
19 | 0.0529 | 6.55 | 0.24 | 1 | 0.3333 | 0.375 |
20 | 0.0201 | 4.35 | 0.205 | 0.4148 | 0.5103 | 0.6667 |
21 | 0.0304 | 4.38 | 0.2 | 0.5082 | 0.5066 | 0.75 |
22 | 0.0073 | 2.78 | 0.195 | 0.3377 | 0.8214 | 0.8571 |
23 | 0.0283 | 6.38 | 0.225 | 0.4859 | 0.3425 | 0.4615 |
24 | 0.0101 | 5.9 | 0.24 | 0.352 | 0.3714 | 0.375 |
25 | 0.0278 | 3.27 | 0.19 | 0.4809 | 0.69 | 1 |
26 | 0.0064 | 4.21 | 0.22 | 0.3333 | 0.5281 | 0.5 |
From Eq. 4, the three-response is converted into single response, i.e. Grey relation grade. It has been calculated, corresponding to parameter T_{on}, T_{off}, current and wire feed by passing the response MRR, SR and Kerf width.
Grey relation grade
Experiment no. | A (T_{on}) | B (T_{off}) | C (IP) | D (W_{f}) | GRG |
---|---|---|---|---|---|
1 | 40 | 15 | 3 | 30 | 0.5523 |
2 | 30 | 10 | 3 | 40 | 0.5048 |
3 | 40 | 15 | 3 | 50 | 0.5024 |
4 | 40 | 10 | 2 | 40 | 0.4545 |
5 | 20 | 5 | 3 | 50 | 0.522 |
6 | 30 | 10 | 2 | 50 | 0.5822 |
7 | 40 | 15 | 1 | 30 | 0.452 |
8 | 30 | 10 | 2 | 30 | 0.5227 |
9 | 30 | 5 | 2 | 40 | 0.4432 |
10 | 40 | 5 | 1 | 50 | 0.4089 |
11 | 20 | 5 | 1 | 50 | 0.6459 |
12 | 20 | 15 | 3 | 30 | 0.6741 |
13 | 20 | 5 | 3 | 30 | 0.4957 |
14 | 20 | 10 | 2 | 40 | 0.7416 |
15 | 20 | 15 | 3 | 50 | 0.8067 |
16 | 20 | 15 | 1 | 50 | 0.7415 |
17 | 30 | 10 | 2 | 40 | 0.5385 |
18 | 40 | 15 | 1 | 50 | 0.5527 |
19 | 40 | 5 | 3 | 30 | 0.5694 |
20 | 30 | 10 | 1 | 40 | 0.5306 |
21 | 30 | 10 | 2 | 40 | 0.5883 |
22 | 20 | 15 | 1 | 30 | 0.6721 |
23 | 40 | 5 | 3 | 50 | 0.43 |
24 | 40 | 5 | 1 | 30 | 0.3661 |
25 | 30 | 15 | 2 | 40 | 0.7236 |
26 | 20 | 5 | 1 | 30 | 0.4538 |
ANOVA analysis for Grey relation grade
Source | DF | Grey relation grade | ||||
---|---|---|---|---|---|---|
Adj SS | Adj MS | F-value | P value | % contribution | ||
Model | 14 | 0.28801 | 0.020572 | 5.74 | 0.003 | 87.95917 |
Linear | 4 | 0.23287 | 0.058218 | 16.24 | 0 | 71.11924 |
Square | 4 | 0.008239 | 0.00206 | 0.57 | 0.687 | 2.516217 |
2-Way interaction | 6 | 0.046901 | 0.007817 | 2.18 | 0.124 | 14.32372 |
Error | 11 | 0.039426 | 0.003584 | 12.04083 | ||
Lack-of-fit (LOF) | 10 | 0.038186 | 0.003819 | 3.08 | 0.419 | 11.66213 |
Pure error | 1 | 0.00124 | 0.00124 | 0.3787 | ||
Total | 25 | 0.327436 | 100 |
Response optimisation of GRG and optimal parameter setting
Response | Goal | Lower | Target | Upper | Weight | Importance |
---|---|---|---|---|---|---|
GRG | Maximum | 0.3661 | 1 | 1 | 1 | 1 |
Predicted GRG responses = 0.855339
Desirability = 0.771792
Optimised process parameters of WEDM by Grey analysis
Parameter | Value | Units |
---|---|---|
T _{on} | 20 | µs |
T _{off} | 15 | µs |
IP | 2 | A |
Wire feed | 50 | mm/s |
Conclusion
In this paper, the performance parameters namely metal removal rate, surface roughness and kerf width are investigated by varying the machining parameters on workpiece HSS M2 grade steel. Molybdenum wire of 0.18 mm diameter is used as an electrode in WEDM. The performance parameters of pulse-on time (T_{on}), pulse-off time (T_{off}), peak current (IP) and wire feed rate (W_{f}) are analysed. FCCD based on RSM is used for experimental design. Using Grey analysis, WEDM’s parameter was optimised and found that optimal responses were material removal rate (0.03137 g/min), surface roughness (1.79 µm) and Kerf width (0.19 mm) at optimal parameter at pulse-on time 20 µs, pulse-off time 15 µs current 2 A, and wire feed 50 mm/s which are the best parametric combination.
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