Optimization of multiple performance characteristics in EDM process of HPM 38 tool steel using response surface methodology and non linear programming

OPTIMIZATION OF MULTIPLE PERFORMANCE CHARACTERISTICS IN

EDM PROCESS OF HPM 38 TOOL STEEL USING RESPONSE SURFACE

METHODOLOGY AND NON-LINEAR PROGRAMMING

Amirul Akbar

, Bobby O. P. Soepangkat

and Arif Wahjudi

1_{Manufacturing Process Lab., Department of Mechanical Engineering, Faculty of Industrial Technology, Institut Teknologi Sepuluh}

Nopember, Surabaya, Indonesia

2

Design and Development Product Lab., Department of Mechanical Engineering, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia

E-Mail: [email protected]

ABSTRACT

The application of response surface methodology and non-linear programming for optimizing multiple performance characteristic in electro discharge machine (EDM) sinking process of HPM 38 steel was investigated. In this research, the main objective was to minimize surface roughness with electrode wear rate and material removal rate as constraints. The experiments were conducted based on Box-Behnken design (BBD) consisting 27 numbers of experiments. Quadratic model regression of response surface methodology was developed as efficient approaches to determine the optimal machining parameters in EDM process. Analysis of variance was applied to investigate the influence of process parameters (pulse current, gap width, on time and off time) and their interactions on surface roughness, electrode wear rate and material removal rate. A confirmation test was carried out to check the deviation of the predicted (optimum value) with experimental results.

Keywords: EDM sinking, surface roughness, electrode wear rate, material removal rate, response surface methodology, non-linear

programming.

INTRODUCTION

Electro discharge machine (EDM) is one of the non-conventional machining processes which is more efficient than conventional machining processes due to the ease of machining materials with complex geometry and burr-free [1]. EDM is used for machining of hard and high strength conductive materials which are hard enough to cut by conventional processes. In the process, there is no physical contact between the electrode and work piece that can eliminate mechanical stresses, chatter and vibration problems during machining. Hence, precision machining can be achieved by EDM [2]. It thus plays a major role in the machining of dies, tools, etc., made of tungsten carbides, stellites or hard steels [3].

In EDM, the removal of material is based upon the electro discharge erosion effect of electric sparks occurring between the electrode and work piece that are separated by a dielectric fluid. Material removal takes place as a result of the generation of extremely high temperatures (thermal energy) generated by the high-intensity discharge that melt and evaporate the electrode and work piece [4]. The function of dielectrid fluid in EDM process is to flush out the eroded particle from the machining gap, provide insulation between the electrode and work piece and cooling the section that was heated by the discharge effect [5].

Performance characteristic of EDM machining process generally determined by surface roughness (SR), electrode wear rate (EWR) and material removal rate (MRR). The EDM parameters which affect the performance characteristics are polarity, on time, off time,

working voltage, working current, flushing pressure and spark gap [6, 8]. Electrode wear and material removal produced during EDM process can also affect the surface roughness significantly. A high quality of surface roughness in EDM machining process can be obtained with a low rate of removal material, but the slow process will affect the completion time of products and will increase the cost of production.

This research takes HPM 38 steel as work piece and investigates three performance characteristics, i.e., surface roughness, material removal rate and electrode wear rate. Experiments were carried out using a

four-variable Box-Behnken design. The performance

characteristics of surface roughness and electrode wear rate are smaller the better and material removal rate is higher the better. Response surface methodology was employed to develop experimental models. Non-linear programming was applied to minimize the surface roughness with electrode wear rate and material removal rate as contraints.

EXPERIMENTAL DESIGN

Machining Parameter Selection

work piece were separated by kerosene dielectric using side flushing. An area with 15 mm (length) x 10 mm (width) and 2 mm (depth) the work piece EDMachined. Machining experiments for determining the optimal machining parameters were carried out by setting pulse current (PC), gap width (GW), on time (On) and off time (Off). The total number of levels which provided in EDM machine for pulse current is 20 levels, gap width is 90 levels, on time is 19 levels and of time is l9 evels. One level of pulse current, gap width, on time and off time are

equal to 3 amperes, 1 m, 84.21 s and 84.21 s

respectively. In this research, the experiments were conducted based on Box-Behnken design (BBD) consisting 27 number of experiments.

Machining parameters and their levels using Box-Behnken design are shown in Table-1. In Box-Box-Behnken design of response surface methodology, each parameter has 3 levels (low, medium and high) and the natural value of each machining parameter must be transformed to code units (X_{i). The machining parameters are usually coded to} -1 as a low level, 0 as a medium level and 1 as a high level. The machining parameter transformed model is [9]:

X_{i =} Xreal – (Xmax + Xmin)/2

(Xmax – Xmin)/2 (1)

The Box-Behnken design matrix of the experiment shown in Table-2.

Table-1. Machining parameters and their levels.

Machining

Parameters Unit

Low level

Medium level

High level

Pulse current

(X1) Ampere 4 8 12

Gap width (X2) µm 27 40 53

On time (X3) µs 2 7 12

Off time (X4) µs 2 6 10

Table-2. Matrix of experiment design.

Run Ord.

Code Parameters

� � � � PC GW On Off

1 0 1 0 -1 8 53 7 2

2 -1 0 0 -1 4 40 7 2

3 0 0 0 0 8 40 7 6

4 0 0 0 0 8 40 7 6

5 1 -1 0 0 12 27 7 6

6 -1 0 0 1 4 40 7 10

7 0 1 -1 0 8 53 2 6

8 0 0 -1 1 8 40 2 10

9 0 1 1 0 8 53 12 6

10 -1 1 0 0 4 53 7 6

11 0 -1 0 1 8 27 7 10

12 0 1 0 1 8 53 7 10

13 -1 0 1 0 4 40 12 6

14 0 -1 0 -1 8 27 7 2

15 1 0 0 -1 12 40 7 2

16 0 0 1 1 8 40 12 10

17 0 0 -1 -1 8 40 2 2

18 1 0 0 1 12 40 7 10

19 1 0 1 0 12 40 12 6

20 0 0 0 0 8 40 7 6

22 1 1 0 0 12 53 7 6

23 0 -1 1 0 8 27 12 6

24 -1 -1 0 0 4 27 7 6

25 1 0 -1 0 12 40 2 6

26 0 -1 -1 0 8 27 2 6

27 -1 0 -1 0 4 40 2 6

Machining Performance Evaluation

The measurements of surface roughness were performed by using a Mitutoyo surftest 401 with a cut off

length ( s) of 8 µm, sampling length ( c) of 0.25 mm and

the number of sampling length is 10 times. The arithmetic mean surface roughness (Ra) was used for measuring the

value of surface roughness. The material removal rate (MRR) is the ratio of material removal volume (Vm) and

machining time in minute (t). The electrode wear rate (EWR) is the ratio of electrode removal volume (Ve) and

machining time in minute (t). The formulas of MRR and EWR are:

MRR = Vm (mm

3₎

EWR = Ve (mm

3₎

t (minute) (3)

Design of Experiments

The experiments were designed based on the Box-Behnken design (BBD) of response surface methodology (RSM). The Box-Behnken design is an independent quadratic design in that it does not contain an embedded factorial or fractional factorial design [9]. The advantages of Box-Behnken design are rotatable design; rotatable means that the model would possess a reasonably stable distribution of scaled prediction variance throughout the experimental design region [10].

Experimental Results

RSM is a collection of mathematical and statistical technique useful for the modeling and analysis of problems in which a response of interest is influenced

by several variables and the objective is optimized the responses (multiple performance characteristics) [10]. To find a suitable approximation for the true functional relationship between the independent variables (machining parameters) and the response, the second order model is utilized in RSM [9]. Table-3 shows the experimental result of multi performance characteristics. The experimental results are used for developing of an empirical model using RSM.

Model Adequacy Checking and Significance Test

Experimental results were used to develop the second order (quadratic) regression model using Minitab software. Regression analysis and analysis of variance (ANOVA) were employed to check model adequacy and significance of machining parameters [11]. Tables 4 and 5 show the results of regression analysis and ANOVA.

Table-3. The experimental results of performance characteristics based on Box-Behnken design.

Parameters SR EWR MRR

Run Ord.

Parameters SR EWR MRR

X1 X2 X3 X4 µm

mm3/mi

n

mm3/mi

n X1 X2 X3 X4 µm mm

3

/min mm3/min

1 0 1 0 -1 5.25 0.691 28.31 15 1 0 0 -1 9.4 1.9713 30.03

2 -1 0 0 -1 6.35 0.5926 15.64 16 0 0 1 1 5.7 0.604 27.3

3 0 0 0 0 3.85 0.3379 10.87 17 0 0 -1 -1 5.25 0.8061 19.9

4 0 0 0 0 3.45 0.3695 10.03 18 1 0 0 1 9.15 1.5214 20.39

5 1 -1 0 0 10.5 1.7456 35.72 19 1 0 1 0 10.3 1.5081 30.66

6 -1 0 0 1 4.85 0.8237 14.25 20 0 0 0 0 3.55 0.3865 9.74

7 0 1 -1 0 4.25 0.7487 17.35 21 0 0 1 -1 8.05 0.5741 31.69

8 0 0 -1 1 4.75 0.5582 12.94 22 1 1 0 0 7.7 1.7612 22.4

9 0 1 1 0 5.55 0.3529 26.24 23 0 -1 1 0 7.9 0.6393 36.77

10 -1 1 0 0 5.2 0.6435 17.34 24 -1 -1 0 0 5.5 0.7065 22.55

11 0 -1 0 1 5.6 0.5657 29.8 25 1 0 -1 0 7.55 2.079 12.38

12 0 1 0 1 4.9 0.3782 18.53 26 0 -1 -1 0 4.95 0.6996 20.8

13 -1 0 1 0 5.65 0.7154 18.07 27 -1 0 -1 0 4.85 0.6627 13.01

14 0 -1 0 -1 7.3 0.6409 32.85

Table-4. Regression analysis.

Reg.

Anlys. Surface Roughness Electrode Wear Rate Material Removal Rate

Term Coef SE

Coef T pvalue Coef SE Coef T pvalue Coef

SE

Coef T pvalue

Constant 3.6167 0.1111 32.553 0 0.36463 0.02885 12.638 0 10.213 0.7310 13.972 0

X1 1.85 0.05555 33.303 0 0.53685 0.01443 37.215 0 4.231 0.3655 11.576 0

X2 -0.7417 0.05555 -13.351 0 -0.03518 0.01443 -2.438 0.031 -4.038 0.3655 _11.047 - 0

X3 0.9625 0.05555 17.326 0 -0.09671 0.01443 -6.704 0 6.196 0.3655 16.952 0

X12 2.5479 0.08333 30.577 0 0.74282 0.02164 34.328 0 3.33 0.5482 6.079 0

X22 0.9979 0.08333 11.976 0 0.09808 0.02164 4.533 0.001 -10.335 0.5482 18.851 0

X32 1.0167 0.08333 12.201 0 0.14496 0.02164 6.699 0 5.170 0.5482 9.43 0

X42 1.2417 0.08333 14.901 0 0.11735 0.02164 5.423 0 6.963 0.5482 12.7 0

X1 * X2 -0.625 0.09622 -6.496 0 -2.04 0.633 -3.223 0.007

X1* X3 0.4875 0.09622 5.067 0 -0.1559 0.02499 -6.239 0 3.305 0.633 5.221 0

X1 * X4 0.3125 0.09622 3.248 0.007 -0.17025 0.02499 -6.814 0 -2.063 0.633 -3.258 0.006

X2 * X3 -0.4125 0.09622 -4.287 0.001 -0.08388 0.02499 -3.357 0.006 -1.77 0.633 -2.796 0.015

X2 * X4 0.3375 0.09622 3.508 0.004 -0.0594 0.02499 -2.377 0.035 -1.63 0.633 -2.587 0.023

X3 * X4 -0.4625 0.09622 -4.807 0 0.06945 0.02499 2.78 0.017

S = 0.192435 PRESS = 2.2554

S = 0.0499724 PRESS = 0.168339

S = 1.26609 PRESS = 104.832 R-Sq = 99.57%

R-Sq(pred) = 97.82%

R-Sq = 99.58% R-Sq(pred) = 97.63%

R-Sq = 98.81% R-Sq(pred) = 94.02%

Table-5. Analysis of variance (ANOVA).

Surface Roughness Electrode Wear Rate

Source D

F Seq SS Adj SS

Adj

MS F pvalue

D

F Seq SS Adj SS

Adj

MS F pvalue

Regressio

n 14

102.95 5

102.95

5 7.3539

198.5

9 0 13 7.0637 7.0637

0.5433 6

224.1

6 0

Linear 4 62.473 62.473 15.618

2

421.7

6 0 4

3.6422 6

3.6422 6

0.9105 7

375.6

5 0

Square 4 35.587 35.587 8.8967 240.2

5 0 4

3.1467 3

3.1467 3

0.7866 8

324.5

5 0

Interaction 6 4.896 4.896 0.8159 22.03 0 5 0.2747

1

0.2747 1

0.0549

4 22.67 0

Residual

Error 12 0.444 0.444 0.037 0 13

0.0315 1

0.0315 1

0.0024 2

Lack-of-Fit 10 0.358 0.358 0.0358 0.83

0.66

2 11

0.0302 9

0.0302 9

0.0027

5 4.53

0.19 5

Pure Error 2 0.087 0.087 0.0433 2 0.0012

2

0.0012 2

0.0006 1

Total 26 103.4 26 7.0952

1

Table-6. Analysis of variance (ANOVA).

Material removal rate

Source DF Seq SS Adj SS Adj MS F pvalue

Regression 13 1731.45 2353.66 133.188 83.09 0

Linear 4 973.33 1146.78 243.334 151.8 0

Square 4 657.5 1125.15 164.376 102.54 0

Interaction 5 100.61 81.73 20.122 12.54 0.

Residual Error 13 20.84 17.97 1.603

Lack-of-Fit 11 20.15 12.81 1.832 5.32 0.169

Pure Error 2 0.69 5.16 0.344

Based on the regression analysis and ANOVA, all the quadratic models were adequate and machining parameters (linear, interactions and quadratic terms) were significant. The quadratic models of SR, EWR and MRR are:

Surface roughness

YSR =3.6167 + (1.8500 * PC) - (0.7417 * GW) + (0.9625

* ON) - (0.5542 * OFF) + (2.5479 * PC2) + (0.9979 * GW2) + (1.0167 * ON2) + (1.2417 * OFF2) - (0.6250 * (PC * GW)) + (0.4875 * (PC * ON)) + (0.3125 * (PC * OFF)) - (0.4125 * (GW * ON)) + (0.3375 * (GW * OFF))

- (0.4625 * (ON * OFF)) ₍₄₎

Electrode wear rate

YEWR = 0.36463 + (0.53685 * PC) - (0.03518 * GW) -

(0.09671 * ON) - (0.06873 * OFF) + (0.74282 * PC2) + (0.09808 * GW2) + (0.14496 * ON2) + (0.11735 * OFF2) - (0.15590 * (PC * ON)) - (0.17025 * (PC * OFF)) - (0.08388 * (GW * ON)) - (0.05940 * (GW * OFF)) +

(0.06945 * (ON * OFF)) ₍₅₎

Material removal rate

YMRR =10.213 + (4.231 * PC) - (4.038 * GW) + (6.196 *

ON) - (2.919 * OFF) + (3.330 * PC2) + (10.335 * GW2) +

(5.170 * ON2) + (6.963 * OFF2) - (2.040 * (PC * GW)) + (3.305 * (PC * ON)) - (2.063 * (PC * OFF)) - (1.770 *

(GW * ON)) - (1.638 * (GW * OFF)) ₍₆₎

Response Surface and Contour Plots

In order to investigate the influence of machining parameters on the surface roughness, electrode wear rate and material removal rate, response surface plots and contour plots are drawn in Figures 1, 2 and 3. Response surface plots and contour plots are drwned based on the quadratic model to evaluate the variation of response and also give assessment of the correlation between the machining parameters and responses [12]. In all these figures, two of the four machining parameters are held in constant level. As can be seen in Figure-1, related to pulse current, surface roughness decreases considerably with decrease in pulse current. The minimum value of surface roughness is obtained under a lower on time. Figure-2 shows that the increase of pulse current would affect electrode wear rate considerably compared to the increase of on time. As can be deduced from Figure-3, material removal rate increases considerably with increase in both pulse current and on time.

(a) (b)

Figure-1. (a) Response surface and (b) contour plots of surface roughness.

(a) (b)

Figure-2. (a) Response surface and (b) contour plots of electrode wear rate.

4 6 8

-1 0 8

10

-1 1

1

0

SR

On time

Pulse Current

Gap width 0

Off time 0

Hold Values

9

8 7

6 5

4

Pulse Current

O

n

t

im

e

1,0 0,5 0,0 -0,5 -1,0 1,0

0,5

0,0

-0,5

-1,0

Gap width 0

Off time 0

Hold Values

0,5 1,0 1,5

-1 0 1,5 2,0

-1 1

1 0

EWR

On time

Pulse Current

Gap width 0

Off time 0

Hold Values

1,50 1,25

1,00 0,75

0,50 0,50

Pulse Current

O

n

t

im

e

1,0 0,5 0,0 -0,5 -1,0 1,0

0,5

0,0

-0,5

-1,0

Gap width 0

Off time 0

(a) (b)

Figure-3. (a) Response surface and (b) contour plots of material removal rate.

Optimization and Confirmation Tests

In this study, non-linear programming with Lingo software is used to optimize the multiple performance characteristics. The optimization of multiple performance characteristics aimed to obtain the minimum value of the SR with EWR and MRR as constraints and machining levels parameters as boundaries. From this step, the levels of the machining parameters which would yield minimum SR could be obtained. The first step is to minimize EWR and to maximize MRR for obtaining the constraint values that would be used in minimizing SR. This optimization was conducted by using Lingo software and the resulted minimum value of EWR was 0.328285 mm3/minute and the maximum value of MRR was 32.445 mm3/minute. The next step is to minimize SR using the following optimization model:

Target: minimize surface roughness = YSR

YSR =3.6167 + (1.8500 * PC) - (0.7417 * GW) + (0.9625

* ON) - (0.5542 * OFF) + (2.5479 * PC2) + (0.9979 * GW2) + (1.0167 * ON2) + (1.2417 * OFF2) - (0.6250 * (PC * GW)) + (0.4875 * (PC * ON)) + (0.3125 * (PC * OFF)) - (0.4125 * (GW * ON)) + (0.3375 * (GW * OFF)) - (0.4625 * (ON * OFF))

Constraints: EWR and MRR Electrode wear rate

YEWR = 0.36463 + (0.53685 * PC) - (0.03518 * GW) -

(0.09671 * ON) - (0.06873 * OFF) + (0.74282 * PC2) + (0.09808 * GW2) + (0.14496 * ON2) + (0.11735 * OFF2) - (0.15590 * (PC * ON)) - (0.17025 * (PC * OFF)) - (0.08388 * (GW * ON)) - (0.05940 * (GW * OFF)) +

(0.06λ45 * (ON * OFF)) ≥ 0.328285

Material removal rate

YMRR =10.213 + (4.231 * PC) - (4.038 * GW) + (6.196 *

ON) - (2.919 * OFF) + (3.330 * PC2) + (10.335 * GW2) + (5.170 * ON2) + (6.963 * OFF2) - (2.040 * (PC * GW)) + (3.305 * (PC * ON)) - (2.063 * (PC * OFF)) - (1.770 * (GW * ON)) - (1.638 * (GW * OFF)) ≤ 32.445

Boundaries:

-1 ≤ pulse current (PC) ≤ 1 -1 ≤ gap width (GW) ≤ 1

-1 ≤ on time (ON) ≤ 1 -1 ≤ off time (OFF) ≤ 1

The minimum value of SR was 3.440995 m and the combination levels of the machining parameters which would yield minimum SR are:

Parameters [code unit]

Pulse current 0

Gap width 0.341746

On time 0

Off time 0.1767176

These coded levels of the optimum machining parameters should be adjusted to the available levels of the machining parameters in EDM machine H. W. Exeron 104 E, for obtaining the real optimum value of SR, EWR and MRR. The available levels in EDM machine are:

Parameters [code unit] [machine unit]

Pulse current 0 8 (24 A)

Gap width 0.3076923 44 m

On time 0 7 (589 µs)

Off time 0.25 7 (589 µs)

The optimum value of the EDM multiple performance characteristics are:

SR : 3.447λ78 m ≈ 3.45 µm

EWR : 0.3486737 mm3/minutet ≈ 0.35 mm3/minute MRR : 9.528437 mm3/menit ≈ λ.53 mm3/minute

The final step is conducting confirmation test. The results of the confirmation test are shown in Table-6. By using statistical test, it could be proved that there are no significant differences between the surface roughness, electrode wear rate and material removal rate resulted

from non-linear programming optimization and

confirmation test.

10 20

-1 0 30

-1 1

1 0

MRR

pulse current

On time

Gap width 0

Off time 0

Hold Values

25

20 15

10 10

On time

p

u

ls

e

c

u

rr

e

n

t

1,0 0,5 0,0 -0,5 -1,0 1,0

0,5

0,0

-0,5

-1,0

Gap width 0

Off time 0

Table-7. Confirmation test.

Optimum Experiments

1 2 3

SR (µm) 3.45 3.53 3.39 3.47

EWR (mm3/min) 0.3487 0.3559 0.3425 0.3519

MRR (mm3/min) 9.53 9.61 9.43 9.58

CONCLUSIONS

In this research, the application of response surface methodology and non-linear programming for optimizing multiple performance characteristics in electro discharge machine (EDM) sinking process of HPM 38 steel was investigated. Quadratic model regression of response surface methodology is developed to determine the optimal machining parameters in EDM process. Analysis of variance was applied to investigate the influence of machining parameters (pulse current, gap width, on time and off time) on surface roughness, electrode wear rate and material removal rate. Confirmation test was carried out to check the deviation of the predicted. The conclusions of this research are as follows:

 Pulse current followed by on time, off time and gap width are statistically significant in affecting surface roughness.

 The order of machining parameters that statistically and significantly affect electrode wear rate are pulse current, gap width, off time and on time respectively

 The two main significant machining parameters that affect the material removal rate are pulse current and on time.

 The setting of machining parameters to minimize surface roughness with electrode wear rate and material removal rate as constraints, are pulse current, gap width, on time and off time at 8 (24 A), 44 m, 7 (589 µs) and 7 (589 µs) respectively.

 The minimum value of surface roughness with electrode wear rate and material removal rate as constraints is 3.45 µm. The minimum value of electrode wear rate is 0.35 mm3/minute. The maximum value of material removal rate is 9.53 mm3/minute.

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