Multicriteria Optimization of Surface Roughness Produced in Electro Chemical Machining

Multicriteria Optimization of Surface Roughness Produced in Electro Chemical Machining

1. Bishnu.M.Jha*#

2. A.Mandal*

* Deptt. of Manufacturing Engineering,NIFFT,Hatia,Ranchi, India.

#Corresponding author

Abstract Surface roughness has strong influence on functional performance of engineering components in service. A single surface texture parameter is not sufficient to analyze the functional properties of the part surface such as friction & wear or lubrication. Hence, combination of parameters is necessary to characterize the functional property of a surface. The objective of this work is to locate optimal values of process parameters for ECM namely applied potential, inter-electrode gap and machining time for low coefficient of friction in this study two cases i.e. dry and lubricated conditions have been considered. In dry case, the constraints used are maximum Sq, SHTp and minimum Ssk, Sku . For lubricated case the constraints used are minimum Sq, Ssk, SHTp and maximum Sku. It is observed that Overall Desirability Function as implemented in Design- Expert

® software together with Box-Behnken design can be used effectively for simultaneous optimization four surface roughness parameters Sq, Ssk, Sku and SHTp based on constraints referred above. The effects of ranges, weights, importance of response variables on the results have been studied.

Keywords ECM, surface roughness, multicriteria optimization, desirability function.

1. INTRODUCTION

   Electrochemical machining (ECM), a nontraditional machining process offers a number of advantages. The advantages include ability to machine very complex features in hard and difficult to machine materials with negligible tool wear, reasonable accuracy and acceptable surface finish.

   However, there are many parameters both controllable and uncontrollable that dictate the material removal rate, accuracy and surface texture. [1-12]. Functional performance of engineering components in service is strongly influenced by surface roughness [13-17] and hence, it is treated as an index of product quality. 2D parameters have been used extensively to characterize the surface roughness. However, 3D parameters or combination of different 3D/ areal parameters [14,18-22] are found to be more effective for surface characterization than a combination of 2D parameters. There are a large number of 3D surface texture parameters/ areal parameters. A single surface texture parameter is not sufficient to reflect true quality of the product [13-16, 18]. Combination of parameters is necessary to characterize the functional property of a surface. For example friction and wear has been reported to

   be influenced by surface roughness parameters such as (Ra, Rq), (Rt,Rz), Rsk, Rku, RDelA,Wa [13]. Wear is reported [15] to be larger when the initial values of the amplitude parameters Sa, Sq and SHtp as well as rms. slope SDq are high. It is reported [16] that in case of dry wear test, coefficient of friction is low when roughness is high. In lubricated case, when roughness is low, then coefficient of friction is low. It is found [16] that increase in parameter Rku led to increase in friction in lubricated case and decrease in friction in dry tests. Friction also is observed to be lower when the parameter Rsk tends to be more negative in lubricated tests.

   Based on the above reports it is decided to locate optimal process parameters for ECM namely applied potential, inter- electrode gap and machining time for low coefficient of friction for the two cases i.e. dry and lubricated conditions. The constraints used are:

   1. Dry case-maximize Sq, SHTp and minimize Ssk, Sku.

   2. Lubricated case- minimize Sq, Ssk, SHTp and maximize Sku.

   The first step is to develop mathematical models to predict the effect of process variables on surface roughness parameters- Sq, Sz, Ssk, Sku, SHtp. The models will be used to calculate the values of roughness parameters at any point in the allowable design space.

   The second step is to use these models to generate optimum levels of process parameters for minimum coefficient of friction for dry and lubricated conditions.

2. MATHEMATICAL MODEL

The mathematical models used in this work are taken from reference [23]. The essential details and truncated results are presented here. The matrix is a fifteen point Box Behnken design [24]. The fifteen experiments allowed estimation of the linear, quadratic and two-way interaction effects of the variables on the surface parameters. The actual and coded values of the different variables are listed in Table-1. The design matrix is shown in Table-2.

ECM machine model ECMAC – II, manufactured by MetaTech Industries, Pune, is used along with flat hexagon

shaped tool made of copper. Electrolyte used is KCl solution (250 grams of KCl / litre of tap water).

Table-1. The Actual and Coded Values of Different Variables

Table- 2. Design Matrix

values. The coefficients of the models developed and model statistics are given in Table 3.

Table-3:The Coefficients of the Models Developed and the Statistical Model Parameters for KCl electrolyte.

The variance for the mean estimated values can be calculated using equation (2) [25].

To validate the models further three experiments were carried out at levels different than those of design matrix. The conditions and results are given in Table 4. The confidence interval is calculated based on the equation (3).

1. Work-piece material specification:

   SG Iron: Chemical Composition:

   %C	%Si	%Mn	%S	%P
   3.60- 3.63	2.30- 2.38	0.35- 0.36	0.014- 0.013	0.083- 0.080

   Hommel Tester T-8000 is used for measuring the surface texture parameters.

   To correlate the effects of the variables and the response factor i.e. the surface roughness parameters Sq, Ssk, Sku, and SHtp the following second order polynomial is used.

   Y = Bo + B1T+ B2V +B3G+ B11T2 + B22V2 +B33G2

   +B12TV+B13TG+B23VG . . . . . . . (1)

   Where, B's are the regression coefficients. The controllable ECM parameters T, V, G and their combinations are in coded

   Where,

   .(3)

   The experimental values are within the confidence interval. Design- Expert ®[26] is used For locating the optimum levels of ECM process parameters for minimum coefficient of friction for dry and lubricated conditions. Design- Expert uses an optimization method developed by Derringer and Swich [27], as described by Meyrs,Montgomery and Anderson-Cook[28].

   Derringer and Swich [27] has developed an overall desirability function (D) by combining the quality attribute from multiple responses. For measuring single quality attribute three types of desirability functions (D) were defined. The individual desirability function di varies over the range [29].

   Table 4: Model Validation.

   	Sl.N o	1		Confidnce interval (±)	2		Confidnce interval (±)	3		Confidnce interval (±)
   ECM Parameters		cod ed	actua l		code d	act ual		co de d	act ual
   	T (min )	0.15	3.15		0.5	3.5		-1	3.5
   	V (volt )	-0.4	18		-0.2	19		0.5	19
   	G (mm )	-1	0.64		1	1.2 8		0.3 43 75	19
   From Experiments Models	Sq	4.99			4.99			8.52
   	Ssk	0.262			-0.55			-0.259
   	Sku	2.51			3.06			2.7
   	SHtp	9.08			8.58			14.8
   From Model	Sq	5.6		1.515	5.533		1.5268	9.288		1.535
   	Ssk	0.199		0.6	-0.5656		0.6043	-0.7412		0.6075
   	Sku	2.516		0.385	2.873		0.388	2.511		0.39
   	SHtp	9.26		4.11	9.55		4.14	13.909		4.165

   [29]

   1. For the response y is maximum:

(iii) The two sided desirability function:

Where, L, U, T stand for lower limit, upper limit, target or objective of the response y. r, r1 & r2 are the weights.

The overall desirability function (D) is calculated as .

The design variables are then chosen to maximize the overall desirability.

The overall desirability function as implemented in Design Expert depends on a number of factors: (i) Range of the individual parameters (ii) weights assigned to the parameters and (iii) relative importance of the parameters. Design Expert, however calculates the desirability functions from -1 to 1 limits for all the parameters. The models developed can be used for estimating the roughness parameters reliably as long as the coded values of T,V and G satisfy the relation.

For all experimental and desirability values presented here this constraint has been satisfied.

Case 1: Dry Case

Table 5. Constraints used in Dry Case

Lower Upper Lower Upper

Name Goal Limit Limit Weight Weight Importance

range

range range

Table:6 Optimized Parameters for dry case.

A:T 1

B:V 1

C:G 1

A:T 1

B:V 1

C:G 1

Sq 1

Sq Ssk Sku

Shtp

0.791698

0.994038

0.946803

0.907354

Ssk Sku

Shtp 1

Combined 2

Combined

0.906775

0.000 0.250 0.500 0.750 1.000

0.000 0.250 0.500 0.750 1.000

Fig.2.a.

Fig.1.a

0.928202

0.928202

1

D e s i r a b i l i t y

0.8

0.6

0.4

0.2

0

1 1

0.5 0.5

0 0

B: V (volt)

-0.5

-1 -1

-0.5

A: T (sec)

Fig.2.b.

Fig.1.b

range range

Table_8: Optimized Parameters for dry case with modified constraints.

Table-9: Effect of weights on the overall desirability function

(D) and the optimized parameters.

A:T 1

B:V 1

In the above case all the factors have been given equal weight. Next the effects of weights on the overall desirability function (D) and its position in the design space have been studied.

C:G

Sq

Co

1

0.000 0.250 0.500 0.750 1.000

1

D e s i r a b i l i t y

0.8

0.6

Fig.3.a

0.70774

0.70774

Table:12 Optimized Parameters for lubricaed case.

0.4

0.2

0

Table-13: of weights on the overall desirability function (D)

1

0.5

B: V (volt)

0

-0.5

-1 -1

0

-0.5

1

0.5

A: T (sec)

Fig.3.b.

Table 10. Effect of changing the importance of the parameters.

Case 2:Lubricated Case

Table 11. Constraints used in Lubricated Case.

Sq minimize 3.21333 12.375 1 1 3

Ssk minimize -1.009 0.48876 1 1 3

Sku maximize 1.7524 4.09373 1 1 3

Shtp minimize 5.31714 20.6819 1 1 3

Table-14: Effect of weights on the overall desirability function (D) and its position in the design space.

For dry case the highest value of D calculated is 0.906 when all factors have equal weight of 1 and have same importance value of three. Under the same conditions highest value of D calculated is 0.708 in lubricated case (Table 6 & 12). The ideal value of D is 1.00. In the experimental space under the constraints considered, dry case is closer to ideal condition than lubricated one. With changing limits, value of D changed appreciably (Table 7 & 13). For dry case it has improved from 0.906 to 0.952; where as in lubricated case it has decreased from 0.708 to 0.608. In case of dry, Ssk and Sku values have changed in opposite direction (Table 6 & 8). Though D value is greater in case of modified constraint but relative importance of the two parameters will decide which condition will be the best. In case of lubricated case, value of D has decreased from 0.708 to 6.08 when the constraints have been modified. Though D has decreased but, there is substantial reduction in Sq , SHTp values and a very large increase in Ssk value (Table 12 & 13). Again the relative importance of Sq, SHTP in one hand and Ssk on the other hand will decide the selection of optimum conditions.

The other interesting result is that as weights of all the parameters are increased equally (Table 9 & 14) value of D

has decreased continuously. But, there is little change in values of, Sq, Ssk, Sku and SHTp. Giving more weight to Ssk than other parameters has pulled the value of Ssk towards the absolute minimum. Under same weight of Ssk when the weights of all other parameters are increased from 2 to 3 , value of Ssk has increased slightly from -0.9446 to -0.9362

i.e. moved in reverse direction.

Changing the importance of parameter (Table 10) shows that when Ssk status is changed from (****) to (*****) keeping all other parameters at status of (**) Ssk value has changed from -0.267 to -0.93874. A very large change. However, when status of all other parameters except Ssk are changed to (***) a negligible change occurred in the value of Ssk. Between importance and weight, it is found that weight is slightly more effective in satisfying the constants than importance of parameters.

CONCLUSION

1. Overall desirability function together with Box-Behnken design can be used effectively for simultaneous optimization of several response parameters. In this study four surface roughness parameters Sq, Ssk, Sku and SHTp have been optimized based on constraints selected to minimize the coefficient of friction. The model verification results confirmed that the predictions of Box- Behnken models are reliable and hence can be used for optimization.

2. Design-Expert is used to locate the values of ECM process variables – applied potential, inter-electrode gap and machining time which will give lowest value of the functional characteristic i.e. coefficient of friction based on constraint applied to four surface roughness parameters Sq,Ssk,Sku and SHTp.

3. Highest value of D calculated for dry case is 0.9523 for the ECM process variables: time at -1 level, potential at 0.59538 level and gap at -0.76617 level.

Box-Behnken design it should be limited to spherical radius of 2. Outside this range the prediction from Box- Behnken design is not reliable.

9. The software by default selects the maximum and minimum value from the given design points. However, those values may not be the global maximum and minimum. For each response, maximum and minimum may be calculated and the constraints may be formulated suitably.

Roughness Parameter:

All parameters starting with S is 3D extension of R roughness profile parameter: for example Sq is the 3D extension of Rq

RDelA : Average Slope of the Profile. Rt : Maximum Height of Profile.

Sa: Arithmetic Mean Deviation of the Surface ,µm SDq : Root mean square gradient of the surface

Sku: Kurtosis of the Topography Height Distribution.

Sq: Root-Mean-Square (RMS) Deviation of the Surface,µm SHTp: Surface section height difference (20% – 80%)

Ssk: Skewness of the Topography Height Distribution.

Wa : Mean Value of the Waviness of the Unfiltered Profile.

Experimental Variables

T : Time of machining (minutes) V : Applied potential(volts)

G : Inter electrode gap(mm)

: Variable (T,V,G) Statistical Analysis Parameters

1. For lubricated case the highest value of D calculated is 0.708 for the ECM process variables time at 1 level, potential at -0.04 level and gap at 0.999 level.

2. As weights of all the parameters are increased equally value of D has decreased continuously. However, there is little change in values of Sq, Ssk, Sku and SHTp.

   (

   x30)

   = variance of estimated response at a point given by

   )

   = Mean Square of Residual

   = Mean estimated response at a point given by (x10, x20,

   = Confidence interval for single estimated response at a

3. Giving more weight to Ssk than others parameters has pulled the value of Ssk to towards the absolute minimum. Under same weight of Ssk when the weights of all other parameters are increased from 2 to 3 , value of Ssk has increased slightly from -0.9446 to -0.9362 i.e. moved in reverse direction. This shows the sensitivity of the optimization method.

4. Weight has slightly more effect than importance (for setting up of effective constraints :ranges, weights, importance of response variables) knowledge of relative effects of the four roughness parameters on the coefficient of friction in dry and lubricated cases are important.

5. Design Expert searches the design space of -1 to +1 for all the ECM process variables for optimization. In case of

   point given by (x10, x20, x30)

   = F ratio

   = Mean Square of Experimental Error

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