 Open Access
 Total Downloads : 4
 Authors : Naveenkumara, Vengatesha, Nexon Brissaca, Madhanrajb
 Paper ID : IJERTCONV3IS22038
 Volume & Issue : NCEASE – 2015 (Volume 3 – Issue 22)
 Published (First Online): 24042018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Mathematical Modelling and Optimization of Electro CoDeposition Process Parameters Using Response Surface Methodology and Genetic Algorithm
1.NaveenKumara,2.Vengatesha, 3.Nexon Brissaca, 4.MadhanRajb
a Student, Department of Mechanical Engineering, Christ College Of Engineering and Technology, Moolakulam, Pondicherry 605 010.
bAssistant Professor, Department of Mechanical Engineering, Christ College Of Engineering and Technology, Moolakulam, Pondicherry 605 010.
Abstract: The Process electro codeposition is a ceramic matrix composites processing method having ability to coat nonmetallic ceramic particles in the substrate along with metals. The mathematical modelling of responses of a process helps us to predict the process and further used as the objective functions for optimization.
In this paper, Response Surface Methodology is used for making empirical relation for each response by taking Current Density, W/L of SiC Added and Voltage as a governing parameters. The responses were analysed and discussed by ANOVA and Surface Plots. The wear rate for micro DC and micro PC is optimized as 4.78580E9 and 2.13633E9 using Genetic Algorithm. The optimized wear rates are found to be approximate to actual value. The Actual value and the Predicted Value are compared.

INTRODUCTION
Electro codeposition is a chemical process in which atoms of metallic materials will be deposited on the surface of another material along with the nonmetallic (ceramic) atoms in the electrolytic bath. In this process one of the materials is taken as anode and other as cathode. And this works by the principle of faradayss law of electrolysis. This method is more advantageous than conventional electroplating process, because by electro codeposition method we can make nonmetallic atoms to be deposited on the substrate.
RSM is a collection of mathematical and statistical techniques that are useful for the modelling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response. RSM also quantifies relationships among one or more measured responses and the vital input factors. The Design Expert version7 software was used to develop the experimental plan for RSM. The same software was also used to analyse data collected.
Genetic algorithm(GA) is a nonconventional optimization method which is based on the darwins theory of survival of the fittest. The biological terms like genes, chromosomes were used to represent the values of the parameters. Using GA we can solve constrained and unconstrained optimization problems to find the maximum or minimum of an objective function. The solution converges or diverges by repeatedly modifies a population of individual solution. The GA is applicable to solve
variety of optimization problems that are not well suited for standard optimization algorithms, including problems in which the objective function is discontinuous, non differentiable, stochastic or highly nonlinear

MATHEMATICAL MODELLING
There are many methods to plan and design an experiment. Response Surface Methods are design and models for working with continuous treatments when finding optima or describing the response is the goal.
RSM is an important subject in the statistical design which is a collection of mathematical and statistical techniques used to model and analyze a problem in which
response is influenced by several input variables and the objective is to optimize this response.
The second order polynomial regression equation is to fit the non linear curve. The equation contains interaction of the variables and the square of them.
The second order equation is represented as
follows:
Composite Method Design Matrix is used for all the Experiments. The Experiments are,

Micro SiC DC Supply

Micro SiC PC Supply
The parameters are almost same only differences are the Type of Current Supplied (DC or PC) and the Size of the SiC Particle Supplied in the Bath.
Y = b
+ b x + b x 2 + b x x
Table 1 Important Codeposition process parameters
0 i i
ii i
ij i j (a)
Factors
Unit
Variable s
2
1
0
1
2
Current Density (DC/PC)
A/dm
2
A
0.5
1
1.5
2
2.5
W/L of SiC (Micro)
%W/ L
B
0
5
10
15
20
Voltage
Volts
C
0.5
1
1.5
2
2.5
Factors
Unit
Variable s
2
1
0
1
2
Current Density (DC/PC)
A/dm
2
A
0.5
1
1.5
2
2.5
W/L of SiC (Micro)
%W/ L
B
0
5
10
15
20
Voltage
Volts
C
0.5
1
1.5
2
2.5
In this paper, mathematical model were developed and optimized the parameters to find the operating condition to get minimum wear rate. This analysis has three dependent such as %Wt of SiC incorporation in the coating, Specific Wear Rate and Wear Coefficient are related to the three independent variables Current Density, W/L of SiC and Voltage.
Responses = b
+ b (A) + b (B) + b (C) + b
(A2)
0 1 2 3 11
+ b22(B2) + b33(C2) + b12(AB) + b13(AC)+b23(BC) (b)
The second order polynomial Equations were developed using DESIGN EXPERT – 7 software for the prediction of %Wt of SiC incorporation in the coating, Specific Wear Rate and Wear Coefficient in terms of three independent variables.
A Current Density
B W/L of SiC supplied C Voltage
The Regressions equations are created for the two different experiments values, since the input and output parameters are same for these experiments the same Central composite design can be used.
Table 2 Experimental design matrix and respones

MicroSiC for DC supply
The current supply to the electrolyte bath is Direct current and the experimental values are taken from the Literature [1]. The responses are obtained for varying current and amount of SiC in Electrolyte bath. The voltage also changed during experiment.

MicroSiC for PC supply
In this experiment method every parameters are same as in the microSiC for DC supply except the type of current . The Pules Current is supplied during the deposition process. Other parameters like W/L added and Voltage are maintained unchanged.
Voltag e
Micro DC
Micro PC
Current Densit y
W/ L of SiC
Voltag e
%Wt of SiC incorpo ration in the coating
Specific Wear Rate
Wear Co efficient
Current Densit y
W/ L of SiC
%Wt of SiC incorpor ation in the coating
Specific Wear Rate
Wear Co efficient
1
1
1
27.31
5.06E09
2.86E07
1
1
1
30.23
3.01E09
2.45E07
1
1
1
22.41
5.72E09
3.43E07
1
1
1
24.78
4.34E09
3.23E07
1
1
1
24.56
5.15E09
3.12E07
1
1
1
27.01
4.12E09
3.01E07
0
0
0
22.38
8.58E09
5.43E07
0
0
0
25.12
6.55E09
5.12 E07
2
0
0
16.35
1.74E08
1.45E06
2
0
0
18.95
1.43E08
1.99E06
1
1
1
18.27
1.20E08
8.51E07
1
1
1
19.79
1.10E08
8.23E07
0
0
0
22.38
8.58E09
5.43E07
0
0
0
25.12
6.55E09
5.12E07
0
0
0
22.38
8.58E09
5.43E07
0
0
0
25.12
6.55E09
5.12E07
0
0
0
22.39
8.69E09
5.92E07
0
0
0
25.11
6.25E09
4.98E07
1
1
1
19.21
1.14E08
7.72E07
1
1
1
22.44
1.00E08
7.00E07
0
2
0
0
2.23E08
2.03E06
0
2
0
0
1.28E08
1.12E06
1
1
1
19.5
1.23E08
8.86E07
1
1
1
22.21
1.12E08
8.56E07
0
0
0
22.39
8.69E09
5.92E07
0
0
0
25.12
6.55E09
5.12E07
0
2
0
30.24
8.58E09
2.03E06
0
2
0
32.34
6.32E09
4.01E07
2
0
0
16.3
1.54E08
9.25E07
2
0
0
18.61
1.21E08
9.01E07
0
0
2
21.28
1.01E08
6.00E07
0
0
2
23.23
1.00E08
5.97E07
1
1
1
20.72
1.08E08
7.10E07
1
1
1
22.87
1.01E08
7.43E07
0
0
2
25.54
6.86E09
2.57E07
0
0
2
27.32
5.83E09
2.34E07
0
0
0
22.37
8.47E09
5.01E07
0
0
0
25.13
6.65E09
5.45E07
1
1
1
29.97
4.56E09
2.73E07
1
1
1
30.98
3.52E09
2.45E07


DEVELOPING EMPIRICAL RELATION
The %W/T of SiC incorporated in the substrate, Wear rate and Wear coefficient are the responses. For this responses the second order polynomial regression equation were created in terms of Current Density(A), W/L of SiC Added in electrolyte(B) and Voltage(C) to predict. The empirical relation for coded values are shown below for microSiC DC and PC supply.

For MicroSiC DC supply
%W/L of SiC incorp=+23.00+0.52*A+5.44*B+0.74*C+1.56*A*B+0.57
*A*C0.28*B*C1.20*A21.50*B2+0.57*C2 (c)
WearRate=+7.884E009+2.974E010*A3.353E009*B 4.174E010*C4.118E010*A*B2.122E
011*A*C+3.963E011*B*C+1.615E009*A2+1.367E
009*B23.719E010*C2(d)
Wear Coefficient=+4.547E007+7.561E008*A1.254E 007*B4.345E008*C4.398E008*A*B+6.783E
009*A*C+5.628E009*B*C+1.159E007*A2+3.275E
007*B27.382E008*C2 (e)

For MicroSiC PC supply
%W/LofSiCincorp=+25.79+0.42*A+5.65*B+0.60*C+1.59
*A* B+0.62*A*C0.54*B*C1.25*A21.90*B2+0.38* C2
(f)
WearRate =+6.131E009+2.870E010*A2.519E 009*B4.546E010*C5.035E010*A*B+5.207E
011*A*C+5.142E011*B*C+1.479E009*A2+5.705E
010*B2+1.552E010*C2 (g)
WearCoefficient =+4.688E007+1.436E007*A2.159E 007*B3.926E008*C4.617E008*A*B4.034E
009*A*C6.759E009*B*C+2.103E007*A2+3.868E
008*B24.818E008*C2 (h)
The above equations are obtained at 95% confidence level and Central composite design is used to obtain the coefficients


OPTIMIZATION BY GENETIC ALGORITHM The Genetic Algorithm is a nonconventional
search and optimization method based on natural selection
mechanics. The genetic algorithm is ease in operation, global perspective and it can solve problems which are difficult to solve in conventional methods.
The Genetic Algorithm parameters are: Population Size = 100, Selection operator = Roulette Method, Crossover operator = Single point operator, Crossover Probability =0.9, length of chromosome = 90 and fitness parameter = Wear rate.
The objective function is the form of:
Wear Rate = f (Current Density, W/L of SiC added, Voltage)
The constraints are: Current Density 0.5 2.5 W/L of SiC Added 0 20 Voltage 0.5 2.5
The optimization is carried out in the MATLAB software using GA tool. The objective function for wear rate is taken from the empirical relation developed through RSM in this previous work. The optimization is done for the wear rate of both DC supply and PC supply.
The Fitness value and generation plot is plotted while optimizing and the solution converges at around
50thGeneration. Before this many local minima are reached and the average distance of the population decrease with the increase in the generation.

RESULTS AND DISCUSSION

MicroSiC for DC supply
Fig. 1.Surface Plo for Wear Rate
The Surface Plot for the wear rate of micro SiC under DC supply is shown in Fig. 1. This plot indicates that the wear rate is minimum for the maximum deposition of the SiC (15% addition) on the substrate and the respective current range is also found as around 1.50. The voltage factor is set to 1.50. It is inferred that wear rate is maximum for the minimum amount of SiCadded in the bath even though the current supply is maximum(2.0).
Fig. 2.Surface Plot for W/L of SiC Incorporated
The surface plot for the SiC incorporation for the microSiC DC supply in Fig.2.shows that the deposition of the SiC on the substrate is maximum at the 15% of SiC added and 2A/dm2 of Current. The amount of SiC deposited is 30.24. And the minimum deposition is attained at minimum addition of SiC(5%) on the bath and the minimum current supply(1A/dm2). The plot also shows that the deposition of the SiC on the substrate increases
linearly proportional to the increase in the SiC addition in the bath and the current supply.

MicroSiC for PC supply
Fig. 5. Surface Plot for Wear Rate
This surface plot in Fig.5.is for the wear rate of the substrate obtained by microSiC for PC supply in the bath. The wear rate is minimum at 15% of SiC addition in the bath and the respective current supply is around 1.52A/dm2. At 5% of SiC the wear rate is maximum at both 1A/dm2 and 2A/dm2. At the center of the surface plotthe wear rate is 1.21102E008 where the SiC added is 10% and the current supply is 1.5A/dm2.
Fig. 6. Surface Plot for W/L of SiC Incorporated
The surface plot for the SiC incorporated in microSiC for PC supply in Fig.6. shows that the SiC deposition is maximum at 15% of SiC added in the bath and 2A/dm2 of current supply. The SiC deposition in the substrate increases linearly as the increase in the current and SiC addition in the bath. It is also found the deposition of SiC on the substrate is minimum at 1A/dm2 even though the SiC addition in bath is maximum(15%). So that the SiC addition and current should be mutually increased to get maximum deposition and hence to minimize the wear rate.

Genetic Algorithm optimization
The optimized input parameters range are used to calculate the respective Incorporation of SiC on the substrate by substituting the optimized Current density,, %W/L of SiC added and Voltage values in the
%W/L of SiC incorporated empirical relation developed through RSM. Both the Wear Rate and the respective incorporation of SiC obtained by mathematical method are approximate with the experimental value.


CONCLUSION

Empirical relation are developed to predict the
%W/L of SiC deposited in the substrate, Wear rate and Wear coefficient for both DC and PC supply.

Surface Plots were developed to study the responses with respect to the governing parameter.

It is found that PC supply produces optimum SiC deposition and also has minimum wear than DC supply.

The wear rate is optimized by GA and found that PC has minimum wear rate.

The predicted values of the governing parameters are in good agreement with the experimental values.
REFERENCES

PradeepDevaneyan S, T.Senthilvelan, An Experimental Study of the Effect of Nickel with SiCCodeposited on Aluminium 7075 under Direct Current and Pulse Current, International Journal of Composite Materials 2014,4(5)

D.C.Montgomery, Design and Analysis of Experiments, 4th ed., Wiley, New York, 1997.

G.MAHENDRAN, V.BALASUBRAMANIAN, T.SENTHILVELAN, Influences of diffusion bonding process parameters on bond characteristics of MgCu dissimilar joints, Trans. Nonferrous Met. Soc. China 20(2010) 9971005.

M.Y.Noordin, V.C.Venkatesh, S.Sharif, S.Elting, A.Abdullah, Application of response surface methodology in describing the performance of coated carbide tools when turning AISI 1045 steel, Journal of Materials Processing Technology 145 (2004) 4658.

G.Padmanaban,V.Balasubramanian, Optimization of laser beam welding process parameters to attain maximum tensile strength in AZ31B magnesium alloy.