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26-02-2011, 12:33 PM

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Optimization of operating parameters is an important step in machining, particularly for operating unconventional machining procedure like Wire EDM .The economy of machining mainly depends on the machining parameters. Optimization of machining parameters is an important step and has been dealt by many researchers. In this paper Genetic algorithm (GA), Simulated annealing (SA) and Continuous Ants Colony algorithm (CACO) based optimization procedures have been developed to optimize machining parameters viz. pulse on time, pulse off time, peak current, wire feed rate and machining speed. The Objective functions considered for the optimization of cutting parameters are viz. maximization of Metal Removal Rate (MRR) and minimization of surface roughness . This paper deals with the employment of CACO for optimization process and the results are compared with other algorithms.
KEYWORDS: WEDM, GA, SA, CACO. Machining parameters, MRR, surface finish.
1. Introduction
The tool nd die making industry has always been faced with an increasing demand for precision and accuracy. The necessity to machine hard materials, complex shapes and contours which are difficult by conventional methods has created the need for Wire Electro Discharge Machine (WEDM).
Wire electrical discharge machining involves complex physical process including heating and cooling. The electrical discharge energy, affected by the spark plasma intensity and the discharging time, will determine the crater size, which in turn will influence the machining efficiency and surface quality [1 – 3]. Hence, the operating parameters including pulse on time, pulse off time, table feed rate, flushing pressure, wire tension, wire velocity etc. should be chosen properly so that a better performance can be obtained. However, the selection of appropriate machining parameters for WEDM is difficult and the operation has more role to play.
Scott, Boyina and Rajurkar [4] used a factorial design method to determine the optimal combination of control parameters in WEDM, the measures of machining parameter being the metal removal rate and the surface finish
By means of regression analysis, mathematical models relating the machining performance are established [5] Based on the mathematical models developed the objective functions are obtained. A feed forward neural network has been used to associate the cutting parameters with the cutting performance [6]. A simulated annealing algorithm is then applied to the neural network for solving the optimal cutting parameters based on a performance index within the allowable working conditions.
A CAD/CAM mathematical model has been proposed to design ruled surfaces for wire cut electrical discharge machining [7]. The trend of variation of the geometrical inaccuracy caused due to wire lag with various machine control parameters has been established [8]. Taguchi method is used to find the optimal parametric settings for the different machining conditions.
The methods discussed above for the optimization of cutting parameters uses traditional approaches. In this work non-traditional optimization techniques are used. Genetic algorithm a powerful tool for the optimization of engineering design problems and the methodology is explained [9 – 10]. Considering the drawbacks of traditional optimization techniques an attempt has been made to determine the optimal machining parameters for machining of a continuous finished profile from bar stock using GA & SA is being presented [11].
The SA algorithm and the physical analogy on which it is based are discussed [12]. An overview of implementation & choices facing the user of this method is presented. The steps involved and the implementation of Ants colony optimization algorithm in engineering applications is presented [13 – 14]. Manna et [15] al has discussed about optimization design of parameters for EDM using Taguchi and ANOVA.
2. Problem Formulation
The formulation of an optimization problem begins with identifying the underlying design variables, which are primarily varied during the optimization process. In this paper machining speed, pulse on time, pulse off time and peak current are considered as design variables.
2.1 Machining Model
With reference to [5] by using regression and correlation analysis, the mathematical models are obtained for mild steel specimens. Evidence shows that the mathematical models derived by the regression analysis are sufficiently precise to present the real machining performance. The objective functions for metal removal rate and surface roughness are obtained based on the mathematical models. The cutting parameters considered for optimization in this work are given below and their ranges are given in table 2.1
(A) Machining speed
(B) Pulse on time
© Pulse off time
(D) Peak current
(E) Wire feed rate
The objective of this model is to minimize the surface roughness and maximize the material removal rate. The formulae for calculating the surface roughness and material removal rate is given by
2.1.1 Response equation for surface roughness
Ra = 1.6592 + 0.687 [A – 1.375] [1 – 4.07 (D – 3.5)
- 0.0061 [C – 20] + 0.0374 [((D – 3.5) 2 / 0.25) – (8/12)]

For Ra , out of five input cutting parameters, only three parameters namely machining speed, pulse off time, and peak current are significant in surface roughness.
2.1.2 Response equation for MRR
MRR = 1.6184 – 0.0404 {[(A – 1.375) 2/0.01] – (8/12)}
- 0.0138 (B – 20)-0.0465 {[(D – 3.5) 2/0.25] – (8/12)}
For MRR, out of five input cutting parameters, only three parameters namely machining speed, pulse on time, and peak current are significant in material removal rate.
2.2 Machining Constraints
The constraints represent some functional relationship among the design variables and other design satisfying certain physical phenomenon and certain resource are greater than or equal to, a resource value. In this paper, work piece material and material thickness are considered as constraints.
3. Solution Methodology
The natural metaphor on which ant algorithms are based is that of the ant colonies. Ants could establish the shortest route from their nests to the food source and back. And therefore, ant colony algorithms suited really very well for solving Traveling Salesman Problem . Many authors have been trying to bring out the utility and advantages of genetic algorithm and simulated annealing. It is in this spirit, it is proposed to use the new evolutionary approach viz., the ant colony optimization algorithm for the machining optimization problems. This paper also compare the results of ant colony algorithm with the genetic algorithm and Simulated Annealing .
3.1 Genetic Algorithm Methodology
In this work, a standard optimization procedure has been developed using the new popular approach called Genetic Algorithm (GA) for solving wide variety of machining optimization problem. CNC wire electrical discharge machine parameters optimization is considered in this work. The quality of the solution is illustrated with suitable examples.
3.1.1 Steps in the Genetic Algorithm Method
1. Choose a coding to represent problem parameter, a selection operator, a crossover operator and a mutation operator. Choose population size N, crossover probability pc, and mutation probability pm. Initialize a random population of strings of size of size 10.
Set it =0.
2. Evaluate each string in the population.
3. If it>itmax (or) other termination criteria is satisfied, terminate.
4. Perform reproduction on the population.
5. Perform crossover on the random pairs of strings.
6. Perform bit wise mutation.
7. Evaluate strings in the new population. Set it = it + 1 and go to step 3.

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