Cutting Parameters Optimization by Using Particle Swarm Optimization (PSO)

Cutting parameters play an essential role in the economics of machining. In this paper, particle swarm optimization (PSO), a novel optimization algorithm for cutting parameters optimization (CPO), was discussed comprehensively. First, the fundamental principle of PSO was introduced; then, the algorithm for PSO application in cutting parameters optimization was developed; thirdly, cutting experiments without and with optimized cutting parameters were conducted to demonstrate the effectiveness of optimization, respectively. The results show that the machining process was improved obviously. Introduction Cutting parameters composed of cutting speed, feed rate, cutting depth and cutting width (for milling operation), have essential effects on the machining productivity and cost. The selection of cutting parameters has long depended on the skills and experience of machine tool operators or handbooks, and conservative cutting parameters are usually selected. This situation would cause significant productivity loses and lead to a costly machining operation. The determination of optimum cutting parameters is a combinatorial optimization problem and is usually realized by applying optimization algorithms. These algorithms include neural network [1], geometric programming [2], simulated annealing [3], genetic algorithm (GA) [4], particle swarm optimization (PSO)[5], etc. GA was considered as a suitable algorithm for solving any type of machining process optimization problem [6]. However, encoding and decoding operations for each individual are involved and the complexity of genetic operations will be increased when variables to be optimized are more than two. It will decrease the process efficiency greatly. PSO is discovered through simulation of the social behavior of bird flocking for food. It was used for optimization of continuous nonlinear functions. In PSO, the variables to be optimized need not to be encoded. Therefore, PSO will be more efficient when the number of variables to be optimized is more than two. Because of the convenience of realization and promising optimization ability in various problems, it has been paid more and more attention [7]. Opposite to the well-developed optimization algorithms, “PSO is still in its infancy and there are many associated problems that need further study” [8]. In this paper, CPO by using PSO will be discussed comprehensively in section 2 and section 3. In the following section, cutting experiments without and with cutting parameters optimization were conducted and analyzed. Conclusions were drawn in the last section. Particle Swarm Optimization (PSO) PSO is firstly introduced by Eberhart and Kennedy [9] and used for optimization of continuous nonlinear functions. The swarm is composed of volume-less particles with stochastic velocities, each of which represents a feasible solution. The algorithm finds the optimal solution through moving the particles in the solution space. Each particle in PSO flies in the solution space with a velocity dynamically adjusted according to its own and its companions’ flying experience. Given a swarm of N particles, the ith particle is represented as Xi=(xi1, xi2, ..., xiD) (D is the number of decision parameters of an optimum Applied Mechanics and Materials Vols. 10-12 (2008) pp 879-883 online at http://www.scientific.net © (2008) Trans Tech Publications, Switzerland Online available since 2007/Dec/06 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.34-16/04/08,09:42:55) problem). In PSO, not only the best particle among the swarm but also the best previous position for each particle needs to be recorded. The best previous position (the position giving the best fitness value) of the ith particle is represented as Pi = (pi1, pi2, ..., piD) and the best particle among the swarm is represented as Pg = (pg1, pg2, .., pgD). The rate of position change (velocity) for the ith particle is represented as Vi = (vi1, vi2, ..., viD). The particles are manipulated according to the following equation [10] id id 1 id id 2 gd id v (k+1) = w v (k)+c rand( ) (p -x (k))+c Rand( ) (p -x (k)) i (1, 2, ..., N) d (1, 2, ..., D) × × × × × ∈ ∈ (1) id id id x (k+1) = x (k)+v (k+1) (2) where w is the inertia weight. c1 and c2 are two positive constants, and rand( ) and Rand( ) are two random functions with return value in range[0, l] independently. The first part of Eq.1 is the previous velocity of the particle. The second represents the exploiting of its own experience, where c1 is the individual learning factor. And the third represents the shared information and mutual cooperation among the particles, where c2 is the social learning factor. Algorithm of Cutting Parameters Optimization by Using PSO In NC programming, generally, cutting depth and cutting width are specified firstly according to the cutting tool and the workpiece; then spindle speed and feed rate are determined, which depends much on the programmer’s experience. Therefore, spindle speed and feed rate are considered as variables to be optimized. CPO is a process to searching for the optimal solutions in the solution space within the bounds defined by practical constraints [11] by using an optimization algorithm. Fig.1 shows the framework of methodology of CPO. In Fig.1, the Given cutting parameter(s) is the parameter(s) that has been specified, such as cutting depth and cutting width. The Algorithm parameters are the initial value of parameters for the optimization algorithm, such as population size, the maximum number of iterations, etc. The Objective is a goal that the optimal cutting parameters can produce the extreme value. The Cutting database provides adequate information for the prediction of cutting force, tool-life, etc. Based-on the cutting parameters carried by each individual, the Prediction of machining performance is used to predict the machining performances so that optimal cutting parameters can be searched and evaluated. The Constraints, including power, tool-life, surface finish, etc. determines the solution space so that cutting parameters optimally determined must be limited in the bounds. The Optimization methodology is the kernel of optimization, by using which optimum cutting parameters are searched. Based-on the prediction of machining performance, the optimal cutting parameters are evaluated in the Evaluation module. The diagram of CPO by using PSO is sketched as shown in Fig.2. Optimization methodology Cutting database Constraints Given cutting parameter(s) Objective Best individual Algorithm parameters Prediction of machining performance