【文章內(nèi)容簡介】 order linear model, developed from the above functional relationship using least squares method, can be represented as follows: Y1 = Y?∈ =b0x0 +b1x1+b2x2+b3x3 +b4x4 (3) where Y1 is the estimated response based on the firstorder equation, Y is the measured surface roughness on a logarithmic scale, x0 = 1 (dummy variable), x1, x2, x3 and x4 are logarithmic transformations of cutting speed, feed rate, radial rake angle and nose radius respectively, ∈ is the experimental error and b values are the estimates of corresponding parameters. The general second order polynomial response is as given below: Y2 = Y?∈ =b0x0 +b1x1+b2x2 +b3x3+b4x4 +b12x1x2 +b23x2x3 +b14x1x4 +b24x2x4 +b13x1x3 +b34x3x4 +b11x21 +b22x22 +b33x23 +b44x24 (4) where Y2 is the estimated response based on the second order equation. The parameters, . b0, b1, b2, b3, b4, b12, b23, b14, etc. are to be estimated by the method of least squares. Validity of the selected model used for optimizing the process parameters has been tested with the help of statistical tests, such as Ftest, chi square test, etc. [10]. Optimization using geic algorithms Most of the researchers have used traditional optimization techniques for solving machining problems. The traditional methods of optimization and search do not fare well over a broad spectrum of problem domains. Traditional techniques are not efficient when the practical search space is too large. These algorithms are not robust. They are inclined to obtain a local optimal solution. Numerous constraints and number of passes make the machining optimization problem more plicated. So, it was decided to employ geic algorithms as an optimization technique. GA e under the class of nontraditional search and optimization techniques. GA are different from traditional optimization techniques in the following ways: work with a coding of the parameter set, not the parameter themselves. search from a population of points and not a single point. use information of fitness function, not derivatives or other auxiliary knowledge. use probabilistic transition rules not deterministic rules. is very likely that the expected GA solution will be the global solution. Geic algorithms (GA) form a class of adaptive heuristics based on principles derived from the dynamics of natural population geics. The searching process simulates the natural evaluation of biological creatures and turns out to be an intelligent exploitation of a random search. The mechanics of a GA is simple, involving copying of binary strings. Simplicity of operation and putational efficiency are the two main attractions of the geic algorithmic approach. The putations are carried out in three stages to get a result in one generation or iteration. The three stages are reproduction, crossover and mutation. In order to use GA to solve any problem, the variable is typically encoded into a string (binary coding) or chromosome structure which represents a possible solution to the given problem. GA begin with a population of strings (individuals) created at random. The fitness of each individual string is evaluated with respect to the given objective function. Then this initial population is operated on by three main operators – reproduction cross over and mutation – to create, hopefully, a better population. Highly fit individuals or solutions are given the opportunity to reproduce by exchanging pieces of their geic information, in the crossover procedure, with other highly fit individuals. This produces new “offspring” solutions, which share some characteristics taken from both the parents. Mutation is often applied after crossover by altering some genes (. bits) in the offspring. The offspring can either replace the whole population (generational approach) or replace less fit individuals (steady state approach). This new population is further evaluated and tested for some termination criteria. The reproductioncross over mutation evaluation cycle is repeated until the termination criteria are met. 4 Experimental details For developing models on the basis of experimental data, careful planning of experimentation is essential. The factors considered for experimentation and analysis were cutting speed, feed rate, radial rake angle and nose radius. Experimental design The design of experimentation has a major affect on the number of experiments needed. Therefore it is essential to have a well designed set of experiments. The range of values of each factor was set at three different levels, namely low, medium and high as shown in Table 1. Based on this, a total number of 81 experiments (full factorial design), each having a bination of different levels of factors, as shown in Table 2, were carried out. The variables were coded by taking into account the capacity and limiting cutting conditions of the milling machine. The coded values of variables, to be used in Eqs. 3 and 4, were obtained from the following transforming equations: where x1 is the coded value of cutting speed (S), x2 is the coded value of the feed rate ( f ), x3 is the coded value of radial rake angle(α ) and x4 is the coded value of nose radius (r). Experimentation A high precision ?Rambaudi Rammatic 500? CNC milling machine, with a vertical milling head, was used for experimentation. The control system is a CNC FIDIA12 pact. The cutting tools, used for the experimentation, were solid coated carbide end mill cutters of different radial rake angles and nose radii (WIDIA: DIA20 X FL38 X OAL 102 MM). The tools are coated with TiAlN coating. The hardness, density and transverse rupture strength are 1570 HV 30, gm/cm3 and 3800 N/mm2 respectively. AISI 1045 steel specimens of 100 75 mm and 20 mm thickness were used in the present study. All the specimens were annealed, by hold