1、 1 毕业论文中英文资料外文翻译文献 附录 附录 1： 英文原文 Selection of optimum tool geometry and cutting conditions using a surface roughness prediction model for end milling Abstract Influence of tool geometry on the quality of surface produced is well known and hence any attempt to assess the performance of end milling sh
2、ould include the tool geometry. In the present work, experimental studies have been conducted to see the effect of tool geometry (radial rake angle and nose radius) and cutting conditions (cutting speed and feed rate) on the machining performance during end milling of medium carbon steel. The first
3、and second order mathematical models, in terms of machining parameters, were developed for surface roughness prediction using response surface methodology (RSM) on the basis of experimental results. The model selected for optimization has been validated with the Chi square test. The significance of
4、these parameters on surface roughness has been established with analysis of variance. An attempt has also been made to optimize the surface roughness prediction model using genetic algorithms (GA). The GA program gives minimum values of surface roughness and their respective optimal conditions. 1 In
5、troduction End milling is one of the most commonly used metal removal operations in industry because of its ability to remove material faster giving reasonably good surface quality. It is used in a variety of manufacturing industries including aerospace and automotive sectors, where quality is an im
6、portant factor in the production of slots, pockets, precision moulds and dies. Greater attention is given to dimensional accuracy and surface roughness of products by the industry these days. Moreover, surface finish influences mechanical properties such as fatigue behaviour, wear, corrosion, lubric
7、ation and electrical conductivity. Thus, measuring and characterizing surface finish can be considered for predicting machining performance. Surface finish resulting from turning operations has traditionally received considerable research attention, where as that of machining processes using multipo
8、int cutters, requires attention by researchers. As these processes involve large number of parameters, it would be 2 difficult to correlate surface finish with other parameters just by conducting experiments. Modelling helps to understand this kind of process better. Though some amount of work has b
9、een carried out to develop surface finish prediction models in the past, the effect of tool geometry has received little attention. However, the radial rake angle has a major affect on the power consumption apart from tangential and radial forces. It also influences chip curling and modifies chip fl
10、ow direction. In addition to this, researchers 1 have also observed that the nose radius plays a significant role in affecting the surface finish. Therefore the development of a good model should involve the radial rake angle and nose radius along with other relevant factors. Establishment of effici
11、ent machining parameters has been a problem that has confronted manufacturing industries for nearly a century, and is still the subject of many studies. Obtaining optimum machining parameters is of great concern in manufacturing industries, where the economy of machining operation plays a key role i
12、n the competitive market. In material removal processes, an improper selection of cutting conditions cause surfaces with high roughness and dimensional errors, and it is even possible that dynamic phenomena due to auto excited vibrations may set in 2. In view of the significant role that the milling
13、 operation plays in todays manufacturing world, there is a need to optimize the machining parameters for this operation. So, an effort has been made in this paper to see the influence of tool geometry (radial rake angle and nose radius) and cutting conditions (cutting speed and feed rate) on the sur
14、face finish produced during end milling of medium carbon steel. The experimental results of this work will be used to relate cutting speed, feed rate, radial rake angle and nose radius with the machining response i.e. surface roughness by modelling. The mathematical models thus developed are further
15、 utilized to find the optimum process parameters using genetic algorithms. 2 Review Process modelling and optimization are two important issues in ma nufacturing. The manufacturing processes are characterized by a multiplicity of dynamically interacting process variables. Surface finish has been an
16、important factor of machining in predicting performance of any machining operation. In order to develop and optimize a surface roughness model, it is essential to understand the current status of work in this area. Davis et al. 3 have investigated the cutting performance of five end mills having var
17、ious helix angles. Cutting tests were performed on aluminium alloy L 65 for three milling processes (face, slot and side), in which cutting force, surface roughness and concavity of a machined plane surface were measured. The central composite design was used to decide on the number of experiments t
18、o be conducted. The cutting performance of the end mills was assessed using 3 variance analysis. The affects of spindle speed, depth of cut and feed rate on the cutting force and surface roughness were studied. The investigation showed that end mills with left hand helix angles are generally less co
19、st effective than those with right hand helix angles. There is no significant difference between up milling and down milling with regard tothe cutting force, although the difference between them regarding the surface roughness was large. Bayoumi et al. 4 have studied the affect of the tool rotation
20、angle, feed rate and cutting speed on the mechanistic process parameters (pressure, friction parameter) for end milling operation with three commercially available workpiece materials, 11 L 17 free machining steel, 62- 35-3 free machining brass and 2024 aluminium using a single fluted HSS milling cu
21、tter. It has been found that pressure and friction act on the chip tool interface decrease with the increase of feed rate and with the decrease of the flow angle, while the cutting speed has a negligible effect on some of the material dependent parameters. Process parameters are summarized into empi
22、rical equations as functions of feed rate and tool rotation angle for each work material. However, researchers have not taken into account the effects of cutting conditions and tool geometry simultaneously; besides these studies have not considered the optimization of the cutting process. As end mil
23、ling is a process which involves a large number f parameters, combined influence of the significant parameters an only be obtained by modelling. Mansour and Abdallaet al. 5 have developed a surface roughness model for the end milling of EN32M (a semi-free cutting carbon case hardening steel with imp
24、roved merchantability). The mathematical model has been developed in terms of cutting speed, feed rate and axial depth of cut. The affect of these parameters on the surface roughness has been carried out using response surface methodology (RSM). A first order equation covering the speed range of 303
25、5 m/min and a second order equation covering the speed range of 2438 m/min were developed under dry machining conditions. Alauddin et al. 6 developed a surface roughness model using RSM for the end milling of 190 BHN steel. First and second order models were constructed along with contour graphs for
26、 the selection of the proper combination of cutting speed and feed to increase the metal removal rate without sacrificing surface quality. Hasmi et al. 7 also used the RSM model for assessing the influence of the workpiece material on the surface roughness of the machined surfaces. The model was dev
27、eloped for milling operation by conducting experiments on steel specimens. The expression shows, the relationship between the surface roughness and the various parameters; namely, the cutting speed, feed and depth of cut. The above models have not considered the affect of tool geometry on surface ro
28、ughness. Since the turn of the century quite a large number of attempts have been made to find optimum values of machining parameters. Uses of many methods have been reported in the literature to solve optimization problems for machining parameters. Jain and Jain 8 have used 4 neural networks for mo
29、deling and optimizing the machining conditions. The results have been validated by comparing the optimized machining conditions obtained using genetic algorithms. Suresh et al. 9 have developed a surface roughness prediction model for turning mild steel using a response surface methodology to produc
30、e the factor affects of the individual process parameters. They have also optimized the turning process using the surface roughness prediction model as the objective function. Considering the above, an attempt has been made in this work to develop a surface roughness model with tool geometry and cut
31、ting conditions on the basis of experimental results and then optimize it for the selection of these parameters within the given constraints in the end milling operation. 3 Methodology In this work, mathematical models have been developed using experimental results with the help of response surface
32、methodology. The purpose of developing mathematical models relating the machining responses and their factors is to facilitate the optimization of the machining process. This mathematical model has been used as an objective function and the optimization was carried out with the help of genetic algor
33、ithms. 3.1 Mathematical formulation Response surface methodology (RSM) is a combination of mathematical and statistical techniques useful for modelling and analyzing the problems in which several independent variables influence a dependent variable or response. The mathematical models commonly used
34、are represented by: where Y is the machining response, is the response function and S, f , , r are milling variables and is the error which is normally distributed about the observed response Y with zero mean. The relationship between surface roughness and other independent variables can be represen
35、ted as follows， where C is a constant and a, b, c and d are exponents. To facilitate the determination of constants and exponents, this mathematical model will have to be linearized by performing a logarithmic transformation as follows: The constants and exponents C, a, b, c and d can be determined
36、by the method of least squares. The first order linear model, developed from the above functional relationship using least squares method, can be represented as follows: where Y1 is the estimated response based on the first-order equation, Y is the measured surface roughness on a logarithmic scale,
37、x0 = 1 (dummy variable), x1, x2, x3 and x4 are logarithmic transformations of cutting speed, feed rate, radial rake angle and nose radius 5 respectively, is the experimental error and b values are the estimates of corresponding parameters. The general second order polynomial response is as given bel
38、ow: where Y2 is the estimated response based on the second order equation. The parameters, i.e. 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 stati
39、stical tests, such as F-test, chi square test, etc. 10. 3.2 Optimization using genetic 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
40、 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 complicated. So, it was decid
41、ed to employ genetic algorithms as an optimization technique. GA come under the class of non-traditional search and optimization techniques. GA are different from traditional optimization techniques in the following ways: 1.GA work with a coding of the parameter set, not the parameter themselves. 2.
42、GA search from a population of points and not a single point. 3.GA use information of fitness function, not derivatives or other auxiliary knowledge. 4.GA use probabilistic transition rules not deterministic rules. 5.It is very likely that the expected GA solution will be the global solution. Geneti
43、c algorithms (GA) form a class of adaptive heuristics based on principles derived from the dynamics of natural population genetics. 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
44、 is simple, involving copying of binary strings. Simplicity of operation and computational efficiency are the two main attractions of the genetic algorithmic approach. The computations are carried out in three stages to get a result in one generation or iteration. The three stages are reproduction,
45、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 ea
46、ch 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 6 opportunity to repro
47、duce by exchanging pieces of their genetic 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 (i.e. bits) i
48、n 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 reproduction-cross over mutation- evaluation cycle is repeate
49、d 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. 4.1 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 lo
