外文翻譯選擇最佳工具幾何形狀和切削條件利用表面粗糙度預(yù)測(cè)模型端銑

1、附錄selection of optimum tool geometry and cutting conditionsusing a surface roughness prediction model for end millingreceived: 14 october 2003 / accepted: 22 january 2004 / published online: 12 january 2005. springer-verlag london limited 2005abstract influence of tool geometry on the quality of sur

2、face produced is well known and hence any attempt to assess the performance of end milling should 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

3、feed rate) on the machining performance during end milling of medium carbon steel. the first 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 mode

4、l selected for optimization has been validated with the chi square test. the significance of 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 pr

5、ogram gives minimum values of surface roughness and their respective optimal conditions.keywords end milling genetic algorithms modelling radial rake anglenomenclaturea cutting speed exponent in mathematical modelb feed rate exponent in mathematical modelc radial rake angle exponent in mathematical

6、modelc constant in mathematical modeld nose radius exponent in mathematical modeldof degree of freedomf feed rate, mm/minmrr material removal rate, mm3/sr nose radius, mmra surface roughness measured, mrae surface roughness estimated, ms cutting speed, m/minx1 logarithmic transformation of cutting s

7、peedx2 logarithmic transformation of feed ratex3 logarithmic transformation of radial rake anglex4 logarithmic transformation of nose radiusy machining response, my1 estimated response based on first order model, my2 estimated response based on second order model, mgreek letters response function ra

8、dial rake angle, degree experimental error1 introductionend 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 a

9、nd automotive sectors, where quality is an important 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

10、as fatigue behaviour, wear, corrosion, lubrication 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

11、 as that of machining processes using multipoint cutters, requires attention by researchers. as these processes involve large number of parameters, it would be difficult to correlate surface finish with other parameters just by conducting experiments. modelling helps to understand this kind of proce

12、ss better. though some amount of work has been 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 i

13、nfluences chip curling and modifies chip flow 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 othe

14、r relevant factors.establishment of efficient 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

15、 of machining operation plays a key role in 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 vie

16、w of the significant role that the milling 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 condition

17、s (cutting speed and feed rate) on the surface 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 math

18、ematical models thus developed are further utilized to find the optimum process parameters using genetic algorithms.2 literature reviewprocess modelling and optimization are two important issues in manufacturing. the manufacturing processes are characterized by a multiplicity of dynamically interact

19、ing process variables. surface finish has been an 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 th

20、e cutting performance of five end mills having various 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

21、 was used to decide on the number of experiments to be conducted. the cutting performance of the end mills was assessed using 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 w

22、ith left hand helix angles are generally less cost 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.

23、 4 have studied the affect of the tool rotation 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 202

24、4 aluminium using a single fluted hss milling cutter. 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 paramet

25、ers. process parameters are summarized into empirical 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

26、 optimization of the cutting process.as end milling 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-fr

27、ee cutting carbon case hardening steel with improved 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

28、 order equation covering the speed range of 3035 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

29、 were constructed along with contour graphs for 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 roughn

30、ess of the machined surfaces. the model was developed 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 consi

31、dered the affect of tool geometry on surface roughness.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

32、 and jain 8 have used neural networks for modeling 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 us

33、ing a response surface methodology to produce 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 surfac

34、e roughness model with tool geometry and cutting 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 methodologyin this work, mathematical models have been developed using experimental

35、results with the help of response surface 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

36、carried out with the help of genetic algorithms.3.1 mathematical formulationresponse 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

37、. the mathematical models commonly used are represented by:y = (s, f, , r)+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 rou

38、ghness and other independent variables can be represented as follows:ra = csa f bcrd , (1)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

39、 follows:ln ra = ln c+a ln s+b ln f +c ln +d ln r . (2)the constants and exponents c, a, b, c and d can be determined 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:y1 = y=b0x0 +

40、b1x1+b2x2+b3x3 +b4x4 (3)where y1 is the estimated response based on the first-order 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 respecti

41、vely, 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

42、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 statistical tests, such as f-test,

43、chi square test, etc. 10.3.2 optimization using genetic algorithmsmost 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

44、 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 decided to employ genetic algorithms

45、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.ga search from a population of poi

46、nts 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.genetic algorithms (ga) form a class of adap

47、tive 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 is simple, involving copying of binar

48、y 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, crossover and mutation.in order to use

49、 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

50、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 geneti

51、c 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) in the offspring. the offspring can either

52、 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 repeated until the termination criteria are met.

53、4 experimental detailsfor 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 designthe design of experimentati

54、on 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 (ful

55、l factorial design), each having a combination 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 ob

56、tained 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() and x4 is the coded value of nose radius (r).4.2 experimentationa high precision rambaudi rammatic 500 cnc mil

57、ling machine, with a vertical milling head, was used for experimentation. the control system is a cnc fidia-12 compact. 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 t

58、ools are coated with tialn coating. the hardness, density and transverse rupture strength are 1570 hv 30, 14.5 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 holding them at 850 c

59、for one hour and then cooling them in a furnace. the chemical analysis of specimens is presented in table 3. the hardness of the workpiece material is 170 bhn. all the experiments were carried out at a constant axial depth of cut of 20 mm and a radial depth of cut of 1 mm. the surface roughness (response) wa