外文翻译--选择最佳工具，几何形状和切削条件利用表面粗糙度预测模型端铣

外文翻译--选择最佳工具，几何形状和切削条件利用表面粗糙度预测模型端铣 附录 Selection of optimum tool geometry and cutting conditions using a surface roughness prediction model for end milling Received: 14 October 2003 / Accepted: 22 January 2004 / Published online: 12 January 2005 -Verlag London Limited 2005 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 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 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 model 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 program gives minimum values of surface roughness and their respective optimal conditions. Keywords End milling Genetic algorithms Modelling Radial rake angle Nomenclature a Cutting speed exponent in mathematical model b Feed rate exponent in mathematical model c Radial rake angle exponent in mathematical model C Constant in mathematical model d Nose radius exponent in mathematical model dof Degree of freedom f Feed rate, mm/min MRR Material removal rate, mm3/s r Nose radius, mm Ra Surface roughness measured, μm Rae Surface roughness estimated, μm S Cutting speed, m/min x1 Logarithmic transformation of cutting speed x2 Logarithmic transformation of feed rate x3 Logarithmic transformation of radial rake angle x4 Logarithmic transformation of nose radius Y Machining response, μm Y1 Estimated response based on first order model, μm Y2 Estimated response based on second order model, μm Greek letters ? Response function α Radial rake angle, degree ? Experimental error 1 Introduction 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 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 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 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 process 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 influences 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 other 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 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 view of the significant role that the milling operation plays in today?s 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 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 mathematical models thus developed are further utilized to find the optimum process parameters using genetic algorithms. 2 Literature review Process modelling and optimization are two important issues in manufacturing. The manufacturing processes are characterized by a multiplicity of dynamically interacting 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 the 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 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 with 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. [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 2024 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 parameters. 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 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-free 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 order equation covering the speed range of 30–35 m/min and a second order equation covering the speed range of 24–38 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 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 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 considered 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 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 using 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 surface 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 Methodology In this work, mathematical models have been developed using experimental 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 carried out with the help of genetic algorithms. 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 are represented by: Y = ?(S, f, α, r)+? where Y is the machining response, ? is the response function and S, f , α, 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 represented as follows: Ra = CSa f bαcrd , (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 follows: ln Ra = ln C+a ln S+b ln f +c ln α+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 +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 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, 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, 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 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 decided 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.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. Genetic 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 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, 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 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) 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 reproduction-cross 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. 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 low, medium and high as shown in Table 1. Based on this, a total number of 81 experiments (full 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 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). 4.2 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 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 tools 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 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) was measured with Talysurf-6 at a 0.8 mm cut-off value. An average of four measurements was used as a response value. 5 Results and discussion The influences of cutting speed, feed rate, radial rake angle and nose radius have been assessed by conducting experiments. The variation of machining response with respect to the variables was shown graphically in Fig. 1. It is seen from these figures that of the four dependent parameters, radial rake angle has definite influence on the roughness of the surface machined using an end mill cutter. It is felt that the prominent influence of radial rake angle on the surface generation could be due to the fact that any change in the radial rake angle changes the sharpness of the cutting edge on the periphery, i.e changes the contact length between the chip and workpiece surface. Also it is evident from the plots that as the radial rake angle changes from 4? to 16?, the surface roughness decreases and then increases. Therefore, it may be concluded here that the radial rake angle in the range of 4? to 10? would give a better surface finish. Figure 1 also shows that the surface roughness decreases first and then increases with the increase in the nose radius. This shows that there is a scope for finding the optimum value of the radial rake angle and nose radius for obtaining the best possible quality of the surface. It was also found that the surface roughness decreases with an increase in cutting speed and increases as feed rate increases. It could also be observed that the surface roughness was a minimum at the 250 m/min speed, 200 mm/min feed rate, 10? radial rake angle and 0.8 mm nose radius. In order to understand the process better, the experimental results can be used to develop mathematical models using RSM. In this work, a commercially available mathematical software package (MATLAB) was used for the computation of the regression of constants and exponents. 5.1 The roughness model Using experimental results, empirical equations have been obtained to estimate surface roughness with the significant parameters considered for the experimentation i.e. cutting speed, feed rate, radial rake angle and nose radius. The first order model obtained from the above functional relationship using the RSM method is as follows: The transformed equation of surface roughness prediction is as follows: Equation 10 is derived from Eq. 9 by substituting the coded values of x1, x2, x3 and x4 in terms of ln s, ln f , lnα and ln r. The analysis of the variance (ANOVA) and the F- ratio test have been performed to justify the accuracy of the fit for the mathematical model. Since the calculated values of the F-ratio are less than the standard values of the F-ratio for surface roughness as shown in Table 4, the model is adequate at 99% confidence level to represent the relationship between the machining response and the considered machining parameters of the end milling process. The multiple regression coefficient of the first order model was found to be 0.5839. This shows that the first order model can explain the variation in surface roughness to the extent of 58.39%. As the first order model has low predictability, the second order model has been developed to see whether it can represent better or not. The second order surface roughness model thus developed is as given below: where Y2 is the estimated response of the surface roughness on a logarithmic scale, x1, x2, x3 and x4 are the logarithmic transformation of speed, feed, radial rake angle and nose radius. The data of analysis of variance for the second order surface roughness model is shown in Table 5. Since F cal is greater than F0.01, there is a definite relationship between the response variable and independent variable at 99% confidence level. The multiple regression coefficient of the second order model was found to be 0.9596. On the basis of the multiple regression coefficient (R2), it can be concluded that the second order model was adequate to represent this process. Hence the second order model was considered as an objective function for optimization using genetic algorithms. This second order model was also validated using the chi square test. The calculated chi square value of the model was 0.1493 and them tabulated value at χ2 0.005 is 52.34, as shown in Table 6, which indicates that 99.5% of the variability in surface roughness was explained by this model. Using the second order model, the surface roughness of the components produced by end milling can be estimated with reasonable accuracy. This model would be optimized using genetic algorithms (GA). 5.2 The optimization of end milling Optimization of machining parameters not only increases the utility for machining economics, but also the product quality toa great extent. In this context an effort has been made to estimate the optimum tool geometry and machining conditions to produce the best possible surface quality within the constraints. The constrained optimization problem is stated as follows: Minimize Ra using the model given here: where xil and xiu are the upper and lower bounds of process variables xi and x1, x2, x3, x4 are logarithmic transformation of cutting speed, feed, radial rake angle and nose radius. The GA code was developed using MATLAB. This approach makes a binary coding system to represent the variables cutting speed (S), feed rate ( f ), radial rake angle (α) and nose radius (r), i.e. each of these variables is represented by a ten bit binary equivalent, limiting the total string length to 40. It is known as a chromosome. The variables are represented as genes (substrings) in the chromosome. The randomly generated 20 such chromosomes (population size is 20), fulfilling the constraints on the variables, are taken in each generation. The first generation is called the initial population. Once the coding of the variables has been done, then the actual decoded values for the variables are estimated using the following formula: where xi is the actual decoded value of the cutting speed, feed rate, radial rake angle and nose radius, x(L) i is the lower limit and x(U) i is the upper limit and li is the substring length, which is equal to ten in this case. Using the present generation of 20 chromosomes, fitness values are calculated by the following transformation: where f(x) is the fitness function and Ra is the objective function. Out of these 20 fitness values, four are chosen using the roulette-wheel selection scheme. The chromosomes corresponding to these four fitness values are taken as parents. Then the crossover and mutation reproduction methods are applied to generate 20 new chromosomes for the next generation. This processof generating the new population from the old population is called one generation. Many such generations are run till the maximum number of generations is met or the average of four selected fitness values in each generation becomes steady. This ensures that the optimization of all the variables (cutting speed, feed rate, radial rake angle and nose radius) is carried out simultaneously. The final statistics are displayed at the end of all iterations. In order to optimize the present problem using GA, the following parameters have been selected to obtain the best possible solution with the least computational effort: Table 7 shows some of the minimum values of the surface roughness predicted by the GA program with respect to input machining ranges, and Table 8 shows the optimum machining conditions for the corresponding minimum values of the surface roughness shown in Table 7. The MRR given in Table 8 was calculated by where f is the table feed (mm/min), aa is the axial depth of cut (20 mm) and ar is the radial depth of cut (1 mm). It can be concluded from the optimization results of the GA program that it is possible to select a combination of cutting speed, feed rate, radial rake angle and nose radius for achieving the best possible surface finish giving a reasonably good material removal rate. This GA program provides optimum machining conditions for the corresponding given minimum values of the surface roughness. The application of the genetic algorithmic approach to obtain optimal machining conditions will be quite useful at the computer aided process planning (CAPP) stage in the production of high quality goods with tight tolerances by a variety of machining operations, and in the adaptive control of automated machine tools. With the known boundaries of surface roughness and machining conditions, machining could be performed with a relatively high rate of success with the selected machining conditions. 6 Conclusions The investigations of this study indicate that the parameters cutting speed, feed, radial rake angle and nose radius are the primary actors influencing the surface roughness of medium carbon steel uring end milling. The approach presented in this paper provides n impetus to develop analytical models, based on experimental results for obtaining a surface roughness model using the response surface methodology. By incorporating the cutter geometry in the model, the validity of the model has been enhanced. The optimization of this model using genetic algorithms has resulted in a fairly useful method of obtaining machining parameters in order to obtain the best possible surface quality. References 1. Chung SC (1998) A force model for nose radius worn tools with a chamfered main cutting edge. Int J Mach Tools Manuf 38:1467–1498 2. Perez CJL (2002) Surface roughness modeling considered uncertainty in measurements. Int J Prod Res 40(10):2245–2268 3. Davies R, Ema S (1989) Cutting performance of end mills with different helix angles. Int J Mach Tools Manuf 29:217–227 4. Guven Y, Bayoumi AE (1993) Determination of process parameters through a mechanistic force model of milling operations. Int J Mach Tools Manuf 33:627–641 5. Mansour A, Abdalla H (2002) Surface roughness model for end milling: a semi-free cutting carbon case hardening steel (EN32) in dry condition. J Mater Process Technol 124:183–191 6. Alauddin M, Hasmi MSJ (1995) Computer aided analysis of a surface roughness model for end milling. J Mater Process Technol 55:123–127 7. Hasmi MSJ, (1996) Optimization of surface finish in end milling inconel 718. J Mater Process Technol 56:54–65 8. Jain RK, Jain VK (2000) Optimum selection of machining conditions in abrasive flow using neural networks. J Mater Process Technol 108:62–67 9. Suresh PVS, Venkateswara Rao P, Deshmukh SG (2002) A genetic algorithmic approach for optimization of surface roughness prediction model. Int J Mach Tools Manuf 42:675–680 10. Montgomery DC (1996) Introduction to statistical quality control. Wiley, New York11. Goldberg DE (1999) Genetic algorithms. Addison-Wesley, New Delhi 选择最佳工具，几何形状和切削条件 利用表面粗糙度预测模型端铣 收到日期: 2003年10月14日/接受: 2004年1月22日/网上公布: 2005年1月12日 施普林格出版社，伦敦有限公司2005年 , 摘要: 刀具几何形状对工件表面质量产生的影响是人所共知的，因此，任何成型面端铣应包括刀具的几何形状。在当前的工作中，实验性研究的进行已看到刀具几何(径向前角和刀尖半径)和切削条件(切削速度和进给速度) ，对加工性能，和端铣中碳钢影响效果。第一次和第二次为建立数学模型，从加工参数方面，制订了表面粗糙度预测响应面方法(丹参) ，在此基础上的实验结果。该模 已得到证实，并通过了卡方检验。这些参数对表面粗糙度的建型取得的优化效果 立，方差极具意义。通过尝试也取得了优化表面粗糙度预测模型，采用遗传算法( GA ) 。在加文的程式中实现了最低值，表面粗糙度及各自的值都达到了最佳条件。 关键词 端铣;遗传算法;塑造;径向前角 命名法 a 切削速度指数的数学模型 b 进给速度指数在数学模型 径向前角指数的数学模型 c C 常数的数学模型 d 刀尖半径指数的数学模型 dof 自由度 f 进给速度，毫米/分钟 MRR 材料去除率，立方毫米/秒 r 刀尖半径，毫米 Ra 表面粗糙度测量，μm Rae 表面粗糙度的估计, μm S 切割速度，米/分钟 x1 对数变换切削速度 x2 对数变换的进给速度 x3 对数变换的径向前角 x4 对数变换的刀尖半径 Y 加工回应, μm Y1 估计响应基于一阶模型, μm Y2 估计响应基于二阶模型, μm Φ 响应函数 α 径向前角，程度 ? 实验误差 1 导言 端铣是最常用的金属去除作业方式，因为它能够更快速去除物质并达到合理良好的表面质量。它可用于各种各样的制造工业，包括航空航天和汽车这些以质量为首要因素的行业，以及在生产阶段，槽孔，精密模具和模具这些更加注重尺寸精度和表面粗糙度产品的行业内。此外，表面光洁度还影响到机械性能，如疲劳性能，磨损，腐蚀，润滑和导电性。因此，测量表面光洁度，可预测加工性能。 车削过程对表面光洁度造成的影响历来倍受研究关注，对于加工过程采用多刀，用机器制造处理，都是研究员需要注意的。由于这些过程涉及大量的参数，使得难以将关联表面光洁度与其他参数进行实验。在这个过程中建模有助于更好的理解。在过去，虽然通过许多人的大量工作，已开发并建立了表面光洁度预测模型，但影响刀具几何方面受到很少注意。然而，除了切向和径向力量，径向前角对电力的消费有着重大的影响。它也影响着芯片冰壶和修改芯片方向人流。此外，研究人员[ 1 ]也指出，在不影响表面光洁度情况下，刀尖半径发挥着重要作用。因此，发展一个很好的模式应当包含径向前角和刀尖半径连同其他相关因素。 对于制造业，建立高效率的加工参数几乎是将近一个世纪的问题，并且仍然是许多研究的主题。获得最佳切削参数，是在制造业是非常关心的，而经济的加工操作中及竞争激烈的市场中发挥了关键作用。在材料去除过程中，不当的选择切削条件造成的表面粗糙度高和尺寸误差，它甚至可能发生动力现象:由于自动兴奋的震动，可以设定在[ 2 ] 。鉴于铣削运行在今天的全球制造业中起着重要的作用，就必要优化加工参数。因此通过努力，在这篇文章中看到刀具几何(径向前角和刀尖半径)和切削条件(切削速度和进给速度) ，表面精整生产过程中端铣中碳钢的影响。实验显示，这项工作将被用来测试切削速度，进给速度，径向前角和刀尖半 径与加工反应。数学模型的进一步利用，寻找最佳的工艺参数，并采用遗传算法可促进更大发展。 2文献回顾 建模过程与优化，是两部很重要的问题，在制造业。生产过程的特点是多重性的动态互动过程中的变数。表面光洁度一直是一个重要的因素，在机械加工性能预测任何加工操作。为了开发和优化表面粗糙度模型，有必要了解目前在这方面的工作的状况。 迪维斯等人[ 3 ]调查有关切削加工性能的五个铣刀具有不同螺旋角。分别对铝合金L65的3向铣削过程(面，槽和侧面)进行了切削试验，并对其中的切削力，表面粗糙度，凹状加工平面进行了测量。所进行的若干实验是用来决定该中心复合设计的。切削性能的立铣刀则被评定采用方差分析。对主轴速度，切削深度和进给速度对切削力和表面粗糙度的影响进行了研究。调查显示铣刀与左手螺旋角一般不太具有成本效益比。上下铣方面切削力与右手螺旋角，虽然主要区别在于表面粗糙度大，但不存在显著差异。 拜佑密等人[ 4 ]研究过工具对旋转角度，进给速度和切削速度在机械工艺参数(压力，摩擦参数)的影响，为端铣操作常用三种商用工件材料， 11L17易切削钢，62-35-3易切削黄铜和铝2024年使用单一槽高速钢立铣刀。目前已发现的压力和摩擦法对芯片-工具接口减少，增加进给速度，并与下降的气流角，而切削速度已微不足道，对一些材料依赖参数，工艺参数，归纳为经验公式，作为职能的进给速度和刀具旋转角度为每个工作材料。不过，研究人员也还有没有考虑到的影响，如切削条件和刀具几何同步，而且这些研究都没有考虑到切削过程的优化。 因为端铣过程介入多数f参量，重大参量的联合只能通过塑造得到。曼苏尔和艾布达莱特基地[ 5 ]已开发出一种表面粗糙度模式，为年底铣EN32M(半自由切削 碳硬化钢并改进适销性)。数学模型已经研制成功，可用在计算切削速度，进给速度和轴向切深。这些参数对表面粗糙度的影响已进行了响应面分析法(丹参)。分别制定了一阶方程涵盖的速度范围为30-35米/分，一类二阶方程涵盖速度范围的24-38米/分的干切削条件。 艾尔艾丁等人[ 6 ]开发出一种表面粗糙度模型，用丹参，为端铣190BHN钢。为选择适当的组合，切割速度和伺服，增加金属去除率并不牺牲的表面质量，多此进行了模型建造并绘制随层等高线图。 瀚斯曼等人[ 7 ] ，还使用了丹参模式来评估工件材料表面粗糙度对加工表面的影响。该模型是铣操作进行实验钢标本。表明表面粗糙度及各项参数，即切削速度，饲料和切削深度之间的关系。上述模式并没有考虑到对刀具几何形状对表面粗糙度的影响。 自从世纪之交的相当多的尝试已找到了最佳值的加工参数。许多方法已经被国内外文献报道，以解决加工参数优化问题。乔恩和贾殷[ 8 ]用神经网络建模和优化加工条件。结果已得到验证，通过比较优化的加工条件得到了应用遗传算法。 (苏瑞等人[ 9 ]已开发出一种表面粗糙度预测模型，将软钢用响应面方法，验证生产因素对个别工艺参数的影响。他们还优化了车削加工用表面粗糙度预测模型为目标函数。考虑到上述情况，已试图在这方面的工作，以发展一个表面粗糙度的模型与工具几何形状和切削条件，在此基础上的实验结果，然后再优化，在端铣操作中，它为选拔这些参数给定了限制。 3 方法论 在这项工作中，数学模型已经开发使用的实验结果与帮助响应面方法论。旨在促进数学模型与加工的反应及其因素，是要促进优化加工过程。这个数学模型已被作为目标函数和优化进行了借助遗传算法 3.1数学表达 响应面分析法(丹参)是一种有益建模和分析问题的组合数学和统计技术的方法，在这几个独立变量的影响力供养变或反应。数学模型常用的是代表: Y = ?(S, f, α, r)+? 而Y是加工回应，?是响应函数和S，f，α ， R的铣削变数和?是错误，通常是发给约观测响应y为零的意思。 之间的关系，表面粗糙度及其他独立变量可以发生情况如下: Ra = CSa f bαcrd (1) 其中c是一个常数，并为A ， B ， C和D的指数 为方便测定常数和指数，这个数学模型，必须由线性表演对数变换如下: ln Ra = ln C+a ln S+b ln f +c ln α+d ln r (2) 常数和指数c，为A,B,C和D都可以由最小二乘法。一阶线性模型，发展了，从上述的功能关系用最小二乘法，可派代表作为如下: Y1 = Y??=b0x0 +b1x1+b2x2+b3x3 +b4x4 (3) 在估计响应y1的基础上，一阶方程，Y是衡量表面粗糙度对对数的规模x0=1(虚拟变量)的x1,x2,x3和x4分别为对数变换切削速度，进给速度，径向前角和刀尖半径,?是实验误差和b值是估计相应的参数。 一般二阶多项式的回应是，作为提供以下资料: Y2 = Y??=b0x0 +b1x1+b2x2 +b3x3+b4x4 +b12x1x2 +b23x2x3 +b14x1x4 +b24x2x4 +b13x1x3 +b34x3x4 +b11x21 +b22x22 +b33x23 +b44x24 (4) 如Y2型是估计响应的基础上的二阶方程。参数，即本B0中，B1，B2的，B3的，B4的，B12的，b23的，b14等，要估计由最小二乘法。有效性选定的模型用于优化工艺参数，是经过检验的帮助下统计测试，如F检验，卡方检验等[10] 。 3.2优化中的应用遗传算法 大部分的研究人员一直使用传统的优化技术，为解决加工问题。传统方法的优化和搜索并不收费，以及点多面广的问题域。传统的技术是没有效率的时候，实际的搜索空间过大。这些算法并不强劲。他们倾向于获得局部最优解。众多的制约因素和月票数目，使加工优化问题更加复杂化。因此，决定使用遗传算法作为优化技术。加文来根据类别的非传统的搜索和优化技术。加文不同于传统优化技术在以下几个方面: 1.GA的工作，用编码的参数集，而不是参数本身。 2.搜索从一个人口中的要点，并没有一个单一的点。 3.GA利用信息的健身功能，而不是衍生工具或其他辅助知识。 4.GA使用概率转换规则不确定性的规则。 5.很可能预期的GA解决将成为全球性的解决办法。 遗传算法( GA )一类是自适应启发式原则的基础上得出的，从动态的人口自然遗传学。搜索过程模拟自然的评价生物的动物，和原来是一个智能开发的一个随机搜索。力学一加文很简单，其中涉及抄袭的二进制字符串。操作更方便和 计算效率是两个主要景点的遗传算法的方法。计算是分三个阶段进行，以获得结果在一代人或迭代。这三个阶段是复制，交叉和变异。 为了使用GA解决所有问题，可变物典型地被输入入代表可能解决方案对特定问题的串(二进制编制程序)或染色体结构。GA开始有(个体)的人口随机被创造的串。每单独串的健身评估关于特定目标函数。那么，这个初始种群的运作形式，由三个主要运营商-突变-创造，我们希望更好的人口。非常适合个人或解决方案是给予机会，以复制，交换件，其遗传信息，在交叉的程序，与其他高度合适的个人。这将产生新的"后代"的解决方案，并分享一些特点，从父母双方。基因突变是经常被采用交叉后，通过改变某些基因(即比特)后代可以取代整个人口(两代人的方法)或取代少适合个人( 独立的做法)。这个新的人口，是进一步的评估和测试，为一些终止准则。复制-实现评价周期重复，直至终止准则。 4 实验细节 为在此基础上的实验数据发展模式，周密筹划的试验是必不可少的。所考虑的因素，对实验和分析切削速度，进给速度，径向前角和刀尖半径。 4.1实验设计 设计实验对一系列实验需要有着重大的影响。因此，它必须有精心设计的一套实验。范围值的每一项因素是定于三个不同层次，即低，中和高如表1所示。在此 基础上，总人数81实验(全阶乘设计) ，每相结合的不同层次的因素，如表2所示，进行了。 变量进行编码，考虑到容量，并限制切削条件的铣床。编码值的变量，可用于环境质量标准。第3和第4 ，获得了来自下列转化方程: 凡x1是编码的价值切削速度( s )和x2是编码值的进给速度(f) ， x3就是编码值的径向前角( α )和x4是编码值的刀尖半径(r) 。 4.2 实验 一种高精度“rambaudi rammatic 500 ”数控铣床，有垂直铣削头，是用于试验。该控制系统是一个数控FIDIA–12协定。切削工具，用来为试点，分别为固体涂层硬质合金立铣刀刀具的不同径向倾斜角度和鼻子半径(尺寸 :DIA20 X FL38×OAL102 mm)。这些工具是有一层TiAlN膜层。硬度，密度和横向断裂强度是1570高压30,14.5gm/cm3和3800n/mm2 。 100×75mm和20mm AISI 1045钢标本厚度用于本研究。 所有标本通过在在850?C熔炉加热一个小时然后冷却锻炼。对标本的化学分析在表3.被提出。 制件材料的坚硬度为170BHN。所有实验材料进行了20mm裁减的恒定的轴向深度和1mm裁减的辐形深度。地面粗糙度(反应)测量了与在0.8mm切除Talysurf-6的值。 平均四次测量使用了反应值。 5 结果与讨论 做实验以估计切削速度，进给速度，径向前角和刀尖半径的影响。加工方面的反应变数生动地显示在图1。从这些数字可以看出径向前角，表面粗糙度，加工用铣刀对四个变参数具有一定的影响。有人认为径向前角对表面生成原因有突出的影响，可能是一个事实，即任何变化，在径向前角的变化，改变了接触长度之间的芯片和工件表面。也很明显，由于径向前角从4?至16?的变化，表面粗糙度降低，然后增加。因此，可以得出结论，径向前角在4?至10?范围内将提供更好的表面光洁度。图1还表明，表面粗糙度使刀尖半径先减小，然后增加。这表明，有一定范围内，寻找最佳值的径向前角和刀尖半径可获取尽可能好的表面质量。实验还发现，表面粗糙度下降，增加了切割速度及加工时间。可以观察到，表面粗糙度最低时是250米/分钟的速度， 200毫米/分钟进给速度，10?径向前角和0.8毫米刀尖半径。了解过程可以看处，实验结果可用于开发的数学模型，用丹参。在这项工作中，在商业上可用的数学软件包( MATLAB的) ，是用来计算的回归常数和指数。 5.1粗糙度模型 利用实验结果，已经获得了估计表面粗糙度经验公式，考虑符合重大的参数，即切削速度，进给速度，径向前角和刀尖半径。从一阶模型得到，从上述的功能关系用丹参方法如下: 化方程的表面粗糙度预测如下: 等式10 从Eq 获得。9 替代x1 的代码值, x2 、x3 和x4 根据ln s, ln f , lnα 和 ln r算得 ，分析中的变异(方差分析)和F -比检验已完成，适合作精确的数学模型。由于计算值的F比率都远低于标准值的F比率为表面粗糙度如表4所示，模型是足够在99 ,的信心水准下，以代表之间的关系，加工回应，并考虑将加工参数年底铣削过程。 多元回归系数的一阶模型被指定为0.5839 。这表明，一阶模型可以解释变异 的表面粗糙度，为58.39, 。作为一阶模型具有较低的可预测性，二阶模型已经研 制成功就看它是否能代表更好。 二阶表面粗糙度模型通过以下资料建立。 如Y2型，是估计的反应，表面粗糙度对对数尺度,x1,x2,x3和x4是对数变换速度，伺服，径向前角和刀尖半径。数据方差分析，为二阶表面粗糙度模型表5所示。 因为Fcal大于F0.01 ，在99 ,的标准下，响应变量与自变量，有一定的关系。多元回归系数的二阶模型被裁定为0.9596 。在此基础上的多元回归系数(er2),可以得出结论认为，二阶模型足以代表这一进程。因此二阶模型被认为是一个客观的功能，为优化利用遗传算法。这二阶模型，还验证了用卡方检验。计算卡方值该模型是0.1493和他们表价值在χ2 0.005是52.34 ，如表6所示，这表明， 99.5 ,的变异性，表面粗糙度解释了这一模式。 用二阶模型，其表面粗糙度的组成部分所产生的端铣可估计合理性及准确性。这种模式将利用遗传算法( GA )得以优化 。 5.2优化端铣 优化加工参数，不仅增加了实用性，为加工经济，还对产品质量的TOA有很大程度的影响。在这方面已作出努力来估计最佳工具，几何形状和加工条件，以产生最佳的表面质量，内部制约因素。 约束优化问题，说明如下:尽量减少利用该模型考虑在这里: 凡xil和xiu上下界过程中的变数及x1 ， x2 ， X3， x4是对数变换的切削速度，进给，径向前角和刀尖半径。 GA开发利用Matlab 。这种方法使一个二进制编码系统为代表的变数切削速度( s )和进给速度(f) ，径向前角( α )和刀尖半径( R )的，即每这些变数都代表了一个10位的二进制当量，限制总字串长度为40.据了解，作为一个染色体。变数就派代表作为基因( substrings )在染色体上。随机产生20个染色体(人口规模是20个) ，完成制约变数，是采取在各代。第一代是所谓初始种群。一旦编码的变数就已经做了，那么，实际的解码值为变数，估计使用的公式如下: xi是解码后的实际价值的切削速度，进给速度，径向前角和刀尖半径，X( l ) i是下限和X ( u )的i是上限和李应生是子长，这是相当于十年样子。 用现在这一代人的20个染色体，健身价值，是按以下转变: 这里f ( x )是健身功能和RA是目标函数。 出于这20个健身价值，有四个选择使用轮盘轮甄选。染色体对应于这四个健身价值观是采取家长。然后交叉和变异繁殖的方法，是适用于产生20个新的染色体，为下一代。这个过程的生成新的人口从旧的人口，是所谓的一代人。很多这样的一代，都运行到最大数目的，是几代人达到或平均4个选定的健身价值，在每一代人变得平稳。这确保了优化的所有变量(切削速度，进给速度，径向前角和刀尖半径) ，是同步进行的。最后统计显示，在结束所有迭代。为了优化目前的问题，利用加文，以下参数已选定，以取得最佳的解决方案与最不计算努力: 表7显示，一些最起码的价值，表面粗糙度预测，由加文程序方面的投入，加工范围，并表8显示了最佳加工条件，为相应的最低值，表面粗糙度表7所示。该MRR给出表8计算 其中f是工作台进给速度(毫米/分钟) ，机管局正轴向切深( 20毫米)和AR是径向切深(1毫米) 。 可以得出这样的结论，从优化结果的GA程序，是有可能选择相结合的切削速度，进给速度，径向前角和刀尖半径为取得最佳的表面光洁度给予一个合理良好的物质去除率。对GA计划提供最佳加工条件，相应给予最低值的表面粗糙度。应用遗传算法的方法，以获得最佳的加工条件，将是非常有益的，在计算机辅助工艺设计( CAPP )阶段，在生产高品质的货品，紧公差，由各种各样的值。 改换行动，并在自适应控制的自动机床。与已知的边界表面粗糙度及加工条件，加工，可表演了一个比较高的成功率，与选定的加工条件。 6 结论 调查研究表明，该参数切削速度，进给，径向前角和刀尖半径是主要受行动者的影响，表面粗糙度的中碳钢端铣。该文提供了n动力，以发展分析模型，根据实验结果，可以获得表面粗糙度模型，用响应面方法论。通过把刀具几何模型，该模型的有效性有了较大的提高。优化模型采用遗传算法，导致在一个相当有用的方法获取加工参数，以获得最佳的表面质量。 参考文献 1. Chung SC (1998) A force model for nose radius worn tools with a chamfered main cutting edge. Int J Mach Tools Manuf 38:1467–1498 2. Perez CJL (2002) Surface roughness modeling considered uncertainty in measurements. Int J Prod Res 40(10):2245–2268 3. Davies R, Ema S (1989) Cutting performance of end mills with different helix angles. Int J Mach Tools Manuf 29:217–227 4. Guven Y, Bayoumi AE (1993) Determination of process parameters through a mechanistic force model of milling operations. Int J Mach Tools Manuf 33:627–641 5. Mansour A, Abdalla H (2002) Surface roughness model for end milling: a semi-free cutting carbon case hardening steel (EN32) in dry condition. J Mater Process Technol 124:183–191 6. Alauddin M, Hasmi MSJ (1995) Computer aided analysis of a surface roughness model for end milling. J Mater Process Technol 55:123–127 7. Hasmi MSJ, (1996) Optimization of surface finish in end milling inconel 718. J Mater Process Technol 56:54–65 8. Jain RK, Jain VK (2000) Optimum selection of machining conditions in abrasive flow using neural networks. J Mater Process Technol 108:62–67 9. Suresh PVS, Venkateswara Rao P, Deshmukh SG (2002) A genetic algorithmic approach for optimization of surface roughness prediction model. Int J Mach Tools Manuf 42:675–680 10. Montgomery DC (1996) Introduction to statistical quality control. Wiley, New York11. Goldberg DE (1999) Genetic algorithms. Addison-Wesley, New Delhi