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曲柄压力机曲柄滑块工作机构设计【4张图纸】【优秀】

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关键词：: 曲柄压力机曲柄滑块工作机构设计图纸曲柄滑块工作机构

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曲柄压力机曲柄滑块工作机构设计

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前言………………………………………………………………………..

1 曲柄压力机构成及工作原理和相关参数

1.1曲柄压力机构成及工作原理……………………………………………..

1.1.1曲柄压力机一般有工作部分构成……………………………………

1.1.2.曲柄压力机工作原理…………………………………………………

1.2 曲柄压力机的主要技术参数…………………………………………….

1.2.1曲柄压力机的主要技术参数…………………………………………

1.2.2曲柄压力机的型号介绍………………………………………………

2 曲柄压力机滑块机构的运动分析与受力分析

2.1压力机曲柄滑块机构的构成………………………………………………

2.2曲柄压力机滑块机构的运动规律分析……………………………………

2.2.1滑块的位移和曲柄转角之间的关系…………………………………..

2.2.2滑块的速度和曲柄转角的关系……………………………………….

2.3曲柄压力机滑块机构的受力分析…………………………………………

2.3.1忽略摩擦情况下滑块机构主要构件的力学分析……………

2.3.2考虑摩擦情况下滑块机构主要构件的力学分析……………

3 齿轮传动

3.1齿轮传动的介绍…………………………………………………………..

3.1.1齿轮在应用的过程中对精度要求………………………………….

3.2直齿轮传动……………………………………………………………….

3.2.1齿轮参数确定

3.2.2齿轮的尺寸初步计算

3.2.3 齿轮的强度校核

3.3锥齿轮传动………………………………………………………………

3.3.1几何参数的计算........................................

3.3.2 核算弯曲应力..........................................

3.4蜗杆蜗轮传动……………………………………………………………

3.4.1蜗杆传动的特点.......................................

3.4.2蜗杆蜗轮的材料.......................................

3.4.3蜗杆蜗轮尺寸的计算...................................

3.4.4 校核蜗轮蜗杆..........................................

4 曲柄压力机滑块机构的设计与计算。

4.1曲柄压力机滑块机构的构成……………………………………………

4.1.1选定轴的材料…………………………………………………………

4.1.2估算曲轴的相关尺寸

4.1.3 设计轴的结构并绘制结构草图

4.1.4 校核轴劲尺寸

4.1.5曲轴的危险阶面校核

4.2曲轴设计与计算…………………………………………………………

4.2.1 连杆和调节螺杆初步确定

4.2.2校核调节螺杆的和连杆尺寸

4.3连杆设计与计算…………………………………………………………

4.4导轨的设计与计算……………………………………………………..

4.5高度调节装置的设计……………………………………………………

5 轴承的选用

5.1滑动轴承的选用………………………………………………………….

5.1.1连杆大端滑动轴承选用与校核

5.1.2曲轴颈上滑动轴承选用与校核

5.2滚动轴承的选用………………………………………………………….

翻译………………………………………………………………………….

英语原文………………………………………………………………………..

后记………………………………………………………………………….

致谢………………………………………………………………………………

参考资料………………………………………………………………………

前言

制造业是一个国家经济发展的重要支柱，其发展水平标志着该国家的经济实力、科技水平和国防实力。压力机是机械制造业的基础设备。随着社会需求和科学技术的发展，对机床设计要求越来越高。尤其是模具制造的飞速出现，使机床向高速、精确，智能化的方向发展。因此，对压力机的精度和生产率等各方面的要求也就越来越高。

本次设计是结合中型压力机的工作实际，对JB31-160型曲柄压力机进行改造性设计。由于传统JB31-160型曲柄压力压力机，存在滑块运动精度底，装模高度调节麻烦，滑块行程量小等缺点，严重影响了生产效率。本次设计鉴于以上缺点对其进行了如下改正：1改进部件结构设计，采用新型材料。例如离合器部件，尽量减小其从动惯量，采用新兴摩擦材料。2调节装置方面，采用二级的锥齿——蜗杆蜗轮调节，节省了工人劳动量，又提高了精度。3采用了曲轴代替同类型的偏心轴，用变位齿轮代替普通齿轮，这样就减小了机身的高度，更方

内容简介：: 响应曲面法在最优化切削条件下获得最小表面粗糙度的应用摘要：这篇文章主要讨论：在模具表面的铣削中，综合运用响应曲面法和常规算法相结合这样一种有效的方法，在最佳的切削条件下获得最小的表面粗糙度。响应曲面法被用于创造一种有效的模型来分析表面粗糙度，即切削参数：进给量、切削速度、轴向切深、径向切深和机器公差。为了收集表面粗糙度值，做了大量基于三个等级的，大部分因素的试验方法设计的机械试验和数据统计。一个有效的第四等级的响应曲面模具的型腔在试验中被测量。最优化切削条件下的常规算法对响应曲面模具获得预想表面粗糙度有很大的影响。常规算法使模具型腔的表面粗糙度值有过去降到现在的，相对降低了10%。基于常规算法的最优化切削条件下的生产被实验测量证实具有一致性。关键词：铣削、切削条件、表面粗糙度、注射模、响应曲面法、遗传算法.1、引言目前生产塑料制品的模具零件需要铣削加工，而制造工业的发展主要取决于数控加工技术的发展。在用铝合金7075T6制造机械模具零件时也常用数控铣削加工中心。在本次的研究中用的也是铝合金7075T6，由于它具有像高抗变形、良好的传导性、较高的拉伸强度等优点，所以在飞行器和模具工业中广泛应用。塑料注射模生产的塑料产品的质量受模具表面铣削质量的影响，这些产品的质量通常与表面粗糙度值和表面粗糙度的测量有关。各种机床加工出来的工件的表面粗糙度是不规则的。表面粗糙度值即平均表面粗糙度，常用符号Ra表示。理论上，Ra是离轮廓中心线的长度的算术平均值。Ra也是控制机器工作的重要因素。刀具几何尺寸、进给量、切削条件和其它不规则的机器运转因素，如：刀具的涂层、振动、刀具挠度、切削液和工件特性等都会影响表面粗糙度。这里研究的主要是切削条件的影响（进给量、切削速度、轴向、径向切深和机床公差）。一些学者已经研究过铣削条件在铣削和塑料注射模制造中的影响。例如真空封蜡模的制造。为了预测表面粗糙度和刀具寿命，也就是在铣削钢材时的切削速度、进给量和轴向切深，建立了分析模型。在铣削铬镍铁合金718时，提出了一种优化表面光洁度的有效方法。在这个研究中，建立了一个四等级的响应曲面模型，能够在铣削铝合金7075T6材料的模具表面时获得预期的表面粗糙度。通常利用响应曲面法统计响应曲面模型，实验测量证实了响应曲面模具的精确度。在寻找最佳切削条件获得最小表面粗糙度上，成熟的响应曲面模型和成熟的遗传算法有很大的联系。切削条件用进给量、切削速度、轴向和径向切深及机器公差表示。用遗传算法预期的最佳切削条件可用实验测量证实。目前，在这个研究中创造和利用响应曲面模型和常规算法比手册中的其它方法有许多优点。响应曲面模型是一个具有足够精确度的高等级、更富经验性的多项式模型，遗传算法去除了在遗传算法中存在的需用户定义的参数。用响应曲面法和遗传算法得到的最优化加工所生成的响应曲面模具的细节在下面的章节中给出。2、试验过程2.1试验规划响应曲面法生成响应曲面模具的一个重要阶段是试验规划。在这个研究中，计划用三个等级的全部因素的设计来统计切削实验数据。切削实验表现为5个参数：进给量（）、切削速度（）、轴向切深（）、径向切深（）和机器公差（）。进行所有35=243个切削实验。切削余量分为高中低三个等级的全部因素试验设计的切削参数在表1中列出。切削参数的取值范围都是从Sandvik Tool Catalogue中的推荐值选取的。铣削加工是在已设置完毕切削参数的DECKEL MAHO DMU 60P五轴铣削加工中心上进行的，表面粗糙度Ra从模具的表面上量取。2.2刀具和材料实验中的刀具是铣头直径为10mm的平头四齿铣刀，刀具材料是PVD AlTiN，表面渗碳处理。刀具的螺旋角为45，前倾角为10。机械实验都是在尺寸为12012050的铝合金（7075T6）锭上的模腔上进行的。后面所用的试件材料化学成分是：1.6%的铜，2.5%的镁，0.23%的铬，5.4%的锌。工件的硬度值为布氏硬度150。铝合金的机械特性是：拉伸强度为570MPa，屈服强度为505MPa，剪切强度为330MPa，延伸率为11%.用Surftest 301表面粗糙度测量仪通过一条沿中心线为2.5的样条测量表面粗糙度，把测量结果转化为Ra数值。由于这种方法比较简便，通用，这个研究也采用这种方法。每个Ra的测量至少重复三次，三个Ra的平均值作为响应曲面模具的表面粗糙度值记录下来。2.3模具零件用于该研究的模具零件是用于生产应用于生物力学上的矫正部件的组成部分。如图1所示。矫正部件常用于行走器械上用于保持人腿在行走时的平稳。它配备有一根直径为12，长度为300的铝制圆棒，绑到膝盖的区域。矫正部件由三个主要组成部分。本次研究的对象就是其中之一。2.4制造矫正部件的零件用一套完整的方法制造矫正部件的组件，用了三道机械加工工序。首先，在数控铣削加工中心上加工选定的部件，表面粗糙度值Ra从模具型腔表面量取。其次，用ARBURG把塑料注射进塑料注射模中，Polyacetal (POM)C902是常用的注射用聚合材料。这种材料熔化后的密度为，注射温度是165，粘度为50 Pa s，熔化后的填充流速是。最后，为了获得模具铸件，进行浇铸。模具部件、塑料产品和模铸件都在图2中给出了。3、响应曲面模具的表面粗糙度在用响应曲面法获得预期的表面粗糙度中，响应曲面模型是一个分析函数。在模具的生产阶段响应曲面法利用了试验数值统计法和最小正方形填充法。它被总结在图3中。响应曲面法最初被Box和Draper用于物理实验的填充中，后来在其它领域也被采用。响应曲面模型可用下面的多项式函数表示：式中，和为切削参数，是模型的参数(例如：加工参数)。在这个研究中，建立一个响应曲面模型，必须用MATLAB语言编写一个计算机程序，如果有足够的数据，响应曲面程序具有创建多达第十等级多项式的能力。在模型中所有的交叉条件都能考虑到（例如：参数的相互影响）。响应曲面模型同样能在参数相反的条件下生成，即：如果需要的话能用取代。在建立响应曲面模型中，为5个参数（、和）设计的基于3个等级的全部因素试验决定了243个表面粗糙度值，将其分为训练数组和检验数组两部分。训练数组包括236个用于模具安装中的粗糙度。为了节省空间，大量的训练数组值用图4表示，而不用表格。在图4中横坐标表示数组数，纵坐标表示相应的表面粗糙度值。检验数组包括7个表面粗糙度值，用于检验响应曲面模具的精度。检验数组如表2所示。它们都选自243个数组，显示了切削参数空间上良好的分布状况和在响应曲面模具精度上的良好检验。在这个研究中，用设计的程序建立和检验从第一等级到第四等级的响应曲面模型。表3中几个响应模型的建立显示了各自精度上的误差。在表3中相反的部分中：0表示参数，1表示它的倒数。四等级的全部多项式方程为：用测量数组得到最好的安装结果，用检验数组检查响应曲面模具的精度。最大的精度误差大约为2.05%。这一结果表明切削参数在允许的变化范围内响应曲面模具获得预期的表面粗糙度值具有足够的可能性。4、最优切削条件下获得的表面粗糙度4.1最优化问题的公式化由于表面粗糙度值表示模具铣削质量的高低，因此希望得到尽可能低的表面粗糙度。在合适的数学优化条件方法的帮助下通过调整切削条件，很容易得到较低的表面粗糙度。为了获得最小的表面粗糙度必须将这个问题用标准的数学形式公式化。如下：参数：、最小化方程：Ra（、）限制条件：Ra0.412m参数取值范围：0.08 0.13100 3000.3 0.71 20.001 0.01在等式3中Ra值是在第三章中获得的响应曲面模具的表面粗糙度。、和都是切削参数。在最优化问题定义如上的同时，迫切需要通过约束来定义一个解决方案。限制定义一个表面粗糙度值Ra，如果可以的话使它小于243个数组中的最小值。243个数组中最小表面粗糙度值是0.412m。基于Sandvik Tool Catalogue 的推荐，选择最优化切削参数的范围。4.2最优化的解决方法用成熟的响应曲面模型和成熟的遗传算法来解决等式3表示的最优化问题。如图5基于自然界生物进化过程的演变，交互式的遗传算法解决优化问题。在解决这个问题的过程中，需要无规律地选择一套参数。设定取决于它们表面粗糙度值的等级（如遗传算法中的值）。获得最小的表面粗糙度取决于最优的参数组合，新参数的组合是用模仿生物后裔结构的交叉变异而成的。这个过程一直重复直到表面粗糙度值和新的参数组合不再产生。最优化解决方法就是参数的最后组合，遗传算法的重要参数：种群大小、变异比率、重复次数等，它们的值都在表4中给出。用MATLAB编写遗传算法，染色体的选择基于对象值和限制等级，合适的种群大小偏向于最小目标值和在它们的后代中最不可出现提趋势。大部分遗传算法在获得解之前，通过处罚函数把限制优化的问题转化为非限制优化的形式。这就引出了选择合适的处罚系数的难题，它需要使用者的经验。在这次研究的程序中不需要处罚系数，所以这个难题被避免了。4.3优化结果及对它的讨论解决这个优化问题后，遗传算法使表面粗糙度从降到，和原始切削条件下的表面粗糙度相比降幅几乎是10%。最优化切削条件获得的表面粗糙度在表5中列出。通过遗传算法所获得的最优化切削条件被物理测量所证实。在图6中把预期的表面粗糙度和物理测量作了比较。从图6中可以看出物理测量和遗传算法的结果非常接近。5、结论在这个研究中，在铣削铝合金7075T6制成的模具表面时，为了获得预期的表面粗糙度，应用了一个第四等级的响应曲面模型。在生成响应曲面模型时，用了数理统计响应曲面法。响应曲面模型的精确度被试验测量所证实。精确度的误差很小，只有2.05%。成熟的响应曲面模型和成熟的遗传算法在寻找最优化切削条件，获得最小表面粗糙度上有很大的联系。模具和表面粗糙度由优化前的降到优化后的。遗传算法使表面粗糙度提高了10%，预期的最优化切削条件被试验测量证实。研究发现遗传算法的预测结果和实验结果相差很小，误差小于1.4%。这表示在这个研究中用到的成熟的响应曲面模型和成熟的遗传算法获得最优化方法是有效的，它还可以用于解决其它机械方面的问题，如：刀具寿命、尺寸误差等等。致谢作者感谢卡卡里大学的Dr. Mustafa COL提供了该项目，也感谢吉布兹工业技术学院的Dr. Fehmi ERZINCANLI为本项目提供了数控铣削加工中心。Journal of Materials Processing Technology 170 (2005) 1116Application of response surface methodology in the optimizationof cutting conditions for surface roughnessH.Oktema, T. Erzurumlub, H. KurtaranbaDepartment of Mechanical Engineering, University of Kocaeli, 41420 Kocaeli, TurkeybDepartment of Design and Manufacturing Engineering, GIT, 41400 Gebze, Kocaeli, TurkeyReceived 16 July 2004; received in revised form 12 March 2005; accepted 12 April 2005AbstractThis paper focuses on the development of an effective methodology to determine the optimum cutting conditions leading to minimumsurface roughness in milling of mold surfaces by coupling response surface methodology (RSM) with a developed genetic algorithm (GA).RSM is utilized to create an efficient analytical model for surface roughness in terms of cutting parameters: feed, cutting speed, axial depthof cut, radial depth of cut and machining tolerance. For this purpose, a number of machining experiments based on statistical three-level fullfactorial design of experiments method are carried out in order to collect surface roughness values. An effective fourth order response surface(RS) model is developed utilizing experimental measurements in the mold cavity. RS model is further interfaced with the GA to optimize thecutting conditions for desired surface roughness. The GA reduces the surface roughness value in the mold cavity from 0.412?m to 0.375?mcorresponding to about 10% improvement. Optimum cutting condition produced from GA is verified with the experimental measurement. 2005 Elsevier B.V. All rights reserved.Keywords: Milling; Cutting conditions; Surface roughness; Injection molding; Response surface methodology; Genetic algorithm1. IntroductionRecentdevelopmentsinmanufacturingindustryhavecon-tributed to the importance of CNC milling operations 1,2.Milling process is required to make mold parts used for pro-ducingplasticproducts.ItisalsopreferredinmachiningmoldpartsmadeofAluminum7075-T6material.Aluminum7075-T6 material as chosen in this study is commonly utilized inaircraft and die/mold industries due to some advantages suchashighresistance,goodtransmission,heattreatableandhightensile strength 3,4.The quality of plastic products manufactured by plas-tic injection molding process is highly influenced by thatof mold surfaces obtained from the milling process. Sur-face quality of these products is generally associated withsurface roughness and can be determined by measuring sur-face roughness 5. Surface roughness is expressed as theirregularities of material resulted from various machiningCorresponding author. Tel.: +90 262 742 32 90; fax: +90 262 742 40 91.E-mail address: .tr (H.Oktem).operations. In quantifying surface roughness, average sur-face roughness definition, which is often represented with Rasymbol, is commonly used. Theoretically, Rais the arith-metic average value of departure of the profile from themean line throughout the sampling length 6. Rais alsoan important factor in controlling machining performance.Surface roughness is influenced by tool geometry, feed, cut-tingconditionsandtheirregularitiesofmachiningoperationssuch as tool wear, chatter, tool deflections, cutting fluid, andworkpiece properties 7,11,16. The effect of cutting con-ditions (feed, cutting speed, axialradial depth of cut andmachining tolerance) on surface roughness is discussed inthis study.Several researchers have studied the effect of cutting con-ditions in milling and plastic injection molding processessuch as in vacuum-sealed molding process 5. Analyticalmodels have been created to predict surface roughness andtool life in terms of cutting speed, feed and axial depth of cutinmillingsteelmaterial8,9.Aneffectiveapproachhasalsobeen presented to optimize surface finish in milling Inconel718 10.0924-0136/$ see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2005.04.09612H.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 1116In this study, a fourth order response surface (RS) modelfor predicting surface roughness values in milling the moldsurfaces made of Aluminum (7075-T6) material is devel-oped. In generating the RS model statistical response surfacemethodology (RSM) is utilized. The accuracy of the RSmodel is verified with the experimental measurement. Thedeveloped RS model is further coupled with a developedgeneticalgorithm(GA)tofindtheoptimumcuttingconditionleadingtotheleastsurfaceroughnessvalue.Cuttingconditionis represented with cutting parameters of feed, cutting speed,axialradial depth of cut and machining tolerance. The pre-dicted optimum cutting condition by GA is validated with anexperimental measurement.TheRSmodelandGAdevelopedandutilizedinthisstudypresent several advantages over other methods in the litera-ture. The RS model is a higher order and more sophisticatedpolynomial model with sufficient accuracy. The GA elimi-nates the difficulty of user-defined parameters of the existingGAs. Details of the RS model generation by RSM and theoptimization process by GA are given in the following sec-tions.2. Experimental procedures2.1. Plan of experimentsAn important stage of RS model generation by RSM isthe planning of experiments. In this study, cutting experi-ments are planned using statistical three-level full factorialexperimentaldesign.Cuttingexperimentsareconductedcon-sidering five cutting parameters: feed (ft), cutting speed (Vc),axial depth of cut (aa), radial depth of cut (ar) and machin-ing tolerance (mt). Overall 35=243 cutting experiments arecarried out. Lowmiddlehigh level of cutting parameters incuttingspaceforthree-levelfullfactorialexperimentaldesignisshowninTable1.Rangesofcuttingparametersareselectedbased on recommendation of Sandvik Tool Catalogue 12.Milling operations are performed at the determined cuttingconditions on a DECKEL MAHO DMU 60 P five axis CNCmillingmachine.Surfaceroughness(Ra)valuesaremeasuredfrom the mold surfaces.2.2. Tool and materialCutting tool used in experiments has the diameter of10mm flat end mill with four teeth. The material of the toolTable 1Lowmiddlehigh levels of cutting parameters in three-level full factorialdesign of experimentCutting parametersThree- level valuesFeed, ft(mm/tooth)0.080.1050.13Cutting speed, Vc(m/min)100200300Axial depth of cut, ar(mm)Radial depth of cut, ar(mm)11.52Machining tolerance, mt(mm)0.0010.00550.01Fig. 1. Mold part.is PVD AlTiN coated with solid carbide. It has the helixangle of 45and rake angle of 10. Machining experimentsare performed in the mold cavity on aluminum (7075-T6)block with dimensions of 120mm120mm50mm. Thechemical composition of workpiece material is given in thefollowingspecification(wt.%):1.6Cu,2.5Mg,0.23Cr,5.40Zn. The hardness of workpiece is measured as 150BHN.The mechanical properties of aluminum material are: ten-sile strength of 570MPa, yield strength of 505MPa, shearstrength of 330MPa and elongation of 11%.Surface roughness is measured with Surftest 301 pro-filometerattraverselengthof2.5mmalongcenterlineofsam-pling. Converting the measurement into a numerical value,mathematical definition of Rais used. Since this way of con-version is common in the literature it is adopted in this studyas well 79. Each Rameasurement is repeated at least threetimes. Average of three Ravalues is saved to establish RSmodel.2.3. Mold partsThe mold part used in this study is utilized to producethe components of an orthose part in biomechanical appli-cations. It is shown in Fig. 1. Orthose parts are generallyutilized in walking apparatus that holds human legs in stableposition during walking. It binds the kneecap region of legand is equipped with cylindrical bars that are made of alu-minum material in diameter of 12mm and length of 300mm.Orthose part consists of three main components; one of themis employed as the working model in this study.2.4. Manufacturing the components of orthose partThree machining processes are implemented in order tomanufacture each component of the orthose part in an inte-gratedmanner.Firstly,theselectedcomponentismachinedinCNC milling machine. Ravalues are then taken from the sur-faces in the mold cavity. Secondly, plastic product is injectedH.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 111613Fig. 2. The parts obtained from three machining process.Fig. 3. The stages taken in creating a response surface model by RSM.in plastic injection machine produced by ARBURG. Poly-acetal (POM) C 9021 material is used to inject the polymermaterial. The properties of polymer material has the den-sity of solution 1.2g/cm3, the ejected temperature of 165C,viscosity of 50Pas and melt flow-fill rate of 0.8cm3/min.Finally, net casting process is applied for producing die cast-ing part. Mold part, plastic product and die casting part areillustrated in Fig. 2.3. Response surface model for surface roughnessRS model, which is an analytical function, in predictingsurfaceroughnessvaluesisdevelopedusingRSM.RSMusesstatistical design of experiment (experimental design) tech-nique and least-square fitting method in model generationphase. It is summarized in Fig. 3. RSM was originally devel-oped for the model fitting of physical experiments by Boxand Draper 13 and later adopted in other fields. RS modelis formulated as following polynomial function:f = a0+n?i=1aixi+n?i=1n?j=1aijxixj+ (1)wherea0,aiandaijaretuningparametersandnisthenumberof model parameters (i.e. process parameters). In this study,to create RS model, a computer program has been written inMATLAB programming language.The RS program developed has the capability of creat-ing RS polynomials up to 10th order if sufficient data exist.All cross terms (i.e. interactions between parameters) in themodels can be taken into account. RS models can also begenerated in terms of inverse of parameters. That is, xicanbe replaced as1xi(i.e. inversely) in RS model if desired, increating the RS models, 243 surface roughness values deter-mined based on three-level full factorial experimental designfor five parameters (ft, Vc, aa, arand mt) are used The 243data sets for surface roughness are divided into two parts;training data set and the check (i.e. test) data set. Trainingdata set includes 236 surface roughness values and is uti-lized in model fitting procedure. Because of large number ofvalues and to save space, training data is shown in Fig. 4,rather than in a table. In Fig. 4, abscissa indicates the dataset number and the ordinate indicates the corresponding sur-face roughness value. Check data sets include seven surfaceroughness values and are used in checking the accuracy ofthe RS model. Check data sets are shown in Table 2. TheyFig. 4. Comparison of experimental measurements with RS prediction for surface roughness.14H.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 1116Table 2The data set used for checking the accuracy of RS modelSet numberCutting conditionsRa(?m)ftVcaaarmtMeasurement resultsRSM modelMaximum test error (%)10.1052000.710.0010.5910.5892.0520.105200010.6290.62730.1052000.310.00550.7810.77540.082000550.8990.89550.081000.720.00550.9780.99660.0820011.6741.70670.1052000.520.011.8561.893Table 3The accuracy error of several RS modelsReciprocal flagFirst orderSecond orderThird orderFourth order000002774.82.70010025.97.285.82.950000152.410.94.02.991100027.26.634.82.050110025.97.05.52.550001154.91110025.87.035.72.50111027.57.05.92.81111153.03are selected from 243 data sets to show a good distributionin the cutting parameters space and thereby to have a goodcheck on the accuracy of the RS model.In this study, RS models of varying orders from first orderto fourth order are created and tested with the developedprogram. Several RS model created are demonstrated alongwith their accuracy errors in Table 3. In reciprocal section inTable3,0indicatesaparameter(xi),1indicatestheinverseofa parameter (1xi). The full fourth order polynomial functionof the form:Ra= a0+ a11ft+ a21Vc+ a3aa+ a4ar+ a5mt+ +an?1ft1Vcaaarmt?4+ + am(mt)4(2)fits best (with minimum fitting error) to the training data set.The accuracy of the RS model was checked using the checkdata set. The maximum accuracy error is found to be about2.05%. This indicates that RS model generated has sufficientaccuracy in predicting surface roughness within the range ofcutting parameters.4. Optimization of cutting conditions for surfaceroughness4.1. Optimization problem formulationSince it is indicator of surface quality in milling of moldsurfaces, surface roughness value is desired to be as low aspossible. Low surface roughness values can be achieved effi-ciently by adjusting cutting conditions with the help of anappropriate numerical optimization method. For this, mini-mization of surface roughness problem must be formulatedin the standard mathematical format as below:Find : ft,Vc,aa,ar,mt(3a)Minimize : Ra(ft,Vc,aa,ar,mt)(3b)Subjected to constraints : Ra 0.412?m(3c)Within ranges :0.08mm ft 0.13mm100mm Vc 300mm0.3mm aa 0.7mm1mm ar 2mm0.001mm mt 0.01mm.In Eq. (3), Rais the RS model developed in Section 3.ft, Vc, aa, arand mtare the cutting parameters. In the opti-mization problem definition above, a better solution is alsoforcedthroughtheconstraintdefinition.Constraintdefinitionsearches a surface roughness value (Ra), which is less thanthelowestvaluein243datasetifpossible.Minimumsurfaceroughness value in 243 data set is 0.412?m. The ranges ofcutting parameters in optimization have been selected basedon the recommendation of Sandvik Tool Catalogue.4.2. Optimization problem solutionTheoptimizationproblemexpressedinEq.(3)issolvedbycouplingthedevelopedRSmodelwiththedevelopedgeneticalgorithm as shown in Fig. 5.The genetic algorithm 14 solves optimization problemiteratively based oh biological evolution process in nature(Darwinstheoryofsurvivalofthefittest).Inthesolutionpro-cedure, a set of parameter values is randomly selected. Set isranked bashed on their surface roughness values (i.e. fitnessFig.5. Interactionofexperimentalmeasurements,RSmodelandGAduringsurface roughness optimization.H.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 111615Table 4GA parametersSubjectValuesPopulation size50Crossover rate1.0Mutation rate0.1Number of bit16Number of generations540values in the GA literature). Best combination of parametersleading to minimum surface roughness is determined. Newcombination of parameters is generated from the best com-bination by simulating biological mechanisms of offspring,crossover and mutation. This process is repeated until sur-face roughness value with new combination of parameterscannot be further reduced anymore. The final combination ofparameters is considered as the optimum solution. The criti-calparametersinGAsarethesizeofthepopulation,mutationrate,numberofiterations(i.e.generations),etc.andtheirval-ues are given in Table 4.The GA written in MATLAB programming languageselects chromosomes based on the objective value and thelevel of constraint violation. Fitness values of the popula-tion are biased towards the minimum objective value andthe least infeasible sets in offspring phase. Most of GAs inthe literature converts the constrained optimization probleminto an unconstrained optimization problem through penaltyfunction before the solution. This brings the difficulty ofappropriate selection of problem dependent penalty coeffi-cient which requires user experience. In the program used inthis study, this difficulty is avoided since no problem depen-dent coefficient is needed 15.4.3. Optimization results and discussionBy solving the optimization problem, the GA reducesthe surface roughness of mold surfaces from 0.412?m to0.375?m by about 10% compared to the initial cutting con-dition. The best (optimum) cutting condition leading to theminimum surface roughness is shown in Table 5. The pre-dicted optimum cutting condition by GA is further validatedwith a physical measurement. Predicted surface roughnessvalue is compared with the measurement in Fig. 6. FromTable 5The best cutting conditionParametersAfter optimizationCutting conditionft(m/tooth)0.083Vc(m/min)200aa(mm)0.302ar(mm)1.002mt(mm)0.002Ra(?m)Measurement0.370GA0.375Fig. 6. Surface roughness measurement.Fig. 6 it is seen that GA result agrees very well with themeasurement.5. ConclusionsIn this study, a fourth order RS model for predicting sur-face roughness values in milling mold surfaces made ofAluminum (7075-T6) material was developed. In generat-ing the RS model statistical RSM was utilized. The accuracyof the RS model was verified with the experimental mea-surement. The accuracy error was found to be insignificant(2.05%). The developed RS model was further coupled witha developed GA to find the optimum cutting condition lead-ingtotheleastsurfaceroughnessvalue.Surfaceroughnessofthe mold surfaces, which was 0.412?m before optimization,was reduced to 0.375?m after optimization. GA improvedthe surface roughness by about 10%. The predicted optimumcutting condition was validated with an experimental mea-surement. It was found that GA prediction correlates verywell with the experiment. Difference was found to be lessthan 1.4%. This indicates that the optimization methodologyproposed in this study by coupling the developed RS modelandthedevelopedGAiseffectiveandcanbeutilizedinothermachiningproblemssuchastoollife,dimensionalerrors,etc.as well.AcknowledgementsThe aut

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