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基于 proe 齿轮 减速器 设计 动态 仿真

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基于proe的齿轮减速器设计与动态仿真,基于,proe,齿轮,减速器,设计,动态,仿真

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陕西理工学院毕业设计论文任务书院（系） 机械工程学院 专业 机械设计制造及其自动化 学生姓名 王华 一、 毕业设计题目 齿轮减速器设计与动态仿真 二、 毕业设计工作自 2009 年 3 月 15 日起至 2006 年 6 月 15 日止三、 毕业设计进行地点： 校 内 四、 毕业设计内容要求： 齿轮减速器具有传动效率高、结构紧凑、传动平稳等优点，因此被广泛地应用于各类机器设备。齿轮减速器系统动力学研究的目标，是确定和评价齿轮系统的动态特性，从而为设计高质量的齿轮系统提供理论依据。 主要技术指标： 1. 在题目要求下进行二级齿轮减速器的结构设计,绘制装配图和零件图。 2. 在三维软件环境下建立整机模型。 3.对指定的齿轮和轴进行应力分析和齿轮的模态分析。 结果形式 1. 0号装配图一张,2号零件图1张(箱体)、3号零件图2张（齿轮、轴) 2. 编写毕业论文一本, 不得少于20000字; 3. 译英文资料一份(不少于3万印刷符)。 进度与要求1.第3-4周 翻阅相关资料，掌握毕业设计内容要求,写开题报告；2.第5-7周 进行二级齿轮减速器的结构设计， 绘制减速器装配图与零件图3.第8-13周 在三维软件环境下建立整机模型： 6.第14-15周 对指定的齿轮和轴进行应力分析和齿轮的模态分析；7,第16-17周 撰写毕业论文,准备毕业论文答辩。 指 导 教 师 系（教研室） 机械设计教研室 系（教研室）主任签名 批准日期 接收论文（设计）任务开始执行时间 学生签名 王华 齿轮减速器设计及动力学仿真【摘要】： 本文在虚拟样机技术理论的指导下，在国外高新软件CAD/CAE/CAM特征造型工具Pro/E (PRO/ENGINEER )、有限元分析软件ANSYS集成系统基础上，对圆柱齿轮减速器进行了研究。首先利用Pro/E软件对其进行了三维参数化建模和装配，并进行了运动学分析，验证了模型的正确性和合理性;然后利用有限元分析元件ANSYS对圆柱齿轮减速器的关键零部件齿轮、轴等进行了有限元静力学和动力学分析，校核了其各项性能，为优化设计提供了理论依据;最后利用有限元分析软件ANSYS对输出轴进行了优化设计，并阐述了利用虚拟样机技术对圆柱齿轮减速器进行系统优化设计的理论思想和方法。【关键词】:虚拟样机技术、齿轮减速、有限元分析、仿真Software in the nowadays world-Pro/E (Pro/ENGINEER) and ANSYS(the finite element analysis software)【Abstract】: This paper studies and the optimization designing of The Cylindrical Gear Reducer. With the advanced。First, the 3D models of the Reducer is built up with the software Pro/E realizing 3D parameterized modeling, and the 3D assembly models are built up accordingto related assembly character, and validates the correctness of the models bydong the kinematics analysis. Then the dynamics analysis is made for calculatingforces on the gears and axes, which are the boundary conditions for the FEA.Based the boundary conditions, the FEA static and dynamics analysis of the key A parts of the Reducer-gear and axe is made with the FEA software ANYSY. Theseanalysises provide the theory bases for the optimization designing by severalcharacteristics testings. In the end, the optimization designing of the axe is did with the FEA software ANSYS and the method and theory of the system optimization designing is expatiated. The method and theory used in this paper can also be used in other products and systems.【Keywords】: Cylindrical Gear Reducer、the finite element analysis、Simulation目录1 绪论41.1 本设计的目的及意义41.2 减速器的发展状况51.3 减速器的发展趋势52 传动装置总体设计62.1 确定传动方案62.1.1 电动机的容量选择72.1.2 电动机转速的选择82.1.3 电动机型号的确定82.1.4 传动比的分配92.1.5 传动系统的运动和动力参数计算92.2 传动零件的设计102.2.1 高、低速级齿轮的参数计算102.2.2 齿轮结构设计及绘制齿轮零件图162.3轴及轴承装置的设计计算172.3.1轴的设计172.3.2轴的校核212.3.3 轴承的寿命计算312.4 箱体上个部分尺寸计算；323 Pro/E三维参数化设计353.1概述353.2建立模型363.3基于Pro/E的圆柱齿轮减速器装配过程393.3.1产品装配过程393.3.2减速器机构运动仿真413.4选择“测量结果”以图形方式查看位置结果424 减速器关键零部件的有限元分析434.1 ANSYS的简介434.1.1 ANSYS10.0的新特点444.1.2 ANSYS软件功能模块444.2 ANSYS分析主要步骤454.3结构静力分析464.4模态分析简介474.5输出轴有限元静力学分析474.6大齿轮模态分析50参考文献52设计小结53致 谢541 绪论随着社会的发展和人民生活水平的提高，人们对产品的需求是多样化的，这就决定了未来的生产方式趋向多品种、小批量。在各行各业中十分广泛地使用着齿轮减速器，它是一种不可缺少的机械传动装置. 它是机械设备的重要组成部分和核心部件。目前，国内各类通用减速器的标准系列已达数百个，基本可满足各行业对通用减速器的需求。国内减速器行业重点骨干企业的产品品种、规格及参数覆盖范围近几年都在不断扩展，产品质量已达到国外先进工业国家同类产品水平，承担起为国民经济各行业提供传动装置配套的重任，部分产品还出口至欧美及东南亚地区，推动了中国装配制造业发展。1.1 本设计的目的及意义目的： 1） 通过设计熟悉机器的具体操作，增强感性认识和社会适应能力，进一步巩固、 深化已学过的理论知识，提高综合运用所学知识发现问题、解决问题的能力。2）学习机械设计的一般方法，掌握通用机械零件、机械传动装置或简单机械的设计原理和过程。Journal of Materials Processing Technology 153154 (2004) 821828Development of a computer-aided-design system ofcold forward extrusion of a spur gearJ.H. Song, Y.T. ImComputer Aided Materials Processing Laboratory, Department of Mechanical Engineering, ME3227 Korea Advanced Instituteof Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, South KoreaAbstractIn this study, a computer-aided-design system for manufacturing a spur gear in cold forward extrusion was developed under a graphicaluser interface environment. The influence of gear geometry such as total tooth number, profile shift coefficient, and module on deformationmechanics was investigated by the three-dimensional finite element (FE) program CAMPform3D in terms of complete formation of theteeth and the level of forming loads. From such investigations and literature survey on existing design practices, necessary rule basesincluding limiting extrusion ratio at the cross-section of the root and limiting ratio between extrusion ratios of the addendum and root ofa gear were established and applied for process design of extrusion of solid or hollow spur gears. The developed system can provide afeasible set of gear and pinion geometries for a given input data satisfying required product capacities such as contact ratio and bendingstrength. Thus, design engineer can easily select the better product design depending on individual priority of the product and reduces thelead time and cost required at the initial design stage of extrusion of spur gears at practice. 2004 Elsevier B.V. All rights reserved.Keywords: Computer-aided-design; Spur gear; Extrusion ratio; Rule base1. IntroductionCold extrusion of a solid or hollow spur gear or pinionhas economic advantages such as material saving and highproductivity compared to conventional machining. Also, ex-truded gears or pinions have better wear and fatigue prop-erties than those machined. Because of this, the process hasbeen widely used in production of pinion for automobilestarter. In cold extrusion, the acquisition of die design skillobtaining complete formation of a tooth under the allowableforming load is essential to achieve the competitiveness ofa formed product. Due to rapid development of computers,the application of computer-aided engineering such as finiteelement (FE) analyses has been actively used in industry re-cently.In particular, the improvement of computer speed en-ables the three-dimensional FE analysis, from which reli-able knowledge of the formation of a product with com-plex geometry can easily be obtained. In the area of gearmanufacture, there have been many studies reported apply-ing three-dimensional FE simulations. Since various designparameters must be considered, design method merely rely-Corresponding author. Tel.: +82 42 869 3227; fax: +82 42 869 3210.E-mail address: ytimwebmail.kaiist.ac.kr (Y.T. Im).ing on the analysis leads to the waste of development time.Instead, development of a computer-aided-design system isnecessary for the product and die designs of a solid or hol-low spur gear or pinion.In the field of metal forming, process design systemsbased on rule base or knowledge base have been activelydeveloped for an axi-symmetric geometry so far 15. Inaddition, in order to improve the flexibility of the system,various design methodologies in connection with heuristicsearching algorithm, neural network, and FE analyses havebeen applied. Kim and Altan 6 utilized a commercial FEprogram as the verification tool of the designed process se-quence. Osakada et al. 7 have designed a cold forging se-quence by hybriding FE simulation results with the designsystem using neural network. Kim and Im 8,9 have devel-oped an expert system for a multi-stage process sequencedesign system, in which Aand depth-first search techniquewere introduced for obtaining uniform forming load andstrain distribution during the process. However, the devel-opment of design system for complex three-dimensional ge-ometry like gears and pinions is not available so far.In the present investigation, a computer-aided-design sys-tem in cold extrusion of solid or hollow spur gears and/orpinions was developed under the graphical environment.Various extrusion ratios were introduced to establish a de-sign rule in order to achieve complete formation of a tooth.0924-0136/$ see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2004.04.178822J.H. Song, Y.T. Im/Journal of Materials Processing Technology 153154 (2004) 821828An in-house FE simulator CAMPform3D 10 was used toinvestigate the influence of gear geometry such as the num-ber of teeth, module, profile shift coefficient, pressure angle,and clearance ratio on the deformation mechanics. Basedon FE simulation results and the literature survey, rule basewas constructed based on the limiting extrusion ratio at thecross-section of the root and limiting ratio between extrusionratios of the addendum and root of a gear. In order to de-termine the forming load requirement, an existing empiricalformula for the axi-symmetric geometry was modified. Inresult, a case study designing a set of gear and pinion basedon the rule base determined and product capacities such ascontact ratio and bending strength was performed. Finally,the effect of elastic deformation of a die on the profile of atooth was investigated through numerical simulations.2. BackgroundIn general, the design procedure of a spur gear and/orpinion called product design can be divided into two stages,initialanddetaildesign.Attheinitialdesignstage,thevaluesof basic specification such as the number of teeth n, modulem, profile shift coefficient p, pressure angle , and clearanceratio c should be either provided by the user or determinedautomatically by the design system if not provided.Once these are given as input, then, detail design can bemade in terms of calculating detail specification such as theradii of addendum Ro, pitch Rp, base Rb, and root RrasfollowsRo=nm2+ (p + 1)m,Rp=nm2,Rb=nm2cos,Rr=nm2 (c + 1 p)m.(1)Thisequationapplieseitherforagearorpinion,respectively.The graphical representation of such data for a gear is givenFig. 1. (a) Schematic diagram of extrusion die of a spur gear and (b) calculation of bending strength available in reference 11.in Fig. 1(a). In this figure R represents the radius of billetcontainer and Rmthe radius of mandrel if necessary forhollow ones.Normally, detail design should satisfy the required prod-uct capacities such as contact ratio and allowable bendingstrength of the material used. If not, the values of basic spec-ification should be modified for a successful design. Contactratio indicates the level of overlapping between their con-tacting teeth and can be calculated through the followingequation.Mc= f?2nmg2Ro mng?2Ro mng2m?+f?2mnp2ro mnp?2Ro mnp2m? f?ng+ npy?y,wherey =Dcm?ng+ np2?andf(x)=?(x + 2)2 x2cos2 xsin2cos.(2)Here, Mcis the contact ratio, Dcthe center distance betweengear and pinion, rothe radius of addendum of the pinion, ngthe teeth number of gear, and npthe teeth number of pinion.To assure a smooth and continuous contact between thetwo, it is desirable to design a set of gear and pinion witha higher contact ratio. In addition, bending strength appliedshould be less than the allowable bending strength of thematerial to prevent the possible fracture of a tooth during theoperation. Thus, it is important to decide the bending stressacting on a tooth under the operating environment. In thepresent investigation, an empirical formula available in theliterature 11 was used in calculating its value as indicatedin Fig. 1(b).Forextrusiondiedesignofthespurgearorpinion,anothermajor issue is to achieve complete filling of a tooth underJ.H. Song, Y.T. Im/Journal of Materials Processing Technology 153154 (2004) 821828823the acceptable forming load in consideration of the machinecapacity used. Therefore, it is very important to determinea guideline to guarantee the complete filling after extrusionand predict the extrusion load required in a simple empiricalequation.For this purpose, several extrusion ratios defined as theratio between cross-sectional areas of the initial billet be-fore and after extrusion are introduced in the following toconsider the effect of gear or pinion geometry on formingcharacteristics during the process.2.1. Prediction of complete fillingNormally, there are two kinds of gears such as solid orhollow types. In order to manufacture the hollow type gears,mandrel will be used in the extrusion process. Thus, in thefollowinginvestigationtwoextrusionprocesseswithorwith-out mandrel will be considered. For solid types, Rm= 0 willbe applied in the following derivation.Since the material flows are different at the tooth and rootof a gear or pinion, extrusion ratios at the cross-section ofaddendum (ERo) and root (ERr) were defined, respectively,as followsERr=(R2 R2m)(R2r R2m),ERo=(R2 R2m)(R2o R2m).(3)Here, R and Rmare the radius of billet container and mandrelused, respectively.When the extrusion ratios are calculated at an arbitrarycross-section of a die in gear extrusion, ERrhas the highestvalue among them. In general, the risk of making formingdefect increased as the extrusion ratio increased because ofsevere deformation of the billet. Therefore, ERrwas selectedas one of design rules in the design system developed foravoiding forming defect in this study.In order to predict the likeliness of under-filling at thetooth die cavity, the ratio between extrusion ratios of theCompletefilling of atoothUnderfilling of a tooth68101214161820221.52.02.53.03.54.0ERr/oNumber of teethComplete filling zoneFig. 2. The relationship between ERr/oand filling state of a tooth obtained from FE simulations.addendum and root introduced in the former equation wasdefined asERr/o=(R2o R2m)(R2r R2m).(4)In Fig. 2, this value was obtained for various cases of thenumber of teeth by three-dimensional FE simulations. Ac-cordingtothisfigure,itwasconstruedthatthevalueofERr/oshould be higher than 2.6 to guarantee the complete forma-tion of a tooth numerically. Thus, this value was used as thelimiting value of ERr/oin the developed design system.2.2. Prediction of forming loadFor development of useful design system, the requiredforming load should be determined reasonably in a simpleway before die trial not to break the machine used. For thispurpose, an existing empirical rule available in the literature12 was modified as follows.P = CA0 o(3.45lnERe+ 1.15),(5)where P is the forming load required, C the coefficient (1.1and 1.2 for solid and hollow types, respectively), A0the areaof the initial billet, and othe yield stress of the materialused.In order to define ERein the present investigation, anequivalentcylindricalcross-sectionhavingthesameareaofagiven gear geometry was introduced and its radius defined asthe equivalent radius of the three-dimensional gear geometryRe. Then, the extrusion ratio ERefor such an equivalentcross-section can be defined asERe=(R2 R2m)(R2e R2m).(6)Comparisons of forming load estimations using Eq. (5),axi-symmetricFEsimulationsusingtheequivalentcross-section Re, and three-dimensional FE simulations aregiven in Table 1. It can be seen in this table that the required824J.H. Song, Y.T. Im/Journal of Materials Processing Technology 153154 (2004) 821828Table 1The comparison between required loads obtained from the three-dimen-sional FE simulation, axi-symmetric FE simulation, and empirical equationNumber ofteethERe3D FEsimulation(MN)Axi-symmetricFE simulation(MN)Empiricalequation(MN)1026.297.517.207.921231.379.629.2010.121436.4411.5011.2012.321641.4613.6214.1015.511846.4817.4016.6018.26forming load can be conveniently predicted using the mod-ified empirical equation or axi-symmetric FE simulationsinstead of three-dimensional FE simulations.3. Design system developmentIn this study, a computer-aided-design system for coldforward extrusion of solid or hollow spur gear and/or pin-ion was developed using the Visual C+language in theWindows environment. Fig. 3 shows the overall structure ofthe system developed, in which the system is composed ofmodules for input, product and die designs, and output.Since the design engineer provides either all the basicspecification or some important parameters such as the num-ber of teeth, module, and pressure angle to determine theproduct specification, the developed system was designed intwo ways as follows:At first, when the user inputs all the design variable val-ues, the system will check whether contact ratio and bend-ing strength are acceptable for the given input data. If it isfound to be satisfactory, then the design system will proceedwith the die design stage based on design rules stored in theInputMaterialLimiting contact ratio (Mc limit )Applied load (P)Angle of applied load ( )Center distance (Dc)Limiting bending strength( )Liming forming load (Llimit)Number of teeth (n)Module (m)Pressure angle ( )Profile shift coefficient (p)Clearance ratio (c)Radius of a billet container (R)Radius of a mandrel (Rm )Product design variablesTooth width (b)Die design variablesitb limRule baseLimiting value of ERrLimiting ratio of extrusionratios of addendum and rootof ERr/oDesign a set of gear and pinionAre limiting product capacities satisfied?NYAre all the basicspecifications given?YNChange value of product design variables within the limiting rangesText fileDxf fileDesign a dieAre design rule basessatisfied?NOutputChange value of die designvariables within the limiting rangesYFig. 3. Overall structure of the developed system for cold forward extrusion of a spur gear.system. Depending on the given data provided, several pos-sible die designs from which the user can choose the bestcandidate according to his own choice will be available inthe developed system.In other cases when the designer provided some importantparameters, a range of values for each missing parameterof basic specification can be input into the current systeminstead. In this case, the product design module will generatevarious possible product designs within these ranges thatwill satisfy the required product capacities of contact ratioand bending strength as described in the following. Then, diedesigns for each of these product designs will be availableto the user as before.3.1. InputIn the input module, for product design the user shouldprovide the basic specification of the gear and/or pinion. Asmentioned, the user can provide an exact value or a rangeof values of each product design variable as desired. Also,the center distance between the gear and pinion to calculatethe contact ratio using Eq. (2) and the limiting contact ratiovalue needed to be specified by the user. Likewise, the usershould provide the applied load, angle of applied load, andtooth width for calculating the bending strength. For the diedesign stage, the user can provide either the fixed valuesor allowable ranges of billet container and mandrel radii.Also, the type of material can be chosen from the materialdatabase in the current system.3.2. Product designContact ratio and bending strength were considered to bemajor product constraints to be satisfied in the current in-vestigation. If the basic specification data of the gear and/orJ.H. Song, Y.T. Im/Journal of Materials Processing Technology 153154 (2004) 821828825Basic specificationof gear and pinionCalculate detail specificationMc limitMcStartYvariminvari varimaxSave in the system memoryArrange product design variablesgiven as the ranges by the uservar1var2varn.Calculate contact ratio McCalculate bending stressbbitb limYEndiiivarvarvar+=NNEndCalculate Ro, Rr of a productDesigned sets ofgear and pinionCalculate ERr, ERo, ERe, and ERr/o ERrERr limitERr/o Err/o limitMaterial databaseStartRule baseCalculate forming loadLoad LlimitYYYRmin= Max (Ro, Rinputmin), Rmax= Min (Rtrap, Rinputmax)Calculate limiting range of the radius of billet container NNRmin RRmaxRm min Rm Rm maxRm =Rm +NR =R+Rm =Rm minRm min= Max (Rmf, Rm inputmin), Rm max= Min (Rr, Rm inputmax)Calculate limiting range of mandrel mRmRSave in the system memory(a)(b)Fig. 4. Flow chart of the developed system: (a) product design and (b) die design.pinion set are available, then, the designer can simply usethe current system to check whether these data satisfy theproduct constraints. However, in most cases it is more likelythat the designer does not know the exact basic specifica-tion to be used for the gear and/or pinion set. Selectingappropriate specification for a gear and/or pinion set thatwill satisfy required product constraints is usually very dif-ficult since the effects of many variables are coupled to eachother.Thus, in the currently developed product design system,the user can assign a range of allowable values of designvariable instead of just a fixed value. Or the user can usecombinations of fixed variables and variables with allowableranges as desired.When using ranges of design variables, the designer mustassign an incremental factor variof design variables alongwith their allowable ranges as presented in Fig. 4(a). Amongthe numerous combinations of design variable values thatare acceptable, the design system finds all the combinationsof variables that will satisfy both the limiting contact ratioMclimitand bending strength blimit. The list of satisfactoryproduct designs and their values of contact ratio and bendingstress can be provided to the designer. Thus, the designercan select the most suitable design depending on his ownchoice. The product design that gives the greatest contactratio or smallest bending stress will be indicated by thecurrent design system as well.3.3. Die designCompletefillingofteethunderanacceptableformingloadwas the main design objective in the die design stage of thecurrent system. The radii of billet container R and mandrelRmwere taken as the two design variables to achieve this.If the user provided R and Rmas fixed values, then, fillingstatus of the product was merely checked and made knownto the user.In the more likely case where the designer must find ap-propriate values of R and Rm, the current design system pre-scribes allowable ranges of R and Rmvalues according tothe product geometry determined by the previous productdesign module. The user can directly provide limiting val-ues for R and Rmat this level. If not, the upper and lowerlimits of R and Rm, respectively, were determined automat-ically by the system as shown in Fig. 4(b). In this figure,Rtrapand Rmfwere calculated as followsRtrap= Rr?ERrlimit,Rmf=?(ERr/olimitR2r R2o)(ERr/olimit 1).(7)Here, ERrlimitis the limiting extrusion ratio of the selectedmaterial in trapped cold forward extrusion and ERr/olimitthelimiting ratio between extrusion ratios of the addendum androot of the gear or pinion.826J.H. Song, Y.T. Im/Journal of Materials Processing Technology 153154 (2004) 821828Once these allowable ranges of design variables were set,the design procedure proceeded by making repetitive calcu-lations with incrementally varying values of R and Rmasshown in Fig. 4(b) to determine design variables that wouldresult in complete filling with acceptable forming load. Insuch iterations, the increments, R and Rmneeded to beprovided by the user. The rule base used to adjust values ofdesign variables can be summarized as followsRule 1. If ERris greater than ERrlimit, then R is increasedby R and Rmis set as Rmmin.Rule2.IfERr/oislessthanERr/olimit,thenRmisincreasedby R.Rule 3. If forming load is greater than Llimit, then R isincreased by R and Rmis set as Rmmin.Here, Llimitis the limiting forming load given by the user ac-cording to the machine capacity and the value of ERr/olimitwas set to be 2.6 from FE simulation results of Fig. 2 as pre-viously mentioned. In the above rules 2 and 3 were used toensure complete filling of teeth. Then, the designs that satis-fied the prescribed forming load limit were saved in the sys-tem memory and made available to the designer. The abovewas continuously repeated until R and Rmhave reached theirupper limits prescribed.3.4. OutputThe final information of product and die designs such assets of gear and pinion, the radii of billet container and man-drel, forming load, and bending strength can be displayedas graphic representations or tables on the PC monitor. Inaddition, the results can be stored as text files or .dxf filesto generate drawings using commercial AutoCAD.4. ApplicationsAnexampleofthespurgearandpiniondesignwascarriedout to illustrate the capabilities of the currently developedFig. 5. (a) Designed set of gear and pinion and (b) the radii of billet container and mandrel graphically displayed for the gear.design system. In this example the design variables of profileshift coefficient and clearance ratio were given in terms ofallowableranges,whiletheotherdesignvariablesweregivenas fixed values. Fig. 5(a) shows the product design that wasfound to satisfy the limiting contact ratio of 1.3 and bearingstrength of 70MPa. In this figure, designed product set alongwith geometric information of basic and detail specificationswas graphically displayed. In Fig. 5(a), the applied loadwas assumed to be 900N, the applied load angle 60, andthe tooth width 10mm. With these assumptions of workingcondition, the bending stress in the pinion and gear werecalculated to be 50.1 and 30.0MPa, respectively.The table shown in Fig. 5(b) lists the possible radii of thebillet container and mandrel that can be used to form thegear designed in Fig. 5(a) when the type of material usedwas AISI1010. In this table shown in Fig. 5(b), the use ofmandrel was determined to avoid the incomplete formationof gear teeth. The design case of using mandrel and billetcontainer radii of 32 and 56mm is graphically represented inthis figure as well. The forming loads determined by Eq. (5)were 2.7MN and 5.8MN for the solid pinion and hollowgear, respectively.In order to examine the validity of the above designs,three-dimensional FE simulations were carried out to checkcomplete filling of teeth and forming load.Fig. 6(a) and (b) show the distributions of effective strainwhen forming the gear and pinion of Fig. 5(a). As previouslymentioned, the gear and pinion were formed with and with-out using the mandrel, respectively. In these simulations, theconstant shear friction factor was assumed to be 0.2 and theflow stress equation of AISI1010 ( = 650 0.25MPa) wasused. The predicted forming loads by 3D FE simulationswere 2.3 and 5.7MN for the solid pinion and hollow gear,respectively.Finally, elastic analysis was conducted to investigate thedeformation of a tooth profile caused by elastic deformationof the die in Fig. 7. Super hard material having chemicalcomposition of 90% tungsten carbide and 10% cobalt wasused as a die material 13. This figure shows the simulationJ.H. Song, Y.T. Im/Journal of Materials Processing Technology 153154 (2004) 821828827Fig. 6. The distribution of effective strain obtained from FE simulations in the designed products for (a) hollow gear and (b) solid pinion.Fig. 7. The elastic simulation condition and deformed dimensions at the root and addendum of the hollow gear and solid pinion.conditions and deformed dimensions at the addendum androot region of the hollow gear and solid pinion. As can beseen in this figure, the deformation level was more severe atthe root than that at the addendum.5. ConclusionsIn this study, a computer-aided-design system for designof cold forward extrusion of solid or hollow spur gearswas develope