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X53K机床变速箱体的加工工艺及镗削纵向孔φ50，φ30孔 夹具设计 X53K 机床 变速 箱体 加工 工艺 纵向 50 30 夹具 设计

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X53K机床变速箱体的加工工艺及镗削纵向孔φ50φ30孔 夹具设计,X53K机床变速箱体的加工工艺及镗削纵向孔φ50,φ30孔,夹具设计,X53K,机床,变速,箱体,加工,工艺,纵向,50,30,夹具,设计

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南京理工大学泰州科技学院毕业设计（论文）任务书学院(系)：机械工程学院专 业：机械制造与自动化学 生 姓 名：余磊学 号：1001010136设计(论文)题目：机床变速箱体的加工工艺 及夹具设计 起 迄 日 期:2014.2.242014.5.31设计(论文)地点:南京理工大学泰州科技学院指 导 教 师:黄晓华专业负责人:李连波发任务书日期: 2014 年 2 月 24 日任务书填写要求1毕业设计（论文）任务书由指导教师根据各课题的具体情况填写，经学生所在专业的负责人审查、院（系）领导签字后生效。此任务书应在第七学期结束前填好并发给学生；2任务书内容必须用黑墨水笔工整书写或按教务处统一设计的电子文档标准格式（可从教务处网页上下载）打印，不得随便涂改或潦草书写，禁止打印在其它纸上后剪贴；3任务书内填写的内容，必须和学生毕业设计（论文）完成的情况相一致，若有变更，应当经过所在专业及院（系）主管领导审批后方可重新填写；4任务书内有关“学院（系）”、“专业”等名称的填写，应写中文全称，不能写数字代码。学生的“学号”要写全号；5任务书内“主要参考文献”的填写，应按照国标GB 77142005文后参考文献著录规则的要求书写，不能有随意性；6有关年月日等日期的填写，应当按照国标GB/T 74082005数据元和交换格式、信息交换、日期和时间表示法规定的要求，一律用阿拉伯数字书写。如“2009年3月15日”或“2009-03-15”。毕 业 设 计（论 文）任 务 书1本毕业设计（论文）课题应达到的目的：1、 培养学生调查研究、中外文献检索与阅读的能力；2、 综合运用专业理论知识、专业知识分析解决实际问题的能力；3、 定性、定量相结合的独立研究与论证的能力；4、 培养学生对复杂机械零件加工工艺设计与夹具设计的能力；5、 逻辑思维与形象思维相结合的文字表达能力；6、 撰写设计论文的能力。2本毕业设计（论文）课题任务的内容和要求（包括原始数据、技术要求、工作要求等）：为了能够更好地、直观地了解和研究机床变速箱体的加工工艺及夹具设计，本课题以X53K变速箱体为研究对象进行设计。本课题主要设计任务为：1、机床变速箱体加工总体方案的设计；2、机床变速箱体加工的具体工艺卡片设计与编制；3、机床变速箱体加工的辅助夹具设计，并绘制装配图；4、夹具关键零部件的设计与校核。 本课题对学生的要求：1、 具备加工工艺的基本知识；2、 熟悉工夹具设计；3、 熟悉PROE软件。毕 业 设 计（论 文）任 务 书3对本毕业设计（论文）课题成果的要求包括毕业设计论文、图表、实物样品等：l 机床变速箱体零件图0一张；l 箱体加工工艺流程图1张，工艺、工序卡多张，采用标准的工序卡的格式；l 夹具的总体装配图纸A0一张；l 夹具关键零部件的设计图纸8张。4主要参考文献：l 要求按国标GB 77142005文后参考文献著录规则书写，例如：1 刘谋佶, 吕志咏, 丘成昊, 等. 边条翼与旋涡分离流M. 北京: 北京航空学院出版社, 1988. 2427. 2 傅惠民. 二项分布参数整体推断方法J. 航空学报，2000，21（2）： 155158. 请按照以上的格式，查阅相关文献资料，并将查阅的参考文献写下来。毕 业 设 计（论 文）任 务 书5本毕业设计（论文）课题工作进度计划：起 迄 日 期工 作 内 容2014年2月25日 3月15日3月16日 3月18日3月19日 3月30日3月31日 4月13日4月14日 4月15日4月16日 4月24日4月25日 4月27日4月28日 4月30日5月1日 5月2日5月3日 5月4日下发任务书，完成文献综述以及课题报告，完成外文文献的翻译；并查阅相关资料，了解主轴传动箱体的加工方式；检查开题报告、外文翻译； 箱体加工工艺流程图以及工艺、工序卡多张，采用标准的工序卡的格式；夹具的总体装配图纸A0一张；毕业设计进行中期检查；夹具关键零部件的设计图纸；论文初稿撰写；修改完成设计稿；毕业设计成果全部校验；完成评审与答辩。所在专业审查意见：负责人： 年 月 日学院（系）意见：院（系）领导： 年 月 日 南京理工大学泰州科技学院毕业设计(论文)外文资料翻译学院 (系)： 机械学院 专 业： 机械制造及自动化 姓 名： 余磊 学 号： 1001010136 (用外文写)外文出处： International Joumal of Machine Tools & Manufacture 附 件： 1.外文资料翻译译文；2.外文原文。 指导教师评语： 签名： 年 月 日注：请将该封面与附件装订成册。附件1：外文资料翻译译文国际机床与制造39（1999）33-53一个立体的CAD/CAM/CAE集成系统空心冷挤压模具的雕塑表面许进忠模具工程系，国立高雄技术学院。415建公路，高雄807，台湾，中华名国于1997年6月30日收，于1998年1月28日定摘要在本文中，一个CAD/CAM/CAE集成系统的空心冷挤压模具的曲面已经研制了利用C语言的Windows。一个曲面模型变量的控制点与一般的三维流场分析挤压过程相结合。该产品的配置和钢坯在CAD模块中产生的。拟合点的生成是限定产品的分布和钢坯。控制点的初始猜测是通过使用相应的拟合点的轴向偏移而创建的。自动变化的控制点采用上限法和优化程序来获得最佳的模具表面。凸轮模块通过优化模具表面模型生成刀具位置。刨削区的工具路径检测与删除。计算刀具位置是通过刀具路径模拟验证的。利用免费刨的刀具位置自动生成数控代码，然后直接发送到一个三轴数控机床中心来制造EDM电极。挤压模具型腔是由使用EDM加工过程制造的。挤压实验验证了所提出的CAD/CAM/CAE集成系统是成功的。关键词：CAD/CAM/CAE集成；上限；冷挤压；雕塑表面命名法a,b,c,d,e,h 速度场的最佳参数p,q 控制点的入口边界优化之前和优化之后 增量出口部分 出口边界的控制点 埃尔米特形式混合功能 ，形状函数的Z向速度 内齿翅片管的高度 允许的最大尖端高度 共挤出功耗 总耗能模具长度和模具相对长度 定的剪切摩擦系数 所需的挤出压力 成分的位置，U-，V-导数和向量 雕塑表面的拟合点 拟合点的表面补丁 拟合点的入口和出口边界，分别 雕塑表面模型 模具表面 翅片管的基圆半径 ，芯棒坯的半径 纵向平均速度 平均纵向速度的导数W,R,T,Z 在R向，Z向，U向速度 内存速度和出口速度 内部力量，摩擦的模具表面和芯棒 圆柱坐标 表面模型的归一化参数 沿着U向的低和上的集成 平面的出口部分 在出口处平均有效的应变部分 应变集成在一个常数的最后流线型结构 应变速率组件 应变速率组件 有效的应变率 有效和平均有效压力流 (, z) 1. 介绍 对于非轴对称挤压模具的传统设计是一个圆锥形或平面模。结果是,高挤压载荷是必须的，物质流控制不好。设计面模是非常依赖于经验和耗时的。CADCAMCAE一体化系统已经被开发，以缩短模具设计和制造的交货时间。有研究人员提出了许多模具设计和材料流预测方法。该上限法是一种简单而适用的方法来分析物料流挤出工艺。Kiuchi et al. 1-4提出了一种线性收敛的模具，用假设轴向均匀流来分析许多非轴对称部分挤压。Nagpal et al.5有用一个多项式函数来设计一个精简的“T”模具的部分挤压。Hoshino 和Gunasekera 6,7提出多边形挤出速度与线性收敛和立方流线型模具的申请。Yang 和 Lange8提出了一个更一般的速度字段具有均匀的轴向速度的假设。 Yang et al. 911提出了一种可以由一个解析函数来表示通用三维速度场的模具表面。Yang et al. 9使用傅里叶级数展开的方法来描述该模具的表面，也不能解析表达。Yang et al. 12曾提出了一个一般的三维速度场预测去解析表达模具表面的中空挤压工艺。线性汇聚模具有突然的速度间断，并需要额外的剪切消费。模具表面与解析函数描述中的应用有其局限性。立方流线型模具忽略模具的几何形状在圆周上的物料流动方向的影响。傅立叶级数展开的方法是灵活的，但模具表面切割路径的生成却呈现的不自然。Sheu et al. 13提出了张力参数曲面模型并通过一个通用的三维速度场预测固体挤压工艺。在本文中，具有可变控制点的复杂曲面模型被用来设计空心挤压的模具表面。它是方便灵活地描述产品的形状和模具的几何形状。曲面模型的NC刀具路径计算也非常发达。该最佳的模具表面数据直接用于规划刀具路径和在CAM模块中计算刀具位置。表面模型使CAD / CAE / CAM一体化系统 顺利的被提出。产生切割位置和数控码有许多方法和注意事项用于三维表面的制造。Faux and Pratt 14提出了偏移曲面法计算刀具位置。Broomhead 15考虑了在前向和侧方向上的公差，在切割方向上计算的步长和使用迭代方法邻近刀具路径。Loney and Ozsoy 16应用弦误差的方法来确定沿切割路径刀具中心的增量。该相邻路径切割步骤是考虑扇贝高度来确定。干扰路径被除去，以产生气刨 - 自由切割位置（Choi et al.17）。在本文中，NC刀具路径复杂曲面的参数空间的规划。前进方向的参数增量设定为0.05，然后通过使用弦偏差法过滤。切割位置法线矢量的计算来优化模具表面。刀具路径的刨区域是通过曲率检查和自我循环检测来检查和去除。显示刀具位置的痕迹图形模拟切割过程。切削条件，如切割器的进给速度和刀具的位置都使用CAM模块生成NC代码自动完成。2. 该集成系统的结构所提出的集成系统的框图如图所示。 1。一般的图形用户界面（GUI）已经建立与用户沟通，并显示的CAD / CAE/ CAM模块结果采用C语言编写。该产品与钢坯访问使用直线和圆弧实体绘制。生成的拟合点和对应的控制点自动在CAD模块产生的表面模型进行内插的访问和控制的V型衍生物。表面模型是注册成立的速度场，在CAE模块中利用上限法和优化过程来优化模具表面。最佳模具表面用阴影算法或删除隐藏线时方案显示。该材料特性和润滑条件在CAE模块中输入。电源法被用来呈现该材料的流动应力。恒定的剪切摩擦系数m ，是用来考虑摩擦的条件。模具长度可以在模具表面优化程序中是固定的或变化的。一个优化的模具表面是在CAE模块中使用上结合分析，以最小化时的挤载荷自动设计的。刀具的几何形状和切割参数，就像在CAM模块中输入容差和切削速度。最佳模具表面的数据直接使用CAM模块来规划所述切割路径，并计算刀具的位置。用干涉检查和拆卸程序来检测和删除刀的计量。 NC程序是通过欺诈无刀位置和切削参数自动生成的。数控码被发送到一个三轴数控加工中心制造电火花加工电极。模具表面（阴影，隐线） 挤压参数（摩擦，滑块速度） 优化（速度场，模具表面） 具有可变控制点面模型 上界分析（物料流） CAE模块NC代码生成干涉检查切削仿真 刀位计算切割路径规划切削条件刀具几何CAM模块Windows 95的图形用户界面 圆坯 产品简介 DXF接口 图（线，弧） CAD模块 图1 所提出的CAD / CAM/ CAE一体化系统的示意图3. 可变控制点的曲面模型 用复杂曲面模型变量控制点来描述模几何。用图片格式来表示雕刻表面和嵌合点的示意图。2.所述表面模型是由装配点和修补程序组成。在表面上表示它通过使用参数空间的U方向和V方向曲面曲线（U，V）。该雕塑表面的数学表达式如下： （1a）其中，为埃尔米特形式的混合函数给定为 (1b) （1c）在方程（1c）中，拟合点的扭转矢量被设置为零，以获得光滑的模具表面。 U和v衍生物的载体是通过相邻的色块和边界条件的斜率连续性要求获得的。在U方向表示模具表面的圆周方向。拟合点的U衍生物通过使用该产品和坯料剖面的样条拟合得到的。 V方向指模具表面轴向的纵向方向延伸。装配点的v型衍生物是通过改变对应的控制点的位置来控制。最佳的模具表面通过改变控制点的位置获得较低的能量消耗。图3显示出了拟合点和对应的控制点 在V型曲线的方向上。在x， y坐标控制点是一样的记者拟合点，但z坐标是不同的。该控制点z坐标上的变化，改变了对应的v型衍生物的配合点和作为一个结果，在模具表面被改变。原来v型曲线上的控制点由实线和不同的V形曲线表示，对照的的点在图3中用虚线表示。控制点的z坐标是被除以模头长度L得到的归一化参数，从而表面优化。该控制点的最终位置是通过使用一个优化过程和上限分析确定的。点U方向参数空间一个修补程序点v方向图2 雕刻的表面和拟合点的示意图隐藏线移除和渲染方案是用来更加全面的显示最佳模具表面。众所周知的z缓冲区方案被采用，以除去隐藏线。发达的Gourand阴影算法通过恒定着色进行渲染表面和消除强度的不连续性。4.上界分析上界分析方法采用模拟空心冷挤压工艺。表面模型中装有机动容许速度场12预测物料流。速度场应满足材料挤出过程中的边界条件和体积稳定性。在以下假设得出速度场： 模具长度模具出口模具入口轴轴可变的控制点 图3 表面优化的表面曲线的可变控制点1.该材料在模具入口处的横截面和模具出口都是平面2.该材料是不可压缩的，服从冯米斯屈服准则3.材料的变形跟随刚塑性模型 通过参照在图4中的符号，并使用上述的假设，速度字段如下获得：(a)该非均匀的轴向速度（纵向速度）被假定为 (2a) (2b) (2c) (2d) (2e) (2f) 出进图4 动可容速度场的表示法和边界 中空挤出速度形函数图5 对中空挤压z方向上的速度的形状函数其中是在模具表面上，Rm是心轴的半径，是平均纵速度，是ram速度，a，b，c，d，e，h，p是速度场的最佳参数，是的形状的功能。图5示出中空挤压轴向速度的形状函数。通过将不可压缩的情况下，参数a，b和c是不独立的，关系由下式给出： (3a) (3b) （b）该角速度假定为 (4) （c）该径向速度从不可压缩假设派生和由下式给出 (5a) (5b) (5c) (5d)其中，（）指z的一阶导数。为了获得平滑的模具表面，该模具入口与模具出口v方向的切向量在模的入口和出口边界应为零，其结果是，装配点和对应的控制点应该具有相同的（X，Y）坐标。应变速率场是由上述推导得到输入的速度场，给出如下： (6a) (6b) (6c) 速度场是在入口和出口连续部分并没有剪切功耗消失在这里。所需的总功率挤压由内部电源和摩擦力由下式给出 (7) 变形的内部功耗由下式给出 (8)其中L是模具长度，电子是应变率分量和是平均有效压力对于加工硬化的材料，并且和下面的公式近似： (9) 其中是平均总有效应变出口段，并获得 (10)其中是由有效应变率沿一个恒定的流线整合的最终应变。摩擦功率沿模具表面消散由下式给出 (11)其中m是坯料和模具表面之间的恒定剪切摩擦系数。摩擦电源与芯棒表面消散由下式给出 (12)其中m是坯料和所述心轴的表面之间的摩擦系数。的参数速度场和模具表面参数的确定是通过使用优化的方法，以减少所需的挤压力。这里，采用变量度量优化方案18来获得优化模具表面。由此得到的挤出压力 (13)5.数控刀具路径规划和刀位计算 刀具路径是以圆周方向顺时针转动。粗加工刀具路径计划在恒定的Z平面。平头立铣刀，用于粗加工，以便获得一个高材料去除率。精加工的刀具路径是沿着流线产生恒v参数。球头立铣刀是通过精加工操作使表面顺利进行建模。精切削的刀具位置是通过计算表面正常偏移。弦误差的容差用于确定在圆周切割步骤方向。该算法如下：1.生成的测试点：所产生的插补点在两个接头点间与一个小U间隔（0.05） 2.计算内插点的偏差：发现对插的弦偏差相对于线下实体点建设的起点和行军点 3.过滤插补点：如果弦偏差小于公差，内插点旁边的行进点被设置为一个新的行进点 4.重复（2）和（3）：迭代直到和弦偏差大于公差，前点向行进的一点是该步骤的终止点，并开始点下一步在z方向上的切割步骤是通过检查该近似尖点来确定，即在切割工序必须比较小，其中是允许的风口浪尖高度。刀具位置的干扰区域通过检查主曲率淘汰和最小曲率17。6.实验 缸镦粗试验和环压试验，进行了确定模具材料接口之间的的铝1100 F和恒定剪切摩擦系数m的流应力。从压缩试验中铝1100 F中的流动应力是兆帕，摩擦系数0.18。进行挤出实验验证了理论结果。图6中所示的鹭宫100吨液压机负载，速度和位移控制被用于压缩和挤压试验。空心钢坯挤压测试，分别为30mm外径，50mm高，10mm、14 mm或18mm内径。心轴的直径为10、14或18mm。挤出模头组的部件被显示在图7，包括容器，冲压，心轴，加强和模腔。7.结果与讨论7.1.产品概要文件的描述和模具表面的优化设计 图8显示了齿轮样条的配置文件和拟合点创建使用CAD功能所提出的系统。Z轴控制点的坐标会自动变化，以找到最佳的模具的几何形状，以尽量减少所需的挤压力。图9示出了自动取得最佳的模具表面具有在模具入口处和模具出口处平稳过渡。模具图6 鹭宫的100吨液压机进行压缩和挤压测试表面的不同意见和底纹结果显示，以帮助修真的设计师。这两个数字显示系统所提出的使用的CAD和CAE模块的模具表面自动设计的功能。7.2.模具制造 在图10（a，b）中显示切割操作的刀具路径模拟。扁平头立铣刀用于粗切削和一个球头立铣刀用于精切削。主轴转速是1200转，进给速度为100毫米/分钟，精加工的津贴为0.1毫米。切割的凝视点位于电极的顶部中心。在切割位置的图7 挤压模具集（集装箱，冲压，心轴，加强和模腔）的组成部分图8 该产品与钢坯访问和齿轮花键的嵌合点干涉在精切削应予删除。图11（a）显示出了刀具路径的计量发生在精加工操作的过渡区域。图11（b）显示滤波干扰后，没有计量的切刀位置。在NC代码发送到三轴数控机床中心通过使用RS 232接口用电火花电极切割。图12显示出了精切削操作。机械加工后，电极研磨，以获得更精细的表面质量。对模腔的内壁进行抛光，并进行热处理，以获得光滑和坚硬的模具表面。图9 最佳的模具表面的齿轮花键的空心挤压7.3.挤压实验固体和空心管坯被用于挤压试验。在图13中，上半部分示出了钢坯，下半部示出了挤压的结果。该产品是直的，不弯曲或扭转。这意味着该物质流量使用建议表面模具已顺利通过控制。在图14中显示了理论的压力和实验结果的比较相对于不同面积减少率的结果。挤压力的理论倾向相对于该区域的减速比与实验结果吻合。理论曲线比实验曲线高是因为上限法被采用。7.4.的模具表面设计的翅片管挤出应用一种模具表面的翅片管式挤出是考虑到演示申请的提出制度。挤压力的关系 ，有效应变和面积的减少对于相对齿高度在图15中表示。挤出压力的倾向和有效应变正在下降而相对齿高在增加，直到相对齿高达到0.2。挤出压力和有效应力的倾向，然后上升而增加的相对齿的高度。它表明面积的减少占主导地位平头刀盘直径粗加工模拟图10 （a）粗切削的电极制造刀具路径模拟 （b）刀具路径模拟 的完成切割的电极制造在相对低齿高的情况下变形，即较高的面积减少需要更高挤压力。有效应变增大后的相对齿高度大于0.2，挤压力的趋势也是往上走。这意味着邻近非均匀流动的牙齿主导的材料变形。在图16（a，b）中显示变形网格和速度场的零度截面。在图16（C，D）中显示变形网格和速度场45度的截面。这些数字表明附近齿顶物质流不像近圆形区域物质流动的顺风顺水。一种非均匀的轴向速度被观察，因为有在模具材料的区域和模芯材料界面摩擦的效果。干扰（计量） 避免干扰（计量删除）图11 （a）完成刀具路径无干扰消除（计量发生） （b）完成刀具路径与干扰去除（无计量发生）图12 电火花加工（球头立铣刀）电极的精加工8.结论 一个CAD / CAE / CAM一体化系统的雕塑表面的设计和制造 冷挤压模具已经研制成功。用可变控制点提出的雕塑表面与是能够自动设计的空心冷挤压模具表面。利用上限法和优化技术来优化雕塑模具的表面，以得到较低的功耗。切刀的位置被计算和干扰刀具路径的区域将被删除。电火花加工电极顺利晋级核实所提出的适用于表面的立体裁剪系统产生的NC代码。理论结果的趋势是与挤压试验吻合良好。模具表面翅片管挤压的设计是考虑到验证了该系统的应用。致谢笔者要感谢国科会的资助，项目编号为NSC85-2212-E-269-001。图13 空心坯和挤压产品具有不同的内半径参考文献1 M. Kiuchi, H. Kishi, M. Ishikawa, J. of Japan Society Tech. Plasticity 24 (266) (1983) 290.2 M. Kiuchi, M. Ishikawa, J. of JSTP 24 (270) (1983) 722.3 M. Kiuchi, Proceeding of 12th North American Metalworking Research, 1984, p. 111.4 M. Kiuchi, S. I-i-jima, Advanced Technology of Plasticity, vol. 1, 1987, p. 507.5 V. Nagpal, C.H. Billhardt, T. Altan, J. of Engng. Ind. ASME 101 (1979) 319.6 S. Hoshino, J.S. Gunasekera, Proceeding of the 21st Int. Machine Tool Design and Res. Conf., Swansea, England,1980, p. 97.7 J.S. Gunasekera, S. Hoshino, J. of Eng. for Ind., ASME 107 (Aug. 1985) 229.8 D.Y. Yang, K. Lange, Int. J. Mech. Sci. 26 (1984) 1.9 D.Y. Yang, C.H. Han, M.U. Kim, Int. J. Mech. Sci. 28 (8) (1986) 517.10 C.H. Han, D.Y. Yang, M. Kiuchi, Int. J. Mech. Sci. 28 (4) (1986) 201.11 C.H. Han, D.Y. Yang, Int. J. Mech. Sci. 30 (1) (1988) 13.12 D.Y. Yang, H.S. Kim, C.M. Lee, C.H. Han, Int. J. Mech. Sci. 32 (2) (1990) 115.13 J.J. Sheu, R.S. Lee, Int. J. Mach. Tools Manufact. 31 (4) (1991) 521.14 I.D. Faux, M.J. Pratt, Computational Geometry for Design and Manufacture, Halsted Press, New York, Ellis Horwood, 1979, p. 198.15 P. Broomhead, M. Edkins, Int. J. Prod. Res. 24 (1) (1986) 11.16 G.C. Loney, T.M. Ozsoy, Computer-Aided Design, 19 (2) (1987) 85.17 B.K. Choi, C.S. Jun, Computer-Aided Design, 21(6) (1989) 371.18 G.N. Vanderplaats, Numerical Optimization Techniques for Engineering Design: with Application, McGraw-Hill,New York, 1984, p. 92. 面积减少率 实验结果 理论结果 挤压载荷（KN）图14 理论挤压的比较加载与理论结果相对的齿高减少的面积减少的面积有效应变相对的挤压力相对的挤压力，有效应变图_15 相对挤出压力和有效应力相对于相对的齿高轴顶杆度轴轴 顶杆度 轴图16 （a）0截面的变形网格 （H/R1=0.2，RM= 3毫米） （b）0截面的速度场 （H/R1=0.2，RM= 3毫米） （c）45截面的变形网格（H/R1=0.2，RM= 3毫米） （d）45截面的速度场 （H/R1=0.2，RM= 3毫米）轴顶杆度轴轴顶杆度轴图16 继续International Journal of Machine Tools & Manufacture 39 (1999) 3353A three-dimensional CAD/CAM/CAE integration system ofsculpture surface die for hollow cold extrusionJinn-Jong SheuDepartment of Mold and Die Engineering, National Kaohsiung Institute of Technology, 415 Chien-Kung Road,Kaohsiung 807, Taiwan, R.O.C.Received 30 June 1997; in final form 28 January 1998AbstractIn this paper, a CAD/CAM/CAE integration system for a sculptured surface die for hollow cold extrusionhas been developed by using C language for Windows. A sculptured surface model with variable controlpoints is incorporated with a general three-dimensional velocity field to analyze the extrusion process. Theprofiles of the product and the billet are generated in the CAD module. The fitting points are generatedto interpolate the profiles of the product and the billet. The initial guess of control points are created by usingthe offset of corresponding fitting points in the axial direction. The control points are varied automatically toobtain the optimum die surface by using the upper-bound method and optimization procedure. The CAMmodule generates the cutter locations by using the optimized die surface model. The gouging areas of thetool path are detected and removed. The calculated cutter locations are verified through the tool pathsimulation. The NC codes are generated automatically by using the gouging-free cutter locations and thensent directly to a three-axis CNC machine centre to manufacture the EDM electrodes. The extrusion diecavity is made by using an EDM process. Extrusion experiments have verified the proposedCAD/CAM/CAE integration system is successful. 1998 Elsevier Science Ltd. All rights reserved.Keywords: CAD/CAM/CAE integration; Upper-bound; Cold extrusion; Sculpture surfaceNomenclaturea,b,c,d,e,h, the optimum parameters of velocity fieldp,qC(u,z)R2m2Vm(z) +Rq + 1mq + 1V(u,z)uB*,B*9control points of the entrance boundary before and after optimization0890-6955/99/$see front matter 1998 Elsevier Science Ltd. All rights reserved.PII: S0890-6955(98)00029-734J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353dAincremental area on the exit sectionE*control points of the exit boundaryF(u)Hermite form blending functiong(b)b3+ ab2+ bb + c, shape function of the z-direction velocityHthe tooth height of a fin-tubehmaxthe allowable maximum cusp heightJ*total extrusion power consumptionL, L/Rbthe die length and the relative die lengthmconstant shear friction factorPthe extrusion pressure requiredP*composition of the position, u-, v-derivative and twist vectorsPifitting points of a sculpture surfacePlb, Plt,fitting points of a surface patchPrb, PrtQ*, P*fitting points of the entrance and the exit boundaries, respectivelyR(u,v)sculpture surface modelR, R(u,z)the die surfaceR1the base circle radius of a fin-tubeRb, Rm,the radius of the billet, the mandrel, hR(u,z) + (1 h)RmRh(u,z)Vm(z)the average longitudinal velocityVm9(z)the derivative of average longitudinal velocity w.r.t. zVr, Vz, Vuthe velocities in the r-, z-,u-directionsVram, Vexitthe ram speed and the exit velocityWi, Wfd,internal power, frictional powers of die surface and mandrelWfmr, z,uthe cylindrical coordinateu, vnormalized parameters of surface modelub,uelower and upper bound of integration along theudirectionsa(z)dz2(z e)(z L)2b(r Rm)/R(u,z) RmGexitthe plane of the exit sectionefavgthe average total effective strain at the exit sectionef= et0edtthe final strain integrated along a constant stream-lineer,ez,eustrain rate componentserz,eru,ezustrain rate componentseeffective strain rates,smeffective and mean effective flow stressh(u, z)Rph(u,z)D (u, z)R(u,z) RmV(u, z) (q + 1)2(Rq + 1 Rq + 1m)eu0(R2Vm R2mVm)zdu35J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 33531. IntroductionThe traditional design for a non-axisymmetric extrusion is a conical or a flat-face die. As aresult, a high extrusion load is required and the material flow is not well controlled. The designof a flat-face die is very experience-dependent and time consuming. A CAD/CAM/CAE inte-gration system has been developed to shorten the lead times of die design and manufacturing.There are many die design and material flow prediction methods proposed by researchers. Theupper bound method is a simple and applicable approach to analyze the material flow of theextrusion process. Kiuchi et al. 14 have proposed a linearly converging die with the assumptionof uniform axial flow to analyze many non-axisymmetric section extrusion. Nagpal et al. 5 haveused a polynomial function to design a streamlined die for the extrusion of T sections. Hoshinoand Gunasekera 6,7 have proposed a velocity filed for polygon shape extrusion with the linearlyconverging and the cubic streamlined dies. Yang and Lange 8 proposed a more general velocityfield with the assumption of uniform axial velocity. Yang et al. 911 has proposed a generalthree-dimensional velocity field for the die surface that can be expressed by an analytical function.Yang et al. 9 used a Fourier series expansion method to describe the die surface that cant beexpressed analytically. Yang et al. 12 had proposed a general three-dimensional velocity filedto predict the hollow extrusion process with an analytical expression of die surface. The linearlyconverging dies had the abrupt velocity discontinuity and additional shear consumption required.The application of die surface with analytical function description has its limitation. The cubicstreamlined die neglects the effect of die geometry on the material flow in the circumferencedirection. The Fourier series expansion method is flexible but unnatural to present a die surfacefor cutting path generation. Sheu et al. 13 had proposed a surface model with tension parameterand adopted a general three-dimensional velocity field to predict the solid extrusion process. Inthis paper, a sculptured surface model with variable control points is proposed to design a diesurface for hollow extrusion. It is convenient and flexible to describe the shape of product andthe geometry of die. The NC tool path calculation of a surface model is also well-developed. Theoptimum die surface data is directly used to plan the tool path and calculate the cutter locationsin the CAM module. The surface model enables the smooth CAD/CAE/CAM integration of theproposed system.There are many approaches and considerations to generate the cutter locations and the NCcodes for the manufacturing of a three-dimensional surface. Faux and Pratt 14 proposed theoffset surface method to calculate the cutter locations. Broomhead 15 considered the tolerancesin the forward and the side directions and calculated the step length in the cutting direction andin the neighbouring tool path by using an iteration method. Loney and Ozsoy 16 applied thechord error method to determine the increment of the cutter centre along the cutting path. Thecutting step of the neighbouring paths is determined by considering the scallop height. The inter-ference paths are removed to generate the gouging-free cutter locations (Choi et al. 17).In this paper, the NC tool path is planned on the parametric-space of the sculptured surface.The parameter increment is set to 0.05 in the forward direction and then filtered by using thechord deviation method. The cutter locations are calculated by using the normal vector of theoptimized die surface. The gouging areas of the tool path are checked and removed by using thecurvature examination and the self-loop detection. The traces of cutter locations are displayedgraphically to simulate the cutting process. The cutting conditions, such as the dimension of cutter36J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353and the feed rate, and the cutter locations are used by the CAM module to generate the NCcodes automatically.2. The structure of the integration systemThe block diagram of the proposed integration system is shown in Fig. 1. A general graphicuser interface (GUI) has been established to communicate with users and show the results of theCAD/CAE/CAM modules by using C language. The product and the billet profiles are drawn byusing line and arc entities. The fitting points and the correspondent control points are generatedautomatically in the CAD module to interpolate the profiles and to control the v-derivatives ofthe surface model. The surface model is incorporated with the velocity field, the CAE moduleuses the upper-bound method and the optimization process to optimize the die surface. The opti-mum die surface is displayed with the shading algorithm or the hidden line removal scheme.The material property and the lubrication condition are input in the CAE module. The powerlaw is used to present the flow stress of the material. The constant shear friction factor, m, isused to consider the friction conditions. The die length can be fixed or varied during the diesurface optimization procedures. An optimization die surface is automatically designed in theCAE module by using the upper-bound analysis to minimize the extrusion load. The cuttergeometry and the cutting parameters, such as tolerance and cutting speed, are input in the CAMmodule. The optimum die surface data is directly used by the CAM module to plan the cuttingpath and to calculate the cutter locations. The gauging of cutter is detected and removed by usingthe interference checking and removal procedure. The NC program is generated automatically byusing the gouging-free cutter locations and the cutting parameters. The NC codes are sent to athree-axis CNC machine centre to manufacture the electrodes of EDM.Fig. 1.The schematic diagram of the proposed CAD/CAM/CAE integration system.37J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 33533. The surface model with variable control pointsA sculptured surface model with the variable control points is proposed to describe the diegeometry. The schematic diagram of a sculpture surface and the fitting points is shown in Fig.2. The surface model is composed from the fitting points and the patches. The surface is rep-resented by using u-direction and v-direction surface curves in the (u,v) parameter space. Themathematical representation of a sculpture surface is as follows:R(u,v) = F(u)P*FT(v)(1a)where F(u) is the Hermite form blending function, F(u) is given asF(u) = 1 u u2u310000010 33 2 12 211(1b)P*=Fposition vectorsv derivative vectorsu derivative vectorstwisting vectorsG(1c)In Eq. (1c), the twisting vectors of the fitting points are set to zero to obtain a smooth diesurface. The vectors of the u-derivative and the v-derivative are obtained by using the slopecontinuity requirement of the neighbouring patches and the boundary conditions. The u-directionmeans the circumference direction of the die surface. The u-derivatives of the fitting points areobtained by using the spline fitting of the product and billet profiles. The v-direction means theaxial longitudinal direction of the die surface. The v-derivative of the fitting points are controlledFig. 2.The schematic diagram of the sculptured surface and fitting points.38J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353by varying the positions of the correspondent control points. The optimum die surface with lowerenergy consumption is obtained by changing the positions of control points. Fig. 3 shows thefitting points Q*, P*and the correspondent control points B*, E*on a v-direction curve. The x,y-coordinates of the control points are same as the correspondent fitting points, but the z-coordinateis different. The variation of the z-coordinate of control points B*, E*changes the correspondentv-derivative of the fitting points Q*, P*and as a result, the die surface is changed. The original v-curve with the control point B*is shown by a solid line and the varied v-curve with the controlpoint B*9 is shown by a dashed line in Fig. 3. The z-coordinate of the control points B*, E*aredivided by the die length L to obtain the normalized parameters for surface optimization. Thefinal position of the control points are determined by using an optimization process and the upperbound analysis.The hidden line removing and the rendering schemes are used to display the optimum diesurface more comprehensively. The well-known z-buffer scheme is adopted to remove the hiddenlines. The well-developed Gourand shading algorithm is adopted to render the surface and elimin-ate the intensity discontinuities caused by the constant shading.4. The upper bound analysisThe upper bound analysis method is adopted to simulate the hollow cold extrusion process.The surface model is incorporated with a kinematically admissible velocity field 12 to predictthe material flow. The velocity field should satisfy the boundary conditions and the volume con-stancy of material during the extrusion process. The following assumptions are made to derivethe velocity field:Fig. 3.The variable control points of a surface curve for surface optimization.39J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 33531. The cross-section of the material in the die entrance and the die exit are all planes.2. The material is incompressible and obey the von Mises yield criterion.3. The material deformation follows the rigid-plastic model.By referring to the notations in Fig. 4 and using the above mentioned assumptions, the velocityfield is obtained as follows:(a) the non-uniform axial velocity (longitudinal velocity) is assumed to beVz(r,u,z) = Vm(z) + a(z)Rph(u,z)g(b)(2a)Vm(z) =vramE2p0R2(u,0)duE2p0R2(u,z)du(2b)a(z) = dz2(z e)(z L)2(2c)b= (r Rm)/R(u,z) Rm(2d)Rh(u,z) = hR(u,z) + (1 h)Rm(2e)g(b) =b3+ ab2+ bb+ c(2f)Fig. 4.The notation and boundaries of the kinematically admissible velocity field.40J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353Fig. 5.The shape function of z-direction velocity for hollow extrusion.where R(u,z) is the die surface, Rmis the radius of the mandrel, Vm(z) is the average longitudinalvelocity, Vramis the ram speed, a, b, c, d, e, h, p are the optimum parameters of the velocityfield, g(b) is the shape function of Vz. Fig. 5 shows the shape function of axial velocity for hollowextrusion. By applying the incompressible conditions, the parameters a, b and c are not inde-pendent, the relations are given as follows:3/20 + a/6 + b/6 = 0(3a)1/4 + a/3 + b/2 + c = 0(3b)(b) the angular velocity is assumed to beVu(r,u,z) = rqV(u,z)(4)(c) the radial velocity is derived from the incompressible assumption and is given byVr(r,u,z) = r2Vm9 Dr(a9h+ah9)FDSb55+ab44+bb33+cb22D+ RmSb44+ab33+bb22+ cbDG+ahrS3b44+2ab33+bb22DR9(u,z)Rm(5a)41J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353+ahDrS3b55+2ab44+bb33DR9(u,z)rqq + 1V(u,z)u+C(u,z)rD(u,z) = R(u,z) Rm(5b)h(u,z) = Rph(u,z)C(u,z) =R2m2Vm(z) +Rq + 1mq + 1V(u,z)u(5c)V(u,z) = (q + 1)2(Rq + 1 Rq + 1m)Eu0(R2Vm R2mVm)zdu(5d)where (9) means first derivative with respect to z. In order to obtain a smooth die surface, the v-direction tangent vectors in the die entrance and the exit boundaries should be zero at the dieentrance and die exit, as a result, the fitting points and the correspondent control points shouldhave the same (x,y) coordinates. The strain rate field is obtained by the derivation of the abovementioned velocity field and is given as follows:er= Vr/rez= Vz/z(6a)eu= Vr/rerz=12Vz/r + Vr/zeru=12F1rVr/u+ Vu/r Vu/rG(6b)ezu=12F1rVz/u+ Vu/zGe=F23(e2r+e2u+e2z+e2ru+e2uz+e2zr)G1/2(6c)42J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353The velocity field is continuous at the entrance and the exit sections and no shear power con-sumption vanishes here. The total extrusion power required consists of the internal power andthe frictional powers and is given byJ*= Wi+ Wfd+ Wfm(7)The internal power consumption of deformation is given byWi=Evsedv =!23smEL0E2p0ER(u,z)Rm(eijeij)1/2rdrdudz(8)where L is the die length,eij is the strain rate components, andsmis the mean effective stressfor work-hardening material and is approximated by the following equation:sm=Eefavg0sde/efavg(9)whereefavgis the average total effective strain at the exit section Gexitand is obtained byefavg=EGexitefdA/EGexitdA(10)whereef=Et0edt is the final strain by integrating the effective strain rate along a constant stream-line. The frictional power dissipated along the die surface is given byWfd=2pm3smEL0V2r+ V2z1/2r = RRF1 +SRRuD2+SRzD2G1/2dzdu(11)where m is the constant shear friction factor between the billet and the die surfaces. The frictionalpower dissipated along the mandrel surface is given byWfm=2pm3smRmLV2r+ V2z1/2r = Rm(12)where m is the friction factor between the billet and the mandrel surfaces. The parameters of thevelocity field and the die surface are determined by using the optimization method to minimizethe extrusion pressure required. Here, the variable metric optimization scheme 18 is adopted toobtain the optimization die surface. The extrusion pressure is obtained byP = (Wi+ Wfd+ Wfm)/p(R2b R2m)V0(13)43J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 33535. The NC tool path planning and the cutter location calculationThe tool paths are calculated in the circumference direction clockwise. The roughing tool pathis planned on the constant Z planes. The flat-end mill is used for roughing in order to obtain ahigh material removal rate. The tool paths of finishing are generated along the stream lines ofconstant v parameter. The ball-end mill is adopted in the finishing operation to follow the surfacemodel smoothly. The cutter locations of the finish cutting are calculated by using the surfacenormal offset. The tolerance of chord error is used to determine the cutting step in the circumfer-ential direction. The algorithm is as follows:1. Generate the testing points: the interpolation points are generated with a small u interval (0.05)between two fitting points.2. Calculate the deviation of the interpolation points: find the chord deviation of the interpolationpoints with respect to the line entity construct by the start and the marching points.3. Filter the interpolation points: if the chord deviation is smaller than the tolerance, the interp-olation point next to the marching point is set to a new marching point.4. Repeat (2) and (3): iterate until the chord deviation is larger than the tolerance, the point priorto the marching point is the stop point of this step and start point of next step.The cutting step in the z-direction is determined by checking the approximation cusp, i.e. thecutting step must be smaller than 2hmax(2Rc hmax), where hmaxis the allowable cusp height.The interference areas of the cutter location are eliminated by checking the principal curvatureand the minimum curvature 17.6. ExperimentationCylinder upsetting tests and the ring compression tests were carried out to determine the flowstress of the aluminum 1100 F and the constant shear friction factor m between the die-materialinterface. The flow stress of aluminum 1100 F was found to be 162.3290.41381eMPa and thefriction factor 0.18 from the compression tests. The extrusion experiments were carried out toverify the theoretical results. A Saginomiya 100-ton hydraulic press shown in Fig. 6 with load,speed and displacement control was used for the compression and extrusion tests. The hollowbillets for extrusion tests were 30 mm outer diameter, 50 mm high and either 10 mm, 14 mm or18 mm inner diameter. The diameters of the mandrel were either 10, 14 or 18 mm, respectively.The components of the extrusion die set are shown in Fig. 7 including the container, ram, man-drels, bolster and die cavity.7. Results and discussion7.1. Description of the product profiles and the optimum design of die surfaceFig. 8 shows the profiles and the fitting points of a gear spline created by using the CADfunctions of the proposed system. The z coordinate of the control points are varied automatically44J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353Fig. 6.The Saginomiya 100-ton hydraulic press for compression and extrusion tests.to find an optimum die geometry to minimize the required extrusion load. Fig. 9 shows theoptimum die surface obtained automatically which has a smooth transition at the die entrance anddie exit. The different views and the shading results of the die surface are displayed to help thecomprehension of the designers. These two figures have shown the ability of die surface designautomation of the proposed system by using the functions of CAD and CAE modules.7.2. Die manufacturingThe tool path simulation of the cutting operations are shown in Fig. 10(a,b). A flat-end cutteris used for the rough cutting and a ball-end cutter is used for the finish cutting. The spindle speedis 1200 rpm, the feed rate is 100 mm/min, the allowance for finishing is 0.1 mm. The staringpoint of the cutting is at the top centre of the electrode. The interference of the cutter locationsin the finish cutting should be removed. Fig. 11(a) shows the gauging of the tool path occurred45J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353Fig. 7.The components of the extrusion die set (container, ram, mandrels, bolster and die cavity).Fig. 8.The product and the billet profiles and the fitting points of a gear spline.at the transition areas in finishing operation. After the filter of interference, the cutter locationswithout gauging are shown in Fig. 11(b). The NC codes are sent to the three-axis CNC machinecenter by using a RS 232 interface to cut the EDM electrodes. Fig. 12 shows the finish cuttingoperation. After machining, the electrodes are polished in order to obtain a finer surface quality.46J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353Fig. 9.The optimum die surface for the hollow extrusion of gear spline.The inner walls of the die cavity are polished and are heat treated to obtain a smooth and harddie surface.7.3. Extrusion experimentsThe solid and the hollow billets are used for the extrusion tests. In Fig. 13, the upper halfshows the billets and the lower half shows the extrusion results. The products are straight withoutbending or twisting. It means the material flows have been controlled smoothly by using theproposed surface die. The comparison of the theoretical pressures and the experimental resultswith respect to the different area reduction ratio is shown in Fig. 14. The theoretical tendency ofthe extrusion pressure with respect to the area reduction ratio is in good agreement with theexperimental results. The theoretical curve is higher than the experimental curve because theupper-bound method is adopted.7.4. Applications of die surface design for a fin-tube extrusionA die surface for the fin-tube extrusion is given to demonstrate the application of the proposedsystem. The relations of the extrusion pressure, the effective strain and the reduction of area withrespect to the relative tooth height is shown in Fig. 15. The tendency of the extrusion pressureand the effective strain is going down with increasing the relative tooth height until the relativetooth height achieved 0.2. The tendency of extrusion pressure and effective strain is then goingup with increasing the relative tooth height. It shows that the reduction of area dominates thedeformation in the case of low relative tooth height, i.e. higher area reduction requires higherextrusion pressure. The effective strain is increased after the relative tooth height is larger than0.2 and the tendency of extrusion pressure is going up too. It means the non-uniform flow near47J.-J. Sheu/International Journal of Machine Tools & Manufacture 39 (1999) 3353Fig. 10.(a) The tool path simulation of rough cutting for the electrode manufacturing. (b) The tool path simulationof finish cutting for the electrode manufacturing.the teeth dominates the deformation of material. The deformed grids and the velocity field on thesection of zero degrees are shown in Fig. 16(a,b). The deformed grids and the velocity field onthe section of 45 degrees are shown in Fig. 16(c,d). These figures show the material flows nearthe tooth top are not so smooth as the material flows near the circular areas. A non-uniform axial48J.-J. Sheu/International Journal of M