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外 文 翻 译自动化夹具的规划系统的发展系 别： 专 业 名 称： 学 生 姓 名： 学 号： 指导教师姓名、职称： 完成日期：2016年 月 日摘要：夹具是一个很重要的工业步骤。计算机辅助夹具设计技术在涉及制造规划中迅速发展。自动化的夹具外形设计系统发展成被用来挑选自动组合夹具元件和把它们合适的放在装配关系的位置上。在这篇论文里，一个自动化夹具设计系统只是呈现了夹具在基于工件几何和可操作性上，夹具表面和位置都是自动化的。夹具的可及性、表面特征准确、夹具稳定所面临的主要问题都在夹具规划中这个系统的开发在这篇论文里，夹具规划和实施例被提出来了。 关键词：精确度；夹具；夹具规划；定位1.介绍 夹具是一个重要的工业生产活动在工业周期中。计算机辅助夹具设计被广泛应用在CAD/CAM中1。CAFD的发展对于减少交货时间，制造运转和审核的制造过程中的有很大的贡献2。CAFD在柔性制造系统(FMS)和计算机集成制造系统(CIMS)中扮演了一个很重要的角色3。图1 夹具设计制造系统 图1概括了活动在夹具设计制造系统，它们包含三个主要领域：设置规划，夹具规划、夹具结构设计4。目标规划，是决定设置机构的数量，定位及发展方向的工件在每个设置，在每个加工面的也占有一席之地。 夹具规划定位和夹紧点了工件表面上。夹具结构设计的任务是选择夹具元件和把它们安置在贴合位置然后夹紧工件。一个自动组合夹具结构设计系统，在选定的工件摸具的表面和夹紧位置上，夹具单元和放置在自动生成位置协助夹具组件装配关系上被广泛的应用发展4,5，本文论述了夹具规划当夹具工件表面及位置时自动选择的内容。 对夹具设计以往已经出版了的文献分析中，只有综合夹具规划系统，是主要用于产生夹具计划还没有发展工业领域中的应用。前期工作包括：自动测定方法的夹具定位和夹紧源自数学模型 6；一种算法选择的定位和夹紧的职位提供最大限度的机械杠杆作用7；基于运动学分析夹具的计划8,9；一个夹具的等级和精度等级建立在夹具夹紧能力的分析上；在夹具设计中，自动选择中安装要考虑到定位误差因素夹具设计11,而且最后结合2D几何夹具计划系统12。在我们先前的研究中，夹具的特点13，夹具的精度14,15，几何约束16，和夹具可及性表面17都被研究过了。设置规划和夹具设计的整体结构被提出来了18。 在这篇论文里，当工件模型和设置规划信息输入系统时，自动夹具规划体系，夹具设计在夹具的表面和关键点中被定义了。2.夹具设计的基本要求 在工程实践中，夹具设计的规划是由许多因素组成的，包括工件的几何信息和公差，设置规划信息，就像加工特征，机床，和每个位置的刀具，在每个位置对于工件所产生的影响以及可夹紧的元件，确保一个夹具在一个合适的位置能夹紧，所以生产过程中可以根据国家标准而且必须满足以下夹具要求来进行设计。1.当工件被固定住的时候，工件的自由度必须完全约束住。2.在当前的设置中要满足加工精度的要求。3.夹具设计稳定在抵制外部的影响力及力矩平衡。4.夹具表面和位置可以被可夹具元件轻易地通过5.在工件与夹具之间没有干扰，以及在夹具和刀具之间。 在本研究中，我们首先关注4个条件。夹具的计划是基于以下进行考虑：1.尽管工件几何是复杂的，但是在工业生产中，当工件是固定的时在大多数夹具设计、平面和圆柱表面(内部和外部)被作为定位，夹紧表面，是靠着多方面的这些特性的测量。在本研究中，平面和圆柱表面都使用在夹具的计划中。2.许多数控机床、特别是加工中心，可以用来在一个设置中做不同的作业。在大多数情况下，刀具轴机床是固定的。在考虑夹具稳定性时、定位表面最好是反向正常的，还是垂直于刀具轴。锁紧特征、法线方向应符合，还是垂直于刀具轴，所以在夹具设计，应该是与定位器夹紧力相反。3.给表面加工，都应该有从尺寸和公差及其他的测量数据作为定位及发展方向的参考。在夹具规划里、高精度的表面作为优先选择，作为定位表面，方便于，后面的加工误差缩小，而且所要求的加工特征更方便实现。4.在夹具规划中，在一个步骤里，超过一个工件表面是必须选择用来夹紧和定位的，用来限制一个工件的自由度。因此，除了结合个人表面的条件以外，以可用的定位表面来结合现状对于工件的精确定位是很重要的。5.因为夹具和定位器与工件有接触，在保障夹具稳定中，这些点的分布在夹具中起着至关重要的作用。6.一种可行的夹具设计，夹具表面必须要被与夹具元件所接触。有效的使用夹具表面应该是大得足以容纳功能表面的夹具和定位器的表面。除了考虑夹具表面，在表面上的一些潜在的可接触点对于决定最终的夹具点分布也是很重要的。3. 夹具表面装置的概念已经被广泛的应用于设计和制造业，一个经过机器加工的工件可以看作是诸如位面，步幅，多格行置地纸架，插槽和空洞的装置的结合。在一个特殊的运转装置中，用来固定工件的装置可以定义为定位装置或者是表面定位。事实上，大部分的定位装置都是二维圆柱形的曲面。根据夹具的功能，夹具的表面可以分类为定位，夹和合支撑夹具。与设计和制造业的家居装置不同，夹具表面是从属方向定位。他们在制造过程中不扮演相同的角色。一整套的表面装置可以用于装置组合中的夹具表面，但是可能不用于夹具本身或者在其他装置组合中有不同功能的夹具。夹具装置的概念允许与夹具几何学有关的夹具需求。在一个基础特征的家具模型中的装置信息也可以直接用来表示夹具设计的目的。对于制造装置来讲，需要描述一个夹具装置的信息包含几何学和非几何学的方面。前者包括型号，形状和空间参数，也包括工件的定位和方向。厚着包括表面装饰，水平面精确和加工装置和表面操作性的关系。3.1 夹具曲面的离散化 在大多数的夹具设计中，夹具装置，尤其是定位表面，是曲面和圆柱形表面。为了估计夹具表面装置的可行性和夹具表面的决定性定位目标，一个备用夹具表面被抽象化为有着相同间隔的网格排列的离散的点T。如果T足够小，离散的抽样点将会大部分的持续。 为了让抽样算法变得普遍化，一个在表面外部边框的长方形矩阵用于取样区域。因为在大多数情况下，初始定位表面是垂直于其他定位表面，尤其是在动态反应的夹具设计中，定位表面被看作是底部定位，顶部夹紧和侧别定位，侧边加紧表面。对于有着标准方向Z的底部定位/顶部夹紧的表面，外部边框的长方形区域的两边必须要平行于X轴，其他的两个边必须与这两个边垂直的平行于Y轴。对于底部定位/夹紧的表面，必须有2个边平行于z轴，尽管其他的两个边必须垂直于前面两条。图形2展示了有着表面外部边框长方形矩阵区域的备用抽样定位表面的抽样。Z轴在表面定位备用系统中的正常这一猜想，在外部边框长方形矩阵的内部的重要之处可以表示为：x = Xmin + T u, u = 1，2， %, Nuy = Ymin + T v, v = 1，2， %, Nv (1)这些是在X和Y轴中的点nu和nv ，分别的是Nu = int (Xmax- Xmin)/T and Nv = int (Ymax - Ymin)/T。图2 一个夹具表面外边框矩形的抽样3.2 可及性表面的可及性 夹具表面的可及性是一种无论夹具表面是否是夹具组成的一部分的衡量标准。三个主要因素必须考虑：1.夹具的几何表面涉及有效面积和形状的表面。2.法线方向上阻塞工件几何形状或者围绕着夹具的几何区域的表面。3.为达到夹具元件的功能，夹具元件的尺寸和形状。 在实际情况中, 工件的一个平面有复杂的形状且法线上或者其他区域有完整或者局部的阻碍。因此需要，一个模型应该全面反映这些事实以便一个合理的可及性与价值可广泛应用于个个夹具表面。 表面可及性被定义为建立于在表面上每一个有效的采样点的可及性的统计值，PA由两部分组成：SIA和NRA。SLA符合大部分的夹具点中的单独的可及性，然而NRA反映了夹具点的可延长性。SLA的一个样本点以来于三个标签的基础上，标签s1用于表明无论方形网格标签的中心是在夹具里面,表面或者外面，中心目前的采样点就在里面，在,或在和家具的表面。三个离散值被指定代表它的地位，那就是，0、1、2，分别。 如果存在在表面正常的方向和周围采样点上阻塞性工件几何成型，会影响采样点的可及性。举个例子，在图3中所看到的，在工件的一个表面上，采样点p1是不是可以因为并沿工件底部位置的阻塞性几何学的发展方向，P2无论它周围是不是有阻碍都无法进入。在表面法线方向，自动的评估是否存在的障碍物，一个虚拟的体积是在表面法线方向被由方形测试网格转化成固体。通过使用一种检测方法两种固体实体之间是否有干扰，如图3(b)中所示的阻碍被确认。这种挤压方法是方形网格标签在侧面定位和夹紧表面上有一点不同，这个面上方形网格标签起初沿着底部定位方向，然后伸直标签是沿着侧面定位和夹紧表面上被挤压成型，如图4所示。属性标签s2是用来记录检查的结果在采样点阻塞的结果。当这些受阻被检测到，s2 = 1，否则，s2 = 0的图片标签。Detected， s2 = 1， otherwise， s2 = 0。检测到，s2 = 1，否则，s2 = 0的图片标签。 如果发现测试网格上面采样点不阻碍，其个体可触性很大程度上取决于测试表面和夹具元件，由属性标签s 3表示，s3的定义公式是AreaI是接触面积，T是边长。在此基础上三个属性标签，也是采样点的pu、v可以赋予一个数值根据以下规则：图3. 阻塞检查在样本的有效点底部表面定位。（pi意味着被点Pi沿着其可接触的方向执行挤压成型。）图4 阻碍在样本点在边缘定位或者夹紧表面时的检查如果侧面定位/夹紧而且 s1 OutsideOuterLoop则 在v反映了影响的重点的高度一边定位/装夹。在采样点的周围区域也会影响其可及性。在一个夹具的表面，当前的采样点与周围的其他采样点的位置关系可以用3*3地图来表示，在Pc是当前采样点的地方用一个离散型(u， v)来表示，P1P8是8个周围点， 他们的位置如图5所表示。NAR在当前点P u，v 可以使用公式：由于Fk和kth周围有接近关系的因素，可以建立在SLA的基础上确定以及测量（s1， s2，s3）。在底部定位或者顶部定位时，当侧面定位或者夹紧时， 一个有效的采样点，一旦SLA，NRA同时知道，PA也能根据方程式被计算出来：图 5. 在3 X 3方位图中的当前点Pc和8个相临样本点P1P8 从SLA和NRA定义SIA在射程为0 1，NRA的范围为-1 1。因此，PA必须在范围-1 2。当PA是少数非零系数，采样点严重阻碍一种可行的夹具点。整体可访问性（OA）家具表面的定义是通过值的总和检验样本点，即： 由于整体可及性是通过表面上，样本点的可及性影响来判断的，这些信息关于有效面积和形状复杂的表面在模型上所展示。一般来说，模型，满足标准的表面以较大的可及性数值比较小的可及性数值更加满足要求。3.3 夹具精度的总体性特征最重要的任务之一是为夹具加工工件保证公差要求。特征的准确性被他们的公差和表面处理。一般来说，公差的功能分为两种类型：尺寸精度和几何公差。尺寸公差的大小表达关系的两个特点的工件。如果有一个特征尺寸公差严格对加工特征，这意味着特征可以使用作为操作数据可能,即定位表面的设定。基于数据的特点是是否有需要，这次的公差可以进一步分成形式公差和位置公差。形式公差是只有特色的有关本身指定允许几何变化特点。个人特征的适用性的夹具的数据。位置公差是相同的重要性夹具尺寸公差的计划，因为它代表之间的一种关系的特点。为了评估特征的准确性和有效利用时间的方法在即可规划、广义精度等级是应用于特征这次调查的定义是：都是重要因素。Tg = (w1Td + w2Tp) * (w3Tf + w4Tr) (10)Td,p,Tf的尺寸精度等级，位置公差等级和形式分别公差等级。Tr是公差等级等同于表面光洁度，w1， w2， w3， and w4都是重要因素。这多个操作“*”代表了一个主导的关系的地方一个零值可导致最后的结果，而经营“+”代表着一个相对薄弱的关系偏好。Td，Tp、Tf，与Tr可以通过阴影算法11，18中描述。4.自动化设备的发展规划系统概述夹具计划系统自动的展现为图6。程序为夹具规划可以是分开的到五个阶段，包括输入、分析、计划、验证、输出。输入的数据包括一个工件CAD模型含有几何和宽容的信息特点和工艺设定工件，规划信息包括特点和加工机床类型的特殊设置。这些数据可以提取也从CAD数据库和用户交互地通过了计算机辅助设计系统。分析涉及候选人的提取夹具相关信息的特点，精度和评价访问夹具的特点。在这一研究中，平面和圆柱表面都考虑夹具的目的。 任务的规划，是决定自动主要定位方向，选择最优定位/夹紧表面和分在当前的设定。算法规划发展的底(头)和侧定位/夹紧安排。 精确定位是主要的原因，以确保，工件的加工精度。一旦定位/夹紧方案，确定相应的夹具单元对夹具产生的分，均可使用夹具结构设计系统(Fix-Des)发展以前19。一个综合项目被发展出来，为了最后的夹具设计，明确夹具元件的累计公差和工件精度的影响。图6 夹具设计的步骤夹具设计的输出量是一个在格式化的夹具设计中的夹具表面或者点用于夹具结构设计。尽管夹具设计是建立在一些优化规则上生成的，替代夹具设计也提供了进一步优化或用户证明。4.1 基本定位方向的定良分析在设备设计中，通常有3个参考定位的表面，那些表面决定工件的位置和方向。基本定位表面是主要定位基准面，为了决定在当前的设置中立体位置和工件的方向，和约束工件3个自由度。基本定位表面是垂直于其他表面的，尤其是被用来应用在模块花夹具中。一般案例，基本定位表面可以是一个单独的面或者是在同意方向上的多个在同一个或不同高度的面。基本定位表面的通常方向被称为基本定位方向，需要在夹具规划中第一个被决定。它应该平行或垂直机床的刀具轴。假定工具轴是Vt=(Vx，Vy，Vz)。这些面与普通方向平行或与工具轴垂直，这些面被提取于工件模型中，他们的分类如下：Sfn代表一组表面，在基本定位方向上的法线方向上；fi(Vi，Tgi，Ai)代表法向矢量Vi,广义的精度等级Tgi和一个可用区域Ai；Nf是这组里特点的数目的集合；Ns是这组里的特点数。如果基本定位方向是由V1(V1x，V1y，V1z)和V1Vi所决定的，以下指标是用于鉴定Vi是否有按优先顺序排列：WA和WT1是表面的重量因素和精确度，maxSA是这组区域里的最大限度的面，maxST是总体性的精度等级特征的最大值。如果得到In_V1，那么相应的正常向量在基本定位方向上被确定。4.2底部定位和顶部定位的规划夹具规划在这个阶段的任务是决定合适的主要位置和在表面上的定位点的分布，夹紧面和点与基准方向一致，在图7中表示。图. 7 垂直方向的一个夹具规划程序所有基准面的集合能被表示为： Fi(Vi，Tgi，Ci)由一个正常向量Vi，一个广义精度Tgi，等高线Ci而且这个公式里Nf代表集点。 当包含多个平面的时候，这些平面投射在基准方向上，形成了一个虚拟平面，通过他们的边界实体就像线段和弧线。当这些面在离散点上被取样的时候，一个外界区域在虚拟平面生成了。因为定位点不能太过于接近工件的外边沿。矩形区域的大小被还原成向向它的中心边界移动。最终定位点的投影将要在这个新区域被确定。然而，也有一些点可能是在表面之外，检测是否是这个点标准算法是在一个特定的区域里。在基准定位方向中，3个方向上必须被约束3个自由度。3个点画成一个3角形，而且工件的中心，为了保证定位的稳定性，重心应该在3角中被确定。最理想的定位方案由下面因素决定：1 三角形区域越大越好，公式：当S=0.5*(l1+l2+l3)，而且l1，l2，l3是三角形三条边长。 2.工件重心到三角形三个边缘的距离要尽可能的大，公式为： 这里Di是三角形的边缘到工件重心的距离。3.位面广义精度上的定位点的位置要尽可能的高（公差值要尽可能的小）。公式为： 4.三个定位点的可及性要尽可能的。公式为：这里ACCi，ACCj，ACCk，是定位点的可及性。5.定位点的均衡应该尽可能的一致。公式为：当上诉因素的值被获得时，证明指数被用来定义最优定位点，其中最小值是：这里Ws，WT2，WC1，和WH分别是夹具稳定性，精确度，可及性和统一高度的重力因素；maxTA，maxTL，和maxTT是所有垂直定位的标准因素。一旦确定了最后的定位点，包含了与三个定位点相对应的定位表面。值得注意的是通过使用一个或更多的程序能被选择作为主要定位条件。夹具类型的选择主要涉及到加工方向上的力和可夹紧装置的表面。加紧表面的确定基于以下的几点因素：1，表面相对于底部表面定位。2，表面就是当前的加工表面。3，如果表面被投射进定位三角区域将重合。4，在装夹的时候表面是容易处理的。一旦夹紧表面被确定，最优夹紧点被选中以至于夹紧力就是对一个方向的底定位器或者在底定位三角形。在上诉步骤后，产生了所有可行的对底部定位和对顶部定位的夹紧计划并且被优先确定。每一个夹紧计划的文件包含了夹紧信息，例如，夹具功能，定位夹紧表面，表面位置和定位夹紧点的坐标。4.3侧定位夹紧规划在水平方向的夹紧计划包括侧定位和夹紧计划。侧定位是用来确定非主要的定位点与定位表面。侧定位最普遍的方法是标准的3-2-1定位原理。在这样的情况下，侧定位计划选择两条相互垂直的边作为第二和第三定位表面，并且这些边分别包含了两个和一个定位表面。当设计一个夹紧装置时这些夹紧方案是优先的用来控制定位精度，因为其是在不同自由度上是独立约束的。然而，在很多情况下，是非常困难的去发现这种相互垂直的定位夹具设计。一个非常普遍的情况，有时柱面和不、垂直的边也被用来作为定位表面。这三个侧定位点分布在三个不同的表面。在这项研究中提供了解决情况，包括标准的3-2-1情况作为有限的解决方案。为了选择合适的侧定位表面，一般情况下，考虑到广义的精度等级，可及性价值和候选表面形状。这些负荷侧边定位原理的的特性被表示为：这里fi（Vi，Tgi，Acci，Ci）是一个一般向量Vi，一般精度等级Tgi，一个可及性Acci和轮廓Ci的特性；Nf是特性的数量。为了限制来自于主要定位的剩余的三个自由度，需要多个加工表面来作为侧定位。如上所诉，除了个别表面的情况，结合现状，候选加工表面在工件定位时也是一个重要的因素。对于这两种定位特点，有许多组合能被使用在侧定位中。以下是部分优先组合的列表：1. 互相垂直得两个位面2. 不垂直的两个位面3. 三个位面4. 一个位面和一个柱面5. 两个柱面6. 一个位面和两个柱面，显示在图8中。基于这些组合的类型，特征群体能够建立表示为：图8 包含了6种类型，1号为两个垂直面，2号为两个非垂直面，3号为两个非平行面，4号为一个圆周面跟两个平面相交，5号为两个圆周平面，6号为一个平面跟两个圆周面。LHCm=fii=1，2or1，2，3，fi LH， （21）m=1，2，Nm在这个公式里面，fi起着主导作用，Nm为一个数集。每个特征组里面包含了两到三个特征，衡量特征组的标准包含以下几点：1.特征组合形式，一重量系数，HF，被指定到不同定位面的组合类型中，如果特征组包含了两个垂直面，则为最优先选择，如果包含了三个圆周面，则相反。2. 特征组的广义精度等级划分。广义上的特征组通常都被用于所有的特征当中，HT=Ti的总和，在特征组里面，Ti是广义的精度等级，而i是1，2，3的数。3.特征组的重要性。在特征组里面，没个面的重要性都有被考虑，HC=Accii=1,2or3，在所选的水平面特征中，Acci是极重要的。当以上的参数都被包含进去时，下面的公式则可以用于确定最好的基准面。In_Hl=HF+WT3*HTi/maxHT+WC2*HCi，Nsil （22）在公式里面，WT3和WC2是分别的并且可以达到的重量系数，而maxHT是标准系数。当定位基准平面分类于每个组中时，定位高度就会被确定。预期结果是所有的定位元件，跟夹具一样，都被放置在同一个高度，或者定位点的高度差为最小。图9. 工件模型和侧交叉定位平面一旦定位高度被确定，有效的定位基准平面在2D直线与圆弧或者圆之间，这些2D定位区域能直接在CAD加工模型中反映出来。图9所显示的是一个定位高度的横截面。在2D线性片段中，定位点的位置是确定的，建立在不同的表面跟点上面，要想解决定位问题，必须满足两个条件16，第一，在正常加工过程中，定位的基准平面是不会绝对平行的。第二，当给出一个含糊不清的工作位置时，三个基准点是不会重合于一点的。对于通用夹具的稳定性来说，当这个平面为基准面的对立面时，面夹具就比较适合，当在决定夹紧面与定位点的时候，一个完整的解决方案就会被提出。图10显示的是面夹具的定位选择过程。图. 10 在水平方向夹具规划的一个程序.5. 实例和结论 Fix-Des是一个夹具设计系统，它的发展结合了CAD系统和自动化设备配置系统。CAD系统作为平台，适用于提供系统与输入必要信息，Fix-Des是用来产生夹具结构设计用于Fix-Planning的输出。图11具体体现了系统菜单显示8功能模块。SysSetup被用来在执行任务计划之前初始化系统。系统初始化的一个例子被显示在图12，规划条件在定制的地方被设置，如夹紧类型、最小面积为定位器的高度和最低位置定位器在水平位置和影响着垂直位置的主要因素是先后顺序。文件是用来从CAD数据库读取工件规格的，是用来储存夹具外形设计的夹具方案的。LocatingDir是为了确定工件主要定位的方向。可及性是夹具的特点和目的中的辅助功能。该算法对于侧面和底部定位/夹紧在水平定位，水平夹紧，垂直定位和垂直夹紧的模块中固定。当夹具设计完成的时候，结果优先也被显示出来。图11 整体的Fix-Planning系统图12 系统初始化的例子标签1 可及性分析的结果（BL 底部定位；SL 边上定位；SC 边上夹紧；TC 顶部夹紧）。例如工件在图9（a）中在F46表面上所执行的加工步骤。标签1中显示了后补加工面的易用性评估,而且图13显示，在后补加工面的底部定位中可及性点的分布。在水平和垂直方向，夹具规划的结果如图14。可能结果并不是一定的。在图14中表示夹具结构设计中，替补计划一样是不可少的。图15显示了夹具的设计。 在例子中所见，夹具表面和点的自动化选择建立在很多因素的考虑中，包括精度等级，夹具稳定性还有夹具表面可及性。在系统中，工件的几何信息直接从CAD模型中引出，机构的设计信息被输入，而且平面和圆柱表面都被视为夹具表面。夹具表面组织建立了垂直和水平的计划。替代方案提供了进一步的优化和使用准确。在使用先前的发展系统Fix-Des时，接触点也被自动确定，为了夹具结构设计而被输出。该系统的应用程序将导致减少交货时间的伟大计划，因此也会响应在生产设计中对于制造系统的能力的增强的改变。图 13. PA是在以底部面F23定位时，样本点的静态值（a）在F23表面上样本点的分布。（b）PA是在面F23上所有样本点的静态值。图14（a） 水平定位/装夹的例子。（b） 垂直定位例子。（c）对应垂直定位的垂直夹紧的例子。图15 夹具结构设计的最后结果。（a）2D俯视图。（b）3D消除隐藏线视图。参考文献1. A. J. C. Trappey and C. R. Liu, “A literature survey of fixturedesign automation”, International Journal of Advanced Manufacturing Technology, 5(3), pp. 240255, 1990.2. Y. Rong and Y. Zhu, “Computer-aided modular fixture design and management in computer-integrated manufacturing systems, Japan-USA Symposium on Flexible Automation, Kobe, Japan, 1118 July, pp. 529534, 1994.3. B. S. Thompson and M. V. Gandhi, “Commentary on flexible fixturing”, Applied Mechanics Review, 39(9), pp. 13651369,1986.4. Y. Rong and Y. Bai, “Automated generation of modular fixture configuration design”, Journal of Manufacturing Science and Engineering, 119, pp. 208219, May 1997.5. Y. Bai and Y. Rong, “Modular fixture element modeling and assembly relationship analysis for automated fixture configuration design”, Journal of Engineering Automation, 4(2), pp. 147162,1998.6. Y. C. Chou, V. Chandru and M. M. Barash, “A mathematical approach to automatic configuration of machining fixtures: analysis and synthesis”, Journal of Engineering for Industry, 111, pp. 299306, 1989.7. E. C. De Meter, “Selection of fixture configuration for the maximization of mechanical leverage”, Manufacturing Science and Engineering, ASME WAM, New Orleans, LA, 28 November2 December 1993, PED-4, pp. 491506, 1993.8. R. J. Menassa and W. DeVries, “A design synthesis and optimization method for fixtures with compliant elements”, Advances in Integrated Product Design and Manufacture. ASME WAM, PED-47, Dallas, TX, 2530 November, pp. 203218, 1990.9. M. Mani and W. R. D. Wilson, “Automated design of workholding fixtures using kinematic constraint synthesis”, 16th NAMRC, pp. 437444, 1988.10. S. K. Ong and A. Y. C. Nee, “A systematic approach for analysing the fixturability of parts for machining”, ASME WAM, San Francisco,CA, 1217 November 1995.11. J. R. Boerma and H. J. J. Kals, “Fixture design with FIXES: the automated selection of positioning, clamping and support features for prismatic parts”, Annals CIRP, 38, pp. 399402, 1989.12. R. C. Brost and K. Y. Goldberg, “A complete algorithm for synthesizing modular fixtures for polygonal parts”, IEEE Transactions on Robots and Automation, 12(1), pp. 3146, 1996.13. Y. Rong, J. Zhu and S. Li, “Fixturing feature analysis for computeraided fixture design”, Intelligent Design and Manufacturing, ASME WAM, New Orleans, LA, 28 November3December, PED-64, pp. 267271, 1993.14. Y. Rong and Y. Bai, “Machining accuracy analysis for computeraidedfixture design”, Journal of Manufacturing Science and Engineering,118, pp. 289300, August 1996.15. Y. Rong, W. Li and Y. Bai, “Locator error analysis for fixturing accuracy verification”, Computer in Engineering, Boston, MA, 1721 September, pp. 825832, 1995.16. Y. Wu, Y. Rong, W. Ma and S. LeClair, “Automated modular fixture design: geometric analysis”, Robotics and Computer-Integrated Manufacturing, 14, pp. 1726, 1998.17. J. Li, W. Ma and Y. Rong, “Fixturing surface accessibility analysis for automated fixture design”, 26th NAMRC, Atlanta, GA, 1922 May 1998.18. Y. Rong, X. Liu, J. Zhou and A. Wen, “Computer-aided setup planning and fixture design”, International Journal of Intelligent Automation and Soft Computing, 3(3), pp. 191206, 1997.19. W. Ma, Z. Lei and Y. Rong, “Fix-Des: a Computer-aided Modular Fixture Configuration Design System”, International Journal of Advanced Manufacturing Technology, 1988; partially presented at ASME Computer in Engineering Conference, Sacramento, CA,1417 September 1997, DETC97/CIE-4281.20. Y. Wu, Y. Rong, W. Ma and S. LeClair, “Automated modular fixture design: accuracy analysis and clamping design”, Robotics and Computer-integrated Manufacturing, 14, pp. 115, 1998; partially presented at ASME IMECE, Dallas, TX, 1621 November 1997.外文翻译原文Development of Automated Fixture Planning SystemsW. Ma, J. Li and Y. RongDepartment of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USAFixturing is an important manufacturing activity. The computeraided fixture design technique is being rapidly developed to reduce the lead time involved in manufacturing planning. An automated fixture configuration design system has been developed to select automatically modular fixture components and place them in position with satisfactory assembly relationships.In this paper, an automated fixturing planning system is presented in which fixturing surfaces and points are automatically determined based on workpiece geometry and operational information. Fixturing surface accessibility, feature accuracy, and fixturing stability are the main concerns in the fixture planning. The system development, the fixture planning decision procedure, and an implementation example are presented in the paper.Keywords: Accuracy; Clamping; Fixture planning; Locating1. Introduction Fixturing is an important manufacturing activity in the production cycle. A computer-aided (or automated) fixture design (CAFD) technique has been developed as part of CAD/CAM integration 1. The development of CAFD contributes to the reduction of manufacturing lead time, the optimisation of manufacturing operations, and the verification of manufacturing process designs 2. CAFD plays an important role in flexible manufacturing systems (FMS) and computer-integrated manufacturingsystems (CIMS) 3. Figure 1 outlines the activities for fixture design in manufacturing systems which include three major aspects: set-up planning, fixture planning, and fixture configuration design 4. The objective of set-up planning is to determine the number of setups, the position and orientation of the workpiece in each setup, and also the machining surfaces in each set-up. Fixture planning determines the locating and clamping points on workpiece surfaces. The task of fixture configuration design is to select fixture components and place them into a final configuration to fulfil the functions of locating and clamping theworkpiece. An automated modular fixture configuration design system has been developed in which, when fixturing surfaces and points are selected on the workpiece model, fixture units are automatically generated and placed into position with the assistance of fixture component assembly relationships 4,5. This paper deals with fixture planning when the fixturing surfaces and positions on the workpiece are selected automatically.Fig. 1. Fixture design in manufacturing systems. Previous papers on fixture design analysis have been published,but a comprehensive fixture planning system which can be used to generate fixture plans for industrial applications hasnot been developed. Previous work includes: a method for the automated determination of fixture location and clamping derived from a mathematical model 6; an algorithm for theselection of locating and clamping positions which provide the maximum mechanical leverage 7; kinematic analysis based fixture planning 8,9; a fixturing grade and dependency grade based fixturability analysis 10; automated selection of set-ups with consideration of tolerance factors of orientation errors in fixture design 11, and finally a geometric analysis based 2D fixture planning system 12. In our previous research, fixturing features 13, fixturing accuracy 14,15, geometric constraints 16, and fixturing surface accessibility 17 have been studied. A framework has been developed for set-up planning andfixture design 18. In this paper, an automated fixture planning system, Fix-Planning, is presented where fixturing surfaces and points are determined when the workpiece model and set-up planning information is input to the system.2. Basic Requirements of FixturePlanning In engineering practice, fixture planning is governed by a number of factors, including workpiece geometric information and tolerance; set-up planning information such as machining features, the machine tool and cutting tools to be used in each set-up; initial and resulting forms of the workpiece in each set-up; and available fixture components. To ensure that the fixture can hold the workpiece in an acceptable position so that the manufacturing process can be carried out according to the design specifications, the following conditions should be satisfied for a feasible fixture plan. 1. The degrees of freedom (DOF) of the workpiece are totally constrained when the workpiece is located. 2. Machining accuracy specifications can be ensured in the current set-up. 3. Fixture design is stable to resist any effects of external force and torque. 4. Fixturing surfaces and points can be accessed easily by available fixture components. 5. There is no interference between the workpiece and the fixture, and between the cutter tool and the fixture. In this investigation, we focus on the first four requirements.Fixture planning is carried out based on the following considerations: 1. Although the workpiece geometry can be complex in industrial production, in most fixture designs, planar and cylindrical surfaces (internal and external) are used as the locating and clamping surfaces because of the ease of access and measurement of these features when the workpiece is fixed. In this investigation, planar and cylindrical surfaces are used in fixture planning. 2. Many CNC machines, especially machining centres, can be used to perform various operations within one set-up. In most cases, the cutting-tool axis of the machine tool is fixed. When considering fixturing stability, the locating surfaces are preferably those with normal directions opposite to, or perpendicular to, the cutting-tool axis. For clamping features, the normal directions should be in line with, or perpendicular to, the cutting-tool axis, because, in fixture design, clamping forces should be against locators. 3. For the surfaces to be machined, there should exist datum surfaces which serve as position and orientation references from which other dimensions and tolerances are measured. In fixture planning, surfaces with high accuracy grades should be selected preferentially as locating surfaces so that the inherited machining error is minimised and the required tolerances of the machining features are easily attained. 4. In fixture planning, more than one workpiece surface must be selected for the locating and clamping surfaces for restricting the DOF of the workpiece in a set-up. Therefore, besides the conditions for individual surfaces, the combination status of the available locating surfaces is also important for the accurate location of the workpiece. 5. Since the locators and clamps are in contact with the workpiece, the distribution of fixturing points plays a critical role in ensuring fixturing stability. 6. For a feasible fixture design, the fixturing surfaces must be accessible to the fixture components. The usable (effective) area of the fixturing surface should be large enough to accommodate the functional surfaces of the locators and clamps. Besides considering a fixturing surface, the accessibility of potential fixturing points on the surface is also important for the determination of the final fixturing point distribution.3. Fixturing Surfaces The concept of features has been widely used in design and manufacturing. A workpiece to be machined can be viewed as a combination of features such as planes, steps, pockets, slots, and holes. In a particular operation set-up, features used for fixturing the workpiece can be defined as fixturing features or fixturing surfaces. In practice, most fixturing features are planar and cylindrical surfaces. According to the fixturing functions,the fixturing surfaces can be classified into locating, clamping, and supporting features. Unlike design and manufacturing features, fixturing surfaces are orientation-dependent. They do not play the same role throughout the manufacturing processes. A set of surfaces may serve as fixturing surfaces in a set-up, but may not be used for fixturing or have different fixturing functions in another set-up. The concept of fixturing features allows the fixturing requirements to be associated with the workpiece geometry. Feature information in a feature-based workpiece model can also be used directly for fixture design purposes. For manufacturing features, the information necessary for describing a fixturing feature contains geometric and non-geometric aspects. The former includes feature type, shape and dimensional parameters,and position and orientation of the workpiece. The latter includes the surface finish, accuracy level and relationships with machining features, and surface accessibility.3.1 Discretisation of Fixturing Surfaces In most fixture designs, the fixturing features, especially the locating surfaces, are planar and cylindrical surfaces. In order to evaluate fixturing surface accessibility and determine locating/clamping points on fixturing surfaces, a candidate fixturing surface is sampled into grid-arrayed discrete points with equal interval T. If T is small enough, the discrete sample points will be almost continuous. In order to make the sampling algorithm generic, an outerbounding rectangle on the surface is used as the sampling region. Since in most cases, the primary locating surface is perpendicular to the other locating surfaces, especially in modular fixture designs, the fixturing surfaces are considered as bottom-locating, top-clamping, side-locating, and side-clampingsurfaces. For a bottom-locating/top-clamping surface with a normal Z (or 2Z) direction, two edges of the outer-bounding rectangle must be parallel to the X-axis and two other edges parallel to the Y-axis. For a side-locating/clamping surface, there must be two edges parallel to the Z-axis, while the other two edges must be perpendicular to the first two edges. Figure2 shows an example of sampled candidate fixturing surfaces with the outer-bounding rectangle. With the assumption that the Z-axis is normal to the surface in the surface local coordinate system, the points within the outer-bounding rectangle can be represented as:where Nu and Nv are the numbers of points in the X- and Y directions, respectively, which are: Nu = int (Xmax - Xmin)/T and Nv = int Ymax - Ymin)/T.Fig. 2. Sampling of a candidate fixturing surface with an outer-bounding rectangle.3.2 Fixturing Surface AccessibilityFixturing surface accessibility is a measure of whether a candidate fixturing surface is accessible to a regular fixture component. Three major factors must be taken into account:1. The geometry of the fixturing surface which involves the effective area and shape of the surface.2. Possible obstruction of the workpiece geometry along the normal direction and/or around the geometric region of the fixturing surface.3. The size and shape of the functional fixture components. In practical situations, it is possible that a planar surface of the workpiece has a complex shape and has a full/partial obstruction along its normal direction and/or around its geometric region. It is thus required that the accessibility model should comprehensively reflect these facts so that a reasonably comparable accessibility value can be applied for every candidate fixturing surface. The surface accessibility is defined as a statistical value based on the point accessibility (PA) of every valid sample point on the surface, where PA consists of two parts: the point self individual accessibility (SIA) and the point neighbour related accessibility (NRA). The SIA corresponds mainly to the isolated accessibility of the fixturing point, whereas the NRA reflects the extended accessibility of the fixturing point. The SIA of a sample point is defined on the basis of three attribute tags. The tag s1 is used to indicate whether the square test grid with its centre at the current sample point is inside, on, or outside the outer-loop of the fixturing surface. Three discrete values are assigned to represent its status, i.e. 0, 1, and 2, respectively. If there exists obstructive workpiece geometry in the surface normal direction or surrounding the sample point, this affects the surface accessibility at the sample point. For example, as shown in Fig. 3(a), on a candidate bottom-locating surface of a workpiece, sample point p1 is not accessible because of the obstructive geometry of the workpiece along the bottom-locating direction, and p2 is not accessible either because of the obstructions surrounding it. To evaluate automatically whether an obstruction exists in the surface normal direction, a virtual volume is generated by extruding the square test grid to asolid entity in the surface normal direction. By employing a technique for detecting the interference between two solid entities, the obstruction can be identified, as shown in Fig.3(b). The extruding method is a little different for the square test grid on the side-locating/clamping surface, where the square test grid is first stretched along the bottom-locating direction, and then the stretched grid is extruded along the side-locating/clamping direction as illustrated in Fig. 4. The attribute tag s2 is used for recording the result of obstruction checking at a sample point. When such an obstruction isdetected, s2 = 1, otherwise, s2 = 0.Fig. 3. Obstruction checking at virtual sample points on a bottomlocating surface. (Kpi means the extrusion is carried out at point pi along its accessible direction.)Fig. 4. Obstruction checking at sample points on a side-locating/ clamping surface. If the test grid at the sample point is found to be not obstructed, its individual accessibility is largely dependent on the contact area between the test surface and the fixture components, which is represented by the attribute tag s3. The definition of s3 is where AreaI is the contact area and T is the edge length of the test grid. On the basis of above three attribute tags, the SIA of a sample point pu,v can be given by a numerical value according to the following rules: if s1 = OutsideOuterLoop, SIA = -1 (inaccessible); if s1 OutsideOuterLoop AND s2 = Obstructed, SIA =- 1 (inaccessible); if bottom-locating/top-clamping AND S1 OutsideOuterLoop AND s2 = NotObstructed, SIA = s3; if side-locating/clamping AND s1 OutsideOuterLoop AND s2 = NotObstructed, SIA = 0.5vs3; where v reflects the height effect of the point in side locating/clamping. Fig. 5. 3 X 3 position map of current point Pc and 8-neighbour sample points P1P8. The accessibility in the surrounding area of the sample point also affects the accessibility of the point. On a fixturing surface, the positional relationship between the current sample point and all the neighbouring sample points can be represented by a 3 X 3 map where Pc is the current sample point with a discrete position of (u, v), P1 P8 are 8-neighbour sample points, and their locations are all labelled in Fig. 5. The NRA at sample point pu,v can be calculated using the equation: where Fk is the related-access factor of kth neighbour, which can be determined based on the SIA as well as its measure (s1, s2, s3).For bottom-locating/top-clamping,For side-locating/clamping,For a valid sample point, once the SIA and NRA are obtained, the PA can also be calculated according to the equation: From the definitions of SIA and NRA, SIA is in the range of 0 1 and NRA is in the range of -11. Therefore, PA must be in the range of -12. When the value of PA is less than zero, the sample point is severely obstructed and is not a feasible fixturing point. The overall accessibility (OA) of the fixturing surface is defined as the sum of the PA values at all valid sample points, i.e., As OA is statistically measured by the overall effect of the accessibility of the sample points on the surface, the information about the effective area and shape complexity of the surface is represented in the model. Generally, the model satisfies the criterion that the surface with the larger OA is more accessible than the one with the smaller OA.3.3 Generalised Accuracy of the Fixturing FeaturesOne of the most important tasks for fixture planing is to guarantee that the tolerance requirements are met when the workpiece is machined. The accuracy of features can be characterised by their tolerance and surface finish, and the tolerance between features. Generally, the tolerance of features can be classified into two types: dimensional tolerance and geometric tolerance. The magnitude of the dimensional tolerance may express the relationship between two features on the workpiece. If there is a feature with a tight dimensional tolerance with respect to a machining feature, this implies that the feature may be used potentially as an operational datum, i.e. a locating surface in the set-up. Based on whether a datum feature isneeded, the geometric tolerance can be further divided into form tolerance and positional/orientation tolerance. The form tolerance is associated only with the feature itself, which specifies the allowable geometric variation of individual features. The form tolerance, e.g. surface finish, of a feature affects the suitability of the feature to be the fixturing datum. The positional/orientation tolerance is of the same importance as the dimensional tolerance for fixture planning since it also represents a relationship between features. In order to evaluate the accuracy of a feature and use it efficiently in fixture planning, a generalised feature accuracy grade is applied in this investigation, which is defined as:Tg = (w1Td + w2Tp) * (w3Tf + w4Tr) (10)where Td, Tp and Tf are the dimensional tolerance grade, positional tolerance grade and form tolerance grade, respectively; Tr is the tolerance grade equivalent to the surface finish of the feature. w1, w2, w3, and w4 are the weight factors. The multiple operation “*” represents a dominant relationship where a zero value can contribute to the final result, while the operation “+” represents a relatively weak relationship with preferences. Td, Tp, Tf, and Tr can be obtained by applying the algorithms described in 11,18.4. Development of Automated FixturePlanning Systems An overview of the automated fixture planning system is shown in Fig. 6. The procedure for fixture planning can be divided into five stages, i.e. input, analysis, planning, verification, and output. The input data includes a workpiece CAD model containing the geometric and tolerance information of the features of the workpiece, and set-up planning information including the features to be machined and the machine tool type for the specific set-up. The data can be extracted either from a CAD database or entered interactively by the user ina CAD system. Analysis involves the extraction of the candidate fixturing features with related accuracy information and an evaluation of the accessibility of the fixturing features. In this study, planar and cylindrical surfaces are considered for fixturing purposes. The task of planning is to determine automatically the primary locating direction and to select the optimal locating/clamping surfaces and points in the current set-up. Algorithms are developed for the planning of the bottom (top) and side locating/clamping arrangements. Accurate location is the major contributor in ensuring the machining accuracy of the workpiece. Once the locating/clamping scheme is determined, the fixture units corresponding to the fixturing points can be generated by using the fixture configuration design system (Fix-Des) developed previously 19. A comprehensive program has been developed to analyse the final fixture design in terms of the cumulative tolerances of fixture components and the effects on workpiece accuracy.The output of the fixture planning is the fixturing surfaces/points in the format of a fixture plan which can be used in fixture configu