关 键 词：

含CAD图纸、文档所见所得 摩托车 后轮 轮毂 低压 铸造 模具设计 CAD 图纸 文档 所得

资源描述：

购买设计请充值后下载，，资源目录下的文件所见即所得，都可以点开预览，，资料完整，充值下载就能得到。。。【注】：dwg后缀为CAD图，doc,docx为WORD文档，有不明白之处，可咨询QQ:414951605

内容简介：

注塑模具自动装配造型注塑模具自动装配造型 X. G. Ye, J. Y. H. Fuh and K. S. Lee机械和生产工程部，新加坡国立大学，新加坡注射模是一种由与塑料制品有关的和与制品无关的零部件两大部分组成的机械装置。本文提出了（有关）注射模装配造型的两个主要观点，即描述了在计算机上进行注射模装配以及确定装配中与制品无关的零部件的方向和位置的方法，提出了一个基于特征和面向对象的表达式以描述注射模等级装配关系，该论述要求并允许设计者除了考虑零部件的外观形状和位置外，还要明确知道什么部份最重要和为什么。因此，它为设计者进行装配设计（DFA）提供了一个机会。同样地，为了根据装配状态推断出装配体中装配对象的结构，一种简化的特征几何学方法也诞生了。在提出的表达式和简化特征几何学的基础上，进一步深入探讨了自动装配造型的方法。关键字：装配造型；基于特征；注射模；面向对象。1、简介注射成型是生产塑料模具产品最重要的工艺。需要用到的两种装备是：注射成型机和注射模。现在常用的注射成型机即所谓的通用机，在一定尺寸范围内，可以用于不同形状的各种塑料模型中，但注射模的设计就必须随塑料制品的变化而变化。模型的几何因素不同，它们的构造也就不同。注射模的主要任务是把塑料熔体制成塑料制品的最终形状，这个过程是由型芯、型腔、镶件、滑块等与塑料制品有关的零部件完成的，它们是直接构成塑料件形状及尺寸的各种零件，因此，这些零件称为成型零件。（在下文，制品指塑料模具制品，部件指注射模的零部件。）除了注射成型外，注射模还必须完成分配熔体、冷却、开模、传输、引导运动等任务，而完成这些任务的注射模组件在结构和形状上往往都是相似的，它们的结构和形状并不取决于塑料模具，而是取决于塑料制品。图 1 显示了注射模的结构组成。 图 1 注射模的结构成型零件的设计从塑料制品中分离了出来。近几年，CAD/CAM 技术已经成功的应用到成型零件的设计上。成型零件的形状的自动化生成也引起了很多研究者的兴趣，不过很少有人在其上付诸实践，虽然它也象结构零件一样重要。现在，模具工业在应用计算机辅助设计系统设计成型零件和注射成型机时，遇到了两个主要困难。第一，在一个模具装置中，通常都包括有一百多个成型零部件，而这些零部件又相互联系，相互限制。对于设计者来说，确定好这些零部件的正确位置是很费时间的。第二，在很多时候，模具设计者已想象出工件的真实形状，例如螺丝，转盘和销钉，但是 CAD 系统只能用于另一种信息的操作。这就需要设计者将他们的想法转化成CAD 系统能接受的信息(例如线，面或者实体等)。因此，为了解决这两个问题，很有必要发展一种用于注射模的自动装配成型系统。在此篇文章里，主要讲述了两个观点：即成型零部件和模具在计算机上的防真装配以及确定零部件在模具中的结构和位置。这篇文章概括了关于注塑成型的相关研究，并对注射成型机有一个完整的阐述。通过举例一个注射模的自动装配造型，提出一种简化的几何学符号法，用于确定注射模具零部件的结构和位置。2.相关研究在各种领域的研究中，装配造型已成为一门学科，就像运动学、人工智能学、模拟几何学一样。Libardi 作了一个关于装配造型的调查。据称，很多研究人员已经开始用图表分析模型会议拓扑。在这个图里，各个元件由节点组成的，再将这些点依次连接成线段。然而这些变化矩阵并没有紧紧的连在一起，这将严重影响整体的结构，即，当其中某一部分移动了，其他部分并不能做出相应的移动。Lee and Gossard 开发了一种新的系统，支持包含更多的关于零部件的基本信息的一种分级的装配数据结构，就像在各元件间的“装配特征”。变化矩阵自动从实际的线段间的联系得到，但是这个分级的拓扑模型只能有效地代表“部分”的关系。自动判别装配组件的结构意味着设计者可避免直接指定变化的矩阵，而且，当它的参考零部件的尺寸和位置被修改的时候，它的位置也将随之改变。现在有三种技术可以推断组件在模具中的位置和结构：反复数值技术,象征代数学技术，以及象征几何学技术。Lee and Gossard 提出一项从空间关系计算每个组成元件的位置和方向的反复数值技术。他们的理论由三步组成：产生条件方程式，降低方程式数量，解答方程式。方程式有：16 个满足未知条件的方程式，18 个满足已知条件的方程式，6 个满足各个矩阵的方程式以及另外的两个满足旋转元件的方程式。通常方程式的数量超过变量的数量时，应该想办法去除多余的方程式。牛顿迭代法常用来解决这种方程式。不过这种方法存在两种缺点：第一，它太依赖初始解；第二：反复的数值技术在解决空间内不能分清不同的根。因此，在一个完全的空间关系问题上，有可能解出来的结果在数学理论上有效，但实际上却是行不通的。Ambler 和 Popplestone 提议分别计算每个零部件的旋转量和转变量以确定它们之间的空间关系，而解出的每个零部件的 6 个变量(3 个转变量和 3 旋转量)要和它们的空间关系一致。这种方法要求大量的编程和计算，才能用可解的形式重写有关的方程式。此外，它不能保证每次都能求出结果，特别是当方程式不能被以可解答的形式重写时。为了能确定出满足一套几何学限制条件的刚体的位置与方向，Kramer 开发了一种特征几何学方法。通过产生一连串满足逐渐增长的限制条件的动作推断其几何特征，这样将减少物体的自由度数。Kramer 使用的基本参考实体称为一个标识，由一个点和两正交轴构成。标识间的 7 个限制条件（coincident, in-line, in-plane, parallelFz,offsetFz, offsetFx and helical)都被定了义。对于一个包括独立元件、相互约束的标识和不变的标识的问题来说，可以用动作分析法来解决问题，它将一步一步地最后求出物体的最终的几何构造。在确定物体构造的每一个阶段，自由度分析将决定什么动作能提供满足限制物体未加限制部位的自由度。然后计算该动作怎样能进一步降低物体的自由度数。在每个阶段的最后，给隐喻的装配计划加上合适的一步。根据 Shah 和 Rogers 的分析，Kramer 的理论代表了注射模具最显著的发展，他的特征几何学方法能解出全部的限制条件。和反复的数值技术相比，他的这种方法更具吸引力。不过要实行这种方法，需要大量的编程。现在虽然已有很多研究者开始研究注射成型机，但仍很少有学者将注意力放在注射模设计上。Kruth 开发了一个注射模的设计支援系统。这个系统通过高级的模具对象(零部件和特征)支持注射模的成型设计。因为系统是在 AUTOCAD 的基础上设计的，因此它只适于线和简单的实体模型操作。3.注射模装配概述主要讲述了关于注射模自动装配造型的两个方面：注射模在电脑上的防真装配和确定结构零件在装配中的位置和方向。在这个部分，我们基于特征和面向对象论述了注射模装配。注射模在电脑上的防真装配包含着注射模零部件在结构上和空间上的联系。这种防真必须支持所有给定零部件的装配、在相互关联的零部件间进行变动以及整体上的操作。而且防真装配也必须满足设计者的下列要求：1支持能表达出模具设计者实体造型想象的高级对象。2成型防真应该有象现实一样的操作功能，就如装入和干扰检查。为了满足这些要求，可用一个基于特征和面向对象的分级模型来代替注射模。这样便将模型分成许多部分，反过来由多段模型和独立部分组成。因此，一个分级的模型最适合于描述各组成部分之间的结构关系。一级表明一个装配顺序，另外，一个分级的模型还能说明一个部分相对于另一个部分的确定位置。与直观的固体模型操作相比，面向特征设计允许设计者在抽象上进行操作。它可以通过一最小套参数快速列出模型的特征、尺寸以及其方位。此外，由于特征模型的数据结构在几何实体上的联系，设计者更容易更改设计。如果没有这些特征，设计者在构造固体模型几何特征时就必须考虑到所有需要的细节。而且面向特征的防真为设计者提供了更高级的成型对象。例如，模具设计者想象出一个浇口的实体形状，电脑就能将这个浇口造型出来。面向对象造型法是一种参照实物的概念去设计模型的新思维方式。基本的图素是能够将数据库和单一图素的动作联系起来的对象。面向对象的造型对理解问题并且设计程序和数据库是很有用的。此外，面向对象的装配体呈现方式使得“子”对象能继承其“父”对象的信息变得更容易。图形2说明以特性为基础和面向对象的分层的表示一种插入模具。 表示是多重水平的提取的一种分层的结构，从低水平的几何学的实体(形成特性)到高水平的组件。 在盒子中被封入的项目代表“装配对象”； 固体线代表“部分”关系； 同时，猛冲的线代表其它关系。 组件( SUBFA )包括部分( PART )。 一部分能被认为是形式特性( FF )的一种“装配”。 表示把一个以特性为基础的几何学的模型的力与面向对象的模型的那些相结合。 它不仅包含父对象和子对象之间的“部分”关系，也包括富有的套结构的关系和装配对象的一群操作的功能。 在段中3.1，在装配对象之间有有关一种装配对象的定义的较进一步的讨论，而详尽的关系在3.2段中被提出。3.1装配对象的定义在我们的工作中，一种装配对象，O，以如下形式被定义为一个唯一而可辨认的实体：O = ( Oid，A，M，R ) ( 1 )在此式中：Oid是一种装配对象( O )的一个唯一的标识符。A是一套三元组，( t，a，v )。 每一元素a被称为O的一种属性，与每一属性有关是一类型，t，和一种价值，v。M是一套元组，( m，tc1，tc2，%，tcn，tc)。 M中每一个元素都有唯一识别方法。 符号m代表一种方法名称； 同时，方法定义有关对象的操作。 符号tc (i= 1，2，%，n )规定争论类型和符号tc退回的价值类型。3.2形式特性之间的关系模具设计在本质中是一个智力的过程； 模具设计者大多数时间在真实客观的对象诸如金属板，螺丝钉，槽，斜面，和孔等思索设想。因此，用形式特性建设所有产品独立部分的几何学的模型是必要。 模具设计者能容易地改变一部分的大小和形状，因为形式特性之间的关系保持在部分表示中。 图形3(a )显示一个金属板带有一个含有公差等级要求的孔。 这部分被两个形式特性定义，即一个块和含有公差等级要求的孔。 关于块特性计数器开掘洞( FF2 )被放置FF1，使用他们本地分别地协调F2和F1，。 方程( 2) ( 5 )显示计数器开掘洞( FF2 )和块特性( FF1 )之间的空间的关系。 对于形式特性，没有他们之间的空间的约束，因此空间的关系被设计者直接指定。 两形式特性之间的详尽的装配关系被定义如下：4.在装配中推断部分配置一种装配中的若干部分的位置和方向最后通过转换矩阵来表达。为了方便的缘故，空间的关系通常被诸如“伙伴”，“结盟”和“平行”的高水平的铺席子的条件指定。 这样，从含蓄的约束关系自动地引出若干部分之间的清晰明确的转换矩阵是十分重要。推断一种装配中的若干部分的配置三种技术在段2.中已被讨论了因为象征性几何学的接近能以多项式时间复杂性定位所有关于约束方程的解决方案，我们使用这接近来确定位置和一种装配中的若干部分的方向。 为了在装配模拟软件中执行这接近，大量的编写程序被要求。因此，一种简化的几何学的接近被建议确定位置和一种装配中的若干部分的方向。在象征性几何学的接近中，确定位置和若干部分的方向被产生一系列行动执行符号满足每一逐渐增长的约束。被要求来满足每一逐渐增长的约束的信息储存在“计划片段”的一个表格中。 每一计划片段是规定一系列测量方法和行动的一个过程按照这样一种方式移动部分对于满足相应的约束。 计划片段也记录新的自由度和联系不变量的几何不变式。 由于这些限制约束序列，我们的计划片段桌子中的输入的数字基本上被减少。 为了为了一，两或者三个约束解决在我们的系统中允许，九种输入仅仅被要求。 为了交互式的增加组成部分装配，更多约束类型和自由的序列将为了用户增加灵活性。 然而，在为了一种插入模具模拟的自动装配中，当空间的关系被预先规定在装配对象中时，一些序列限制不有关系。 有了上述的定义的合成约束，一个组成部分部分的结构的关系能指定在组成部分的数据库中。 当把一个组成部分部分添加到模具装配时，系统将首先分解进入原始的约束的合成约束，然后产生一群片段计划将组成部分指明方向并且定位在装配中。5.注射模的自动装配任何注射模具的装配都由产品的局部和整体两部分组成。产品的局部依赖产品的整体设计基于塑料的部分 1,2 的几何学。 产品依赖部分通常有与那个同样的方向顶端水平装配，而他们的位置被设计者直接指定。 对于产品独立部分的设计，常规，模具设计者从目录中选择结构，为了产品若干部分的选择的结构建设几何学的模型，而然后把产品独立部分添加到插入模具的装配。 这设计过程是时间消耗的和差错容易倾向于。 在我们的系统中，一个数据库为了所有产品独立部分根据装配表示被建造，而对象定义在段3.中不仅描述这数据库包含产品独立部分的几何学的形状和大小，也包括他们之间的空间的约束。 此外，一些日常事务发挥作用诸如干扰检查和装在衣袋内被封装在数据库中。 因此，模具设计者必须从用户接口中选择产品独立部分的结构类型，而然后软件将为了这些部分自动地计算方向和位置矩阵，而把他们添加到装配。5.1模具基础组件 正如图1所示，产品的独立部分可以更进一步被分为摸具基础和标准部分。摸具基础是由一群金属板，插脚，导套等等组成的。除了塑型产品，模具必须具有一系列功能，诸如，箝位，校准，冷却，注塑等等。大多数产品不得不合并相同的功能，这导致了相似结构的树立。一些模具建筑形成的标准已经被采用了。模具基础起因于这个标准。 根据以特性为基础和面向对象的装配表示，模具基础组成部分的以特性为基础的固体模具首先被建造；其次，装配对象被定义为在成分和压缩功能一部分功能在组成零件之间建立关系；然后，利用这些组装对象，一个分层的组装对象模具基础能被形成。这些模具基础对象能通过目录数据库被例示。表4列出了模具基础对象来产生指定的模具基础的例子。这个指定的模具基础实例能自动地添加到模具装配。模具基础部件和最高装配的结构关系能通过Eqs被表达。Mp和Mr所在的（8）和（9）式是单元矩阵。5.2 标准零件的自动增加 一个标准零件是一个组装对象。它可以通过章节3.1的公式（1）来定义。在数据库中，空间约束用 mate，平面aling和轴align，而不像模具基础，标准件的位置和方向的矩阵是未知的。在示例中，软件通过利用单一的符号几何来自动推断章节4中描述的结构关系。5.3 装配对象的包装 自动装配设计的一个重要问题是自动包装过程。包装是一个在相应组成部分提供附着成分的真空区的操作。当一个驱动者被添加到装配时，一个空的空间被要求在EA盘上调节驱动者，如表5所示。 由于面向对象的表示法被采取，每一个装配对象能被描述为两个实体，实物和虚拟物。虚拟物通过被实物占据的空间模仿。只要一个装配对象被添加到装配中，它的虚拟对象也被添加到装配中。操作发挥作用中的pocketFplate( ) M O将从相应的组成部分(参看公式（1）和表1)。此外，因为在相应的组成部分上在虚拟对象和真正的对象之间有联系，包装将随真正的对象的修正而变化。这种自动包装功能更进一步显示了面向对象表示法的优势。6.基于Unigraphics系统 13 ，所提出的以特性为基础和面向对象的装配计划和自动化装配模拟的系统在新加坡的国立大学被开发的IMOLD系统 14 中已被执行。UG系统提供了一个友好的用户应用程序接口。通过这个接口，用户可以调用UG的内部功能，诸如增加装配部件，修正参数等等。 图6显示的是一个注塑模具产品，这个产品的注塑模具组装设计显示在图7（a）。固定一半组件的相应的父子关系图显示在图7（b）。装配是由IMOLD系统设计。每一个模具基础的零件都在装配中自动定位。Unigraphics系统提供一个用户友好应用编写程序接口(应用程序接口)。 通过这接口，虽然Unigraphics为了给条件铺席子提供功能，用户能呼叫诸如把部分添加到一种装配的Unigraphics内部的功能，修改参数等等，所提出的接近仍然被需要推断组成部分配置，因为在组成部分能被添加到装配之前，计算自由的度是必要，而检查给条件铺席子的有效性。 图6个展览一种插入铸造产品，因为图被领进来，和设计的插入模具装配这产品7(a )。 固定一半组件的相应的“父与子”关系被领进来图7(b )。 这装配被系统设计。 每一模具基础的盘子自动地被定位在装配中。 诸如定位的圆环和驱逐者的标准的部分自动地被添加到装配，因为这些标准部分也自动地被建立，和口袋。7.结论注射模具装配以所提出的特性为基础和面向对象的分层的表示不仅把特性范例扩展到装配，由于扩展特性范例而给条件，插入和方向限制等等铺席子到装配设计设计，而且是封装操作的功能和几何学的约束，诸如自由的程度，诸如集合的组成部分的模糊变化修正甚至能在完成装配过程之后被制定。 装配对象的封装有如下两种优势： 首先，因为装配的条件被封装在装配对象中，自动装配设计容易执行； 其次，对象装配的封装操作的功能使诸如装在衣袋内与干扰检查的装配设计的日常事务过程自动化。 所提出的简单化的动作分析能基本上减少为了自动检测校对模具装配之内组成部分干扰所需要的规划设计的努力。Int J Adv Manuf Technol (2000) 16:739747 2000 Springer-Verlag London LimitedAutomated Assembly Modelling for Plastic Injection MouldsX. G. Ye, J. Y. H. Fuh and K. S. LeeDepartment of Mechanical and Production Engineering, National University of Singapore, SingaporeAn injection mould is a mechanical assembly that consists ofproduct-dependent parts and product-independent parts. Thispaper addresses the two key issues of assembly modellingfor injection moulds, namely, representing an injection mouldassembly in a computer and determining the position andorientation of a product-independent part in an assembly. Afeature-based and object-oriented representation is proposedto represent the hierarchical assembly of injection moulds.This representation requires and permits a designer to thinkbeyond the mere shape of a part and state explicitly whatportions of a part are important and why. Thus, it providesan opportunity for designers to design for assembly (DFA). Asimplified symbolic geometric approach is also presented toinfer the configurations of assembly objects in an assemblyaccording to the mating conditions. Based on the proposedrepresentation and the simplified symbolic geometric approach,automatic assembly modelling is further discussed.Keywords: Assemblymodelling;Feature-based;Injectionmoulds; Object-oriented1.IntroductionInjection moulding is the most important process for manufac-turing plastic moulded products. The necessary equipment con-sists of two main elements, the injection moulding machineand the injection mould. The injection moulding machines usedtoday are so-called universal machines, onto which variousmoulds for plastic parts with different geometries can bemounted, within certain dimension limits, but the injectionmould design has to change with plastic products. For differentmoulding geometries, different mould configurations are usuallynecessary. The primary task of an injection mould is to shapethe molten material into the final shape of the plastic product.This task is fulfilled by the cavity system that consists of core,cavity, inserts, and slider/lifter heads. The geometrical shapesCorrespondence and offprint requests to: Dr Jerry Y. H. Fuh, Depart-ment of Mechanical and Production Engineering, National Universityof Singapore (NUS), 10 Kent Ridge Crescent, Singapore 119260.E-mail: mpefuhyhK.sgand sizes of a cavity system are determined directly by theplastic moulded product, so all components of a cavity systemare called product-dependent parts. (Hereinafter, product refersto a plastic moulded product, part refers to the component ofan injection mould.) Besides the primary task of shaping theproduct, an injection mould has also to fulfil a number oftasks such as the distribution of melt, cooling the moltenmaterial, ejection of the moulded product, transmitting motion,guiding, and aligning the mould halves. The functional partsto fulfil these tasks are usually similar in structure and geo-metrical shape for different injection moulds. Their structuresand geometrical shapes are independent of the plastic mouldedproducts, but their sizes can be changed according to theplastic products. Therefore, it can be concluded that an injectionmould is actually a mechanical assembly that consists ofproduct-dependent parts and product-independent parts. Figure1 shows the assembly structure of an injection mould.The design of a product-dependent part is based on extractingthegeometryfrom theplasticproduct.Inrecentyears,CAD/CAM technology has been successfully used to helpmould designers to design the product-dependent parts. TheMouldMouldbaseCoolFillLayoutPlugSocketCav_1Cav_2CA-plateGuild-bushTCP-plateBep-plateCb-plateEa-plateEb-plateGuid-pinIp-plateRet-pinSliderbodyguideStop-blkHeel-blkheadCoreCavityProduct-independent partProduct-dependent partMove-halfFixed-halfFig. 1. Assembly structure of an injection mould.740X. G. Ye et al.automatic generation of the geometrical shape for a product-dependent part from the plastic product has also attracted alot of research interest 1,2. However, little work has beencarried out on the assembly modelling of injection moulds,although it is as important as the design of product-dependentparts. The mould industry is facing the following two difficult-ies when use a CAD system to design product-independentparts and the whole assembly of an injection mould. First,there are usually around one hundred product-independent partsin a mould set, and these parts are associated with each otherwith different kinds of constraints. It is time-consuming forthe designer to orient and position the components in anassembly. Secondly, while mould designers, most of the time,think on the level of real-world objects, such as screws, plates,and pins, the CAD system uses a totally different level ofgeometrical objects. As a result, high-level object-oriented ideashave to be translated to low-level CAD entities such as lines,surfaces, or solids. Therefore, it is necessary to develop anautomatic assembly modelling system for injection moulds tosolve these two problems. In this paper, we address the follow-ing two key issues for automatic assembly modelling: rep-resenting a product-independent part and a mould assembly ina computer; and determining the position and orientation of acomponent part in an assembly.This paper gives a brief review of related research inassembly modelling, and presents an integrated representationfor the injection mould assembly. A simplified geometric sym-bolic method is proposed to determine the position and orien-tation of a part in the mould assembly. An example of auto-matic assembly modelling of an injection mould is illustrated.2.Related ResearchAssembly modelling has been the subject of research in diversefields, such as, kinematics, AI, and geometric modelling. Lib-ardi et al. 3 compiled a research review of assembly model-ling. They reported that many researchers had used graphstructures to model assembly topology. In this graph scheme,the components are represented by nodes, and transformationmatrices are attached to arcs. However, the transformationmatrices are not coupled together, which seriously affects thetransformation procedure, i.e. if a subassembly is moved, allits constituent parts do not move correspondingly. Lee andGossard 4 developed a system that supported a hierarchicalassembly data structure containing more basic informationabout assemblies such as “mating feature” between the compo-nents. The transformation matrices are derived automaticallyfrom the associations of virtual links, but this hierarchicaltopology model represents only “part-of” relations effectively.Automatically inferring the configuration of components inan assembly means that designers can avoid specifying thetransformation matrices directly. Moreover, the position of acomponent will change whenever the size and position of itsreference component are modified. There exist three techniquesto infer the position and orientation of a component in theassembly: iterative numerical technique, symbolic algebraictechnique, and symbolic geometric technique. Lee and Gossard5 proposed an iterative numerical technique to compute thelocation and orientation of each component from the spatialrelationships. Their method consists of three steps: generationof the constraint equations, reducing the number of equations,and solving the equations. There are 16 equations for “against”condition, 18 equations for “fit” condition, 6 property equationsfor each matrix, and 2 additional equations for a rotationalpart. Usually the number of equations exceeds the number ofvariables, so a method must be devised to remove the redundantequations. The NewtonRaphson iteration algorithm is used tosolve the equations. This technique has two disadvantages:first, the solution is heavily dependent on the initial solution;secondly, the iterative numerical technique cannot distinguishbetween different roots in the solution space. Therefore, itis possible, in a purely spatial relationship problem, that amathematically valid, but physically unfeasible, solution canbe obtained.Ambler and Popplestone 6 suggested a method of comput-ing the required rotation and translation for each componentto satisfy the spatial relationships between the components inanassembly.Sixvariables(threetranslationsandthreerotations) for each component are solved to be consistent withthe spatial relationships. This method requires a vast amountof programming and computation to rewrite related equationsin a solvable format. Also, it does not guarantee a solutionevery time, especially when the equation cannot be rewrittenin solvable forms.Kramer 7 developed a symbolic geometric approach fordetermining the positions and orientations of rigid bodies thatsatisfy a set of geometric constraints. Reasoning about thegeometric bodies is performed symbolically by generating asequence of actions to satisfy each constraint incrementally,which results in the reduction of the objects available degreesof freedom (DOF). The fundamental reference entity used byKramer is called a “marker”, that is a point and two orthogonalaxes. Seven constraints (coincident, in-line, in-plane, parallelFz,offsetFz, offsetFx and helical) between markers are defined.For a problem involving a single object and constraints betweenmarkers on that body, and markers which have invariant attri-butes, action analysis 7 is used to obtain a solution. Actionanalysis decides the final configuration of a geometric object,step by step. At each step in solving the object configuration,degrees of freedom analysis decides what action will satisfyone of the bodys as yet unsatisfied constraints, given theavailable degrees of freedom. It then calculates how that actionfurther reduces the bodys degrees of freedom. At the end ofeach step, one appropriate action is added to the metaphoricalassembly plan. According to Shah and Rogers 8, Kramerswork represents the most significant development for assemblymodelling. This symbolic geometric approach can locate allsolutionsto constraintconditions, andis computationallyattractive compared to an iterative technique, but to implementthis method, a large amount of programming is required.Although many researchers have been actively involved inassembly modelling, little literature has been reported on fea-ture based assembly modelling for injection mould design.Kruth et al. 9 developed a design support system for aninjection mould. Their system supported the assembly designfor injection mouldsthrough high-level functionalmouldobjects (components and features). Because their system wasAutomated Assembly Modelling741based on AutoCAD, it could only accommodate wire-frameand simple solid models.3.Representation of Injection MouldAssembliesThe two key issues of automated assembly modelling forinjection moulds are, representing a mould assembly in com-puters, and determining the position and orientation of a pro-duct-independent part in the assembly. In this section, wepresent an object-oriented and feature-based representation forassemblies of injection moulds.The representation of assemblies in a computer involvesstructural and spatial relationships between individual parts.Such a representation must support the construction of anassembly from all the given parts, changes in the relativepositioning of parts, and manipulation of the assembly as awhole. Moreover, the representations of assemblies must meetthe following requirements from designers:1. It should be possible to have high-level objects ready touse while mould designers think on the level of real-world objects.2. The representation of assemblies should encapsulate oper-ational functions to automate routine processes such aspocketing and interference checks.To meet these requirements, a feature-based and object-orientedhierarchical model is proposed to represent injection moulds.An assembly may be divided into subassemblies, which in turnconsists of subassemblies and/or individual components. Thus,a hierarchical model is most appropriate for representing thestructural relations between components. A hierarchy impliesa definite assembly sequence. In addition, a hierarchical modelcan provide an explicit representation of the dependency ofthe position of one part on another.Feature-based design 10 allows designers to work at asomewhat higher level of abstraction than that possible withthe direct use of solid modellers. Geometric features areinstanced, sized, and located quickly by the user by specifyinga minimum set of parameters, while the feature modeller worksout the details. Also, it is easy to make design changes becauseof the associativities between geometric entities maintained inthe data structure of feature modellers. Without features,designers have to be concerned with all the details of geometricconstruction procedures required by solid modellers, and designchanges have to be strictly specified for every entity affectedby the change. Moreover, the feature-based representation willprovide high-level assembly objects for designers to use. Forexample, while mould designers think on the level of a real-world object, e.g. a counterbore hole, a feature object of acounterbore hole will be ready in the computer for use.Object-oriented modelling 11,12 is a new way of thinkingabout problems using models organised around real-world con-cepts. The fundamental entity is the object, which combinesboth data structures and behaviour in a single entity. Object-oriented models are useful for understanding problems anddesigning programs and databases. In addition, the object-oriented representation of assemblies makes it easy for a“child” object to inherit information from its “parent”.Figure 2 shows the feature-based and object-oriented hier-archical representation of an injection mould. The represen-tation is a hierarchical structure at multiple levels of abstraction,from low-level geometric entities (form feature) to high-levelsubassemblies. The items enclosed in the boxes represent“assembly objects” (SUBFAs, PARTs and FFs); the solid linesrepresent “part-of” relation; and the dashed lines representother relationships. Subassembly (SUBFA) consists of parts(PARTs). A part can be thought of as an “assembly” of formfeatures (FFs). The representation combines the strengths of afeature-based geometric model with those of object-orientedmodels. It not only contains the “part-of” relations betweenthe parent object and the child object, but also includes aricher set of structural relations and a group of operationalfunctions for assembly objects. In Section 3.1, there is furtherdiscussion on the definition of an assembly object, and detailedrelations between assembly objects are presented in Section Definition of Assembly ObjectsIn our work, an assembly object, O, is defined as a unique,identifiable entity in the following form:O = (Oid, A, M, R)(1)Where:Oid is a unique identifier of an assembly object (O).A is a set of three-tuples, (t, a, v). Each a is called anattribute of O, associated with each attribute is a type,t, and a value, v.M is a set of tuples, (m, tc1, tc2, %, tcn, tc). Eachelement of M is a function that uniquely identifies amethod. The symbol m represents a method name; andmethods define operations on objects. The symbol tci(iFig. 2. Feature-based, object-oriented hierarchical representation.742X. G. Ye et al.= 1, 2, %, n) specifies the argument type and tc specifiesthe returned value type.R is a set of relationships among O and other assemblyobjects.Therearesixtypesofbasicrelationshipsbetween assembly objects, i.e. Part-of, SR, SC, DOF,Lts, and Fit.Table 1 shows an assembly object of injection moulds, e.g.ejector. The ejector in Table 1 is formally specified as:(ejector-pinF1, (string, purpose, ejecting moulding),(string, material, nitride steel), (string, catalogFno,THX),(checkFinterference(), boolean), (pocketFplate(), boolean),(part-of ejectionFsys), (SR Align EBFplate), (DOF Tx,Ty).In this example, purpose, material and catalogFno areattributes with a data type of string; checkFinterference andpocketFplate are member functions; and Part-of, SR and DOFare relationships.3.2Assembly RelationshipsThere are six types of basic relationships between assemblyobjects, Part-of, SR, SC, DOF, Lts, and Fit.Part-ofAn assembly object belongs to its ancestor object.SRSpatial relations: explicitly specify the positionsandorientationsofassemblyobjectsinanassembly.Foracomponentpart,itsspatialrelationship is derived from spatial constraints(SC).SCSpatial constraints: implicitly locate a componentpart with respect to the other parts.DOFDegrees of freedom: are allowable translational/rotational directions of motion after assembly, withor without limits.LtsMotion limits: because of obstructions/interferences,the DOF may have unilateral or bilateral limits.FitSize constraint: is applied to dimensions, in orderto maintain a given class of fit.Table 1. Definition of an assembly object-ejector.Object Oidejector-pinF1Instance-ofEjectorFpinDerived from ejector classAPurpose “ejecting moulding” Type stringMaterial “nitrided steel”Type stringCatalogFno “THX”Type stringMCheckFinterferenceCheck interference(coolFobj)between ejectors andcooling linesPocketFplate()Make a hole on plate toaccommodate ejector pinsRPart-ofejectorFsysSRalign with EBplateDOFTx, TyAmong all the elements of an assembly object, the relation-ships are most important for assembly design. The relationshipsbetween assembly objects will not only determine the positionof objects in an assembly, but also maintain the associativitiesbetween assembly objects. In the following sub-sections, wewill illustrate the relationships at the same assembly level withthe help of examples.3.2.1Relationships Between Form FeaturesMould design, in essence, is a mental process; mould designersmost of the time think on the level of real-world objects suchas plates, screws, grooves, chamfers, and counter-bore holes.Therefore, it is necessary to build the geometric models of allproduct-independent parts from form features. The moulddesigner can easily change the size and shape of a part,because of the relations between form features maintained inthe part representation. Figure 3(a) shows a plate with acounter-bore hole. This part is defined by two form features,i.e. a block and a counter-bore hole. The counter-bore hole(FF2) is placed with reference to the block feature FF1, usingtheir local coordinates F2and F1, respectively. Equations (2)(5) show the spatial relationships between the counter-borehole (FF2) and the block feature (FF1). For form features,there is no spatial constraint between them, so the spatialrelationships are specified directly by the designer. The detailedassembly relationships between two form features are definedas follows:SR(FF2, FF1):F2i= F1i(2)F2j= F1j(3)Fig. 3. Assembly relationships.Automated Assembly Modelling743F2k= F1k(4)r2F= r1F+ b22*F1j+ AF1*F1i(5)DOF:ObjFhasF1FRDOF(FF2, F2j)The counter-bore feature can rotate about axis F2j.LTs(FF2, FF1):AF1, b11 0.5*b21(6)Fit (FF2, FF1):b22= b12(7)WhereF and r are the orientation and position vectors of fea-tures.F1= (F1i, F1j, F1k),F2= (F2i, F2j, F2k).bijis the dimension of form features, Subscript i isfeature number, j is dimension number.AF1is the dimension between form features.Equations (2)(7) present the relationships between the formfeature FF1and FF2. These relationships thus determine theposition and orientation of a form feature in the part. Takingthe part as an assembly, the form feature can be consideredas “components” of the assembly.The choice of form features is based on the shape character-istics of product-independent parts. Because the form featuresprovided by the Unigraphics CAD/CAM system 13 can meetthe shape requirements of parts for injection moulds and thespatial relationships between form features are also maintained,we choose them to build the required part models. In additionto the spatial relationships, we must record LTs, Fits relation-ships for form features, which are essential to check thevalidity of form features before updating the models in theCAD system.3.2.2Relationships Between PartsIn an assembly, the position and orientation of a part is usuallyassociated with another part. Figure 3(b) shows a plate (PP1)and a screw (PP2). The relative placement of the screw isconstrained by the counter-bore hole on the plate. The relation-ships between the screw and the plate are defined as follows:SR(PP2, PP1):P2= MpP1(8)r2= Mrr1(9)SC(PP2, PP1):mate(f1,f2) axisFalign(axisF1, axisF2)DOF:ObjFhasF1FRDOF(PP2, P2j)The screw can rotate about P2jof the plate.LTs(PP2, PP1):A22, A12(10)Fits(PP2, PP1):A13= A21+ cc(11)Where:P1and P2are the orientation vectors of the plate andthe screw, and P1= (P1i, P1j, P1k), P2= (P2i, P2j, P2k).Mpand Mrare the transformation matrix between thescrew and the plate. is a Boolean operator.mate and axisFalign are constraints (detailed discussionabout them are given in the next section).r is a position vector.Aijis dimension of parts. Subscript i is part number, andj is dimension number.cc is the clearance between the screw and the plate.As we can see in Eqs. (8) and (9), it is essential to calculatethe matrix Mpand Mrto determine the position and orientationof the screw with reference to the plate. Mpand Mrcan bederived from the spatial constraints (SC). This derivationrequires the task of inferring the configuration of a part in anassembly, which will be discussed in the next section.We have presented a representation of the injection mouldassembly in a computer. At this stage, it might be worthwhileto summarise the benefits of this representation. Assembliesare represented as a collection of subassemblies that in turnmay consist of subassemblies and/or component parts, and acomponent part can further be considered as the assembly ofform features. Such hierarchical relationships imply an orderingon the assembly sequence and a parentchild link. The feature-based representation not only allows designers to work at ahigh-level of abstraction while designing individual parts, butalso extends the feature paradigm to assembly modelling,because this representation allows a component to be changedparametrically with the other components consequently havingtheir positions changed accordingly. The object-oriented rep-resentation can combine both the data structure and operationin an object. The encapsulated operational functions in anassembly object can help to automate the routine processessuch as the pocketing and interference check.4.Inferring Part Configuration in theAssemblyAs we can see from Eqs (8) and (9), the positions andorientations of parts in an assembly are eventually representedby the transformation matrices. For the sake of convenience,the spatial relationships are usually specified by the high-levelmating conditions such as “mate”, “align” and “parallel”. Thus,it is essential to derive automatically the explicit transformationmatrices between parts from implicit constraint relationships.Three techniques to infer the configurations of parts in anassembly have been discussed in Section 2. Because the sym-bolic geometric approach can locate all solutions to constraintequations withpolynomial time complexity, we use thisapproach to determine the positions and orientations of partsin an assembly. To implement this approach in assemblymodelling software, a large amount of programming is required.Therefore, a simplified geometric approach is proposed todetermine the positions and orientations of parts in an assembly.744X. G. Ye et al.In the symbolic geometric approach, determining positionsand orientations of parts is performed symbolically by generat-ing a sequence of actions to satisfy each constraint incremen-tally. The information required to satisfy each constraintincrementally is stored in a table of “plan fragments”. Eachplan fragment is a procedure that specifies a sequence ofmeasurements and actions that move parts in such a way asto satisfy the corresponding constraint. The plan fragment alsorecords the objects new degrees of freedom (DOFs) andassociated geometric invariants. Conceptually, Kramers planfragment table is a 3D dispatch table. We use TDOF torepresent translational degrees of freedom and RDOF to rep-resent rotational degrees of freedom. Then an entry in the planfragment table has the following form:planFfragment: kTDOF, RDOF, constraintFtypelTDOF = 0, 1, 2, 3RDOF = 0, 1, 2, 3constraintFtype=coincident,in-line,in-plane,parallelFz, offsetFz, offsetFx and helicalThe plan fragment table is an exhaustive enumeration of allthe states in the search space for the problem of moving anobject to satisfy a series of constraints between markers onthe object and markers fixed in the global coordinate frame.To enumerate the combination of different values of the abovethree parameters, 82 entries will be generated 7. If the searchspace for the problem can be reduced the number of entriesin a plan fragment table will decrease. To achieve this, thenumber of enumerate values for entry parameters must bedecreased. For example, for a specified constraint type, if theenumeration values of TDOF change from 0,1,2,3 to 0,3,then the search space is reduced.After a careful analysis of the constraints between compo-nents of an injection mould, four basic primitive constraints areintroduced: in-line, parallelFz, parallelFz1 and parallelFoffset.Their definitions and algebraic equations are as follows:in-line(M1, M2): M1lies on the line through M2parallel to theZ-axis of M2.ugmp(M1) gmp(M2)u gmz(M2)u = 0(12)parallelFz(M1, M2): the Z-axes of markers M1and M2areparallel and have the same direction.gmz(M1) gmz(M2) = 1(13)parallelFz1(M1, M2): the Z-axes of markers M1and M2areparallel and have the opposite direction.gmz(M1) gmz(M2) = 1(14)paralleFoffset(M1, M2, d): Applicable only in conjunctionwith parallelFz or parallelFz1, specifies the distancebetween M1position and M2position.gmp(M1) gmp(M2) = d(15)Where:M1and M2are markers.gmp(M) is the global marker position.gmz(M) is the global marker Z-axis.gmx(M) the global marker X-axis.d is the distance between M1and M2.In our simplified symbolic geometric approach, the enumer-ation vales of constraint types are inFline, parallelFz, par-relFz1, paralleFoffset. Compared with Kramers symbolic geo-metric approach, our constraint types are reduced from sevento four. This simplification will reduce the number of entriesin the plan fragment table. Based on these four primitiveconstraints, three high-level constraints were synthesised fortheusersconvenience.Theyaremate(M1,M2,d),planeFalign(M1, M2, d), and axisFalign(M1, M2). Their defi-nitions are given as follows:mate(M1, M2, d):parallelFz1(M1, M2) parallelFoffset(M1, M2, d)planeFalign(M1, M2, d):parallelFz(M1, M2) parallelFoffset(M1, M2, d)axisFalign(M1, M2):parallelFz(M1, M2) inFline(M1, M2)The assembly objects in an injection mould can have one,two or three synthesised constraints. For two and three syn-thesised constraints, the constraint sequence is further restricted.The sequences are as follows:mate(M1, M2, d) planeFalign(M3, M4, d2)mate(M1, M2, d1) axisFalign(M3, M4)planeFalign(M1, M2, d) axisFalign(M3, M4)mate(M1,M2,d1)axisFalign(M3,M4,d2)axisFalign(M5, M6).Because of these restrictions on the constraint sequences,the number of entries in our plan fragment table is substantiallyreduced. To solve for one, two or three constraints allowed inour system, only nine entries are required. For interactiveaddition of components to the assembly, more constraint typesand free sequences will increase the flexibility for users. How-ever, in automatic assembly modelling for an injection mould,as the spatial relationships are predefined in assembly objects,some of the sequence restrictions do not matter. With theabove-defined synthesised constraints, the structural relation-ships of a component part can be specified in the database ofthe components. When adding a component part to the mouldassembly, the system will first decompose the synthesisedconstraints into primitive constraints, then generate a groupof fragment plans to orient and position the component inthe assembly.5.Automated Assembly Modelling ofInjection MouldsAnyassemblyofinjectionmouldsconsistsofproduct-independent parts and product-dependent parts. The design ofindividual product-dependent parts is based on the geometryof the plastic part 1,2. Usually the product-dependent partshave the same orientation as that of the top-level assembly,and their positions are specified directly by the designer. Asfor the design of product-independent parts, conventionally,mould designers select the structures from the catalogues,Automated Assembly Modelling745build the geometric models for selected structures of product-independent parts, and then add the product-independent partsto the assembly of the injection mould. This design process istime-consuming and error-prone. In our system, a database isbuiltforallproduct-independentpartsaccordingtotheassembly representation and object definition described in Sec-tion 3. This database not only contains the geometric shapesand sizes of the product-independent parts, but also includesthe spatial constraints between them. Moreover, some routinefunctions such as interference check and pocketing are encapsu-lated in the database. Therefore, the mould designer must selectthe structure types of product-independent parts from the userinterfaces, and then the software will automatically calculatethe orientation and position matrices for these parts, and addthem to the assembly.5.1Mould Base SubassemblyAs can be seen from Fig. 1, the product-independent parts canbe further classified as the mould base and standard parts. Amould base is the assembly of a group of plates, pins, guidebushes, etc. Besides shaping the product, a mould has to fulfila number of functions such as clamping the mould, leadingand aligning the mould halves, cooling, ejecting the product,etc. Most moulds have to incorporate the same functionality,which results in a similarity of the structural build-up. Someform of standardisation in mould construction has been adopted.A mould base is the result of this standardisation.According to the feature-based and object-oriented assemblyrepresentation, the feature-based solid models for componentparts of the mould base are first constructed; next, the assemblyobjectsaredefinedbyestablishingrelationshipsbetweencomponents and encapsulating some functions in the componentparts; then, using these assembly objects, a hierarchical subas-sembly object a mould base can be formed. This mouldbase object can be instantiated by a group of data from thecatalogue database. Figure 4 shows the instantiation of themould base object to generate the specified mould base. Thisspecified mould base instance can be added automatically tothe mould assembly. The structural relations between the mouldbase subassembly and top assembly can be expressed by Eqs.(8) and (9), where Mpand Mrare the unit matrices.5.2Automatic Addition of Standard PartsA standard part is an assembly object. It can be definedaccording to Eq. (1) in Section 3.1. In the database, the spatialconstraints are specified by mate, planeFalign and axisFalign,but unlike the mould base, the position and orientation matricesof a standard part are left unknown. During instantiation,the software then automatically infers the explicit structuralrelationshipsbyusingthesimplifiedsymbolicgeometricapproach described in Section 4.5.3Pocketing for Assembly ObjectsOne of the important issues for automatic assembly design isthe automation of the pocketing process. Pocketing is anFig. 4. Instantiation of mould base.operation that makes an empty space in corresponding compo-nents to accommodate the inserted components. When an ejec-tor is added to the assembly, an empty space is required onthe EA plate to accommodate the ejector, as shown in Fig. 5.Since an object-oriented representation is adopted, eachassembly object can be represented by two solids, the realobject and the virtual object. The virtual object is modelledaccording to the space that a real object will occupy. Wheneveran assembly object is added to an assembly, its virtual objectisalsoaddedtotheassembly.TheoperationfunctionpocketFplate() in M of O will subtract the virtual object fromthe corresponding components (see Eq. (1) and Table 1).Moreover, because there are associativities between the virtualobject and real object, the pockets on the corresponding compo-nents will change with the modification of the real object.Fig. 5. Pocketing of assembled objects.746X. G. Ye et al.This automatic pocketing function further demonstrates theadvantage of an object-oriented representation.6.System ImplementationBased on the Unigraphics system 13, the proposed feature-based and object-oriented assembly scheme and automation ofassembly modelling have been implemented in the IMOLDsystem 14 developed at the National University of Singapore.The Unigraphics system provides a user-friendly applicationprogramming interface (API). Through this interface, t