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譯文題目： Automated Assembly Modelling for Plastic Injection Moulds
注塑模具自動裝配造型
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Automated Assembly Modelling for Plastic Injection Moulds
X. G. Ye, J. Y. H. F uh and K. S. Lee
Department of Mechanical and Production Engineering, National University of Singapore, Singapore
An injection mould is a mechanical assembly that consists of product-dependent parts and product-independent parts. This paper addresses the two key issues of assembly modelling for injection moulds, namely, representing an injection mould assembly in a computer and determining the position and orientation of a product-independent part in an assembly. A feature-based and object-oriented representation is proposed to represent the hierarchical assembly of injection moulds.This representation requires and permits a designer to think beyond the mere shape of a part and state explicitly what portions of a part are important and why. Thus, it provides an opportunity for designers to design for assembly (DFA). A simplified symbolic geometric approach is also presented to infer the configurations of assembly objects in an assembly according to the mating conditions. Based on the proposed representation and the simplified symbolic geometric approach,automatic assembly modelling is further discussed.
Keywords: Assembly modelling; Feature-based; Injection moulds; Object-oriented
1. Introduction
Injection moulding is the most important process for manufacturing plastic molded products. The necessary equipment consists of two main elements, the injection moulding machine and the injection mould. The injection moulding machines used today are so-called universal machines, onto which various moulds for plastic parts with different geometries can be mounted, within certain dimension limits, but the injection mould design has to change with plastic products. For different moulding geometries, different mould configurations are usually necessary. The primary task of an injection mould is to shape the 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 shapes and sizes of a cavity system are determined directly by the plastic moulded product, so all components of a cavity system are called product-dependent parts. (Hereinafter, product refers to a plastic molded product, part refers to the component of an injection mould.) Besides the primary task of shaping the product, an injection mould has also to fulfil a number of tasks such as the distribution of melt, cooling the molten material, ejection of the molded product, transmitting motion,guiding, and aligning the mould halves. The functional parts to fulfil these tasks are usually similar in structure and geometrical shape for different injection moulds. Their structures and geometrical shapes are independent of the plastic molded products, but their sizes can be changed according to the plastic products. Therefore, it can be concluded that an injection mould is actually a mechanical assembly that consists of product-dependent parts and product-independent parts. Figure 1 shows the assembly structure of an injection mould.
The design of a product-dependent part is based on extracting the geometry from the plastic product. In recent years,CAD/CAM technology has been successfully used to help mould designers to design the product-dependent parts. The automatic generation of the geometrical shape for a product dependent part from the plastic product has also attracted a lot of research interest [1,2]. However, little work has been carried out on the assembly modelling of injection moulds,although it is as important as the design of product-dependent parts. The mould industry is facing the following two difficulties when use a CAD system to design product-independent parts and the whole assembly of an injection mould. First,there are usually around one hundred product-independent parts in a mould set, and these parts are associated with each other with different kinds of constraints. It is time-consuming for the designer to orient and position the components in an assembly. 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 of geometrical objects. As a result, high-level object-oriented ideas have to be translated to low-level CAD entities such as lines,surfaces, or solids. Therefore, it is necessary to develop an automatic assembly modelling system for injection moulds to solve these two problems. In this paper, we address the following two key issues for automatic assembly modelling: representing a product-independent part and a mould assembly in a computer; and determining the position and orientation of a component part in an assembly.
This paper gives a brief review of related research in assembly modelling, and presents an integrated representation for the injection mould assembly. A simplified geometric symbolic method is proposed to determine the position and orientation of a part in the mould assembly. An example of automatic assembly modelling of an injection mould is illustrated.
2. Related Research
Assembly modelling has been the subject of research in diverse fields, such as, kinematics, AI, and geometric modelling. Libardietal. [3] compiled a research review of assembly modelling.They reported that many researchers had used graph structures to model assembly topology. In this graph scheme,the components are represented by nodes, and transformation matrices are attached to arcs. However, the transformation matrices are not coupled together, which seriously affects the transformation procedure, i.e. if a sub assembly is moved, all its constituent parts do not move correspondingly. Lee and Gossard [4] developed a system that supported a hierarchical assembly data structure containing more basic information about assemblies such as “mating feature” between the components. The transformation matrices are derived automatically from the associations of virtual links, but this hierarchical topology model represents only “part-of” relations effectively.
Automatically inferring the configuration of components in an assembly means that designers can avoid specifying the transformation matrices directly. Moreover, the position of a component will change whenever the size and position of its reference component are modified. There exist three techniques to infer the position and orientation of a component in the assembly: iterative numerical technique, symbolic algebraic technique, and symbolic geometric technique. Lee and Gossard [5] proposed an iterative numerical technique to compute the location and orientation of each component from the spatial relationships. Their method consists of three steps: generation of 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 equations for each matrix, and 2 additional equations for a rotational part. Usually the number of equations exceeds the number of variables, so a method must be devised to remove the redundant equations. The Newton–Raphson iteration algorithm is used to solve the equations. This technique has two disadvantages:first, the solution is heavily dependent on the initial solution; secondly, the iterative numerical technique cannot distinguish between different roots in the solution space. Therefore, it is possible, in a purely spatial relationship problem, that a mathematically valid, but physically unfeasible, solution can be obtained. Ambler and Popplestone [6] suggested a method of computing the required rotation and translation for each component to satisfy the spatial relationships between the components in an assembly. Six variables (three translations and three rotations) for each component are solved to be consistent with the spatial relationships. This method requires a vast amount of programming and computation to rewrite related equations in a solvable format. Also, it does not guarantee a solution every time, especially when the equation cannot be rewritten in solvable forms.
Kramer [7] developed a symbolic geometric approach for determining the positions and orientations of rigid bodies that satisfy a set of geometric constraints. Reasoning about the geometric bodies is performed symbolically by generating a sequence of actions to satisfy each constraint incrementally, which results in the reduction of the object’s available degrees of freedom (DOF). The fundamental reference entity used by Kramer is called a “marker”, that is a point and two orthogonal axes. Seven constraints between markers are defined. For a problem involving a single object and constraints between markers on that body, and markers which have invariant attributes, action analysis [7] is used to obtain a solution. Action analysis 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 satisfy one of the body’s as yet unsatisfied constraints, given the available degrees of freedom. It then calculates how that action further reduces the body’s degrees of freedom. At the end of each step, one appropriate action is added to the metaphorical assembly plan. According to Shah and Rogers [8], Kramer’s work represents the most significant development for assembly modelling. This symbolic geometric approach can locate all solutions to constraint conditions, and is computationally attractive compared to an iterative technique, but to implement this method, a large amount of programming is required.
Although many researchers have been actively involved in assembly modelling, little literature has been reported on feature based assembly modelling for injection mould design. Kruth et al. [9] developed a design support system for an injection mould. Their system supported the assembly design for injection moulds through high-level functional mould objects (components and features). Because their system was based on AutoCAD, it could only accommodate wire-frame and simple solid models.
3. Representation of Injection Mould Assemblies
The two key issues of automated assembly modelling for injection moulds are, representing a mould assembly in computers, and determining the position and orientation of a product- independent part in the assembly. In this section, we present an object-oriented and feature-based representation for assemblies of injection moulds.
The representation of assemblies in a computer involves structural and spatial relationships between individual parts. Such a representation must support the construction of an assembly from all the given parts, changes in the relative positioning of parts, and manipulation of the assembly as a whole. Moreover, the representations of assemblies must meet the following requirements from designers:
1. It should be possible to have high-level objects ready to use while mould designers think on the level of realworld objects.
2. The representation of assemblies should encapsulate operational functions to automate routine processes such as pocketing and interference checks. To meet these requirements, a feature-based and object-oriented hierarchical model is proposed to represent injection moulds. An assembly may be divided into sub assemblies, which in turn consists of sub assemblies and/or individual components. Thus, a hierarchical model is most appropriate for representing the structural relations between components. A hierarchy implies a definite assembly sequence. In addition, a hierarchical model can provide an explicit representation of the dependency of the position of one part on another.
Feature-based design [10] allows designers to work at a somewhat higher level of abstraction than that possible with the direct use of solid modellers. Geometric features are instanced, sized, and located quickly by the user by specifying a minimum set of parameters, while the feature modeller works out the details. Also, it is easy to make design changes because of the associativities between geometric entities maintained in the data structure of feature modellers. Without features, designers have to be concerned with all the details of geometric construction procedures required by solid modellers, and design changes have to be strictly specified for every entity affected by the change. Moreover, the feature-based representation will provide high-level assembly objects for designers to use. For example, while mould designers think on the level of a real world object, e.g. a counter bore hole, a feature object of a counter bore hole will be ready in the computer for use.
Object-oriented modelling [11,12] is a new way of thinking about problems using models organied around real-world concepts. The fundamental entity is the object, which combines both data structures and behaviour in a single entity. Object oriented models are useful for understanding problems and designing programs and databases. In addition, the object oriented representation of assemblies makes it easy for a “child” object to inherit information from its “parent”.
References
[1]. K. H. Shin and K. Lee, “Design of side cores of injection moulds from automatic detection of interference faces”, Journal of Design and Manufacturing, 3(3), pp. 225–236, December 1993.
[2]. Y. F. Zhang, K. S. Lee, Y. Wang, J. Y. H. F uh and A. Y. C. Nee, “Automatic slider core creation for designing slider/lifter of injection moulds”, CIRP International Conference and Exhibition on Design and Production of Dies and moulds, pp. 33–38, Turkey, 19–21 June 1997.
[3]. E. C. Libardi, J. R. Dixon and M. K. Simmon, “Computer environments for design of mechanical assemblies: A research review”, Engineering with Computers, 3(3), pp. 121–136, 1988.
[4]. K. Lee and D. C. Gossard, “A hierarchical data structure for representing assemblies”, Computer-Aided Design, 17(1), pp. 15– 19, January 1985.
[5]. K. Lee and D. Gossard, “Inference of position of components in an assembly”, Computer-Aided Design, 17(1), pp. 20–24, January
1985.
[6]. A. P. Ambler and R. J. Popplestone, “Inferring the positions of bodies from specified spatial relationships”, Artificial Intelligence, 6, pp. 157–174, 1975.
[7]. G. Kramer, Solving Geometric Constraint Systems: A Case Study in Kinematics, MIT Press, Cambridge, MA, 1992.
[8]. J. J. Shah and M. T. Rogers, “Assembly modelling as an extension of feature-based design”, Research in Engineering Design, 5(3&4), pp. 218–237, 1993.
[9]. J. P. Kruth, R. Willems and D. Lecluse, “A design support system using high level mould objects”, CIRP International Conference and Exhibition on Design and Production of Dies and moulds, pp. 39–44, Turkey, 19–21 June, 1997.
[10]. J. J. Shah, “Assessment of feature technology”, Computer-Aided Design, 23(5), pp. 331–343, June 1991.
[11]. S. R. Gorti, A. Gupta, G. J. Kim, R. D. Sriram and A. Wong, “An objection-oriented representation for product and design process”, Computer-Aided Design, 30(7), pp. 489–501, June 1998.
[12]. J. Rumbaugh, M. Blaha, W. Premerlani, et al. Object-Oriented Modeling and Design, Prentice Hall, Englewood Cliffs, NJ, 1991.
[13]. Unigraphics Essentials User Manual, Unigraphics Solution Co., Maryland Heights, MO, 1997.
[14]. IMOLD homepage http:://www.eng.nus.edu.sg/imold, Manusoft Plastic Pte Ltd. Singapore.
注塑模具自動裝配造型
X. G. Ye, J. Y. H. F uh and K. S. Lee
機(jī)械和生產(chǎn)工程部，新加坡國立大學(xué)，新加坡
注射模是一種由與塑料制品有關(guān)的和與制品無關(guān)的零部件兩大部分組成的機(jī)械裝置。本文提出了（有關(guān)）注射模裝配造型的兩個主要觀點(diǎn)，即描述了在計算機(jī)上進(jìn)行注射模裝配以及確定裝配中與制品無關(guān)的零部件的方向和位置的方法，提出了一個基于特征和面向?qū)ο蟮谋磉_(dá)式以描述注射模等級裝配關(guān)系，該論述要求并允許設(shè)計者除了考慮零部件的外觀形狀和位置外，還要明確知道什么部份最重要和為什么。因此，它為設(shè)計者進(jìn)行裝配設(shè)計（DFA）提供了一個機(jī)會。同樣地，為了根據(jù)裝配狀態(tài)推斷出裝配體中裝配對象的結(jié)構(gòu)，一種簡化的特征幾何學(xué)方法也誕生了。在提出的表達(dá)式和簡化特征幾何學(xué)的基礎(chǔ)上，進(jìn)一步深入探討了自動裝配造型的方法。
關(guān)鍵字：裝配造型；基于特征；注射模；面向?qū)ο蟆?
1、簡介
注射成型是生產(chǎn)塑料模具產(chǎn)品最重要的工藝。需要用到的兩種裝備是：注射成型機(jī)和注射?！，F(xiàn)在常用的注射成型機(jī)即所謂的通用機(jī)，在一定尺寸范圍內(nèi)，可以用于不同形狀的各種塑料模型中，但注射模的設(shè)計就必須隨塑料制品的變化而變化。模型的幾何因素不同，它們的構(gòu)造也就不同。注射模的主要任務(wù)是把塑料熔體制成塑料制品的最終形狀，這個過程是由型芯、型腔、鑲件、滑塊等與塑料制品有關(guān)的零部件完成的，它們是直接構(gòu)成塑料件形狀及尺寸的各種零件，因此，這些零件稱為成型零件。（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，注射模還必須完成分配熔體、冷卻，開模，傳輸、引導(dǎo)運(yùn)動等任務(wù)，而完成這些任務(wù)的注射模組件在結(jié)構(gòu)和形狀上往往都是相似的，它們的結(jié)構(gòu)和形狀并不取決于塑料模具，而是取決于塑料制品。圖1顯示了注射模的結(jié)構(gòu)組成。
成型零件的設(shè)計從塑料制品中分離了出來。近幾年，CAD/CAM技術(shù)已經(jīng)成功的應(yīng)用到成型零件的設(shè)計上。成型零件的形狀的自動化生成也引起了很多研究者的興趣，不過很少有人在其上付諸實(shí)踐，雖然它也象結(jié)構(gòu)零件一樣重要?，F(xiàn)在，模具工業(yè)在應(yīng)用計算機(jī)輔助設(shè)計系統(tǒng)設(shè)計成型零件和注射成型機(jī)時，遇到了兩個主要困難。第一，在一個模具裝置中，通常都包括有一百多個成型零部件，而這些零部件又相互聯(lián)系，相互限制。對于設(shè)計者來說，確定好這些零部件的正確位置是很費(fèi)時間的。第二，在很多時候，模具設(shè)計者已想象出工件的真實(shí)形狀，例如螺絲，轉(zhuǎn)盤和銷釘，但是CAD系統(tǒng)只能用于另一種信息的操作。這就需要設(shè)計者將他們的想法轉(zhuǎn)化成CAD系統(tǒng)能接受的信息(例如線，面或者實(shí)體等)。因此，為了解決這兩個問題，很有必要發(fā)展一種用于注射模的自動裝配成型系統(tǒng)。在此篇文章里，主要講述了兩個觀點(diǎn)：即成型零部件和模具在計算機(jī)上的仿真裝配以及確定零部件在模具中的結(jié)構(gòu)和位置。
這篇文章概括了關(guān)于注塑成型的相關(guān)研究，并對注射成型機(jī)有一個完整的闡述。通過舉例一個注射模的自動裝配造型，提出一種簡化的幾何學(xué)符號法，用于確定注射模具零部件的結(jié)構(gòu)和位置。
2、相關(guān)研究
在各種領(lǐng)域的研究中，裝配造型已成為一門學(xué)科，就像運(yùn)動學(xué)、人工智能學(xué)、模擬幾何學(xué)一樣。Libardi作了一個關(guān)于裝配造型的調(diào)查。據(jù)稱，很多研究人員已經(jīng)開始用圖表分析模型會議拓?fù)?。在這個圖里，各個元件由節(jié)點(diǎn)組成的，再將這些點(diǎn)依次連接成線段。然而這些變化矩陣并沒有緊緊的連在一起，這將嚴(yán)重影響整體的結(jié)構(gòu)，即，當(dāng)其中某一部分移動了，其他部分并不能做出相應(yīng)的移動。Lee and Gossard開發(fā)了一種新的系統(tǒng)，支持包含更多的關(guān)于零部件的基本信息的一種分級的裝配數(shù)據(jù)結(jié)構(gòu)，就像在各元件間的“裝配特征”。變化矩陣自動從實(shí)際的線段間的聯(lián)系得到，但是這個分級的拓?fù)淠Ｐ椭荒苡行У卮怼安糠帧钡年P(guān)系。
自動判別裝配組件的結(jié)構(gòu)意味著設(shè)計者可避免直接指定變化的矩陣，而且，當(dāng)它的參考零部件的尺寸和位置被修改的時候，它的位置也將隨之改變?，F(xiàn)在有三種技術(shù)可以推斷組件在模具中的位置和結(jié)構(gòu)：反復(fù)數(shù)值技術(shù),象征代數(shù)學(xué)技術(shù)，以及象征幾何學(xué)技術(shù)。Lee and Gossard提出一項(xiàng)從空間關(guān)系計算每個組成元件的位置和方向的反復(fù)數(shù)值技術(shù)。他們的理論由三步組成：產(chǎn)生條件方程式，降低方程式數(shù)量，解答方程式。方程式有：16個滿足未知條件的方程式，18個滿足已知條件的方程式，6個滿足各個矩陣的方程式以及另外的兩個滿足旋轉(zhuǎn)元件的方程式。通常方程式的數(shù)量超過變量的數(shù)量時，應(yīng)該想辦法去除多余的方程式。牛頓迭代法常用來解決這種方程式。不過這種方法存在兩種缺點(diǎn)：第一，它太依賴初始解；第二：反復(fù)的數(shù)值技術(shù)在解決空間內(nèi)不能分清不同的根。因此，在一個完全的空間關(guān)系問題上，有可能解出來的結(jié)果在數(shù)學(xué)理論上有效，但實(shí)際上卻是行不通的。
Ambler和Popplestone提議分別計算每個零部件的旋轉(zhuǎn)量和轉(zhuǎn)變量以確定它們之間的空間關(guān)系，而解出的每個零部件的6個變量(3個轉(zhuǎn)變量和3旋轉(zhuǎn)量)要和它們的空間關(guān)系一致。這種方法要求大量的編程和計算，才能用可解的形式重寫有關(guān)的方程式。此外，它不能保證每次都能求出結(jié)果，特別是當(dāng)方程式不能被以可解答的形式重寫時。
為了能確定出滿足一套幾何學(xué)限制條件的剛體的位置與方向，Kramer開發(fā)了一種特征幾何學(xué)方法。通過產(chǎn)生一連串滿足逐漸增長的限制條件的動作推斷其幾何特征，這樣將減少物體的自由度數(shù)。Kramer使用的基本參考實(shí)體稱為一個"標(biāo)識"，由一個點(diǎn)和兩正交軸構(gòu)成。標(biāo)識間的7個限制條件都被定了義。對于一個包括獨(dú)立元件、相互約束的標(biāo)識和不變的標(biāo)識的問題來說，可以用動作分析法來解決問題，它將一步一步地最后求出物體的最終的幾何構(gòu)造。在確定物體構(gòu)造的每一個階段，自由度分析將決定什么動作能提供滿足限制物體未加限制部位的自由度。然后計算該動作怎樣能進(jìn)一步降低物體的自由度數(shù)。在每個階段的最后，給隱喻的裝配計劃加上合適的一步。根據(jù)Shah和Rogers的分析，Kramer的理論代表了注射模具最顯著的發(fā)展，他的特征幾何學(xué)方法能解出全部的限制條件。和反復(fù)的數(shù)值技術(shù)相比，他的這種方法更具吸引力。不過要實(shí)行這種方法，需要大量的編程。
現(xiàn)在雖然已有很多研究者開始研究注射成型機(jī)，但仍很少有學(xué)者將注意力放在注射模設(shè)計上。Kruth開發(fā)了一個注射模的設(shè)計支援系統(tǒng)。這個系統(tǒng)通過高級的模具對象(零部件和特征)支持注射模的成型設(shè)計。因?yàn)橄到y(tǒng)是在AUTOCAD的基礎(chǔ)上設(shè)計的，因此它只適于線和簡單的實(shí)體模型操作。
3、注射模裝配概述
主要講述了關(guān)于注射模自動裝配造型的兩個方面：注射模在電腦上的仿真裝配和確定結(jié)構(gòu)零件在裝配中的位置和方向。在這個部分，我們基于特征和面向?qū)ο笳撌隽俗⑸淠Ｑb配。
注射模在電腦上的仿真裝配包含著注射模零部件在結(jié)構(gòu)上和空間上的聯(lián)系。這種仿真必須支持所有給定零部件的裝配、在相互關(guān)聯(lián)的零部件間進(jìn)行變動以及整體上的操作。而且仿真裝配也必須滿足設(shè)計者的下列要求：
1） 支持能表達(dá)出模具設(shè)計者實(shí)體造型想象的高級對象。
2）成型仿真應(yīng)該有象現(xiàn)實(shí)一樣的操作功能，就如裝入和干擾檢查。
為了滿足這些要求，可用一個基于特征和面向?qū)ο蟮姆旨壞Ｐ蛠泶孀⑸淠?。這樣便將模型分成許多部分，反過來由多段模型和獨(dú)立部分組成。因此，一個分級的模型最適合于描述各組成部分之間的結(jié)構(gòu)關(guān)系。一級表明一個裝配順序，另外，一個分級的模型還能說明一個部分相對于另一個部分的確定位置。
與直觀的固體模型操作相比，面向特征設(shè)計允許設(shè)計者在抽象上進(jìn)行操作。它可以通過一最小套參數(shù)快速列出模型的特征、尺寸以及其方位。此外，由于特征模型的數(shù)據(jù)結(jié)構(gòu)在幾何實(shí)體上的聯(lián)系，設(shè)計者更容易更改設(shè)計。如果沒有這些特征，設(shè)計者在構(gòu)造固體模型幾何特征時就必須考慮到所有需要的細(xì)節(jié)。而且面向特征的仿真為設(shè)計者提供了更高級的成型對象。例如，模具設(shè)計者想象出一個澆口的實(shí)體形狀，電腦就能將這個澆口造型出來。
面向?qū)ο笤煨头ㄊ且环N參照實(shí)物的概念去設(shè)計模型的新思維方式。基本的圖素是能夠?qū)?shù)據(jù)庫和單一圖素的動作聯(lián)系起來的對象。面向?qū)ο蟮脑煨蛯斫鈫栴}并且設(shè)計程序和數(shù)據(jù)庫是很有用的。此外，面向?qū)ο蟮难b配體呈現(xiàn)方式使得“子”對象能繼承其“父”對象的信息變得更容易。