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桂林電子科技大學(xué)畢業(yè)設(shè)計(jì)用紙
自動裝配模型注塑模具
注射模具是包含產(chǎn)品生產(chǎn)部分和自動化裝配的組件,本篇論文論述了注射成型模塑的兩個(gè)關(guān)鍵的裝配組件,也就是由計(jì)算機(jī)設(shè)計(jì)模擬出來,并且決定非生產(chǎn)部件在裝配組件中的位置和取向。這種從本質(zhì)特征和客觀取向所設(shè)計(jì)的組件,是為了表現(xiàn)出注射成型裝配組件的。這種設(shè)計(jì)允許設(shè)計(jì)者忽略模塑制件的細(xì)節(jié),直接描述制件重點(diǎn)的那一部分及其原因,因此它給設(shè)計(jì)者提供了一次設(shè)計(jì)裝配的機(jī)會,一個(gè)系統(tǒng)的簡單幾何方法通??梢栽谙嗤臈l件下推斷出一個(gè)客觀配件在裝配組件中的位置。在這種粗略設(shè)計(jì)和系統(tǒng)簡單的幾何方法的基礎(chǔ)上,模塑自動化裝配組件被進(jìn)一步研究。
關(guān)鍵詞:模塑組裝,表觀現(xiàn)象,注射成型,客觀取向
1. 前言
注射成型是塑料制造業(yè)中最重要的一個(gè)環(huán)節(jié)。它所必要的設(shè)備包含兩個(gè)部分:注射成型機(jī)和注射模具。今天所用的注射模具機(jī)就是所謂的萬能機(jī),在一定的范圍內(nèi)不同尺寸的塑件通過它生產(chǎn)出來,但是模具設(shè)計(jì)時(shí)需要根據(jù)塑件的要求進(jìn)行改變。不同的模具布局對于不同的模具形狀是必要的。注射成型模具的最基本的任務(wù)就是將熔化了的材料生產(chǎn)成不同形狀的制品,這個(gè)任務(wù)是由包含了陽模、型腔、嵌件、一級頂出機(jī)構(gòu)的型腔系統(tǒng)完成的。型腔系統(tǒng)的幾何形狀和尺寸是由塑件直接決定的,因此一個(gè)型腔所有的構(gòu)件稱為產(chǎn)品生產(chǎn)部件(產(chǎn)品就是指塑件,部件就是指注射模具的構(gòu)件),另外產(chǎn)品成型是最基本任務(wù),注射成型機(jī)需要完成很多任務(wù),例如,分配、熔料、冷卻融化物注射塑件,功能部件所完成的這些任務(wù)與注射成型不同結(jié)構(gòu)和尺寸的塑件非常相似,他們的結(jié)構(gòu)和幾何形狀與塑件成型模具不相關(guān),但是他們的尺寸可以根據(jù)塑件的尺寸而不斷改變,因此我們可以從中得到結(jié)論:注射成型機(jī)包含了塑件生產(chǎn)部分和與之相關(guān)的非生產(chǎn)部分的自動化裝配組件。圖1所示為注塑模具的裝配機(jī)構(gòu):
圖1 注塑模具的裝配機(jī)構(gòu)
設(shè)計(jì)作為產(chǎn)品依賴的一部分是基于塑件的幾何形狀,最近幾年,CAD/CAM技術(shù)已經(jīng)被成功的應(yīng)用在幫助模具設(shè)計(jì)者設(shè)計(jì)塑件生產(chǎn)部分。塑件的自動化生產(chǎn)作為塑件生產(chǎn)的一部分給人們帶來很大的研究興趣,然而在塑料模具裝配建模上卻很少有行動,盡管它和產(chǎn)品的設(shè)計(jì)一樣很重要。當(dāng)應(yīng)用CAD系統(tǒng)設(shè)計(jì)產(chǎn)品生產(chǎn)部分和所有的注射成型裝配組件時(shí)模具工業(yè)面臨以下兩種困難,第一,在一個(gè)模具系統(tǒng)中往往有一百多個(gè)產(chǎn)品生產(chǎn)部分,并且這些部分之間互相聯(lián)系互相制約,模具設(shè)計(jì)者在一個(gè)裝配組件取向和安排這些組件時(shí)浪費(fèi)了很多時(shí)間,第二,模具設(shè)計(jì)者利用大部分的時(shí)間來思考實(shí)際存在的客觀部件的選用原則,例如,螺絲、底座、釘子時(shí),CAD系統(tǒng)應(yīng)用了一個(gè)完全不同的客觀無體幾何水平。結(jié)果高水平的客觀取向想法不得不翻譯成低水平的CAD系統(tǒng),例如,線、面、塊,因此,對于解決上面的兩個(gè)問題,發(fā)展一個(gè)模塑自動化裝配組件是非常重要的。在這篇論文中我們論述了模塑自動化組建的兩個(gè)關(guān)鍵因素。在計(jì)算機(jī)中涉及模具生產(chǎn)部分和模具生產(chǎn)裝配組件,并且決定組成部分在一個(gè)裝配組件中的位置和客觀取向。
這篇論文簡要的描述了模塑裝配組件的相關(guān)研究,并且論述了注射成型模塑裝配組件的一個(gè)不可缺少的設(shè)計(jì),一個(gè)簡單的幾何方法被用來決定一個(gè)部件在模具裝配組件中的位置和客觀取向,介紹了注塑成型模塑的自動化裝配組件的一個(gè)例子。
2.相關(guān)的研究
模具裝配已經(jīng)在很多領(lǐng)域廣泛研究,例如,動力機(jī)體學(xué)、人工智能和幾何建模學(xué)。Libardi等人編輯了一本模塑組件的書,他們在其中報(bào)道了許多研究者在模具裝配研究中利用圖標(biāo)機(jī)構(gòu)。在這個(gè)圖標(biāo)方案中,一些組件被比喻成鼻子,一些感觀機(jī)體被弧線連接起來。然而,這些感官機(jī)體并沒有重合在一起,這就嚴(yán)重的影響了改性過程。例如,一個(gè)幾何裝配移動,所有與之相關(guān)的部件沒有相應(yīng)的移動。Lee 和 Gossard發(fā)明了一種支持包含了最基本信息的數(shù)據(jù)庫的有等級差別的裝配組建系統(tǒng),這些最基本的信息包含了兩個(gè)部件之間的墊片,這些改型基體取決于與之相關(guān)的實(shí)體,但是這些有等級模具差別的模具組建僅僅代表了這些模具中的一部分。
自動化推斷配置部件在裝配中的作用,意味著模具設(shè)計(jì)者可以避免直接定義這些改性機(jī)體,另外,一個(gè)部件位置的改變,將會隨著與之相連的任意一個(gè)部件的形狀和位置的改動而變動,存在著三種技術(shù)推斷計(jì)算一個(gè)部件在一個(gè)裝配組件中的位置和取向,這三種技術(shù)分別是數(shù)字迭代技術(shù)、系統(tǒng)代數(shù)技術(shù)、和系統(tǒng)幾何技術(shù)。 Lee和 Gossard指出數(shù)字迭代技術(shù)使用計(jì)算存在與空間關(guān)系中任何一個(gè)部件的位置和取向,他們的方法包含了三個(gè)步驟:產(chǎn)生約束等式、減少約束等式的數(shù)量和解決這些等式,存在著16個(gè)等式與條件不符,18個(gè)等式符合條件,6個(gè)對任何機(jī)體合適的等式,還有2個(gè)附加等式符合旋轉(zhuǎn)部分,通常這些等式的數(shù)量超過了可以利用的等式,因此這就需要一種技術(shù)篩選到不需要的公式,牛頓力學(xué)公式被用來解決這個(gè)問題。這種技術(shù)有兩個(gè)缺點(diǎn):第一、這種方法嚴(yán)重的依賴這前面的方法;第二、數(shù)字迭代技術(shù)不能區(qū)別不同的數(shù)字基礎(chǔ),因此,它很可能用在空間關(guān)系的問題上,這個(gè)領(lǐng)域不是數(shù)學(xué)方面的空白,但是在理論上還很模糊。
Ambler 和Popplestone提出了一種方法用來計(jì)算裝配組建中的每一個(gè)部件在兩個(gè)部件之間轉(zhuǎn)換和改觀方面所需要的空間關(guān)系,每一個(gè)部件存在著關(guān)于空間關(guān)系的六個(gè)轉(zhuǎn)變?nèi)齻€(gè)移動和三個(gè)旋轉(zhuǎn))。這種技術(shù)需要大量的計(jì)算機(jī)程序應(yīng)用和數(shù)據(jù)計(jì)算,同樣他不能用來解決在任何時(shí)間出現(xiàn)的所用問題,尤其是當(dāng)一個(gè)等式不能在程序中被重寫的時(shí)候。
Kramer發(fā)明了一種能夠決定一個(gè)剛性物體的位置和取向的集合方法,這種方法滿足一套的幾何約束。這種幾何方法是通過產(chǎn)生一系列沒任何約束的系統(tǒng)方法來解決問題的。這就導(dǎo)致了DOF數(shù)量的下降,Kramer利用了一種解決問題的技術(shù)稱作“上帝”,這是一個(gè)包含了一個(gè)點(diǎn)和兩條直交軸線的技術(shù)。7條約束現(xiàn)在圖標(biāo)間被定義出來,對于一個(gè)涉及到單個(gè)對象與約束在那個(gè)機(jī)構(gòu)上的標(biāo)記與不變屬性和實(shí)驗(yàn)分析的標(biāo)記的問題獲得了解決。經(jīng)試驗(yàn)分析后確定一個(gè)幾何物體的最終布局,再一步一步的解決客觀物體的布局,自由度決定哪一種方法將會滿足一個(gè)物體沒有約束,這考慮到將來減小物體的自由運(yùn)行,在每一步的結(jié)尾,一個(gè)可行的的法案增加到裝配計(jì)劃中。根據(jù)Shah和 Rogers的方法,Kramer的描述在塑裝配組建技術(shù)中起到了重大的作用,這種系統(tǒng)的幾何方法可以解決所有的約束條件,并且與數(shù)字迭代技術(shù)相比他擁有更吸引人的數(shù)字計(jì)算技術(shù),但是要應(yīng)用這種方法就需要大量的應(yīng)用程序。
盡管很多的設(shè)計(jì)者積極的投入到模塑裝配組建技術(shù)上,但是關(guān)于塑料注射成型模塑裝配組建技術(shù)的成果很少被系統(tǒng)的報(bào)道。Kruth等人發(fā)明一種支持注射成型的設(shè)計(jì)系統(tǒng),他們的系統(tǒng)通過高水平的功能模塑組建支持了注射成型模塑技術(shù),因?yàn)樗麄兊募夹g(shù)是建立在AUTOCAD的基礎(chǔ)上,所以只能通過簡單的塊和線框表示出來。
3.注射成型裝配組件的表征
注射成型模塑的自動化裝配組件的兩個(gè)關(guān)鍵技術(shù)是在計(jì)算機(jī)中將模塑裝配組件表示出來以及決定部件的生產(chǎn)部分在裝配組件中的位置和方向。在這個(gè)階段我們可以利用客觀取樣和表觀現(xiàn)象來代表注射成型的裝配組件。
在計(jì)算機(jī)中會使每個(gè)部件的結(jié)構(gòu)與空間關(guān)系變?yōu)楝F(xiàn)實(shí),這種設(shè)計(jì)必須支持所有的部件在裝配組件中的配合,所有部件間的改變關(guān)系和裝配組件作為一個(gè)整體的操作要求。另外,裝配組件的這種設(shè)計(jì)要求設(shè)計(jì)者在設(shè)計(jì)師必須滿足以下的要求:
1、要求模具設(shè)計(jì)者有高水平的技術(shù)來應(yīng)對實(shí)際存在的物體水平;
2、裝配組件的這種設(shè)計(jì)必須能夠正確的表現(xiàn)出自動生產(chǎn)過程的功能;
為了滿足這些要求一種具有表觀現(xiàn)象和客觀取向的有等級差別的模具被應(yīng)用在注射成型技術(shù)中,一個(gè)裝配組件可以被分成很多集合裝配,這個(gè)集合裝配有包含了很多的構(gòu)件,因此有等級差別的模具能夠分成合適的代表兩個(gè)構(gòu)件之間的結(jié)構(gòu)。一個(gè)等級差別的模具暗示了一個(gè)明確的裝配組件組,另外,一個(gè)等級差別的膜具能夠直接表現(xiàn)出一個(gè)構(gòu)件對另一個(gè)構(gòu)件的依賴。
基于特征的設(shè)計(jì)要求設(shè)計(jì)者站在一個(gè)比實(shí)際應(yīng)用模具更高的水平線。幾何形狀是直接的、有尺寸的,當(dāng)功能建模設(shè)計(jì)出來細(xì)節(jié),使用者能夠很快的通過一系列參數(shù)直接定位。當(dāng)然,由于幾何形狀之間的關(guān)系,它同樣也可以使設(shè)計(jì)者比客觀取向的模具設(shè)計(jì)者容易做出變動。沒有客觀取向設(shè)計(jì)者就要根據(jù)模具要求考慮到所有的幾何結(jié)構(gòu),因此,每一次設(shè)計(jì)改變可直接根據(jù)模具要求改變而改變。另外,客觀取向的設(shè)計(jì)能夠給設(shè)計(jì)者提供更高水平的組件物體,例如,當(dāng)模具設(shè)計(jì)者考慮到物體的真實(shí)水平時(shí),如一個(gè)冷卻水孔相關(guān)的客觀表象在計(jì)算機(jī)中模擬使用。
客觀取向模具設(shè)計(jì)是一個(gè)在考慮到現(xiàn)實(shí)事件中的模具技術(shù)的基礎(chǔ)上所應(yīng)用的一種新的方法,它的基礎(chǔ)是客觀物體,這個(gè)物體結(jié)合了數(shù)據(jù)結(jié)構(gòu)和性能客觀取向方法被用來理解問題和設(shè)計(jì)程序和數(shù)據(jù)庫,另外,客觀取向代表了裝配組件制造時(shí)單位客觀物體和總的組件的包含與被包含關(guān)系。
圖2表示了模具裝配中的表觀現(xiàn)象與客觀取向,代表性就是抽象的層次結(jié)構(gòu)來自低水平的幾何實(shí)體到高水平的組件。項(xiàng)目圖包含方格代表裝配模具,實(shí)線代表部件的關(guān)系,虛線代表其它的關(guān)系,部件組成實(shí)體。它聯(lián)合了表觀現(xiàn)象與客觀取向的優(yōu)點(diǎn),它不僅包含部件與整體的關(guān)系,更擁有一些模具裝配的結(jié)構(gòu)關(guān)系和使用功能。在3.1中將進(jìn)一步分析模具裝配的意義,而在3.2中詳細(xì)的介紹各部件之間的關(guān)系。
圖2 模具裝配中的表觀現(xiàn)象與客觀取向
3.1.裝配模具的定義
在我們的工作中,把模具裝配“O” 在下面的公式中是獨(dú)一無二的實(shí)體:
O = (Oid, A, M, R) (1)
在這里:
Oid是模具裝配的唯一標(biāo)識符(O);
A是一個(gè)三元組合(t,a,v), 其中a是O的一個(gè)屬性,每個(gè)與之相關(guān)的元素就是字符t, a和v;
M是一個(gè)數(shù)組,(m, tc1, tc2, %, tcn, tc)。每一個(gè)元素都是每個(gè)功能的唯一標(biāo)識符。
R是O與其它元素之間的關(guān)系,這兒又六種基本的關(guān)系在模具裝配中。即:Part-of, SR, SC, DOF, Lts, and Fit.
3.2.裝配模具的關(guān)系
在模具的裝配中有六種關(guān)系,分別是:Part-of, SR, SC, DOF, Lts, Fit。
Part-of—模具裝配本身的一種性質(zhì);
SR—明確規(guī)定的方向與裝配部件的客觀取向之間的關(guān)系,對于一個(gè)組成部分,它們特殊的空間關(guān)系來源于特殊的限制(SC);
SC —一個(gè)部件與其它的裝配組件之間的限制關(guān)系;
DOF —在裝配完成后允許的旋轉(zhuǎn)自由度;
Lts —由于旋轉(zhuǎn)的自由度,單方向或多方向的限制;
Fit —尺寸的限制為了保持某種狀態(tài);
在模具裝配的所有元素中,模具的裝配各部件之間的關(guān)系是非常重要的,這種關(guān)系不僅決定部件的方位,而且能夠保持模具裝配的關(guān)系。接下來,我們將要進(jìn)一步通過例子來闡述這種關(guān)系。
3.2.1.形狀特征間的關(guān)系
從本質(zhì)上說,模具設(shè)計(jì)就是一種思想,模具設(shè)計(jì)師們大部分時(shí)間在想一些實(shí)際的東西,例如底板、螺絲釘、溝槽、斜面和孔。所以,非常的有必要利用所有的標(biāo)準(zhǔn)部件建立幾何模型。模具設(shè)計(jì)師可以很容易的對部件的方位以及形狀進(jìn)行改變,因?yàn)槟切┎考g的關(guān)系都顯示在模型上。圖3a顯示一個(gè)平板上有個(gè)孔,這個(gè)部件有兩個(gè)特征:階段性和反鉆孔,反鉆孔(FF1)在F2和 F1的坐標(biāo)系中可用FF1表示,公式(2)~(5)表示了二者之間的關(guān)系。對于形狀特征,這里沒有什么特殊的限制,所以設(shè)計(jì)者直接指定這種關(guān)系。這種詳細(xì)的關(guān)系如下:
圖3 裝配關(guān)系
公式(2)-(7)顯示了FF1與FF2之間的關(guān)系,這些關(guān)系最終決定在這一部件中的方位和方向,如果把這一部件看做是模具裝配,形狀特征便是模具裝配中的一個(gè)“元件”。
形狀特征的選擇是建立在標(biāo)準(zhǔn)零部件的尺寸的基礎(chǔ)之上的,因?yàn)镃AD/CAM系統(tǒng)技術(shù)的支持,形狀特征不僅滿足模具裝配的尺寸和位置,而且體現(xiàn)了我們選擇的模具部件之間的特殊關(guān)系。為了增加那種特殊的關(guān)系,我們必須記錄邏輯關(guān)系,為模具裝配配備合適的關(guān)系。在CAD系統(tǒng)更新前, 檢查合適的形狀特征都是必要的。
3.2.2.各部件之間的關(guān)系
在模具裝配中,某部件的方向和方位是與其它部件相關(guān)聯(lián)的。圖3b顯示了一個(gè)模板(PP1)與螺絲釘(pp2)。螺釘?shù)南鄬ξ恢帽荒0迳系目姿拗疲@種模板與螺釘之間的關(guān)系如下:
就像我們從公式(8)和(9)所看到的一樣,通過計(jì)算Mp 和Mr決定螺釘在平板上的位置和方向是非常重要的。Mp 和Mr來自空間的限制,這種推導(dǎo)需要推斷模具裝配中的配置,這個(gè)問題將在下一階段進(jìn)行討論。
我們已經(jīng)介紹了一種注塑模具裝配的計(jì)算機(jī)模型。在這一階段,總結(jié)計(jì)算機(jī)模型的長處是有必要的。裝配模具作為組件的代表,反過來卻包括了組件,這個(gè)組件可以進(jìn)一步代表裝配的形狀特征,如此等級關(guān)系暗示裝配順序以及包含關(guān)系。這種基礎(chǔ)特征不僅要求設(shè)計(jì)師們能夠高水平的設(shè)計(jì)單個(gè)部件,而且擴(kuò)展了模具裝配的功能,因?yàn)檫@種性質(zhì)允許部件隨同其他部件位置和方向的改變而改變。表觀現(xiàn)象可以聯(lián)合某個(gè)對象的數(shù)據(jù)庫以及操作。模具裝配中封裝的功能就像頂出機(jī)構(gòu)與干涉檢查一樣能夠使的例行程序自動化。
4.注射成型模塑的裝配部件推斷
我們從等式8和9中可以看出,裝配模具中部件的方位與方向最終會被變換母體所取代。為了方便,特別的機(jī)構(gòu)關(guān)系通常是一些高水平的交配條件,就像伙伴、共線和平行。所以,在部件之間的隱含約束關(guān)系間自動獲取明確轉(zhuǎn)變條件是很必要的。在第二部分中已經(jīng)對三種推斷模具裝配部件的技術(shù)進(jìn)行了分析。因?yàn)閹缀文P湍軌蛘页鏊袉栴},并同時(shí)間的復(fù)雜性組成等式,我們用這種方法去確定裝配模具部件的方位與方向,要將這種方法在模具裝配中付之于行動,需要大量的規(guī)劃。然而,一種簡化幾何的方法被提議去確定模具裝配時(shí)的部件方位與方向。
在這種簡化幾何的方法中,通過產(chǎn)生一系列的行動去滿足那些約束來確定模具裝配時(shí)的部件方位與方向。滿足約束的所需資料被存儲在“計(jì)劃碎片”中,每個(gè)計(jì)劃碎片就是一個(gè)能夠指定順序和能夠使移動部件按照預(yù)定的路線移動的程序,計(jì)劃碎片還可以記錄物體的新自由度和相關(guān)的幾何變量。從概念上說,Kramer的計(jì)劃是一個(gè)三維調(diào)度表。我們用TDOF來代表自由度的平移度,RDOF來代表自由度的旋轉(zhuǎn)度。
這種計(jì)劃表詳盡的例舉了所有空間的狀態(tài),為了滿足一系列的約束在物體上的標(biāo)記和球坐標(biāo)系中的標(biāo)記而移動物體。例舉了上面三個(gè)因素相結(jié)合的不同,將導(dǎo)致82中差異。如果研究的空間減少的話,將會降低計(jì)劃表中的差異。為了實(shí)現(xiàn)這一目標(biāo),那些因素的例舉數(shù)量需減少。例如,對于一定的約束類型,如果TDOF由{0,1,2 ,3}變?yōu)閧0,3}后,這樣研究空間就嚴(yán)重的降低。經(jīng)過仔細(xì)的分析模具裝配部件的組成,四個(gè)基礎(chǔ)的約束被引用,他們的定義和代數(shù)方程如下:
由于那些相關(guān)的限制,我們計(jì)劃表中的參數(shù)充分的下降了,在我們的計(jì)劃表中去解決一個(gè)、兩個(gè)和三個(gè)的限制,必須有九個(gè)參數(shù)。模具裝配中為了互相增加組件,更多的限制約束和自由度將會增加使用者的適應(yīng)性。然而,在自動化模具裝配中,許多特殊的模具裝配關(guān)系將會事先確定,許多順序關(guān)系也不太重要。通過上面的約束限制,各部件之間的結(jié)構(gòu)關(guān)系將會被資料庫中數(shù)據(jù)指定。當(dāng)增加模具裝配中增加部件時(shí),系統(tǒng)將會第一時(shí)間分解復(fù)雜的約束為簡單的約束,然后,生成一組碎片計(jì)劃使部件在模具裝配中有確定的方向和方位。
5.模具非標(biāo)準(zhǔn)的集合裝配
許多注塑成型的裝配組件包含了生產(chǎn)部分和非生產(chǎn)部分, 生產(chǎn)部分單個(gè)組件的設(shè)計(jì)是在塑件幾何性能的基礎(chǔ)上得到的,通常產(chǎn)品生產(chǎn)部分應(yīng)有與高水平裝配組件相同的取向,通常這些構(gòu)件的位置和大小直接由設(shè)計(jì)者制定,對于產(chǎn)品省成本的設(shè)計(jì),傳統(tǒng)的方法是設(shè)計(jì)者從手冊中直接選擇所需要的模型,對這些選擇的產(chǎn)品生產(chǎn)部分建立幾何模型塊,然后再將這些塊加入到注射成型裝配組件中,這樣的設(shè)計(jì)既浪費(fèi)時(shí)間又錯(cuò)誤百出。在我們所應(yīng)用的新的設(shè)計(jì)方法中,所有生產(chǎn)部分的設(shè)計(jì)數(shù)據(jù)是在裝配組件和客觀需要的基礎(chǔ)上得到的,這些數(shù)據(jù)不僅包含了幾何形狀和生產(chǎn)部分的尺寸,而且還包含了部件之間的空間約束。另外,許多部件有固定的路線,例如:頂出和復(fù)位同樣也在這個(gè)數(shù)據(jù)庫中,因此,模具設(shè)計(jì)必須選則應(yīng)用這要求的模具生產(chǎn)部分而確定它的結(jié)構(gòu),然后計(jì)算機(jī)軟件會自動的確定出這些部分所要求部件的取向和位置,最后再將這些部件加入到裝配組件中。
5.1.模架組件
就像我們從圖1中看到的那樣,產(chǎn)品的生產(chǎn)部分可以進(jìn)一步分為標(biāo)準(zhǔn)件和非標(biāo)準(zhǔn)件。這些非標(biāo)準(zhǔn)件是由一系列底座、導(dǎo)向機(jī)構(gòu)等裝配組件構(gòu)成的。除了確定產(chǎn)品的性狀外,一個(gè)模具還必須同時(shí)完成許多其他的功能,例如冷卻、注射產(chǎn)品、頂出、合模導(dǎo)向等,許多的模具應(yīng)有相似的性能,因此這就導(dǎo)致了他們在結(jié)構(gòu)上的相似,模具結(jié)構(gòu)設(shè)計(jì)中有許多標(biāo)準(zhǔn)要求,模具非標(biāo)準(zhǔn)部件就是在這些標(biāo)準(zhǔn)組件的基礎(chǔ)上設(shè)計(jì)而成的。
根據(jù)裝配組件設(shè)計(jì)師的客觀取樣和表觀現(xiàn)象,模具組件的表觀現(xiàn)象是非標(biāo)準(zhǔn)件首先應(yīng)該考慮到的,另外,客觀組件的設(shè)計(jì)受到組件構(gòu)件之間的相互關(guān)系和構(gòu)件的功能的限制,然后利用這些客觀組件,一個(gè)有等級差比的集合裝配(模具的非標(biāo)準(zhǔn)部件)就形成了,這些模具的生產(chǎn)部分可以直接由目錄數(shù)據(jù)庫中的數(shù)據(jù)確定,圖4表示模具實(shí)際情況對立于模具的特殊組件,這種特殊的模具組件的例子被自動的添加的模具裝配中,模具部件與整體之間的結(jié)構(gòu)關(guān)系可以以Mp和Mr為單元表示出來。
圖4 模具設(shè)計(jì)實(shí)例
5.2.標(biāo)準(zhǔn)件的自動添加
一個(gè)標(biāo)準(zhǔn)件就是一個(gè)自動組件,這個(gè)可以依據(jù)3.1中的公式1定義。在數(shù)據(jù)庫中的空間約束是由交差、平面直線和弧線確定的,但是它與非標(biāo)準(zhǔn)件不同,標(biāo)準(zhǔn)件的位置和客觀取向并不確定。在設(shè)計(jì)時(shí)軟件通過簡單的公式直接推斷出標(biāo)準(zhǔn)件的幾何形狀。
5.3.模具裝配中的復(fù)位機(jī)構(gòu)
自動化設(shè)計(jì)的一個(gè)關(guān)鍵考慮因素是復(fù)位過程,復(fù)位是指嵌件在設(shè)計(jì)過程中留出相應(yīng)的一定空間使之歸位的操作。當(dāng)一個(gè)頂出設(shè)備加入到裝配組件中就要求在設(shè)計(jì)過程中留出相應(yīng)的孔,以便復(fù)位。如圖5所示:
圖5 模具頂出機(jī)構(gòu)
既然利用了客觀取向技術(shù),每一個(gè)裝配組件都可以有兩種表示方式:實(shí)際存在和客觀設(shè)計(jì)。實(shí)際存在的物體空間是根據(jù)一個(gè)真實(shí)物體所要占據(jù)的空間決定的,無論何時(shí)一個(gè)客觀構(gòu)件被加入到裝配組件中,它的真實(shí)空間尺寸也同時(shí)被設(shè)計(jì)出來,復(fù)位操作技術(shù)是根據(jù)相關(guān)構(gòu)件的相互關(guān)系而設(shè)計(jì)的。另外由于實(shí)際空間和真實(shí)空間的關(guān)系,復(fù)位技術(shù)的設(shè)計(jì)也要根據(jù)實(shí)際物體做出相應(yīng)的改變,這種自動復(fù)位功能進(jìn)一步說明了客觀取向的優(yōu)點(diǎn)。
6.系統(tǒng)實(shí)施
在客觀取樣和表觀取向基礎(chǔ)上設(shè)計(jì)而出的模塑自動化裝配組件技術(shù),已經(jīng)在美國國立大學(xué)被應(yīng)用在IMOLD領(lǐng)域內(nèi)。這種繪圖技術(shù)是提高應(yīng)用程序的一個(gè)有效方式,通過這種技術(shù)的使用這可以將其它部分加入到裝配組件中修改參數(shù)等。盡管繪圖技術(shù)提供了很好的功能,但是上文提到的方法仍然被用來推斷構(gòu)件的布局,因?yàn)樵谠O(shè)計(jì)過程中必須考慮到構(gòu)件自由運(yùn)行的程度和檢查構(gòu)件在加入到裝配組件以前所需要的空間。這種系統(tǒng)的約束條件和圖表約束是相輔相成的。
圖6顯示為一種注塑產(chǎn)品,圖7a中顯示成型這種塑件的注塑模具,圖7b中指出了各個(gè)組件在裝配時(shí)的父子關(guān)系。這種裝配組件使用IMOLD技術(shù)設(shè)計(jì)的,模具中的每一個(gè)非標(biāo)準(zhǔn)件被自動的安置在裝配組件中。同樣,標(biāo)準(zhǔn)件(例如:螺釘)也是被自動的加入到裝配組件中,復(fù)位技術(shù)也不例外。
圖6 注塑產(chǎn)品
圖7 成型注塑產(chǎn)品6的模具
7. 結(jié)論
在表觀現(xiàn)象和客觀取向技術(shù)上所設(shè)計(jì)的具有等級差別的注射模塑裝配組件,不僅僅提高了裝配組件設(shè)計(jì)技術(shù),而且同時(shí)提高了操作功能和幾何約束性,例如:自由的程度,配合條件、鑲嵌和取向約束。因?yàn)?,裝配組件設(shè)計(jì)的這一技術(shù)的提高,裝配組件中某一構(gòu)件的尺寸變化可以在整體設(shè)計(jì)完以后再做出變動。裝配組件構(gòu)件的封裝有以下兩個(gè)特點(diǎn):1、配合技術(shù)在裝配構(gòu)件中封裝自動化裝配組件設(shè)計(jì)時(shí)可以被容易的利用;2、裝配組件的封裝使得裝配組件的設(shè)計(jì)在應(yīng)用過程中自動完成,例如:復(fù)位和構(gòu)件檢查。提出的簡單的統(tǒng)計(jì)方法可以直接降低自動化設(shè)計(jì)過程中程序的難度。
DVD-ROM上蓋的建模和注塑成型工藝對收縮率影響的分析
塑料注射成型在生產(chǎn)高品質(zhì)塑料零件中發(fā)揮著關(guān)鍵的作用。收縮是影響注塑成型零件質(zhì)量最重要的因素之一。本文通過評估丙烯腈-丁二烯-苯乙烯共聚物(ABS)材質(zhì)的DVD-ROM上蓋質(zhì)量著重研究建模和注塑成型工藝對收縮率的影響。通過數(shù)據(jù)分析確定工藝參數(shù)(模具溫度、熔點(diǎn)、注射壓力、注射時(shí)間和冷卻時(shí)間)與收縮率之間的數(shù)學(xué)關(guān)系開發(fā)一個(gè)有效的回歸模型。有限元 (FE) 分析 (L27)田口所設(shè)計(jì)Mold?ow仿真程序中運(yùn)行的正交數(shù)組。通過方差分析(ANOVA)校驗(yàn)回歸模型并確定工藝參數(shù)對收縮率的影響。通過Mold?ow仿真分析,可獲得有限元分析與控制的回歸模型的準(zhǔn)確性。結(jié)果顯示回歸模型與有限元分析實(shí)驗(yàn)的結(jié)果高度一致。由此可以得出結(jié)論這項(xiàng)建模的收縮問題在我們的應(yīng)用程序中研究成功。
關(guān)鍵詞:塑料注塑成型,回歸建模和方差分析,收縮。
1 前言
注射成型是批量生產(chǎn)制造薄殼塑料零件常用的加工方法之一。塑料部件的質(zhì)量取決于材料的特性、 模具設(shè)計(jì)和最重要的工藝參數(shù)。幾項(xiàng)研究發(fā)現(xiàn),注射成型的工藝參數(shù)對塑料部件的質(zhì)量都有關(guān)鍵的影響。他們調(diào)查注射成型工藝在生產(chǎn)過程中零部件的收縮、 彎曲、 熔合紋、凹陷和殘余應(yīng)力等問題。他們的研究還顯示影響塑料部件質(zhì)量的最重要參數(shù)是保壓、 熔化溫度和模具溫度。然而,這些研究沒有充分考慮到其他包括注射時(shí)間和冷卻時(shí)間等工藝參數(shù)的影響。此外,德米雷爾有對收縮和翹曲變形導(dǎo)致部件質(zhì)量問題的計(jì)算進(jìn)行實(shí)驗(yàn)研究。這項(xiàng)研究還表明了收縮和翹曲變形隨著溫度的升高和注射壓力的降低而增加。在這個(gè)研究中,雖然沒有考慮到主要影響工藝參數(shù)注射時(shí)間和冷卻時(shí)間,但是這些實(shí)驗(yàn)條件足夠得出寶貴的結(jié)論。許多發(fā)表的論文指出,在薄殼塑料部件的注射成型中,工藝參數(shù)和影響零塑件質(zhì)量問題的收縮與彎曲可以建立物理關(guān)系。在以往的研究中,進(jìn)行一系列的試驗(yàn)來測量收縮和翹曲變形下的工藝參數(shù)的值。通過數(shù)學(xué)模型利用測量的值確定最佳工藝參數(shù)。以類似的方式,利用回歸分析取得薄殼塑料零件注射成型工藝參數(shù)與通過實(shí)驗(yàn)獲得的收縮率之間的關(guān)系。通過工藝參數(shù)與收縮率的數(shù)學(xué)關(guān)系式創(chuàng)建二階廣義多項(xiàng)式回歸方程。由此發(fā)現(xiàn),工藝對零塑件的質(zhì)量起著至關(guān)重要的影響。另一方面,在上述研究中,它沒有經(jīng)過任何成型仿真工具(模流分析)對實(shí)驗(yàn)結(jié)果進(jìn)行校核。然而,有許多研究工藝參數(shù)對質(zhì)量的影響的仿真塑料注塑成型的文章。
其中一篇由Chen et al寫的文章具有典型代表性。這篇文章涉及到計(jì)算機(jī)輔助工程結(jié)合統(tǒng)計(jì)技術(shù)應(yīng)用,用以減少塑料注塑參數(shù)引起的翹曲變形。為此,一些依賴田口正交數(shù)組的模塑仿真分析、回歸方程和方差分析(ANOVA) 可以結(jié)合預(yù)測各種注塑參數(shù)引起的翹曲變形。但是,這篇文章只是簡單說明了塑料注塑過程中的翹曲變形而未提到收縮。然而,由Chen等人寫的另一篇文章負(fù)責(zé)通過利用一系列模塑仿真分析研究注塑模制品收縮率變化有影響的有效參數(shù)。與上述研究結(jié)果不同的是,由阿爾坦做的一項(xiàng)研究使用田口方法、方差分析和模擬腦神經(jīng)網(wǎng)絡(luò)使注塑成型收縮減小。進(jìn)行了二十七次注射成型試驗(yàn)獲得的聚丙烯 (PP)、 聚苯乙烯 (PS) 兩種不同的聚合物材料的收縮量。從這項(xiàng)研究可以看到通過綜合辦法可以獲得最佳工藝條件對應(yīng)的最小收縮量。與從上述論文不同的是,一些研究人員只研究電火花加工(EDM) ??傊?,即使這些研究者工作在不同領(lǐng)域,但他們有采用和塑料注射成型類似的方法。從這項(xiàng)研究中,從模塑仿真分析模擬得到以有限元分析為基礎(chǔ)的有效回歸模型可獲得塑料注塑工藝參數(shù) (模具溫度、 熔化溫度、 注射壓力、 注射時(shí)間和冷卻時(shí)間) 和使用 ABS 高分子材料的體積收縮率之間的數(shù)學(xué)關(guān)系。大多數(shù)研究文獻(xiàn)中沒有考慮到所有這些過程參數(shù)。在不同學(xué)者的論文內(nèi)工藝參數(shù)的范圍也不同。方差分析是塑料注塑成型測量工藝參數(shù)和評估回歸模型最有效的方法。此外,通過四次DVD-ROM上蓋塑件的注塑成型實(shí)驗(yàn)得到的理論值和實(shí)際測量值進(jìn)行比較來驗(yàn)證創(chuàng)建的回歸模型的準(zhǔn)確性。
2.實(shí)驗(yàn)研究方法
2.1田口正交數(shù)組設(shè)計(jì)實(shí)驗(yàn)
利用正交數(shù)組的實(shí)驗(yàn)設(shè)計(jì)方法,在大多數(shù)情況下,高效方便的實(shí)驗(yàn)方法與傳統(tǒng)的試驗(yàn)設(shè)計(jì)方法相比,有必要減少和控制實(shí)驗(yàn)次數(shù)。此外,當(dāng)工藝參數(shù)增加時(shí),必須要進(jìn)行大量的實(shí)驗(yàn)。在此研究中,27 FE 分析基于田口正交數(shù)組(L27)對塑料注塑工藝參數(shù)的研究,包括:模具溫度 (T 模),運(yùn)行熔融溫度 (T 熔體),注射壓力 (P 注射用),(I 時(shí)間),注射時(shí)間和冷卻時(shí)間 (C) 如表 1 所示。收縮參數(shù)值對應(yīng)回歸模型中的響應(yīng)值。在表 2 中提供了從模塑仿真分析軟件模擬有限元分析取得的收縮率結(jié)果。
2.2模具設(shè)計(jì)制造
當(dāng)生產(chǎn)一個(gè)塑料部件的時(shí)候,模具必須經(jīng)過各種機(jī)械設(shè)計(jì)和制造。在此研究中,適用于制造DVD-ROM上蓋塑料產(chǎn)品的的步驟說明如圖1所示。在塑料注射成型中,用Pro/Engineer CAD/CAM 程序設(shè)計(jì)DVD-ROM上蓋塑料制品的CAD模型。此外,DVD ROM上蓋模具設(shè)計(jì)包括了兩個(gè)夾緊板、核心板和針腳。在制作模具組件中,會用到一些機(jī)械設(shè)備,如數(shù)控銑床、電火花加工、鉆和磨。DIN 1.2738 (IMPAX) 鋼被選為模具元件的材料。用沃伯特英斯特朗儀器測量此材料的硬度達(dá)到31HRC,表3中列出了它的化學(xué)成分。
2.3 有限元 (FE) 分析和成型周期
2.3.1 FE 的預(yù)先處理,DVD-ROM蓋。
3D模型的DVD-ROM上蓋部分被導(dǎo)入到Moldflow Plastic Insight 5.0(MPI 5.0)塑料仿真模擬軟件。DVD-ROM上蓋的尺寸為153mm×45.17mm×7mm。DVD-ROM上蓋的材料高分子聚合物(ABS)由模流分析類似的推測而來,在表4中列出了其材料屬性。在成型之前需要用干燥機(jī)烘高分子材料ABS四個(gè)小時(shí)。DVD-ROM 部件的有限元模型是利用離散幾何由較小的簡單元素創(chuàng)建的。有限元融合網(wǎng)格模型,如圖 2 所示由 2726年節(jié)點(diǎn)、69 梁元素和5318三角元素組成。
2.3.2 DVD-ROM上蓋的成型周期。
模具組件的設(shè)計(jì)和制造是為了可以注入制造DVD-ROM上蓋部分的材料,這個(gè)上蓋是安裝在計(jì)算機(jī)機(jī)箱前部DVD安裝部位。這項(xiàng)研究所用的塑料注塑機(jī)是瑞士制造的NETSTAL (600 H-110 60 噸 1.66 盎司 (25 毫米))。這種塑料注塑機(jī)器技術(shù)規(guī)格最大夾緊力543噸、 243 MPa的最大注射壓力、 491 cm3/s最大注射率、螺釘直徑為25毫米和0.2 s的機(jī)液壓響應(yīng)。
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桂林電子科技大學(xué)畢業(yè)設(shè)計(jì)用紙
Automated Assembly Modelling for Plastic Injection Moulds
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 moulded 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 moulded 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 oftasks such as the distribution of melt, cooling the molten material, ejection of the moulded 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 moulded 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
Fig. 1. Assembly structure of an injection mould
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. Lib-ardi et al. [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 subassembly 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 (coincident, in-line, in-plane, parallelFz, offsetFz, offsetFx and helical) 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. 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 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 com- puters, 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 real-world 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 subassemblies, which in turn consists of subassemblies 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 counterbore hole, a feature object of a counterbore hole will be ready in the computer for use.
Object-oriented modelling [11,12] is a new way of thinking about problems using models organised 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”.
Figure 2 shows the feature-based and object-oriented hier- archical representation of an injection mould. The representation is a hierarchical structure at multiple levels of abstraction, from low-level geometric entities (form feature) to high-level subassemblies. The items enclosed in the boxes represent “assembly objects” (SUBFAs, PARTs and FFs); the solid lines represent “part-of” relation; and the dashed lines represent other relationships. Subassembly (SUBFA) consists of parts (PARTs). A part can be thought of as an “assembly” of form features (FFs). The representation combines the strengths of a feature-based geometric model with those of object-oriented models. It not only contains the “part-of” relations between the parent object and the child object, but also includes a richer set of structural relations and a group of operational functions for assembly objects. In Section 3.1, there is further discussion on the definition of an assembly object, and detailed relations between assembly objects are presented in Section 3.2
Fig. 2. Feature-based, object-oriented hierarchical representation
3.1 Definition of Assembly Objects
In 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 an attribute 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). Each element of M is a function that uniquely identifies a method. The symbol m represents a method name; and methods define operations on objects. The symbol tci(i= 1, 2, %, n) specifies the argument type and tc specifies the returned value type.
R is a set of relationships among O and other assembly objects. There are six types of basic relationships between 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 are attributes with a data type of string; checkFinterference and pocketFplate are member functions; and Part-of, SR and DOF are relationships.
3.2 Assembly Relationships
There are six types of basic relationships between assembly objects, Part-of, SR, SC, DOF, Lts, and Fit.
Part-of An assembly object belongs to its ancestor object.
SR Spatial relations: explicitly specify the positions and orientations of assembly objects in an assembly. For a component part, its spatial relationship is derived from spatial constraints (SC).
SC Spatial constraints: implicitly locate a component part with respect to the other parts.
DOF Degrees of freedom: are allowable translational/ rotational directions of motion after assembly, with or without limits.
Lts Motion limits: because of obstructions/interferences, the DOF may have unilateral or bilateral limits.
Fit Size constraint: is applied to dimensions, in order to maintain a given class of fit.
Among all the elements of an assembly object, the relation-ships are most important for assembly design. The relationships between assembly objects will not only determine the position of objects in an assembly, but also maintain the associativities between assembly objects. In the following sub-sections, we will illustrate the relationships at the same assembly level with the help of examples.
3.2.1 Relationships Between Form Features
Mould design, in essence, is a mental process; mould designers most of the time think on the level of real-world objects such as plates, screws, grooves, chamfers, and counter-bore holes. Therefore, it is necessary to build the geometric models of all product-independent parts from form features. The mould designer can easily change the size and shape of a part, because of the relations between form features maintained in the part representation. Figure 3(a) shows a plate with a counter-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, using their local coordinates F2and F1, respectively. Equations (2)–(5) show the spatial relationships between the counter-bore hole (FF2) and the block feature (FF1). For form features, there is no spatial constraint between them, so the spatial relationships are specified directly by the designer. The detailed assembly relationships between two form features are defined as follows:
Fig. 3. Assembly relationships.
F2k= 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)
Where
F and r are the orientation and position vectors of features.
F1= (F1i, F1j, F1k), F2= (F2i, F2j, F2k).
bij is the dimension of form features, Subscript i ifeature number, j is dimension number.
AF1is the dimension between form features.
Equations (2)–(7) present the relationships between the form feature FF1 and FF2. These relationships thus determine the position and orientation of a form feature in the part. Taking the part as an assembly, the form feature can be considered as “components” of the assembly.
The choice of form features is based on the shape characteristics of product-independent parts. Because the form features provided by the Unigraphics CAD/CAM system [13] can meet the shape requirements of parts for injection moulds and the spatial relationships between form features are also maintained, we choose them to build the required part models. In addition to the spatial relationships, we must record LTs, Fits relationships for form features, which are essential to c