【溫馨提示】====【1】設(shè)計(jì)包含CAD圖紙 和 DOC文檔，均可以在線預(yù)覽，所見即所得，，dwg后綴的文件為CAD圖，超高清，可編輯，無(wú)任何水印，，充值下載得到【資源目錄】里展示的所有文件======【2】若題目上備注三維，則表示文件里包含三維源文件，由于三維組成零件數(shù)量較多，為保證預(yù)覽的簡(jiǎn)潔性，店家將三維文件夾進(jìn)行了打包。三維預(yù)覽圖，均為店主電腦打開軟件進(jìn)行截圖的，保證能夠打開，下載后解壓即可。======【3】特價(jià)促銷，，拼團(tuán)購(gòu)買，，均有不同程度的打折優(yōu)惠，，詳情可咨詢QQ：1304139763 或者 414951605======【4】 題目最后的備注【JA系列】為店主整理分類的代號(hào)，與課題內(nèi)容無(wú)關(guān)，請(qǐng)忽視
畢業(yè)設(shè)計(jì)(論文)
題 目 銳意車工具箱蓋雙型腔注射模模具設(shè)計(jì)
院（系） 機(jī)械工程學(xué)院
專業(yè)班級(jí) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化
學(xué)生姓名
指導(dǎo)教師
成 績(jī)
年 月 日
用于塑料注射模具設(shè)計(jì)和生產(chǎn)的自動(dòng)基準(zhǔn)尺寸
摘要：基準(zhǔn)尺寸（或者坐標(biāo)尺寸）技術(shù)在表面有大量必須有規(guī)定的孔特征的注射模具畫圖方面應(yīng)用非常廣泛。盡管商業(yè)CAD/CAM系統(tǒng)提供了半自動(dòng)工具來(lái)協(xié)助設(shè)計(jì)者進(jìn)行尺寸確定，但它仍然是個(gè)非常復(fù)雜的過(guò)程。作為使用者，不得不進(jìn)行規(guī)定每個(gè)尺寸標(biāo)記的位置。這篇文章講的是一種最優(yōu)的尺寸標(biāo)記的全自動(dòng)方法。這種方法采用的是動(dòng)態(tài)工程技術(shù)，在尊重用戶所選擇的標(biāo)準(zhǔn)前提下，使尺寸確定最優(yōu)化。這種方法已經(jīng)作為一種工具插到了商業(yè)CAD/CAM系統(tǒng)中，并且給出了一些實(shí)例來(lái)說(shuō)明這個(gè)技術(shù)的重要特征。
關(guān)鍵字：自動(dòng)尺寸 基準(zhǔn)尺寸 動(dòng)態(tài)工程 最優(yōu)尺寸 坐標(biāo)尺寸
1介紹 CAD/CAM系統(tǒng)現(xiàn)在在塑料模具注射制造業(yè)應(yīng)用非常廣泛，許多公司可用一種實(shí)體模擬系統(tǒng)來(lái)設(shè)計(jì)注射模具。他們用CAD系統(tǒng)來(lái)設(shè)計(jì)，不僅僅是核心和孔插入到模具（他們是形成模具最重要部分），同時(shí)也是在模具裝配中其他所有部分。伴隨著互聯(lián)網(wǎng)技術(shù)的進(jìn)步和最近CAD網(wǎng)絡(luò)通信的發(fā)展，注射模具的設(shè)計(jì)信息可以在產(chǎn)品工程師（設(shè)計(jì)塑料部件）和刀具工程師（設(shè)計(jì)注射模具），甚至他們位于世界上不同區(qū)域。在設(shè)計(jì)信息通過(guò)電子方式在產(chǎn)品設(shè)計(jì)和刀具設(shè)計(jì)中可以有效的交流，制造信息通信在電子和傳統(tǒng)技術(shù)共同作用下在車間完成。數(shù)控機(jī)床刀具軌跡或者檢查指令可以直接從CAD/CAM和互聯(lián)網(wǎng)下載給數(shù)控控制器進(jìn)行加工或者進(jìn)行檢查工作。然而，對(duì)于一個(gè)專門機(jī)器來(lái)說(shuō)建立一個(gè)說(shuō)明書或許在工程圖紙中規(guī)定。另外，不是所有的加工任務(wù)都是在數(shù)控機(jī)床上完成。出于成本預(yù)算的考慮，一些傳統(tǒng)機(jī)床，例如鉆床和磨床等，可以方便用傳統(tǒng)刀具完成。通常工程圖紙也在車間里的工程信息通信中扮演重要角色。正交投影工程圖紙可以從CAD模型中自動(dòng)產(chǎn)生。零件尺寸自動(dòng)工具同樣由商業(yè)CAD系統(tǒng)提供。然而，就像有chen指出的，那些尺寸工具不能夠根據(jù)圖紙標(biāo)準(zhǔn)和工廠通常采用的工程方法來(lái)生成尺寸。
在注射模具的特殊要求中，孔特征的基準(zhǔn)尺寸（或坐標(biāo)尺寸）應(yīng)用得非常廣泛。圖1展示了一張?jiān)谝粋€(gè)模具制造公司的工廠中可以找到的典型詳細(xì)的圖紙。在圖中表明了孔特征和用來(lái)規(guī)定這些孔位置的基準(zhǔn)尺寸?？梢园l(fā)現(xiàn)這些尺寸顯得非常擁擠，并且人工的來(lái)確定這些基準(zhǔn)尺寸的位置是非常繁重的工作。最終這張滿帶尺寸的圖紙的質(zhì)量很大程度上依賴于這張圖紙繪圖員的經(jīng)驗(yàn)。這項(xiàng)研究的目的是發(fā)明一種能夠從一個(gè)給定的注射模具的零件上自動(dòng)的產(chǎn)生基準(zhǔn)尺寸。尺寸結(jié)果必須滿足兩個(gè)要求：第一，任意兩個(gè)尺寸標(biāo)記不能夠重疊；第二，尺寸標(biāo)記必須盡可能的接近被測(cè)特征。這個(gè)問(wèn)題的關(guān)鍵是研究一種使基準(zhǔn)尺寸位置的最優(yōu)化的方法。
2.相關(guān)工作
在規(guī)定機(jī)械零件或組裝特征的大小或位置信息中尺寸標(biāo)記和公差分析是兩個(gè)非常接近的工作，并且大多數(shù)的研究工作都集中于公差上。公差的主要研究問(wèn)題是顯示、分析和合成。公差顯示與把公差信息合并產(chǎn)品模型草圖中相關(guān)。實(shí)例中包括由Requicha發(fā)明的實(shí)體偏移法、Turner的可行性空間法和Desrocher和Dlement的TTRS法。在Roy和Yu的文章中有更加詳細(xì)的觀點(diǎn)。公差分析的目的是確定公差中決定零件公差的合并效果。它被用來(lái)證實(shí)已知或猜想的給定設(shè)計(jì)單個(gè)零件尺寸變化的功能性。公差分析的技術(shù)實(shí)例包括Monte，Carlo總結(jié)和指出的線性方法。它的主要觀點(diǎn)是綜合合成或公差分配，它是用來(lái)確定基于給定裝配的功能性要求的零件公差。最近，Is Lam同時(shí)發(fā)表了一個(gè)工程方法來(lái)解決這個(gè)問(wèn)題。從工程性考慮，根據(jù)不同用戶需求和技術(shù)需求在系統(tǒng)的分析功能性需求基礎(chǔ)上，提出了一種解決尺寸需求的方法。FDT軟件也是用來(lái)支持實(shí)現(xiàn)這種方法。FDT向功能需求或尺寸基礎(chǔ)中提供用來(lái)代表功能需求、尺寸、公差或過(guò)程能力的工具。在這個(gè)基礎(chǔ)上，這種獲取的函數(shù)方程被分成若干組，并且每組都用來(lái)解決所涉及到的函數(shù)需求和公差問(wèn)題的專一方法策略。在公差公差分析和合并中更多詳細(xì)的觀點(diǎn)可以在Roy、Ngoi、Ong，Hong和Chang的文章中找到。
從一個(gè)CAD模型中自動(dòng)的產(chǎn)生尺寸的方法已經(jīng)被提出。在立體幾何學(xué)實(shí)體模型技術(shù)上的零件自動(dòng)顯示尺寸上Yuen做過(guò)一些早期的嘗試。從實(shí)體模型上提取一些來(lái)自二維表面和剪切剪切圓柱上的點(diǎn)。這些點(diǎn)的坐標(biāo)被安排在一個(gè)樹型結(jié)構(gòu)上來(lái)產(chǎn)生線性尺寸，并刊登了一個(gè)為直徑和半徑尺寸的簡(jiǎn)單例子。其他早期的自動(dòng)尺寸方面的工作由Yu總結(jié)了。最近，Chen發(fā)表了一個(gè)更加在自動(dòng)尺寸方面具有深度的研究。他們的方法是分析多余尺寸，對(duì)稱特性的尺寸草圖。，選擇適當(dāng)?shù)囊暯莵?lái)規(guī)定尺寸，并且用一種專業(yè)級(jí)系統(tǒng)的方法來(lái)確定尺寸定位。這個(gè)專業(yè)級(jí)系統(tǒng)分析被測(cè)特征的幾何形狀和布局，并且確定一個(gè)合適的位置來(lái)放置一個(gè)基于一套規(guī)則的相關(guān)被測(cè)特征的尺寸。在一個(gè)尺寸位置完成后，構(gòu)造一個(gè)禁區(qū)使所有隨后的尺寸不會(huì)放在此區(qū)域中。這就避免了兩個(gè)尺寸的重疊或交叉。
現(xiàn)存的尺寸放置方法是有限的，取決于這個(gè)方法的自然連續(xù)性。例如，在Chen的方法中，特征的測(cè)量是被優(yōu)先考慮的，但尺寸的位置是隨后考慮的。這種方法不適合確定坐標(biāo)尺寸的位置，特別是在注射模具表面尺寸非常擁擠的情況下。這是因?yàn)橐粋€(gè)基準(zhǔn)尺寸的位置影響到其他尺寸的位置。這篇文章講述了我們?cè)诮鉀Q坐標(biāo)尺寸位置方面的工作。使用了動(dòng)態(tài)程序方法使其最優(yōu)化，這種新的方法克服了在現(xiàn)存方法中連續(xù)方法的限制。
3.在基準(zhǔn)尺寸中，特征位置通過(guò)特征的參考位置和參考基準(zhǔn)的水平和垂直距離來(lái)確定?；鶞?zhǔn)尺寸的缺省形式在圖2a中表示。當(dāng)被測(cè)兩特征的垂直距離小于尺寸標(biāo)記大?。ǔ叽缥谋靖叨鹊暮秃拖噜弮沙叽缥谋镜淖钚】臻g）,圖2b中的被選形式就需要了。為了防止不重疊，這個(gè)尺寸標(biāo)記則從缺省位置向上或向下轉(zhuǎn)換。就像圖2c中，尺寸標(biāo)記的轉(zhuǎn)換是尺寸的單一延長(zhǎng)線打斷成了三個(gè)部分：被一個(gè)傾斜部分相連的兩個(gè)水平部分。通過(guò)三個(gè)參數(shù)使尺寸標(biāo)記的范圍能夠變換調(diào)整：（i）傾斜部分和尺寸線的水平部分的折角α；（ii）尺寸文本和零件邊緣距離m；（iii）特征的位置和最低位置由下式給出：
=
= （1）
4．自動(dòng)基準(zhǔn)尺寸
自動(dòng)基準(zhǔn)尺寸的目的是尋找一種使每個(gè)基準(zhǔn)尺寸位置都達(dá)到最優(yōu)的方法。每個(gè)過(guò)程包括兩個(gè)階段：準(zhǔn)備階段和最優(yōu)化階段。在準(zhǔn)備階段，使最優(yōu)化過(guò)程得到簡(jiǎn)化的主要參數(shù)將被建立。所有特征使用給出的折角、邊緣偏移和尺寸標(biāo)記大小將會(huì)進(jìn)行尺寸位置的可行化測(cè)試。在最優(yōu)化階段，使用的是動(dòng)態(tài)程序方法。尺寸標(biāo)記位置最優(yōu)化是在最重不同的基準(zhǔn)系列，包括從他們的缺省位置中每個(gè)尺寸轉(zhuǎn)移的最小量，或者從缺省形式使用的盡可能多的最大量。
4.1準(zhǔn)備階段
被測(cè)特征首先被分成一個(gè)或更多的特征系列。對(duì)于一個(gè)特征系列的每一個(gè)特征來(lái)說(shuō)，在此特征系列中至少存在另一個(gè)特征以便使他們之間的垂直距離小于尺寸標(biāo)記的大小。換句話說(shuō)，在一個(gè)特征系列中的所有特征，沒(méi)有重疊的情況下在相鄰兩尺寸標(biāo)記不能用缺省的專用形式測(cè)量。相反，至多一個(gè)特征能用一個(gè)叫做尺寸塊的特征相關(guān)聯(lián)。尺寸快的構(gòu)造涉及到每個(gè)在尺寸塊中的基準(zhǔn)尺寸的形式和位置。對(duì)于一個(gè)尺寸塊的每個(gè)位置，它的構(gòu)造是唯一確定的。圖3表示在兩個(gè)構(gòu)造中的兩個(gè)特征系列和它們的尺寸塊
定義1：構(gòu)造的正確性。假如在一個(gè)尺寸塊中任意兩個(gè)尺寸標(biāo)記間沒(méi)有重疊，并且每個(gè)尺寸標(biāo)記位于它們的末端位置，則這個(gè)尺寸塊的構(gòu)造就是正確的。
在圖3b中表示的尺寸塊就是正確的。圖4表示的兩個(gè)尺寸塊是不正確的。因?yàn)樵趫D4a中的尺寸標(biāo)記有重疊所以不正確，圖4b的構(gòu)造中，14.00尺寸標(biāo)記的延伸線的位置太高，而尺寸要求的位置標(biāo)記在它之下。
定義2：構(gòu)造末端。有兩種構(gòu)造末端：最高構(gòu)造和最低構(gòu)造。假如一個(gè)尺寸是正確的，并且任何再高點(diǎn)（或低點(diǎn)）的位置都是不正確的構(gòu)造則稱此尺寸塊是最高（或最低）構(gòu)造。尺寸塊的末端構(gòu)造取決于和。
圖5a里的構(gòu)造處于它的最高構(gòu)造。因?yàn)?9.5是它的最高位置，它不能再向上移動(dòng)了。圖5b表示的是最低構(gòu)造，因?yàn)?4.00是它的最低位置，它不能向下移動(dòng)了。
尺寸塊的末端構(gòu)造有兩個(gè)在最優(yōu)化階段所應(yīng)用的重要參數(shù)。在兩個(gè)尺寸標(biāo)記中沒(méi)有任何重疊的情況下，看測(cè)量所有特征是否可行的過(guò)程中，這兩個(gè)參數(shù)是非常有用的。在形成一種測(cè)量末端構(gòu)造中可以看到這兩個(gè)參數(shù)是非常有用的。
特點(diǎn)1：在一個(gè)尺寸標(biāo)記處于它的最高（或最低）的位置上，最少有一個(gè)尺寸標(biāo)記處于最高（或最低）的位置。
特點(diǎn)2：只要尺寸塊有末端構(gòu)造，則它就是不正確的。
特點(diǎn)1可以由反證法證明。假如一個(gè)尺寸處于它的最高（或最低）構(gòu)造上，并且沒(méi)有尺寸標(biāo)記處于最高（或最低）位置。因此所有它的尺寸標(biāo)記都不處于它們的最高（或最低）位置，它們能夠同時(shí)向上（或向下）移動(dòng)相同距離直到它們中的任意一個(gè)達(dá)到了最高（或最低）位置上。因?yàn)樗械某叽鐦?biāo)記都是同時(shí)移動(dòng)了相同的距離，尺寸標(biāo)記就不會(huì)重疊，并且因此構(gòu)造結(jié)果仍然是正確的，并且在一個(gè)比它初始構(gòu)造更高點(diǎn)（或低點(diǎn)）的位置上。這就違反了初始構(gòu)造處于最高或最低的假設(shè)。
特點(diǎn)2可以直接證明。給定的一個(gè)正確構(gòu)造、尺寸塊移動(dòng)更高（或低）直到一個(gè)或更高的尺寸標(biāo)記達(dá)到最高（或最低）位置。因此所有尺寸標(biāo)記都同時(shí)移動(dòng)相同距離，重疊也不會(huì)發(fā)生。另外，因?yàn)橹辽偎囊粋€(gè)尺寸標(biāo)記達(dá)到最高（或最低）位置，尺寸塊在沒(méi)有不正確構(gòu)造的情況下，尺寸塊不能被移動(dòng)更高（或更低）。根據(jù)定義2，構(gòu)造的結(jié)果也是最高（或最低）位置。另一方面，尺寸塊是否有末端構(gòu)造就很明顯了，因?yàn)槟┒藰?gòu)造定義是正確的所以該尺寸塊就是正確構(gòu)造。
特點(diǎn)1表明尺寸塊的末端構(gòu)造可以由通過(guò)觀察塊中的尺寸標(biāo)記的末端位置的方法獲得。尺寸塊的構(gòu)造可以通過(guò){}來(lái)規(guī)定，i=1，2，3，……，n，是特征系列中第i個(gè)特征的尺寸標(biāo)記的位置。這說(shuō)明了{(lán)}是按照他們的垂直上升順序排布的（假如i﹥j，則﹥）。然而，為了避免尺寸標(biāo)記的重疊，第i個(gè)尺寸標(biāo)記的位置由下式給出：
； n≥i≥2 （2）
式中SIZE是尺寸標(biāo)記的大小，是該系列中的第一個(gè)特征（）尺寸標(biāo)記的位置。也同樣被用作尺寸塊的參考位置。
如果構(gòu)造是正確的，通過(guò)式（1）得出所有尺寸標(biāo)記必須位于其自己最高位置的下端，如下：
≥
因此
以上關(guān)系必須通過(guò)所有i證明。因此，最高允許值通過(guò)給出：
（3）
的值通過(guò)式（2）給出，一個(gè)或更多的都等于。所有其他的都小于它的。沒(méi)有更大的值因此構(gòu)造滿足≥，假如正確，這個(gè)最終構(gòu)造就是它的最高構(gòu)造。然而，在此構(gòu)造中通過(guò)式（2）給出的中的一些值可能小于。因此，每個(gè)必須驗(yàn)證。假如所有的i的≥，則這個(gè)最高構(gòu)造成立。假如一些i的，則這個(gè)構(gòu)造成立就是不正確的，并且沒(méi)有最高位置成立。通過(guò)特性2特征系列{}不存在任何正確構(gòu)造。
為了尋找最低位置，對(duì)于所有i的≥，最低允許值由下式給出：
對(duì)于一個(gè)零件來(lái)說(shuō)，它的尺寸塊是多樣化的，假如所有尺寸塊中的兩個(gè)末端構(gòu)造能夠成功建立，則在每個(gè)沒(méi)有任何重疊尺寸塊中放置尺寸標(biāo)記就是可行的。然而，一個(gè)尺寸塊中的一個(gè)尺寸標(biāo)記可能與另一個(gè)尺寸塊中的尺寸標(biāo)記重疊。因此下一步就是測(cè)試所有沒(méi)有任何重疊的尺寸塊的放置是否可行。下面所講的特點(diǎn)3在解釋這個(gè)測(cè)試過(guò)程就是十分有用的。
特點(diǎn)3：在一個(gè)尺寸塊中的兩個(gè)末端構(gòu)造之間通常建立一個(gè)正確的構(gòu)造。
在特點(diǎn)3中很容易發(fā)現(xiàn)，從最低位置開始，在尺寸塊中的尺寸標(biāo)記能夠同時(shí)移動(dòng)相同的距離，以使它的尺寸標(biāo)記能夠達(dá)到它的最高位置。根據(jù)定義1，此位置的構(gòu)造是正確的，當(dāng)它的一個(gè)尺寸標(biāo)記達(dá)到了最高位置，就達(dá)到了尺寸塊的最高位置。
為了測(cè)試放置沒(méi)有重疊的所有尺寸塊的可行性，一個(gè)特征系列的所有特征首先參考按照它們特征的上升順序挑選。然后所有特征系列根據(jù)它們的第一個(gè)特征的位置按照上升順序排列。第一個(gè)尺寸塊被放置在它們最低構(gòu)造的位置。對(duì)于第二個(gè)特征系列，假如比的頂端高，尺寸塊也被放置在它們最低構(gòu)造的位置，否則在和的范圍內(nèi)放在的頂端。根據(jù)特點(diǎn)3，對(duì)于后者也是正確構(gòu)造。否則，作為正確的構(gòu)造在沒(méi)有與尺寸塊重疊的情況下也不能夠建立。對(duì)于下個(gè)尺寸塊來(lái)說(shuō)是一個(gè)重復(fù)的過(guò)程，直到所有正確的尺寸塊都已建立，否則無(wú)論對(duì)于一個(gè)尺寸塊正確的構(gòu)造不能建立的話都將中止。
4.2最優(yōu)化階段
在準(zhǔn)備階段之后，每個(gè)尺寸塊的邊緣構(gòu)造已經(jīng)建立，并且使在一個(gè)尺寸塊和兩個(gè)相鄰尺寸塊確定避免。使用一種動(dòng)態(tài)工程方法來(lái)確定每個(gè)尺寸塊最優(yōu)構(gòu)造。像上面假設(shè)一樣，根據(jù)尺寸塊的參考位置用上升順序來(lái)挑選尺寸塊。確定尺寸塊構(gòu)造的過(guò)程被分為步，i=1，2，3，……，n，在第i步確定了尺寸塊的構(gòu)造。在每個(gè)步，的每個(gè)可能構(gòu)造與其狀態(tài)相聯(lián)系。換句話說(shuō)，狀態(tài)與第i個(gè)尺寸塊的第j個(gè)構(gòu)造相聯(lián)系。選取第步的狀態(tài)，的費(fèi)用通過(guò)一個(gè)總的費(fèi)用函數(shù)來(lái)反映，它是通過(guò)下式給出：
是費(fèi)用函數(shù)用來(lái)反映：（i）在獨(dú)立的狀態(tài)和的情況在兩尺寸塊和的相互作用；（ii）尺寸塊從它缺省構(gòu)造中的偏差范圍；（iii）兩尺寸塊和之間的重疊；（iv）尺寸塊與被稱為禁區(qū)的一系列區(qū)域之間的重疊。禁區(qū)由用戶規(guī)定，并且禁區(qū)通常為由用戶放置的其他尺寸標(biāo)記的區(qū)域，因此不允許把尺寸標(biāo)記放置在遠(yuǎn)的地方。最優(yōu)的解決方法從中獲得。這個(gè)步驟系列=1，2，3，……，n使最優(yōu)化得以提高，同時(shí)這一系列構(gòu)造使尺寸標(biāo)記的放置位置得到最優(yōu)化。
4.3狀態(tài)解決方法
通過(guò)特點(diǎn)3，一個(gè)尺寸塊的兩個(gè)邊緣構(gòu)造之間的構(gòu)造是正確的構(gòu)造，因此每一步都有無(wú)數(shù)種選擇。為了使動(dòng)態(tài)工程方法起作用，必須使用離散化使無(wú)數(shù)的狀態(tài)為每個(gè)步。離散化最簡(jiǎn)單的方法是從 和的位置中提取一個(gè)合適的數(shù)字，這種方法對(duì)利用計(jì)算機(jī)資源來(lái)說(shuō)不是一個(gè)有效的方法。這是因?yàn)槌叽鐗K的范圍（由-給定）可以很大限度的改變，從式1中可以明顯的看出尺寸塊給出了一個(gè)很大的范圍，而很少值的給了一個(gè)很小的范圍。在有合適數(shù)量的狀態(tài)下，那些有較大范圍的尺寸塊會(huì)得到近似的解決方法。另一方面，對(duì)于一個(gè)有很大范圍的尺寸塊來(lái)說(shuō)，就像大多數(shù)在兩邊緣構(gòu)造的正確構(gòu)造將在它們的尺寸塊重疊。通過(guò)一個(gè)例子最好的解釋：假如在尺寸塊最高構(gòu)造的頂端高于尺寸塊最高位置構(gòu)造的底端，則尺寸塊在構(gòu)造上必然與的最高端重疊。相似的問(wèn)題在最低構(gòu)造上。因此，對(duì)于每個(gè)尺寸塊來(lái)說(shuō)，一個(gè)合適的范圍，由和之間的不同來(lái)定義：
=
=
式中和是尺寸塊和中尺寸標(biāo)記的數(shù)量且是獨(dú)立的。使用這種可行的范圍定義，那些在兩相鄰尺寸塊之間經(jīng)常導(dǎo)致重疊的構(gòu)造從可行范圍內(nèi)排除。
4.4費(fèi)用函數(shù)
一個(gè)階段的費(fèi)用和費(fèi)用函數(shù)都是矢量和矢量值函數(shù)。一個(gè)費(fèi)用矢量包括按重要性由高到低排列的5個(gè)部分，i=1，2，3，……，5。動(dòng)態(tài)的實(shí)施階段要求最小的費(fèi)用選擇，因此必須在兩矢量間進(jìn)行對(duì)比。兩個(gè)費(fèi)用函數(shù)通過(guò)比較它們的組成來(lái)比較。比較從認(rèn)為最重要的第一部分開始。假如兩矢量的第一部分相等，則比較認(rèn)為是次重要的下一部分。當(dāng)相關(guān)聯(lián)的兩部分不相等時(shí)就停止比較。在費(fèi)用矢量尖的比較是建立在不相等的第一對(duì)部件上的。
費(fèi)用函數(shù)的第一組成部分等式應(yīng)該減少相鄰兩尺寸塊和和尺寸塊和禁區(qū)之間的重疊。由下式給出：
式中如果在和之間沒(méi)有重疊=0。如果有重疊，則就是一個(gè)很大的值。費(fèi)用函數(shù)用來(lái)減少與狀態(tài)相關(guān)聯(lián)的尺寸塊和禁區(qū)之間的重疊。的所有和m認(rèn)為是與所有禁區(qū)相重疊的值。在和如果沒(méi)有重疊，則=0；如果有重疊，則就是一個(gè)很大的值。
接下來(lái)的四個(gè)等式和，是分配四個(gè)可選的亞費(fèi)用函數(shù)，這些函數(shù)根據(jù)四個(gè)不同的基準(zhǔn)通過(guò)返回值來(lái)反映構(gòu)造的。的布局與亞費(fèi)用函數(shù)由用戶確定。這就給了用戶的可行性來(lái)決定準(zhǔn)則的重要聯(lián)系。
要求尺寸塊放置在特征的中間部分能夠被測(cè)缺省構(gòu)造測(cè)量的位置，這就認(rèn)為是尺寸塊的缺省構(gòu)造。亞費(fèi)用函數(shù)是用來(lái)測(cè)量尺寸塊在它的第j個(gè)構(gòu)造處偏移的程度。這個(gè)偏移值可以從特征的平均位置上來(lái)測(cè)量，并且是第j個(gè)構(gòu)造尺寸標(biāo)記的平均位置
=
式中為尺寸塊中尺寸標(biāo)記的數(shù)量，為在第j個(gè)構(gòu)造上尺寸標(biāo)記的位置，為特征的位置。和是所有尺寸標(biāo)記和特征的數(shù)量。
在只被用作亞費(fèi)用函數(shù)的時(shí)候，不能通過(guò)費(fèi)用函數(shù)來(lái)確定。因?yàn)樵诿績(jī)蓚€(gè)狀態(tài)下偏移的數(shù)是確定的費(fèi)用函數(shù)是僅建立在能夠給出相同費(fèi)用的可選費(fèi)用函數(shù)上的，可以忽略這個(gè)問(wèn)題?？梢苑峙涞搅硪粋€(gè)可以給出一個(gè)較低狀態(tài)費(fèi)用函數(shù)的部件等式。假如尺寸塊在狀態(tài)時(shí)不在它的缺省狀態(tài)，取1，否則取0。
可能要求由用戶規(guī)定一個(gè)可行范圍的百分比來(lái)限制尺寸塊由缺省位置偏移的范圍。亞費(fèi)用函數(shù)是用來(lái)減少過(guò)大的偏移。假如>p×︳YFmaxi ?YFmin ︳，則的值為1，否則為0。
當(dāng)兩個(gè)相鄰尺寸塊在它們的缺省位置重疊，某個(gè)值a，則在此重疊中向上移動(dòng)距離為，并且向下移動(dòng)到，距離為，其中+=。其中要求=。這就要求兩尺寸塊移動(dòng)量相等。亞費(fèi)用函數(shù)不能達(dá)到這個(gè)目的，因?yàn)檫@僅是測(cè)量移動(dòng)值不是相鄰尺寸塊移動(dòng)值的分配。則要求兩相鄰尺寸塊的移動(dòng)值相等。在兩相鄰尺寸塊移動(dòng)值的范圍通過(guò)下式設(shè)置不同值：
這四個(gè)可選的亞費(fèi)用函數(shù)可以由用戶自由的選擇，安排第二到第五部分來(lái)達(dá)到目的。在下一部分中，通過(guò)例子來(lái)說(shuō)明選擇不同的亞費(fèi)用函數(shù)達(dá)到不同的結(jié)束。
5.實(shí)例說(shuō)明
合適的最優(yōu)化方法已經(jīng)被執(zhí)行，并且通過(guò)API插入到UG2系統(tǒng)中。為了說(shuō)明亞費(fèi)用函數(shù)的作用，思考圖6中的作用。圖6中有5個(gè)尺寸塊，所有尺寸塊都處于它們的缺省構(gòu)造，并且在和之間，和
DOI 10 1007 s00170 004 2374 2 ORIGINAL ARTICLE Int J Adv Manuf Technol 2006 28 370 378 C L Li K M Yu Y H Lee Automatic datum dimensioning for plastic injection mould design and manufacturing Received 7 May 2004 Accepted 10 August 2004 Published online 20 April 2005 Springer Verlag London Limited 2005 Abstract Datum dimensioning or ordinate dimensioning tech nique is very popular in plastic injection mould drawings where the location dimensions of a large number of hole features must be specified in the drawings of the mould plates Although com mercial CAD CAM systems provide semi automatic tools to as sist the designer in the dimensioning process it is still a very tedious process as the user has to specify the location of each di mension tag This paper reports a completely automatic method where optimal placements of the dimension tags can be deter mined The method employs dynamic programming technique to optimize the dimension process with respect to several criteria that can be selected by the user The method has been imple mented and incorporated into a commercial CAD CAM system and examples are given to illustrate the important features of the program Keywords Automatic dimensioning Datum dimensioning Dynamic programming Optimal dimensioning Ordinate dimensioning 1 Introduction CAD CAM systems are now widely used in the plastic injec tion mould making industry Many companies are using a solid modeling system to design the injection mould They use a CAD system to model not only the core and cavity inserts of the mould which are the most important components that form the im pression of the mould but also all other components in the C L Li a117 Y H L e e Department of Manufacturing Engineering and Engineering Management City University of Hong Kong Tat Chee Avenue Kowloon Hong Kong E mail meclli cityu edu hk Tel 8 52 27888432 Fax 8 52 27888423 K M Yu Department of Industrial and Systems Engineering The Hong Kong Polytechnic University entire mould assembly With the advance in Internet technology and the recent development of Internet enabled CAD the de sign information of the injection mould can be communicated electronically between the product engineer who designs the plastic part and the tooling engineer who designs the injection mould even though they may be located in different geographic regions of the world While flow of design information between product design and tooling design are communicated effectively through an electronic means the communication of manufac turing information to the shop floor is done by both electronic and traditional techniques Computer Numerical Control CNC machining toolpath or inspection instructions can be generated directly from the CAD CAM system and downloaded through a network to the CNC controller for the machining or inspection operations However set up instructions for a particular machin ing job may be specified in an engineering drawing Moreover not all machining tasks are done using CNC machine tools Some traditional machining processes such as drilling and grinding are done using conventional machine tools because of cost con sideration Conventional engineering drawings are thus still play ing an important role in communicating engineering information to the shop floor The orthographic projections in engineering drawings can be generated automatically from the CAD model of the parts Automatic tools for dimensioning of the parts are also provided by many commercial CAD systems However as pointed out by Chen et al 1 those automatic dimensioning tools are not able to generate dimensions according to the draw ing standards and engineering practices adopted in the shop floor In the specific application of injection mould design datum dimensioning or ordinate dimensioning of hole features are used extensively Figure 1 shows a typical detail drawing that can be found on the shop floor of a mould making company Shown in the figure are the hole features and datum dimensions which are used to specify the locations of the holes It can be seen that the dimensions are very crowded and it is a tedious task to manually adjust the placement of all the datum dimensions The quality of the final fully dimensioned drawing thus depends very much on the experience of the draftsman who produces the draw ing The purpose of this research is to develop a tool that can 371 Fig 1 Use of datum dimensioning in a drawing of a plastic injection mould part generate the datum dimensions automatically from a given part of the injection mould The resulting dimensions must satisfy two obvious requirements first that no two dimension tags may overlap and second that a dimension tag be placed as close as possible to the feature being dimensioned The key issue in this research is to develop a method that can optimize the placement of the datum dimensions 2 Related work While dimensioning and tolerancing are two closely related pro cesses in specifying the size and location information of the features in a mechanical part or an assembly most of the past research work has focused on tolerancing The major research issues in tolerancing are representation analysis and synthesis Tolerancing representation is concerned with the incorporation of tolerance information into a product modeling scheme Exam ples include the solid offset approach developed by Requicha 2 the feasibility space approach proposed by Turner 3 and the TTRS by Desrochers and Clement 4 More detailed review can be found in Roy et al 5 and Yu et al 6 Tolerance analy sis aims to determine the combined effect of part tolerances on the assembly tolerance It can be used to verify the functional ity of a design given known or assumed variations of individual part dimensions Examples of technique in tolerance analysis in clude Monte Carlo simulation 7 and the direct linearization method 8 The main objective of tolerance synthesis or tol erance allocation is to allocate part tolerances based on given functional requirements of the assembly Recently Islam 9 re ported a concurrent engineering approach to address this prob lem Based on a systemic analysis of the functional requirements from different customer requirements and the technical require ments from engineering considerations a methodology for ex tracting dimensional requirements is developed A software pro totype FDT 10 is also developed for supporting the implemen tation of the methodology FDT provides tools for representing the functional requirements dimensions tolerances and process capability into a functional requirement dimensions matrix The functional equations captured in the matrix are then separated into groups and each group is then solved using a solution strat egy specific to the functional requirement and the tolerancing problem involved More detailed review in tolerance analysis and synthesis can be found in Roy et al 5 Ngoi and Ong 11 and Hong and Chang 12 Several methods have been developed for generating dimen sions automatically from the CAD model of a part Yuen et al 13 reported an early attempt in automatic dimensioning of parts represented in Constructive Solid Geometry CSG solid modeling technique Points from planar faces and axes of cylin ders are extracted from the solid model The coordinates of the points are arranged in a tree structure to generate linear dimen sions in the three principal directions A simple technique for diametric and radial dimensions was also reported Other early works in automatic dimensioning have been summarized by Yu et al 6 Recently Chen et al 1 14 reported a more in depth study of automatic dimensioning Their method analyzed di mension redundancy determined dimensioning schemes that are specific to feature patterns selected appropriate views for spec ifying the dimension and determined the appropriate location of the dimension using an expert system approach 15 The ex pert system analyses the geometry and topology of the feature to be dimensioned and determined a position for placing the dimension based on a set of rules that is relevant to the cur rent dimensioning feature With the placement of one dimension a forbidden region is constructed so that all subsequent dimen sions will not be placed in this region This avoids overlap or intersection between two dimensions 372 A limitation in the existing approach for the placement of the dimension is due to the sequential nature of the method For example in Chen s 1 14 method the features to be dimen sioned are prioritized and the positions of the dimensions are determined one after another The approach is not appropriate for determining the placement of datum dimensions especially when the dimensions are very crowded as in the case of injection mould plates This is because the placement of one datum di mension may have an effect on the placement of another dimen sion that may be located far away from the current dimension This paper reports our work in solving the placement problem in datum dimensioning The major contribution of our work is the development of a new method that determines the optimal placement of each datum dimension Using the dynamic pro gramming approach to optimization this new method overcomes the limitation of the sequential approach used in the existing method 3 Basic characteristic of datum dimensioning In datum dimensioning the location of a feature is specified by the horizontal and vertical distances from the reference lo cation of the feature and a reference datum The default form of datum dimension is shown in Fig 2a When the vertical dis tance between two features to be dimensioned is less than the dimension tag size i e the sum of the dimension text height and the minimum spacing between adjacent dimension texts Fig 2 Basic characteristics of datum dimensioning the alternative forms shown in Fig 2b are required 1 The di mension tags are shifted upward or downward from the default location to prevent overlap As shown in Fig 2c the shifting of the dimension tag is achieved by breaking the single exten sion line of the dimension into three segments two horizontal segments which are connected by one inclined segment The ex tent to which a dimension tag can be shifted is governed by three parameters i the dogleg angle which is the angle be tween the inclined segment and the horizontal segments of the dimension line ii the margin distance m between the dimen sion text and the part boundary and iii the location x f i y f i of the feature f i The two extreme positions i e the uppermost pos ition y max i and lowermost position y min i of the dimension tag are given by y max i y f i x f i m tan y min i y f i x f i m tan 1 4 Automatic datum dimension The objective of the automatic datum dimensioning system is to find an optimal position for each datum dimension The process consists of two phases of operation the preparation phase and the optimization phase In the preparation phase major param eters that facilitate the optimization process will be established Feasibility for placing the dimensions for all the features using the given dogleg angle margin offset and dimension tag size will also be tested In the optimization phase a dynamic pro gramming approach is used The dimension tag locations can be optimized with respect to different sets of criteria including the minimization of the shift of every dimension from their default locations or maximization of the use of the default form as much as possible 4 1 The preparation phase The features to be dimensioned are first grouped into one or more feature sets For each feature in a feature set there exist at least one other feature in the set such that the vertical dis tance between them is less than the dimension tag size In other words the features in a feature set cannot be dimensioned using the default form exclusively without overlap between adjacent dimension tags Instead at most one feature can use the de fault form while all others require the use of the alternative form The set of dimension tags associated with a feature set is called a dimension block The configuration of a dimension block refers to the forms and locations of each datum dimen sion within the dimension block For each position of a dimen sion block its configuration is uniquely defined Figure 3 shows two feature sets and their dimension blocks at two different configurations 1 To simplify the explanation of the technique only vertical dimensions placed on the left hand side of the part are discussed The method developed is general and can be applied to the other sides of the part 373 Fig 3 Feature sets and different con figurations of dimension blocks Definition 1 Validity of a configuration A configuration of a di mension block is valid if there is no overlap between any dimen sion tags in the dimension block and each dimension tag lies within its extreme positions The configurations of the dimension blocks shown in Fig 3b are valid Two examples of invalid configuration are shown in Fig 4 The configuration shown in Fig 4a is invalid because two of the dimension tags overlap For the configuration shown in Fig 4b the extension line of the dimension tag 14 00 is at its lowermost position while the required position for the dimen sion tag is beyond this lowermost position Fig 4 Invalid configurations of a dimension block Fig 5 Dimension block at extreme configurations Definition 2 Extreme configurations There are two extreme configurations the uppermost and lowermost configurations A dimension block is at its uppermost lowermost configuration if the dimension block is valid and is at a position such that any other higher lower position results in an invalid configuration The extreme configurations of a dimension block d i are denoted by Y max i and Y min i Figure 5a shows a dimension block at its uppermost config uration It cannot move further upward because the dimension tag 29 5 is at its highest position Figure 5b shows a dimen sion block at its lowermost configuration It cannot move fur 374 ther downward because the dimension tag 14 00 is at its lowest position The extreme configurations of a dimension block are the two important parameters that will be used by the optimization pro cess They are also useful in testing whether it is feasible to dimension all the features without any overlap between the di mension tags It is observed that two properties are useful in developing a method to determine the extreme configurations Property 1 For a dimension block at its uppermost lowermost configuration at least one of its dimension tags is at its upper most lowermost position Property 2 A dimension block has a valid configuration if and only if it has extreme configurations Property 1 can be proved by contradiction Assume that a di mension block is at its uppermost lowermost configuration and none of its dimension tags are at their uppermost lowermost positions Since all the dimension tags are not at their uppermost lowermost positions they can all be moved upwards down wards simultaneously by the same amount until any one of them reaches its uppermost lowermost position As all dimension tags are moved simultaneously by the same amount the dimen sion tags do not overlap and thus the resulting configuration is still valid and at a higher lower position than its original configuration This violates the assumption that the original con figuration is the uppermost lowermost configuration Property 2 can be verified directly Given a valid configura tion the dimension block is moved upward downward until one or more of its dimension tags reach its uppermost lowermost position Since all the dimension tags are moved simultaneously by the same amount overlap does not occur Moreover the di mension block cannot be moved upwards downwards any fur ther without invalidating the configuration because at least one of its dimension tags is at its uppermost lowermost position According to Definition 2 the resulting configuration is thus the uppermost lowermost configuration On the other hand it is ob vious that if a dimension block has extreme configurations then it has a valid configuration because the extreme configurations are by definition valid Property 1 indicates that the extreme configurations of a di mension block can be obtained by investigating the extreme pos itions of the dimension tags in the block The configuration of a dimension block can be specified by y i i 1 2 n where y i is the location of the dimension tag of the ith feature in the feature set f i Thisassumesthat f i are arranged in ascend ing order by their vertical positions i e y f i y f j if i j Then to avoid overlap between dimension tags the location of the ith dimension tag is given by y i i 1 SIZE y 1 n i 2 2 where SIZE is the dimension tag size and y 1 is the location of the dimension tag for the first feature f 1 oftheset y 1 is also used as the reference location of the dimension block For a configuration to be valid all dimension tags must lie below its own uppermost position given by Eq 1 That is y max i y i and thus y max i i 1 SIZE y 1 The above relationship must be satisfied by all i Therefore the highest allowable value for y 1 is given by Min i y max i i 1 SIZE 3 with the y 1 value given by Eq 2 and one or more y i equal to y max i All other y i are less than its y max i Since no other larger value of y 1 results in a configuration that satisfies y max i y i the resulting configuration if valid is the uppermost configuration However it is possible that at this configuration some of the y i given by Eq 2 is less than y min i Therefore a check is performed for each y i Ify i y min i for all i then the uppermost configura tion is found If y i i Y max j SIZE n i YF min i Max Y min i Max i j 1 Y min j SIZE n j where n i and n j are the number of dimension tags in dimension blocks d i and d j respectively Using this definition of the feas ible range those configurations that always cause overlap with adjacent dimension blocks are excluded from the feasible range A fixed resolution say 0 5 mm is specified and the number of states for a given stage is obtained by dividing the feasible range by the given resolution 4 4 Cost functions The overall cost of a stage and the cost function C i t i j t i 1 k are vector and vector valued functions respectively A cost vec tor consists of five components c i i 1 5arrangedinde scending order of importance That is c i is considered more important than c j if i p vextendsingle vextendsingle YF max i YF min i vextendsingle vextendsingle and is set to zero otherwise When two adjacent dimension blocks at their default loca tions overlap for a certain amount a the overlap can be removed by shifting d i upwards by a i and shifting d i 1 downwards by a i 1 such that a i a i 1 a It may be desirable that a i a i 1 That is the required total shift is being shared equally between two dimension blocks The sub cost function D V t i j is not able to achieve this purpose because it only measures the total shift amount and not the distribution of the amount between adjacent dimension blocks D E t i j is devised to equalize the amount of shift between adjacent dimension blocks It is set to the differ ence between the extent of deviations of the adjacent dimension blocks D E t i j t i 1 k D V t i j D V t i 1 k The four optional sub cost functions are freely selected and assigned to the second to fifth cost components by the user to achieve different objectives In the next section examples are given to illustrate the different results obtained by choosing dif ferent optional sub cost functions 5 Illustrative examples The proposed optimization method has been implemented using C and incorporated into the Unigraphics II CAD CAM system through its Application Program Interface API To illustrate the effects of the sub cost functions consider the example illustrated in Fig 6 There are five dimension blocks in the figure All the dimension blocks are at their default configuration