呼機(jī)上蓋的塑件注射模具設(shè)計【一模兩腔】【側(cè)抽芯】【說明書+CAD】

呼機(jī)上蓋的塑件注射模具設(shè)計【一模兩腔】【側(cè)抽芯】【說明書+CAD】,一模兩腔,側(cè)抽芯,說明書+CAD,呼機(jī)上蓋的塑件注射模具設(shè)計【一模兩腔】【側(cè)抽芯】【說明書+CAD】,呼機(jī),注射,模具設(shè)計,說明書,仿單,cad 畢業(yè)設(shè)計用紙摘 要本次畢業(yè)設(shè)計的題目是：呼機(jī)上蓋的塑件注射模。本次設(shè)計主要是通過對塑件的形狀、尺寸及其精度的要求來進(jìn)行注射成型工藝的可行性分析。塑件的成型工藝性主要包括塑件的壁厚，斜度和圓角以及是否有抽芯機(jī)構(gòu)。通過以上的分析來確定模具分型面、型腔數(shù)目、澆口形式、位置大小；其中最重要的是確定型芯和型腔的結(jié)構(gòu)，例如是采用整體式還是鑲拼式，以及它們的定位和固緊方式。此外還分析了模具受力，脫模機(jī)構(gòu)的設(shè)計，合模導(dǎo)向機(jī)構(gòu)的設(shè)計，冷卻系統(tǒng)的設(shè)計等。最后繪制完整的模具裝配總圖和主要的模具零件土及編制成型零部件的制造加工工藝過程卡片。關(guān)鍵詞：分型面、澆口、型腔，型芯，鑲塊，脫摸力,潛伏澆口。ABSTRACTThis graduate that design is:The piece that shout the on board cap injects the mold.This design primarily passeses to piece viability assessment for request for of shape, size and its accuracy coming proceeding injecting type craft.the piece the wall for of type craft primarily including the piece is thick, slope and circle angle and whether to have core-pulling or not mechanism.Pass the above analysis to come the certain molding tool cent the type the surface, type the number, gate the form, place the size;The among them and most important is a certain type core and the construction of the type , for example adopt the whole the type of type still , and their fixed position and tight way of .In addition and still analyzed the molding tool to suffer force, mold that design that the design of the pattern draw mechanism, match the design etc. to lead to the mechanism, cooling system.Finally draw the production that complete molding tool assemble the general drawing sum the soil and establishment of prinipal molding tool parts type zero the parts process the craft process the card.Keywords: parting line,the gate, cavity,core,mold insert,ejection force,submarinegate. 目 錄摘要1ABSTRACT2目 錄3前 言5概 論6第一章 塑件分析6第二章 塑件材料的成型特性與工藝參數(shù)7第一節(jié) 塑件材料的特性7第二節(jié) 成型特性7第三節(jié) 工藝參數(shù)8第四節(jié) 塑料制件的結(jié)構(gòu)工藝性8第五節(jié) 塑件在模具中的位置9第三章 設(shè)備的選擇10第一節(jié) 最大注射量10第二節(jié) 注射量校核10第三節(jié) 塑件在分型面上的投影面積與鎖模力的校核11第四節(jié) 注射壓力的校核11第五節(jié) 開模行程的校核11第六節(jié) 注射機(jī)的技術(shù)規(guī)格11第四章 澆注系統(tǒng)的設(shè)計12第一節(jié) 澆注系統(tǒng)的功能闡述12第二節(jié) 主流道的設(shè)計12第三節(jié) 分流道的設(shè)計13第四節(jié) 澆口形式的選擇13第五節(jié) 冷料穴的設(shè)計14第六節(jié) 排溢系統(tǒng)的設(shè)計14第七節(jié) 模架組合的選擇15第五章 成型零件工作部分尺寸的計算15第一節(jié) 成型零件的結(jié)構(gòu)設(shè)計15第二節(jié) 成型工作零件的工作尺寸15第三節(jié) 模具型腔側(cè)壁和底板的厚度的計算19第六章 推出機(jī)構(gòu)與復(fù)位機(jī)構(gòu)20第一節(jié) 推出機(jī)構(gòu)的組成20第二節(jié) 推出機(jī)構(gòu)的設(shè)計原則20第三節(jié) 簡單推出機(jī)構(gòu)21第七章 合模導(dǎo)向機(jī)構(gòu)的設(shè)計23第八章 冷卻系統(tǒng)的設(shè)計24總結(jié)25致 謝26參 考 文 獻(xiàn)26前 言一、本次設(shè)計的任務(wù)本次的設(shè)計是畢業(yè)生的最后一次課程設(shè)計，是我們對以前所學(xué)的理論知識和技能的一次綜合性訓(xùn)練。模具設(shè)計是一項很復(fù)雜的工作，它要求我們在掌握理論知識的基礎(chǔ)上要有更好的實踐經(jīng)驗。設(shè)計一付好的模具，其中牽涉到許多的內(nèi)容，一套模具有好多種方案，在進(jìn)行的比較中需要考慮的內(nèi)容包括對塑件成型工藝的分析，如何確定分型面、型腔數(shù)目以及選擇注射機(jī)型號。確定模具的總體結(jié)構(gòu)、型腔型芯的結(jié)構(gòu)，同時還考慮了模具制造工藝的可行性以及模具制造的經(jīng)濟(jì)性；澆注系統(tǒng)的設(shè)計，確定澆口形式及位置大??；確定主流道，分流道和冷料穴的形式及尺寸；脫模機(jī)構(gòu)的設(shè)計，脫模力的計算；側(cè)向分型及抽芯機(jī)構(gòu)的設(shè)計，導(dǎo)向機(jī)構(gòu)的設(shè)計，冷卻系統(tǒng)的設(shè)計。二、設(shè)計要求1、在設(shè)計過程中要理論聯(lián)系實際，扎實的掌握理論基礎(chǔ)知識，以便靈活應(yīng)用解決實際問題。2、在設(shè)計過程中要不斷地修改，擬定幾種方案以便進(jìn)行比較，在保證塑件使用要求和外觀精度的基礎(chǔ)上盡量采用簡單的模具結(jié)構(gòu)。3、在設(shè)計過程中要不斷地查取有關(guān)的設(shè)計資料，在努力采用以前的模具結(jié)構(gòu)的基礎(chǔ)上要進(jìn)行大膽的修改，以便設(shè)計出有新穎的模具。、4、設(shè)計中遇到的問題要多與指導(dǎo)老師交流，要合理、認(rèn)真、獨立地完成。 5、設(shè)計中應(yīng)盡量采用標(biāo)準(zhǔn)件，這樣就可以減少模具的制造難度。.概 論模具是工業(yè)生產(chǎn)中的重要工藝裝備模具工業(yè)是國民經(jīng)各部門發(fā)展的重要基礎(chǔ)之一。塑料模具是指用于成型塑料制件的模具，它是型腔模的一種類型。模具設(shè)計水平的高低、加工設(shè)備的好壞、制造力量的強弱模具質(zhì)量的優(yōu)劣，直接影響著許多新產(chǎn)品的開發(fā)和老產(chǎn)品的更新?lián)Q代，影響著產(chǎn)品質(zhì)量和經(jīng)濟(jì)效益的提高。在現(xiàn)代塑料制件的生產(chǎn)中，采用合理的加工工藝，高效設(shè)備，先進(jìn)的模具。塑料成型技術(shù)的發(fā)展趨勢是：一、模具的標(biāo)準(zhǔn)化1.為了適應(yīng)大規(guī)模成批生產(chǎn)塑料成型模具和縮短模具制造周期的需要，模具的標(biāo)準(zhǔn)化工作十分重要。二、模具加工技術(shù)的革新。1.為了提高加工精度，縮短模具制造周期，塑料模成型零件加工廣泛應(yīng)用仿行加工，電加工，數(shù)控加工及微機(jī)控制加工等先進(jìn)技術(shù)，并使用坐標(biāo)鏜，坐標(biāo)磨和三坐標(biāo)測量儀等精密加工與測量設(shè)備。三、各種新材料的研制和應(yīng)用。1.模具材料影響模具加工成本使用壽命和塑件成型質(zhì)量等。四、CAD/CAM/CAE技術(shù)的應(yīng)用。 第一章 塑件分析參看產(chǎn)品零件圖如（圖1）圖1 呼機(jī)上蓋 從零件圖來看，塑件的外表面精度要求較高，而內(nèi)表面的精度要求一般，由于是采用上下蓋配合而成，從而避免了側(cè)向凹凸，簡化了模具結(jié)構(gòu)。塑件的四個角和各側(cè)面采用了圓角過渡，這樣使塑件的外觀變得更加圓滑，而且可避免在尖角處產(chǎn)生應(yīng)力集中或在脫摸過程中由于成型內(nèi)應(yīng)力而開裂。綜合以上各點分析，采用一模兩件，以提高生產(chǎn)率和降低制造成本。第二章 塑件材料的成型特性與工藝參數(shù)本章著重介紹塑料成型的工藝特點以及塑件的工藝要求，塑件結(jié)構(gòu)設(shè)計方面的知識。為后面幾章的模具設(shè)計奠定了基礎(chǔ)。對零件的分析得塑件材料取ABS（丙烯腈-丁二-苯乙烯共聚物）。第一節(jié) 塑件材料的特性 ABS是由丙烯腈、丁二烯、苯乙烯共聚而成的。這三種組分的各自特性使ABS具有良好的性能。ABS無毒、無味，呈微黃色，成型的塑件有較好的光澤。密度為1.021.05g/cm. ABS有極好的抗沖擊強度，且再低溫下也不迅速下降。有良好的機(jī)械強度和一定的耐磨性、耐寒性、耐油性、耐水性、化學(xué)穩(wěn)定性和電器性能。 ABS在機(jī)械工業(yè)上用來制造齒輪、泵葉輪、軸承、把手、管道、電機(jī)外殼、儀表殼、儀器盤、水箱外殼等。ABS還用來制作水表殼、紡織器材、電器零件、文教用品、玩具、電子琴及收錄機(jī)殼體、食品包裝容器、農(nóng)藥噴霧器及家具等。第二節(jié) 成型特性ABS在升溫是粘度增高，所以成型壓力較高，塑料上的脫模斜度宜稍大；ABS易吸水，成型加工前應(yīng)進(jìn)行干燥處理；易產(chǎn)生熔接痕，模具設(shè)計是應(yīng)注意盡量減小澆注系統(tǒng)對料流的阻力；在正常的成型條件下，壁厚、熔料溫度及收縮率影響極小。要求塑件精度高時，模具溫度可控制在5060，要求塑件光澤和耐熱時，應(yīng)控制在6080。第三節(jié) 工藝參數(shù)塑料性能ABS（苯乙烯共聚）塑料性能ABS（苯乙烯共聚）屈服強度 /Mpa50玻璃化溫度 /拉伸強度 /Mpa38熔點（粘流溫度） /130160斷裂伸長率 /%35熱變形溫度/45 N/cm108 N/cm90108拉伸彈性模量 /Gpa1.883103彎曲強度 /Mpa80線膨脹系數(shù)/（105/）7.0彎曲彈性模量 /Gpa1.4比熱容/J/(kgK)1470簡支架沖擊強度/（kJ/m） 無缺口缺口261熱導(dǎo)率/W/(mK)0.26311燃燒性/(cm/min)慢氏硬度HBS9.7 R121體積電阻/cm6.910密度/（g/cm）1.021.16擊穿電壓/(Kv/mm)比體積/(cm/g)1.021.16成型收縮率/%0.40.7吸水性 /% （24h） 長時間0.20.4拉伸模量E/101.911.98泊松比0.38透明度或透光率不透明與鋼的摩擦因子f0.200.25 第四節(jié) 塑料制件的結(jié)構(gòu)工藝性 要想獲得合格的塑料制件，除選擇合理的塑件材料外，還必須考慮塑件的結(jié)構(gòu)工藝性。塑件的 結(jié)構(gòu)工藝性與模具設(shè)計有直接關(guān)系，只有塑件設(shè)計滿足成型工藝要求， 才能設(shè)計出合理的模具結(jié)構(gòu)。一、 尺寸及精度塑件尺寸的大小取決于塑料的流動性。在注射成型華中，薄壁塑件的尺寸不能設(shè)計的過大。塑件的尺寸精度是指所獲得的塑件尺寸與產(chǎn)品圖中尺寸的符合程度，及所獲得塑件尺寸的準(zhǔn)確度。根據(jù)本次設(shè)計的要求，結(jié)合表3-9（參一）初步選定該零件的三個表面的精度分別為4、5、6級。二、 表面粗糙度塑件的外觀要求越高，表面粗糙度應(yīng)越低。一般模具表面粗糙度,要比塑件的要求低1-2級。塑件的表面粗糙度一般為Ra0.8-0.2um。三、 形狀塑件的內(nèi)外表面形狀應(yīng)盡可能保證有利于成型。四、 斜度為了便于從塑件中抽出型心或從型腔中脫出塑件，防止脫模時拉傷塑件，在設(shè)計時必須使塑件內(nèi)外表面沿脫模方向留有足夠的斜度，由于本次設(shè)計所選材料為ABS，內(nèi)外表面均取拔模斜度為1度。五、 壁厚塑件的壁厚對塑件的質(zhì)量有很大的影響，塑件壁厚盡可能均勻。本次設(shè)計的壁厚非均勻，盡量保證兩側(cè)均勻，且滿足塑件的最小壁厚。六、 圓角塑件除了使用上要求采用尖角外，其余所有轉(zhuǎn)角處均應(yīng)盡可能采用圓角過渡，本設(shè)計未注圓角處均為R3。第五節(jié) 塑件在模具中的位置一、 型腔數(shù)量及排列方式塑件的設(shè)計已完成，根據(jù)塑件品種，形狀及尺寸分析，塑件的材料、形狀尺寸于澆口的位置和形狀有關(guān)，同時也對分型面和脫模位置有影響，此外質(zhì)量控制要求，塑件的成本，注射機(jī)技術(shù)規(guī)范對型腔均有影響。本次設(shè)計初步選定型腔數(shù)目為2個，采用平衡式布局，可直接達(dá)到各個型腔均衡進(jìn)料的目的。二、分型面的設(shè)計 1、分型面設(shè)在零件開口最大輪廓處2、分型面設(shè)在零件 開口處以使塑件開模以后留在動模。便于順利脫模3、在分型面上設(shè)有1度的拔模斜度，可以保證塑件外觀質(zhì)量和塑件精度要求 第三章 設(shè)備的選擇第一節(jié) 最大注射量一次設(shè)計先確定型腔數(shù)目，然后根據(jù)生產(chǎn)條件，如注射機(jī)的有關(guān)技術(shù)規(guī)范進(jìn)行校核。據(jù)4-2（參1）n=KmK注射機(jī)最大注射量的利用系數(shù)，一般K=0.8M注射機(jī)額定塑化量（g/h）M2澆注系統(tǒng)所需塑料的質(zhì)量或體積（g）Mn注射機(jī)允許的最大注射量本次設(shè)計采用UG進(jìn)行三維造型，利用實體測得M1=10g所以 2（0.8Mn-2）/10Mn27.5g初步選定注射機(jī)為XSZ60 （見表4-1）第二節(jié) 注射量校核 nm1+m20.8m (參1，4-4)m27.5m 注射機(jī)的最大注射量（g 或cm3 第三節(jié) 塑件在分型面上的投影面積與鎖模力的校核 （n*A1+A2）F (參1 46)A2澆注系統(tǒng)在分型面上的投影面積A1單個塑件在模具分型面上的投影面積F注射機(jī)額定鎖模力P塑料熔體對型腔成型壓力，其大小一般為注射壓力的80%經(jīng)校核，注射機(jī)額定鎖模力已足夠，不會發(fā)生漲模溢料的現(xiàn)象。第四節(jié) 注射壓力的校核 塑件材料為ABS，注射壓力一般為7090，取80KN，而注射機(jī)額定壓力為122，注射機(jī)最大注射壓力能滿足塑件成型的要求。第五節(jié) 開模行程的校核 SH1+H2+(510)H1推出距離（mm）H2包括澆注系統(tǒng)凝料在內(nèi)的塑件高度（mm）S15+50+10=75（mm）而XZS60 的最大開模距離為180mm 故開模距離滿足要求第六節(jié) 注射機(jī)的技術(shù)規(guī)格注射機(jī)技術(shù)規(guī)格為：額定注射量cm： 60螺桿直徑mm： 38注射壓力MPa： 122注射行程mm： 170合模力KN: 500最大成型面積cm：130最大開模行程mm：160模具最大厚度mm：200模具最小厚度mm：70動模固定板尺寸mm：330440第四章 澆注系統(tǒng)的設(shè)計第一節(jié) 澆注系統(tǒng)的功能闡述澆注系統(tǒng)是熔體從注射機(jī)噴嘴射出后到達(dá)型腔之前在模具中流經(jīng)的通道，澆注系統(tǒng)的設(shè)計是注射模具設(shè)計的一個重要環(huán)節(jié)，它對獲得優(yōu)良性能和理想外觀的塑料制件以及最佳的成型效率有直接的影響，是模具設(shè)計者十分重視的技術(shù)問題。 澆注系統(tǒng)分為普通流道的澆注系統(tǒng)和熱流道的澆注系統(tǒng)，前者較為常用， 一般由主流道、分流道、澆口和冷料穴等四部分組成。它的主要作用為將來自注射機(jī)噴嘴的塑料熔體均勻而平穩(wěn)地輸送到型腔，同時使型腔內(nèi)的氣體能及時順利地排出。在塑件熔體填充及凝固的過程中，將注射壓力有效地傳遞到型腔的各個部位，以獲得形狀完整，內(nèi)外在質(zhì)量優(yōu)良的塑料制件。第二節(jié) 主流道的設(shè)計主流道是澆注系統(tǒng)中從注射機(jī)噴嘴與模具相接觸的部位開始到分流道為止的塑料熔體的流動通道。在臥式注射機(jī)上使用的模具中，主流道垂直于分型面，為使凝料能從其中順利拔出，需設(shè)計成圓錐形，錐角為26，表面粗糙度為Ra0.8um 主流道的尺寸為： d=注射機(jī)噴嘴直徑+1=5mm SR=噴嘴球面直徑+1=15mm h=35 a=2 L=60mm D=10mm如圖：主流道襯套與定位圈設(shè)計成整體式。第三節(jié) 分流道的設(shè)計 由于所設(shè)置的模具為一模四件，屬于多型腔模具，應(yīng)設(shè)置分流道，分流道是指主流道末斷與澆口之間這一段塑料熔體的流動通道，所選分流道為半圓形分流道，直徑為6。第四節(jié) 澆口形式的選擇 澆口是連接分流道與型腔的一段細(xì)短通道，它是澆注系統(tǒng)的關(guān)鍵部分，澆口形狀、數(shù)量、尺寸和位置對塑件 的質(zhì)量影響很大。澆口主要有兩個作用：一是塑料熔體流徑的通道；二是澆口的適時凝固可控制保壓時間。由于塑件的外觀質(zhì)量要求較高，所以澆口本身設(shè)在模具內(nèi)的隱蔽處，塑料熔體通過型腔側(cè)面斜向注入型腔，因而塑件外表不受損傷，不致因澆口痕跡而影響塑件的表面質(zhì)量及美觀效果第五節(jié) 冷料穴的設(shè)計 冷料穴一般位于主流道對面的動模板上，或處于分流道的末端。其作用是存放料流前端的“冷料”，防止冷料進(jìn)入型腔而形成冷接縫。開模時又能將主流道中的凝料拉出。并采用與推桿匹配的冷料穴。這里采用Z字的冷料穴。這樣在開摸時推桿將澆注系統(tǒng)凝料推出模外。推料桿和冷料穴的具體形式如圖 所示: 第六節(jié) 排溢系統(tǒng)的設(shè)計當(dāng)塑料熔體填充型腔時，如果型腔內(nèi)的氣體因各種原因不被排除干凈的話，一方面將會在塑件上形成氣泡、接縫、表面輪廓不清等成型缺陷，另一方面氣體受壓，體積縮小而產(chǎn)生高溫會導(dǎo)致塑件局部表面炭化，同時積存的氣體還會產(chǎn)生反向壓力而降低充模速度，因此設(shè)計型腔時必須考慮排氣問題。 此塑件可以利用拉料桿，推件桿等利用間隙排氣。第七節(jié) 模架組合的選擇根據(jù)注射機(jī)固定模板尺寸和各項工藝參數(shù)，以及塑件尺寸形狀凸凹模尺寸的計算，注射模架選取基本型A2（見參2 表2-95），定模和動模均 由兩快模板組成，推桿推出塑件。注射模中小型模架組合選為 250250第五章 成型零件工作部分尺寸的計算第一節(jié) 成型零件的結(jié)構(gòu)設(shè)計凹模是成型塑件外表面的主要零件，本次設(shè)計采用組合式型腔，并采用整體嵌入式凹模。小型塑件用多型腔模具成型時，各單個凹模采用機(jī)械加工、冷擠壓3、電加工等方法加工制成，然后壓入模板中，這種結(jié)構(gòu)加工效率高，裝拆方便，可以保證各個型腔形狀、尺寸一致。 凸模和型心均是成型塑件內(nèi)表面的零件，凸模又稱主型芯。在一般模具中采用將型芯單獨加工，在鑲?cè)肽０逯?，為了便于加工，形狀?fù)雜的型芯往往采用鑲拼式結(jié)構(gòu)。小型芯成型塑件上的小孔或槽，小型芯單獨制造，在嵌入模板中。第二節(jié) 成型工作零件的工作尺寸成型零件工作尺寸是指成型零件上直接用來構(gòu)成塑件的尺寸，主要有型腔和型芯的徑向尺寸，型腔的深度尺寸和型芯的高度尺寸，型芯和型腔的位置尺寸等。一、型腔和型芯的徑向尺寸（1）型腔徑向尺寸 利用平均收縮率法LM+z =（1+Scp）LS-3/4+z LM凹模徑向尺寸（mm）LS塑件徑向公稱尺寸（mm）Scp塑料的平均收縮率（）塑件公差值（mm）z凹模制造公差（mm） 查表得：ABS的收縮率為0.40.7則塑料的平均收縮率Scp =0.55%型腔的徑向尺寸：實踐證明：成型零件的制造公差約占 塑件總公差的1/31/4，因此在確定成型零件工作尺寸公差值時可取塑件公差的1/31/4。為了保持較高精度選1/4。 由于外表面精度較高，1=0.32 mm 2=0.28 mm 3=0.18 mmz1=0.250.32=0.08 mm z2=0.250.28=0.07 mmz3=0.250.18=0.045 mm則： LM1+z=（1+Scp）L1-3/4+z =（1+0.55%）64.3-3/40.32 +0.08 =64.4+0.08mmLM12+z =（1+Scp）LS-3/4+z =（1+0.55%）43.5-3/40.28 +0.07 =43.53+0.07 mmLM13+z =（1+Scp）LS-3/4+z =（1+0.55%）12-3/40.18 +0.045 =53.2+0.045 mm二、型芯的徑向尺寸 同樣運用平均收縮率法：LMz =（1+Scp）LS+3/4 z LM 型芯徑向尺寸（mm）z 型芯徑向制造公差（mm）其余符號同上 取IT6精度時1=0.64mm 2=0.56mm3=0.36mm 由z=1/4得：z1=0.16 mm z1=0.14 mm z1=0.09mm則：LM4z =（1+Scp）LS+1/2z =（1+0.55%）60.3+1/20.640.16 =60.95 0.16 mmLM4z =（1+Scp）LS+1/2z =（1+0.55%）39.5+1/20.560.14 =39.900.0.14 mmLM4z =（1+Scp）LS+1/2z =（1+0.55%）10+1/20.360.09 =10.23 0.09 mmL=36 =0.52 LM4z =（1+Scp）LS+1/2z =36.460.13 mmL=11 =0.36 LM4z =（1+Scp）LS+1/2z =11.240.09 mmL=40 =0.56 LM4z =（1+Scp）LS+1/2z =40.50.16 mm L=15 =0.40 LM4z =（1+Scp）LS+1/2z =15.280.1 mm三、中心距尺寸：塑件上凸臺之間，凹槽之間或凸臺到凹槽的中心線之間的距離稱為中心距，該類尺寸屬于定位尺寸。由于模具上中心距尺寸和塑件中心距公差都是雙向等植公差，同時磨損的結(jié)果不會使中心距尺寸發(fā)生變化，在計算中心距尺寸時不必考慮磨損量。m=(1+s)Cs標(biāo)注上制造公差后得：(Cm) z =(1+s)Csz10 (Cm) z =(1+s)Csz =1.0055101/21/40.32 =10.00550.046 (Cm) z =(1+s)Csz =1.005561/21/40.28=6.030.0357.1 (Cm) z =(1+s)Csz =1.00557.11/21/40.32 =7.130.048.2 (Cm) z =(1+s)Csz =1.00558.21/21/40.28 =8.250.03510 (Cm) z =(1+s)Csz =1.0055101/21/40.32 =10.0550.0424 (Cm) z =(1+s)Csz =1.0055241/21/40.44 =24.130.05522 (Cm) z =(1+s)Csz=1.0055221/21/40.44 =22.120.055四、型芯高度尺寸同樣運用平均收縮率法： HM+z =（1+Scp）LS+3/4zHM型芯高度尺寸（mm）z型芯高度制造公差（mm）其余符號同上由：H=2mm 如（圖13） 取IT3精度時 =0.06 mm 由z=1/4得：z=0.015 mm 則：HMz =（1+Scp）hs+3/4z =（1+0.55%）2+3/40.060.015 =2.056 0.015 mm第三節(jié) 模具型腔側(cè)壁和底板的厚度的計算塑料模具型腔在成型過程中受到熔體的高壓作用，應(yīng)具有足夠的強度和剛度，如果型腔側(cè)壁和底版厚度過小，可能因強度不足而產(chǎn)生塑料變性甚至破壞，也可能因為剛度不足而產(chǎn)生撓曲變形，導(dǎo)致 溢料和出現(xiàn)飛邊，降低塑件尺寸精度并影響順利脫模。對于小尺寸的模具型腔，在發(fā)生大的彈性變形前，其內(nèi)應(yīng)力往往超過了模具材料的許多應(yīng)力，因此，強度不夠是主要矛盾，設(shè)計型腔壁厚應(yīng)以強度為準(zhǔn)。本次設(shè)計采用組合式型腔，由于型腔壁厚計算比較麻煩，見（參一）表5-17，經(jīng)驗推薦數(shù)據(jù)選取凹模壁厚S1=10mm，模套壁厚S=25 mm。（2）底版厚度的計算：按強度條件，型腔底板厚度計算式為： h= 如（圖15）式中：h矩形底板的厚度 （mm）B底板總寬度 （mm）L雙支腳間距 （mm）P型腔內(nèi)塑料熔體壓力 （MPa） 模具材料的許用應(yīng)力 （MPa） 圖 15 h25 mm 第六章 推出機(jī)構(gòu)與復(fù)位機(jī)構(gòu)塑件在從模具上取下以前，還有一個從模具的成型零件上脫出的過程，使塑件從成型零件上脫出來的機(jī)構(gòu)稱為推出機(jī)構(gòu)。推出機(jī)構(gòu)的動作是通過裝在注射機(jī)合模機(jī)構(gòu)上的頂桿或液壓缸來完成的。第一節(jié) 推出機(jī)構(gòu)的組成推出機(jī)構(gòu)主要由推出零件推出零件固定板和推板、推出機(jī)構(gòu)的導(dǎo)向與復(fù)位零件等組成。推出機(jī)構(gòu)中，凡直接與塑件相接觸、并將塑件推出型腔或型芯的零件稱為推出零件。本次設(shè)計采用推桿推出機(jī)構(gòu)。第二節(jié) 推出機(jī)構(gòu)的設(shè)計原則 1、推出機(jī)構(gòu)應(yīng)盡量設(shè)置在動模一側(cè)，由于推出機(jī)構(gòu)的動作是通過裝在注射機(jī)合模機(jī)構(gòu)上的頂桿來驅(qū)動的，所以一般情況下，推出機(jī)構(gòu)設(shè)在動模一側(cè)。2、保證塑件不因推出而變形損壞，為了保證塑件在推出過程中不變形、不損壞，設(shè)計時要仔細(xì)分析塑件對模具的包緊力和粘附力的大小，合理的選擇推出方式及推出位置，從而使塑件受力均勻、不變形、不損壞。3、機(jī)構(gòu)簡單動作可靠 推出機(jī)構(gòu)應(yīng)使推出動作可靠、靈活、制造方便，機(jī)構(gòu)本身要有足夠的強度、剛度和硬度，以承受推出過程中的各種力的作用，確保塑件順利脫模。4、合模時的正確復(fù)位 設(shè)計推出機(jī)構(gòu)時，還必須考慮合模時機(jī)構(gòu)的正確復(fù)位，并保證不與其他模具零件相干涉。一、脫模力的計算 注射成型后，塑件在模具內(nèi)冷卻定型，由于體積的收縮，對型芯產(chǎn)生包緊力，塑件要從模腔中脫出，就必須克服因包緊力而產(chǎn)生的摩擦阻力。一般而論，塑料制件剛開始脫模時，所需克服的阻力最大，即所需的脫模力最大。Ft=Fb(cos_sin)式中 塑料對鋼的摩擦系數(shù)，約為0.1-0.3 A塑件包容型芯的面積；P塑件對型芯的單位面積上的包緊力，一般情況下，模外冷卻的塑件約為2.4-3.910Pa，模內(nèi)冷卻的塑件約為0.81.210PaFt=43642.510000000(0.1cos1-sin1) =5680000000Pa第三節(jié) 簡單推出機(jī)構(gòu) 簡單推出機(jī)構(gòu)包括推桿推出機(jī)構(gòu)、推管推出機(jī)構(gòu)、推件板推出機(jī)構(gòu)、活動鑲塊及凹模推出機(jī)構(gòu)，多元推出機(jī)構(gòu)等等。一、推桿推出機(jī)構(gòu)由于推桿位置的自由度很大，因而推桿推出機(jī)構(gòu)是最常用的推出機(jī)構(gòu)，常用來推出各種塑件。推桿的截面形狀根據(jù)塑件的推出情況而定，可設(shè)計成圓形，矩形。本次設(shè)計采用圓形截面推桿。1、推桿位置的設(shè)置 （1）推桿應(yīng)均勻布置 當(dāng)塑件脫模力相同時，應(yīng)均勻布置推桿，保證塑件被推桿推出時受力均勻，推出平穩(wěn)、不變形。（2）推桿應(yīng)設(shè)置在脫模力大的地方 型芯周圍塑件對型芯包緊力很大所以可在型芯外側(cè)塑件的端面上設(shè)置推桿，也可在型芯靠近側(cè)壁處設(shè)推桿。（3）推桿應(yīng)設(shè)在塑件強度較大處 推桿不宜設(shè)在塑件薄壁處，盡可能設(shè)在塑件壁厚、凸緣、加強肋處。二、推桿的直徑 推桿在推出塑件時，應(yīng)具有足夠的剛性，以承受推出力，為此，推桿的直徑不宜太小。三、推桿的形狀四、推出機(jī)構(gòu)的導(dǎo)向和復(fù)位為了保證推出機(jī)構(gòu)在工作中靈活、平穩(wěn)，每次合模后，推出元件能回到原來的位置，通常還需要設(shè)計推出機(jī)構(gòu)的導(dǎo)向與復(fù)位裝置。（一） 導(dǎo)向零件推出機(jī)構(gòu)的導(dǎo)向零件，通常由推板導(dǎo)柱和推板導(dǎo)套所組成，導(dǎo)向，零件使各推出零件得以保持一定的配合間隙，從而保證推出和復(fù)位動作順利進(jìn)行。（二） 復(fù)位零件1、復(fù)位桿復(fù)位 為了使推出元件合模后能回到原來的位置，推桿固定板上同時裝有復(fù)位桿， 常用的復(fù)位桿采用圓形截面，一一般每副模具設(shè)置四根復(fù)位桿，其位置盡量設(shè)置在推桿固定板的四周以便推出機(jī)構(gòu)合模時復(fù)位平穩(wěn)，復(fù)位桿端面與所在動模分型面平齊。二、復(fù)位桿的形狀 第七章 合模導(dǎo)向機(jī)構(gòu)的設(shè)計導(dǎo)向機(jī)構(gòu)是保證動定模或上下模合模時，正確定位和導(dǎo)向的零件。合模導(dǎo)向機(jī)構(gòu)主要有導(dǎo)柱導(dǎo)向和錐面定位兩種形式。通常采用導(dǎo)柱導(dǎo)向定位。導(dǎo)向機(jī)構(gòu)在模具閉合過程中保證動定模位置正確，保證型腔的形狀和尺寸精確 ；同時起了定位作用，便于裝配和調(diào)整。合模時，首先是導(dǎo)向零件接觸，引導(dǎo)動定模準(zhǔn)確閉合，避免型芯先進(jìn)入型腔造成成型零件損壞。此外，導(dǎo)向機(jī)構(gòu)還承受一定的側(cè)向壓力，保證了模具的正常工作。導(dǎo)柱導(dǎo)向機(jī)構(gòu)的主要零件是導(dǎo)柱和導(dǎo)套。一、導(dǎo)柱1、導(dǎo)柱的結(jié)構(gòu)形式 2、導(dǎo)柱的結(jié)構(gòu)和技術(shù)要求 導(dǎo)柱的導(dǎo)向部分的長度應(yīng)比凸模端面高出812mm，以避免出現(xiàn)導(dǎo)柱未導(dǎo)正方向而型芯先進(jìn)入型腔。 導(dǎo)柱前端應(yīng)作成錐臺或半球形，以使導(dǎo)柱順利地進(jìn)入導(dǎo)向孔。導(dǎo)柱應(yīng)合理均勻在模具分型面的四周，導(dǎo)柱中心至模具邊緣應(yīng)足夠的距離，以保證模具強度。導(dǎo)柱既可以設(shè)在動模一側(cè)，也可以設(shè)置在定模一側(cè)，在不防礙脫模取件的條件下，導(dǎo)柱通常設(shè)在型芯高出分型面較多的一側(cè)。二、導(dǎo)套1、導(dǎo)套的結(jié)構(gòu)形式、導(dǎo)套的結(jié)構(gòu)和技術(shù)要求為使導(dǎo)柱順利的進(jìn)入導(dǎo)套，在導(dǎo)套的前端應(yīng)倒圓角。導(dǎo)柱孔最好作成通孔，以利于排除孔內(nèi)空氣及廢料殘渣。第八章 冷卻系統(tǒng)的設(shè)計一、在設(shè)計冷卻系統(tǒng)時，應(yīng)注意以下原則：（一）冷卻水道應(yīng)盡量多，截面尺寸應(yīng)盡量大。2、冷卻水道至型腔表面距離應(yīng)盡量相等，此塑件壁厚相等，所以冷卻水道到型腔表面距離相等，且距離應(yīng)在1215 mm，這里取15mm。3、澆口處加強冷卻。塑料熔體充填型腔時，澆口附近溫度最高，所以要加強冷卻澆口。4、冷卻水道出入口溫差應(yīng)最小，盡量縮短冷卻水道長度，降低出入口冷卻水的溫差，提高冷卻效果。5、冷卻水道應(yīng)沿著塑料收縮的方向設(shè)置，此外，在設(shè)計冷卻水道時還要避免塑料的熔融部位，以免產(chǎn)生熔接痕，并且還要易于清理，冷卻水道孔徑取10 mm。總結(jié)經(jīng)過一個月的時間，我完成了畢業(yè)設(shè)計。在這短短的一個月內(nèi)，我學(xué)到了很多東西，可說是受益非淺。雖說是短短的一個月，但我認(rèn)為通過實踐所得比從書本上學(xué)到的東西要有價值的多。通過畢業(yè)設(shè)計使我真正做到了理論聯(lián)系實際。在XX老師耐心、認(rèn)真的教導(dǎo)下，使我獨立地完成了這次畢業(yè)設(shè)計。在此設(shè)計中我還學(xué)會了如何查閱設(shè)計手冊，如何對塑件的工藝分析，如何模具設(shè)計。在張老師的帶領(lǐng)下，還看到了型腔、型芯、滑塊等各種模具零部件。這樣在我腦海里有了一個深刻的印象，不至于對模具模棱兩可。同時也清楚的看到了實踐與理論的差別。更重要的是經(jīng)過這次設(shè)計，使我更加牢固、扎實的掌握了專業(yè)理論知識，對我以后的學(xué)習(xí)工作上有了更大的幫助，并奠定了扎實的基礎(chǔ)。由于本人水平有限，時間倉促，本次設(shè)計難免有錯誤和欠妥之處，懇請老師們批評指正。最后我誠摯的感謝老師們對我的教導(dǎo)。 致 謝在本次設(shè)計過程中，我得到了老師們的指導(dǎo)和幫助，在研究過程中，同學(xué)們給了我很多獨特的見解和幫助。使我有了很大的進(jìn)步，在此本人一并表示誠摯的、衷心的感謝。愿他們在 以后的工作中一切順利，一帆風(fēng)順！參 考 文 獻(xiàn)(1)屈華昌 主編, 塑料成型工藝與模具設(shè)計。 北京：機(jī)械工業(yè)出版社，2000(2)賈潤禮、程志遠(yuǎn) 主編, 實用注射模設(shè)計手冊。北京：中國輕工業(yè)出版社，2000(3)馮炳蕘、韓泰榮、蔣文森 主編, 模具設(shè)計與制造簡明手冊。 上海：上?？茖W(xué)技術(shù)出版社，1998共 27 頁 第 27 頁常州輕工職業(yè)技術(shù)學(xué)院模具系畢業(yè)設(shè)計 常州輕工職業(yè)技術(shù)學(xué)院常州輕工職業(yè)技術(shù)學(xué)院 題 目 呼機(jī)上蓋的塑件注射模設(shè)計 姓 名 學(xué) 號 班 級 指導(dǎo)教師 職 稱 日 期 C Z IL I 畢業(yè)設(shè)計(論文)說明書 Computer-Aided Design 40 (2008) space C.L. producti moulded part. Despite the various research efforts that have been directed towards the analysis, optimization, and fabrication of cooling systems, support for the layout design of the cooling system has not been well developed. In the layout design phase, a major concern is the feasibility of building the cooling system inside the mould insert without interfering with the other mould components. This paper reports a configuration space (C-space) method to address this important issue. While a high-dimensional C-space is generally required to deal with a complex system such as a cooling system, the special characteristics of cooling system design are exploited in the present study, and special techniques that allow C-space computation and storage in three-dimensional or lower dimension are developed. This new method is an improvement on the heuristic method developed previously by the authors, because the C-space representation enables an automatic layout design system to conduct a more systematic search among all of the feasible designs. A simple genetic algorithm is implemented and integrated with the C-space representation to automatically generate candidate layout designs. Design examples generated by the genetic algorithm are given to demonstrate the feasibility of the method. c 2007 Elsevier Ltd. All rights reserved. Keywords: Cooling system design; Plastic injection mould; Configuration space method 1. Introduction The cooling system of an injection mould is very important to the productivity of the injection moulding process and the quality of the moulded part. Extensive research has been conducted into the analysis of cooling systems 1,2, and commercial CAE systems such as MOLDFLOW 3 and Moldex3D 4 are widely used in the industry. Research into techniques to optimize a given cooling system has also been reported 58. Recently, methods to build better cooling systems by using new forms of fabrication technology have been reported. Xu et al. 9 reported the design and fabrication of conformal cooling channels that maintain a constant distance from the mould impression. Sun et al. 10,11 used CNC Despitethevariousresearcheffortsthathavefocusedmainly on the preliminary design phase of the cooling system design process in which the major concern is the performance of the cooling function of the system, support for the layout design phase in which the feasibility and manufacturability of the cooling system design are addressed has not been well developed. A major concern in the layout design phase is the feasibility of building the cooling system inside the mould insert without interfering with the other mould components. Consider the example shown in Fig. 1. It can be seen that many different components of the various subsystems of the injection mould, such as ejector pins, slides, sub-inserts, and so forth, have to be packed into the mould insert. Finding the best location for each channel of the cooling circuit to optimize Plastic injection mould cooling configuration C.G. Li, Department of Manufacturing Engineering and Engineering Received 3 May 2007; accepted Abstract The cooling system of an injection mould is very important to the milling to produce U-shaped milled grooves for cooling channels and Yu 12 proposed a scaffolding structure for the design of conformal cooling. Corresponding author. E-mail address: mecllicityu.edu.hk (C.L. Li). 0010-4485/$ - see front matter c 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cad.2007.11.010 334349 system design by the method Li Management, City University of Hong Kong, Hong Kong 18 November 2007 vity of the injection moulding process and the quality of the the cooling performance of the cooling system and to avoid interference with the other components is not a simple task. Another issue that further complicates the layout design problem is that the individual cooling channels need to be connected to form a path that connects between the inlet and the outlet. Therefore, changing the location of a channel may 335 Fig.1. Thecoolingsystem components. require changing the example shown in to optimize the cooling in Fig. 2(a). Assume other mould components mould component As C1 cannot be mo interference with other C2 is moved and C connectivity, as sho C3 is found to interfere mould components, is very tedious. that supports the this new technique, used to provide a layout designs. The an efficient method the layout design to generate layout system developed w C-space method to conduct a more layout designs. is the space that system is treated the configuration free region. Points of the the components correspond to of the system initially formalized planning problems shortened and further modification is needed, which results in the final design shown in Fig. 2(c). Given that a typical injection mould may have more than ten cooling channels, with each channel (a) Interference occurs between cooling channel C1 and mould component O1 at the ideal location of C1. (c) C3 is moved and C2 is design. Fig. 2. An example showing the tediousness and a survey in this area of research has been reported by Wise and Bowyer 16. The C-space method has also been used to solve problems in qualitative reasoning (e.g., 17,18) (b) Channel C1 is shortened, C2 is moved, and C3 is elongated. to give the final C.G. Li, C.L. Li / Computer-Aided Design 40 (2008) 334349 insideamouldinsertpackedwithmanyothermould other channels as well. Consider the Fig. 2. The ideal location of each channel performance of the system is shown that when the cooling system and the are built into the mould insert, a O1 is found to interfere with channel C1. ved to a nearby location due to the possible components, it is shortened. As a result, 3 is elongated accordingly to maintain the wn in Fig. 2(b). Owing to its new length, with another mould component, O2, potentially interfering with a few other finding an optimal layout design manually This paper reports a new technique automation of the layout design process. In a configuration space (C-space) method is concise representation of all of the feasible C-space representation is constructed by that exploits the special characteristics of problem. Instead of using heuristic rules designs, as in the automatic layout design previously by the authors 13,14, this ne enables an automatic layout design system systematic search among all of the feasible 2. The configuration space method In general, the C-space of a system results when each degree of freedom of that as a dimension of the space. Regions in space are labeled as blocked region or in the free regions correspond to valid configurations system where there is no interference between of the system. Points in the blocked regions invalid configurations where the components interfere with one another. C-space was by Lozano-Perez 15 to solve robot path of the layout design process. 336 and (e.g., automatic 23 2.1. the y c 3 se (e) a cooling system. Fig. 3 gives an example. The preliminary design of this cooling system consists of four cooling channels. To generate a layout design from the preliminary design, the centers and lengths of the channels are adjusted. As shown in Fig. 3, the center of channel C1 can be moved along the X1 and X2 directions, and its length can be adjusted along the X3 direction. Similarly, the length of C2 can be adjusted along the X4 direction, while its center adjustment is described by X1 and X3 and thus must be the same as the adjustment of C1 to maintain the connectivity. By applying similar arguments to the other channels, it can be seen that the cooling system has 5 (a) Channel Ci and three mould components inside the mould insert. (b) Offsets of the mould Ci represented by line (d) The initial free region of Ci. Fig. 4. The major steps in the construction considered. To account for the diameter D, Oi is first offset by D/2 + M to give Oprimei, where M is the minimum allowable distance between the channel wall and the face of a component. This growing of Oi in effect reduces channel Ci to a line Li. Consider the example illustrated in Fig. 4. Fig. 4(a) shows a channel Ci and three mould components, O1, O2, and O3, that may interfere with Ci. Fig. 4(b) shows the offsets Oprime1, Oprime2, and Oprime3 of the mould components, and the reduction of Ci to a line segment Li that is coincident with the axis of Ci. If there is no intersection between Li and the offsets of the mould components, then the original channel Ci will not intersect with components and gment Li. (c) Sweeping the offsets of the mould components and Ci represented by point Pi. Subtracting Oprimeprimei from Bprimei. (f) The free region FRi of Ci. C.G. Li, C.L. Li / Computer-Aided Design 40 (2008) 334349 Fig. 3. An example showing the degrees of freedom of a cooling system. the analysis and design automation of kinematic devices 1921).TheauthorinvestigatedaC-spacemethodinthe design synthesis of multiple-state mechanisms 22, in previous research. C-space of a cooling system A high-dimensional C-space can be used to represent all of feasible layout designs of a given preliminary design of degreesoffreedom,andtheyaredenotedas Xi,i = 1,2,.,5. In principle, the C-space is a five-dimensional space and an point in the free region of this space gives a set of coordinate values on the Xi axes that can be used to define the geometry of the channels without causing interference with the other mould components.Todeterminethefreeregioninahigh-dimensional C-spaceofacoolingsystem,thefirststepistoconstructthefree regions in the C-spaces of the individual channels. 2.2. C-space construction of individual cooling channels When an individual channel Ci is considered alone, it has three degrees of freedom, say X1 and X2 for its center location and X3 for its length. As the ideal center location and length have already been specified in the preliminary design, it is reasonable to assume a fixed maximum allowable variation for X1, X2, and X3. The initial free region in the C-space of channel Ci is thus a three-dimensional cube Bi with the dimensionsc c c. To avoid any possible interference with a mould component Oi when channel Ci is built into the mould insert by drilling, a drilling diameter D and drilling depth along X have to be of the free region FRi of a channel Ci. C.G. Li, C.L. Li / Computer-Aided the mould components. This growing or offset of an obstacle is a standard technique in the C-space method 15. A channel is formed by drilling from a face of the mould insert, and any obstacle Oi within the drilling depth will affect the construction of the channel. To account for the drilling depth, the offset Oprimei of Oi is swept along the drilling direction until the opposite face of the mould insert is reached to generate Oprimeprimei . This sweeping of Oprimei in effect reduces line Li to a point Pi located at the end of Li. As shown in Fig. 4(c), if the point Pi is outside Oprimeprimei , the drilling along Li to produce Ci is feasible. The free region FRi of channel Ci is obtained as follows. First, the initial free region Bi is constructed with its center at Pi as shown in Fig. 4(d). Bi then intersects with the mould insert to obtain Bprimei. Bprimei represents all of the possible variations of Ci when only the geometric shape of the mould insert is considered. Then, FRi is obtained by subtracting from Bprimei the Oprimeprimei of all of the obstacles. Fig. 4(e) and (f) show the subtraction and the resulting FRi of the example. 2.3. Basic approach to the construction of the C-space of cooling system To determine the free region FRF in the C-space of a cooling system, the free regions of each cooling channel have to be “intersected” in a proper manner so that the effect of the obstacles to all of the channels are properly represented by FRF. However, the standard Boolean intersection between the free regions of two different channels cannot be performed because their C-spaces are in general spanned by different sets of axes. Referring to the example in Fig. 3, the C-spaces of C1 and C2 are spanned by X1, X2, X3 and X1, X3, X4, respectively. To facilitate the intersection between free regions in different C-spaces, the projection of a region from the C- space of one channel to that of another channel is needed. The following notations are first introduced and will be used in the subsequent discussions on projections and the rest of the paper. Notations used in describing high-dimensional spaces Sn denotes an n-dimensional space spanned by the set of axes Xn = X1, X2,., Xn. Sm denotes an m-dimensional space spanned by the set of axes Xm = Xprime1, Xprime2,., Xprimem. pn denotes a point in Sn and pn = (x1,x2,.,xn), where xi denotes a coordinate on the ith axis Xi. Rn denotes a region in Sn(Rn Sn). Rn is a set of points in Sn. PROJSm(pn) denotes the projection of a point pn from Sn to Sm. PROJSm(Rn) denotes the projection of a region Rn from Sn to Sm. Notations used in describing a cooling system nC denotes the number of channels in the cooling system. nF denotes the total degrees of freedom of the cooling system. Ci denotes the ith channel of the cooling system. Si denotes the C-space of Ci. Design 40 (2008) 334349 337 FRi denotes the free region in Si. That is, it is the free region of an individual channel Ci. SF denotes the C-space of the cooling system. FRF denotes the free region in SF. That is, it is the free region of the cooling system. Consider the projection of a point pn in Sn to a point pm in Sm. Fig. 5(a) illustrates examples of projection using spaces of one dimension to three dimensions. Projections are illustrated forthreecases:(i) Xm Xn;(ii) Xm Xn;and(iii) Xm negationslash Xn, Xn negationslash Xm, and Xn Xm negationslash= . For (i), each coordinate of pm is equal to a corresponding coordinate of pn that is on the same axis. For (ii) and (iii), the projection of pn is a region Rm. For each point pm in Rm, a coordinate of pm is equal to that of pn if that coordinate is on a common axis of Sn and Sm. For the other coordinates of pm, any value can be assigned. The reason for this specific definition of the projections, in particular, for cases (ii) and (iii), is as follows. Consider two adjacent channels Cn and Cm. As they are adjacent, they must be connected and thus their C-spacesSn and Sm share some common axes. Assume that a configuration that corresponds to a point pn in Sn has been selected for Cn. To maintain the connectivity, the configuration for Cm must be selected such that the corresponding point pm in Sm shares the same coordinates with pn on their common axes. This implies that pm can be any point within the projection of pn on Sm, where the method of projection is defined above. The projections of a region Rn in Sn to Sm are simply the projections of every point in Rn to Sm. Fig. 5(b) illustrates the region projections. The formal definition of projection is given below. Definition 1 (Projection). 1.1. If Xm Xn, PROJSm(pn) is a point pm = (xprime1,xprime2,.,xprimem), where for Xprimei = X j, xprimei = xj for all i 1,m. To simplify the notations in subsequent discussion, this projection is regarded as a region that consists of the single point pm. That is, PROJSm(pn) = pm. 1.2. If Xm Xn, PROJSm(pn) is a region Rm = pm|PROJSn(pm) = pn. 1.3. If Xm negationslash Xn, Xn negationslash Xm, and Xn Xm negationslash= , PROJSm(pn)is a region Rm = pm|PROJSI (pm) = PROJSI (pn), where SI is the space spanned by Xn Xm. If Xn Xm = , PROJSm(pn) is defined as Sm. 1.4. PROJSm(Rn) is defined as the region Rm = pm|pm PROJSm(pn), pn Rn. As discussed in Section 2.1, any point pF in FRF gives a value for each degree of freedom of the cooling system so that the geometry of the channels is free from interference with the other mould components. In other words, the projection of pF to each Si is in the free region FRi of each Ci. Thus, FRF is defined as follows. Definition 2 (Free Region in the C-space of a Cooling System). FRF = pF|PROJSi (pF) FRi,i 1,nC -Aided Note that according to to Si always contains only that span Si is always a subset The construction of the already been explained in the following theorem is useful. Theorem 1. FRF = nCintersectiondisplay i=1 PROJSF(FRi). Intuitively, this theorem says first projected to the C-space can then be obtained by performing among the projections. The used in the proof are given of the C-space F and to facilitate the between the regions can use a kind of cell used in 21,24. The region RF in Each box is defined by SF. The intersection of of the two sets of high-dimensional boxes intervals of each of the by m three- OJSF(FRi) can then be boxes. The construction Fig. 5. The projections of points and regions in Sn to Sm. Definition 1.1, the projection of pF a single point because the set of axes of the axes that span Sn. free region FRi of each Ci has Section 2.2. To find FRF from FRi, that to find FRF, all of the FRi are of the cooling system SF. FRF the Boolean intersections proof of Theorem 1 and the lemmas 2.4. Representation and computation To represent the free region FR computation of the Boolean intersections in a high-dimensional space, we enumeration method similar to the one basic idea is to approximate a high-dimensional SF by a set of high-dimensional boxes. specifying an interval on each axis of two regions is achieved by the intersection boxes. The intersection between two is simply the intersection between the boxes in each axis. Assuming that each FRi is approximated dimensional boxes, the projection PR approximated by mnF-dimensional 338 C.G. Li, C.L. Li / Computer in the Appendix. Design 40 (2008) 334349 of FRF that uses Theorem 1 then requires mnC intersections between nF-dimensional maximum of mnCnF of boxes used to represent intersections and FR is anticipated that the are still major problems improved method is 3. An efficient technique To avoid the high for the representation . Instead, we process to example shown in is assumed in this along the Z direction hasfourdegrees each channel Ci are shown in Fig. 6(b). channel C1. First, a (a) A simple cooling system with four channels and four degrees of freedom. (b) The free region FRi of each channel in its configuration space Si. Fig. 6. A simplified example of a cooling system design. boxes, and FRF is represented by a -dimensional boxes. Although the number the intermediate results of the F can be reduced by special techniques, it memory and computational requirements of this method. In the next section, an developed. for C-space construction to represent and not to compute FRF explicitly focus on a technique that enables the computational work on the C-spaces of each individual channel. First, consider the simplified design Fig. 6. For the purpose of illustration, it example that there is no variation in FRi ofthemouldinsertandthusthecoolingsystem of freedom as shown in Fig. 6(a). The Si of two dimensional and the assumed FRi are Consider a simple method for designing C.G. Li, C.L. Li / Computer-Aided memory and computational requirements and construction of FRF, we choose not Design 40 (2008) 334349 339 point p1 can be selected from within FR1 so that C1 is free from interference with any obstacle. However, S1 is spanned -Aided continued even though their C-spaces of C1, (i.e., they are as well, because the system are connected. have an effect in the cooling system. To develop a design of each individual channels, selection of a point always exist a corresponding that all of the channels system. To address this Si is needed. Definition 3. PRi is PRi = PROJSi (FRF Obviously, for an always a correspondi FR2. Again, as p2 x3 must have a value FR3. Also, as must also be inside p1, p2, p3, and p4 C1. determine the valid designs for C1, the The effect of FR4 valid region in FR3, finally in S1. The all of the effects of is formally channels Ci and of their free regions do