帶液壓缸的帶式輸送機(jī)液壓拉緊系統(tǒng)設(shè)計(jì)【含5張CAD圖紙、說(shuō)明書(shū)】,含5張CAD圖紙、說(shuō)明書(shū),液壓缸,輸送,液壓,拉緊,系統(tǒng),設(shè)計(jì),CAD,圖紙,說(shuō)明書(shū) 畢業(yè)設(shè)計(jì)（論文）開(kāi)題報(bào)告 課 題 名 稱(chēng)： 帶液壓缸的帶式輸送機(jī)液壓拉緊系統(tǒng)設(shè)計(jì) 學(xué) 生 姓 名： 學(xué)號(hào)： 指 導(dǎo) 教 師： 職稱(chēng)： 副教授 所 在 學(xué) 院： 機(jī)電工程學(xué)院 專(zhuān) 業(yè) 名 稱(chēng)： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 2018 年 3 月 16 日 說(shuō) 明 1．根據(jù)《畢業(yè)設(shè)計(jì)(論文)管理規(guī)定》，學(xué)生必須撰寫(xiě)《畢業(yè)設(shè)計(jì)（論文）開(kāi)題報(bào)告》，由指導(dǎo)教師簽署意見(jiàn)、教研室審查，學(xué)院教學(xué)院長(zhǎng)批準(zhǔn)后實(shí)施。 2．開(kāi)題報(bào)告是畢業(yè)設(shè)計(jì)（論文）答辯委員會(huì)對(duì)學(xué)生答辯資格審查的依據(jù)材料之一。學(xué)生應(yīng)當(dāng)在畢業(yè)設(shè)計(jì)（論文）工作前期內(nèi)完成，開(kāi)題報(bào)告不合格者不得參加答辯。 3．畢業(yè)設(shè)計(jì)開(kāi)題報(bào)告各項(xiàng)內(nèi)容要實(shí)事求是，逐條認(rèn)真填寫(xiě)。其中的文字表達(dá)要明確、嚴(yán)謹(jǐn)，語(yǔ)言通順，外來(lái)語(yǔ)要同時(shí)用原文和中文表達(dá)。第一次出現(xiàn)縮寫(xiě)詞，須注出全稱(chēng)。 4．本報(bào)告中，由學(xué)生本人撰寫(xiě)的對(duì)課題和研究工作的分析及描述，沒(méi)有經(jīng)過(guò)整理歸納，缺乏個(gè)人見(jiàn)解僅僅從網(wǎng)上下載材料拼湊而成的開(kāi)題報(bào)告按不合格論。 5. 課題類(lèi)型填：工程設(shè)計(jì)類(lèi)；理論研究類(lèi)；應(yīng)用（實(shí)驗(yàn)）研究類(lèi)；軟件設(shè)計(jì)類(lèi)；其它。 6、課題來(lái)源填：教師科研；社會(huì)生產(chǎn)實(shí)踐；教學(xué)；其它 畢業(yè)設(shè)計(jì)（論文）開(kāi)題報(bào)告 課題名稱(chēng) 帶液壓缸的帶式輸送機(jī)液壓拉緊系統(tǒng)設(shè)計(jì) 課題來(lái)源 社會(huì)生產(chǎn)實(shí)踐 課題類(lèi)型 工程設(shè)計(jì)類(lèi) 1．選題的背景及意義： 帶式輸送機(jī)是煤礦港口碼頭等散裝物料的主要運(yùn)輸設(shè)計(jì)，帶式輸送機(jī)是通過(guò)摩擦傳遞動(dòng)力的，傳動(dòng)滾筒的摩擦力來(lái)源于輸送帶與滾筒之間的張緊，該張緊力是通過(guò)拉緊系統(tǒng)實(shí)現(xiàn)的，通過(guò)對(duì)張緊系統(tǒng)的設(shè)計(jì)，可以掌握典型的通用機(jī)械的設(shè)計(jì)過(guò)程。 2．研究?jī)?nèi)容擬解決的主要問(wèn)題： 完成總體方案的設(shè)計(jì)；調(diào)研并選定傳動(dòng)機(jī)構(gòu)主要參數(shù)；給定部分參考圖；完成傳動(dòng)系統(tǒng)總圖及主要零部件圖的設(shè)計(jì)；完成論文的撰寫(xiě)。繪制圖紙若干張，包括總裝配圖及其主要零部件圖，圖紙量折合3張零號(hào)圖；撰寫(xiě)畢業(yè)設(shè)計(jì)論文，字?jǐn)?shù)不少于1.5萬(wàn)字；完成4000英文原文的翻譯。參考文獻(xiàn)不低于15篇,其中英文原文兩篇。 3．研究方法技術(shù)路線： 帶式輸送機(jī)液壓拉緊系統(tǒng)原理-帶式輸送機(jī)傳動(dòng)系統(tǒng)的運(yùn)動(dòng)及力學(xué)計(jì)算-帶式輸送機(jī)液壓拉緊系統(tǒng)設(shè)計(jì)與計(jì)算-液壓拉緊裝置的關(guān)鍵零部件的結(jié)構(gòu)設(shè)計(jì)與計(jì)算 4．研究的總體安排和進(jìn)度計(jì)劃： 寒假 實(shí)習(xí)、查資料、英文翻譯 1~2周 完成開(kāi)題報(bào)告； 3~4周 確定方案，進(jìn)行總體方案設(shè)計(jì) 5~6周 總圖繪制，說(shuō)明書(shū)編寫(xiě) 7~12周 部件圖繪制，說(shuō)明書(shū)編寫(xiě) 13周 填寫(xiě)論文副本，完成說(shuō)明書(shū)、圖紙繪制，準(zhǔn)備答辯 5．主要參考文獻(xiàn)： [1]徐灝．機(jī)械設(shè)計(jì)手冊(cè).北京：機(jī)械工業(yè)出版社，2000． [2]許福玲，陳堯明.液壓與氣壓傳動(dòng)，機(jī)械工業(yè)出版社，2007 [3]陳國(guó)定，吳立顏.機(jī)械設(shè)計(jì)，高等教育出版社，2013 [4]裘新建，機(jī)械原理課程設(shè)計(jì)，高等教育出版社，2010 [5]孫恒，陳作模，葛文杰.機(jī)械原理，高等教育出版社，2015 [6]朱顏，張雨震.礦車(chē)清掃機(jī)應(yīng)用現(xiàn)狀分析[J].湖南農(nóng)機(jī)，2013 [7]陳文，孫召瑞.一種礦車(chē)清車(chē)裝置設(shè)計(jì)[J]，煤礦機(jī)械，2007 [8]金豐民，王瑀，張榮建等編著.帶式輸送機(jī)實(shí)用技術(shù)[M].北京：冶金工業(yè)出版社.2012. [9]武予魯主編.帶式輸送機(jī)綜合保護(hù)裝置的工作原理與使用[M].北京：煤炭工業(yè)出版社.2003. [10]孫可文著.帶式輸送機(jī)的傳動(dòng)理論與設(shè)計(jì)計(jì)算[M].北京：煤炭工業(yè)出版社.1991. [11]林壯著.帶式輸送機(jī)皮帶自動(dòng)糾偏裝置設(shè)計(jì)研究[M].徐州：中國(guó)礦業(yè)大學(xué)出版社.2011 [12]劉成效，李和林主編.強(qiáng)力帶式輸送機(jī)操作工[M].北京：煤炭工業(yè)出版社.2005. [13]白曉滿(mǎn)著.帶式輸送機(jī)轉(zhuǎn)彎關(guān)鍵技術(shù)研究[M].徐州：中國(guó)礦業(yè)大學(xué)出版社.2010. [14]FredE.Meyers，MatthewP.Stephens著.制造設(shè)施設(shè)計(jì)和物料搬運(yùn) 第2版[M].北京：清華大學(xué)出版社.2002. [15]WilliamA.Nash，Ph.D.著.Theory and Problems of Strength of Materials Fourth Edition[M].北京：清華大學(xué)出版社.2003. 指導(dǎo)教師意見(jiàn)： 對(duì)“文獻(xiàn)綜述”的評(píng)語(yǔ)：符合規(guī)定要求 對(duì)總體安排和進(jìn)度計(jì)劃的評(píng)語(yǔ)：規(guī)劃合理 指導(dǎo)教師簽名： 2018 年 3 月 16 日 教研室意見(jiàn)： 通過(guò)，同意開(kāi)題 教研室主任簽名： 2018年 5 月 26 日 學(xué)院意見(jiàn)： 教學(xué)院長(zhǎng)簽名： 年 月 日 6 學(xué)生畢業(yè)設(shè)計(jì)（論文）中期情況檢查表 學(xué)院名稱(chēng)：機(jī)電工程學(xué)院 檢查日期：2018 年 6 月 6 日 學(xué)生姓名 專(zhuān) 業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 指導(dǎo)教師 設(shè)計(jì)（論文）題目 帶液壓缸的帶式輸送機(jī)液壓拉緊系統(tǒng)設(shè)計(jì) 工作進(jìn)度情況 基本思路已經(jīng)清楚，下面在老師指導(dǎo)下開(kāi)始寫(xiě)論文，畫(huà)圖。同時(shí)對(duì)于前期出現(xiàn)的理論知識(shí)匱乏情況有了填補(bǔ)。另外還需要進(jìn)一步的查閱資料來(lái)開(kāi)展中后期的工作。 是否符合任務(wù)書(shū)要求進(jìn)度 是 能否按期完成任務(wù) 是 工作態(tài)度情況 (態(tài)度、紀(jì)律、出勤、主動(dòng)接受指導(dǎo)等) 該生工作態(tài)度較為端正，基本遵守學(xué)校的有關(guān)規(guī)章制度，按照指導(dǎo)老師規(guī)定的時(shí)間出勤，對(duì)不會(huì)的問(wèn)題能主動(dòng)的聯(lián)系指導(dǎo)老師并請(qǐng)教，具有查閱資料解決問(wèn)題的能力，具有一定的分析解決問(wèn)題的能力，能熟悉使用計(jì)算機(jī)軟件，動(dòng)手能力較強(qiáng)。 質(zhì)量 評(píng)價(jià) (針對(duì)已完成的部分) 已完成的總體方案基本可行，計(jì)算基本正確，完成了一定的圖紙工作量。另外在論文的書(shū)寫(xiě)和畫(huà)圖的過(guò)程中一定要注意格式的修改，這也是我們后期重點(diǎn)去做的。 存在問(wèn)題和解決辦法 論文問(wèn)題：撰寫(xiě)剩余部分并需要進(jìn)一步修改完善；論文格式：論文格式圖紙需要按學(xué)校格式修改；圖紙的格式以及尺寸需要進(jìn)一步的修改；基礎(chǔ)知識(shí)需要進(jìn)一步的提高，有利于論文的續(xù)寫(xiě)。 檢查人簽名 教學(xué)院長(zhǎng)簽名 1 學(xué)生畢業(yè)設(shè)計(jì)（論文）中期匯報(bào)表 學(xué)生姓名 專(zhuān) 業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 學(xué) 號(hào) 設(shè)計(jì)（論文）題目 帶液壓缸的帶式輸送機(jī)液壓拉緊系統(tǒng)設(shè)計(jì) 畢業(yè)設(shè)計(jì)（論文）前期工作小結(jié) 主要通過(guò)查閱資料了解了課題設(shè)計(jì)的背景以及來(lái)源，了解了帶式輸送機(jī)在國(guó)內(nèi)外的發(fā)展趨勢(shì)，通過(guò)開(kāi)始的設(shè)計(jì)，使我們了解可課題的研究意義及背景。接下來(lái)我們會(huì)考慮課題是如何分析的。我們應(yīng)當(dāng)設(shè)計(jì)最佳設(shè)計(jì)方案，按時(shí)完成前期的工作計(jì)劃，為下一步設(shè)計(jì)做好準(zhǔn)備。 指導(dǎo)教師意見(jiàn) 該生在指定的時(shí)間內(nèi)完成了論文的撰寫(xiě)及修改工作，總體基本符合設(shè)計(jì)要求，在查閱資料方面能夠多方位全面的考慮。在語(yǔ)言表達(dá)上還需要進(jìn)一步的提升，爭(zhēng)取做到語(yǔ)言表達(dá)清晰。在材料選取方面能合理應(yīng)用材料，對(duì)一些問(wèn)題有自己的看法。在設(shè)計(jì)說(shuō)明書(shū)上還有一些細(xì)節(jié)問(wèn)題，希望進(jìn)一步改正。 簽名： 2018 年 6 月 6 日 1 畢業(yè)設(shè)計(jì)（論文）任務(wù)書(shū) 學(xué)? 院 （系）： 機(jī)電工程學(xué)院 專(zhuān) 業(yè)： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 學(xué) 生 姓 名： 學(xué) 號(hào)： 設(shè)計(jì)（論文）題目： 帶 液 壓 缸 的 帶 式 輸 送 機(jī) 液 壓 拉緊 系 統(tǒng) 設(shè) 計(jì) 起 迄 日 期：2018年2月26日~2018年5月26日 指 導(dǎo) 教 師： 教研室主任： 發(fā)任務(wù)書(shū)日期： 2018 年 3 月 4 日 畢 業(yè) 設(shè) 計(jì)（論 文）任 務(wù) 書(shū) 1.畢業(yè)設(shè)計(jì)的背景： 帶式輸送機(jī)是煤礦港口碼頭等散裝物料的主要運(yùn)輸設(shè)計(jì)，帶式輸送機(jī)是通過(guò)摩擦傳遞動(dòng)力的，傳動(dòng)滾筒的摩擦力來(lái)源于輸送帶與滾筒之間的張緊，該張緊力是通過(guò)拉緊系統(tǒng)實(shí)現(xiàn)的，通過(guò)對(duì)張緊系統(tǒng)的設(shè)計(jì)，可以掌握典型的通用機(jī)械的設(shè)計(jì)過(guò)程。 2.畢業(yè)設(shè)計(jì)(論文)的內(nèi)容和要求： 完成總體方案的設(shè)計(jì)；調(diào)研并選定傳動(dòng)機(jī)構(gòu)主要參數(shù)；給定部分參考圖；完成傳動(dòng)系統(tǒng)總圖及主要零部件圖的設(shè)計(jì)；完成論文的撰寫(xiě)。繪制圖紙若干張，包括總裝配圖及其主要零部件圖，圖紙量折合3張零號(hào)圖；撰寫(xiě)畢業(yè)設(shè)計(jì)論文，字?jǐn)?shù)不少于1.5萬(wàn)字；完成4000英文原文的翻譯。參考文獻(xiàn)不低于15篇,其中英文原文兩篇。 3.主要參考文獻(xiàn)： [1]徐灝．機(jī)械設(shè)計(jì)手冊(cè).北京：機(jī)械工業(yè)出版社，2000． [2]許福玲，陳堯明.液壓與氣壓傳動(dòng)，機(jī)械工業(yè)出版社，2007 [3]陳國(guó)定，吳立顏.機(jī)械設(shè)計(jì)，高等教育出版社，2013 [4]裘新建，機(jī)械原理課程設(shè)計(jì)，高等教育出版社，2010 [5]孫恒，陳作模，葛文杰.機(jī)械原理，高等教育出版社，2015 [6]朱顏，張雨震.礦車(chē)清掃機(jī)應(yīng)用現(xiàn)狀分析[J].湖南農(nóng)機(jī)，2013 [7]陳文，孫召瑞.一種礦車(chē)清車(chē)裝置設(shè)計(jì)[J]，煤礦機(jī)械，2007 4.畢業(yè)設(shè)計(jì)(論文)進(jìn)度計(jì)劃(以周為單位)： 寒假 實(shí)習(xí)、查資料、英文翻譯 1~2周 完成開(kāi)題報(bào)告； 3~4周 確定方案，進(jìn)行總體方案設(shè)計(jì) 5~6周 總圖繪制，說(shuō)明書(shū)編寫(xiě) 7~12周 部件圖繪制，說(shuō)明書(shū)編寫(xiě) 13周 填寫(xiě)論文副本，完成說(shuō)明書(shū)、圖紙繪制，準(zhǔn)備答辯 教研室審查意見(jiàn)： 同意。 室主任簽名： 2018 年 3 月 5 日 學(xué)院審查意見(jiàn)： 教學(xué)院長(zhǎng)簽名： 年 月 日 3 外文資料翻譯 Overview of adaptable die design for extrusions W.A. Gordon.C.J. Van Tyne.Y.H. Moon ABSTRACT The term “adaptable die design” is used for the methodology in which the tooling shape is determined or modified to produce some optimal property in either product or process. The adaptable die design method, used in conjunction with an upper bound model, allows the rapid evaluation of a large number of die shapes and the discovery of the one that produces the desired outcome. In order for the adaptable die design method to be successful, it is necessary to have a realistic velocity field for the deformation process through extrusion dies of any shape and the velocity field must allow flexibility in material movement to achieve the required material flow description. A variety of criteria can be used in the adaptable die design method. For example, dies which produce minimal distortion in the product. A double optimization process is used to determine the values for the flexible variables in the velocity field and secondly to determine the die shape that best meets the given criteria. The method has been extended to the design of dies for non-axisymmetric product shapes. 2006 Elsevier B.V. All rights reserved. Keywords: Extrusion; Die design; Upper bound approach; Minimum distortion criterion 1. Introduction New metal alloys and composites are being developed to meet demanding applications. Many of these new materials as well as traditional materials have limited workability. Extrusion is a metalworking process that can be used to deform these difficult materials into the shapes needed for specific applications. For a successful extrusion process, metalworking engineers and designers need to know how the extrusion die shape can affect the final product. The present work focuses on the design of appropriate extrusion die shapes. A methodology is presented to determine die shapes that meet specific criteria: either shapes which pro-duce product with optimal set of specified properties, such as minimum distortion in the extrudate, or shapes which produce product by an optimized process, such as minimum extrusion pressure. The term “adaptable die design” is used for the method nology in which the die shape is determined or modified to produce some optimal property in either product or process. This adaptable die design method, used in conjunction with anupper bound model, allows the rapid evaluation of a large number of die shapes and the discovery of the one that can optimize the desired outcome. There are several conditions that need to be met for the adaptable die design method to be viable. First, a generalized but realistic velocity field is needed for use in an upper bound model to mathematically describe the flow of the material during extrusion through dies of any shape. Second, a robust crite- rion needs to be established for the optimization of the die shape. The criterion must be useable within an upper bound model. The full details of the method are presented elsewhere 16. In the present paper, following a review of previous models for extrusion, the flexible velocity field for the deformation region in a direct extrusion will be briefly presented. This velocity field is able to characterize the flow through a die of almost any configuration. The adaptable equation, which describes the die shape, is also presented. The constants in this die shape equation are optimized with respect to a criterion. The criterion, which can be used to minimize distortion, is presented. Finally, the shape of an adaptable die, which produces of an extruded product with minimal distortion, is presented. The objective of the present paper is to provide a brief overview of the adaptable die design method. 2. Background 2.1. Axisymmetric extrusion Numerous studies have analyzed the axisymmetric extrusion of a cylindrical product from a cylindrical billet. Avitzur710 proposed upper bound models for axisymmetric extrusion through conical dies. Zimerman and Avitzur 11 modeled extrusion using the upper bound method, but with generalized shear boundaries. Finite element methods were used by Chen et al. 12 and Liu and Chung 13 to model axisymmetric extrusion through conical dies. Chen and Ling 14 and Nagpal 15 analyzed other die shapes. They developed velocity fields for axisymmetric extrusion through arbitrarily shaped dies. Richmond16 was the first to propose the concept of a streamlined die shape as a die profile optimized for minimal distortion. Yang et al. 17 as well as Yang and Han 18 developed upper bound models for streamlined dies. Srinivasan et al.19 proposed a controlled strain rate die as a streamlined shape, which improved the extrusion process for materials with limited workability. Lu and Lo 20 proposed a die shape with an improved strain rate control. 2.2. Distortion and die shape analysis Numerous analytical and experimental axisymmetric extrusion investigations have examined the die shape and resulting distortion. Avitzur 9 showed that distortion increases with increasing reduction and die angle for axisymmetric extrusion through conical dies. Zimerman and Avitzur 11 and Pan et al. 21 proposed further upper bound models, including ones with flexibility in the velocity field to allow the distorted grid to change with friction. They found that increasing friction causes more distortion in the extruded product. Chen et al.12 con-firmed that distortion increases with increasing reduction, die angle, and friction. Other research work has focused on non-conical die shapes. Nagpal 15 refined the upper bound approach to study alter-native axisymmetric die shapes. Chen and Ling 14 used the upper bound approach to study the flow through cosine, elliptic, and hyperbolic dies in an attempt to find a die shape, which minimized force and redundant strain. Richmond and Devenpeck 16,22,23, instead of assuming a particular type of die shape, decided to design a die based upon some feature of the extruded product. Using slip line analysis and assuming ideal and frictionless conditions, Richmond 16 proposed a stream-lined sigmoidal die, which has smooth transitions at the die entrance and exit. The streamlined die shape is the basis for many efforts in axisymmetric extrusion die design. Yang et al. 17 , Yang and Han 18 , and Ghulman et al. 24 developed upper bound models using streamlined dies. Certain materials, such as metal matrix composites, can be successfully extruded only in a narrow effective strain rate range, leading to the development of controlled strain rate dies. The control of the strain rate in the deformation zone came from studies that showed fiber breakage during the extrusion of whisker reinforced composites decreases when peak strain rate was minimized 25 . Initially developed by Srinivasan et al. 19 , the streamlined die shape attempts to produce a constant strain rate throughout a large region of the deformation zone. Lu and Lo 20 used a refined slab method to account for friction and material property changes in the deformation zone. Kim et al. 26 used FEM to design an axisymmetric controlled strain rate die. They used Bezier curves to describe the die shape and minimized the volumetric effective strain rate deviation in the deformation zone. 2.3. Three-dimensional non-axisymmetric extrusion analysis Both the upper bound and finite element techniques have been used to analyze three-dimensional non-axisymmetric extrusions. Nagpal 27 proposed one of the earliest upper bound analyses for non-axisymmetric extrusion. Upper bound and finite element models were developed Basily and Sansome28 , Boer et al.29 , and Boer and Webster 30 . Kiuchi 31 studied non-axisymmetric extrusions through straight converging dies. Gunasekera and Hoshino 3234 used an upper bound model to study the extrusion of polygonal shapes through converging dies as well as through streamlined dies. Wu and Hsu 35 proposed a flexible velocity field to extrude polygonal shapes through straight converging dies. Han et al. 36 created a velocity field from their previous axisymmetric upper bound model 37 in order to study extrusion through streamlined dies that produced clover-shaped sections. Yang et al. 37 applied a general upper bound model to study extrusion of elliptic and rectangular sections. Han and Yang 38 modeled the extrusion of trocoidal gears. Yang et al. 39 also used finite element analysis to con-firm the experimental and upper bound analysis of the clover sections. Non-axisymmetric three-dimensional extrusions have been studied further by using upper bound elemental technique 40 and spatial elementary rigid zones 41,42 . Streamlined dies have been the proposed die shape for most three-dimensional extrusion. The shape of the die between the entrance and exit has been selected by experience and feel rather than rigorous engineering principles. Nagpal et al. 43 assumed that the final position of a point that was initially on the billet is determined by ensuring that area reduction of local segments was the same as the overall area reduction. Once the final position of a material point was assumed, a third order polynomial was fit between the die entrance and exit points. Gunasekera et al.44 refined this method to allow for re-entrant geometries. Ponalagusamy et al. 45 proposed using Bezier curves for designing streamlined extrusion dies. Kang and Yang46 used finite element models to predict the optimal bearing length for an“L” shape extrusion. Studies on the design of three-dimensional extrusion dies have been limited. The controlled strain rate concept has only been applied to axisymmetric extrusions and not to three-dimensional extrusions 19,20,26. 3. The adaptable die design method The adaptable die design method has been developed and is described in detail in a series of papers 15. The method has been extended to non-axisymmetric three-dimensional extrusion of a round bar to a rectangular shape 6. The major criterion used in developing the method was to minimize the distortion in the product. The present paper provides a brief overview of the method and results from these previous studies. Fig. 1. Schematic diagram of axisymmetric extrusion using spherical coordinate system through a die of arbitrary shape 3.1. Velocity field An upper bound analysis of a metal forming problem requires a kin matically admissible velocity field. Fig. 1 shows the process parameters in a schematic diagram with a spherical coordinate system (r, , ) and the three velocity zones that are used in the upper bound analysis of axisymmetric extrusion through a die with an arbitrary die shape. The material is assumed to be a perfectly plastic material with flow strength,0.he friction, which exists between the deformation zone in he work piece and the die, is characterized by a frictional shear tress, 0/3mf, where the constant friction factor, mf, can take values from 0 to 1. The material starts as a cylinder of radius Ro and is extruded into a cylindrical product of radius fR. Rigid body flow occurs in zones I and III, with velocities of 0v and fv , respectively. Zone II is the deformation region, where the velocity is fairly complex. Two spherical surfaces of velocity discontinuity 1 and 2 separate the three velocity zones. The surface 1 is located a distance 0r from the origin and the surface 2 is located a distance fr from the origin. The coordinate system is centered at the convergence point of the die. The convergence point is defined by the intersection of the axis of symmetry with a line at angle that goes through the point where the die begins its deviation from a cylindrical shape and the exit point of the die. Fig. 1 shows the position of the coordinate system origin. The die surface, which is labeled (r) in Fig. 1, is given in the spherical coordinate system. (r) is the angular position of the die surface as a function of the radial distance from the origin. The die length for the deformation region is given by the parameter L. The best velocity field to describe the flow in the deformation region is the sine-1 velocity field 1,2 . This velocity field uses a base radial velocity, rv , which is modified by an additional term comprised to two functions with each function containing pseudo-independent parameters to determine the radial velocity component in zone II: rrUv (1) The function permits flexibility of flow in the radial, r, direction, and the function permits flexibility of flow in the angular, , direction. The value of rv is determined by assuming proportional distances in a cylindrical sense from the centreline: 2002sincossinrrvvr (2) This velocity field was found to be the best representation of the flow in the deformation region of an extrusion process for an arbitrarily shaped die. The function is represented as a series of Legendre polynomials that are orthogonal over deformation zone. The representation of is: 0aniiiAP x (3) Where 0002/11/ffRRrxwithRRr ia being the coefficients of the Lengendre polynomials Pi(x) and an being the order of the representation. There is a restriction that: 13anoddiiAA ，02aneveniiAA (4) The remaining higher order coefficients (A2 to Aan ) are the pseudo-independent parameters, with values determined by minimization of the total power. Legendre polynomials are used so that higher order terms can be added to the function without causing significant changes in the coefficients of the lower order polynomials. This feature of the Legendre polynomials occurs because they are orthogonal over a finite distance. The function that satisfies the boundary conditions and allows the best description of the flow is: 011 cos1 cosbiniiBB (5) where 011bniiBBi and the high order coefficients B1 to Bbn are pseudo-independent parameters with values determined by minimization of the total power. The order of the representation is bn . It has been shown 3 that an = 6 and bn = 2 are usually sufficient to provide reasonable flexibility for the flow field in the deformation region. 3.2. Die shape The die shape is described by the function (r). The adaptable die shape is described by a set of Legendre polynomials: 0cniiic px (6) where 0002/11/ffRRrxwithrRRand ic being the coefficients of the Legendre polynomials Pi(x). The order of the Legendre polynomial representation is cn . The boundary conditions at the entrance and exit of the deformation region require that: At r = 0r , = At r = fr , = (7) If a streamlined die is used then this function must meet two additional boundary conditions: At r = 0r , 0tanrr At r = fr , 00tanfRrrR (8) 3.3. Distortion criteria The criterion that was found to minimize the distortion in the extrusion product involves minimizing the volumetric effective strain rate deviation 4,5 . The volumetric effective strain rate deviation in the deformation zone is: Where with: (10) and ij are the components of the strain rate field. 3.4. Determining the adaptable die shape The search for the optimal coefficients for the Legendre polynomials representing the die shape is not constrained. A nested optimization routine is used with the velocity field (inside loop) being minimized with respect to the externally supplied power for the process, and the die shape (outside loop) being adapted to minimize the distortion criterion. The final shape is called an adaptable die shape, since the shape has adapted to meet the specified criterion. Fig. 2. Streamlined adaptable die shape with no adaptation in the rotational directiowith red = 0.60, L/Ro= 1.0,mf= 0.1,Rr/Ro= 0.1 and = 1.5. The area reduction ratio is red, Rr is the cornered radius of the rectangular product, and is the height to width ratio of the rectangular product. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.) 3.5. Extension to three-dimensional non-axisymmetric shapes In extending the adaptable die design method from axisymmetric flow to non-axisymmetric three-dimensional flow in the deformation region requires several special considerations 6. First, the velocity field needs to be modified to allow for rotational movement in the deformation region. Second, the bearing region on the exit side of the die needs to be analyzed properly. Third, the functions used to describe the die shape need to have some flexibility in the rotational direction (i.e. (r, ). This flexibility allows die shape adaptation with respect to the rotational coordinate, . 4. Die shape to minimize distortion To illustrate the adaptable die design method a specific three-dimensional example is presented. An extrusion upper bound model was used to determine adaptable die surface shapes, which minimize distortion through minimizing the volumetric effective strain rate deviation in the deformation zone for the extrusion of a cylindrical billet into a round cornered rectangular product. Two schemes were used. In the first method there was no flexibility allowed in the rotational direction, (r), whereas in the second method the die shape was able to adapt in the rotational direction, (r, ). In both methods a streamlined condition was used at the entrance and exit regions of the die. The quarter sections ( =0 to /2) of both die shapes are given in Figs. 2 and 3. Fig. 2is the die shape with no rotational flexibility and in Fig. 3 the die was allowed to adapt its shape in the rotational direction to reduce distortion. For both of these examples the area reduction was 60% and the rectangular product had a width to height ratio, , of 1.5. In Fig. 4, the extrusion die surface shape on the two rectangular symmetry planes of the product is presented. The adaptable die shape with rotational flexibility is different from the die shape obtained without adaptation in the rotational direction especially along the = /2 symmetry plane. The adaptable die shape geometry along the = /2 symmetry plane increases the speed of the material in the deformation zone near the exit. Fig. 5 shows the resulting distorted grid in the extrudate on the two symmetry planes. The adaptable die shape shows a smaller difference in distortion as compared to the die shape without the rotational flexibility. Fig. 3. Streamlined adaptable die shape with adaptation of the die shape in the rotational direction with red = 0.60, L/Ro= 1.0,mf= 0.1,Rr/Ro= 0.1 and = 1.5. Fig. 4. Streamlined die shape with no adaptation as the rotational direction compared to streamlined die shape with adaptation as a function of the rotational directionplotted along rectangular symmetry planes. Fig. 5. Extrudate distorted grid along rectangular symmetry planes for extrusion through a streamlined die shape with no adaptation as the rotational direction compared to a streamlined die shape with adaptation as a function of the rota-tional directionplotted along rectangular symmetry planes. Ar is the width of he extrudate and Br is the height of the extrudate. 5. Summary This paper presented an overview of the “adaptable die design” methodology. The full details of the method are given elsewhere 16. In order to use the adaptable die design method in conjunction with an upper bound analysis, it is necessary to have a velocity field in the deformation region with sufficient flexibility so that the model can be closer to the real flow. The specific criterion of producing a product with minimal distortion involves minimizing the volumetric strain rate deviation. A double optimization process is used (1) to determine the values for the flexible variables in the velocity field and (2) to determine the die shape that best meets the minimum distortion criterion. An example of the method for the design of dies for the extrusion of a cylindrical billet into a round cornered rectangular shape has been presented. 擠壓模具設(shè)計(jì)概述 擠壓模具設(shè)計(jì)概述 摘 要 術(shù)語(yǔ)“適應(yīng)”是用于模具設(shè)計(jì)的方法，在結(jié)果或過(guò)程中確定加工 形 狀或改良來(lái)產(chǎn)生最佳 的性能。模具設(shè)計(jì)方法的適應(yīng)性，使用一個(gè) 上 界，允許快速評(píng)價(jià)一大 批二維模型和發(fā)現(xiàn)那個(gè)想要的結(jié)果。為了 成 功得到合適的擠壓模 具的設(shè)計(jì)方法，擁有一個(gè)現(xiàn)實(shí)的速度場(chǎng)，通 過(guò) 擠 壓 模 具 變 形 過(guò) 程 中 的 任 何 形 狀 和 速 度 場(chǎng) 一 定 要 讓 彈 性 材 料