裝配圖懲罰函數(shù)法二級圓柱齒輪減速器的優(yōu)化設計

裝配圖懲罰函數(shù)法二級圓柱齒輪減速器的優(yōu)化設計,裝配,懲罰,函數(shù),二級,圓柱齒輪,減速器,優(yōu)化,設計 一、 選題的依據(jù)及意義： 齒輪減速器是原動機和工作機之間的獨立的閉式傳動裝置，用來降低轉(zhuǎn)速和增大轉(zhuǎn)矩，以滿足工作需要，在某些場合也用來增速，稱為增速器。其特點是減速電機和大型減速機的結(jié)合。無須聯(lián)軸器和適配器，結(jié)構(gòu)緊湊。負載分布在行星齒輪上，因而承載能力比一般斜齒輪減速機高。滿足小空間高扭矩輸出的需要。廣泛應用于大型礦山，鋼鐵，化工，港口，環(huán)保等領(lǐng)域。與K、R系列組合能得到更大速比。按照齒形分為圓柱齒輪減速器、圓錐齒輪減速器和圓柱—圓錐齒輪減速器; 二級圓柱齒輪減速器就是按其分類來命名的。圓柱齒輪減速器的設計是按傳統(tǒng)方法進行的。設計人員按照各種資料、文獻提供的數(shù)據(jù)，結(jié)合自己的設計實驗，并對已有減速器做一番對比，初步定出一個設計方案，然后對這個方案進行一些驗算，如果驗算通過了，方案便被肯定了。顯然，這個方案是可采用的。但這往往使設計的減速器有很大的尺寸富余量，造成財力、物力和人力的極大浪費。因此，優(yōu)化圓柱齒輪減速器勢在必行。 圓柱齒輪傳動與普通定軸齒輪傳動相比較，具有質(zhì)量小、體積小、傳動比大、承載能力大以及傳動平穩(wěn)和傳動效率高等優(yōu)點，這些已被我國越來越多的機械工程技術(shù)人員所了解和重視。由于在各種類型的圓柱齒輪傳動中均有效的利用了功率分流性和輸入、輸出的同軸性以及合理地采用了內(nèi)嚙合，才使得其具有了上述的許多獨特的優(yōu)點。圓柱齒輪傳動不僅適用于高速、大功率而且可用于低速、大轉(zhuǎn)矩的機械傳動裝置上。它可以用作減速、增速和變速傳動，運動的合成和分解，以及其特殊的應用中；這些功用對于現(xiàn)代機械傳動發(fā)展有著重要意義。因此，圓柱齒輪傳動在起重運輸、工程機械、冶金礦山、石油化工、建筑機械、輕工紡織、醫(yī)療器械、儀器儀表、汽車、船舶、兵器、和航空航天等工業(yè)部門均獲得了廣泛的應用。對這種減速器進行優(yōu)化設計，必將獲得可觀的經(jīng)濟效益。 選做這個畢業(yè)設計，一方面對于減速器的內(nèi)部結(jié)構(gòu)和工作原理也有一定的了解和基礎(chǔ)，其次通過對圓柱齒輪減速器這一畢業(yè)課題設計可以鞏固我大學4年來所學的專業(yè)知識，對于我也是一種檢驗?？梢匀鏅z驗我大學所學的知識是否全面，是否能靈活運用到實際生活工作中。在做的過程中我還可以不斷學習和拓寬視野和思路，做到理論與實際相結(jié)合的運用。最重要的是對于即將離校走向社會的我是一種挑戰(zhàn)，培養(yǎng)我獨立思考，樹立全局觀念，為以后的我奠定堅實的基礎(chǔ)。 二、 國內(nèi)外研究概況及發(fā)展趨勢（含文獻綜述）： 隨著時代進步，科技與時俱進，對于齒輪的傳動越來越多的科技因素在起 著主導地位。世界上一些工業(yè)發(fā)達國家，如日本、德國、英國、美國和俄羅斯等，對齒輪傳動的應用，生產(chǎn)和研究都十分重視，在結(jié)構(gòu)優(yōu)化、傳動性能，傳動功率、轉(zhuǎn)矩和速度等方面均處于領(lǐng)先地位，并出現(xiàn)一些新型的圓柱傳動技術(shù)，如封閉圓柱齒輪傳動、圓柱齒輪變速傳動和微型圓柱齒輪傳動等早已在現(xiàn)代化的機械傳動設備中獲得了成功的應用。圓柱齒輪傳動在我國已有了許多年的發(fā)展史，很早就有了應用。然而，自20世紀60年代以來，我國才開始對圓柱齒輪傳動進行了較深入、系統(tǒng)的研究和試制工作。無論是在設計理論方面，還是在試制和應用實踐方面，均取得了較大的成就，并獲得了許多的研究成果。 近20多年來，尤其是我國改革開放以來，隨著我國科學技術(shù)水平的進步和發(fā)展，我國已從世界上許多工業(yè)發(fā)達國家引進了大量先進的機械設備和技術(shù)，經(jīng)過我國機械科技人員不斷積極的吸收和消化，與時俱進，開拓創(chuàng)新地努力奮進，使我國的齒輪傳動技術(shù)有了迅速的發(fā)展。國內(nèi)減速器行業(yè)重點骨干企業(yè)的產(chǎn)品品種、規(guī)格及參數(shù)覆蓋范圍近幾年都在不斷擴展，產(chǎn)品質(zhì)量已達到國外先進工業(yè)國家同類產(chǎn)品水平。?縱觀國內(nèi)減速器行業(yè)的現(xiàn)狀，為保持行業(yè)的健康可持續(xù)發(fā)展在充分肯定行業(yè)不斷發(fā)展、進步的同時，更應看到存在的問題，并積極研究對策，采取措施，力爭在較短時間內(nèi)能有所進展。目前，同外減速器行業(yè)存在的比較突出的問題是，行業(yè)整體新產(chǎn)品開發(fā)能力弱、工藝創(chuàng)新及管理水平低，企業(yè)管理方式較為粗放，相當比例的產(chǎn)品仍為中低檔次、缺乏有國際影響力的產(chǎn)品品牌、行業(yè)整體散、亂情況依然較為嚴重?；诖耍七M行業(yè)優(yōu)勢企業(yè)間的購并、整合，盡快形成有著一定的市場影響力的品牌、有較大規(guī)模的和實力、有較強產(chǎn)品研發(fā)和技術(shù)支持能力的這樣若干個集團型企業(yè)，如此放能在與國外同行的競爭中保持一定的優(yōu)勢并不斷得以發(fā)展。? 國內(nèi)減速器行業(yè)重點骨干企業(yè)的產(chǎn)品品種、規(guī)格及參數(shù)覆蓋范圍近幾年都在不斷擴展，產(chǎn)品質(zhì)量已達到國外先進工業(yè)國家同類產(chǎn)品水平，完全可承擔起為國民經(jīng)濟各行業(yè)提供傳動裝置配套的重任，部分產(chǎn)品還出口至歐美及東南亞地區(qū)。? 目前，國內(nèi)各類通用減速器的標準系列已達數(shù)百個，基本可滿足各行業(yè)對通用減速器的需求。在第一代通用硬齒面齒輪減速器及圓弧圓柱蝸桿減速器系列產(chǎn)品的基礎(chǔ)上，由西安重型機械研究落開發(fā)并完成標準化的新一代圓柱及圓錐——圓柱齒輪減速器及圓弧圓柱蝸桿減速器業(yè)已投方市場。新一代減速器的突出特點為不僅在產(chǎn)品性能參數(shù)上進一步進行于優(yōu)化，而且在系列設計上完全遵從模塊化的設計原則，產(chǎn)品造型更加美觀，更宜于組織批量生產(chǎn)，更適應現(xiàn)代工業(yè)不斷發(fā)展而對基礎(chǔ)件產(chǎn)品提出的愈來愈高的配套要求。此外，南京高精齒輪股份有限公司也推動了PR系列的模塊式齒輪減速器系列產(chǎn)品。但總體而言，國內(nèi)同外減速器系列產(chǎn)品的開發(fā)及更新工作近幾年進展緩慢，與國外同行在此方面的差距有拉大的趨勢。而且與市場的需求也很不適應，西安重型機械研究所及國內(nèi)其他單位今年已著手開始這方面的開發(fā)級標準化工作。????? 在通用減速器的制造方面，國內(nèi)目前生產(chǎn)廠家數(shù)目眾多，如對各種類型的圓柱齒輪機圓錐——圓柱齒輪或者齒輪——蝸桿減速器系列產(chǎn)品，國內(nèi)主要廠家有南京高精齒輪股份有限公司、寧波東力傳動設備有限公司、江陰齒輪箱制造有限公司、江蘇泰星減速器有限公司、江蘇金象減速機有限公司、山西平遙減速機廠等。對象蝸桿減速器，目前國內(nèi)主要生產(chǎn)圓弧圓柱蝸桿減速器、錐面包絡圓柱蝸桿減速器、平面二次包絡環(huán)面蝸桿減速器等多種類型，主要生產(chǎn)廠家有江蘇金象減速機有限公司、首鋼機械制造公司、杭州減機廠、杭州萬杰減速劑有限公司、天津萬新減速機廠、上海浦江減速機有限公司等，對各種通用圓柱齒輪減速器、包括標準的NGW系列圓柱齒輪減速器，也包括各類回轉(zhuǎn)圓柱減速器及封閉式圓柱齒輪檢錄其等，主要生產(chǎn)廠家有荊州巨鯨動機械有限公司、洛陽中重齒輪箱有限公司、西安重型機械研究所、石家莊科一重工有限公司、內(nèi)蒙興華機械廠等。? 在各類專用傳動裝置的開發(fā)機制造方面，國內(nèi)近幾年取得的明顯的進展，如重慶齒輪箱有限責任公司生產(chǎn)的MDH28型磨機邊緣驅(qū)動傳動裝置，其最大功率已達7000KW，傳動轉(zhuǎn)矩達5000KN.m，總重46噸，生產(chǎn)的1700熱連軋主傳動齒輪箱子的最大模數(shù)為30，重量達180噸。由杭州前進齒輪箱有限公司生產(chǎn)的gwc70/76型1.2萬噸及裝箱船用齒輪箱，傳動功率已達6250KW。(轉(zhuǎn)載中國鍛壓網(wǎng))由南京高精齒輪股份有限公司及重慶齒輪箱有限公司生產(chǎn)的里磨系列齒輪箱最大功率已達3800KW，由西安重型機械研究所、洛陽重重齒輪箱有限公司、荊州巨鯨傳動機械有限公司等開發(fā)制造的重載圓柱齒輪箱系列產(chǎn)品在礦山、冶金、建材、煤炭及水電等行業(yè)也都得到了廣泛應用，其中西安重型機械研究所開發(fā)的水泥行業(yè)輥壓機懸掛系列圓柱齒輪箱的輸入功率已達1250KW，用于鋁造軋機的圓柱齒輪箱有司責任公司、杭州前進出論箱有限公司、西安重型機械研究所開發(fā)的風力發(fā)電增速箱系列產(chǎn)品也逐步取代進口產(chǎn)品，廣泛應用于國內(nèi)風電行業(yè)。在大型齒圈的制造方面，國內(nèi)目前最大直徑為9.936米，凈重達80噸的齒圈已由中信重機制造完成，并用于武鋼集團年產(chǎn)500萬噸氧化球生產(chǎn)線，至此用于大型燒結(jié)機、磨機、回轉(zhuǎn)窯的大型驅(qū)動裝置以及用于轉(zhuǎn)爐及燒結(jié)設備的大型柔性傳動裝置國內(nèi)均可圈套供貨，而無需再行進口。???????? 在其他類型新產(chǎn)品的開發(fā)方面，行業(yè)企業(yè)也取得了不少成果，如西安重型機械研究所開發(fā)的工程車輛變速箱和風機及泵用差動節(jié)能調(diào)速裝置、洛陽中重齒輪箱有限公司的大型礦井提升機圓柱齒輪箱、江蘇金象減速機公司的磨機驅(qū)動齒輪箱、北京太富力傳動有限公司的大型三環(huán)傳動齒輪箱及傳動裝置等，也都受到了市場的歡迎并得以廣泛應用。? ???????在行業(yè)企業(yè)的產(chǎn)能擴展及技術(shù)改造方面，近幾年呈現(xiàn)出跨越式的發(fā)展，這一方面得益于近幾年市場強勁需求的拉動，另一方面也是受企業(yè)擴大生產(chǎn)規(guī)模、提升加工制造水平、進而提升企業(yè)競爭力的主觀愿望的驅(qū)動，國內(nèi)主要產(chǎn)品廠家近二年購進的關(guān)鍵加工設備，如大型磨齒機、鏜銑床、技工中心及熱處理設備等，累計超過200余臺（套），預計行業(yè)產(chǎn)能擴大一倍以上，技改工作的開展固然有提審行業(yè)企業(yè)規(guī)模和生產(chǎn)集中度及競爭力的客觀效果，但由于仍存在行業(yè)企業(yè)數(shù)量多、規(guī)格小及水平參差不齊等實際問題，因之隨著市場需求的回落和國外同行廠商大規(guī)模進入國內(nèi)市場，行業(yè)競爭必將進一步加劇，這也必將促進行業(yè)企業(yè)間的購并、整合甚至轉(zhuǎn)型。 據(jù)有關(guān)資料介紹，人們認為目前齒輪傳動技術(shù)的發(fā)展方向如下： （1） 標準化、多品種 目前世界上已經(jīng)有50多個漸開線圓柱齒輪傳動系列設計；而且還演化出多種形式的圓柱減速器、差速器和圓柱變速器等多種產(chǎn)品。 （2） 硬齒面、高精度 圓柱傳動機構(gòu)中的齒輪廣泛采用滲碳和氮化等化學熱處理。齒輪制造精度一般均在6級以上。顯然，采用硬齒面、高精度有利于進一步提高承載能力，使齒輪尺寸變得更小。 （3） 高轉(zhuǎn)速、大功率 圓柱齒輪傳動機構(gòu)在高速傳動中，如在高速汽輪中已獲得日益廣泛的應用，其傳動功率也越來越大。 大規(guī)格、大轉(zhuǎn)矩 在中低速、重載傳動中，傳遞大轉(zhuǎn)矩的大規(guī)格的圓柱齒輪傳動已有了較大的發(fā)展。 三、 研究內(nèi)容及實驗方案： 在圓柱齒輪傳動的設計時，應該根據(jù)設計任務書所要求該圓柱傳動的要求（原始數(shù)據(jù)及設計技術(shù)要求），進一步分析該傳動所需的使用要求、工作狀況和所需齒輪的機械特性，首先應了解和掌握該圓柱齒輪傳動的已知條件；通常，已知的其原始數(shù)據(jù)為輸入功率、輸入轉(zhuǎn)速、傳動比、工作特性和載荷工況等。 建立優(yōu)化設計模型，優(yōu)化問題的數(shù)學是實際優(yōu)化設計問題的數(shù)學抽象。在明確設計變量、約束條件、目標函數(shù)之后，優(yōu)化設計問題就可以轉(zhuǎn)化成一般數(shù)學問題。采用懲罰函數(shù)法對設計參數(shù)進行約束優(yōu)化，以中心距最小為目標進行優(yōu)化設計，并與常規(guī)設計進行比較。進而繪制出減速器裝配圖及主要零件圖。 二級圓柱齒輪減速器的優(yōu)化設計的一般原則是： （1）各級傳動的承載能力大致相等（可以最大性能的發(fā)揮減速器的承載能力）； （2）在一定承載能力下，減速器具有最小的外形尺寸和重量； （3）各級傳動中大齒輪的浸油深度大致相等。 四、目標、主要特色及工作進度 1、設計目標： 設計出的圓柱齒輪減速器：其輸入功率P=6.2kW，輸入轉(zhuǎn)速n1=1450r/min，總傳動比i=16.5，齒輪的寬度系數(shù)φa=0.4，工作壽命10年，每年工作300天。結(jié)構(gòu)緊湊、傳動功率較高，采用懲罰函數(shù)法，以中心距最小為目標進行減速器優(yōu)化設計 2、圓柱齒輪減速器主要特色： 1、重量輕、體積小，結(jié)構(gòu)緊湊、承載能力大 2、傳動效率高 3、傳動功率范圍大，可以實現(xiàn)運動的合成與分解 4、運動平穩(wěn)、抗沖擊和振動的能力較強 5、采用硬齒面技術(shù)，使用壽命長，使用性廣。 3、工作進度： 1. 收集資料、開題報告、外文翻譯 3.05－3.25 第1周—第3周 2. 建立優(yōu)化設計的數(shù)學模型 3.26－4.8 第4周—第6周 3．編寫優(yōu)化設計程序、計算 4.11－4.24 第 7周—第9周 4. 減速器常規(guī)設計計算、結(jié)果分析 4.25－5.6 第10周—第12周 5. 繪制減速器裝配圖及主要零件圖 5.9－5.20 第13周—第14周 6. 撰寫畢業(yè)設計論文 5.21－5.31 第15周—第16周 7．答辯準備及論文答辯 6.1－6.2 第17周 五、參考文獻 [1]、璞良貴，紀名剛主編.機械設計.第八版.北京：高等教育出版社，2007 [2]、孫靖民主編.機械優(yōu)化設計.第三版.北京：機械工業(yè)出版社，2005 [3]、方世杰，綦耀光主編.機械優(yōu)化設計.北京：機械工業(yè)出版社，1997.2 [4]、王昆等主編. 機械設計課程設計手冊.北京：機械工業(yè)出版社，2004 [5]、Carrol, R., and Johnson, G.,“Optimal design of compact spur gear sets”, ASME Journal of mechanisms, transmissions and automation in design. Vol.106, No.1, March 1984, pp.95-101 6 畢業(yè)設計（論文）開題報告 題目 懲罰函數(shù)法二級圓柱齒輪減速器的優(yōu)化設計 專 業(yè) 名 稱 機械設計制造及其自動化 班 級 學 號 078105214 學 生 姓 名 江 崇 文 指 導 教 師 朱 保 利 填 表 日 期 2011 年 3 月 23 日 懲罰函數(shù)法二級圓柱齒輪減速器的優(yōu)化設計 學生姓名：江崇文 班級：0781052 指導老師：朱保利 摘要：減速器是各類機械設備中廣泛使用的傳動裝置。其主要特點為傳遞功率大、制造簡單、維修方便和使用壽命長等優(yōu)點。傳統(tǒng)的減速器設計一般通過反復的試湊、校核確定設計方案，雖然也能獲得滿足給定條件的設計方案，實踐證明，按照傳統(tǒng)設計方法作出的設計方案，大部分都有改進的余地，不是最佳方案。 本文將對二級圓柱齒輪減速器進行優(yōu)化設計?？紤]到以中心距最小為目標，在此采用了懲罰函數(shù)法。通過設計變量的選取、目標函數(shù)和約束條件的確定，建立了圓柱齒輪減速器設計的數(shù)學模型。編寫了優(yōu)化設計程序，通過在計算機上運行和計算，得出優(yōu)化設計各參數(shù)的大小。從理論上對圓柱齒輪減速器的結(jié)構(gòu)進行了分析并作了常規(guī)設計，并對其它的一些附件進行了相應的設計，設計完畢，對其齒面、齒根彎曲強度進行校核，結(jié)果滿足要求。結(jié)果表明，采用優(yōu)化設計方法后，在滿足強度要求的前提下，減速器的尺寸大大降低了，減少了用材及成本，提高了設計效率和質(zhì)量。 關(guān)鍵詞：圓柱齒輪減速器 優(yōu)化設計 懲罰函數(shù)法 中心距 常規(guī)設計 指導老師簽名： Penalty function Optimal Design for Two-Grade Helical Cylindrical Gear Redactor Student name：Jiang Chong Wen Class：0781052 Supervisor：Zhu Bao Li Abstract：Reducer is a transmission device which is widely found in mechanical equipment. The main characteristics of it is large power transmission、manufacture simple、easy maintenance and long life. Traditionally, in order to get satisfied design data of reducer, you must cut and try again and again. Although this design can satisfy conditions given. Proved by the practice, according to the traditional design method to the design, most of them have room for improvement, it is not optimal. In this article we will two-grade helical cylindrical gear redactor conduct optimal design . Taking account the minimum distance of center into the goal, penalty function used in this method . In this paper, by the way of selecting design variable , setting up goal function and restriction condition , the mathematical model of cylindrical gear reducer is established . The preparation of the optimal design program , run by the computer and calculating the optimal design parameters . The structure of the gear reducer is analyzed and made conventional design in theory, and some other accessories for the corresponding design , which proved reasonable for the the checking of Tooth surface and tooth root bending strength after the designation completed . The results show that the optimal design methods , strength requirements are met under the premise of the size reducer greatly reduced, reducing the timber and the cost , improve the design efficiency and quality. Key words: Helical Cylindrical Gear Redactor optimal design penalty function Center distance Conventional Design Signature of supervisor: Optimal Design of Compliant Trailing Edge for Shape Changing Abstract: Adaptive wings have long used smooth morphing technique of compliant leading an d trailing edge to improve their aerodynamic characteristics．This paper introduces a systematic approach to design compliant structures to carry out required shape changes under distributed pressure loads．In order to minimize the deviation of the deformed shape from the target shape，this method uses M ATLAB and ANSYS to optimize the distributed compliant mechanisms by way of the ground approach and genetic algorithm (GA)to remove the elements possessive of very low stresses．In the optimization process，man y factors should be considered such as air loads，input displacements，and geometric nonlinearities。Direct search method is used to locally optimize the dimension an d input displacement after the GA optimization。The resultant structure could make its shape change from 0 to 9．3degreesTheexperimental data of the model confirm s the feasibility of this approach． Keywords： adaptive wing；compliant mechanism；genetic algorithm ；topology optimization；distributed pressure load；geometric nonlinearity 1 Introduction： As conventional airfoil contours are usually designed with specific lift coefficients and M ach numbers，they could not change in accordance with the environment changing．Siclari and Austin indicated that the variable camber trailing edge would produce the drag about sixty percent less than the conventional fixed camber airfoil There are three methods used to design able camber wings．Of them．one is conventional hinged mechanism，which，however, will create discontinuities over the wings surface leading to earlier airflow separation an d drag increase． The others are smart material and the compliant mechanism，of which both could realize smooth shape changing．Nevertheless，compared to the compliant mechanism，the smart—material—made actuators have many disadvantages，such as deficient in energy ,slow in response，strong in hysteresis，limited by temperature，and difficult to control too many actuators．Musolff from Industry University of Berlin used Ni—Ti shape—memory—alloy wire to make an adaptive variable camber wing，which could quickly change its shape，but could not perform highly frequent alteration because of its resilience depend en ton the heat exchange with the outside environment。 Compliant mechanism is a kind of one-piece flexible structure，which can transfer motion and power through its own elastic deformation．It is not only flexible enough to deform，but also has enough stiffness to withstand external loads．Thanks to its joint—free nature，it does not have the trouble some problems confronted by conventional mechanism such as friction，lubrication，noise and recoiling，thereby achieving smooth shape changing. In 1 994，Kota，a professor from University of Michigan，firstly pointed out that compliant mechanism could be used to control static shape changing under the sponsorship of the Air Force Of ice of Scientific Research in USA．Saggere and Kota suggested a new method to design compliant adaptive structures，which made the least square errors between the shape—changed curve and the target curve as the objective function for optimization．Based on their work，Lu put forward a load path representation method．However, her work was limited to only linear analysis under consideration of nodal loads．Good[ from Virginia Polytechnic Institute of State University used the compliant mechanism and the Moving Asymptotes method to design the fuselage tail within the allowable range of its tip maximal deflection．Kota and He trick in2004 designed a compliant trailing edge on the base of the F16s data，which can change from 0。to 15。and obtained a patent．Campanile from German Aerospace Center presented a modal procedure to design synthetic flexible mechanisms for airfoil shape control，and pointed out that the future re—search should take into account the air load and the geometric nonlinearity．Buhl from Riso National Laboratory of the Wind Energy Department in Denmark used the SIM P method and geometrically nonlinear finite element method to design compliant trailing edge flaps．FlxSys Inc in 2006 produced an adaptive compliant wing，which stood the test on the White Knight airplane．The results indicated that the compliant trailing edge could change+10 ．In China，the research of adaptive wing has been concentrated on smart material and conventional mechanism．Few people，it seems，have worked on designing adaptive wings with the compliant mechanism．Yang is an exception．He analyzed the active aero—elastic wings based on the aero—servo— elasticity technology．Chen and Huang separately investigated the morphing of the compliant leading edge from the viewpoints of discreteness and continuity. This paper presents a method to design the shape changeable structure by MATLAB and AN—SYS associated with distributed compliant mechanism on the base of the ground structure approach and genetic algorithm (GA)taking into account the external distributed loads and geometric nonlinearity. 2 Optimization Process: 2．1 Defining the trailing edge model and objective function As shown in Fig．1，both curves represent two ideal shapes of the trailing edge in the different flying states．One side point)of the structure is supposed to be fixed，and the other side point) to be sliding horizontally. Firstly, the design domain should be defined by the initial curve shape．the input location and the boundary conditions．Then．it is divided with abeam element network simulating the bird’s feather as shown in Fig．2．This is termed the partial ground structure method. Fig．1 Initial shape and target shape Fig．2 Discretization of the design domain The simplest and most effective way to manufacture the planar compliant mechanism is to use wire—cutting technology．In the optimization pro—gram，all the elements are of rectangular beams with the same width equal to the thickness of the material，every beams height being a design variable． In order to make the structure’s deformation come close to the target shape curve，the least square error(LSE)between the deformed curve and the target curve is defined as the objective function．LSE is the sum of squares of position differences of various points along the curves Its expression is where I (=1，2，?，P)is the number of the points along the curves，P is the total number of points．a(chǎn)ndare the coordinates of it h node on the target and deformed boundary curve respectively． The constraints are Where J (=1，2，?， )is the number of elements，miss the tota1 number of elements，，hi the dimension variable，hmin and hmax are the lower and upper bounds of the element beam height for all elements with the value dependent on manufacturing，hb the height of the boundary elements， the maximumnoda1 deformation of the nodes on the curve boundary when the input point is inactive，and should be smaller than[d]to ensure structure stiffness，[d] the allowable maximum displacement when the input point is inactive，O'max the maximum stress of al1 the elements which must be smaller than Tj to prevent yielding，Tj the topology variable equal to 1，or else0 when the element is eliminated． 2．2 GA optimization GA is an optimization method which simulates the heuristic selection rule in nature，where the fit．test living things have the most chance to survive，but the inferior ones also have the opportunity to exist． Different from the continuous optimization method，it does not require the gradient-based in—formation of the objective function. Every element could be expressed as a topology variable and a dimension variable． There—fore，each individua1 could be coded as follows where ，2 is the number of elements except the boundary ones．With the same heights，the boundary elements throughout the optimizing process are represented by only one variable，hb. The fitness is the criterion of the GA optimization．It could be transformed from the objective function into where βis a coefficient deciding the compulsive selection of the betterindividua1．The smaller the value，the more different would be between the two individuals’fitness thus increasing the compulsiveness of choosing the individual of higher fitness． The selection of control parameters plays an important role in the convergence of the GA．Generally speaking．the cross probability ranges 0．40—0．99；the mutation probability is 0．000 01-0．01．a(chǎn)nd the number of individuals 1 0．200． The variable would be updated through the crossover and mutation，so the possible design could generate in the GA process． 2．3 Finite element analysis(FEA) Because of the limited design variables and the target function，the optimization module of FEA software could not be used to design the compliant morphing mechanism．Therefore，this paper programmed the GA in MATLAB and the FEA in ANSYS．In the FEA，taking only account of geo—metric nonlinearities and the material being of linear elasticity, ANSYS could solve the node displacements and the element stresses．Then by deleting the elements with low stress，the fitness could be calculated．Fig．3 shows the detailed process． Fig．3 Flowchart of the structural optimization program． 2．4 Second optimization Although the GA could optimize the topology and dimension simultaneously in a large solution space，the dimension usually could not directly converge to the optimization．In order to solve this problem，after the GA，the Direct Search method should be used to find the best values of the input displacement and the dimensions of the elements which remain in the results after the GA． For morphing of compliant mechanism，F(xiàn)ig．3describes the whole optimization process．It mainly contains initialization of the design domain，F(xiàn)EA，GA optimization and second optimization. 3 Presentation of Results: Adopted from Ref，the sizes of the initial and the target trailing edge are reduced by sixty percent．，I1ab1e 1 lists the design parameters. Because the displacement is used as the input，the nonlinear analysis could hardly converge and the stress of the initia1 solutions is very large．Which should be considered after thirtieth generation. Table 1 Design parameters Fig．4 and Fig．5 illustrate the results from the GA optimization and the second optimization respectively． Fig．4 Results after the GA optimization Fig．5 Results after the second optimization． Form Table 2，it could be found that through the second optimization of the input displacement and the dimension，the LSE is reduced by 1．352 8mmand improved by 3．13％ ．The altered angle is increased by 1．049 3 Table 2 Results after the two optimization Fig．6 Stability of final optimal structure Fig．6 shows the influences of the parameters when the outside distributed pressure load changes from 0 to 1 0 N／mm and the input displacement re—mains 1 1．389 7 mm on the optimal structure．It could be seen that the optimal structure has a good stability if the load is kept in the range Of 0—5 N／mm．As the external load exceeds 5 N／mm，the max stress is likely to exceed the yield stress． Because this optimization program is based on the M ATLAB and ANSYS．in order to verify the results．a(chǎn)n attempt is made to introduce the analytical results of the optimized structure into ANSYS and PATRAN respectively, and then a comparison is made between them．As shown in Fig．7 and Fig．8，the two altered shapes are in good agreement：for in ANSYS the tip displacement is 54．97mm and in PATRRAN 54．50mm．The minor difference between them is from the software． Fig．7 Results of FEA in ANSYS Fig．8 Results of FEA in PATRAN On the other hand，a model is made by wire—cutting technology to verify the analytical results．The material of the mode1．identical with that of the design，is 5 mm thick．In the experiment，the distributed pressure load is assumed to be zero．The input displacement 11．389 7mm with the required input load 146 N．Fig．9 shows the model and the experimental result．The altered angle is measured9．3。．a(chǎn)nd the tip displacement 53mm．The altered shape well accords to the optimized result．If a displacement of 11．3897mm is imposed on the model，the theoretical tip displacement is 54．796 mm． Be．cause of the friction there is between the model and the experiment table a tiny difference will take place between the measured data and the calculated results． Fig．9 The model and experimental result 4 Conclusions： Proved by the simulation and experiments，the proposed method to design morphing compliant mechanism is effectual in turning out a trailing edge with required morphing effects and ability of with—standing external loads．The combination of MAT—LAB and ANSYS in the optimization renders the program simple and universa1．There is no need for frequent changes of the rigid matrix．It also avoids the complexity of programming the nonlinear FEA and the transforming distributed loads into nodal loads．Using the mixed code，the topology and the dimension could simultaneously be optimized by the GA．Removing the free elements after the FEA could speed up the optimization．The second optimization could improve the GA results． 20