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1 動(dòng)力與背景 1.1 介紹 最近，對(duì)工程師有用的著作中，行星齒輪傳動(dòng)就像一個(gè)簡(jiǎn)單明了的運(yùn)動(dòng)學(xué)解答一樣給予了一個(gè)明確的分析。不幸的是沒有一個(gè)出版機(jī)構(gòu)愿意出版一個(gè)簡(jiǎn)單的設(shè)計(jì)與分析技術(shù)。這一技術(shù)考慮到了在普通的例子中動(dòng)力在齒輪傳動(dòng)中表現(xiàn)。這論文目的是想彌補(bǔ)這樣一個(gè)空缺，在大多數(shù)的例子中，能找到全部的速度以及周轉(zhuǎn)輪系力的解決方法的技術(shù)。在這方法發(fā)展后，列線圖表可被用作產(chǎn)生直覺設(shè)計(jì)裝置，允許設(shè)計(jì)者通過視覺去分析齒輪傳動(dòng)的運(yùn)動(dòng)形式，而不許不需重復(fù)的去解方程來(lái)完成。終于,方法設(shè)計(jì)與解決裝置的出現(xiàn)，在新的一系列雙軸自行車中，把使用行星輪系的實(shí)際性當(dāng)作能源單位來(lái)聯(lián)結(jié)。 1.2 動(dòng)力 2002 年研究這項(xiàng)上述方法。很大程度上激發(fā)了被承擔(dān)由弗吉尼亞技術(shù)人的供給動(dòng)力的車隊(duì)。在多用車早期設(shè)計(jì)期間進(jìn)入了每年ASME 競(jìng)爭(zhēng), 這表明，對(duì)于兩名車手相對(duì)不一致輸入動(dòng)力最有效的辦法是使用行星輪系。概念在設(shè)計(jì)之后由人力車隊(duì)試圖將使用一列行星齒輪象那個(gè)被顯示在上圖1 創(chuàng)造近似地會(huì)允許兩個(gè)車手對(duì)腳蹬以同樣速度和近似地會(huì)貢獻(xiàn)產(chǎn)品力量的同樣百分比的系統(tǒng)。行星輪系容納在速度和功率輸入上的區(qū)別由二個(gè)車手。輪系特點(diǎn)的本質(zhì)是這份論文焦點(diǎn)。 圖1 圖1: 齒輪傳動(dòng)被使用在人供給動(dòng)力的車的Team..s 設(shè)計(jì)項(xiàng)目中 運(yùn)用Willis的方法為發(fā)現(xiàn)齒輪傳動(dòng)的運(yùn)動(dòng)學(xué)解答, 它被發(fā)現(xiàn)機(jī)制被控制了。 那里..代表在齒輪傳動(dòng)中各個(gè)元素的旋轉(zhuǎn)的速度, 并且R 是齒輪傳動(dòng)的基本的傳輸比率。 執(zhí)行一個(gè)靜態(tài)分析, 扭矩被發(fā)現(xiàn)被控制 那里代表轉(zhuǎn)矩 在各個(gè)元素在傳動(dòng), 并且N 代表齒輪傳動(dòng)中的齒數(shù)。使用這些等式, 它變得明顯, 達(dá)到力量均衡的目標(biāo)以相等和相反輸入速度是不可能的。 如果和被認(rèn)為是相等和相反, 然后達(dá)到力量均衡, T2 和T5 必須并且是相等和對(duì)立的。 根據(jù)等式3, 這意味著R 必須是1 。 不幸地, 這采取分母等式1 到零, 可以驅(qū)動(dòng)到無(wú)限。什么直覺地似乎一個(gè)簡(jiǎn)單的問題解決導(dǎo)致了唯一的解答空間。 以最后期限為競(jìng)爭(zhēng)結(jié)束, 設(shè)計(jì)計(jì)劃被摒棄了傾向于一種更加簡(jiǎn)單的解答。研究完成在試圖設(shè)計(jì)一系列齒輪傳動(dòng)，成為了一個(gè)更加寬廣的研究計(jì)劃的基礎(chǔ)。 這個(gè)項(xiàng)目驅(qū)動(dòng), 而不是系列齒輪傳動(dòng)的設(shè)計(jì)為一個(gè)具體目的, 是創(chuàng)造將允許行星齒輪傳動(dòng)發(fā)展為任一個(gè)可能的應(yīng)用的數(shù)字的一個(gè)簡(jiǎn)明的設(shè)計(jì)方法。 由處理行星在最一般的例子中, 這個(gè)項(xiàng)目以及允許探索HPV 隊(duì)的失敗的原因，設(shè)計(jì)工程師定義運(yùn)動(dòng)學(xué)關(guān)系在行星齒輪傳動(dòng)中的三個(gè)分支之間沒有首先選擇齒輪的一個(gè)物理安排。 1.3背景 一列行星齒輪傳動(dòng)被定義作為任一列齒輪傳動(dòng)中，包含至少循軌道運(yùn)行由轉(zhuǎn)動(dòng)關(guān)于它自轉(zhuǎn)和并且關(guān)于的軸的一個(gè)齒輪, 或載體。 基本行星, 或周轉(zhuǎn)圓, 齒輪傳動(dòng)被顯示在表2, 與被簡(jiǎn)化的表示法一起被使用為這份論文剩下的人。 基本的傳動(dòng)包括二個(gè)齒輪, 太陽(yáng)(1) 和行星(2) 齒輪, 并且第三名成員, 此后指行星載體或架(3)。 圖2 圖2: (a) 基本的周轉(zhuǎn)圓的齒輪傳動(dòng)和(b) 它的運(yùn)動(dòng)學(xué)表示法。 因?yàn)樗茈y直接地把轉(zhuǎn)動(dòng)傳送到從行星齒輪, 基本的周轉(zhuǎn)圓的齒輪傳動(dòng)有些被限制在實(shí)際應(yīng)用。然而，更加有用的是，周轉(zhuǎn)圓傳動(dòng)指簡(jiǎn)單和復(fù)雜行星齒輪傳動(dòng), 那里第二個(gè)太陽(yáng)齒輪被使用。 這些齒輪傳動(dòng)可能會(huì)在任何十二個(gè)安排被指出的圖3. 是依照由L..vai 最初提出。 圖3 圖3: 簡(jiǎn)單和復(fù)雜周轉(zhuǎn)圓的齒輪傳動(dòng)。 傳動(dòng)在象限I 和III 被分類作為簡(jiǎn)單的周轉(zhuǎn)圓傳動(dòng), 因?yàn)樾行驱X輪是在與兩個(gè)太陽(yáng)齒輪嚙合。那些在象限II 和IV 代表復(fù)雜齒輪傳動(dòng), 那里行星齒輪部份地是在互相嚙合和部份地在嚙合與二個(gè)太陽(yáng)齒輪。 注意那, 不管安排, 只一個(gè)行星載體也許被使用。 當(dāng)這個(gè)圖清楚地顯示周轉(zhuǎn)圓的齒輪傳動(dòng)的十二個(gè)可能的排列, 記法使用很被難掌握。 為了援助在實(shí)際傳動(dòng)的形象化模擬, 圖4 顯示更低的布置在象限I的一級(jí)齒輪傳動(dòng)。 圖4 圖4: 象限I 的更低布置的周轉(zhuǎn)圓的齒輪傳動(dòng)在表3。 行星齒輪傳動(dòng)第一次出現(xiàn)在古老中國(guó), 是大約2600BC ,。 當(dāng)磁性指南針?biāo)Q生時(shí)候, 中國(guó)人面對(duì)了難題是運(yùn)用它，橫跨一望無(wú)際的戈壁沙漠。 克服這個(gè)困難,這機(jī)器被發(fā)展了。 這個(gè)設(shè)備使用了一列相對(duì)地復(fù)雜行星齒輪傳動(dòng)，附有驅(qū)動(dòng)的二個(gè)輪子維護(hù)一個(gè)圖在推車上面指向在同樣方向, 不管道路怎樣，都向前運(yùn)動(dòng)。這個(gè)設(shè)備的復(fù)雜似乎表明, 中國(guó)人使用有差別的驅(qū)動(dòng)相當(dāng)一段時(shí)間的傳動(dòng)的裝置的誕生之前。 這時(shí)，行星齒輪傳動(dòng)消失從歷史相當(dāng)一段時(shí)間。 這更加可能歸結(jié)于缺乏目標(biāo), 而不是實(shí)際原則的不用。 在裝置以后, 下次出現(xiàn)行星傳動(dòng)是在什么被命名了安尼可雅機(jī)器。1901 年由海綿潛水者發(fā)現(xiàn)在離Antikythera 希臘海島的沿海的附近, 它由學(xué)者辨認(rèn)了作為類型計(jì)算器被使用為預(yù)言蝕和其它占星術(shù)事件。這個(gè)特殊設(shè)備建于大約82BC, 留下期間行星齒輪傳動(dòng)通過相對(duì)地未被注意的由人類歷史大致2500 年的空白在 行星齒輪的傳動(dòng)原理在遠(yuǎn)東拯救了歐洲的黑暗年代, 由設(shè)備的發(fā)現(xiàn)上見證相似與Antikythera 機(jī)器由伊朗savant 說出Al Biz4una 名字在第一個(gè)世紀(jì)廣告晚期。 在巨大新生期間, 行星被獲取的廣泛用途在星盤和時(shí)鐘里。機(jī)制的用途和發(fā)展在新生過程中一直持續(xù)到當(dāng)今天。 在這點(diǎn)可以有趣的表明, 從2600BC行星原理成功地被使用了, 在1841機(jī)制的衛(wèi)利斯的原則出版之前，任一目的都是為了創(chuàng)造設(shè)備的一個(gè)分析模型。 1.4 文學(xué)回顧 羅伯特?衛(wèi)利斯1857 年的出版物,即機(jī)制的原則, 廣泛被看待如同第一出版物單一地致力現(xiàn)在叫動(dòng)力學(xué)領(lǐng)域。 在他的工作中, 衛(wèi)利斯第一次在出版文學(xué)里談?wù)摲治鏊茉煲恢苻D(zhuǎn)圓的行星齒輪傳動(dòng)。因?yàn)檫@工作純粹地在研究一關(guān)于機(jī)制的, Willis 提出唯一一種解答為旋轉(zhuǎn)的速度在齒輪傳動(dòng)。 在研究這種解答以后, 作者讓剩下的致力周轉(zhuǎn)圓的齒輪傳動(dòng)的人去談?wù)摍C(jī)制的應(yīng)用。當(dāng)這次討論很好被設(shè)想時(shí), 它報(bào)道四種齒輪的周轉(zhuǎn)傳動(dòng)卓而又模糊的應(yīng)用, 由于工作年齡的關(guān)系。 依照早先的陳述, 這工作研究的僅僅是齒輪傳動(dòng)的動(dòng)力學(xué),在機(jī)制中任一次關(guān)于扭矩的討論都沒有提出。 在他的博士論文關(guān)于技術(shù)大學(xué)的建筑中, 民用和運(yùn)輸工程學(xué)在匈牙利, 周轉(zhuǎn)圓的齒輪和周轉(zhuǎn)圓的變速齒輪的理論, Dr Z 。 L..vai 試圖成利用所有早先書面文學(xué)關(guān)于周轉(zhuǎn)齒輪傳動(dòng)并且他稱.周轉(zhuǎn)傳動(dòng)的變速齒輪傳動(dòng), 哪些看來(lái)簡(jiǎn)單地都是些多速度傳輸。 在對(duì)讀者解釋構(gòu)成一周轉(zhuǎn)圓傳動(dòng)時(shí)L..vai第一次確切地指出, 周轉(zhuǎn)圓傳動(dòng)有一十二種可能。他還解釋到, 這十二可能清楚地被劃分為有沒有輔助行星或行星對(duì)。在第一版中的任一目的都是為了清楚而簡(jiǎn)捷的行星傳動(dòng)的所有可能的排列。 在周轉(zhuǎn)圓傳動(dòng)定義以后, L..vai 突然改變了對(duì)它的解答的關(guān)注。 在簡(jiǎn)要地談?wù)摻獯鸱椒ㄒ院笥蒞illis 計(jì)劃, 并且通過Kutzbach的圖解方法，作為它適用于沒有輔助行星輪的傳動(dòng)。最后，他充分談了兩種不同的定義，這定義可能進(jìn)行適用于Kutzbach方法有輔助行星輪的傳動(dòng)。再者，他沒提供在這一系統(tǒng)中的解決扭矩的辦法。 麻省理工學(xué)院,機(jī)械工程Deane Lent教授在1961 年出版了他的著作—— 機(jī)制解析和設(shè)計(jì)。 在這著作中Lent教授再次詳細(xì)提出Willis 關(guān)于找到有三個(gè)與四個(gè)齒輪傳動(dòng)的特別設(shè)計(jì)方法周轉(zhuǎn)圓齒輪傳動(dòng)每一級(jí)的轉(zhuǎn)動(dòng)速度。當(dāng)這些技術(shù)很好的被寫和簡(jiǎn)單應(yīng)用后, 在這一系統(tǒng)中還是沒有關(guān)于扭結(jié)的討論。在這出版書中包括了及比所有Willis 談?wù)摰母嚓P(guān)的幾種行星齒輪傳動(dòng)的應(yīng)用。 約瑟夫?Shigley 和約翰?Uicker 在1980 年出版了他們的動(dòng)力學(xué)文本, 機(jī)器和機(jī)制的理論。 在這著作中不僅Willis..s 方法學(xué)的分析, 而且對(duì)周轉(zhuǎn)圓的齒輪傳動(dòng)有一個(gè)更加完全的定義。他們不僅對(duì)這個(gè)定義進(jìn)行了相當(dāng)數(shù)量的討論,而且他們?cè)俅紊媪薒..vai.的圖象描述行星齒輪傳動(dòng)的十二可能的變異。然而，最重要地是他們?cè)诋?dāng)前齒輪傳動(dòng)中提出了扭矩的一個(gè)解答技術(shù)。不幸地，他們不能把相近的靜態(tài)力量分析作為一般事件; 他們?yōu)橐粋€(gè)特別的安排行星輪，通過根據(jù)自由體圖可提出解答。 這個(gè)方法相對(duì)地簡(jiǎn)單, 它限制設(shè)計(jì)師在早期設(shè)計(jì)過程中對(duì)一對(duì)齒輪排布。機(jī)制和機(jī)械動(dòng)力學(xué), 哈密爾頓Mabie 和查爾斯?Reinholtz 的出版物,出版了大量和Shigley 和Uicker 一樣的信息。 當(dāng)動(dòng)力學(xué)的解析和機(jī)制的靜態(tài)力量是幾乎相同的, Mabie 和Reinholtz 并且提出一個(gè)簡(jiǎn)要的部分來(lái)考慮在從行星輪系中的流通功率。 當(dāng)這次討論沒有直接應(yīng)用這份論文, 它暗示其中使用的方法在齒輪傳動(dòng)中解決靜態(tài)力量為一般事例。 1981 年約翰?Molnar 出版了他的計(jì)算圖。 這著作給出了對(duì)計(jì)算圖優(yōu)秀介紹, 并且充分談?wù)撍麄兊挠猛竞徒ㄖ?這著作在計(jì)算圖的建筑此中被提出是有幫助的。當(dāng)大多數(shù)這出版物致力于計(jì)算圖的再生產(chǎn)，包括問題寬廣的一般類別處理空氣, 水, 并且相關(guān)的機(jī)械設(shè)備, 介紹為新手比足夠的信息提供更多完全地了解對(duì)計(jì)算圖的建筑和用途為幾乎任一個(gè)問題的解答。 2 CAD/CAM 2.1 CAD/CAM導(dǎo)論 縱觀工業(yè)社會(huì)的發(fā)展歷史，諸多發(fā)明都被申請(qǐng)為專利，并且新的技術(shù)體系也逐步進(jìn)化。其中比以前任何一項(xiàng)技術(shù)能對(duì)制造業(yè)產(chǎn)生更迅速、更重大影響的發(fā)明或許就是數(shù)字計(jì)算機(jī)。計(jì)算機(jī)在繪圖部門正在被越來(lái)越多地應(yīng)用于設(shè)計(jì)和工程零部件的詳細(xì)說明中。 計(jì)算機(jī)輔助設(shè)計(jì)(CAD)就是應(yīng)用計(jì)算機(jī)和圖形軟件，在構(gòu)思到文檔形式的過程中來(lái)幫助或改善產(chǎn)品設(shè)計(jì)。計(jì)算機(jī)輔助設(shè)計(jì)通常與一個(gè)交互式計(jì)算機(jī)圖形系統(tǒng)的應(yīng)用聯(lián)系在一起，稱為計(jì)算機(jī)輔助設(shè)計(jì)系統(tǒng)。計(jì)算機(jī)輔助設(shè)計(jì)系統(tǒng)是進(jìn)行產(chǎn)品和零部件的機(jī)械設(shè)計(jì)及幾何建模的強(qiáng)有力的工具。 采用CAD系統(tǒng)支持工程設(shè)計(jì)有以下優(yōu)點(diǎn)： l 提高生產(chǎn)率 l 提高設(shè)計(jì)質(zhì)量 l 統(tǒng)一設(shè)計(jì)標(biāo)準(zhǔn) l 創(chuàng)建制造數(shù)據(jù)庫(kù) l 消除手工繪圖的誤差和不相容性 計(jì)算機(jī)輔助制造（CAM）就是在制造計(jì)劃和控制中有效地使用計(jì)算機(jī)技術(shù)。計(jì)算機(jī)輔助制造是與制造工藝聯(lián)系最緊密的功能，例如工藝過程和生產(chǎn)規(guī)劃、機(jī)械加工、進(jìn)度安排、管理、質(zhì)量控制和數(shù)字控制（NC）零件加工程序。計(jì)算機(jī)輔助設(shè)計(jì)和計(jì)算機(jī)輔助制造經(jīng)常結(jié)合在一起構(gòu)成CAD/CAM系統(tǒng)。 這種結(jié)合在一起的系統(tǒng)允許在制造一種產(chǎn)品時(shí)，從設(shè)計(jì)階段到計(jì)劃階段進(jìn)行信息傳遞，不再需要手工來(lái)輸入零件幾何機(jī)構(gòu)數(shù)據(jù)。在計(jì)算機(jī)輔助設(shè)計(jì)期間建立的數(shù)據(jù)庫(kù)被儲(chǔ)存起來(lái)，然后通過計(jì)算機(jī)復(fù)制造進(jìn)行進(jìn)一步的處理，轉(zhuǎn)變?yōu)椴僮骱涂刂粕a(chǎn)機(jī)械、材料處理裝置和進(jìn)行產(chǎn)品質(zhì)量自動(dòng)檢測(cè)所必需的數(shù)據(jù)和指令。 2.2 CAD/CAM的基本原理 CAD/CAM基本原理類似于用于在制造業(yè)中判斷任何基于技術(shù)的改進(jìn)原理。它產(chǎn)生于生產(chǎn)力、產(chǎn)品質(zhì)量和競(jìng)爭(zhēng)力不斷提高的需求。還有如下一些因素促使一家公司將手工加工方式改造為應(yīng)用CAD/CAM系統(tǒng)來(lái)進(jìn)行生產(chǎn)： l 不斷增長(zhǎng)的生產(chǎn)率 l 更好的產(chǎn)品質(zhì)量 l 更方便的信息交流 l 在制造過程中共用數(shù)據(jù)庫(kù) l 降低制造樣機(jī)的費(fèi)用 l 加快對(duì)用戶的反應(yīng) 2.3 CAD/CAM的硬件 CAD/CAM系統(tǒng)的硬件部分由以下幾塊組成：（1）一個(gè)或多個(gè)設(shè)計(jì)工作站，（2）數(shù)字計(jì)算機(jī)，（3）繪圖儀、打印機(jī)和其他輸出設(shè)備，（4）儲(chǔ)存設(shè)備。另外，CAD/CAM系統(tǒng)有一個(gè)通信接口允許從其他計(jì)算機(jī)系統(tǒng)或向其他計(jì)算機(jī)系統(tǒng)傳遞數(shù)據(jù)，因此有利于一些計(jì)算機(jī)集成。 工作站是CAD系統(tǒng)中計(jì)算機(jī)和用戶之間的接口。CAD工作站的設(shè)計(jì)和它的實(shí)用特征對(duì)用戶輸出的方便性、生產(chǎn)率和質(zhì)量將產(chǎn)生很重要的影響。工作站必需包括一個(gè)圖形顯示終端和一套用戶輸入設(shè)備。CAD/CAM系統(tǒng)的應(yīng)用要求有一臺(tái)具有高速中央處理器（CPU）的數(shù)字計(jì)算機(jī)。它包含主存儲(chǔ)器和邏輯/算術(shù)部分。在CAD/CAM中使用最廣泛的輔助存儲(chǔ)介質(zhì)是硬盤、軟盤或它們兩個(gè)的結(jié)合。 在CAD系統(tǒng)理典型的輸入/輸出設(shè)備如圖10.2所示。輸入設(shè)備一半被用來(lái)把信息從人或者儲(chǔ)存介質(zhì)傳遞到一臺(tái)能夠執(zhí)行“CAD功能”的計(jì)算機(jī)中。有兩種基本方法來(lái)輸入已經(jīng)存在的圖形：在圖紙上建?；虬褕D形數(shù)字化。CAD/CAM的標(biāo)準(zhǔn)輸出設(shè)備是陰極射線管顯示器。有兩種主要類型的陰極射線管顯示器：隨機(jī)掃描圖形顯示器和光柵掃描顯示器，除陰極射線管顯示器外，還有等離子平板顯示器和液晶顯示器。 2.4 CAD/CAM的軟件 軟件使用戶從一個(gè)硬件設(shè)備進(jìn)入一個(gè)強(qiáng)有力的設(shè)計(jì)和制造系統(tǒng)。根據(jù)完成的幾何圖形的維數(shù)，CAD/CAM軟件分為兩大類：二維和三維軟件。在二維空間里描繪對(duì)象的CAD設(shè)計(jì)包稱為二維軟件。早期的系統(tǒng)局限于二維空間。這是一個(gè)嚴(yán)重的缺陷，因?yàn)橛枚S空間來(lái)表示三維的物體本身就容易讓人混淆，而且還存在制造人員自己不能正確讀懂和解釋用來(lái)表示三維物體的二維圖形。三維軟件可使零件的三維尺寸---長(zhǎng)、寬和高均可見。 CAD/CAM的發(fā)展趨向于用三維來(lái)表示圖形。這種表示法接近所描繪的物體和實(shí)際形狀和外觀，因此，它們更容易被讀懂和理解。 2.5 CAD/CAM的應(yīng)用 CAD/CAM的出現(xiàn)對(duì)整個(gè)制造業(yè)有很大的影響，它能夠?qū)a(chǎn)品開發(fā)標(biāo)準(zhǔn)化、降低設(shè)計(jì)強(qiáng)度、減少試驗(yàn)和樣機(jī)制造工作，且能夠節(jié)省相當(dāng)多的成本費(fèi)用并提高生產(chǎn)率。 CAD/CAM的一些典型應(yīng)用如下： l 為數(shù)控、計(jì)算機(jī)數(shù)控和工業(yè)機(jī)器人編程； l 在設(shè)計(jì)鑄造的模具和模型時(shí)，可按照預(yù)編程序縮小加工余量； l 工具、固定裝置和EDM（電火花機(jī)床）電極的設(shè)計(jì)； l 質(zhì)量控制和檢測(cè)，例如：在CAD/CAM工作站中進(jìn)行坐標(biāo)測(cè)量機(jī)編程； l 工藝計(jì)劃與進(jìn)度安排。 2.6 CAD/CAM的優(yōu)點(diǎn) 使用CAD的原因有很多，最有效的動(dòng)力就是競(jìng)爭(zhēng)。為了贏得業(yè)務(wù)，公司使用CAD可以創(chuàng)造出更好的設(shè)計(jì)，并且在設(shè)計(jì)速度上比競(jìng)爭(zhēng)對(duì)手更快，在成本上花費(fèi)更少，。通過使用CAD,生產(chǎn)率得到了很大的提高，使用戶能夠很容易地畫多邊形、橢圓、多條平行線和多條平行的曲線。在繪制對(duì)稱部分時(shí)、復(fù)制、旋轉(zhuǎn)、鏡象這些工具使用起來(lái)也是很方便的。很多飛機(jī)艙口的樣式就是用CAD程序設(shè)計(jì)的。用各種不同的顏色填充空白的區(qū)域是藝術(shù)和表達(dá)的需要。CAD總是提供許多不同類型的字體。能夠?qū)⒉煌膱D形文件格式和掃描材料（照片）導(dǎo)入CAD也是一大優(yōu)點(diǎn)，特別是可以對(duì)圖像進(jìn)行加工、潤(rùn)飾和加入動(dòng)畫效果。 CAD系統(tǒng)另一個(gè)優(yōu)點(diǎn)是能夠儲(chǔ)存在繪圖中經(jīng)常用到的實(shí)體。常用零件庫(kù)可以另外購(gòu)買或者由繪圖員自己創(chuàng)建。在繪圖中反復(fù)使用的一個(gè)典型的項(xiàng)目可以在數(shù)秒內(nèi)檢索并確定它的位置，也可定位在任一角度，以滿足特定的要求。 使用CAD的產(chǎn)品，可以通過插入現(xiàn)有的零件圖到裝配圖中，然后按照要求把他們放在合適的位置來(lái)繪制裝配圖。 不同零部件之間的間距能夠在圖中直接測(cè)量。如果需要，可以使用裝配圖設(shè)計(jì)出額外的零部件作為參考。 CAD非常適合文件的快速歸檔。以前，工程師和繪圖員們浪費(fèi)大約30%的時(shí)間去尋找圖紙和其他文檔。用CAD產(chǎn)品可以快速而簡(jiǎn)便地編輯圖樣，對(duì)以前的東西進(jìn)行修改，更新零件明細(xì)表。 當(dāng)你用紙繪圖而客戶希望修改圖樣的時(shí)候，你就得全部重畫。使用CAD，你可以馬上進(jìn)行修改，并在幾秒鐘之內(nèi)打印出新圖，或者通過E-mail和互聯(lián)網(wǎng)立即傳送到世界各個(gè)地方。在紙上繪制復(fù)雜的幾何圖形時(shí)，經(jīng)常要進(jìn)行很多測(cè)量并且需要確定參考點(diǎn)。在CAD中，這是一個(gè)輕而易舉的事情，修改也更容易了。許多CAD程序包含“宏”或者允許用戶定制的附加程序語(yǔ)言。 定制你的CAD系統(tǒng)來(lái)你的使它適合你的特定要求，并用它實(shí)現(xiàn)你的天才創(chuàng)意，從而使你的CAD系統(tǒng)區(qū)別于你的競(jìng)爭(zhēng)對(duì)手。CAD能夠使企業(yè)完成更出色的設(shè)計(jì)，而用手工的方式幾乎是不可能，同時(shí)排除了概念設(shè)計(jì)階段的不確定選項(xiàng)。 9 1 MOTIVATION AND BACKGROUND 1.1 Introduction In the current literature available to engineers, planetary gear trains are given a clear treatment as far as a simple kinematic solution. Unfortunately, no publications to date present a simple, concise design and analysis technique that considers both the motion and forces present in a gear train in the general case. This thesis attempts to fill this void by presenting a technique for finding a total speed and force solution to an epicyclic gear train in the most general case possible. After developing this solution, nomographs will be used to create an intuitive design aid, allowing the designer to visualize the performance of a gear train without the need to solve equations repeatedly. Finally, the solution technique and design aids presented will be used to address the practicality of using planetary gear trains as a power coupling element in a new generation of tandem bicycles. 1.2 Motivation The research contained herein was motivated by a design effort undertaken by the Virginia Tech Human Powered Vehicle Team in 2002. During the early design of the multi-rider entry into the annual ASME competition, it was suggested that the most effective method for coupling the relatively inconsistent inputs of two human riders would be to use a planetary gear train. The concept behind the design attempted by the human powered vehicle team was to use a gear train like the one shown in figure 1 to create a system that would allow both riders to pedal at approximately the same speed and contribute approximately the same percentage of the output power. The planetary system accommodates differences in speed and power input by the two riders. The nature of the system behavior is the focus of this thesis. Figure 1 Figure 1: Gear train to be used in the Human Powered Vehicle Team’s design effort Using Willis’s [1] method for finding the kinematic solution of the gear train, it was found that the mechanism was governed by where the ω’s represent rotational speeds of each element in the gear train, and R is the basic transmission ratio of the gear train. Performing a static analysis, the torques were found to be controlled by where the T’s represent torques on each element in the train, and the N’s represent number of teeth in each gear in the train. Using these equations, it became apparent that the goal of achieving power balance at equal and opposite input speeds was impossible. If ω2 and ω5 are assumed to be equal and opposite, then to achieve a power balance, T2 and T5 must also be equal and opposite. According to equation 3, this means R must be 1. Unfortunately, this takes the denominator of equation 1 to zero, which drives ω6 to infinity. What had seemed intuitively a simple problem to solve had led to a singularity in the solution space. With deadlines for competition closing in, the design effort was abandoned in favor of a simpler solution. However, the research done in attempting to design a specific gear train became the foundation of a much broader research project. The drive of this project, rather than the design of a gear train for a specific purpose, is to create a concise design method that will allow development of planetary gear trains for any number of possible applications. By dealing with the planetary in the most general case possible, this project explores the reasons for the failure of the HPV team’s design as well as allowing engineers to define the kinematic relationships between the three branches of the planetary gear train without first selecting a physical arrangement of gears. 1.3 Background A planetary gear train is defined as any gear train containing at least one gear that orbits by rotating about its own axis and also about the axis of an arm, or carrier. The elementary planetary, or epicyclic, gear train is shown in figure 2, along with the simplified representation to be used for the remainder of this thesis. The elementary train consists of two gears, the sun (1) and planet (2) gears, and a third member, hereafter referred to as the planet carrier or arm (3). Figure 2: (a) The elementary epicyclic gear train and (b) its kinematical representation Since it is difficult to directly transmit motion to or from the planet gear, the elementary epicyclic gear train is somewhat limited in practical application. More useful, however, are the epicyclic trains referred to as the simple and complex planetary gear trains, where a second sun gear is used. These gear trains can be realized in any of the twelve arrangements set forth in figure 3, as originally presented by Lévai. The trains in quadrants I and III are classified as simple epicyclic trains, since the planet gears are in mesh with both sun gears. Those in quadrants II and IV represent the complex trains, where the planet gears are partially in mesh with each other and partially in mesh with the two sun gears. Notice that, regardless of arrangement, only one planet carrier may be used. Figure 3 Figure 3: The simple and complex epicyclic gear trains While this figure clearly shows the twelve possible arrangements of the epicyclic gear train, the notation used is difficult to grasp. To aid in the visualization of the actual trains represented, figure 4 shows a gear train of the lower arrangement in quadrant I. Figure 4 Figure 4: Epicyclic gear train of the lower arrangement of quadrant I in figure 3 The planetary gear train first appeared in ancient China, around 2600 BC, in a device referred to as the south pointing chariot. At a time when the magnetic compass was still centuries away from its birth, the Chinese faced the difficult task of navigating across the relatively featureless Gobi Desert. To surmount this difficulty, the south pointing chariot was developed. This device used a relatively complex planetary gear train attached to the two wheels of a cart to maintain a figure atop the cart pointing in the same direction, regardless of the path taken by the cart. The complexity of this device seems to indicate that the Chinese had been using differential drives for quite some time before the birth of the south pointing chariot. At this point, the planetary gear train disappears from history for quite some time. This is more likely due to a lack of writing on the subject, rather than the actual disuse of the principle. After the south pointing chariot, the next appearance of the planetary is in what has been named the Antikythera machine. Discovered by sponge divers off the coast of the Greek island ofAntikythera in 1901, it has been identified by scholars as a type of calculator used for predicting eclipses and other astrological events. This particular device has been dated back to approximately 82 BC, leaving a gap of roughly 2500 years during which the planetary gear train passed relatively unnoticed through human history [8]. The principle of the planetary gear survived Europe’s dark ages in the Far East, evidenced by the discovery of a device similar to the Antikythera machine by an Iranian savant named Al-Biz?na in the late first century AD. During the Great Renaissance, the planetary garnered wide use in astrolabes and clocks. The use and development of the mechanism continued throughout the Renaissance and on until present day. It is interesting to note at this point that, while the planetary has been successfully used since 2600 BC, it was not until the 1841 publication of Willis’s Principles of Mechanism [1] that any attempt was made to create an analytical model of the device. 1.4 Literature Review Robert Willis’s 1857 publication, Principles of Mechanism, is widely regarded as the first publication dedicated solely to the field now called kinematics. In his work, Willis discusses for the first time in published literature the analytical modeling of an epicyclic gear train. As this work is a study purely in mechanism, Willis presents only a solution for the rotational speeds in the gear train. After developing this solution, the author spends the remainder of the work dedicated to epicyclic gear trains in discussing applications of the mechanism. While this discussion is well conceived, it covers four remarkably obscure applications of the epicyclic gear train, owing to the age of the work. As stated previously, this work studied only the pure kinematics of the gear train, without any discussion of the torques present in the mechanism. In his doctoral dissertation for The Technical University of Building, Civil and Transport Engineering in Hungary, Theory of Epicyclic Gears and Epicyclic Change-Speed Gears, Dr Z. Lévai attempts to unify all of the previously written literature on epicyclic trains and what he calls “epicyclic change speed gears”, which appear to simply be multiple speed transmissions. In explaining to the reader exactly what constitutes an epicyclic train Lévai identifies, for the first time, the twelve possible variations on the epicyclic train. It is also stated that these twelve variations can be neatly divided into those with and without auxiliary planets or planet pairs. This is the first publication where any attempt was made to clearly and concisely define all possible arrangements of the planetary train. After defining the epicyclic train, Lévai turns his attention to its solution. After briefly discussing the solution method laid out by Willis, and the graphical method of Kutzbach [5] as it applies to trains without auxiliary planets, he discusses at length two different modifications that can be performed to apply the Kutzbach method to a train with auxiliary planets. Again, he offers no treatment of the torques present in the system. Deane Lent, professor of Mechanical Engineering at Massachusetts Institute of Technology, published his work, Analysis and Design of Mechanisms, in 1961. In this work Lent again presents in detail the methodology of Willis for finding the rotational speeds of each branch of the epicyclic gear train, along with specific methods for the design of three and four gear trains. While these techniques are well written and simple to follow, there is again no discussion of torques present in the system. Also included in this publication are several applications of the planetary gear train, all significantly more relevant than those discussed by Willis. Joseph Shigley and John Uicker published their kinematics text, Theory of Machines and Mechanisms, in 1980. Within this work are not only a treatment of Willis’s methodology, but also a more complete definition of the epicyclic gear train. Not only do they dedicate a significant amount of discussion to this definition, but they also reproduce Lévai’s figure demonstrating the twelve possible variations of the planetary gear train. Most importantly, however, they present a solution technique for the torques present in the gear train. Unfortunately they do not approach the static force analysis for the general case; rather they present the solution in terms of free body diagrams for a specific arrangement of the planetary. While this method is relatively simple, it limits the designer to a single arrangement early in the design process. Mechanisms and the Dynamics of Machinery, the publication of Hamilton Mabie and Charles Reinholtz, presents largely the same information as Shigley and Uicker. While the treatment of the kinematics and static forces of the mechanism are nearly identical, Mabie and Reinholtz also present a brief section considering circulating power flow in controlled planetary gear systems. While this discussion has no direct application to this thesis, it does hint at the methods used herein to solve for the static forces in the gear train for the general case. John Molnar published his Nomographs in 1981. This work presents an excellent introduction to nomographs, as well as discussing at length their use and construction. This work was instrumental in the construction of the nomographs presented herein. While the bulk of this publication is dedicated to the reproduction of nomographs covering the broad general category of problems dealing with air, water, and related mechanical devices, the introduction provides more than enough information for a novice to completely understand the construction and use of nomographs for the solution of nearly any problem. 2 CAD/CAM 2.1 Introduction to CAD/CAM Thoughout the history of our industrial society,many inventions have been patented and whole new technologies have evolved.Perhaps the single development that has impacted manufacturing more quickly and significantly than any previous technology is the digital computer.Computer are being used increasingly for both design and detailing of engineering components in the drawing office. Computer-aided design (CAD) is defined as the application of computers and graphics software to aid or enhance the product design from conceptualization to documentation.CAD is most commonly associated with the use of an interactive computer graphics system,referred to as a CAD system.Computer-aided design systems are powerful tools and are used in the mechanical design and geometric modeling of products and components. There are several good reasons for using a CAD system to support the engineering design function: l To increase the productivity l To improve the quality of the design l To uniform design standards l To eliminate inaccuracies caused by hand-copying of drawings and inconsistency between drawings Computer-aided manufacturing (CAM) is defined as the effective use of computer technology in manufacturing planning and control.CAM is most closely associated with functions in manufacturing engineering,such as process and production planning, machining, scheduling, management, quality control, and numerical control (NC) part programming, Computer-aided design and computer-aided manufacturing are often combined into CAD/CAM systems. This combination allows the transfer of information from the design stage into the stage of planning for the manufacturing of a product,without the need reenter the data on part geometry manually.The database developed during CAD is stored; then it is processed further,by CAM,into the necessary data and instructions for operating and controlling production machinery,material-handling equipment,and automated testing and inspection for product quality. 2.2 Rationale for CAD/CAM The rationale for CAD/CAM is similar to that used to justify any technology-based omprovement in manufacturing.It grows out of a need to continually improve productivity,quality and competitiveness.There are also other reasons why a company might make a conversion from manual processes to CAD/CAM: l Increased productivity l Better quality l Better communication l Common database with manufacturing l Reduced prototype construction costs l Faster response to customers 2.3 CAD/CAM Hardware The hardware part of a CAD/CAM system consists of the following components:(1)oneor more design workstaions,(2)digital computer,(3)plotters,printers and other output devices,and (4)storage devices. The relationship among the components is illustrated in Fig.10.1.In addition,the CAD/CAM system would have a communication interface to permit transmission of data to and from other computer systems,thus enabling some of the benefits of computer integration. The workstation is the interface between computer and user in the CAD system.The design of the CAD workstation and its available features have an important influence on the convenience,productivity,and quality of the user’s output.The workstation must include a graphics display terminal and a set of user input devices.CAD/CAM applications require a digital computer with a high-speed control processing unit(CPU).It contains the main memory and logic/arithmetic section for the system.The most widely used secondary storage medium in CAD/CAM is the hard disk,floppy diskette,or a combination of both. The typical I/O devices used in a CAD system are shown in Fig.10.2. Input devices are generally used to transfer information from a human or storage medium to a computer where “CAD functions”are carried out.There are two basic approaches to input an existing drawing:model the object on a drawing or drawing or digitize the drawing.The standard output device for CAD/CAM is a CRT display.There are two major types of CRT displays:random-scan-line-drawing displays and aster-scan displays.In addition to CRT,there are also plasma panel displays and liquid-crystal displays. 2.4 CAD/CAM Software Software allows the human user to turn a hardware configuration into a powerful design and manufacturing system.CAD/CAM software falls into two broad categories,2-D and 3-D, based on the number of dimensions visible in the finished geometry.CAD packages that represent objects in two dimensions visible in the finished geometrey.CAD packages that represent objects in two dimensions are called 2-D software.Early systems were limited to 2-D.This was a serious shortcoming because 2-D representations of 3-D objects is inherently confusing.Equally problem has been the inability of manufacturing personnel to properly read and interpret complicated 2-D representations of objects.3-D software permits the parts to be viewed with the three-dimensional planes-height,width,and depth-visible.The trend in CAD/CAM is toward 3-D representation of graphic images.Such representations approximate the actual shape and appearance of the object to be produced;therefore,they are easier to read and understand. 2.5 Applications of CAD/CAM The emergence of CAD/CAM has had a major impact on manufacturing,by standardizing product development and by reducing design effort,tryout,and prototype work;it has made possible significantly reduced costs and improved productivity. Some typical applications of CAD/CAM are as follows: l Programming for NC,CNC,and industrial robots; l Design of dies and molds for casting,in which,for example,shrinkage allowances are preprogrammed; l Design of tools and fixtures and EDM(electrical-discharge machining)electrodes; l Quality control and inspection---for instance,coordinate-measuring machines programmed on a CAD/CAM workstation; l Process planning and scheduling. 2.6 Advantage of CAD/CAM There are many reasons for using CAD;the most potent driving force is competition.In order to win business,companies used CAD to produce better designs more quickly and more cheaply than their competitors.Productivity is much improved by a CAD program enabling you to easily draw polygons,ellipses,multiple parallel lines and multiple parallel curves.Copy,rotate and mirror facilities are also very handy when drawing symmetrical parts.Many hatch patterns are supplied with CAD programs. Filling areas in various colors is a requirement in artwork and presentations.Different style fonts for text are always supplies with any CAD programs.The possibility of importing different graphic file formats and scanning of material(photographs)into a CAD program is also an asset especially as the image can be manipulated,retouched and animated. Another advantage of CAD system is its ability to store entities,which are frequently used on drawings.Libraries of regularly used parts can be purchased separately or can be created by the draughtsman.For repetitive use on a drawing,a typical item may be retrieved and positioned in seconds,also oriented at any angle to suit particular circumstances. Using CAD products,assembly drawings can be constructed by inserting existing component drawings into the assembly drawing and positioning them as required. Clearance between different components can be measured directly from the drawing,and if required,additional components designed using assembly as reference. CAD is very suitable for fast doc