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河北建筑工程學院 畢業(yè)設計（論文）開題報告 課題 名稱 ZL50裝載機總體及變速箱設計（第二行星排） 系 別： 機械工程系 專 業(yè)： 機械設計制造及其自動化 班 級： 機094 學生姓名： 張 維 學 號： 2009307405 指導教師： 王少雷 課題來源 導師課題 課題類別 工程設計 一、論文資料的準備 裝載機是一種用途非常廣泛得工程機械，它廣泛應用于鏟裝、搬運、卸載、平整散裝物料，也可以對巖石硬土等進行輕度得鏟掘工作。因此，它被廣泛應用于建筑、公路、鐵路、水電、港口、礦山及國防等工程中。裝載機對加快工程建設速度、減輕勞動強度、提高工程質量、降低工程成本具有重要作用。所以裝載機在國內外不論是品種還是產量，都有飛速發(fā)展，并且成為工程機械的主要品種之一。 我國的輪式裝載機是從20世紀70年代初期發(fā)展起來的，與其他機種工程機械相比，輪式裝載機的橋、箱、泵、閥及缸等零部件產品配套相對成熟，已經形成了比較完整的配套體系。而且自90年代以來，國內外工程機械進入了一個新的發(fā)展時期。工程機械產品以信息技術為先導，在發(fā)動機燃料燃燒與電控、液壓控制系統(tǒng)、自動操縱、可視化駕駛、精確定位與作業(yè)、故障診斷與監(jiān)控、節(jié)能與環(huán)保等方面，有了長足的進步。設計人員開發(fā)出了許多新結構和新產品。ZL50型裝載機作為主導產品，經過多年的發(fā)展，質量水平得到不斷提高，已經形成獨立的產品系列和行業(yè)門類。近年來，國內外裝載機的發(fā)展趨向于采用新結構新技術，并向機電一體化、電子化方向發(fā)展。 然而，我國裝載機在設計上存在很多問題，主要集中在可靠性、結構設計強度等方面。而變速箱對于裝載機來說又是重中之重，所以變速箱的設計好壞直接影響到裝載機的使用壽命以及工作效率。雖然現(xiàn)在市場上的裝載機已經日趨成熟，但對其進行改進設計，尤其是對裝載機的變速箱進行改進設計，仍有非常重要的意義。 ZL50裝載機所采用的是行星式動力換擋變速箱： 首先，星行變速箱的主要優(yōu)點是，可通過在行星排中設計多個行星輪，使載荷由幾對齒共同傳遞，減輕了每對齒上的載荷，以便選用較小的模數(shù)，從而減小齒輪體積，因此行星變速箱在徑向方向尺寸較緊湊。但軸向尺寸則與所采用的行星排數(shù)目有關，當行星排數(shù)較多時，則軸向尺寸較大。另外還可實現(xiàn)輸入與輸出軸同心轉動。 其中簡單行星排是由太陽輪、齒圈、行星架和行星輪組成。由于行星輪軸向旋轉與外界連接困難，故在行星排中只有太陽輪、齒圈和行星架三個元件能與外界相連，并稱為基本元件。在行星排傳遞運動過程中，行星輪只起到傳遞運動的惰輪作用，與傳動比無直接關系。其中三個基本元件的傳遞中僅有兩個是獨立參數(shù)，這表示行星排具有兩個自由度。當以某種方式固定某一個元件后，行星排變成了一自由度系統(tǒng)，即可由轉速方程式確定另外兩元件的轉速比。這樣，通過將行星排三個基本元件分別作為固定件、主動件或從動件，則可組成六種方案。 由于zl50裝載機采用雙渦輪變矩器和機械自動變速裝置相結合，可以得到較大的變矩系數(shù)，且高效率范圍寬，其作用相當于變矩器加上一個二檔自動變速箱（隨外負荷變化，不需人操縱，自動換擋）。因此他后面的行星變速箱檔位數(shù)可以減少，ZL50型裝載機的行星變速箱，有兩個行星排組成，只有兩個前進擋和一個倒檔。輸入軸和輸入齒輪做成一體，與二級渦輪輸出齒輪常嚙合，二檔輸入軸與二檔制動器摩擦片連成一體。前后行星排的太陽輪、行星輪、齒圈的齒數(shù)相同。兩行星排的太陽輪制成一體，通過花鍵與輸入軸、二檔輸入軸相連。前行星排齒圈與后行星排星架、二檔離合器受壓盤三者通過花鍵連成一體。前行星排行星架和后行星排齒圈分別設有倒檔、一檔制動器摩擦片。 變速箱后部是一個分動箱，輸出齒輪用螺栓和二檔油缸、二檔離合器受壓盤連成一體，同變速箱輸出齒輪組成常嚙齒輪副，后者用花鍵和前橋輸出軸連接。后橋輸出軸前端用滑動軸承支撐在前橋輸出軸后面中心孔內；后端則以滾動軸承支撐在殼體上。前、后橋離合套用花鍵和前、后橋輸出軸相連，并可由撥叉波動，當離合套移向前面時，前后輪同時驅動；當離合套移向后面時，則只有前橋驅動。離合套通過拉桿、撥叉來操縱，并有鎖定機構。 相比液力機械傳動系統(tǒng)的裝載機不能拖啟動；當柴油機熄火后，便不能轉向；不能利用柴油機進行排氣制動。ZL50裝載機的傳動系統(tǒng)中設有“三合一”機構，可以解決這些問題。 此構件由以下零件組成，空轉齒輪通過一個滾動軸承支撐在閉鎖離合器被動鼓軸上，滑動嚙合套與閉鎖離合器被動鼓周通過花鍵連接。中間傳動軸，其上固定著齒輪1，此齒輪與另一齒輪2嚙合，齒輪3通過滾珠軸承和自由輪支撐在中間傳動軸上。齒輪3與油泵齒輪相嚙合，而油泵齒輪變矩器泵輪齒圈相嚙合。 當發(fā)動機啟動后，發(fā)動機由被動變?yōu)橹鲃?，它要反過來通過這條傳動路線來驅動車輪。由于自由輪只能單向傳動，反向傳動時，它自動把動力切斷，這樣，防止有可能發(fā)動機通過兩條傳動路線來驅動車輪，發(fā)生干涉，使“三合一”機構受損。三合一機構存有一個缺點，當發(fā)動機突然熄火時，要想利用發(fā)動機制動和保持動力轉向，需將嚙合套迅速連接上，但往往難于結合上。 基于上述內容，此設計主要是改進變速箱，設計過程：變速箱行星機構進行運動學和動力學分析，行星變速箱傳動方案簡圖設計，齒輪傳動部分設計，換擋制動器和閉鎖離合器設計，行星變速箱結構分析。跟緊裝載機行業(yè)向高檔、高技術含量和智能化方向發(fā)展的趨勢，開發(fā)和生產具有自主知識產權、適合我國國情的重型車用變速器。 二、本課題的目的（重點及擬解決的關鍵問題） 輪式裝載機總體設計，是機械設計制造及其自動化專業(yè)學習的一個重要的環(huán)節(jié)。通過設計提高我們對機構的分析能力，機械構造設計的能力，機電一體化系統(tǒng)設計能力，掌握實踐生產過程自動化的設計方法，并鍛煉機械類學生的綜合素質。通過設計，我們將有關課程（如機械原理，機械設計，理論力學，材料力學，液壓與氣壓傳動，工程材料，材料成型，自動控制理論，電氣控制，測試技術，數(shù)控技術，微型計算機原理及應用等）中所獲得的理論知識在實際中綜合地加以運用，并使這些知識得到鞏固和發(fā)展，并使理論知識和生產密切的結合起來。 關鍵問題：了解裝載機的發(fā)展狀況和結構類型，確定裝載機總體參數(shù)、總體布置；分析行星機構的運動學和動力學，其中包括運動分析、力矩分析、功率分析；分析行星齒輪變速箱，其包括行星變速箱組成、自由度和檔位數(shù)分析，行星變速箱轉速分析，行星變速箱力矩分析；設計行星變速箱傳動方案簡圖；設計齒輪傳動部分，包括基本參數(shù)的確定、配齒計算、齒輪的幾何計算；分析行星變速箱結構，包括行星變速箱中不轉動部分的支撐和定位、旋轉零件的支撐和定位。編寫符合要求的設計說明書，并正確繪制機械與液壓工程圖紙，獨立撰寫一分畢業(yè)論文，并繪制有關圖表。 三、主要內容、研究方法、研究思路 （1） 設計任務： ① 裝載機的發(fā)展狀況和結構類別 ② 裝載機總體參數(shù)的確定 ③ 裝載機的總體布置 ④ 裝載機變速箱傳動特性分析 （2） 裝載機變速箱的設計和計算 ① 變速箱結構形式的選擇 ② 變速箱行星排運動和受力分析 ③ 行星變速箱傳動方案簡圖設計 通過對資料的調查、收集、加工與整理，綜合運用多學科的理論、知識與技能，分析解決變速箱設計中的問題。并且經過實習，了解變速箱的實際工作狀況，在對變速箱設計過程中有所幫助外，還能使自己的設計更加接近實際。 四、總體安排和進度（包括階段性工作內容及完成日期） 2013.3.29-2013.4.11 熟悉整理資料 2013.4.12-2013.4.25 方案選擇及總體設計 2013.4.26-2013.5.9 繪制總圖 2013.5.10-2013.5.23 變速箱傳統(tǒng)系統(tǒng)分析 2013.5.24-2013.6.13 行星排設計及受力分析計算 2013.6.14-2013.6.22 繪制零件圖紙 2013.6.23-2013.6.27 準備論文及答辯 五、主要參考文獻 [1]吳永平等.工程機械設計機 北京 化學工業(yè)出版社 2007. 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[18] 聞邦椿.機械設計手冊（第五版）北京 機械工業(yè)出版社，2010. 指導教師意見： 指導教師簽名： 日期： 教研室意見： 教研室主任簽名： 日期： 系意見： 系領導簽名： 日期： 系蓋章 課題來源：導師課題、社會實踐、自選、其他 課題類別：工程設計、施工技術、新品開發(fā)、軟件開發(fā)、科學實驗、畢業(yè)論文。 河北建筑工程學院 畢業(yè)實習報告 系 別 機械工程系 專 業(yè) 機械設計制造及其自動化 班 級 機094班 姓 名 張 維 學 號 2009407405 指導教師 王少雷 實習成績 畢業(yè)實習報告 1.實習目的 通過參觀數(shù)控機床及其操作，將所學專業(yè)知識與實踐相結合，并根據(jù)實習內容不斷總結來豐富自己的經驗；不斷培養(yǎng)獨立思考問題、解決問題、自學能力以及在工作中團隊協(xié)作的精神，最終將自己的所學運用于這次畢業(yè)設計中，設計出符合要求畢業(yè)設計成果，并通過這次實踐來檢驗所學的理論知識。 2.實習內容 本次實習的地點:天津大學；時間：2013年4月2 日；內容：本次實習的主要內容是對數(shù)控機床有一個總體的了解，并對本次所要設計的相關數(shù)控編程和加工程序有一個詳細的了解。本次實習所要解決的主要問題包括：數(shù)控機床的工作原理和其先進性、設計加工零件程序和相關編程。 3.實習結果 在老師的講解下，我們對五軸聯(lián)動數(shù)控機床了解的最多，五軸聯(lián)動數(shù)控機床是一種科技含量高、精密度高專門用于加工復雜曲面的機床，這種機床系統(tǒng)對一個國家的航空、航天、軍事、科研、精密器械、高精醫(yī)療設備等等行業(yè)有著舉足輕重的影響力。 目前，五軸聯(lián)動數(shù)控機床系統(tǒng)是解決葉輪、葉片、船用螺旋槳、重型發(fā)電機轉子、汽輪機轉子、大型柴油機曲軸等等加工的唯一手段。 五軸聯(lián)動機床的使用，讓工件的裝夾變得容易。加工時無需特殊夾具，降低了夾具的成本，避免了多次裝夾，提高模具加工精度。采用五軸技術加工 模具可以減少夾具的使用數(shù)量。另外，由于五軸聯(lián)動機床可在加工中省去許多特殊刀具，所以降低了刀具成本。五軸聯(lián)動機床在加工中能增加刀具的有效切削刃長 度，減小切削力，提高刀具使用壽命，降低成本。采用五軸聯(lián)動機床加工模具可以很快的完成模具加工，交貨快，更好的保證模具的加工質量，使模具加工變得更加 容易，并且使模具修改變得容易。在傳統(tǒng)的模具加工中，一般用立式加工中心來完成工件的銑削加工。隨著模具制造技術的不斷發(fā)展，立式加工中心本身的一些弱點 表現(xiàn)得越來越明顯?，F(xiàn)代模具加工普遍使用球頭銑刀來加工，球頭銑刀在模具加工中帶來好處非常明顯，但是如果用立式加工中心的話，其底面的線速度為零，這樣 底面的光潔度就很差，如果使用四、五軸聯(lián)動機床加工技術加工模具，可以克服上述不足。 五軸聯(lián)動加工中心有高效率、高精度的特點，工件一次裝夾就可完成五面體的加工。若配以五軸聯(lián)動的高檔數(shù)控系統(tǒng)，還可以對復雜的空間曲面進行高精度加工，更能夠適應像汽車零部件、飛機結構件等現(xiàn)代模具的加工。立式五軸加工中心的回轉軸有兩種方式，一種是工作臺回轉軸，設置在床身上的工作臺可以環(huán)繞X軸回轉，定義為A軸，A軸一般工作范圍+30度至-120度。工作臺的中間還設有一個回轉臺，在圖示的位置上環(huán)繞Z軸回轉，定義為C軸，C軸都是360度回轉。這樣通過A軸與C軸的組合，固定在工作臺上的工件除了底面之外，其余的五個面都可以由立式主軸進行加工。A軸和C軸最小分度值一般為0.001度，這樣又可以把工件細分成任意角度，加工出傾斜面、傾斜孔等。A軸和C軸如與XYZ三直線軸實現(xiàn)聯(lián)動，就可加工出復雜的空間曲面，當然這需要高檔的數(shù)控系統(tǒng)、伺服系統(tǒng)以及軟件的支持。這種設置方式的優(yōu)點是主軸的結構比較簡單，主軸剛性非常好，制造成本比較低。但一般工作臺不能設計太大，承重也較小，特別是當A軸回轉大于等于90度時，工件切削時會對工作臺帶來很大的承載力矩。 另一種是依靠立式主軸頭的回轉。主軸前端是一個回轉頭，能自行環(huán)繞Z軸360度，成為C軸，回轉頭上還有帶可環(huán)繞X軸旋轉的A軸，一般可達±90度以上，實現(xiàn)上述同樣的功能。這種設置方式的優(yōu)點是主軸加工非常靈活，工作臺也可以設計的非常大，客機龐大的機身、巨大的發(fā)動機殼都可以在這類加工中心上加工。這種設計還有一大優(yōu)點：我們在使用球面銑刀加工曲面時，當?shù)毒咧行木€垂直于加工面時，由于球面銑刀的頂點線速度為零，頂點切出的工件表面質量會很差，采用主軸回轉的設計，令主軸相對工件轉過一個角度，使球面銑刀避開頂點切削，保證有一定的線速度，可提高表面加工質量。這種結構非常受模具高精度曲面加工的歡迎，這是工作臺回轉式加工中心難以做到的。為了達到回轉的高精度，高檔的回轉軸還配置了圓光柵尺反饋，分度精度都在幾秒以內，當然這類主軸的回轉結構比較復雜，制造成本也較高。 此外，我們還了解到數(shù)控機床許多優(yōu)點，在將來機械發(fā)展領域內，數(shù)控將是重中之重。 與普通機床相比，數(shù)控機床有如下特點： 1、對加工對象的適應性強，適應模具等產品單件生產的特點，為模具的制造提供了合適的加工方法； 2、加工精度高，具有穩(wěn)定的加工質量； 3、可進行多坐標的聯(lián)動，能加工形狀復雜的零件； 4、加工零件改變時，一般只需要更改數(shù)控程序，可節(jié)省生產準備時間； 5、機床本身的精度高、剛性大，可選擇有利的加工用量，生產率高（一般為普通機床的3~5倍）； 6、機床自動化程度高，可以減輕勞動強度； 7、有利于生產管理的現(xiàn)代化。數(shù)控機床使用數(shù)字信息與標準代碼處理、傳遞信息，使用了計算機控制方法，為計算機輔助設計、制造及管理一體化奠定了基礎； 8、對操作人員的素質要求較高，對維修人員的技術要求更高； 9、可靠性高。 與傳統(tǒng)機床相比，數(shù)控具有以下一些特點。 1、具有高度柔性 在數(shù)控機床上加工零件，主要取決于加工程序，它與普通機床不同，不必制造，更換許多模具、夾具，不需要經常重新調整機床。因此，數(shù)控機床適用于所加工的零件頻繁更換的場合，亦即適合單件，小批量產品的生產及新產品的開發(fā)，從而縮短了生產準備周期，節(jié)省了大量工藝裝備的費用。 2、加工精度高 數(shù)控機床的加工精度一般可達0.05—0.1MM，數(shù)控機床是按數(shù)字信號形式控制的，數(shù)控裝置每輸出一脈沖信號，則機床移動部件移動一具脈沖當量（一般為0.001MM），而且機床進給傳動鏈的反向間隙與絲桿螺距平均誤差可由數(shù)控裝置進行曲補償，因此，數(shù)控機床定位精度比較高。 3、加工質量穩(wěn)定、可靠 加工同一批零件，在同一機床，在相同加工條件下，使用相同刀具和加工程序，刀具的走刀軌跡完全相同，零件的一致性好，質量穩(wěn)定。 4、生產率高 數(shù)控機床可有效地減少零件的加工時間和輔助時間，數(shù)控機床的主軸聲速 和進給量的范圍大，允許機床進行大切削量的強力切削。數(shù)控機床正進入高速加工時代，數(shù)控機床移動部件的快速移動和定位及高速切削加工，極大地提高了生產率。另外，與加工中心的刀庫配合使用，可實現(xiàn)在一臺機床上進行多道工序的連續(xù)加工，減少了半成品的工序間周轉時間，提高了生產率。 5、改善勞動條件 數(shù)控機床加工前是經調整好后，輸入程序并啟動，機床就能有自動連續(xù)地進行加工，直至加工結束。操作者要做的只是程序的輸入、編輯、零件裝卸、刀具準備、加工狀態(tài)的觀測、零件的檢驗等工作，勞動強度大降低，機床操作者的勞動趨于智力型工作。另外，機床一般是結合起來，既清潔，又安全。 6、利用生產管理現(xiàn)代化 數(shù)控機床的加工，可預先精確估計加工時間，對所使用的刀具、夾具可進行規(guī)范化，現(xiàn)代化管理，易于實現(xiàn)加工信息的標準化，已與計算機輔助設計與制造（CAD/CAM）有機地結合起來，是現(xiàn)代化集成制造技術的基礎。 4.實習總結 此次實習，我不僅學到了很多數(shù)控方面的知識，而且也看到了很多先進的數(shù)控機床和一些先進的測量儀器，豐富了我們的見識，開闊了我們的視野，讓我將之前所學的數(shù)控知識更好地理解，許多以前學習中出現(xiàn)的疑惑都迎刃而解，對于此次實習看到的不懂的東西，我也通過查找各種圖書資料以及到網(wǎng)上查找相關資料來了解，這樣使我的知識得以豐富和完善。更看到了數(shù)控行業(yè)在國家發(fā)展中的重要作用，這更堅定了我學習數(shù)控研究數(shù)控的決心。 此次實習，雖然時間不長，但是我卻收獲良多，在這里看到了先進的各式各樣的數(shù)控加工設備，增加了我對數(shù)控領域知識的理解，拓寬了我的視野。同時通過這次實習，我認識到了實踐的重要性。實踐中蘊含了無窮無盡的知識，這些知識需要我們在實踐中取發(fā)現(xiàn)、去總結。這些在學校無法學到的知識以及寶貴的人生經歷將激勵我在以后的人生路上勇于實踐，開拓創(chuàng)新。同時，我們應好好珍惜每一個學習的機會，讓自己變的充實而有內涵。 總而言之，此次天津之行，在王老師的指導下，受益匪淺，為我人生的下一次輝煌奠定堅實的基礎，成為我受益終生的寶貴財富。 Science China Press and Springer-Verlag Berlin Heidelberg 2010 Review Mechanical Engineering SPECIAL TOPIC: Huazhong University of Science and Technology October 2010 Vol.55 No.30: 34083418 doi: 10.1007/s11434-010-3247-7 Tool path generation and simulation of dynamic cutting process for five-axis NC machining DING Han 1* , BI QingZhen 2 , ZHU LiMin 2 2 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China Received October 9, 2009; accepted December 29, 2009 Five-axis NC machining provides a valid and efficient way to manufacture the mechanical parts with complex shapes, which are widely used in aerospace, energy and national defense industries. Its technology innovations have attracted much attention in re- cent years. In this paper, the state-of-the-art techniques for five-axis machining process planning are summarized and the chal- lenging problems are analyzed from the perspectives of tool path generation, integrated geometric/mechanistic simulation and machining stability analysis. The recent progresses in accessibility-based tool orientation optimization, cutter location (CL) plan- ning for line contact and three-order point contact machining, shape control of cutter envelope surface and milling stability pre- diction are introduced in detail. Finally, the emerging trends and future challenges are briefly discussed. five-axis machining, tool path generation, integrated geometric/mechanistic simulation, dynamics simulation Citation: Ding H, Bi Q Z, Zhu L M, et al. Tool path generation and simulation of dynamic cutting process for five-axis NC machining. Chinese Sci Bull, 2010, 55: 34083418, doi: 10.1007/s11434-010-3247-7 In conventional three-axis NC machining only the transla- tion motions of the cutter are permitted while the cutter ori- entation is allowed to change in a five-axis machine tool because of the two additional rotational axes. The advan- tages of five-axis NC machining mainly depend on the con- trol of tool orientations: (1) The collision between the part and the cutter can be avoided by selecting the accessible tool orientation, which provides the ability to machine the complicated shapes such as aerospace impeller, turbo blade and marine propeller. (2) A large machining strip width can be obtained if the tool orientation is properly planed so that the tool tip geometry matches the part geometry well. Also, the highly efficient flank milling can be applied to machine aerospace impeller by using a five-axis machine tool. (3) The cutting conditions can be improved in five-axis ma- chining. For example, it is possible to shorten the tool overhang length if the tool orientation is optimized. Deter- mining the safe and shortest tool length is very helpful when *Corresponding author (email: ) the surface is machined in a confined space, in which only the small-diameter cutters can be used. The cutting area of a cutter, which affects the cutting force, cutter wear and ma- chined surface quality can also be controlled by changing the cutter orientation. Besides the above advantages, there exist several chal- lenging problems in five-axis machining. Since the tool orientation is adjustable, it is hard to image the complicated spatial motion of the tool. Thus, it is much more difficult to generate the collision-free and high efficient tool paths, which limits its wide application. Furthermore, the cutting force prediction and dynamics simulation are more complex because the involved cutting parameters are time-varying during the machining process. Current works about five- axis machining fall into three categories 1: tool path gen- eration, integrated geometric/mechanistic simulation and dynamics simulation, as shown in Figure 1. Tool path gen- eration is the process to plan the cutter trajectory relative to the part based on the part model, machining method and tolerance requirement. The cutter trajectory affects greatly DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3409 the cutting efficiency and quality. It is also the foundation of integrated geometric/mechanistic simulation, which de- pends on the cutting geometry and cutting force modeling techniques. The cutting geometry reflects the meshing state between the cutter and the workpiece during the material removing process. By integrating the cutting geometry and cutting force models, the transient cutting force can be pre- dicted. The cutting force then can be applied to dynamics simulation, feedrate scheduling, and prediction and com- pensation of deformation. The goal of dynamics simulation is to predict the cutting stability and the machined surface profile based on the cutting force and the dynamics charac- teristics of the machine tool-cutter-fixture system. Dynam- ics simulation is helpful to optimize the cutting parameters and the tool path. The literatures on five-axis NC machining are enormous. A lot of related commercial systems have been developed, such as the general-purpose CAM softwares UG and CATIA, the special CAM software Max-AB for machining impeller and Turbosoft for machining blade, and the dy- namics simulation software CutterPro. European Commis- sion supported a project about flank milling optimization that is called “Flamingo”. Because of the obvious advan- tages of flank milling in cutting efficiency and surface qual- ity, a number of famous companies (SNECMA, Rolls Royce, Dassault Systmes) and a university (Hannover) participated in this project. The researches on five-axis high-efficiency and high-precision machining have also been carried out in some famous companies, such as United Technologies, Pratt it is difficult to automatically generate the opti- mum tool orientations that consider simultaneously all the Figure 1 Three challenging problems in five-axis NC machining. objectives required by the practical cutting process, such as collision avoidance, large effective cutting width, globally cutter orientation smoothness and shorter tool length. Also, most of the existing works about dynamics simulation aim to three-axis machining. Models and algorithms applicable to five-axis machining need to be explored. 1 Tool path generation Tool path generation is the most important technology in NC programming. The critical problem in five-axis ma- chining is to plan cutter orientations. Theoretically, the tool orientation can be any point on the Gauss Sphere. In fact, the feasible tool orientations are only a limited area on the Gauss Sphere because of the constraints of global collision avoidance and machine joint angle limits. To improve ma- chining efficiency and quality, the tool orientation of each cutter location (CL) data should be optimized by consider- ing the important factors related to a practical cutting proc- ess. The factors consist of geometrical constraints, kine- matic constraints, dynamic characteristics and physical fac- tors. How to take into account these factors is the most challenging issue in the research of tool path generation. 1.1 Collision avoidance Collision avoidance must be first considered in the process of tool path generation. There are mainly two kinds of ideas to avoid interference: (1) First generating and then adjusting cutter orientation to avoid collision. (2) Access-based tool path generation. With the former idea, cutter orientations are first planned according to some strategies. A collision detection method is then used to detect the collision be- tween the tool and the parts. If collision occurs, the tool orientations must be changed as shown in Figure 2. With the latter idea, the cutter orientations are generated directly in the accessibility cones as shown in Figure 3. The research about the first idea focuses on the algo- rithms to improve the collision detection efficiency and ad- just cutter orientations to avoid collision. In practical appli- cations, tool paths are usually composed of thousands to hundred thousands of tool positions. The collision detection often requires large computation time and resource. There- fore lots of algorithms have been proposed to improve the computation efficiency of collision detection 2,3. When machining a complex shape, the detection and adjustment processes usually repeat several times. Collision avoidance is of first concern. It is difficult to consider other factors affect- ing the cutting process when adjusting cutter orientations. The access-based tool path generation method consists of two steps. Collision-free cutter orientations at every cutter contact (CC) point are first computed. The set of colli- sion-free cutter orientations is called accessibility cone. The cutter orientations are then generated in the accessibility 3410 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 Figure 2 Detecting and adjusting cutter orientation to avoid collision 2. (a) Collision detection; (b) adjust cutter orientation. Figure 3 Access-based collision-free tool path generation. (a) Accessi- bility cone; (b) collision-free tool path. cones. The most obvious merit of this method is that the iterative process of adjusting cutter orientations can almost be avoided. Based on the accessibility cone, the manufac- turability can be directly determined. Furthermore, the cut- ter orientation optimization can be carried out in the colli- sion-free space. Other objectives such as cutting forces and velocity smoothness may also be considered. The problem with this idea is the difficulty in efficiently computing ac- cessibility cones. Usually computing accessibilities will cost large computation time because complex shape may consist of hundreds of thousands of polygonal meshes. Some algo- rithms were proposed to improve computation efficiency such as the C-space (Configuration Space) methods 4,5 and visibility-based methods 610. Though C-space is an elegant concept to deal with collision avoidance, the free C-space cannot be explicitly and efficiently computed. Wang et al. 5 showed that the elapsed time to compute an accessibility cone for a part composed of only 10000 trian- gles would be 1190.33 min. Furthermore, the algorithm did not consider the collision of the tool holder. A cutter can be abstracted as a light ray that emits from the CL point if its radius is ignored. Then the problem of collision avoidance is transformed into that of visibility. We 68 described cutters visibility cone using the concept of C-space and proposed three strategies to accelerate the computation speed using the hidden-surface removal techniques in com- puter graphics. The manufacturability of a complex surface was also analyzed based on the visibility cone. However, the conventional visibility is only the necessary condition of accessibility because a milling tool usually consists of sev- eral cylindrical shapes with finite radii. The real accessible directions cannot be directly obtained from the visibility cone, and secondary collision checking and avoidance strat- egies are still needed 9. The accessibility will be equal to the visibility if both the machined surface and the interfer- ence checking surface are replaced by their offset surfaces 10. However, the offset surface is usually not easy to ob- tain and the collision avoidance of the tool holder cannot be guaranteed. Furthermore, the method only applies to ball- end cutters and cannot be extended to other types of cutters. We 11,12 proposed a high-efficient algorithm to compute the accessibility cone using graphics hardware. The algo- rithm has almost linear time complexity and applies to both flat-end and torus-end cutters. Generally, the CL point can be specified by the CC point, outward normal direction of the machined surface and cutter orientation. If the viewing direction is opposite to the cutter orientation, the global ac- cessibility of the cutter is then equal to the complete visi- bilities of the involved cylinders and cones. This equiva- lence provides an efficient method for detecting the acces- sibility of the milling cutter by using the occlusion query function of the graphics hardware. The computation effi- ciencies of the three algorithms are compared in Table 1. It is found that the computation time of our algorithm is less than 2% of that in 9 even though both the number of tri- angles and the number of cutter orientations are greater than 10 times of those in 9. The average computation time for one cutter orientation at one contact point is less than 2 of that in 9. The average computation time is also much less than that in 3 even though the number of inputted triangles is much greater than that in 3. 1.2 Cutting efficiency Nowadays, ball-end cutters are widely employed for five-axis NC machining. The major advantages of ball-end milling are that it applies to almost any surface and it is Table 1 The comparison of computation time Inputted models Method Computation platform Triangle Cutter center point Cutter orientations Computation time Average computa- tion time Ref. 9 SGI work station, Dual CPU 250M 10665 1500 80 51.63 m 2.5810 2 s Ref. 3 CPU 2.4G, RAM 512M 12600 50000 1 61.61s 1.2310 3 s Our method 12 CPU 2.4G, RAM 512M 139754 2000 1026 60.53 s 2.9510 5 s DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3411 relatively easy to generate the tool path. From the manufac- turers point of view, however, the main disadvantage of ball-end milling is that it is very time consuming. It may require more finish passes and each pass removes only a small amount of material. Compared with ball-end cutter, non-ball-end cutter possesses more complex geometry, and exhibits different “effective cutting profiles” at different locations. Thus, it is possible to position the cutter so that its “effective cutting profile” well matches the design surface, which results in a great improvement of the machining strip width. Hence, increasing attention has been drawn onto the problem of tool path optimization for milling complex sur- faces with non-ball-end cutters. In five-axis machining, the machined surface is formed by the swept envelope of the cutter surface. The true ma- chining errors are the deviations between the design surface and the cutter envelope surface. It is well known that the shape of the cutter envelope surface cannot be completely determined unless all the cutter positions are given 13,14. Due to the difficulty and complexity in locally modeling the cutter envelope surface, most works adopted the approxi- mate or simplified models, which formulate the problem of optimal cutter positioning as that of approximating the cut- ter surface to the design surface in the neighborhood of the current CC point 15. These optimization models do not characterize the real machining process. Also, they only apply to certain surfaces or cutters. Only a few works have addressed the cutter positioning problem from the perspective of local approximation of cutter envelope surface to design surface 1517. For a flat-end or disk cutter, Wang et al. 15 and Rao et al. 16 developed the third- and second-order approximate models of the cutter envelope surface, respectively. However, for such a cutter, its envelope surface is swept by the cutting circle, which is not a rotary surface. Therefore, the two me- thods cannot be applied to other types of rotary cutters. Re- cently, Gong et al. 17 developed a mathematical model that describes the second-order approximation of the enve- lope surface of a general rotary cutter in the neighborhood of the CC point, and then proposed a cutter positioning strategy that makes the cutter envelope surface have a con- tact of second-order with the design surface at the CC point. However, theoretically speaking, a third-order contact be- tween the cutter envelope surface and the design surface could be achieved by adjusting the cutter orientation. This means that the cutter location planning based on the sec- ond-order model does not take full advantage of the effi- ciency and power that the five-axis machining offers. The above models are not compatible with each other. Also, the optimal CL is determined by solving two equations derived from the second- and third-order contact conditions. Due to the constraints of machine joint angle limits, global colli- sion avoidance and tool path smoothness, maybe there is no feasible solution to this system of equations. In our recent works 18,19, the geometric properties of a pair of line contact surfaces were investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and the design surface along the characteristic curve and cutter contact (CC) path, respec- tively, a mathematical model describing the third-order ap- proximation of the cutter envelope surface according to just one given cutter location (CL) was developed. It was shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section could be de- termined by those of the cutter surface and the design sur- face. This model characterizes the intrinsic relationship among the cutter surface, the cutter envelope surface and the design surface in the vicinity of the CC point. On this basis, a tool positioning strategy was proposed for effi- ciently machining free-form surfaces with non-ball-end cutters. The optimal CL was obtained by adjusting the in- clination and tilt angles of the cutter until its envelope sur- face and the design surface had the third-order contact at the CC point, which resulted in a wide machining strip. The strategy can handle the constraints of joint angle limits, global collision avoidance and tool path smoothness in a nature way, and applies to general rotary cutters and com- plex surfaces. Numerical examples demonstrated that the third-order point contact approach could improve the ma- chining strip width greatly as compared with the recently reported second-order one. A comparison of the machining strip widths using different CLs for the five-axis machining of a helical surface with a toroidal cutter is summarized in Table 2. The values of the tool parameters chosen for simu- lation are: radius of the torus R=10 mm, and radius of the corner r=2.5 mm. Compared with the point milling, the flank milling can increase the material removal rate, lower the cutting forces, eliminate necessary hand finish and ensure improved com- ponent accuracy. It offers a better choice for machining slender surfaces. Lartigue et al. 20 proposed an approach to globally optimize the tool path for flank milling. The basic idea is to deform the tool axis trajectory surface so that the tool envelope surface fits the design surface ac- cording to the least-squares criterion. To simplify the com- putation, an approximate distance measure was employed. For a cylindrical cutter, Gong et al. 21 presented the error propagation principle, and transformed the problem into that of least-squares (LS) approximation of the axis trajectory surface to the offset surface of the design surface. In these two works, not the local geometric error, but the geometric Table 2 Comparison of the machining strip widths for different CLs Tolerance (mm) Ball-end cutter (R = 5.5 mm) Toroidal cutter (Second order contact) Toroidal cutter (Third order contact) = 0.005 0.69 2.48 5.28 = 0.01 0.98 3.12 6.14 3412 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 error between the envelope surface of the cutter and the design surface, was of the first concern. Thus it was called the global optimization method. Although the LS method was easy for implementation and efficient in computation, it could not incorporate readily the non-over- cut constraint required by semi-finish milling, and more importantly, it did not conform to the minimum zone crite- rion recommended by ANSI and ISO standards for toler- ance evaluation. Fur- thermore, the geometric deviation of the