資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 附錄一 PLC模塊控制回轉(zhuǎn)工作臺(tái)在三軸數(shù)控銑床銑削螺旋傘齒輪中的應(yīng)用 S. Mohsen Safavi & S. Saeed Mirian & Reza Abedinzadeh & Mehdi Karimian Received: 25 November 2008 / Accepted: 23 November 2009 # Springer-Verlag London Limited 2009 摘要 　　　當(dāng)今，數(shù)控機(jī)床在機(jī)電一體化領(lǐng)域中得到了日益廣泛的應(yīng)用。機(jī)械、電氣和數(shù)據(jù)處理系統(tǒng)與數(shù)控技術(shù)相結(jié)合，引領(lǐng)了新的生產(chǎn)加工理念。近年來，數(shù)控技術(shù)的發(fā)展已將非線性校正技術(shù)在切削弧齒錐齒輪中的應(yīng)用變?yōu)榭赡?。在本文中，我們將嘗試采用帶有外加PLC模塊分度臺(tái)的三軸數(shù)控銑床，運(yùn)用帶有索引工作界面的通用銑床的傳統(tǒng)連續(xù)多重切削方法來加工制造出這個(gè)螺旋傘齒輪。該研究包括(a)弧齒錐齒輪的幾何建模，(b)運(yùn)用CAD/CAE系統(tǒng)進(jìn)行傳統(tǒng)或新型非傳統(tǒng)方案的模擬仿真，(c)數(shù)控加工工藝的設(shè)計(jì)與PLC編程，(d)通過三軸數(shù)控銑床的實(shí)驗(yàn)切削來探索新方案的正確性。結(jié)果表明，開發(fā)的螺旋傘齒輪實(shí)驗(yàn)切削方案不僅與先進(jìn)數(shù)控加工相比成本更低，而且相比傳統(tǒng)切削，加工齒輪的時(shí)間也較短。因此，在螺旋傘齒輪加工領(lǐng)域，這是一個(gè)很經(jīng)濟(jì)的方案。 關(guān)鍵詞：齒輪加工，螺旋傘齒輪，CAD/CAM/CAE，數(shù)控技術(shù)，PLC，交流電動(dòng)機(jī)，逆變，接近傳感器，光電傳感器，旋轉(zhuǎn)編碼器 1 引言 齒輪是工業(yè)機(jī)械領(lǐng)域中重要的精密機(jī)構(gòu)，在平行軸、橫向交叉或非交叉軸之間用于傳遞機(jī)械功率和機(jī)械運(yùn)動(dòng)。雖然有時(shí)會(huì)看不見，但齒輪仍是我們工業(yè)文明中最重要的機(jī)械元件之一。在各式各樣的條件下，齒輪會(huì)以幾乎達(dá)到無限的速率運(yùn)轉(zhuǎn)。得到發(fā)展的齒輪加工設(shè)備與工藝流程已經(jīng)非常先進(jìn)與成熟。無論大批量生產(chǎn)還是小批量生產(chǎn)，無論在小型車間還是分批處理的加工車間，加工齒輪的流程按順序都需要以下四步操作 1.下料 2.切齒 3.熱處理 4.研磨 根據(jù)它們的類型、應(yīng)用范圍及強(qiáng)度和剛度要求，通常經(jīng)過鑄造、擠壓、鍛造、粉末冶金、注塑加工和滾齒加工來完成齒輪的加工制造。在這一系列加工流程中，螺旋傘齒輪是最復(fù)雜的一種齒輪，在成角度的橫軸之間，它用來傳遞回轉(zhuǎn)運(yùn)動(dòng)。 沿齒長方向，螺旋傘齒輪有徑向彎曲的齒廓曲線。這類齒輪之所以能夠保證與配合齒輪有光滑的嚙合，主要是因?yàn)樗鼈冇袆龠^直齒輪的曲型齒廓，這樣它們同一時(shí)間接觸并嚙合的齒數(shù)會(huì)更多。螺旋傘齒輪的設(shè)計(jì)與制造仍然是一個(gè)熱門的研究課題，在直升機(jī)運(yùn)輸齒輪系、摩托車齒輪減速器及其他工業(yè)分支中都得到十分重要的應(yīng)用。對于制造而言，這種齒輪通常由一種特殊機(jī)床加工而成，如滾齒機(jī)、成型機(jī)。目前，基于輪齒加工的特種數(shù)控加工機(jī)床已運(yùn)用于工業(yè)實(shí)踐中。這也許就是輪齒加工的相關(guān)文獻(xiàn)在公開的研究領(lǐng)域稀少的原因所在。最近，基于齒輪加工的數(shù)控加工機(jī)床已得到長足發(fā)展并逐漸運(yùn)用于工業(yè)實(shí)踐。然而，它們的運(yùn)動(dòng)結(jié)構(gòu)與工業(yè)數(shù)控銑床還是有著內(nèi)在的差異，前者是為一種特種刀具而設(shè)計(jì)的。 先前對齒輪的研究主要涉及齒輪的設(shè)計(jì)和分析。在對其幾何特征與設(shè)計(jì)參數(shù)進(jìn)行研究的同時(shí)，Tsai和Chin基于切面方向上的齒輪傳動(dòng)和漸開線齒輪幾何學(xué)，提供了一個(gè)關(guān)于錐齒（直齒輪、螺旋傘齒輪）的數(shù)學(xué)曲面模型。后來，這個(gè)方案與A-daccak等人和Shunmugan等人基于精密球面漸開線的齒輪曲面模型進(jìn)行了比較，從而得出了一個(gè)截然不同的模型。依據(jù)標(biāo)稱偏差，其精確度（相比運(yùn)用特種機(jī)床加工的螺旋傘齒輪）得到了驗(yàn)證。 對于冠齒輪，一些結(jié)論是可行的。Litvin和Kim通過改良直齒輪的基圓提出了運(yùn)用范成法獲得漸開曲線。運(yùn)用斜齒輪傳動(dòng)誤差的修正測定值，Umeyama在節(jié)圓上設(shè)計(jì)了一個(gè)標(biāo)準(zhǔn)剖面，在面齒輪的上下表面設(shè)計(jì)了一個(gè)改良剖面。Tamura等人對采用平面齒形的錐齒輪研究得出了一個(gè)點(diǎn)接觸模型。這些研究都與專為加工齒輪而特殊設(shè)計(jì)的那些特種齒輪加工機(jī)床（如滾齒機(jī)、成型機(jī)）返程齒剖面有關(guān)。Suh等人對螺旋傘齒輪加工的雕刻面加工方法的可行性做了研究，并驗(yàn)證了運(yùn)用帶有回轉(zhuǎn)擺動(dòng)升降臺(tái)的四軸數(shù)控銑床生成加工軌跡的可能性。同時(shí)，一種螺旋傘齒輪基于模型的驗(yàn)證法也得以提出。 在本文中，對于螺旋傘齒輪我們將嘗試采用一種新的加工流程，加工時(shí)運(yùn)用帶有可用于控制分度臺(tái)的PLC模塊的三軸銑床。很明顯，這種加工方法的生產(chǎn)率不及特種加工機(jī)床?？沙松a(chǎn)率，這種加工方法的優(yōu)點(diǎn)有以下幾個(gè)方面：(1)傳統(tǒng)加工方法需要消耗大量投資成本來獲得各種特種機(jī)床，所選用刀具加工的齒輪種類、尺寸和幾何形狀也非常有限；(2)運(yùn)用這種新的加工方法，各種類型的齒輪都可通過工業(yè)三軸數(shù)控銑床加工而成；(3)相比運(yùn)用特種加工機(jī)床，采用該方法加工更為經(jīng)濟(jì)。一個(gè)不同于先前的工作重點(diǎn)是，為了模擬全部加工過程并獲得加工參數(shù)，需要開發(fā)自動(dòng)計(jì)算機(jī)模型。所有先前的研究都在計(jì)算復(fù)雜的數(shù)學(xué)方程組和設(shè)計(jì)幾何模型。鑒于上述情況，我們的重點(diǎn)在于螺旋傘齒輪的加工實(shí)驗(yàn)檢驗(yàn)，而不在于提供螺旋傘齒輪的幾何或數(shù)學(xué)模型。這是第一次同時(shí)運(yùn)用機(jī)電一體化機(jī)床和數(shù)控銑床來加工特殊齒輪，甚至一個(gè)機(jī)械元件。 2 螺旋傘齒輪的幾何規(guī)格 通常，一個(gè)齒輪的幾何參數(shù)都由工程圖給出。對于定義其幾何形狀而言，有些參數(shù)（主要參數(shù)）是必須有的。為此，我們采用名為“GearTrax”的驅(qū)動(dòng)元件開發(fā)軟件來算得這些主要參數(shù)。 螺旋傘齒輪的設(shè)計(jì)要求高精度的數(shù)學(xué)計(jì)算，并且生產(chǎn)這種齒輪傳動(dòng)機(jī)構(gòu)不僅需要高質(zhì)量的設(shè)備和加工此類齒輪傳動(dòng)機(jī)構(gòu)的機(jī)床，而且還需要拓展適當(dāng)?shù)臋C(jī)床參數(shù)設(shè)置。這樣的設(shè)置雖然不合乎標(biāo)準(zhǔn)，但也需要由能夠保證符合高質(zhì)量齒輪傳動(dòng)要求的每種情況的設(shè)計(jì)（根據(jù)齒輪傳動(dòng)的幾何參數(shù)和展成工具）來確定。 3 加工螺旋傘齒輪 由引言中的討論，我們知道所有類型的齒輪都能通過加工手法來獲得所需要的所有規(guī)格，其中高精度齒輪的加工手法仍然非常卓越的。成型銑削是加工任意類型齒輪的最常見的加工工序。所使用的道具都具有類似相鄰輪齒間隙的相同形狀。標(biāo)準(zhǔn)刀具通常用于齒輪的成型切削。在美國，這些刀具的每個(gè)徑節(jié)都是原來的8倍，用于加工標(biāo)準(zhǔn)表上指示的多齒齒輪。格利森公司基于為補(bǔ)充冠齒輪范成原理而產(chǎn)生的錐齒輪范成的普遍概念：相互嚙合的大小齒輪可分別考慮，運(yùn)用了表面滾齒的加工手法。 由公式(1)可知，表面滾齒加工的速率比應(yīng)取決于工具齒輪與展成齒輪的齒數(shù)比： （1） 其中，和分別為工具齒輪與展成齒輪的扭轉(zhuǎn)角速度；和分別為工具齒輪和展成齒輪的齒數(shù)。 　　　展成齒輪與工具齒輪的基圓半徑由公式(2)、(3)確定： 　　　　　　　　　　　　　　 （2） 　　　　　　　　　　　　　　 （3） 其中，s為機(jī)床徑向設(shè)定值。 范成的冠齒輪可考慮為螺旋角為90度的特殊斜齒輪。因此，出現(xiàn)了“形齒輪”這個(gè)通用術(shù)語。當(dāng)已生成的大小齒輪的配合吃面共軛時(shí)，可以考慮對范成冠齒輪的概念進(jìn)行補(bǔ)充。在實(shí)踐中，為了使失配的輪齒表面得以匹配，形齒輪的大小齒可能互不相同。形齒輪的旋轉(zhuǎn)由戟齒輪上的搖架旋轉(zhuǎn)體現(xiàn)。 用三軸數(shù)控銑床加工螺旋傘齒輪，我們首先應(yīng)該對開發(fā)的CAD/CAM系統(tǒng)的幾何建模和仿真模塊盡享程序測試。運(yùn)用商業(yè)軟件Solidworks創(chuàng)建CAD模型和MSC。運(yùn)用Visual NASTRAN 4D軟件（運(yùn)用3D模型的CAE機(jī)械運(yùn)動(dòng)分析系統(tǒng)）模擬齒輪加工并得到分析結(jié)果。 對于機(jī)床的結(jié)構(gòu)而言，很明顯，螺旋傘齒輪的數(shù)控機(jī)床上，工件的回轉(zhuǎn)運(yùn)動(dòng)史必要的?；谄淝邢鞯男阅芊治觯ㄟ^一步安裝，螺旋傘齒輪的數(shù)控加工至少也可達(dá)到四軸控制的要求。因此，對于三軸銑床具備回轉(zhuǎn)工作臺(tái)是必要的。成型切削或成型銑削都會(huì)在測試中用到。刀具從齒輪毛坯中心想要得到的齒高徑向進(jìn)給，然后穿過齒面，而回轉(zhuǎn)工作臺(tái)繞其中心旋轉(zhuǎn)工件來獲得所需的齒寬。當(dāng)加工完成一個(gè)齒間時(shí)，刀具后退，分度頭指示齒輪毛坯，繼續(xù)切削下一個(gè)齒間。從根本上說，這種方法是一種簡易而靈活的螺旋傘齒輪加工方法。所需的設(shè)備和刀具都相對簡單，并且只運(yùn)用標(biāo)準(zhǔn)三軸數(shù)控銑床。然而，防止出現(xiàn)任何的工件損壞，就每一工步為短程的刀具進(jìn)給而言，我們有必要做到謹(jǐn)慎考慮。 我們在GearTrax環(huán)境下創(chuàng)建螺旋傘齒輪用以模擬操作工序并估算一些加工參數(shù)，如端銑刀的原始高度、接近傳感器的位置、電動(dòng)機(jī)轉(zhuǎn)矩、電動(dòng)機(jī)轉(zhuǎn)速及轉(zhuǎn)動(dòng)頻率。例如，在Solidworks環(huán)境下，端銑刀與螺旋傘齒輪的齒頂間距為14.7mm，這是我們沿Z軸用來垂直定位主軸的。 同時(shí)，根據(jù)我們使用的CAE系統(tǒng)所提供的圖形報(bào)告，電動(dòng)機(jī)的角速度和轉(zhuǎn)矩分別為1rpm和48Nm。 Mastercam是一種可以生成刀具加工軌跡的機(jī)械專業(yè)軟件。根據(jù)齒輪的總深度和表面寬度，在我們的切削程序中可設(shè)計(jì)出加工輪廓線為矩形的刀具軌跡。 其它加工參數(shù)和刀具的規(guī)格也應(yīng)錄入軟件的刀具軌跡菜單。在加工輪廓線窗口，我們要用到以下兩個(gè)選項(xiàng)： 考慮到對切削量的較大控制，在多通道口允許刀具多工步進(jìn)給。 2、在沒有額外的幾何尺寸條件下，在入口/出口位置變動(dòng)之前，導(dǎo)入/導(dǎo)出拉長的或縮短的刀具軌跡，這樣有助于我們控制加工補(bǔ)償，并能使短時(shí)間編制固定加工輪廓線變?yōu)榭赡堋? 雖然這種齒輪的成型切削一般運(yùn)用萬能銑床上的分度頭來完成，但其加工過程緩慢并需要技術(shù)熟練的工人師傅和操作者。刀具安裝在刀柄軸上，運(yùn)用分度頭來旋轉(zhuǎn)（切削輪齒）并指示齒輪毛坯。工作臺(tái)設(shè)置在螺旋角為35度的角度上，并且分度頭也應(yīng)與工作臺(tái)的縱向絲杠相適應(yīng)，以便使齒輪毛坯得以縱向回轉(zhuǎn)運(yùn)動(dòng)。 針對上述提供的方法，我們采用了連接了蝸輪蝸桿變速箱的交流電動(dòng)機(jī)。蝸輪蝸桿變速箱用來減小交流電動(dòng)機(jī)的輸出速度，并將齒線也節(jié)圓錐面間的角度設(shè)置為螺旋角大小。 只要刀具軌跡編制與蝸輪蝸桿變速箱輸出軸的旋轉(zhuǎn)運(yùn)動(dòng)間的同步性達(dá)到要求，機(jī)電一體化系統(tǒng)便可同時(shí)控制四根軸（一軸用于工作臺(tái)的回轉(zhuǎn)運(yùn)動(dòng)，三軸用于刀具的切削運(yùn)動(dòng)）。 同時(shí)，在機(jī)電一體化系統(tǒng)中我們運(yùn)用梯形圖和通用編程語言來操作PLC。 基于梯形圖，PLC的操作步驟如下： 第一步 讀取外部輸入信號，例如傳感器與旋轉(zhuǎn)編碼器的地址。 第二步 根據(jù)第一步中的輸入信號值，計(jì)算輸出信號并將其傳送給變頻器（反相器），從而驅(qū)動(dòng)交流電動(dòng)機(jī)正反轉(zhuǎn)或通過旋轉(zhuǎn)編碼器使電動(dòng)機(jī)旋轉(zhuǎn)一定的角度（齒距）。配置數(shù)控銑床的同時(shí)，所有系統(tǒng)的程序按以下五個(gè)階段完成： 第一階段 成型刀抵達(dá)第一個(gè)接近傳感器，傳感器一旦檢測到成型刀，就向PLC發(fā)送一個(gè)+5V的信號，正如前面提到的，PLC接收信號并向變頻器發(fā)送一個(gè)輸出信號來驅(qū)動(dòng)電動(dòng)機(jī)正轉(zhuǎn)。 第二階段 以Mastercam中生成的刀具加工軌跡用成型刀加工旋轉(zhuǎn)的工件。 第三階段 刀具抵達(dá)第二個(gè)接近傳感器，傳感器通過檢測刀具來向PLC傳送第二個(gè)信號，同時(shí)PLC接收并向變頻器發(fā)送一個(gè)停止指令。 第四階段 銑刀從停止的工件退刀并回到起始位置。同時(shí)，變頻器驅(qū)動(dòng)電動(dòng)機(jī)反轉(zhuǎn)直到輸出軸回到第一工位，在這個(gè)位置，光電傳感器的接收器可可通過輸出軸的縱向裂紋接收傳輸光線。 第五階段 重復(fù)一至四階段直到第一個(gè)齒間切削完成。PLC根據(jù)運(yùn)行上述四階段的次數(shù)計(jì)數(shù)直到達(dá)到加工程序中的預(yù)設(shè)次數(shù)。然后，PLC向變頻器發(fā)送信號指示齒輪毛坯達(dá)到加工直徑尺寸，接著上述所有階段重復(fù)運(yùn)行。加工直徑由1024脈/轉(zhuǎn)的旋轉(zhuǎn)編碼器測定。 在本次創(chuàng)新的加工方法的有利體現(xiàn)里，加工時(shí)間是主要關(guān)注的指標(biāo)之一。例如，加工完成一個(gè)齒間只需2分鐘。相比較，運(yùn)用傳統(tǒng)方法加工同樣的齒間需要花費(fèi)半個(gè)多小時(shí)。 在本次創(chuàng)新關(guān)于手工切削的深遠(yuǎn)有利體現(xiàn)里，切削刀頭的瞬間角度補(bǔ)償是在跳轉(zhuǎn)程序結(jié)束之前立即設(shè)置的。 4 加工策略 工件為木料，通過車削加工將坯料預(yù)加工為錐狀（齒頂錐角）。用于實(shí)驗(yàn)的5號標(biāo)準(zhǔn)刀安裝在機(jī)床主軸上，齒輪毛坯安裝在蝸輪蝸桿變速箱的輸出軸上。隨后，刀具向齒輪毛坯的中心進(jìn)給以達(dá)到所需齒深（圍繞30條加工程序以避免次品出現(xiàn)）。加工完成一個(gè)齒間，退刀；根據(jù)已編譯的程序由交流電動(dòng)機(jī)指引齒輪毛坯接著切削下一個(gè)齒間。 5 結(jié)論 在本文中，我們嘗試運(yùn)用三軸數(shù)控銑床通過成形銑削的方法加工螺旋傘齒輪。為了達(dá)到這一目的，我們對CAD/CAM模具的切削步驟和刀具軌跡算法做了研究。運(yùn)用復(fù)雜的數(shù)學(xué)程序，所有的預(yù)先工作都與設(shè)計(jì)息息相關(guān)，并沒有依靠經(jīng)驗(yàn)加工理論。從根本上說，成形切削用于加工齒輪簡單而靈活。所需的設(shè)備和刀具相對簡單、廉價(jià)，一臺(tái)標(biāo)準(zhǔn)數(shù)控銑床即可。因而，并不需要技術(shù)熟練的操作者來創(chuàng)建加工系統(tǒng)。與運(yùn)用專業(yè)機(jī)床加工齒輪的常規(guī)方法相比，本文所采用的加工方法用于加工各種規(guī)格的螺旋傘齒輪或其它類型的齒輪，改進(jìn)起來也很容易。與手動(dòng)切削加工相比，這種加工方法又是一個(gè)全自動(dòng)的，因?yàn)樗械募庸⒘慷纪ㄟ^電腦模塊得到。這種加工理念同時(shí)也是一個(gè)多變的系統(tǒng)（運(yùn)用機(jī)電一體化和數(shù)控系統(tǒng)），并且會(huì)源源不斷地發(fā)展下去。 參考文獻(xiàn) 1. De Garmo EP, Black JT.材料與工藝制造. Prentice–Hall, New York. 1957 2. Shigley JE. 機(jī)械工程設(shè)計(jì). McGraw-Hill, New York. 1986 3. Maitra GM. 齒輪設(shè)計(jì)手冊. McGraw-Hill, New York. 1994 4. Tsai Y, Chin P. 垂直表面幾何學(xué)與螺旋傘齒輪. ASME J Mech Trans Autom Des 109(4):443–449. 1987 5. Al-daccak M, Angeles J, Gonzalez-Palacios M.精確球面漸開線的錐齒輪模具. ASME J Mech Des 116:364–368. 1994 6. Shunmugam M, Narayana S, Jayapraksh V. 輪齒幾何平面的創(chuàng)建與正態(tài)偏差: 第一部分——圓柱齒輪. J Mech Mach Theory 33(5):517–524. 1998 7. Shunmugam M, Rao B, Jayaprakash V. 輪齒幾何平面的創(chuàng)建與正態(tài)偏差: 第二部分——錐齒輪. J Mech Mach Theory 33(5):525–534. 1998 8. Litvin F, Kim D. 帶有定位支架連結(jié)的改良漸開線直齒輪嚙合范成與仿真及傳動(dòng)誤差的折算標(biāo)準(zhǔn). ASME JMech Des 119:96–100. 1997 9. Umeyama M.斜齒輪副傳動(dòng)誤差的齒面改質(zhì)效應(yīng)與優(yōu)化. Trans Jpn Soc Mech Eng C 61(582):8–15. 1995 10. Tamura H, Tanaka K. 基于擬補(bǔ)償冠齒輪的螺旋傘齒輪切削方法. Trans Jpn Soc Mech Eng C 58(547):202–208. 1992 11. Tamura H et al. 基于擬補(bǔ)償冠齒輪的直齒錐齒輪切削方法. Trans Jpn Soc Mech Eng C 63(606):259–264. 1997 12. Suh S, Ji W, Chung D. 運(yùn)用數(shù)控銑床的螺旋傘齒輪的曲面加工. Int J Mach Tools Manuf 41:833–850. 2001 13. Suh S, Lee E, Kim H. 運(yùn)用STEP-NC的虛擬齒輪模具測量弧齒錐齒輪的幾何誤差. Int J Mach Tools Manuf 42:335–342. 2002 14. Krenzer TJ. 表面銑削與表面研磨, AGMA. 技術(shù)文獻(xiàn), 90 FTM 13 15. Pitts LS, Boch MJ. 運(yùn)用表面研磨方法的錐齒輪與準(zhǔn)雙曲面齒輪的設(shè)計(jì)與開發(fā). No. 4332, 格林森公司. 1997 16. Suh S, Kang J. 自由表面的多軸數(shù)控加工過程設(shè)計(jì). Int J Prod Res 33:2723–2738. 1995 17. Dudley DW. 達(dá)力齒輪手冊, 齒輪的設(shè)計(jì)、制造與應(yīng)用. McGraw-Hill, New York. 1962 18. Jaeschke R. 電力傳輸控制系統(tǒng). Penton/IPC, Cleveland, pp 210–215. 1978 19. Campbell S. 固態(tài)交流電機(jī)控制. Marcel Dekker, New York, pp 79–189 ISBN 0-8247-7728-X. 1987 附錄二 Use of PLC module to control a rotary table to cut spiral bevel gear with three-axis CNC milling S. Mohsen Safavi & S. Saeed Mirian & Reza Abedinzadeh & Mehdi Karimian Received: 25 November 2008 / Accepted: 23 November 2009 # Springer-Verlag London Limited 2009 Abstract 　　　CNC machining nowadays makes more use of "Mechatronics" increasingly. Combining numerical control with mechanic, electric, and data processing systems can lead to new methods of production. In recent years, the development of CNC has made it possible to perform nonlinear correction motions for the cutting of spiral bevel gears. In this paper, we attempt to manufacture the spiral bevel gear using a three-axis CNC milling machine interfaced with an additional PLC module based on traditional discontinuous multi-cutting method accomplished by using a universal milling machine interfaced with an indexing work head. This research consists of (a) geometric modeling of the spiral bevel gear, (b) simulating the traditional and our new nontraditional method using a CAD/CAE system, (c) process planning for CNC machining and PLC Programming, (d) experimental cuts with a three-axis CNC milling machine were made to discover the validity of the presented method. The results demonstrate that invented experimental cutting method of SBGs not only is less expensive than advanced CNC machining but also produces gears in a shorter time in comparison with the traditional cutting. Thereby, it is an economical method in manufacturing of SBGs. Keywords：Gear manufacturing . Spiral bevel gear .CAD/CAM/CAE . CNC . PLC . AC motor . Inverter .Proximity sensors . Photoelectric sensors . Rotary encoder 1 Introduction 　　　Gears are important and precision mechanisms for industrial machinery as a means for mechanical power or motion transmission between parallel, intersecting and nonintersecting cross-axis shafts. Although hidden from sight, gears are one of the most important mechanical elements in our civilization. They operate at almost unlimited speeds under a wide variety of conditions. The machines and processes that have been developed for producing gears are among the most existing ingenious ones. Whether produced in large or small quantities, in cell, or job shop batches, the sequence of processes for gear manufacturing requires four sets of operations: 　　　1. Blanking 　　　2. Gear cutting 　　　3. Heat treatment 　　　4. Grinding Depending on their type and application or required strength and resistance, gears are manufactured by casting, extruding, forging, powder metallurgy, plastic molding, gear rolling, and machining. Among these processes, machining is more frequently used for high-precise gears. Among the various types of gears, the spiral bevel gears (SBG) are the most complex type and are used to transmit the rotational motion between angularly crossed shafts. 　　　SBGs have teeth curved longitudinally along the length of the teeth. The main advantage of these gears over the straight-toothed varieties lies in the fact that more teeth are in contact at the same time because of the curve-shaped contour of the teeth and so a smoother meshing action between the mating pair is ensured. The design and manufacturing of spiral bevel gears is still a hot topic of research that is vital for application of such gears in helicopter transmissions, motorcycle gears, reducers, and in other branches of industry. As far as manufacturing is concerned, the gears are machined by a special type of machine tools, such as gear hobbing and shaping machines. Recently, special CNC-based gear manufacturing machine tools are used in industrial practice. This may be why literature on gear manufacturing is sparse in the open research domain. Recently, CNC-based gear manufacturing machine tools have been developed and increasingly used in industrial practice. However, their kinematic structure is still inherently different from the industrial CNC milling machine, as the former is designed for a special type of cutter. 　　　Previous studies on gears have been mainly concerned with the design and analysis of gears. The geometric characteristics and design parameters of gears have been studied. Tsai and Chin presented a mathematical surface model for bevel gears (straight and SBGs) based on basic gearing kinematcis and involute geometry along the tangent planes. Later, this method was compared with another model based on exact spherical involute curves by Al-daccak et al. Shunmugan et al. presented a different model, and its accuracy (compared with the spiral bevel gear manufactured by special machine tools) was verified in terms of nominal deviation. 　　　For crown gears, a few results are available. Litvin and Kim suggested a generation method for an involute curve from a modified base circle for a spur gear. Umeyama designed a standard profile at the pitch circle and a modified profile at the top/bottom face gear with a determination of the modification value for transmission error of helical gear. Tamura et al. studied a point contact model for a bevel gear using a flat surface tooth. These studies are concerned with the generation of the tooth profile for special gear machines, such as gear hobbing and shaping machines, which are specially designed for manufacturing gears. Suh et al. investigated the possibility of a sculptured surface-machining method for the manufacture of spiral bevel gears and verified the possibility by presenting tool-path generation using a four-axis CNC milling machine interfaced with a rotary-tilt table. A model-based inspection method for the spiral bevel gears was also presented. 　　　In this paper, we attempt to present a new manufacturing procedure of SBGs by using a three-axis milling machine interfaced with a PLC module which operates as an indexing table. In terms of production rate, it is obvious that this method will be lower than that of the special machine tool. Other than production rate, this method is advantageous in the following respects: (1) the conventional method requires a large investment for obtaining various kinds of special machinery and cutters dedicated to a very limited class of gears in terms of gear type, size, and geometry; (2) by this method, various types of gears can be manufactured with the industrial three-axis CNC milling machine; (3) this method is more economical than using the special machine tool. One of the main points which separate our work from previous ones is developing an automatic computer model in order to simulate the process entirely and obtain machining parameter. All previous studies have been engaged in calculating complicated mathematical equations and designing geometric models. In view of the above, special attention is given to experimental tests rather than presenting geometrical or mathematical model of SBGs. This is the first time that mechatronic tools and a three-axis CNC milling machine are being used simultaneously in manufacturing a special gear and even a mechanical element. 2 Geometric specifications of the spiral bevel gears 　　　Most of the time, the geometric parameters of a gear are provided with an engineering drawing. Some parameters (principal parameters) are required for defining the geometry. To calculate these parameters, we have used “drive component development software” called GearTrax. 　　　The design of spiral bevel gear requires high-accuracy mathematical calculations, and the generation of such gear drives requires not only high-quality equipment and tools for manufacturing of such gear drives but also the development of the proper machine-tool settings. Such settings are not standardized but have to be determined for each case of design (depending on geometric parameters of the gear drive and generating tools) to guarantee the required quality of the gear drives. 3 Manufacturing the SBG 　　　As it was discussed in the introduction, by machining, all types of gears can be made in all sizes, and machining is still unsurpassed for gears having very high accuracy. Form milling is one of the most common machining processes used to manufacture any types of gears. The cutter has the same form as the space between adjacent teeth. Standard cutters usually are employed in form-cutting gears. In the USA, these cutters come in eight sizes for each diametral pitch and will cut gears having the number of teeth indicated in standard tables. Gleason works used the face hobbing process that is based on the generalized concept of bevel gear generation in which the mating gear and pinion can be considered respectively, generated by the complementary generating crown gears. 　　　As it is shown in Eq. 1, velocity ratio of face hobbing process depends on tooth number of tool and generating gear: （1） where, wt and wc denote the angular velocities of the tool and generating gear; Nt and Nc denote the number of the blade groups and the tooth number of the generating gear. 　　　The radii of the rolling circles of the generating gear and the tool are determined by Eqs. 2 and 3: 　　　　　　　　　　　　　　　　 （2） 　　　　　　　　　　　　　　　 （3） where s is the machine radial setting. 　　　The generating crown gear can be considered as a special case of a bevel gear with 90° pitch angle. Therefore, a generic term “generating gear” is used. The concept of complementary generating crown gear is considered when the generated mating tooth surfaces of the pinion and the gear are conjugate. In practice, in order to introduce mismatch of the mating tooth surfaces, the generating gears for the pinion and the gear may not be complementarily identical. The rotation of the generating gear is represented by the rotation of the cradle on a hypoid gear generator. 　　　To manufacture the SBGs with the three-axis CNC milling machine, we first test the process by developing a CAD/CAM system composed of geometric modeling and graphic simulation modules. The commercial software Solidworks is used for creating CAD model and MSC. Visual NASTRAN 4D (CAE system of the kinematic analysis of the mechanisms by means of their 3D models) is used for simulating the process of gear manufacturing and its analytical results. 　　As far as machine tool configuration is concerned, it is obvious that a rotational motion of the workpiece is required for NC machining of the SBGs. Based on the machinability analysis, at least four-axis controls are required for NC machining of SBGs by one setup. Thus, a rotary table to be interfaced with the three-axis milling machine is required. Form cutting or form milling is used in our tests. The tool is fed radially toward the center of the gear blank to the desired tooth depth, then across the tooth face, while the rotary table rotates the workpiece around its center to obtain the required tooth width. When one tooth space has been completed, the tool is withdrawn, the gear blank is indexed using a dividing head, and the next tooth space is cut. Basically, this method is a simple and flexible method of machining SBGs. The equipment and cutters required are relatively simple, and standard three-axis CNC milling machine is used. However, considerable care is required on the part of tool feed which should be a small value in each step to prevent any spoil. 　　　We used spiral bevel gear created in GearTrax in order to simulate operating sequence and then estimate some machining parameters such as initial height of end mill, location of proximity sensors, motor torque, motor speed, and rotation frequency. For example, in SolidWorks, distance between end mill and the apex of SBG was 14.7 mm which we used to locate the spindle vertically along the z-axis. 　　　Also, according to the graph report of CAE system which we used, motor angular velocity and motor torque are 1 rpm and 48 Nm, respectively. 　　　Mastercam is a mechanical software that can be used to generate toolpaths for machining. According to whole depth and face width of the gear, a rectangular contour was designed as toolpath in our cutting procedure. 　　　Other machining parameters and tool’s specifications were also submitted to the Tool Path menu of software. In contour window, there are two options which we use: 　　　1. Multipasses which enable multiple stepovers of the tool, allowing for greater control of stock removal. 　　 2. Lead in/out which extend or shorten the toolpath before making entry/exit moves without creating additional geometry, which is helpful when working with control compensation and makes it possible to program solid contours in less time. 　　　Although the form cutting of this kind of gears is currently done on universal milling machine, using an indexing head, the process is slow and requires skilled labor and operator. The cutter is mounted on an arbor, and a dividing head is used to revolve (required to cut the gear tooth) and index the gear blank.