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中文譯文
虛擬制造的多頭ZA蝸桿傳動(dòng)的參數(shù)設(shè)計(jì)和運(yùn)動(dòng)分析
孫劍萍、湯兆平
華東交通大學(xué)軌道交通學(xué)院，江西省 南昌 330013
sunjianping@ecjtu.jx.cn
摘要：阿基米德蝸桿輪齒面通常是用CAD來(lái)形成和模擬的。本文分析了多頭阿基米德蝸桿的加工特征和形成原則，建立了精確的模型，使設(shè)計(jì)參數(shù)化。并利用Pro/E軟件，應(yīng)用虛擬裝配和組件之間的相關(guān)性質(zhì)，模擬現(xiàn)實(shí)過(guò)程，實(shí)際制作蝸輪，建立準(zhǔn)確的模型。另外，將生成的蝸輪，蝸桿組裝，同時(shí)對(duì)他們的運(yùn)動(dòng)進(jìn)行模擬和分析。
關(guān)鍵詞：計(jì)算機(jī)輔助設(shè)計(jì)、參數(shù)化設(shè)計(jì)、運(yùn)動(dòng)分析、Pro/E、多頭ZA蝸桿傳動(dòng)裝置
1、概述
阿基米德蝸桿輪齒面的制作，目前一般是用CAD軟件模擬制圖來(lái)代替真正的蝸輪齒形制造[1]。但是，繪出復(fù)雜而又精確的輪齒是非常困難的，此外，蝸輪蝸桿配合被歸類為左旋，右旋，單線程和多頭的。這就為簡(jiǎn)歷模型增加了困難。本文主要從阿基米德蝸桿（ZA蝸桿）的加工原理入手，模擬其生產(chǎn)過(guò)程，并利用Pro/E中的關(guān)系函數(shù)，實(shí)現(xiàn)準(zhǔn)確的ZA蝸桿參數(shù)模型。此外，在此基礎(chǔ)上也無(wú)形中制造出了蝸輪，以及蝸輪、蝸桿的組裝以及他們的運(yùn)動(dòng)分析。
2、建立模型的思維過(guò)程
為了模仿ZA蝸桿的傳動(dòng)過(guò)程，繪制大小和形狀同參數(shù)化蝸輪滾刀相似的橫截面，以阿基米德螺旋線為軌跡，利用Pro/E軟件中的“變截面掃描/剪切”功能，在蝸桿毛坯上切一個(gè)槽，然后仿效槽，多頭蝸輪滾刀就生成了。使線程數(shù)和軌跡數(shù)充分參數(shù)化是制造模型的一個(gè)難點(diǎn)。關(guān)鍵點(diǎn)是：第一，要設(shè)置控制參數(shù)（右旋的參數(shù)值是1，左旋值是-1）和線程數(shù)，然后用方程建立阿基米德螺旋線，從而改變線程數(shù)。第二，仿效蝸桿插槽，它是設(shè)計(jì)師選擇路徑的“方向”所必須的，并選擇蝸桿坯料的軸線作為參考，建立第一個(gè)方向，輸入線程數(shù)等于蝸桿頭數(shù)，而且輸入螺距等于蝸桿各頭之間的間隔。
在完成蝸輪滾刀的參數(shù)化模型后，然后再在此基礎(chǔ)上，通過(guò)改變參數(shù)來(lái)產(chǎn)生蝸桿模型。蝸輪和蝸桿滾刀的不同之處在于蝸輪滾刀是刀片槽，而且他們之間的間隙大于蝸輪半徑。
蝸輪模式的獲得是采用蝸輪滾刀虛擬處理的方式。作者的基本思路是：在虛擬環(huán)境中，分別建立蝸輪滾刀和蝸輪毛坯，然后將他們放置于坐標(biāo)系當(dāng)中，通過(guò)裝配幾何關(guān)系理論，使他們能夠互相調(diào)整。然后利用布爾減法計(jì)算在運(yùn)動(dòng)過(guò)程中不同位置時(shí)的參數(shù)，直到蝸輪已制作出整個(gè)外表面[2]。
3、建立相關(guān)參數(shù)
從以上的思路可以知道ZA蝸桿傳動(dòng)的參數(shù)化設(shè)計(jì)與運(yùn)動(dòng)分析需要建立在諸如蝸輪滾刀部分、蝸桿部分，蝸輪滾刀和蝸桿滾刀之間的部件以及蝸輪和蝸桿之間的裝配等方面。為了實(shí)現(xiàn)參數(shù)化設(shè)計(jì)，這些部分需要設(shè)定基本的尺寸。
利用Pro/E提供的參數(shù)和關(guān)系的功能，按照蝸桿與蝸輪之間的參數(shù)關(guān)系，設(shè)置蝸輪、蝸桿的模數(shù)，蝸桿特征數(shù)，頭數(shù)，變位系數(shù)等，如表1所示。
4、建立準(zhǔn)確地ZA蝸輪滾刀參數(shù)化模型
根據(jù)以上所有的思路，首先，設(shè)計(jì)者需要在蝸桿滾刀毛坯上切一個(gè)連續(xù)的刀槽，如圖1（a）所示，然后以蝸桿滾刀軸線為導(dǎo)向線，如同已經(jīng)生成的刀槽一樣繼續(xù)切槽，并連續(xù)幾次，直到達(dá)到一定的線程數(shù)（蝸桿頭數(shù)），而且蝸桿螺距等于蝸桿各頭之間的間距，如圖1（b）所示。
采用嵌入在Pro/E2.0中的程序模塊，用戶可以根據(jù)設(shè)計(jì)示意圖編輯程序，設(shè)計(jì)程序，而且可以驅(qū)動(dòng)它的大小，使其充分和參數(shù)化。根據(jù)系統(tǒng)的提示，用戶導(dǎo)入不同的設(shè)計(jì)變量，蝸輪滾刀就可以生成滿足用戶要求的結(jié)果，如圖2所示。
5、建立虛擬加工和裝配的基準(zhǔn)
5.1建立裝配基準(zhǔn)
在Pro/E中，這些部分之間的組成元件和裝配式互相關(guān)聯(lián)的。為了實(shí)現(xiàn)蝸輪滾刀和蝸輪在裝配時(shí)的相對(duì)運(yùn)動(dòng)，設(shè)計(jì)者必須在組件和裝配部件分別建立相應(yīng)的基準(zhǔn)點(diǎn)和基準(zhǔn)軸，而且使這些數(shù)據(jù)參數(shù)化，如圖3所示。每個(gè)組件在這些數(shù)據(jù)的幫助下組裝。如果參數(shù)發(fā)生變化，蝸輪滾刀和蝸輪將根據(jù)給定的傳動(dòng)比相對(duì)旋轉(zhuǎn)。
一般情況下，蝸輪傳動(dòng)裝置兩角之間的夾角是90°。在裝配時(shí)，設(shè)計(jì)者必須建立兩個(gè)獨(dú)立的縱橫基準(zhǔn)軸線和蝸輪滾刀和蝸輪裝配基準(zhǔn)點(diǎn)，并使這些數(shù)據(jù)參數(shù)化。在裝配時(shí)，除了前面已加以說(shuō)明的所必須的參數(shù)如模數(shù)，齒數(shù)外，驅(qū)動(dòng)蝸輪滾刀和蝸輪公轉(zhuǎn)的角度參數(shù)也是必須要給出的。該參數(shù)設(shè)置成“角”，初始值是0。最后，要輸入關(guān)系如下：
$d3=(m*q/2)*cos(jiao) /* x-蝸輪滾刀的定位點(diǎn)坐標(biāo)；
$d4=(m*q/2)*sin(jiao) /* y-蝸輪滾刀的定位點(diǎn)坐標(biāo)；
d5=m*π*z1*n/2 /* z-蝸輪滾刀的定位點(diǎn)坐標(biāo)；
d2=m*π*z1*n/2 /* z-蝸桿模擬運(yùn)動(dòng)中心定位點(diǎn)的坐標(biāo)APNT0，即x坐標(biāo)和y坐標(biāo)都為0，
/ *蝸桿和蝸輪滾刀的定位軸是通過(guò)點(diǎn)APNT0和垂直線ASM_FRONT，
/ *坐標(biāo)系統(tǒng)ACS0轉(zhuǎn)換為APNT0；
$d7=-m*(q+z2+2*x2)/2 /* 中心定位基準(zhǔn)點(diǎn)APNT2的Y坐標(biāo)在蝸輪模擬毛坯的坐標(biāo)系統(tǒng)ACS0；
d8=m*π*z1*n/2 /*中心定位基準(zhǔn)點(diǎn)APNT2的Y坐標(biāo)在蝸輪模擬毛坯的坐標(biāo)系統(tǒng)ACS0；
/ *蝸輪的定位軸是通過(guò)APNT2對(duì)齊和垂直ASM_RIGHT；
/ *坐標(biāo)系統(tǒng)轉(zhuǎn)換為模擬蝸輪的APNT2，以默認(rèn)坐標(biāo)系統(tǒng)X軸的正方向?yàn)閦軸正方向，y軸正方向與默認(rèn)的坐標(biāo)系統(tǒng)相同；
$d9=m*z2/2*cos(jiao*z1/z2) /*蝸輪定位基準(zhǔn)點(diǎn)的X坐標(biāo)在蝸輪模擬坐標(biāo)系統(tǒng)中；
$d10=m*z2/2*sin(jiao*z1/z2) /*蝸輪定位基準(zhǔn)點(diǎn)的Y坐標(biāo)在蝸輪模擬坐標(biāo)系統(tǒng)中。
5.2建立虛擬加工和組裝每部分所需的基準(zhǔn)
為了建立蝸輪滾刀參考圓的一個(gè)基準(zhǔn)點(diǎn)，在裝配期間，將滾刀軸與在組裝部件已經(jīng)建立好的蝸輪滾刀基準(zhǔn)軸對(duì)齊，將滾刀參考圓的基準(zhǔn)點(diǎn)與在組裝部件已經(jīng)建立好的相應(yīng)的基準(zhǔn)點(diǎn)對(duì)齊，因?yàn)榛鶞?zhǔn)點(diǎn)在組裝部件上已經(jīng)被參數(shù)化，因此設(shè)計(jì)師可以實(shí)現(xiàn)圍繞基準(zhǔn)軸旋轉(zhuǎn)滾刀。
利用函數(shù)關(guān)系是非常有必要的，基準(zhǔn)點(diǎn)的輸入關(guān)系如下：
d69=m*q/2 /*x-蝸輪滾刀的定位基準(zhǔn)點(diǎn)坐標(biāo)；
d71=m*π*z1*n/2 /*z-蝸輪滾刀的定位基準(zhǔn)點(diǎn)坐標(biāo)。
用同樣的方法，建立蝸輪毛坯。為了裝配方便，設(shè)計(jì)師在建立模型時(shí)，他必須按照裝配關(guān)系注意蝸輪毛坯軸的方向以及與坐標(biāo)系統(tǒng)的距離，并設(shè)置必要的組裝和模擬日期，輸入關(guān)系如下：
D74=m*(q+x2*2)/2 /* z-蝸輪毛坯的定位基準(zhǔn)點(diǎn)坐標(biāo)。
6、虛擬加工和裝配
當(dāng)裝配各組件時(shí)，設(shè)計(jì)者需要分別校準(zhǔn)蝸桿軸，蝸輪毛坯軸，蝸桿參考圓的基準(zhǔn)點(diǎn)以及蝸輪毛坯參考圓的基準(zhǔn)點(diǎn)同他們相應(yīng)的軸或者是已經(jīng)建立好的基準(zhǔn)點(diǎn)。由于基準(zhǔn)點(diǎn)已經(jīng)在裝配時(shí)參數(shù)化，設(shè)計(jì)人員可以實(shí)現(xiàn)蝸桿和蝸輪毛坯輪圍繞他們各自已經(jīng)改變參數(shù)的校準(zhǔn)軸旋轉(zhuǎn)。
利用“工具 - 參數(shù)”功能，改變角的參數(shù)值（間隔角越小，蝸輪切割效果越好），該模型就可以生成。
利用“編輯 - 構(gòu)件運(yùn)算 - 剪切”功能，切割坯料，然后，在蝸輪部分，設(shè)計(jì)者需要編輯修改前面已經(jīng)定義過(guò)的ID，并改變其每部分的屬性，確保其不隨參數(shù)值的變化而變化。
重復(fù)上述所有步驟，直到所有蝸輪槽都用蝸輪滾刀完全、均勻的切割出來(lái)。如圖4所示。改變蝸桿和蝸輪毛坯的參數(shù)，就可以生成不同的蝸輪，如圖5所示。
7、蝸桿傳動(dòng)的虛擬裝配和運(yùn)動(dòng)分析
7.1虛擬裝配和模擬運(yùn)動(dòng)
更換蝸輪滾刀，以蝸桿作為基準(zhǔn)組件，蝸輪和蝸桿利用針連接方式進(jìn)行組裝，當(dāng)連接組裝時(shí)，模擬運(yùn)動(dòng)相應(yīng)的校準(zhǔn)軸和基準(zhǔn)點(diǎn)必須分別選擇，如圖6所示。
元件布置完成后，設(shè)計(jì)人員可以添加模塊的相應(yīng)驅(qū)動(dòng)器和模擬運(yùn)動(dòng)。
選擇“應(yīng)用程序 - 機(jī)制”，設(shè)計(jì)師可以輸入機(jī)構(gòu)模塊；單擊“定義伺服電機(jī)”，分別建立新的“伺服電機(jī)1”和“伺服電機(jī)2”按鈕。選擇“類型”標(biāo)簽，在組裝蝸輪和蝸桿時(shí)，分別選擇已經(jīng)定義過(guò)的校準(zhǔn)軸以建立“聯(lián)合軸”，選擇“模擬類型”中的“旋轉(zhuǎn)”，設(shè)計(jì)者還必須注意伺服電機(jī)的兩個(gè)運(yùn)動(dòng)方向，在“配置”選項(xiàng)卡中，需要定義伺服電機(jī)1 “規(guī)范”選項(xiàng)中的“速度”和“等級(jí)”中的“常數(shù)”，“A”值為360乘以蝸桿的線程數(shù)和蝸輪的齒數(shù)。將伺服電機(jī)2的“A”值設(shè)置為360，以確保他們的運(yùn)動(dòng)能滿足蝸輪蝸桿的傳動(dòng)比。
用戶單機(jī)“運(yùn)行分析”按鈕，新建“分析定義1”。在對(duì)話框的“喜好”選項(xiàng)卡中，設(shè)置“開(kāi)始時(shí)間”，“結(jié)束時(shí)間”，“幀計(jì)數(shù)”和“幀速率”，預(yù)設(shè)“結(jié)束時(shí)間”是蝸輪齒數(shù)，其余為默認(rèn)值。
7.2運(yùn)動(dòng)模擬分析
軟件中還有一些在機(jī)構(gòu)模塊中可以測(cè)量的選項(xiàng)，例如“位移”，“速度”，“加速度”，“連接反應(yīng)”，“網(wǎng)絡(luò)負(fù)載”等。
分析蝸輪和蝸桿之間的相對(duì)運(yùn)動(dòng)，設(shè)計(jì)者必須選擇他們相應(yīng)的裝配坐標(biāo)系統(tǒng)；確保坐標(biāo)系統(tǒng)不隨蝸桿傳動(dòng)運(yùn)轉(zhuǎn)。
單擊“測(cè)量結(jié)果的原因分析”按鈕，新建措施1到措施4，選擇“圖形測(cè)量分析”，單擊“圖形測(cè)量結(jié)果”對(duì)話框，測(cè)量值可以通過(guò)圖形和數(shù)據(jù)輸出。它是比較直觀和準(zhǔn)確的，如圖7和圖8。
在機(jī)構(gòu)模塊中，單擊“重播以前運(yùn)行分析”按鈕，選擇對(duì)話框中的“干擾”選項(xiàng)卡，在動(dòng)態(tài)干擾條件下檢測(cè)每個(gè)組件；點(diǎn)擊“播放當(dāng)前結(jié)果集” - “捕獲...”，電腦就可以可以播放MPEG格式的動(dòng)畫（也可以導(dǎo)成mpg電影格式）。
從以上輸出的所有運(yùn)動(dòng)模擬圖可以看出以下三點(diǎn)：
（1）蝸輪，蝸桿的Y坐標(biāo)位移值可以利用改變正弦或余弦的方式來(lái)變化，Y坐標(biāo)的速度值也是如此。當(dāng)他們運(yùn)行時(shí)，他們具有相同的圓周運(yùn)動(dòng)規(guī)律。
（2）蝸輪Y坐標(biāo)的位移值范圍為-132.5至132.5毫米。蝸桿Y坐標(biāo)的位移值范圍是從-45至45毫米。蝸輪Y坐標(biāo)的速度值范圍是從-47.1238至47.1238毫米/秒，蝸桿Y坐標(biāo)的速度值范圍是從-282.743到282.743毫米/秒，這與他們的理論值完全一致。
（3）蝸輪的Y坐標(biāo)有3個(gè)正弦波，而蝸桿的Y坐標(biāo)有53個(gè)正弦波。這與蝸輪蝸桿實(shí)際的傳動(dòng)比相同。
可以看出，所有來(lái)自上述的模擬結(jié)果和他們的理論計(jì)算值是相同的，也與實(shí)際相符。
參考資料
[1]陳閩杰，賴貞華，李志明。“阿基米德蝸桿在UG環(huán)境中的精確建?！保甭殬I(yè)技術(shù)學(xué)院學(xué)報(bào)，2006,21（3）：152?156。
[2]譚欣?！捌矫娑伟j(luò)環(huán)面蝸桿副數(shù)字化造型理論及仿真研究”，武漢：武漢理工大學(xué)，2003,6:17?22。
英文原文
The Parameterization Design and Motion Analysis for Multi-start ZA Worm Gearing Based on Virtual Processing Jianping SUN, Zhaoping TANG School of Railway Transportation East China Jiao Tong University Nanchang, Jiangxi Province 330013, China Abstract Archimedes worm gears teeth surfaces are comply and their models were usually built approximately in CAD. This article analyses the processing character and formation principle of the Multi-start ZA worm, builds the accurate model and makes the full parametric design. In environment of Pro/E, applying the entire relevance character between virtual assembly and component, simulating reality processes, the worm gear was produced virtually, and its model was built accurately. Furthermore, the generated worm gear and worm were assembled virtually and their motions were simulated and analysed. Keywords: Computer aided design, Parameterization design, Motion analysis, Pro/E, Multi-start ZA worm gearing 1. Introduction Archimedes worm gears teeth surfaces are comply. At present, in the common CAD software, it is general that approximate drawing instead of worm gears really jugged 1 . It is very difficult to draw out its complicated and accurate tooth; in addition to, its match worm is classified for left- handed, right-handed, single-thread and multi-start. Those have increased difficulty to build its model. This paper starts mainly from the processing principle of Archimedes column worm (ZA worm), simulate its produce procedure, and make use of relations function in Pro/E, realize the accurate and parametric model of ZA worm. Furthermore, on the basis, the worm gear was produced virtually, and the generated worm gear and worm were assembled virtually and their motions were and analysed. 2. The train of thought to build model To imitate ZA worm turning process, draw cross section with the size and shape of parameterization worm gear hobs cross section, take Archimedes spiral as trajectory, make use of the “Variable Section Sweep/Cut” function in Pro/E, cut off one slot on the worm blank, then pattern the slot, the multi- start worm gear hob is generated. It is the model difficult points to full parameterize its hands and number of threads. The key point is: firstly, to set up the parameters of hands (right-handed value is 1, the left-handed value is -1) and number of threads, to establish the Archimedes spiral by the way of equation which can change with hands and number of threads. Secondly, while pattern worm slot, it is necessary that designer select the pattern way of “Direction”, and select the worm blanks axis as a reference to establish the first direction, enter the number of threads as number of members in the first direction and enter screw pitch as the spacing pattern members in the first direction. After finished worm gear hob parameterized model, on the basis, the worm model can generate by change parameter. The difference between worm and worm gear hob is that the worm gear hob has blade slot, and its radius is a clearance bigger than that of worm gear. The way which get worm gear model is to adopt the worm gear hob virtual processing. The basic train of thought is: in the virtual environment, to establish separately the worm gear blank and the worm hob, then place respectively them in each coordinate system which accord to the theory geometry assembles relation, make them rotate in each regulation, and do the Boole subtraction operation between them at different engagement position in the motion process, until the worm gear has been produced entire envelope surfaces 2 . 3. Build the relevance parameter From all above the train of thought, it can be known that ZA worm gearings parameterization design and motion analyse need to build those files such as the worm gear hob part, the worm part, the assembly between the worm gear hob and worm hob, and the assembly between the worm gear and worm. In order to realize parameterization design, these files need to parameterize their fundamental dimension. Table 1.The parametric table parameter m (modulus) q ( worm characteristic number) z1 (number of threads) xuan (hands) n (number of turns) value 5 18 3 1.0 4 parameter z2 (worm gear teeth number) hax (addendum factor) cx (bottom clearance factor) alpha (pressure angle) x2 (modification coefficient) value 53 1.0 0.2 20 -0.1 Making use of the parameters and relations function which Pro/E provides, according to the parameter relation between _____________________________ 978-1-4244-5268-2/09/$25.00 2009 IEEE Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. Downloaded on May 28,2010 at 05:07:00 UTC from IEEE Xplore. Restrictions apply. the worm and worm gear, parameters need be set up such as worm and worm gears modulus, worm characteristic number, hands, number of threads, number of turns, as shown in table 1. 4. To build the precise and parameterization model for ZA worm gear hob According to all above train of thought, firstly, designer need to cut off one slot on worm gear hob blank, as shown in Fig. 1 (a), then take worm gear hob blank axis as direction, pattern the slot which has generated just a moment ago, and add array relation: taking the number of threads as number of members and taking screw pitch as the spacing pattern members, as shown in Fig. 1 (b). (a) (b) Figure 1.Worm hob with a slot (a) and after pattern (b) (m=5, q=18, n=4, z1=3, left-handed) Adopting the Program module which is embedded in Pro/E Wildfire 2.0, the consumer can edit program according to design intention, design program, and can drive it size-fully and parametrically. According to systematic hint, consumer import the different design variable, the worm gear hob can be generated to satisfy consumers demand, as shown in Fig. 2. Figure 2.The worm hob which parameter has changed (m=2.5, q=11.2, n=6, z1=2, right-handed) 5. Establish the datum of virtual processing and assembly 5.1 Establish the datum in assembly file In Pro/E, those files are entire relevance between component and assembly. In order to realize the relative motion between worm gear hob and worm gear in the assembly, designer must establish separately the corresponding datum point and datum axis in component and assembly files, and parameterize these data, as shown in Fig. 3. Every component can be assembled with the help of these data. If parameters are changed, the worm gear hob and worm gear will rotate relatively according to given transmission ratio. Figure 3.The needed datum in virtual assembly The included angle is generally 90 degrees between two shafts of worm gearings component in space. In assembly, designer must establish separately the two necessary datum axes which crisscrossed mutually and datum points for place the worm gear hob and worm gear to assembly, and parameterize these data. In assembly, besides necessary parameters which have be stated before such as modulus, tooth number, the revolution angle parameter is also necessary to drive worm gear hob and worm gear revolution. The parameter is set up as jiao, initial value is 0. Finally it is necessary to input relations as follows: $d3=(m*q/2)*cos(jiao) /* x-coordinate of alignment point for worm gear hob $d4=(m*q/2)*sin(jiao) /* y-coordinate of alignment point for worm gear hob d5=m*pi*z1*n/2 /* z-coordinate of alignment point for worm gear hob d2=m*pi*z1*n/2 /*z-coordinate of alignment central point APNT0 for worm motion simulation, both x-coordinate and y- coordinate are 0 /*the worm and worm gear hobs alignment axis is through point APNT0 and vertical to ASM_FRONT /* the coordinate system ACS0 translates to APNT0 $d7=-m*(q+z2+2*x2)/2 /* the alignment datum central point APNT2s y-coordinate in the coordinate system ACS0 for the worm gear blank simulation d8=m*pi*z1*n/2 /* the alignment datum central point APNT2s z-coordinate in the coordinate system ACS0 for the worm gear blank simulation /* the worm gears alignment axis is through APNT2 and vertical to ASM_RIGHT /*the coordinate system translates to APNT2 for the worm gear simulation, taking the x axis positive direction of default coordinate system as its z axis positive direction, and its y axis Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. Downloaded on May 28,2010 at 05:07:00 UTC from IEEE Xplore. Restrictions apply. positive direction is the same as that in default coordinate system $d9=m*z2/2*cos(jiao*z1/z2) /*the worm gear alignment datum points x-coordinate in the worm gear simulation coordinate system $d10=m*z2/2*sin(jiao*z1/z2) /*the worm gear alignment datum points y-coordinate in the worm gear simulation coordinate system 5.2 Establish the needed datum in each part file for virtual processing and assembly To build a datum point on reference circle of the worm gear hob, align the hob axis with the hob datum axis which has been set up in assembly file while place it to assembly, align the datum point on the hob reference circle with corresponding datum point which has been set up in assembly file, because the datum point has been parameterized in assembly file, so the designer can realize to revolve the hob round their each alignment axis. Then it is necessary to make use of the relations function and input relations for the datum point as follows: d69=m*q/2 /*x-coordinate of alignment datum point for worm gear hob d71=m*pi*z1*n/2 /* z-coordinate of alignment datum point for worm gear hob Using same method, the worm gear blank is built. To be convenient to the after assembly, while the designer build model, he must pay attention to the worm gear blanks axis direction and the distance with coordinate system according to assembly relation, and build the necessary date to assemble and simulate, input relations as follows: D74=m*(q+x2*2)/2 /* z-coordinate of alignment datum point for worm gear blank 6. Virtual processing and assembly While place the components to assemble, designer need to align separately the worm axis, worm gear blank axis, the datum point on the worms reference circle and the datum point on the worm gear blanks reference circle with their corresponding axis or datum point which have been set up in assembly file. Because the datum points have been parameterized in assembly file, the designer can realize to revolve the worm and the worm gear blank round their each alignment axis by change the parameter. Making use of the “Tools--Parameters” function, changing the value of parameter “jiao” (the interval angle is smaller, the effect of worm gear is cut is better), the model can be regenerated. Making use of the “Edit--Component Operations--Cut Out” function, and cut the blank, then, in worm gear part files, designer edit the definition of the cut out id which has got just a moment ago, and change its attribute from subordinate to independent, ensure that the cut couldnt change follow the after change of the parameter value. To repeat all above step, until all worm gear slots are entirely and homogeneously cut off by the worm gear hob, as Fig.4 shows. To change the parameters of the worm and the worm gear blank, the different worm gear can be generated, as Fig.5 shows. Figure 4.The virtual processing and finished worm gear (m=5, q=18, n=4, z1=3, z2=53, left-handed) Figure 5.To assemble the worm gear with hob (m=5, q=18, n=4, z1=3, z2=53, left-handed) 7. Virtual assembly simulation and motion analysis of worm gearing 7. 1 Virtual assembly and motion simulation Replacing the worm gear hob, taking the worm as a component to place, worm gear is assembled with worm in the pin connection way. When the pin connections assemble, the simulated motion corresponding alignment axis and datum point must be chosen respectively, as Fig.6 shows. Figure 6.Define assemble connection After finished the component placement, the designer can add corresponding drive for them by the mechanism module, and simulate the motion. To choose “Applications--mechanism”, the designer can enter the mechanism module; click the button of “Define Servo Motors”, new built respectively “ServoMotor1” and “ServoMotor2”. In the “Type” label, to set up“Joint Axis” by choose respectively alignment axis which have defined when Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. Downloaded on May 28,2010 at 05:07:00 UTC from IEEE Xplore. Restrictions apply. assemble the worm gear with the worm, “Motion Type” is to “Rotation”, the designer need to pay attention to motion direction of the two electric motors. In “profile option card, the ServoMotor1s “Specification” need to be defined as “Velocity”, the “Magnitude” as the “Constant”, and its “A” as 360 multiply with worms threads number and divide worm gears teeth number. Hover ServoMotor2s “A” is set up as 360, to ensure that the engaging movement can satisfy the transmission ratio need between the worm gear and worm. The designer clicks the button of “Run an Analysis”, new built “AnalysisDefinition1”. In dialog boxs “preferences” option card, to set up “Start time”, “End time”, “Frame count” and “Frame rate”, expect that “End time” is the worm gear teeth number, the others are default. 7.2 Analyse the motion simulation There are some types that may be measured in mechanism module, such as “Position”, “Velocity”, “Acceleration”, “Connect Reaction”, “Net Load” etc. Analysing relative motion between the worm gear and the worm, designer must chose their each corresponding assembly coordinate system; ensure that coordinate system can not revolve following worm drive. To click the button of “Generate measure result of analyses”, new built measures from Measure1 to Measure4, and choose the “Graph measurement separately”, click the button of “Graph selected measures for results sets” in dialog box, measure values can be exported by the graph and the data. It is perceptual intuition and accurate, as Fig.7 and Fig.8 shows. Figure 7.Positions Y component graph and data of an index circle point on worm gear (up) or worm (down) Figure 8.Velocitys Y component graph and data of an index circle point on worm gear (up) or worm (down) In mechanism module, to click the button of “Replay previously run analyses”, In dialog boxs “interference option card , dynamic interference condition among every component can be detected; to click “Play current result set” -- “Capture” , the computer can record the animation to MPEG(export the film of mpg file format). From all above the output graph of motion simulation, there are following three points can be seen. (1)The worm gear and worm Positions Y component change in the way of the sine or cosine regular, so does velocitys Y component. It is identical with actual law which they do circling motion while they run. (2)The worm gear Positions Y component range is from - 132.5 to 132.5 mm. The worm Positions Y component range is from -45 to 45 mm. The worm gear velocitys Y component range is from -47.1238 to 47.1238 mm/s. The worm velocitys Y component range is from -282.743 to 282.743 mm/s. they are consistent with their theory value. (3)The worm gears Y component has 3 sine waves, and the worms Y component has 53 sine waves. It is identical with actual transmission ratio law while the worm gear and worm engage. It can be seen from all above that all emulation results and their theory calculation values are identical, also does their realities. References 1 CHEN Min-jie, LAI Zhen-hua, LI Zhi-ming. “Precise Modeling of Archimedes Worm in the Environment of UG”, Journal of Hubei University of Technology,2006,21(3):152156. 2 Tan Xin. “Research on the Digital Modeling Theory and Simulation Methods of Planar Double-Enveloping Toroid Worm Gear Drive”, Wuhan: Wuhan University of Technology,2003,6: 1722 Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. Downloaded on May 28,2010 at 05:07:00 UTC from IEEE Xplore. Restrictions apply.