具圓形斷面齒形兩齒差擺線傳動減速機齒頂修整與電腦輔助製造之研究

A Study on the Addendum Modifing and Computer Aided Manufacturing of Cycloid Drives with Two Tooth Difference for Circular Cross Section Tooth-Profiles

呂家銘(Jia-Ming Lyu)

國立虎尾科技大學/工程學院/動力機械工程研究所/碩士(2005年)

摘要

本論文提出具圓形斷面齒形兩齒差擺線傳動減速機之幾何設計，並作齒頂修整(Addendum Modifing)與電腦輔助製造(CAM)之研究。首先說明擺線傳動減速機之拓樸構造，進而推導嚙合件曲面方程式。接著，以基本嚙合運動、座標轉換、包絡理論為基礎，求嚙合件之嚙合方程式。聯立曲面方程式與嚙合方程式，可得擺線行星輪齒廓，再根據減速機齒數與周節間之關係，可知兩條相差半個周節的擺線行星輪齒廓，其交集可得兩齒差擺線行星輪齒廓。
由於兩齒差擺線行星輪齒廓之齒頂會造成尖點，本文提出Bezier曲線之數學方法與應用CAD軟體之曲線擬合功能作齒頂修整來消除尖點。應用Bezier曲線數學方法之優點為可經由改變尖點位置，來調整擬合曲線的位置。應用CAD曲線擬合功能之優點為只需得到擺線行星輪齒廓，即可在電腦螢幕作齒頂修整，得到與兩齒差擺線行星輪齒廓接合連續的擬合曲線。兩種齒頂修整方法，可分別得到兩齒差擺線行星輪齒廓的幾何數據資料與CAD圖檔(.*DWG)。而兩者皆可利用CAM軟體或Pro/MFG加工模擬程序得到NC加工程式。
最後，使用電腦輔助設計軟體(Pro/ENGINEER)建構兩齒差擺線傳動減速機之實體模型，再經由Pro/MFG加工模擬程序轉出設計模型的NC加工程式。轉出的NC加工程式可供給數值控制機械作兩齒差擺線行星輪的加工。

並列摘要

This work presents an algorithm on geometric design of cycloid drives with two teeth difference and circular cross section tooth-profiles, as well as a methodology on their addendum modifing and computer aided manufacturing. The topological structure of cycloid drives is derived first. Then, the required surface equation is obtained. Finally, equations of meshing are constructed based on the fundamental gearing kinematics, coordinate transformation, envelope theory, and theory of conjugate surfaces. By combining the surface equation and equations of meshing, the conjugate curve of the meshing elements, i.e. the cycloid wheel curve, can be constructed. In order to get a required hyper tooth profile with two tooth difference, two profiles with cycloid wheel curve are generated. They share a common center and differ by a phase shift of half a circular pitch. Consequently, these two wave-like circular curves are crossing with each other. The desired profile is finally obtained by selecting the inner curve between these two twisted curves.
The profile generated by the proposed method will inevitably form undesirable cusps. This research is to develop a mathematic approach based on Bezier curve and to realize addendum modifying using the curve fitting function of CAD. The advantage of applying Bezier curve is that the positions where two wave-like curves are merged can be properly modified by adjusting the position of cusps. Furthermore, the advantage of utilizing the curve-fitting function in CAD is that the hyper tooth profile with two tooth difference can be simply obtained by performing on screen addendum modifying on that with one tooth difference. Two addendum modifing method are introduced here. Both of them can generate geometric data and CAD file with an extension of DWG and combine with CAM software and Pro/MFG process-simulated procedure to get a desired NC Process procedure .
Finally the computer aided design software (Pro/ENGINEER) is used to construct the solid modeling of the proposed cycloid planetary gear with two teeth difference. Then, using the processsimulated procedure in Pro/MFG, this is converted into the NC process procedure that can be provided for NC machine to process cycloid planetary gear with two teeth difference.

參考文獻

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