修整型螺旋內齒輪組之特性分析

Abstract

齒輪為傳遞動力的重要機械元件，其中圓柱型螺旋齒輪由於具有高效率傳遞動力的特性，因此被工業界廣泛地應用在各種傳動機構中。螺旋內齒輪組與外齒輪相比之下由於具有更小之中心距的空間特性，因此內齒輪組為減速機中常見之齒輪機構，而且螺旋齒輪在嚙合時其應力也較小且運轉也較平順。然而由於螺旋內齒輪在實際製造及裝配上之誤差，使其失去原本理想的共軛嚙合條件，造成接觸狀況不佳的情況，所以業界一般會對齒輪齒面進行修整，以達到降低齒輪傳動誤差之目的。 本論文依據齒輪原理及創成機構之關係，在假設齒輪為剛體的前題下，推導出螺旋內齒輪組之齒面數學模式，並開發電腦輔助分析程式來進行該齒輪組之齒輪接觸模擬分析，探討齒輪組經由冠狀及轉位修整之螺旋小齒輪與漸開線螺旋環齒輪，當其齒輪傳動軸具有旋轉軸向之裝配誤差的情形時之嚙合狀態及運動誤差。

The gear is an important mechanical component for transmitting powers. Since the cylindrical helical gear has high efficiency to transmit power, therefore, it is widely used in reduction mechanisms by industry. The internal gear is a gear mechanism usually used for reduction gear box. Compared with the external gear, the center distance of the internal helical gear is smaller, the contact stress is lower and the gear meshing is also more smoother. However, due to the manufacture and assembly errors, the gear set may lose its conjugate meshing condition, which may cause the bad contact situation. Therefore, gear tooth modifications are widely used by the industry to reduce the transmission error of the gear pair. In this thesis, according to the theory of gearing and gear generation mechanism, a mathematical model for internal helical gears with crowned and profile-shifted modification teeth has been developed under the assumption of gear wheel is a rigid body. Based on the gear meshing theory, mathematical model of tooth contact and bearing contact analysis are established.