具冠狀與齒形修整之螺旋齒輪的齒印分析

Abstract

漸開線螺旋齒輪早已普遍使用多時，其相關之齒面修整方式亦有諸多研究及運用，冠狀修整、轉位修整與改變壓力角等均為業界所常用之齒形修整方式。但目前尚未見有具冠狀且具轉位齒形修整之漸開線螺旋齒輪的整合齒面數學模式，亦缺少對此類具齒面修整之齒輪進行接觸研究與齒印分析，因此，建立其齒面數學模式並進行研究分析，以及考量裝配誤差為非定值之偏擺誤差的影響及特性，將可對漸開線螺旋齒輪之齒面修整的特性更為瞭解，並有助於本文所提及齒面修整技術在產業上的運用。 本論文依據齒輪原理與創成機構以推導出具冠狀與齒形修整之螺旋齒輪的齒面數學模式，進而利用齒輪嚙合原理建立齒面接觸分析與齒印分析之數學模式，並輔以電腦分析程式之開發，進行各項齒輪接觸模擬分析。本研究在接觸分析方面已找出修整型螺旋齒輪在理想狀況或具裝配誤差以及發生偏擺時之接觸點的位置與運動誤差，齒印分析則已模擬求得齒輪於嚙合接觸時之齒印形狀與位置，也探討齒面修整方式對於漸開線螺旋齒輪之影響。

Involute helical gears have been widely used for a long time, and there are many researches and applications on the tooth modification methods for that. Tooth crowning, shifting modification and changing pressure angle are frequently used methods for tooth modifications by industry. However, an integrated mathematical model for helical gears with crowned and profile- shifted modification teeth has not been developed yet, and lack of researches on tooth contact and bearing contact analysis on modified tooth gears. Therefore, this study develops a mathematical model and performs the analysis with considerations on the influence and properties of gears with runout errors that the values of misalignment errors are varied. This enables us to increase the understanding of characteristics of tooth modifications, and facilitates the industry applications to this kind of gears. In this thesis, according to the theory of gearing and gear generation mechanism, a mathematical model for helical gears with crowned and profile–shifted modification teeth has been developed. Based on the gear meshing theory, mathematical models of tooth contact and bearing contact analysis have also been established. The location of contact points and kinematic errors of gears with ideal, misalignment and runout assemblies have been investigated. Bearing contact pattern and location as well as the influences of tooth modifications on the involute helical gears have also been studied.