小軸交角之修整型正齒輪與凹面錐形齒輪組設計與負載下齒面接觸分析

Design and loaded tooth contact analysis of a modified spur pinion and a concave conical gear with small intersected axes

陳威呈(Wei-cheng chen)

指導教授 ： 陳怡呈

國立中央大學/工學院/機械工程學系/碩士(2013年)

摘要

首先以相交軸之正齒輪與錐形齒輪為出發，其嚙合具有點接觸之特性。本論文為避免因加工或組裝誤差造成不連續的傳動誤差，與改善於固定軸交角下嚙合應力較高之問題，因此選用由圓弧形法向剖面半徑之假想齒條刀與磨輪創成修整型正齒輪與凹面錐形齒輪，並透過其數學模式進行齒頂變尖與過切分析。
依據所推導修整型正齒輪與凹面錐形齒輪之數學模式，完成軸交角裝配齒輪組之齒面接觸分析與建立有限元素齒面網格分割程式，並由微分幾何與曲率分析求得兩嚙合齒面之主軸方向與主軸曲率，分別以赫茲應力公式與有限元素分析計算結果討論齒輪設計參數對齒面接觸應力之影響。最後為探討齒輪於負載下之嚙合情形，分別以有限元素分析與赫茲公式計算之彈性變形量，整合齒面接觸分析之結果完成負載下傳動誤差。

關鍵字

錐形齒輪 ； 接觸應力 ； 有限元素法 ； 齒面接觸分析

並列摘要

This study investigation a gear set composed of a modified spur pinion and a concave conical gear. The pinion and gear were generated by a rack-cutter with a circular-arc normal section and grinding wheel respectively. The proposed gear set with a small intersected axes exhibits point contact. According to the developed concave conical gear tooth mathematical model, tooth pointing and undercutting were investigated.
Here, tooth contact analysis was applied to explore the contact characteristics of the modified spur pinion and concave conical gear with intersected axes. Based on the differential geometry and curvature analysis, the principal directions and curvatures of the mating tooth surfaces were investigated. A mesh-generation computer program was developed based on the mathematical model of the gear set. This research studied loaded transmission errors and contact stress based on finite element method and Hertzion contact theory. The effects of design parameters various on contact stress were investigated based on the Hertz theory and finite element method.

並列關鍵字

Conical gear ； Contact stress ； Finite Element Method ； tooth contact analysis

參考文獻

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