Mathematical Model and Tooth Undercutting of Curvilinear Gears with Circular-Arc tooth Profiles

以盤狀圓弧刀具創成之曲線齒的數學模式推導與過切分析

吳一正(Yi-Cheng Wu) ； 陳冠宇(Kuan-Yu Chen) ； 蔡忠杓(Chung-Biau Tsay) ； 羅接興(Jie-Shing Lo)

《中國機械工程學刊》 30卷3期 (2009/06) Pp. 181-188

https://doi.org/10.29979/JCSME.200906.0002

摘要

本論文提出一圓弧型曲線齒齒輪(circular-arc curvilinear-tooth gear)。本研究依據齒輪原理來推導出圓弧型曲線齒大小齒輪之齒面數學模式，並依據所推導之齒面數學模式繪製齒輪外形。此外，圓弧型曲線齒齒輪的齒面過切的問題亦加以探討，本研究也以範例來進行齒面過切分析，探討齒面過切之始末奇異點及過切線的位置，同時也計算出齒輪不發生過切的最小齒數。

並列摘要

In this paper, the curvilinear gear with circular-arc tooth profiles is proposed. A mathematical model of the gear is developed based on the theory of gearing. The developed mathematical model of the proposed circular-arc curvilinear gear is then adopted to show the computer graph of gear teeth. Besides, the tooth undercutting is also investigated. Some numerical examples for tooth undercutting analysis of this type of gears are studied and illustrated. The initial tooth undercutting points and tooth undercutting line of the proposed curvilinear gear are investigated. In addition, the minimum number of gear teeth for tooth non-undercutting is also calculated.

並列關鍵字

Mathematical model ； Tooth undercutting ； Curvilinear gear ； Circular-arc tooth profile