改良式戟齒輪設計與齒形模擬研究

徐子評(Tzu-PIing Hsu)

指導教授 ： 馮展華

國立中正大學/工學院/機械工程學系/碩士(2013年)

摘要

本文係根據齒輪原理(Theory of Gearing)與微分幾何(Differential Geometry)，對戟齒輪節錐系統數學模式進行修改。在戟齒輪的設計與製造過程中需計算一些節錐對，例如，大齒輪與小齒輪間之節錐、假想產形輪與大齒輪或小齒輪間之節錐，而傳統的節錐公式在計算產形輪(節錐角為90o)時會產生錯誤。重新檢查交錯軸之節錐相切條件後提出新的節錐計算公式，推導出在數值計算上較穩定之計算公式，並且可以很容易的應用於計算相切錐形對即使是產形輪也可求得。
在計算出節錐對後，可由相對曲率與相對運動關係計算齒面幾何，並由大齒輪齒面上任意指定點之曲率計算小齒輪機械設定與刀具幾何。本研究對於戟齒輪的幾何設計與公式分段模組化進行整理，尤其是相切錐形對的方程組在不同使用場合下皆有較高的數值穩定性，對於開發戟齒切齒輪軟體將有很大的助益。

關鍵字

戟齒輪

並列摘要

Based on the theory of gearing and differential geometry, mathematical model of hypoid gear is improved with novel pitch cone system equations. There are several pitch cones with varied constraints need to be determined during hypoid gear geometry design and manufacturing phases, for example, standard pitch cones between gear and pinion, manufacturing pitch cones between imaginary generating crown gears and the generated gear or pinion. Conventional pitch cone formula is failed when one of the gear pair is a crown gear (i.e., pitch cone angle is 90o). A novel pitch cone formula is proposed by reexamining the tangency condition between pitch cones of crossed axes. The proposed pitch cone formula is numerically stable and can be easily applied to calculate mating pitch cones even when crown gear is encountered. After pitch cones are determined, the geometry of tooth surface is derived by local synthesis with relative curvatures and relative motion. The machine settings and cutter geometry are derived based on the curvatures of the arbitrarily assigned contact point on the gear tooth surface. The tooth contact pattern and motion error curve can be adjusted by modifying the relative curvatures on the pinion tooth surface. The validation of proposed mathematical model for calculating the machine settings and cutter geometry of hypoid gear and mechanical settings are checked by 3D gear solid modelling and the ease-off topography. Several numerical examples are presented in this thesis to show the validation of the proposed mathematical model.

參考文獻

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