臺灣博碩士論文加值系統

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。

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.

摘要 I
Abstract II
目錄 III
圖目錄 VI
表目錄 VIII
參數符號表 IX
第一章 緒論 1
1-1 前言 1
1-2 研究動機與目的 2
1-3 文獻回顧 2
1-4 論文架構 3
第二章 傳統戟齒輪設計方法 5
2-1 節錐面推導 5
2-2 戟齒輪的壓力角和螺旋角 10
第三章 改良之戟齒輪設計方法 16
3-1 戟齒輪大輪設計流程 16
3-2 改良之節錐面推導 18
3-2-1 兩相切錐形設計 18
3-2-2 初始節錐設計 23
3-3 大齒輪機械設定與切削 25
3-4 泛用型座標系 28
第四章 齒面曲率與小齒輪設計 32
4-1 大齒輪齒面曲率計算 33
4-2 計算點之節錐對 35
4-3 完全共軛之小齒輪齒面曲率計算 38
4-4 小齒輪刀具與機械設定 41
4-4-1 小齒輪計算點上螺旋角與壓力角 41
4-4-2 小齒輪切齒節錐 42
4-4-3 小輪刀具 46
第五章 齒輪裝配與接觸分析 47
5-1 齒輪裝配 47
5-2 齒面接觸分析(TCA) 49
5-2-1 大小輪齒齒面接觸點 49
5-2-2 齒面誤差分析之傳動誤差(Transmission error) 51
第六章 數值範例 52
6-1 相切錐形對計算範例 52
6-1-1 範例一 ---- 一般相切錐形對： 52
6-1-2 範例二 ---- 盤形相切錐形對： 54
6-2 初始節錐對計算範例 56
6-3 大輪齒形數值範例 58
6-4 小輪齒形數值範例 60
6-5 齒輪裝配範例 63
6-6 齒面接觸分析(TCA) 64
第七章 結論與未來展望 65
7-1 結論 65
7-2 未來展望 66
參考文獻 67

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