以互補型盤狀圓弧刀具創成之曲線齒齒輪有限元素應力分析

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李致緯(Zhi-uei Li) 查詢紙本館藏

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機械工程學系

論文名稱

以互補型盤狀圓弧刀具創成之曲線齒齒輪有限元素應力分析
(Finite Element Stress Analysis of a Circular-Arc Curvilinear-Tooth Gear Set Generated by Complementary Circular-Arc Disk-Type Cutters)

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摘要(中)

本文主要探討由互補型盤狀圓弧刀具所創成之互補型圓弧曲線齒齒輪的有限元素應力分析。首先，推導互補型圓弧曲線齒齒輪的數學模式，進而利用假想齒條刀配合創成機構推導互補型曲線齒齒輪的齒面數學模式。接著進行互補型曲線齒齒輪之齒面接觸分析，探討刀具參數與組裝誤差對傳動誤差的影響。互補型圓弧曲線齒齒輪是線接觸，且對組裝誤差相當敏感，使用有限元素分析軟體ABAQUS進行互補型圓弧曲線齒齒輪五對接觸齒之應力分析，再將同樣是線接觸型態之正齒輪有限元素分析結果比對，
此外，將互補型圓弧曲線齒齒輪由線接觸修整為點接觸，並利用齒面接觸分析探討傳動誤差和接觸齒印，並探討有限元素應力分析。
最後利用單齒腹測試機針對互補型圓弧曲線齒齒輪和近似線接觸互補型圓弧曲線齒齒輪進行接觸齒印實驗，並與齒面接觸分析和有限元素分析結果互相驗證比對。

摘要(英)

This paper focuses on finite element stress analysis of a complementary circular-arc curvilinear gear set. Firstly, the mathematical model of the complementary circular-arc curvilinear gear set was developed based on the theory of gearing. Tooth contact analysis (TCA) is performed to study the influences of gear design parameters and assembly errors on the transmission error. The original complementary circular-arc curvilinear gear is in line-contact and is sensitive to assembly errors. A commercial finite element analysis (FEA) package, ABAQUS, was utilized to perform stress analysis of five contact teeth pair, and the bending stress of complementary circular-arc curvilinear gear was compared with that of conventional spur gears.
In addition, a method of tooth modification was proposed in this thesis to introduce point contact in a modified complementary circular-arc curvilinear gear set. Tooth contact analysis and FEA were utilized to investigate the transmission error, contact pattern and bending stress of the proposed modified complementary circular-arc curvilinear gear set.
Finally, experimental contact patterns of both original and modified complementary circular-arc curvilinear gear sets were also performed on a single flank testing machine to verify the results from TCA and FEA.

關鍵字(中)

★ 彎矩應力
★ 互補型圓弧曲線齒齒輪
★ AGMA 2001-C95
★ 有限元素分析

關鍵字(英)

★ complementary circular-arc curvilinear-tooth gea
★ root bending stress
★ finite element analysis
★ AGMA standard

論文目次

摘要 i
目錄 iv
圖目錄 vii
表目錄 xii
符號說明 xiii
第1章緒論 1
1-1 研究目的 1
1-2 文獻回顧 1
1-3 研究動機 2
1-4 論文內容 4
第2章互補型圓弧曲線齒齒輪齒面數學模式 5
2-1 假想齒條刀數學模式 5
2-1-1 小齒輪假想齒條刀數學模式 5
2-1-2 大齒輪假想齒條刀數學模式 9
2-2 互補型圓弧曲線齒輪齒面數學模式 11
2-2-1 小齒輪齒面數學模式 11
2-2-2 大齒輪齒面數學模式 17
2-3 互補型曲線齒齒輪齒形特徵 20
2-3-1 不同刀具法向剖面半徑所創成之齒形 20
2-3-2 不同刀盤半徑所創成之齒形 26
2-3-3 齒頂變尖 28
2-3-4 齒根交錯 31
2-4 結論 33
第3章過切分析 35
3-1 過切條件式 35
3-2 公刀具創成之小齒輪過切範例 40
3-2-1 範例一 40
3-2-2 範例二 41
3-2-3 範例三 42
3-2-4 範例四 43
3-2-5 結論 44
3-3 母刀具創成之大齒輪過切範例 46
3-3-1 範例五 46
3-3-2 範例六 47
3-3-3 範例七 49
3-3-4 範例八 50
3-3-5 結論 51
3-4 結論 53
第4章互補型圓弧曲線齒齒輪齒面接觸分析與有限元素分析 55
4-1 前言 55
4-2 互補型圓弧曲線齒齒輪接觸分析數學模式 55
4-3 互補型圓弧曲線齒齒輪接觸分析 59
4-3-1 範例一~範例五 59
4-4 互補型圓弧曲線齒齒輪接觸齒印實驗 63
4-5 接觸率 67
4-6 互補型圓弧曲線齒齒輪有限元素分析 68
4-6-1有限元素分析參數設定 69
4-6-2互補型圓弧曲線齒齒輪齒根彎矩應力有限元素分析 71
4-7 正齒輪有限元素分析 77
4-7-1正齒輪AGMA計算公式 77
4-7-2正齒輪齒根彎矩應力有限元素分析 80
4-8 結論 82
第5章近似線接觸互補型圓弧曲線齒齒輪齒面接觸分析與有限元素分析 84
5-1 近似線接觸互補型圓弧曲線齒齒輪接觸分析數學模式 84
5-2 近似線接觸互補型圓弧曲線齒齒輪接觸齒印 85
5-3 近似線接觸互補型圓弧曲線齒齒輪接觸分析 88
5-3-1 範例六至範例九改變刀具法向剖面半徑 89
5-3-2 範例十至範例十三改變刀盤半徑 91
5-3-3改變公刀具創成之小齒輪刀具法向剖面半徑及刀盤半徑 92
5-4 近似線接觸互補型圓弧曲線齒齒輪接觸齒印實驗 99
5-5 近似線接觸互補型圓弧曲線齒齒輪齒面接觸應力有限元素分析 102
5-6 結論 114
第6章結論與未來工作 116
6-1 結論 116
6-2 未來工作 118
參考文獻 119

參考文獻

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指導教授

陳怡呈(Yi-Cheng Chen)

審核日期

2012-8-31

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