具齒形修整之圓弧形曲線齒輪接觸分析

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古鳴倫(Ming-Lune Gu) 查詢紙本館藏

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機械工程學系

論文名稱

具齒形修整之圓弧形曲線齒輪接觸分析
(Tooth Contact Analysis of a Curvilinear Gear Set with Modification)

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摘要(中)

修整型曲線齒輪係利用具有圓弧法向剖面且具有圓弧齒線的假想齒條刀所創成之齒輪。其特徵為齒面寬中央截面厚度較大，而齒面寬兩端厚度較小，且左右齒面外形不相同，一齒面為凹面，另一齒面為凸面。修整型曲線齒輪組在齒面寬中央為點接觸，能避免發生齒緣接觸。其優點為無軸向推力、彎矩強度較高，且因一齒面為凹面，能有利於潤滑油的殘留，故齒輪潤滑較良好。
本研究首先推導出具圓弧法向剖面齒條刀的數學模式，進而利用假想曲線齒條刀配合創成機構推導修整型曲線齒輪的齒面數學方程式。然後撰寫電腦程式進行修整型曲線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之影響，並且計算出接觸率。
接著以電腦輔助繪圖軟體建立齒輪組實體模型，並使用有限元素分析軟體進行修整型曲線齒輪組之接觸應力分析，探討在不同旋轉角度下的接觸應力與齒根彎矩應力的變化情況，並深入分析刀具參數對齒面接觸應力與齒根彎矩應力之影響。
最後利用五軸CNC加工機製造出修整型曲線齒輪實體模型，使用泛用型齒輪嚙合測試機進行測試，探討不同設計參數下之傳動誤差，並進行齒輪組接觸齒印測試與有限元素分析之結果相互驗證。

摘要(英)

Modified curvilinear gears can be generated by an imaginary rack-cutter with a circular-arc normal section. The tooth thickness of the modified curvilinear gears is larger in the central transverse section, and the left and right tooth surfaces are not symmetric. One of the tooth surfaces is concave and the other is convex. A modified curvilinear gear set has point contact and will not incur point contact under assembly errors.
In this study, firstly the mathematical model of the imaginary rack cutter is developed. The mathematical model of the modified curvilinear gears was derived based on the imaginary rack cutter and the generation mechanism. Tooth contact analysis (TCA) of a modified curvilinear gear set was established to simulate the influences of design parameters and assembly errors on transmission errors. The contact ratio of the gear set was also calculated from the TCA results.
The solid model of the gear set was established by computer aided design software, and finite element analysis (FEA) was performed to analyze the contact stress and root bending stress under different design parameters and different rotational angles.
Finally, the modified curvilinear gears were manufactured by using a 5-Axes CNC Machining Center. Experiments of transmission errors and contact patterns were performed on a universal gear tester to verify the FEA results.

關鍵字(中)

★ 有限元素分析
★ 齒面接觸分析
★ 曲線齒輪
★ 傳動誤差

關鍵字(英)

★ curvilinear gear
★ tooth contact analysis
★ transmission error
★ finite element analysis

論文目次

中文摘要 ………………………………………………………… i
英文摘要 ………………………………………………………… ii
誌謝 ………………………………………………………… iii
目錄 ………………………………………………………… iv
圖目錄 ………………………………………………………… vi
表目錄 ………………………………………………………… x
符號說明 ………………………………………………………… xi
一、緒論…………………………………………………… 1
1-1 研究目的……………………………………………… 1
1-2 文獻回顧……………………………………………… 1
1-3 研究動機……………………………………………… 3
1-4 論文內容……………………………………………… 5
二、齒面數學模式………………………………………… 6
2-1 曲線齒輪創成原理…………………………………… 6
2-2 假想齒條刀數學模式………………………………… 9
2-3 修整型曲線齒輪齒面數學模式……………………… 12
2-4 修整型曲線齒輪齒形特徵…………………………… 18
2-4-1 不同刀具法向剖面半徑所創成之齒輪齒形………… 18
2-4-2 不同刀盤半徑所創成之齒輪齒形…………………… 20
三、齒面接觸分析………………………………………… 23
3-1 前言…………………………………………………… 23
3-2 傳動誤差分析………………………………………… 23
3-3 接觸齒印……………………………………………… 27
3-4 齒面接觸分析範例…………………………………… 30
3-4-1 理想裝配情況………………………………………… 31
3-4-1-1 範例3-1 ……………………………………………… 31
3-4-1-2 範例3-2 ……………………………………………… 32
3-4-1-3 範例3-3 ……………………………………………… 32
3-4-1-4 範例3-4 ……………………………………………… 32
3-4-1-5 範例3-5………………………………………………… 33
3-4-2 組裝誤差……………………………………………… 34
3-5 接觸率………………………………………………… 42
3-6 討論…………………………………………………… 43
3-7 結論…………………………………………………… 45
四、有限元素分析………………………………………… 47
4-1 有限元素模型………………………………………… 47
4-2 接觸面與表面特性定義……………………………… 47
4-3 邊界條件設定………………………………………… 48
4-4 齒輪設計參數對應力值之影響……………………… 48
4-4-1 範例4-1 ……………………………………………… 50
4-4-2 範例4-2 ……………………………………………… 56
4-4-3 範例4-3………………………………………………… 62
4-4-4 討論…………………………………………………… 65
4-5 齒輪組於不同旋轉角度之有限元素分析…………… 69
4-5-1 範例4-4 ……………………………………………… 69
4-5-2 範例4-5 ……………………………………………… 75
4-5-3 討論…………………………………………………… 78
4-6 結論…………………………………………………… 78
五、修整型曲線齒輪製造與實驗………………………… 79
5-1 前言…………………………………………………… 79
5-2 泛用型齒輪測試機之介紹…………………………… 81
5-3 齒輪單齒腹測試原理………………………………… 81
5-4 實驗流程……………………………………………… 84
5-4-1 修整型曲線齒輪齒形誤差…………………………… 86
5-4-2 接觸齒印分析………………………………………… 87
5-4-2-1 無負載之修整型曲線齒輪接觸齒印………………… 87
5-4-2-2 受負載之修整型曲線齒輪接觸齒印………………… 88
5-4-3 討論…………………………………………………… 101
5-5 結論…………………………………………………… 104
六、結論與未來工作……………………………………… 105
6-1 結論…………………………………………………… 105
6-2 未來工作……………………………………………… 106
參考文獻 108

參考文獻

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指導教授

陳怡呈(Yi-Cheng Chen)

審核日期

2011-1-21

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