本論文主要利用有限元素法探討蝸桿蝸輪組嚙合時，導致蝸桿蝸輪組破壞的主要應力變化。一般蝸桿使用的材料強度遠勝於蝸輪材料強度，破壞往往發生在蝸輪嚙合面而非蝸桿，所以應力分析時主要聚焦於蝸輪齒面之破壞。
文中使用有限元素套裝分析軟體Msc.Marc配合蝸桿蝸輪組之創成齒面進行蝸桿蝸輪組的嚙合模擬。探討模數、蝸輪材料、蝸桿輸入負載，對於蝸輪齒面接觸應力及蝸輪齒根彎曲應力的影響。希能提供蝸輪組設計分析之用。
文中將針對現有之蝸輪齒面赫茲接觸應力及齒根彎曲應力的經驗公式，配合Msc.Marc模擬嚙合所得出的嚙合齒輪應力，進行比較並提出一依材料而定之修正係數。對現有蝸輪齒面接觸應力及蝸輪齒根彎曲應力之應力估算公式進行調整修正。希能改善目前常用估算式的精確度，而有助於蝸桿蝸輪組之強度設計及分析。

The contact stress variation during the worm gear set meshing is simulated by using the MARC finite element software in this study. The elastic-plastic finite element model is employed to investigate the stress distribution between engaged worm gear teeth and worm. The effect of worm gear set parameters, i.e. module, worm and gear materials load, on the Hertz and bending stresses of engaged gear teeth has studied.
In this work, the traditional worm gear design formula have also been checked with the simulated stress results. Numerical results indicate that significant difference has been found between the Hertz stress at the contact points. The material dependent modification factors for different worm gear materials have been proposed in this work . The proposed factors may be helpful for the worm-gear designer in the analysis of contact stress variation of an engaged worm-gear set.

謝誌 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 viii
符號說明 ix
第一章 緒論 1
1.1 前言 1
1.2 研究動機 2
1.3 文獻回顧 2
1.4 組織章節 4
第二章 研究理論與方法 6
2.1 有限元素法理論介紹 6
2.2 蝸桿蝸輪組數學模式推導 9
2.2.1 蝸桿齒面數學模式推導 9
2.2.2 蝸輪齒面數學模式推導 21
第三章 有限元素模型建立 32
3.1 幾何外觀與網格切割 32
3.2 邊界條件與接觸設定 39
3.3 斂散性分析 44
第四章 蝸桿蝸輪組強度設計 46
4.1 蝸桿蝸輪組傳動受力分析 46
4.1.1 蝸輪齒面接觸應力公式分析 50
4.1.2 蝸輪齒根彎曲應力公式分析 57
4.2 公式計算結果與有限元素法計算結果比較 67
4.2.1 蝸輪齒面接觸應力比較 67
4.2.2 蝸輪齒根彎曲應力比較 77
第五章 結論與未來工作 87
5.1 結論 87
5.2 未來工作 87
參考文獻 88

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