小軸交角之修整型正齒輪與凹面錐形齒輪組設計與負載下齒面接觸分析

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姓名

陳威呈(Wei-cheng chen) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

小軸交角之修整型正齒輪與凹面錐形齒輪組設計與負載下齒面接觸分析
(Design and loaded tooth contact analysis of a modified spur pinion and a concave conical gear with small intersected axes)

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至系統瀏覽論文 ( 永不開放)

摘要(中)

首先以相交軸之正齒輪與錐形齒輪為出發，其嚙合具有點接觸之特性。本論文為避免因加工或組裝誤差造成不連續的傳動誤差，與改善於固定軸交角下嚙合應力較高之問題，因此選用由圓弧形法向剖面半徑之假想齒條刀與磨輪創成修整型正齒輪與凹面錐形齒輪，並透過其數學模式進行齒頂變尖與過切分析。
依據所推導修整型正齒輪與凹面錐形齒輪之數學模式，完成軸交角裝配齒輪組之齒面接觸分析與建立有限元素齒面網格分割程式，並由微分幾何與曲率分析求得兩嚙合齒面之主軸方向與主軸曲率，分別以赫茲應力公式與有限元素分析計算結果討論齒輪設計參數對齒面接觸應力之影響。最後為探討齒輪於負載下之嚙合情形，分別以有限元素分析與赫茲公式計算之彈性變形量，整合齒面接觸分析之結果完成負載下傳動誤差。

摘要(英)

This study investigation a gear set composed of a modified spur pinion and a concave conical gear. The pinion and gear were generated by a rack-cutter with a circular-arc normal section and grinding wheel respectively. The proposed gear set with a small intersected axes exhibits point contact. According to the developed concave conical gear tooth mathematical model, tooth pointing and undercutting were investigated.
Here, tooth contact analysis was applied to explore the contact characteristics of the modified spur pinion and concave conical gear with intersected axes. Based on the differential geometry and curvature analysis, the principal directions and curvatures of the mating tooth surfaces were investigated. A mesh-generation computer program was developed based on the mathematical model of the gear set. This research studied loaded transmission errors and contact stress based on finite element method and Hertzion contact theory. The effects of design parameters various on contact stress were investigated based on the Hertz theory and finite element method.

關鍵字(中)

★ 錐形齒輪
★ 接觸應力
★ 有限元素法
★ 齒面接觸分析

關鍵字(英)

★ Conical gear
★ Contact stress
★ Finite Element Method
★ tooth contact analysis

論文目次

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vii
表目錄 xii
符號表 xiii
第1章緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 錐形齒輪 2
1.2.2 接觸分析 4
1.3 研究目的 5
1.4 論文架構 6
第2章修整型正齒輪與凹面錐形齒輪數學模式 8
2.1 前言 8
2.2 創成修整型正小齒輪假想齒條刀數學模式 8
2.3 創成凹面錐形大齒輪磨輪之數學模式 11
2.4 修整型正小齒輪齒面數學模式 17
2.5 凹面錐形大齒輪齒面數學模式 20
2.6 修整型正齒輪與凹面錐形齒輪之齒形特徵 23
第3章凹面錐形齒輪齒頂變尖與過切分析 28
3.1 前言 28
3.2 齒頂變尖 28
3.3 過切分析 30
3.4 齒頂變尖與過切分析範例 34
3.5 討論 37
第4章齒面接觸分析 38
4.1 前言 38
4.2 傳動誤差分析 38
4.3 接觸齒印 42
4.4 不發生邊緣接觸之最小磨輪半徑EG 45
4.5 齒面接觸分析範例 47
4.5.1 凹面錐形齒輪避免邊緣接觸之最小磨輪半徑EG 47
4.5.2 標準理想裝配情況 49
4.5.3 組裝誤差 52
4.5.4 討論 54
第5章曲率分析與赫茲接觸應力 56
5.1 前言 56
5.2 修整型正小齒輪與凹面錐形大齒輪之刀面數學模式 57
5.3 曲率分析 58
5.3.1 齒條刀之主軸曲率與主軸方向 58
5.3.2 修整型正齒輪小齒輪之主軸曲率與主軸方向 59
5.3.3 齒條刀主軸曲率與主軸方向 62
5.3.4 凹面錐形大齒輪之主軸曲率與主軸方向 63
5.4 接觸橢圓與赫茲應力 66
5.4.1 單齒對接觸分析 66
5.4.2 兩齒對接觸分析 70
5.4.3 接觸橢圓應力分佈 76
5.4.4 不同旋轉角度之數值範例 76
5.4.5 改變齒輪刀具參數之接觸橢圓與接觸應力 81
5.5 結論 86
第6章負載下齒面接觸分析 88
6.1 前言 88
6.2 單齒對有限元素模型建立 91
6.2.1 接觸敏感區域 91
6.2.2 接觸表面特性定義與邊界條件設定 93
6.3 單齒對有限元素模擬結果 94
6.4 多齒對有限元素模型建立 101
6.5 多齒對模擬結果 102
6.5.1 接觸應力分析 102
6.5.2 齒輪強度分析 106
6.6 負載下傳動誤差 109
6.6.1 有限元素分析計算負載下傳動誤差 110
6.6.2 赫茲應力計算負載下傳動誤差 112
6.6.3 負載下傳動誤差分析範例 112
6.7 結論 117
第7章齒輪修整選用與比較 119
7.1 選用一般漸開線正齒輪與修整型正齒輪之加工誤差分析 119
7.2 選用傳統錐形齒輪與凹面錐形齒輪之接觸應力與接觸橢圓比較 122
7.3 標準理想裝配 127
7.4 組裝誤差 128
7.5 結論 133
第8章修整型正齒輪與凹面錐形齒輪製造與齒印實驗 135
8.1 泛用型嚙合測試機 136
8.2 實驗齒輪參數 137
8.3 實驗流程 138
8.4 接觸齒印 140
8.5 結論 144
第9章實驗傳動誤差數據分析 145
9.1 單齒腹測試 145
9.2 實驗齒輪參數 146
9.3 經驗模態分解法(Empirical Mode Decomposition, EMD) 147
9.4 集成經驗模態分解法(Ensemble EMD, EEMD) 147
9.5 實驗流程與訊號分析步驟 148
9.6 齒形誤差結果與討論 148
第10章結論與未來工作 152
10.1 結論 152
10.2 未來工作 155
參考文獻 156
附錄一標準齒輪檢測報告 160
附錄二修整型正齒輪(RP=500mm)檢測報告 162
附錄三修整型正齒輪(RP=350mm)檢測報告 165
附錄四修整型正齒輪(RP=250mm)檢測報告 167

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指導教授

陳怡呈(Yi-cheng chen)

審核日期

2013-11-15

推文