博碩士論文 102323017 詳細資訊




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姓名 李哲仰(Lee,Che-Yang)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 修整型球面漸開線直傘齒輪對受軸變形與誤差影響之齒面接觸分析
(Tooth contact analysis of modified spherical involute bevel gears considering the shaft deflection and errors)
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摘要(中) 本論文研究之目的,係發展粉末冶金直傘齒輪完整之受載齒面接觸分析模
型,以掌握傘齒輪對在真實狀況下之各種齒面接觸特性。
在本研究中直齒傘齒輪之齒形為球面漸開線,同時並建立齒形移位之設計模式。考慮傘齒輪對多以懸臂支撐方式固定,容易因軸變形影響而造成齒面負載分佈不均,同時也為降低誤差影響,因此採齒線和齒形雙隆起方式修整齒面。
透過所建立之齒面接觸分析方法,在研究中共分析不同組裝、偏心誤差對修整傘齒輪對之接觸點位置及傳動誤差之影響。分析結果顯示,偏位誤差對接觸點在齒面寬方向之位置影響最大,其次分別為大、小齒輪之軸向誤差,而角度誤差僅影響齒形方向之接觸點位置。而無誤差下之傳動誤差曲線呈現拋物線型式,在具偏位誤差、軸交角誤差和大、小齒輪軸向誤差也仍為拋物線型式;但大、小齒輪軸向誤差在誤差值較大情況時,容易產生不連續之傳動特徵。偏心誤差下之傳動誤差曲線,為正弦波形函數與拋物線疊加之結果,且傳動誤差之變化具有週期規律性。論文同時亦製造出測試齒輪進行傳動誤差量測,以印證所建立模型之準確性。
受載齒面接觸分析模型係使用影響係數法建立數值分析方法,此分析模型除考慮齒面接觸變形外,亦納入齒部彎曲變形以及軸變形等影響,除可模擬修整型傘齒輪對之受載齒面接觸應力分佈狀況、接觸斑形狀外,也可以計算負載分配與受載傳動誤差。分析結果顯示齒面上最大接觸應力位置受到軸變形影響往大端偏移。由於齒形修整,嚙合開始與結束之齒面接觸負載與接觸應力皆為零。而隨著扭力增加使傳動誤差曲線偏移量加大,不連續之傳動特徵更加明顯。
摘要(英) The aim of the thesis is to develop a loaded tooth contact analysis model for powder metallurgy straight toothed bevel gears, in order to explore the tooth contact characteristics of the bevel gear pair under real working condition.
In the research, the spherical involute and profile shifting are used for construction of the tooth profile. Because of the shaft deformation due to cantilever supporting of the bevel gears, the load distribution on the contact tooth is not uniform. On the other hand, the influences of errors of PM bevel gears on the tooth contact should be also reduced, Therefore, a double-crowning flank modification, i.e., lead crowning and profile crowning, is introduced in the research.
The tooth contact analysis (TCA) is established based on the geometrical property of spherical involute. The influence of different assembly and eccentric errors on the contact positions and transmission errors of the bevel gear pairs were thus analyzed. The results show that the contact position along the facewidth of the tooth pair due to the offset error is the most sensitive, the next one is due to the mounting distance errors of the gear and the pinion. The shaft angle error only affects the location along tooth profile with the same facewidth. The curve of transmission error (TE) in the ideal case is parabolic; those in the case with errors are also parabolic. With larger mounting distance errors of the gear and the pinion, the TE curves become discontinuous. The TE curve due to the eccentric error is a regular curve with combination of the sinusoidal and the parabolic curve. Test bevel gears were also manufactured for measurement of transmission error to confirm the accuracy of the analysis model.
The loaded tooth contact analysis (LTCA) is conducted with aid of a numerical approach based on the influence coefficient method. The LTCA model involves the influences of the deformations of teeth and shafts as well as the errors. The analysis approach can not only simulate the distribution of the tooth contact stress, the shape of the contact patterns, but also the load sharing and loaded transmission errors. The analysis results show that the position with maximum value of the contact stress is shifted near the heel due to the shaft deflection. The contact stresses at the begin and end of contact are zero due to profile crowning modification. With the increased torque, the average values of the loaded transmission error (LTE) increase. In the case of discontinuous variation of transmission errors, the jump will also increase with the increased torque.
關鍵字(中) ★ 雙隆起修整
★ 偏心誤差
★ 受載齒面接觸分析
★ 傳動誤差
關鍵字(英) ★ Double-crowned flank modification
★ Eccentric error
★ Loaded tooth contact analysis
★ Transmission error
論文目次 摘要 i
Abstract ii
謝誌 iv
目錄 v
圖目錄 ix
表目錄 xv
符號說明 xvi
第1章 前言 1
1.1 研究背景 1
1.2 文獻回顧 2
1.3 研究目的 5
1.4 論文架構 6
第2章 研究方法 7
2.1 傘齒輪移位幾何設計 7
2.1.1 傘齒輪移位定義 7
2.1.2 傘齒輪對嚙合關係 9
2.2 齒面修整和齒面方程式 11
2.2.1 齒線修整 12
2.2.2 齒形修整 17
2.2.3 修整型齒面方程式 19
2.3 修整型傘齒輪對誤差下嚙合關係 21
2.3.1 組裝關係 21
2.3.2 嚙合齒面接觸點求解法 24
2.3.3 偏心誤差之齒面接觸求解 27
2.4 受載齒面接觸分析模型 31
2.4.1 基本分析模型 31
2.4.2 修整傘齒輪對齒面間距 35
2.4.3 齒撓曲變形影響係數 37
2.4.4 軸彎曲變形影響係數 47
2.4.5 軸扭轉變形影響係數 49
第3章 傘齒輪之修整齒面設計 51
3.1 基本分析設定 51
3.1.1 傘齒輪參數 51
3.1.2 傘齒輪軸之設計與配置 51
3.2 齒線修整參數影響 53
3.2.1 形狀係數SF 53
3.2.2 對稱係數Se 54
3.2.3 接觸位置ΔR 55
3.2.4 比例係數Sc 55
3.2.5 修整參數選定 56
3.3 齒形修整參數影響 57
第4章 組裝誤差下嚙合位置 59
4.1 誤差定義 59
4.2 齒面接觸分析 60
4.3 CAD模擬方式 63
4.4 分析結果比較與討論 64
第5章 修整型傘齒輪受載齒面接觸分析 69
5.1 齒面接觸斑變化 69
5.2 嚙合過程負載分配率 70
5.2.1 無誤差下之負載分配率 71
5.2.2 組裝誤差之影響 72
5.3 嚙合過程接觸應力變化 81
5.3.1 無誤差下接觸應力變化 81
5.3.2 組裝誤差之接觸應力變化 83
5.4 特定位置之接觸應力 92
5.4.1 無誤差 93
5.4.2 組裝誤差 95
5.5 傘齒輪對FEM驗證 100
第6章 傳動誤差 102
6.1 傳動誤差定義 102
6.2 無負載下傳動誤差 102
6.2.1 無誤差 102
6.2.2 偏位誤差 103
6.2.3 軸交角誤差 105
6.2.4 大齒輪軸向誤差 105
6.2.5 小齒輪軸向誤差 108
6.2.6 偏心誤差 110
6.2.7 綜合誤差 112
6.3 負載下傳動誤差 113
6.3.1 無誤差 113
6.3.2 偏位誤差 114
6.3.3 軸交角誤差 116
6.3.4 大齒輪軸向誤差 118
6.3.5 小齒輪軸向誤差 120
6.3.6 偏心誤差 122
6.3.7 綜合誤差 124
6.4 傳動誤差試驗與模擬比較 126
6.4.1 實驗用傘齒輪對與實驗機台 126
6.4.2 實驗結果與程式模擬比較 128
第7章 結論與未來展望 130
7.1 結論 130
7.2 未來展望 132
參考文獻 134
附錄 A 傘齒輪對空間配置關係 137
附錄 B 球面漸開線之幾何特性與雙數法 141
附錄 C 組裝誤差之特定位置接觸應力 143

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指導教授 蔡錫錚(Tsai, Shyi-Jeng) 審核日期 2017-4-22
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