平行軸高接觸率正齒輪系統的動態受載齒面接觸分析

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姓名

黃鈺翔(YU-HSIANG HUANG) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

平行軸高接觸率正齒輪系統的動態受載齒面接觸分析
(Dynamically Loaded Tooth Contact Analysis of Parallel Shaft High-Contact-Ratio Spur Gear System)

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摘要(中)

齒輪系統廣泛的運用在各式傳動場合，而為了減低高速運轉中的噪音與震動，提高齒輪的接觸率為其中一種解決方法。高接觸率正齒輪除了繼承正齒輪易於設計與加工的特點，同時因提高接觸率，嚙合剛性變化對系統的影響較小，因此作為解決方案之一受到重視。但也因為正齒輪經常使用加長齒高的方式提高接觸率，高接觸率正齒輪受載情況更容易受軸變形、軸誤差影響。且在現今的高負載高轉速需求下，以往的靜態分析無法滿足需要。
在以往的齒輪動態分析中，通常是利用離散化並配合理論嚙合剛性進行分析，但容易出現模型過於簡化的問題，同時動態模型能提供的資訊有限。而靜態的齒輪分析則是一個已經發展成熟的體系。因此我們希望利用離散-多體模型，並配合以靜態受載齒面接觸分析(SLTCA)，以了解齒輪在動態下的接觸狀況。
分析上，本研究將系統元件離散化，其中齒輪的嚙合剛性由事先以SLTCA方法計算建立的剛性圖得知。而後以數值方法對系統的動態方程式進行求解，在得到齒輪處的軸變形與動態扭力後，再代回SLTCA模組計算瞬時的接觸狀況。
本研究對透過比較高接觸率齒輪系統在各種考慮條件下，研究系統的動態特性。比對修整與無修整齒輪對的結果後，雖然修整會提高動態傳動誤差，但能對系統的嚙合力與扭力振動情形進行改善。在軸誤差案例中，修整能減輕系統振動，並使接觸狀況變回一般的點接觸。最後，在靜止加速案例中，修整也能使啟動時的激振與後續的振動振幅降低。

摘要(英)

Gear systems are widely used in various transmission applications, and to reduce noise and vibration during high-speed operation, increasing the contact ratio is one of the solutions. High-contact ratio spur gears, in addition to keep the advantages of spur gears in terms of ease of design and manufacturing, also its mesh stiffness has smaller effects to system vibration due to the increased contact ratio. As a result, they have received attention as one of the solutions. However, since spur gears often increase the contact ratio by lengthening the tooth height, high contact ratio spur gears are more susceptible to the effects of shaft deformation and misalignment. Moreover, with the increasing demand for high load and high speed, traditional static analysis is no longer sufficient.
In the past, discretization was used along with theoretical mesh stiffness for analysis. However, this approach often oversimplifies the model, and the dynamic models provide limited information. In contrast, static gear analysis is a well-established method. Therefore, this study aims to utilize a discrete multi-body model, combined with statically loaded tooth contact analysis (SLTCA), to understand the stress distribution of gears under dynamic conditions.
In the analysis, this study discretizes the system components, with the gear mesh stiffness determined from stiffness map calculated using the SLTCA method. Then, numerical methods are used to solve the system’s dynamic equations. After obtaining the shaft deformation and dynamic torque at the gears, these results are fed back into the SLTCA module to calculate the instantaneous stress distribution.
This study compares the dynamic characteristics of high-contact ratio gear systems under various conditions. By comparing the results of gears with and without gear modification, it was found that although modification increases dynamic loaded transmission error, it can improve the system’s mesh force and torque vibration behavior. In the case of shaft misalignment, modification helps reduce system vibration and returns the stress distribution to normal point contact. Finally, in the case of static acceleration, modification also helps reduce the excitation during startup and the subsequent vibration amplitude.

關鍵字(中)

★ 高接觸率齒輪對
★ 動態受載齒面接觸分析
★ 剛性圖
★ 齒輪修整
★ 軸誤差
★ 傳動誤差
★ 穩態分析
★ 暫態分析

關鍵字(英)

論文目次

摘　　　要 i
Abstract ii
謝誌 iv
目　　　錄 v
圖　目　錄 viii
表　目　錄 xxiv
符號對照表 xxv
第 1 章緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.3 研究目的與方法 3
1.4 論文架構 4
第 2 章高接觸率正齒輪對 6
2.1 高接觸率正齒輪對接觸分析 6
2.1.1 傳動誤差 7
2.1.2 齒輪修整 7
2.2 齒輪軸及軸誤差 10
2.2.1 軸誤差 10
第 3 章齒輪-軸-軸承動態分析模型 12
3.1 齒輪對動態方程式 12
3.2 軸質量矩陣 13
3.3 軸剛性矩陣 19
3.4 齒輪對質量矩陣 24
3.5 齒輪對剛性矩陣 24
3.5.1 正齒輪對剛性矩陣 24
3.5.2 螺旋齒輪剛性矩陣 34
第 4 章 SLTCA與剛性圖求解方法 56
4.1 靜態受載齒面接觸分析SLTCA 56
4.2 剛性圖法介紹 59
第 5 章動態負載齒面接觸分析(DLTCA) 62
5.1 動態求解流程 62
5.2 穩態傳動求解 72
5.3 暫態傳動求解 73
第 6 章案例數據及KISSsoft分析 83
6.1 案例數據 83
6.2 KISSsoft分析 89
第 7 章穩態分析案例及結果 91
7.1 齒輪修整對系統的影響 91
7.1.1 案例說明 91
7.1.2 分析結果 91
7.2 轉速對系統的影響 98
7.2.1 案例說明 98
7.2.2 分析結果 99
7.3 軸誤差對系統的影響 102
7.3.1 案例說明 102
7.3.2 分析結果 104
第 8 章暫態分析案例及結果 125
8.1 案例說明 125
8.2 分析結果 126
第 9 章結論與展望 134
9.1 結論 134
9.2 未來展望 135
參考文獻 137
附錄 A 無修整齒輪對結果 139
附錄 B 修整齒輪對結果 144
附錄 C 無修整齒輪對-正傾斜結果 149
附錄 D 修整齒輪對-正傾斜結果 155
附錄 E 無修整齒輪對-反傾斜結果 161
附錄 F 修整齒輪對-反傾斜結果 167
附錄 G 無修整齒輪對-正歪斜結果 173
附錄 H 修整齒輪對-正歪斜結果 179
附錄 I 無修整齒輪對-反歪斜結果 185
附錄 J 修整齒輪對-反歪斜結果 191
附錄 K 暫態無修整齒輪對結果 197
附錄 L 暫態修整齒輪對結果 201

參考文獻

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指導教授

蔡錫錚

審核日期

2025-1-21

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