修整型圓柱型齒輪對之動態特性模擬與實驗驗證

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姓名

王志根(Zhigen Wang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

修整型圓柱型齒輪對之動態特性模擬與實驗驗證
(Dynamic Simulation and Experimental Validation of Modified Cylindrical Gears)

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摘要(中)

本研究針對圓柱型齒輪對之動態嚙合特性進行分析，共分兩案例進行研究，包括一組具有齒頂修整與導程隆齒修整之正齒輪對的動態特性模擬與實驗驗證，以及一組具有導程隆齒修整與齒面扭曲修整之螺旋齒輪對的動態特性最佳化設計。首先，正齒輪組方面，提出一套系統化的動態特性模擬方法，基於齒輪原理與微分幾何，從推導具線性齒頂修整與導程隆齒修整的圓柱型齒輪齒面數學模式開始，逐步進行無負載之齒面接觸分析以及基於有限元素分析與KISSsoft兩方法的負載下齒面接觸分析，計算傳動誤差、接觸齒印與嚙合剛性等靜態傳動特性，並建立正齒輪系統動態模型，將齒面接觸分析所得的結果代入動態方程式，求解不同負載與轉速下的模擬動態傳動誤差，計算其均方根值並繪製曲線，並將兩方法所得結果進行比較。此外，利用實驗室建立的動態試驗平台進行實驗驗證，由四個加速規分別鎖固於兩個齒輪上，擷取不同負載與轉速下的振動訊號，經過訊號處理後計算實驗動態傳動誤差之均方根值，並成功驗證模擬結果的正確性，能夠以模擬方法預先評估齒輪對的實際動態表現。
螺旋齒輪組之動態特性研究方面，首先建立具8自由度之動態模型以考慮螺旋角造成的影響，並進一步將動態模擬分析流程自動化以將其與最佳化設計方法結合，分別以窮舉法與基因演算法進行最佳化設計與分析，以窮舉法建立動態特性等高線圖，呈現導程隆齒修整量及齒面扭曲修整參數對於動態特性的影響，並以基因演算法找出在工作轉速下具有最低動態傳動誤差之均方根值的修整參數搭配，最後確認優化設計的改善效果，驗證最佳化設計的可行性。

摘要(英)

This study aims to analyze the dynamic meshing characteristics of cylindrical gear pairs. Two cases were investigated: the dynamic simulation and experimental verification of a pair of spur gears with tooth tip relief and lead crowning modifications, and the dynamic simulation with improved design of a pair of helical gears with lead crowning and bias modifications.
For the spur gear case, a systematic simulation method for analyzing dynamic characteristic was proposed. First, a mathematical model of the cylindrical gear tooth surface with linear tip-relief and lead crowning modifications was derived based on the gear theory and differential geometry. Finite element analysis and KISSsoft software were used to conduct contact analysis under both no-load and loaded conditions, calculating static transmission errors, contact patterns, and mesh stiffness. Subsequently, a dynamic model of the spur gear system was established. The tooth contact analysis results obtained from the finite element analysis and KISSsoft were input into the dynamic equations to simulate the dynamic transmission errors under different loads and speeds. The root-mean-square (RMS) values were calculated and plotted, and the results obtained from both methods were compared.
For experimental verification, a series of dynamic experiments were conducted using a laboratory-built dynamic testing platform. Four accelerometers were mounted on the gears to capture vibration signals under various loads and speeds. After signal processing, the RMS values of experimental dynamic transmission errors were calculated to verify the accuracy of the simulation results. The actual dynamic performance of gear pairs can be pre-evaluated using the proposed simulation method.
In the study of the dynamic characteristics of helical gear pairs, an 8-degree-of-freedom dynamic model was first established, taking into account the influence of the helical angle. Furthermore, the dynamic simulation analysis process was automated and integrated with the optimization design methods. Both exhaustive search and genetic algorithm approaches were employed for optimization design and analysis. Exhaustive search was used to generate the contour maps of dynamic characteristics, illustrating the effects of lead crowning and bias modifications on the dynamic characteristics. Genetic algorithm was utilized to identify the combination of modification parameters that minimizes the RMS value of dynamic transmission error at operating speed. Finally, the improvements of the optimum design were evaluated, confirming the feasibility of the optimization design.

關鍵字(中)

★ 動態特性分析
★ 動態實驗
★ 齒面扭曲修整
★ 最佳化設計

關鍵字(英)

★ Dynamic characteristics analysis
★ Dynamic experiments
★ Bias modification
★ Optimization design

論文目次

摘要 I
Abstract II
致謝 IV
目錄 V
圖目錄 VIII
表目錄 XII
符號對照表 XIII
第1章緒論 1
1.1 前言 1
1.2 文獻回顧 1
1.2.1 齒面修整方法 1
1.2.2 齒輪系統動態模擬與實驗 6
1.2.3 嚙合剛性計算方法 14
1.2.4 最佳化齒輪修整參數設計 15
1.3 研究目的與方法 17
1.4 論文架構 18
第2章圓柱型齒輪齒面數學模式 19
2.1 前言 19
2.2 修整型假想齒條刀數學模式 19
2.3 圓柱型齒輪齒面數學模式 24
2.4 齒面扭曲修整定義 27
第3章正齒輪對之動態模擬與實驗驗證 32
3.1 前言 32
3.2 齒面接觸分析 33
3.2.1 傳動誤差分析 33
3.2.2 接觸齒印分析 37
3.2.3 齒面接觸分析結果 40
3.3 負載下齒面接觸分析 41
3.3.1 有限元素分析方法 42
3.3.2 嚙合剛性計算 44
3.3.3 負載下齒面接觸分析結果 47
3.4 基於有限元素法計算剛性之動態模擬 49
3.4.1 正齒輪系統動態模型 49
3.4.2 模擬之動態傳動誤差結果 51
3.5 基於KISSsoft計算剛性之動態模擬 52
3.5.1 嚙合剛性 52
3.5.2 模擬之動態傳動誤差結果與比較 54
3.6 動態實驗 57
3.6.1 動態實驗流程 57
3.6.2 動態試驗平台與實驗架構 58
3.6.3 訊號處理方法 59
3.6.4 實驗之動態傳動誤差結果 61
3.7 結果與討論 62
第4章具齒面扭曲修整之螺旋齒輪動態特性分析 66
4.1 前言 66
4.2 多自由度之螺旋齒輪系統動態模型 66
4.3 三種齒面扭曲修整之動態特性分析 69
4.4 動態特性最佳化設計 72
4.4.1 窮舉法 72
4.4.2 基因演算法 74
4.5 優化設計之改善效果 76
4.5.1 理想裝配狀態 76
4.5.2 組裝誤差分析 79
4.6 結論 83
第5章結論與未來工作 85
5.1 結論 85
5.2 未來工作 86
參考文獻 88
附錄 93
附錄一、標準齒輪檢測報表 93
Publication List 97
Journal Paper 97
Conference Paper 97

參考文獻

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指導教授

陳怡呈

審核日期

2023-5-30

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