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研究生:劉鴻志
研究生(外文):Hung-Chih Liu
論文名稱:高轉速正齒輪之多目標最佳化與動態特性分析
論文名稱(外文):Multi-Objective Optimization and Dynamic Characteristics of A High-Speed Spur Gear Set
指導教授:陳怡呈陳怡呈引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2019
畢業學年度:108
語文別:中文
論文頁數:142
中文關鍵詞:多目標最佳化齒面接觸分析動態特性動態傳動誤差
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本論文旨在進行高轉速修整型正齒輪之特性分析,並建立最佳化分析流程,探討齒頂修整對於動態特性之影響。首先,由齒輪原理,建立具導程隆齒修整(Lead Crowning)、線性齒頂修整(Linear Tip Relief)與轉位(Profile Shift)之正齒輪齒面數學模式。經由齒面接觸分析,求解靜態傳動誤差(Static Transmission Error, STE),並由有限元素分析軟體與齒輪設計分析軟體進行負載下齒面接觸分析,並探討組裝誤差對於齒面接觸應力之影響。並依據美國齒輪製造協會(American Gear Manufacturers Association, AGMA)所訂定之齒輪相關規範,計算齒輪組之齒面、齒根等安全係數。
其次,在最佳化部分,以負載下傳動誤差之峰谷值(Peak-to-Peak Loaded Transmission Error, PPLTE)作為目標函數,並結合齒輪設計分析軟體KISSsoft與數值分析軟體Matlab,分別以全域搜索演算法(GlobalSearch Algorithm, GS)及基因演算法(Genetic Algorithm, GA)進行最佳化分析,藉以建立最佳化齒形修整參數。
最後,在動態模擬部分,建立齒輪系統動態模型,將齒面接觸分析所得之靜態傳動誤差與嚙合剛性(Meshing Stiffness)代入齒輪系統動態方程式,並利用龍格-庫塔法(Runge-Kutta)求解動態方程式,取得動態傳動誤差(Dynamic Transmission Error, DTE)與加速度振動訊號,並透過均方根值計算(Root Mean Square, RMS)及快速傅立業轉換(Fast Fourier Transform, FFT),探討線性齒頂修整對於動態特性之影響。根據模擬結果顯示,具線性齒頂修整之優化設計,可成功改善齒輪系統之振動幅度。
The purpose of this study is to analyze the characteristics of high-speed spur gear with optimum linear tip-relief. The influence of tip-relief on dynamic characteristics was also discussed. First, the mathematical model of spur gear with lead crowning, linear tip-relief, and profile shift was developed based on the theory of gearing and differential geometry. In addition, tooth contact analysis (TCA) of spur gears was carried out to solve the static transmission error (STE). Loaded tooth contact analysis (LTCA) was carried out by using finite element analysis software and gear design software, and the influence of assembly errors was discussed. The safety factors, including pitting and bending of gear set, were calculated according to the relevant specifications of American Gear Manufacturing Association (AGMA).
Besides, in the optimization aspect, the gear design analysis software KISSsoft was linked with global search algorithm (GS) and genetic algorithm (GA) respectively to determine the optimum gear design parameters.
In the dynamic simulation aspect, a dynamic model of the gear system was established based on the results of the TCA and LTCA, including the STE and meshing stiffness then the dynamic transmission error (DTE) was calculated by using Runge-Kutta method. The influence of the tip-relief on the dynamic characteristics was discussed through the Root Mean Square (RMS) and Fast Fourier Transform (FFT) methods. According to the simulation results, the optimum tip-relief design successfully reduced RMS of DTE and the vibration level.
摘要 I
Abstract II
致謝 III
圖目錄 VIII
表目錄 XII
符號對照表 XIV
第1章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 齒輪系統動態分析 2
1.2.2 嚙合剛性 5
1.2.3 齒輪修整最佳化 5
1.3 研究目的 6
1.4 論文架構 8
第2章 修整型正齒輪齒面數學模式 10
2.1 前言 10
2.2 假想齒條刀法向剖面數學模式 11
2.3 三維假想齒條刀數學模式 -無導程隆齒修整 13
2.4 三維假想齒條刀數學模式 -具導程隆齒修整 15
2.5 修整型正齒輪數學模式 18
2.6 齒輪設計參數 22
第3章 齒面接觸分析 24
3.1 傳動誤差分析 24
3.2 組裝誤差分析 25
3.3 無負載齒面接觸分析 27
3.4 結論 29
第4章 負載下齒面接觸分析 30
4.1 有限元素分析 30
4.1.1 有限元素分析設定 30
4.1.2 有限元素分析結果 32
4.1.3 嚙合剛性 36
4.2 齒輪設計分析軟體 38
4.3 結論 42
第5章 強度分析 43
5.1 安全係數 43
5.1.1 齒面安全係數 43
5.1.2 齒根安全係數 44
5.1.3 刮蝕機率 45
5.2 安全係數分析結果 46
5.3 結論 49
第6章 齒形最佳化分析 50
6.1 最佳化演算法 50
6.1.1 最佳化概論 50
6.1.2 全域搜索演算法 52
6.2.3 基因演算法 54
6.2 最佳化參數 55
6.2.1 全域搜索演算法 57
6.2.2 基因演算法 59
6.2.3 全域搜索演算法與基因演算法之目標函數值比較 59
6.3 基因演算法之優化參數-負載下齒面接觸分析 60
6.4 基因演算法之優化參數-強度分析 68
6.5 結論 70
第7章 齒輪系統動態分析 76
7.1 前言 76
7.2 嚙合剛性 76
7.3 齒輪系統動態模型 78
7.4 齒輪系統動態方程式 80
7.5 齒輪系統動態分析流程 82
7.6 齒輪系統動態分析結果 83
7.6.1動態傳動誤差分析結果 83
7.6.2加速度訊號之頻譜分析與嚙合頻能量計算 88
7.7 結論 91
第8章 實務優化參數與動態分析 92
8.1 實務優化設計 92
8.1.1 實務優化參數 92
8.1.2 現有設計與實務優化參數-強度分析 93
8.2 動態特性分析(一) 96
8.2.1 齒輪設計分析軟體KISSsoft-嚙合剛性 96
8.2.2 動態傳動誤差分析結果 97
8.3 動態特性分析(二) 103
8.3.1 有限元素分析-嚙合剛性 103
8.3.2 動態傳動誤差分析結果 108
8.4 結論 114
第9章 結論 115
9.1 結論 115
9.2 未來工作 117
參考文獻 118
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