博碩士論文 101323102 詳細資訊




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姓名 鄭凱鴻(Kai Hong Jheng)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 修整型正齒輪對動態模擬與實驗
(Dynamic Simulation and Experiment of Modified Spur Gear Pairs)
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摘要(中) 本論文主要目的為探討正齒輪之齒頂修整與齒形誤差對動態特性之影響。首先利用有限元素軟體進行負載下接觸分析,計算其接觸應力與齒輪對之嚙合剛性。接著以等效阻尼(equivalent damping)、嚙合剛性與傳動誤差建立齒輪系統動態模型,並利用龍格庫塔法(Runge-Kutta methods)計算齒輪系統之動態傳動誤差(Dynamic Transmission Error, DTE)與加速度變化,比對不同齒頂修整參數與齒形誤差對於齒輪系統動態特性之影響。
實驗的部分則是於泛用型齒輪嚙合測試機上架設加速規,先量測機台之共振頻率,在避開共振頻率下擷取振動訊號,並運用經驗模態分解法EMD(Empirical Mode Decomposition, EMD)及快速傅立葉轉換FFT(Fast Fourier Transform, FFT)探討嚙合頻能量變化與齒形誤差之關係,並運用所建立之齒輪系統動態模擬流程互相比對,結果顯示模擬之振動訊號與實驗所得振動訊號,在嚙合頻能量變化與齒形誤差趨勢相符。
摘要(英) The main purpose of this thesis is to analyze the dynamic characteristics of spur gear pairs with profile tip relieves or tooth profile errors. The meshing stiffness and contact stress were calculated by loaded tooth contact analysis. A dynamic model of a modified spur gear pair was developed based on the calaulated meshing stiffness, equivalent damping and transmission error. According to the derived equations of motion, the dynamic transmission errors and acceleration were solved by using the Runge-Kutta methods. The effects of various tip relieves and tooth profile errors on the gear dynamic characteristics were investigated and discussed.
In the experimental aspect, the acceleration signals were measured on an universal gear rolling tester. Then the energy levels of meshing frequencies were evaluated by using Empirical Mode Decomposition (EMD) and Fast Fourier Transform (FFT). The results from experiments and dynamic simulation were compared and discussed. Both simulation and experimental results show that the energy levels at meshing frequencies were positively correlated with the magnitudes of tooth profile errors.
關鍵字(中) ★ 嚙合剛性
★ 動態傳動誤差
★ 齒面接觸分析
關鍵字(英) ★ Meshing stiffness
★ Dynamic Transmission Error
★ Tooth contact analysis
論文目次 摘要 I
ABSTRACT II
目錄 IV
圖目錄 VII
表目錄 XIII
符號對照表 XIV
第1章 緒論 1
1.1研究背景 1
1.2文獻回顧 3
1.2.1齒輪系統動態模擬 3
1.2.2齒輪動態測試 5
1.2.3經驗模態分解法 7
1.3研究目的與方法 8
1.4論文架構 9
第2章 齒面數學模式 11
2.1前言 11
2.2修整型正小齒輪之假想齒條刀 數學模式 11
2.3修整型正齒輪之小齒輪數學模式 18
2.4修整型大齒輪之假想齒條刀 之數學模式 22
2.5修整型正齒輪之大齒輪數學模式 26
2.6 大小齒輪齒面數學模式 29
2.6.1小齒輪齒面數學模式(齒頂修整與導程修整正齒輪) 29
2.6.2大齒輪齒面數學模式(齒頂修整正齒輪) 31
2.7 正齒輪齒頂修整特徵與導程修整特徵 33
2.7.1 正齒輪之齒頂修整齒形特徵 33
2.7.2 正齒輪之導程修整齒形特徵 35
第3章 負載下齒面接觸分析 37
3.1 前言 37
3.2 齒面接觸分析 39
3.2.1 傳動誤差分析 42
3.3接觸敏感區域 45
3.4接觸表面特性定義 47
3.5邊界條件設定與材料性質 48
3.6多齒對負載下接觸分析結果 49
3.7 齒根彎矩應力分析結果 64
3.8嚙合剛性計算 65
3.8.1 嚙合剛性計算原理 65
3.8.2 接觸點齒面法向變形量 67
3.8.3 嚙合剛性計算結果 68
3.9結論 70
第4章 齒輪系統動態分析 71
4.1 前言 71
4.2齒輪系統動態模型 72
4.3齒輪系統動態方程式 74
4.4齒輪系統動態分析結果 76
4.4.1動態傳動誤差RMS值比較 77
4.4.2加速度訊號頻譜圖 82
4.5綜合討論 85
4.6結論 86
第5章 動態測試實驗與分析 87
5.1前言 87
5.1訊號分析理論 87
5.1.1 經驗模態分解法 87
5.1.2 集成經驗模態分解法(Ensemble EMD, EEMD) 88
5.1.3集成經驗模態分解法後處理過程(Post-Processing of EEMD) 89
5.2實驗設置與流程 91
5.2.1泛用型齒輪嚙合測試機 91
5.2.2實驗設置 94
5.2.3實驗齒輪參數 96
5.3實驗流程 97
5.3.1實驗校正 98
5.4單齒腹測試結果 99
5.4.1 齒形誤差與偏擺分析結果 100
5.4.2傳動誤差數據FFT頻譜分析結果 102
5.5動態測試實驗與模擬 105
5.5.1機台自然頻率測試 105
5.5.2實驗參數之動態模擬 106
5.5.3 動態測試實驗與分析 113
5.6 實驗結果比較 137
5.7結論 142
第6章 結論與未來展望 143
6.1 結論 143
6.2未來工作 145
參考文獻 146
附錄 151
附錄A CASE 1至CASE 5大齒輪齒面接觸分析結果圖 151
附錄B CASE 1至CASE 5齒根彎矩應力結果 157
附錄C 162
C-1標準齒輪檢測報表 162
C-2實驗1待測齒輪(無齒形修整)檢測報表 164
C-3實驗2待測齒輪(Rp450mm)檢測報表 169
C-4實驗3待測齒輪(Rp350mm)檢測報表 174
附錄D 179
D-1 Case 1至Case 5嚙合剛性計算結果(KISSsoft) 179
D-2實驗1至實驗3嚙合剛性計算結果(KISSsoft) 180
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指導教授 陳怡呈 審核日期 2014-12-3
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