| 摘要: | 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. |
