| 摘要: | 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。
;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. |
