行星齒輪組動態受載齒面接觸分析之研究;Study on Dynamically Loaded Tooth Contact Analysis of Planetary Gear Sets

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Title:	行星齒輪組動態受載齒面接觸分析之研究;Study on Dynamically Loaded Tooth Contact Analysis of Planetary Gear Sets
Authors:	程伯軒;Cheng, Po-Hsuan
Contributors:	機械工程學系
Keywords:	行星齒輪機構;動態受載齒面接觸分析;剛性圖;行星齒輪嚙合相位;傳動誤差;穩態分析;planetary gear mechanisms;dynamically loaded tooth contact analysis;rigidity diagrams;planetary gear engagement;transmission errors;steady state analysis
Date:	2025-06-19
Issue Date:	2025-10-17 12:58:00 (UTC+8)
Publisher:	國立中央大學
Abstract:	行星齒輪機構因其高傳動比、高負載能力與結構緊湊的特性，廣泛應用於各種高負載與高效能的傳動系統中。然而，隨著科技進步，行星齒輪在高轉速與變動負載等複雜工作條件下，其振動特性與齒面接受負載分佈，已成為影響傳動系統穩定性與壽命的關鍵因素。因此，如何提升行星齒輪機構在動態受載條件下的整體效能，已成為當前齒輪傳動領域的重要研究課題。傳統齒輪動態分析多採用離散化的方式建立模型，並結合理論嚙合剛性進行分析。此類模型較為簡化，難以準確反映齒對嚙合特性以及齒面修整對於系統動態行為的影響，且其提供的資訊亦相對有限。相較之下，齒輪在靜態下的接觸分析模型已相對成熟，具有更高的精度與可信度。有鑑於此，本研究提出整合離散化動態模型與靜態受載齒面接觸分析(SLTCA)，以建構一套能反映實際接觸狀況之行星動態受載齒面接觸分析模型。在模型建構方面，本研究將系統各元件進行離散化處理，並利用預先透過 SLTCA 所建立各齒輪對嚙合剛性圖，導入時變嚙合剛性參數。同時，行星齒輪與托架之間的接觸剛性以彈簧支撐方式模擬。隨後，藉由數值方法求解系統動態方程式，得到各元件的動態下位移與負載，並將其代回SLTCA模組，以進一步計算齒面接觸狀況。本研究以四個行星的正齒輪系統為分析對象，探討不同行星齒輪齒數與嚙合相位配置對系統動態特性的影響。結果顯示，在DLTE、太陽扭矩與環齒輪扭矩等動態響應中，等相位配置的的振幅最大，其次為反相位，序列相位配置最小。然而，在齒輪對嚙合力的表現方面，反相位配置則展現出最小的振幅。此外，在加速的暫態分析中發現，齒對交換所引起的剛性變化，對系統動態行為的影響顯著大於加速度本身。 ;Planetary gear mechanisms are extensively utilised in a range of high-load and high-efficiency transmission systems, owing to their high transmission ratios, high-load capacities and compact structures. However, with the advancement of science and technology, the vibration characteristics of planetary gears and the distribution of loads on the tooth surfaces have become the key factors affecting the stability and service life of transmission systems under complex operating conditions, such as high speeds and variable loads. Therefore, the question of how to enhance the overall performance of planetary gear mechanisms under dynamic loaded conditions has become a significant research topic in the field of gear transmission. Conventional dynamic analyses of gears are frequently based on discrete models with theoretical mesh stiffness. Such models are simplified, and they are difficult to accurately reflect the influence of the mesh characteristics of the gear pairs and tooth surface dressing on the dynamic behaviour of the system. Furthermore, the information they provide is relatively limited. Conversely, the contact analysis models of gears in static conditions are more mature and have higher accuracy and credibility. In view of the aforementioned points, the present study proposes a methodology for the integration of a discretised dynamic model with a static loaded tooth contact analysis (SLTCA) in order to construct a set of planetary dynamic loaded tooth contact analysis models. The purpose of this integration is to create models that reflect actual contact conditions. The present study constitutes an analysis of a four-planet spur gear system, with a view to investigating the effects of differing planetary tooth numbers and mesh phase configurations on the dynamic characteristics of the system. The results demonstrate that the amplitude of the dynamic transmission error, solar torque and ring gear torque is maximum for the equal-phase configuration, minimum for the inverse-phase configuration and minimum for the sequential-phase configuration. However, the anti-phase configuration exhibited the most minimal amplitude with regard to gear-to-compression performance. Furthermore, in the transient analysis of acceleration, it was found that the rigidity change caused by the exchange of gear pairs had a significantly greater effect on the dynamic behaviour of the system than the acceleration itself.
Appears in Collections:	[Graduate Institute of Mechanical Engineering] Electronic Thesis & Dissertation

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