Analytical geometry method of planetary gear trains

作     者：CHEN XiaoAn CHEN Hong 

作者机构：State Key Laboratory of Mechanical TransmissionsChongqing UniversityChongqing 400044China 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2012年第55卷第4期

页      面：1007-1021页

核心收录：

学科分类：0810[工学-信息与通信工程] 07[理学] 08[工学] 080203[工学-机械设计及理论] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 0701[理学-数学] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 080201[工学-机械制造及其自动化] 

基　　金：supported by the National Natural Science Foundation of China (Grant No. 51075407) the Fundamental Research Funds for the Central Universities (Grant No. CDJXS11111143) 

主　　题：analytical geometry planetary gear trains kinematics efficiency analysis method 

摘      要：This paper presents an analytical geometry method for kinematics and efficiency of planetary gear trains (PGTs). The novel method which is capable of evolution and contrast analysis of mechanism kinematics, can be applied to any typical one-and two-degree-of-freedom plane PGTs containing any number of simple, compound or complex-compound planetary gear sets. The efficiency analysis of this method features a systematized and programmed process and its independence of the speed ratio. The primary contribution of this work lies in the integration of quantitative calculation, qualitative evolution and comparative analysis of kinematics of PGTs into one diagram, and in the integration of kinematics and efficiency analysis into a single method system. First, the analytical geometry method is defined, its basic properties are given, and the systematization procedure to perform kinematic analysis is demonstrated. As an application, analytical geometry diagrams of common PGTs are exhibited in the form of a list, whose kinematic characteristics and general evolution tendency are discussed. Then, with the mapping of PGTs onto the angular speed plane, the efficiency formula of analytical geometry, which has an extremely concise form, and a simple method for power flow estimation are put forward. Moreover, a general procedure is provided to analyze the efficiency and power flow. Finally, four numerical examples including a complicated eleven-link differential PGTs are given to illustrate the simpleness and intuitiveness of the analytical geometry method.