System Mathematic Model of Epicyclic Gear Trains

XUE Longquan¹  LEI Yarong¹  SONG Nianlong²

(1. School of Mechanical Instrumental Engineering, Xi’an University of Technology, Xi’an 710048;
2. School of Automatization and Communication Engineering, Xi’an University of Technology, Xi’an 710048)

Abstract: On the basis of analyzing structure character and state character of epicyclical gear trains (EGTs) , topological graph is improved. It is realized that gear trains is a physics system , and net problem is presented that is a systems graph theory model applied to solve physics character of EGTs. It is found that topological graph accords with Kirchhoff ’s law. On the basis of analyzing physics and geometry character of topological graph, branch-characteristics matrix and cut-characteristics matrix are presented, the two are applied to create a systems mathematic model, namely loop-equations and cut-equations. A new fundamental theory is presented for structure characteristics and state characteristics of EGTs based on systems research. And it is applied to velocity, torque and bifurcated power characteristics of EGTs with an example.

Key words: Net problem  Graph theory model  Kirchhoff ’s law  Mathematics model

CLC No: TH128

Received 20070413, received in revised form 20070909

References

[1] BUCHSBAUM F, FREUDENSTEIN F. Synthesis of kinematic structure of geared kinematic chain and other mechanisms [J]. Journal of Mechanisms, 1970(5): 357-392.
[2] PENNESTRI E, FREUDENSTEIN F. The mechanical efficiency of epicyclic gear trains [C]//ASME Proceedings: Cam, Gear, Robot and Mechanisms Design, Chi-cago, Illinois DE -1990, 26: 71-79.
[3] HSU C H, LAM K T. Automatic analysis of kinematic structure of planetary gear trains [J]. ASME Transactions, Journal of Mechanical Design, 1993, 115: 631-638.
[4] CHATTERIEE G, TSAI L W. Computer-aided sketching of epicyclictype automatic transmission gear trains [J]. ASME Transactions, Journal of Mechanical Design, 1996, 118: 405-411.
[5] MADAM S R, AMBERKAR A G, JAIN R C. Symbolic notation of planetary gear trains by canonical number approach [J]. International Journal of Mechanical Engineer-ing Education, 2000, 28(1): 47-68.
[6] XUE Longquan, WANG Youming, WANG Huiwu, et al. Study on topological synthesis of epicyclical gear trains based on functional fractionation [J]. Chinese Journal of Mechanical Engineering, 2006, 42(6): 40-45.
[7] [US]CHEN Huikai. Application graph theory[M]. FAN Dingsong, ZHANG Lingling, Translation. Beijing: Posts & Telecom Press, 1990.
[8] КУдрявцев B H. Planetary transmission handbook[M]. CHEN Qisong, ZHANG Zhan, JIANG Genghua, Translation. Beijing: Metallurgical Industry Press, 1998.
[9] LIN Jiande, CHEN Xiaoan. Simplified approach for the determination of the mechanical efficiency in gear trains[J]. Chinese Journal of Mechanical Engineering, 2004, 40(9): 33-37.
[10] YANG Shiru, DUAN Qinhua. A study on inner torque, power-flow and self-locking of epicyclical gear trains[J]. Mechanical Science and Technology, 2004, 23(2): 189-191.