Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion  

作　　者：Xue-Liang Zhang Bang-Chun Wen Chun-Yu Zhao 

机构地区：[1]School of Mechanical Engineering and Automation,Northeastern University

出　　处：《Acta Mechanica Sinica》2012年第5期1424-1435,共12页力学学报（英文版）

基　　金：supported by the National Key Technology R&D Program (2009BAG12A01-F01-3);the National Natural Science Foundation of China (51075063)

摘　　要：In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.

关 键 词：SYNCHRONIZATION Vibrating system Stability Coupling dynamic - Vibratory synchronization transmission 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] O322[自动化与计算机技术—控制科学与工程]