摘要
由弹性连接的直流电机驱动的振动系统体积更小,其自同步理论对于小型化同步装置的研制具有重要意义,本文基于理论、仿真对这类系统进行研究。使用Lagrange方程建立振动系统的动力学模型,并通过小参数法得到两电机的耦合方程,将此类振动系统的同步问题转化为小参数耦合方程零值解的存在性与稳定性问题。根据耦合方程零解的存在条件推导两直流电机达到同步运动的必要性条件,并应用Routh-Hurwitz准则得到两电机同步运动的稳定性条件。最后通过数值仿真对理论进行验证。结果表明:系统满足一定参数条件时可以实现相位差在0°和180°附近的两种稳定同步运动。
The vibration system driven by elastically connected motors is smaller in size,and its self-synchronization theory is of great significance for the development of miniaturized synchronization devices.This paper studied this system theoretically and numerically.The dynamic differential equation of the vibration system was established by applying the Lagrange equation.The coupling equation of the two motors was obtained by the small parameter method,which converts the synchronization problem of this kind of vibration system into the existence and stability problem of the zero solution of the small parameter coupling equation.The necessary synchronization condition for the two DC motors to achieve synchronous motion was obtained according to the existence condition of the zero solution of the coupling equation.The stability condition of synchronous motion of the two motors was derived using the criterion of Routh-Hurwitz.And the theoretical analysis was verified through simulating calculation.The results show that the system can achieve two stable synchronous motions with phase difference around 0°and 180°under certain parameter conditions.
作者
王凯
许佳陆
黄家晟
宋汉文
WANG Kai;XU Jialu;HUANG Jiasheng;SONG Hanwen(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)
出处
《噪声与振动控制》
CSCD
北大核心
2023年第2期9-14,共6页
Noise and Vibration Control
基金
国家自然科学基金资助项目(11872047)。
关键词
振动与波
自同步
同步性
稳定性
振动系统
非线性动力学
vibration and wave
self-synchronization
synchronicity
stability
vibration system
nonlinear dynamics
