双质体双激振器振动系统同步理论与仿真分析

Theoretical and simulation analysis of self-synchronization of double mass vibrating system with dual-exciter

针对单质体振动系统占地面积大和运动轨迹单一的缺点,提出了一种双质体双激振器自同步振动系统。首先,依据Lagrange方程推导出了双质体振动系统的运动微分方程,并求出了其稳态解。然后,由完整非保守系统的Hamilton原理推导出了系统的同步性条件。根据Hamilton作用量具有极值、多元函数系统的稳定性判别及函数的极值理论得出了系统自同步运动的稳定性条件;代入系统相关参数进行数值分析,得出了中间弹簧刚度和电机安装位置对系统同步性及同步相位差角的影响。研究结果表明:系统在一定参数条件下可以实现相位差角波动范围为[-3π/2,-π/2]和[-π/2,π/2]的两种稳定的自同步运动;相对中间弹簧刚度,电机安装位置对同步相位差角的影响更大。最后,对比机电耦合仿真结果和理论研究结果验证理论分析的正确性。

Since the single mass vibration system covered a large area and the trajectory was single, a double mass vibration system of self-synchronization with dual-exciter was proposed. Firstly, the kinematic differential equation of the double mass vibration system was established using Lagrange equation to obtain the stable solution. Then, the self-synchronization qualification was deduced from the Hamilton principle of holonomic non-conservative system. According to Hamilton action extremum,discriminant stability of multivariate function and function extremum theory, the stability condition of self-synchronization motion was obtained. The effects of middle spring stiffness and the motor installation position on self-synchronization and phase difference were analyzed using numerical method. The research results showed that the system could achieve two stable selfsynchronized movement that the phase differences were rad and rad under the certain conditions. The effect of motor installation position on synchronous phase difference was greater than the middle spring stiffness. Finally, the feasibility of theoretical analysis was verified through the comparison between electro-mechanical coupling simulation results and theoretical results.