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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。
In view of the large area of single-body vibration system and the single locus of motion, a double-platen double-exciter self-synchronized vibration system is proposed. First of all, the differential equation of motion of the two mass vibration system is deduced according to the Lagrange equation and its steady-state solution is obtained. Then, the system synchronization condition is derived from the Hamilton principle of a complete non-conservative system. According to the extreme value of Hamilton’s acting quantity, the stability of multivariate functional system and the extremum theory of the function, the stability conditions of self-synchronizing system are obtained. Numerical analysis is made on the relevant parameters of the system, and the relationship between spring stiffness and motor installation Effect of Position on System Synchronization and Synchronization Phase Difference Angle. The results show that the system can realize two stable self-synchronizing motions with the phase angle variation of [-3π / 2, -π / 2] and [-π / 2, π / 2] Intermediate spring stiffness, motor mounting position on the synchronization phase angle greater impact. Finally, the electromechanical coupling simulation results and theoretical research results verify the correctness of the theoretical analysis.