两激振器同一旋转轴线振动系统的自同步理论  

Self-synchronization theory about two exciters on the same rotational axis in a vibration system

作　　者：陈晓哲[1,2] 窦景欣 孔祥希[1] 闻邦椿[1] 

机构地区：[1]东北大学机械工程与自动化学院,沈阳110819 [2]东北大学控制工程学院,秦皇岛066004

出　　处：《振动与冲击》2017年第14期19-25,44,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(51375080)

摘　　要：对两激振器同一旋转轴线振动系统的自同步理论进行了研究。采用拉格朗日方程建立振动系统的运动微分方程。应用小参数平均法获得两激振器的无量纲耦合方程,进而将该类振动系统的同步问题简化为小参数无量纲耦合方程零解的存在性与稳定性问题。由无量纲耦合方程零解存在的条件得出了两激振器实现同步运动的同步性条件,并根据Routh-Hurwitz判据得到了两激振器同步运动的稳定性条件。分析振动系统选择运动特性可知,在远共振的情况下当激振器的旋转中心距离质心的距离大于机体的当量回转半径时,振动系统实现相位差为0°的空间圆周运动;反之,振动系统实现相位差为180°的空间圆锥运动。最后通过试验验证了理论分析的正确性。The self-synchronization theory about two exciters with the same rotational axis in a vibration system wasstudied. The motion equation of the vibration system was derived by applying the Lagrange equation. By introducing the average method of small parameters, a dimensionless coupling equation for the two exciters was deduced, which converts the synchronous problem of this type vibration system into the existence and stability of zero solutions of the dimensionless coupling equation. The synchronization condition of the two exciters carrying out synchronization motion was obtained from the existence of zero solutions, and the stability condition was acquired according to the principle of Routh-Hurwitz. By analyzing the selection motion characteristics of the vibration system, it is concluded that when the distance between the rotating center of the exciters and the mass center of the vibration system is greater than the equivalent radius of the vibration system, the vibration system can carry out a spatial circle motion with 0 degree phase difference, otherwise it can carry out a spatial cone motion with 180 degree phase difference. The correctness of the theoretical analysis was verified by experiment.

关 键 词：自同步 同步性 稳定性 相位差 

分 类 号：TH113[机械工程—机械设计及理论]