手持式振动机械的同步问题  

Self-Synchronization of Hand-Held Vibrating Machinery

作　　者：李叶[1] 李鹤[1] 耿志远[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110004

出　　处：《振动．测试与诊断》2013年第S1期9-14,214-215,共8页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(51175071);教育部新世纪优秀人才支持计划资助项目(NCET-10-0271);机械系统与振动国家重点实验室开放课题资助项目(MSV-2011-19);中央高校基本科研业务费专项资金资助项目(N100503002;N100703001);辽宁省自然科学基金资助项目(201102072);沈阳市人才资源开发专项资金资助项目

摘　　要：提出了一种双电机驱动的手持式振动机模型,研究了该振动系统的自同步理论。首先,利用拉格朗日公式,推导出振动系统的运动微分方程;然后,引入两个扰动小参数,对激振器的角速度和相位差进行平均。通过对两激振器的运动方程在平均周期内进行积分平均计算,推导出了系统频率捕获方程。该方法将两激振器的自同步问题转换成了频率捕获方程零解的存在性和稳定性问题,进而推导出了实现频率捕获和两电机稳定同步运行的条件,还提出频率捕获转矩概念来解释两激振器自同步的特性。结果表明,两激振器之间存在一个频率捕获力矩,对两电机同步运行和稳定性有影响。In the paper, a model of hand-held vibration machinery driven by two exciters was proposed and analyzed to study the self-synchronization theory of the vibration system. At first, the differential equations of systematic motion were derived by applying Lagrange′s equations. Then, with theintroduction of two perturbation small parameters to average angular velocity of two exciters and their phase difference, we deduced the equation of frequency capture by averaging two motion equations of two exciters over their average period. The method converted the synchronization problem of two exciters into that of existence and stability of zero solution for the equation of frequency capture. Then the conditions of implementing frequency capture and that of stabilizing synchronous operation of two motors have been derived. The concept of torque of frequency capture was proposed to explain the peculiarity of selfsynchronization of the two exciters. A conclusion is reached that there is a torques of frequency capture between the two exciters. The torques of frequency capture has an effect on the synchronous operation and stability.

关 键 词：手持式振动模型 自同步 频率捕获 稳定性 

分 类 号：TH113.1[机械工程—机械设计及理论]