三相异步电动机驱动振动系统的Sommerfeld效应分析

提供有限动力的原动机称为非理想原动机。在工程中,几乎所有提供动力的原动机均为非理想原动机。由非理想原动机带动的振动系统称为非理想振动系统。在非理想振动系统中,原动机与振动系统的运动状态是相互作用、相互影响的。Sommerfeld效应是由于非理想原动机在振动系统共振区附近无法提供足够动力而产出的一种非线性跳跃现象。该试验研究了由一种典型原动机——三相异步电动机驱动振动系统的Sommerfeld效应。将三相异步电动机的动力学模型引入到振动系统中,建立了非理想振动系统的动力学模型。采用解析方法,建立了电机供电频率与转速之间的解析表达式,并应用摄动法进行了稳定性分析。基于MATLAB/Simulink进行了仿真验证,说明了所采用解析方法的正确性。分析了偏心质量与电机功率对非理想振动系统的影响规律。通过研究发现,对于非理想振动系统的研究必须充分考虑原动机与振动系统的相互作用,忽略二者之间的相互作用是不合适的。

Sommerfeld effect in a vibration system driven by a three-phase asynchronous motor

The prime movers providing limit power are called non-ideal ones.In engineering,almost all the prime movers are non-ideal ones.The vibration systems driven by non-ideal prime movers are called non-ideal vibration systems.In non-ideal vibration systems,the motion states of the prime movers and the vibration systems interact with each other.Sommerfeld effect is a non-linear jumping phenomenon induced due to the fact that the non-ideal prime mover cannot provide enough power to pass the resonance region of the vibration system.The Sommerfeld effect in a vibration system driven by a typical prime mover,namely a three-phase asynchronous motor,was studied.Firstly,introducing the dynamic model of the three-phase asynchronous motor into the vibration system,a dynamic model of the non-ideal vibration system was established.Then,the analytical relation between the power supply frequency and the rotation speed of the motor was acquired by using the analytical method.Moreover,the stability analysis was carried out by using the perturbation method.Based on MATLAB/Simulink,the simulation results show the correctness of the analytical method.Finally,the influences of the eccentric mass and motor power on the non-ideal vibration system were analyzed.It is found that the interaction between the prime mover and vibration system shouldn’t be ignored but must be fully considered in the study of non-ideal vibration systems.