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丁川, 甘子川, 王笑, 宋汉文. 电机驱动非理想振动系统的索末菲效应. 力学学报, 2024, 56(6): 1-10. DOI: 10.6052/0459-1879-24-088
引用本文: 丁川, 甘子川, 王笑, 宋汉文. 电机驱动非理想振动系统的索末菲效应. 力学学报, 2024, 56(6): 1-10. DOI: 10.6052/0459-1879-24-088
Ding Chuan, Gan Zichuan, Wang Xiao, Song Hanwen. Sommerfeld effect in non-ideal vibration systems driven by motors. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1-10. DOI: 10.6052/0459-1879-24-088
Citation: Ding Chuan, Gan Zichuan, Wang Xiao, Song Hanwen. Sommerfeld effect in non-ideal vibration systems driven by motors. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1-10. DOI: 10.6052/0459-1879-24-088

电机驱动非理想振动系统的索末菲效应

SOMMERFELD EFFECT IN NON-IDEAL VIBRATION SYSTEMS DRIVEN BY MOTORS

  • 摘要: 真实转子系统的电机输出功率有限且无法提供理想恒定驱动, 随着电机输入电压升高, 在系统固有频率附近会出现长时间平均转速停滞和多稳态跳跃, 称为“索末菲(Sommerfeld)效应”. 这类非理想电机启动时会经过索末菲效应作用区, 而长期陷于这一区域时电机转速剧烈波动, 会严重影响电机寿命. 简化忽略转速波动而注重稳态平均转速, 无法观察系统内部受力变化, 因此借助数值分析研究电机系统与振动系统作用过程. 建立了非理想直流电机-质体-不平衡转子系统的机电耦合动力学模型, 通过Matlab/Simulink建模, 分析了振动系统各内力分量的变化规律, 考察了索末菲效应产生、演变和消失过程. 观察到非理想系统进入共振区后, 恢复力、惯性力和阻尼力将突然产生偶数倍频成份, 导致系统在平均转速与固有频率渐进一致的前提下, 产生快转、停转乃至反转剧烈交替切换的现象, 并在输入电压大于临界电压后结束跳跃. 研究描述了在非理想驱动下系统展现的非线性行为, 最后为振动系统动力设计提供指导并确保动力设备正常运行.

     

    Abstract: The motor output power of a real rotor system is limited and cannot provide ideal constant drive force. As the input voltage value of the motor increases, there will be long-term average rotor speed stagnation and the steady-state response of the system appears multiple values and switches by sudden jumps around the natural frequency of the system, which is called "Sommerfeld effect". This kind of non-ideal motor will pass through the Sommerfeld effect zone when starting, and the motor speed will fluctuate sharply when it is trapped in this Sommerfeld zone for a long time, which will seriously affect the performance life of the motor. The theoretical simplification ignores the speed fluctuation and focuses on the steady-state average speed, and cannot observe the internal energy change of the system. Therefore, the interaction process of the motor system and the vibration system is studied by means of numerical analysis method. The electromechanical coupling dynamic model of the non-ideal DC motor, mass and unbalanced rotor system is established. The change law of each internal force component of the vibration system is analyzed by Matlab/Simulink modeling, and the generation, evolution and disappearance process of Sommerfield effect are investigated. It is observed that when the non-ideal system enters the resonance region, the restoring force, inertia force and damping force will suddenly produce an even fold frequency component, resulting in the phenomenon of fast rotation, stop rotation and even reversal of the system under the premise that the rotor average speed is gradually consistent with the natural frequency of the system, and the jump ends when the input voltage value is greater than the critical voltage value. The study describes many nonlinear behaviors due to the non-ideal drive system, and finally provides some guidance for the dynamic design of the vibration system and ensures the normal operation of the power.

     

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