相交轴磁齿轮传动系统含内共振时的自由振动

Free vibration of magnetic gear with intersecting axes under internal resonance

针对构件间磁耦合刚度非线性,建立了磁场调制型相交轴磁齿轮传动系统非线性动力学模型和含平方项的非线性动力学微分方程组,考虑输入、输出转子扭转模态频率间1∶2的倍数关系,采用多尺度法得到了系统存在内共振时的振幅响应曲线及各构件的时域响应规律,结果表明:由于内共振的存在使得能量在输入、输出转子扭转振动模态间相互转化,且初始幅值越大各模态能量交换频率越高,进而使得磁齿轮系统各构件由于外部激励造成的瞬态振动衰减更加缓慢,某种程度上恶化了系统动力学特性。

Considering the nonlinear magnetic coupling stiffness between the components of the field modulated magnetic gear with intersecting axes(FMMGIA),the nonlinear dynamic model and the nonlinear differential equations with quadratic nonlinearities are established.The amplitude curves and the free vibration responses of the FMMGIA system are obtained by using a multi-scale method when the torsional modal frequency of the output rotor is twice as much as that of the input rotor.The results show that the energy in the FMMGIA system continues to be exchanged between the two modes but it is continuously dissipated.The larger the external excitation amplitude is,the higher the energy conversion frequencies are with the existence of internal resonance.Furthermore,the transient vibrations of the FMMGIA system are decayed slowly,which will worsen the dynamic characteristics of the FMMGIA system.