In this article, the nonlinear dynamic characteristics of a rotor–stator rubbing system, which simultaneously considers the dynamical characteristics of rotor and stator as well as their coupled effect produced by rub-impact, are investigated from the perspective of the complex nonlinear modes. The solution method combining harmonic balance and trust region methods is built, based on which the modal characteristics of the rotor–stator rubbing system is obtained. The results show that the system possesses both the rotor-dominated and stator-dominated vibration modes. The coupling effect produced by rub-impact force can significantly change the modal frequencies and modal shapes of these two order modes. Despite that, the modal characteristics of this rubbing system have a feature of interval distribution and can be estimated by the two kinds of derived linear systems. The friction force of the rub-impact may lead to the instability of the backward whirl motions for these two order modes in some cases. Furthermore, the relationship of the nonlinear modes and resonance response of the rotor–stator rubbing system is studied for the first time, based on which a predicted method of the critical speed of the rubbing system is proposed. The method can obtain the critical speed interval of the rubbing system only through the linear modal analysis; therefore, it is very effective in the application of the actual engineering.

在这篇文章中，从复杂的非线性模式的角度研究了转子-定子摩擦系统的非线性动力学特性，该系统同时考虑了转子和定子的动力学特性以及摩擦冲击产生的耦合效应。建立了将谐波平衡和信赖域方法相结合的求解方法，在此基础上获得了转子－定子摩擦系统的模态特征。结果表明，该系统同时具有转子支配和定子支配的振动模式。摩擦力产生的耦合效应可以显着改变这两个阶次模态的模态频率和模态形状。尽管那样，该摩擦系统的模态特征具有区间分布的特征，并且可以通过两种导出的线性系统来估计。在某些情况下，这两种模式的摩擦冲击的摩擦力可能导致向后旋转运动的不稳定性。此外，首次研究了转子-定子摩擦系统的非线性模式与共振响应之间的关系，在此基础上提出了摩擦系统临界转速的预测方法。该方法只能通过线性模态分析获得摩擦系统的临界速度区间。因此，在实际工程应用中非常有效。在某些情况下，这两种模式的摩擦冲击的摩擦力可能会导致后向旋转运动的不稳定性。此外，首次研究了转子-定子摩擦系统的非线性模式与共振响应之间的关系，在此基础上提出了摩擦系统临界转速的预测方法。该方法只能通过线性模态分析获得摩擦系统的临界速度区间。因此，在实际工程应用中非常有效。在某些情况下，这两种模式的摩擦冲击的摩擦力可能导致向后旋转运动的不稳定性。此外，首次研究了转子-定子摩擦系统的非线性模式与共振响应之间的关系，在此基础上提出了摩擦系统临界转速的预测方法。该方法只能通过线性模态分析获得摩擦系统的临界速度区间。因此，在实际工程应用中非常有效。该方法只能通过线性模态分析获得摩擦系统的临界速度区间。因此，在实际工程应用中非常有效。该方法只能通过线性模态分析获得摩擦系统的临界速度区间。因此，在实际工程应用中非常有效。