中文摘要：

针对高速气体轴承-转子系统在主动控制过程中无法避免的时滞现象，建立了含有双时滞控制的三轴向槽动压气体轴承-转子系统的动力学模型。运用微分变换法求解动压气体润滑的 Reynolds 方程，得到了非线性气膜压力分布。基于精细积分法，构造了时滞非线性轴承-转子系统动力响应的求解方法。针对含有双时滞控制的气体轴承-转子系统，运用轨迹图、时间历程图等研究了系统的非线性响应，分析了时滞量和反馈控制增益对系统响应的影响。数值结果表明，当选取的反馈控制增益与气体轴承-转子系统的时滞量相匹配时，时滞系统的振动幅值会变小，运动将更加稳定，达到了较好的控制效果。

英文摘要：

According to the inevitable time delays phenomenon in the active control of high speed gas bearing-rotor system, a dynamical model of the rotor system with double time delays supported on self-acting gas-lubricated bearing with three-axial grooves was established. The time-dependent compressible gas-lubricated Reynolds equation was solved by the differential transformation method, and the distribution of the nonlinear gas film pressure was obtained. A calculation method for the dynamic responses of the nonlinear bearing-rotor system with time delays was proposed based on the precise integration method. The orbit diagram and the time series were employed to investigate the nonlinear responses of the self-acting gas-lubricated bearing-rotor system with double time delays. The influence of time delays and feedback control gains on the dynamic responses of the bearing-rotor nonlinear system was analyzed. The numerical results show that the amplitude of the responses of the system with time delays control is reduced, the motion is more stable and good control effect is achieved when the chosen feedback control gains match the time delays of the bearing-rotor system.