This paper deals with the stability and critical spinning speed of a liquid-filled rotor in thermal environment with nonlinear variable-temperature. The nonlinear temperature field model of the rotor is developed by using Laplace transform. The thermal axial force exerted on the rotor as a result of the thermal effect is calculated as functions of temperature rise rate and rotor thickness ratio. Spinning Timoshenko beam model is employed to establish the structural dynamics equations of the rotor system. The governing equation of the motion is derived by using the Hamilton principle. The validity of the developed model is confirmed by comparing with the numerical solutions available in the literature. The numerical results based on the obtained analytical solutions are given for a better understanding of the effects of the shear deformation, rotary inertia, filling parameters and thermal effect on the system stability and critical spinning speed. The results show that the system stability is dependent on the thermal axial force and cavity ratio. Moreover, the results also highlight the role of thermal effect, rotary inertia, cavity ratio and mass ratio on the critical spinning speed.

本文研究了在非线性温度变化的热环境下充液转子的稳定性和临界旋转速度。利用拉普拉斯变换建立了转子的非线性温度场模型。计算出由于热效应而施加在转子上的轴向热力，作为温度上升速率和转子厚度比的函数。旋转蒂莫申科梁模型被用来建立转子系统的结构动力学方程。利用汉密尔顿原理导出运动的控制方程。通过与文献中可用的数值解决方案进行比较，可以确定所开发模型的有效性。给出了基于获得的解析解的数值结果，以更好地理解剪切变形的影响，旋转惯量，填充参数和热影响系统稳定性和临界纺丝速度。结果表明，系统稳定性取决于热轴向力和空腔比。此外，结果还突出了热效应，旋转惯性，腔比和质量比对临界纺丝速度的影响。