Stability and critical spinning speed of a flexible liquid-filled rotor in thermal environment with nonlinear variable-temperature

Abstract

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.