An analytical study of rotor dynamics coupled with thermal effect for a continuous rotor shaft

• An analytical model to evaluate thermal effect on rotor dynamics is developed.
• This model is applicable to rotors with different asymmetrical temperature field.
• An index of TGs is proposed for occasions with nonlinear asymmetric temperature.
• Thermal vibration is affected by rotor size, thermal and operational factors, etc.

This paper presents an analytical analysis of a continuous rotor shaft subjected to universal temperature gradients. To this end, an analytical model is derived to investigate the generic thermal vibrations of rotor structures. The analytical solutions are obtained in a rotating frame and include parameters related with both the thermal environment and the rotor dynamic structures. This provides an insight into the mechanisms for the rotor thermal vibration. Furthermore, numerical results based on the analytical solutions are given. An index denoting the temperature gradients is proposed for the occasions with nonlinear cross-sectional temperature distributions. Finally, the factors influencing the thermal vibrations are analyzed. The results show that the thermal vibration is affected by many factors including the shaft size, rotational speeds, heating locations, critical speed, etc. Moreover, it is investigated how the convection coefficient and the heat conductivity influence the thermal vibrations in order to provide an insight into the management of thermal vibrations from the perspective of thermal aspects.