Nonlinear thermal behaviors of the inter-shaft bearing in a dual-rotor system subjected to the dynamic load

This paper proposes a new theoretical method to investigate the thermal behaviors of the inter-shaft bearing considering the nonlinear dynamic characteristics of a dual-rotor system by combining heat transfer and nonlinear dynamics. The nonlinearities of the inter-shaft bearing, including the Hertzian contact and the radial clearance, are considered during the dynamic modeling for the system. The dynamic load of the inter-shaft bearing is defined according to the nonlinear dynamic responses of the system. Therefore, some fundamental nonlinear phenomena, i.e., jump and bi-stable phenomena happen to the dynamic load. It makes the dynamic load more appropriate to describe the actual load of the inter-shaft bearing than the static load. Furthermore, a steady-state heat transfer model for the inter-shaft bearing subjected to the dynamic load can be set up with the help of Palmgren's empirical formula. The variation of temperatures with the rotation speed is obtained by using the Gauss-Seidel iteration. Temperatures of the inter-shaft bearing also show nonlinear thermal behaviors, i.e., jump and bi-stable phenomena. It implies the nonlinear dynamic behaviors of the system have a great impact on the thermal behaviors of the inter-shaft bearing. Moreover, an exhaustive parametric analysis for temperatures and nonlinear thermal behaviors of the inter-shaft bearing affected by dynamic parameters (including the rotation speed ratio, unbalances of rotors, the radial clearance, the stiffness and the roller number of the inter-shaft bearing) and thermal parameters (including the lubricant viscosity and the ambient temperature) is carried out. The results show that the rotation speed ratio has a significant influence on both temperatures and nonlinear thermal behaviors, other dynamic parameters mainly affect nonlinear thermal behaviors, while thermal parameters only affect temperatures. This unique discovery indicates the thermal behaviors of the inter-shaft bearing could be much more complex because of the nonlinear dynamic characteristics of the dual-rotor system. The obtained results will contribute to a better understanding of the nonlinear thermal behaviors of bearings and profoundly reveal the mechanism of the nonlinear thermal behaviors of bearings.