Three-Dimensional Thermohydrodynamic Morton Effect Simulation—Part I: Theoretical Model

The present study is focused on accurate prediction of the Morton effect problem including journal asymmetric heating and the corresponding long period amplitude oscillations using a nonlinear time transient rotor-dynamic simulation. This paper presents a theoretical model of thermal induced synchronous instability problems in a nonlinear rotor–bearing system, and suggests a new computational algorithm for the nonlinear transient analysis of the Morton effect where the dynamic and thermal problems are combined. For the analysis of the Morton effect problem, a variable viscosity Reynolds equation and a 3D energy equation are coupled via temperature and viscosity, and solved simultaneously. Three-dimensional heat transfer equations of bearing and shaft are modeled by a finite element method, and thermally coupled with the fluid film via a heat flux boundary condition. Asymmetric heat flux into the synchronously whirling rotor is solved by the orbit time averaged heat flux from fluid film to the spinning shaft surface. The journal orbit is calculated by the nonlinear transient dynamic analysis of a rotor–bearing system with a variable time step numerical integration scheme. For the computation time reduction, modal coordinate transformation is adopted in dynamic and thermal transient analysis. Thermal bow effect makes a significant change to the dynamic behavior of a rotor–bearing system, and a thermal hysteresis bode plot, that is one of the characteristics of the Morton effect problem, is presented with time varying spin speed.