Series solution of the Reynolds equation in finite-length tilting-pad journal bearing including pad deformation

This paper applies the variable separation method to the hydrodynamic pressure calculation of finite-length tilting pad journal bearings under Reynolds boundary conditions, and a series solution of the Reynolds equation is obtained based on the Sturm-Liouville theory, which considers pad deformation. The thermal effect is also taken into account. A comparison of the present solutions is made with the results obtained by other applied methods, as well as past and recent published data, and good agreement is noted. The steady-state and dynamic performance of a four-pad tilting pad journal bearing are investigated by the load capacity, pressure distribution, friction force, lubricant effective viscosity, journal center velocity, journal center orbits, and phase portrait under the proposed series solution of the Reynolds equation. This study contributes to quickly evaluating the nonlinear dynamic performance of a tilting pad journal bearing rotor system and supporting the nonlinear dynamic design of the system.