Finite Journal Bearing With Nonlinear Stiffness and Damping. Part 1: Improved Mathematical Models

Abstract

Finite Journal Bearing With Nonlinear Stiffness and Damping. Part 1: Improved Mathematical Models Two mathematical models for the nonlinear hydrodynamic film forces in a finite bearing are developed including a practical adaptation of the cavitation phenomenon. Using the linearity of the Reynolds equation for incompressible film, the pressure components are effectively decomposed and the Reynolds equation is rearranged for general solution by a finite element program in which only the Lid ratio and the eccentricity ratio are to be specified. The different possibilities of partial film profile location in a general dynamic case are demonstrated. The two partial film models possess the required accuracy of the finite bearing approach with the simplicity of the known long and short bearing approximations which are shown as the upper and lower bounds for the present case. The finite bearing approach presented are particularly suitable for nonlinear dynamic analysis. Journal Equation of MotionThe journal equation of motion can be written for the radial direction as md r =F r + Wcos(fi -\j/) where d r is the journal acceleration in the radial direction and m is the journal mass and similarly for the tangential direction. The radial and tangential film forces F r and F, are