A Matrix Method for Computing the Stiffness and Damping Coefficients of Multi-Arc Journal Bearings

Abstract

A finite element method is used for solving Reynolds equation of hydrodynamic journal bearings. Once a matrix expression for calculating bearing film reaction force, i.e., components f_x, f_y, is obtained, a matrix expression for calculating all the dynamic coefficients can be obtained immediately only by differentiating f_x,f_y expression with respect to the perturbations of displacements x,y and to the velocity u,v respectively. With this “Matrix Method”, we also get a result that both cross damping coefficients, D_xy and D_yx, are equal to each other. This method makes the program very simple and for calculating all these eight dynamic coefficients it is possible to solve Reynolds equation once only.xs