Short Bearing Analysis Applied to Rotor Dynamics—Part I: Theory

A derivation of the Reynolds equation is presented in fixed Cartesian coordinates which allows rapid solution of the fluid-film bearing forces using the short bearing approximation. The solution for the fluid-film pressure profile is given in terms of the instantaneous position and velocities expressed in the fixed reference frame. The effects of cavitation are approximated by deleting subambient pressures when integrating the pressure profile. The equations for the instantaneous whirl rate and curvature are presented and discussed in relation to journal bearing behavior. Three-dimensional plots of the pressure profile for selected dynamic conditions give a vivid picture of the fluid pressure field. Dimensionless plots of the stiffness and damping coefficients for the short bearing are presented. The results of a linearized stability analysis are presented and compared to other published results. Results of transient response analysis will be presented in Part 2.