Considerations for the design of gas-lubricated slider bearings

Abstract

An approach is developed that simplifies calculation of the dynamic characteristics of a self-acting, gas-lubricated slider bearing system. This technique avoids a lengthy simultaneous solution of the equations of motion of the slider and the time-dependent Reynolds' equation, while providing additional design information that is otherwise unobtainable. The equilibrium pressure distribution in the gas film is obtained using the Bunov-Galerkin formulation of the finite element method. By considering small perturbations of the slider bearing system about equilibrium, two coupled, second-order partial differential equations are derived, which define the in-phase and out-of-phase perturbation pressures in the gas film. These perturbation pressures are integrated to obtain the frequency dependent, non-symmetrical stiffness and damping matrices for the slider bearing. Using the stiffness and damping properties of the gas bearing and slider support, the equations of motion for the entire slider bearing system are derived. The frequency dependence of the stiffness and damping matrices renders the eigenvalue problem nonlinear, and the eigensolutions are obtained iteratively using Brent's method. Because of the non-synunetrical stiffness and damping matrices, a similarity transformation based on the left and right modal matrices is used to decouple the equations of motion. This decoupling is approximate because of the frequency dependence of the stiffness and damping matrices, but the resulting damped natural frequencies are shown to be in excellent agreement with published experimental data. Fractions of critical damping obtained for several slider geometries also successfully predict observed instabilities. The mode shapes of slider oscillation, unobtainable with other methods, permit calculation of the center of rotation for the coupled, pitch-heave modes; this information can be used to determine the optimum location for the magnetic transducer. Closed-form solutions are obtained for the response to disk surface displacement, and for the response to a random force applied to the slider body. These forced-response solutions are useful in identifying the critical parameters of slider design.