The Dynamic Behaviour of Passively Compensated, Hydrostatic Journal Bearings with Various Numbers of Recesses

Abstract

A previously established small-perturbation analysis is developed to express the unsteady-state continuity-of-flow equation for an isolated recess in a passively compensated, multirecess, hydrostatic journal bearing in terms of generalized co-ordinates. The concise form of this equation enables motion of the shaft about the concentric position to be described by equations which are derived in closed form for bearings with orifice, capillary or constant flow compensation and any number of recesses. These equations of motion, and hence the expressions for the receptances which describe the response of a bearing to external excitation, are shown to be of exactly the same form for all bearings of the type considered. Furthermore, the damping ratio and natural frequency in any particular case are determined by a single dynamic constant which is shown to be equal to a linear combination of circular functions and a limited number of coefficients which may be found explicitly by routine use of signal flow graphs. The results of the analysis, which is exact within the stated assumptions, are compared with those of other workers and the steady-state solution of the equations of motion is shown to give an expression for static stiffness which is useful for design purposes. Numerical values of the dynamic constant for bearings with between 3 and 20 recesses are given graphically.