On the Role of a Compliant Surface in Long Squeeze Film Bearings

The problem of compliant surface journal bearings with large slenderness ratio (length/diameter → ∞) is analyzed for the case of small journal eccentricities. In this model an elastic circular cylinder has an axial length that is large compared to its diameter. The elastic cylinder is rubber, the inner rubber surface is wetted with a Newtonian lubricant, and the outer rubber surface is bound to a rigid surface. Immersed within the lubricant is a rigid circular journal. The journal is held fixed, and a translatory motion is assigned to the rigidly backed elastomer bearing. The resulting squeeze film is analyzed for near concentricity between the undeformed rubber surface and the rigid journal. The development of the model proceeds from the basic Navier displacement equations for a solid and the Stokes equations for the fluid. The special case of Poisson’s ratio going to 1/2 is used for the solid. The field equations are linear; a nonlinearity is a consequence of the boundary conditions. Discrete distributions of singularities are used to represent the coupled fluid and elastic deformation. Surface stress traction vectors are matched at the liquid-solid interface. Explicit expressions for changes of the fluid film gap due to rubber deformation, together with the associated change in fluid film pressure, are presented.