The Dynamics of a Flexible Beam With a Lubricated Prismatic Kinematic Pair

Abstract

In this article we consider the influence of the prismatic kinematic pair lubrication film on the planar vibrations of a constant cross-sectional straight link that is attached to the joint. The main objective is to develop an analytical model that incorporates the effect of the lubricant film on the vibration of elastic links in mechanisms. It has been assumed that the beam on which the prismatic kinematic pair translates is a linear elastic body. Equations for the translational and rotational motions of the link are developed by applying Hamilton’s principle. Kinetic energy that is required for the application of this principle has been derived by utilizing a generalized velocity field theory for elastic solids. This approach provides means to include the inertia terms directly in the equations of motion. The pressure field exerted through the viscous, incompressible, lubricant film is obtained from the solution of the Reynolds equation of lubrication. We introduce a scheme to solve the resulting two sets of equations for the vibrations of the link and the motion of the fluid. The pressure field is used to compute the external force exerted by the fluid on the link. The utility of the method is demonstrated by considering a planar mechanism that includes an elastic element with a prismatic joint.