THE DYNAMICS OF A FLEXIBLE BEAM WITH A LUBRICATED PRISMATIC KINEMATICPAIR

In this article we consider the influence of the prismatic kinematic p air lubrication film on the planar vibrations of a constant cross-sect ional 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 tran slates is a linear elastic body.. Equations for the translational and rotational motions of the link are developed by applying Hamilton's pr inciple. Kinetic energy that is required for the application of this p rinciple has been derived by utilizing a generalized velocity field th eory for elastic solids. This approach provides means to include the i nertia terms directly in the equations of motion. The pressure field e xerted through the viscous, incompressible, lubricant film is obtained from the solution of the Reynolds equation of lubrication. We introdu ce a scheme to solve the resulting two sets of equations for the vibra tions of the link and the motion of the fluid. The pressure field is u sed to compute the external for ce exerted by the fluid on the link. T he utility of the method is demonstrated by considering a planar mecha nism that includes an elastic element with a prismatic joint.