An exact analytical solution for dynamic loads generated by lubricated long journal bearings

Abstract

Gümbel's solution is utilized by most of the literature addressing the imperfect lubricated joint problem in multibody mechanical systems, this solution involves several approximations in evaluating the lubricant forces. In this work; a new solution for the dynamic characteristics of lubricated long journal bearing under dynamic loading is derived and presented by analytically integrating Reynold's equation for the pressure gradient in lubrication theory, the exact integrations are performed utilizing Sommerfeld's variables without involving approximations or assumptions, new equations to evaluate the lubricant dynamic forces and the zero pressure angles at any eccentric position are presented, the squeeze and the dynamic effects are uncoupled, this uncoupling makes it easier to study the contribution of each effect to the total lubricant forces. The new solution is applied to two different examples; a simple multibody mechanism consists of lubricated long journal bearing under unidirectional constant load, and to crank-slider mechanism with a lubricated imperfect joint. The results are compared to the results obtained by adopting the widely used Gümbel's solution.