Approximate analytical model of oil-film force for finite length elliptical journal bearing

The Reynolds equation of plain journal bearing lubrication was solved by separation of variables method,the pressure distribution expression of oil-film in plain journal bearing was obtained based on dynamic boundary conditions,and the approximate analytical expression of plain journal bearing oil force was deduced.The boundary conditions of elliptical bearing were analyzed.The approximate analytical model of elliptical bearing oil-film was obtained by combining the oil film boundary conditions of elliptical bearing with oil film force expression of plain journal bearing.The oil film force is verified with high accuracy and suitability for any aspect ratio by comparing with the finite difference method,long bearing model,and the short bearing model.The nonlinear rotordynamic behavior of a rigid rotor on elliptical bearing was investigated by Runge-Kutta method,the results of numerical simulation show that the model can describe the dynamic characteristics of elliptical bearing oil film well.