An optimised short bearing theory for nonlinear dynamic analysis of turbulent journal bearings

Abstract

An approximate method for nonlinear dynamic analysis of turbulent journal bearings supporting an unbalanced rigid shaft is proposed. The method is based on two assumptions: the separation of variables for pressure and a parabolic pressure distribution in the axial direction of the bearing. To take into account inertia effects, the well-known algebraic turbulent model based on the Prandtl mixing length hypothesis is used. Using the Constantinescu's approach, the pressure equation is modified by introducing two turbulent coefficients which are depending on the local Reynolds number. The nonlinear equations of motion for the rotor-bearing system are solved by means of the Euler's scheme, and the journal centre trajectories are examined for cases with and without unbalance forces. To illustrate the validity of the present study, three cases of journal bearings are analysed. The accuracy of the minimum film thickness, the dynamic transmissibility coefficient and the peak-to-peak displacement amplitudes obtained by the proposed methodology are comparable to the more elaborate and time consuming 2-D finite difference solution, while the turbulent journal centre orbits are comparable to those obtained experimentally. It is concluded that the optimised short bearing theory shows the advantage of minimising the computation time required for nonlinear dynamic analysis of laminar and turbulent journal bearings without any significant loss of accuracy.