L. Santos F., M. Duarte M., C. Faria M., C. Eduardo A.

Rotating machines are very common in industry. To understand their behaviour is therefore, very important. When considering numerical analysis of such systems, their modelling needs to consider several important effects which are normally disregarded, such as cross-coupled damping and stiffness coefficients associated with the hydrodynamic interactions between the shaft and the supporting bearings. This paper deals with an analysis of the dynamic behaviour of rotating shafts supported on hydrodynamic journal bearings. The model employed to represent the rotor-bearing system is based on the Stodola-Green rotating shaft model, in which the inertia effects associated with the gyroscopic moment and rotary inertia are taken into account, and on the classical Reynolds equation for the hydrodynamic journal bearings. A finite element procedure specially devised to solve the zeroth- and first-order lubrication equations generated from a perturbation technique applied on the Reynolds equation is used to predict the dynamic force coefficients of the hydrodynamic journal bearings. Lagrange equations are used for obtaining the four equations of motion for the rotor lateral vibration. By using the classical method of Runge-Kutta is possible to obtain the frequency response of the system due to the unbalance distribution along the shaft. The influence of the bearing damping and stiffness cross-coupling coefficients on the rotor unbalance response is analysed. Numerical results show that the inclusion of the bearing force coefficients on the dynamic analysis of rotating machines supported on hydrodynamic bearings plays an important role on the determination of the unbalance response of rotors.