Finite element analyses of rotor/bearing system using second-order journal bearings stiffness and damping coefficients

The rotor-bearing system is a crucial component of rotating machinery, such as turbines, pumps, compressors, and turbogenerators, which are widely used in various advanced engineering fields. This work presented a methodology for studying the behavior of an elastic Jeffcott rotor supported by two similar fluid film journal bearings. A finite element model using consistent matrix formulation was employed to simulate the shaft, including the external load, with four degrees of freedom per node. The small perturbation method was used to evaluate the second-order bearing coefficients of a journal bearing of finite length. These coefficients were further integrated with the finite element model to evaluate the dynamic response of the flexible rotors. Moreover, the system equations of motion were presented in dimensional form. The results of the second-order bearing coefficients analysis agreed with nonlinear analysis when the speed was less than the threshold speed, while there was a pronounced difference in second-order analysis when the speed was above the threshold speed. The behavior of the rotor-bearing system was studied using dynamic response and orbit diagrams, revealing that changes in rotational speed significantly affected the rotor's stability.