Nonlinear dynamics and bifurcation analysis of journal bearings based on second order stiffness and damping coefficients

Investigating dynamics and stability of rotors supported on journal bearings is a crucial step in the design of an efficient and reliable rotating machine. In the current work, a model for flexible rotor supported on two symmetric journal bearings is investigated. The nonlinear bearing forces are evaluated by either using direct solution of Reynolds equation or analyzing Reynolds equation to obtain linear and nonlinear bearing stiffness and damping coefficients using time dependent second order perturbation method. These coefficients are obtained for different operating conditions and bearing parameters such as length to diameter ratio, groove angle or applied groove pressure. The present results are validated with the previous literature and a perturbation analysis is used to investigate the validity range of the bearing linear and nonlinear coefficients. A novel technique based on polynomial fitting is used to present the bearing coefficient as a function of the bearing parameters. This enables the investigation of the dynamics of flexible rotor model using numerical continuation technique. Also, the effect of the bearing design parameters such as groove angle, length to diameter ratio and static pressure on the system stability is investigated.