A novel semi-analytical method for the dynamics of nonlinear rotor-bearing systems

• Combination of a continuous rotor with analytically solved finite journal bearings
• Analytical evaluation of the response of a continuous medium in nonlinear bearings
• Incorporation of the rotor's shearing forces into the journal bearing mobility

A semi-analytical simulation of a rotor bearing system that consisted of a multi-segment continuous rotor and plain fluid film bearings with finite length is developed in this paper in order to investigate the system's response under the current proposal of simulation. The rotor is simulated using the continuous medium theory and the bearings with finite length follow a very recent analytical simulation that incorporates the analytical solution of the Reynolds equation for the plain, finite journal bearing. The boundary conditions combine the rotor's shearing force and the fluid film forces at the points where the bearings are located, which are expressed analytically with direct integration of the pressure distribution function.A case study of simulating a multi-segment shaft is used in order to compare the current simulation with corresponding simulations using continuous rotor mounted on linear bearings, or finite bearings numerically simulated using the finite difference method. The time response, the amplitude of the response and the phase during passage through resonance are evaluated for these three cases of bearing simulation using numerical procedures and the differences are notified and remarked.