Stability analysis of rotating shaft under electromagnetic and bearing oil-film forces

Abstract

The stability of the fixed pints of a flexible rotor supported by journal bearings is investigated through the Bifurcation diagrams. In this paper the effect of nonlinear electromagnetic harmonic force is added to the simultaneous consideration of the effects of the nonlinearity in curvature and inertia, mass eccentricity and hydrodynamic forces of the journal bearings. Solution of the Reynolds equation renders the pressure distribution in the bearings. The bearing forces are found from integrating the pressure distribution on the surface of bearings. Derivation of the equations is performed using the Hamilton's principle and the nonlinearity terms are related to the eccentricity and the curvature of shaft. Primary and combination resonances are imposed to the rotor-bearing system and steady state responses show the effects of magnetic and bearing forces on the stability of amplitudes. In combination resonance, frequency of the electromagnetic load is tuned as the average of the forward and backward natural frequencies of the rotor. Existence of unstable Hopf points demonstrates that periodic, quasi-periodic and chaotic motions may be arisen in the nonlinear behavior of rotor.