The Study on Subharmonic Instability of Nonlinear Rotor/Seal Systems

A symmetric rotor/seal system is investigated in this chapter. Calculations for the perfectly balanced system using Poore’s algebraic criteria reveal the supercritical Hopf bifurcation after the threshold speed is exceeded. On considering the small level of imbalance of the rotor, the periodically perturbed Hopf bifurcation in 1/2 subharmonic resonance is dealt with. Analysis of the averaged equation obtained by using the center manifold procedure and the averaging method show that non-synchronized whirl of the unbalanced rotor can either be a quasi-periodic motion resulting from Hopf bifurcation, or a half-frequency whirl from period doubling bifurcation, determined by the structure parameters of the system and operation conditions. Numerical simulation verifies the analytical results.