The stability analysis and nonlinear vibration control of shaft system for hydraulic generating set under multi-source excitation considering effects of dynamic and static eccentricities

Abstract

Aiming at nonlinear vibration problems of shaft system for hydraulic generating set caused by multi-source excitation, based on the construction of unbalanced magnetic pull considering dynamic and static eccentricities, a coupled bending–torsional vibration model of shaft system and corresponding differential equations under the action of multi-vibration sources are established. Nonlinear dynamic analysis is conducted by the shooting method, and the Floquet theory is applied to investigate the stability of system periodic solution. On this basis, discrepancies of dynamic characteristics for systems whether mixed eccentricities are excluded are compared, disclosing that dynamic features of system change dramatically when composited eccentricities are taken into account, and effects from mass eccentricity, excitation current, as well as static and dynamic eccentricities on oscillation response of system are revealed thoroughly by means of numerical method. The magnetorheological fluid damper is incorporated into the system for the purpose of suppressing the nonlinear vibration during operation, and corresponding suppression laws on vibration of rotor and runner are disclosed. While reducing the amplitude of system, fixed eccentricities also increasing the probability of chaotic motion, in addition, the new dynamic phenomena including period 3, period 5 and period 6 are revealed. The rotor displacement will be altered by the fluctuation of excitation current, which affects the dynamic response of runner through stiffness item indirectly. The high dissipation capacity of magnetorheological fluid damper can effectively ameliorate the unsteady dynamic response of system, reduce the amplitude and inhibit the irregular movement of rotor and runner to a certain extent, so as to further increase the stability of unit. The relevant research results can provide references for fault diagnosis and vibration control of hydraulic generating set, as well as for the optimal design.