Abstract: To deeply mine the nonlinear coupling vibration characteristics of the rotor-bearing system in a hydroelectric generator set, this paper extends its damping force from the traditional fixed integer order to the flexible range of fractional order. We constructed a new system dynamic model－coupling the rotor with fractional-order damping and the bearing with a fractional order. Then, the effects of different fractional orders on the system were examined; different motion patterns of the model coupled with fractional-order damping were explored in the order-symmetric system and order-asymmetric system. Distribution diagrams were drawn to illustrate the system's motions under different conditions, and different patterns in the dynamic characteristics of the contact faults were compared between integer-order and fractional-order damping. Our fractional-order damping dynamic model was validated and its superiority was verified through comparison of the touch-and-go faults dynamic characteristics between integer-order and fractional-order damping. The results showed that, compared with integer-order damping, the fractional-order damping had new dynamical features such as nonlocality, memorability, and adaptive nonlinearity.

Key words: hydromechanics, rotor-bearing systems, fractional-order damping, nonlinear dynamics, features of faults