关键词: 机械学, 分数阶微积分, 裂纹转子, 非线性动力学, 非线性涡动, 故障诊断

Abstract: Nonlinear dynamics model of cracked rotor system with fractional order damping under the condition of nonlinear eddy is investigated and simulated by the Runge Kutta method and continued fractional expansion Euler method. The effects of derivative order, rotating speed ratio and crack depth on the nonlinear dynamic characteristics of cracker rotor system with fractional damping are discussed. The simulation results show that the model of cracked rotor system established with fractional order can reveal the nonlinear dynamics characteristics of a rotor system with fractional characteristics. In the same crack depth and fractional order, the rotor system gets chaotic, period-doubling and periodic motions as the factional order increases. In the same rotating speed ratio and fractional order, when the crack depth is small, the rotor system doesn’t appear complex bifurcation and chaos phenomena. With the increase in crack depth, the stiffness of rotor system reduces and the rotor system presents the complex vibration characteristics. The crack fault feature becomes more obvious. The rotor system gets from periodic motion to period-doubling motion. The double frequency component is dominant, and simultaneously other frequency multiplication component also appears. These valuable conclusions provide the important reference for the fault diagnosis of cracked rotor.

Key words: mechanics, fractional calculus, cracked rotor system, nonlinear dynamics, nonlinear eddy, fault diagnosis