基于分数阶微积分的裂纹转子系统非线性动力学特性研究

在考虑非线性涡动的情况下,建立了分数阶阻尼裂纹转子系统的非线性动力学模型,并用龙格-库塔法和连分式Euler法对其进行了数值仿真。讨论了分数阶阶次、转子转速和裂纹深度对分数阶阻尼裂纹转子系统非线性动力学特性的影响。研究结果表明:对于具有分数阶特性的转子系统,采用分数阶来建立裂纹转子系统模型,能更好地揭示系统的非线性动力学特性;在相同的裂纹深度和相同的分数阶阶次下,随着转速比的增加,转子系统依次经历混沌、倍周期和周期运动;在相同的转速比和相同的分数阶阶次下,裂纹深度比较小时,引起的转子刚度变化量不大,一般不会出现复杂的分叉与混沌现象;随着裂纹深度的加深,转子的刚度减小,转子系统呈现复杂的振动特性,裂纹故障特征越来越明显,转子系统由单周期运动变换到倍周期运动,二倍频分量占主导地位,同时其他倍频分量也相继出现。这些有价值的结论对转子裂纹的故障诊断提供了参考。

Nonlinear Dynamic Characteristics of Cracked Rotor System Based on Fractional Order Calculus

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.