分数阶阻尼裂纹转子的非线性动力学特性分析

为了有效地提高转子系统特性的分析精度,使其能够准确地进行故障诊断,以Jeffcott转子模型为基础,建立了带有分数阶阻尼和横向呼吸裂纹故障的转子系统的动力学模型.采用4阶龙格库塔法和10阶连分式欧拉法对转子系统的动力学方程进行数值仿真计算,利用轴心轨迹图、Poin-care截面映射图和分岔图等,研究了阻尼的分数阶次、转速和裂纹深度对裂纹转子动态特性的影响,并通过实验对理论分析结果进行了验证.分析结果表明:在半临界转速附近,由于裂纹的存在,转子的轴心轨迹呈现明显的双环型(或称内8字形),因此响应中的2倍频分量占主导地位.随着分数次阻尼阶次的增加,转子系统依次经历混沌、准周期和周期运动,同时裂纹深度、不平衡量以及转速对转子系统的动态特性具有明显影响.

Influences of Fractional Order Damping on Nonlinear Dynamics of Cracked Rotor

Nonlinear dynamics of cracked rotor system with fractional order damping is investigated with a response-dependent breathing crack model.The fourth order Runge-Kutta method and tenth order continued fraction expansion Euler(CFE-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors.The effects of derivative order of damping,rotating speed ratio,crack depth,orientation angle of imbalance relative to the crack direction and mass eccentricity on the system dynamics are demonstrated by bifurcation diagram,Poincare map and rotor trajectory diagram.The results show that the rotor system gets chaotic,quasi-periodic and periodic as the fractional order increases.It is also found that the imbalance eccentricity level,crack depth,rotational speed,fractional damping and crack angle all exert considerable influence on the nonlinear behaviors of cracked rotor system.