含横向裂纹Jeffcott转子刚度及动力学特性研究

摘 要：以刚性支承的水平Jeffcott裂纹转子为研究对象，建立了不依赖于重力占优假设的动力学方程，在考虑裂纹张开区域对中性轴位置影响的基础上，利用中性轴理论研究裂纹的开闭规律，由截面惯性矩与惯性积得到开闭裂纹截面各方向刚度系数，详细讨论了不同裂纹深度和不同转速下系统的动力学行为。结果表明：裂纹的存在对截面的法向与切向刚度系数的影响较大，而耦合刚度系数则始终接近于零值；随着裂纹深度的增加，裂纹的开闭过渡过程越明显,系统响应的频谱图趋向复杂，高阶谐波分量更加明显；当转速等于一阶临界转速的分数倍时，系统的固有频率被激发，系统响应出现分数次共振现象。

Stiffness and dynamical behavior of Jeffcottrotor with cross crack

The dynamical equations were established to study a horizontal cracked rotor on rigid supports,regardless of the superposition of weight-dominance.By applying the neutral axis theory and considering the influence of the open area of crack on the neutral axis position,the open-close regularity of the crack was presented.Based on the moment of inertia and product of inertia,the shaft stiffness coefficient with an open-close crack was investigated.Also,the dynamical characteristics of the system with different crack depth and under different rotating speeds were studied.The result indicates that the existence of the crack has a major influence on the stiffness in the normal and the tangential directions,while the coupling stiffness is always close to zero.As the depth of crack increases,the switching process of the crack becomes more obvious,and the frequency spectrogram of the response appears more complex with notable high-order harmonic components.When the rotating speed is equal to a fraction of the first-order critical speed,the natural frequency component of the system will be inspired and the subharmonic resonance may arise.