中文摘要：

采用Rayleigh方法计算横向裂纹轴单元的刚度模型，基于有限元法建立具有横向裂纹的多盘柔性转子一轴承系统的数学模型．分析裂纹对多盘柔性转子一轴承系统的动力特性的影响，研究由于裂纹的存在而产生的超谐波共振和亚谐波共振，讨论了这些共振的特点，特别是系统的2倍频和3倍频谐波分量的特性，分析了靠近1／2和1／3倍第一临界转速时的轨迹变化以及裂纹的位置和深度对非线性特性的影响．结果表明，与两端刚性支承的简单Jeff—cott转子相比，利用在次临界转速处2倍频和3倍频超谐波成分作为检测多盘转子系统中的裂纹指标是可行的．

英文摘要：

The stiffness of transverse crack rotor element was calculated by Rayleigh theory. A mathematical model of a multi-disk flexible rotor-bearing system with transverse crack axis was established based on finite element method. The model theoretically analyzed the influence of the crack on the dynamic characteristics of the multi-disk flexible rotor-bearing. The nonlinear resonance of the multi-disk flexible rotor due to the crack was analyzed. The characteristics of the nonlinear resonance was discussed, especially the two times and three times harmonic components of multi-disk flexible rotor system and the rotor orbit at the speed close to 1/2 and 1/3 of the first critical speed. The effect of the crack＇s position and depth on the nonlinear resonance characteristics of the multi-disk flexible rotor-bearing system was analyzed. Results demonstrate that compared to the simple Jeffcott rotor, it is effective to use two times and three times super-harmonic components at the sub-critical speed for the crack detection of multi-disk rotor system.