中文摘要：

基于简单铰链裂纹模型,建立含初始弯曲裂纹转子的动力学模型,将裂纹、质量偏心、初始弯曲转化为外部激励,经量纲一化转换可应用于稳态、瞬态、非线性等不同运动状态下、不同系统参数情形下的裂纹转子的振动特性分析中。利用欧拉方程进行解析求解,对比分析无初始弯曲裂纹转子与含初始弯曲裂纹转子频率成分的差异,研究含初始弯曲裂纹转子的亚临界共振特性。定义一种适用于裂纹转子动力学分析的极坐标圆,可全面反映出振动响应幅值的变化关系;数值仿真计算得到不同参数下的极坐标圆,讨论刚度变化、质量偏心与质量偏心角、初始弯曲与初始弯曲角的影响,可为系统优化或抑制振动提供依据;相应的轴心轨迹与频谱分析验证极坐标圆的有效性和可行性。

英文摘要：

Based on the simple hinge crack model,the dynamic equation of a cracked rotor with initial deflection is modelled,in which the external excitations are derived from the crack,mass eccentricity and initial deflection.Transformed into dimensionless form,it can be applied to the vibration characteristic analysis of cracked rotor with different parameters at stationary,transient or nonlinear state.With Euler equation in analytical solution,the frequency components of the cracked rotor with initial deflection are compared with those without initial deflection,and the subcritical resonance is investigated.The polar circle diagram that is suitable for the vibration analysis of cracked rotor is defined,which can thoroughly demonstrate the amplitude change of vibration responses.By numerical simulation,the polar circles of different parameters are obtained,and the influence of the stiffness variation,mass eccentricity and eccentric angle,the initial deflection and orientation of initial deflection is investigated,which can provide the basis for the system optimization or vibration suppression.The analysis of corresponding axis orbit and spectrum verifies the validity and feasibility of the polar circle diagram.