预变形Jeffcott裂纹转子超谐波共振的动力学响应

doi:10.3969/j.issn.1004-132X.2025.11.010

摘要/Abstract

摘要：

以转子动力学和非线性动力学理论为基础，针对刚性支承的水平Jeffcott 裂纹转子，研究1∶1内共振条件下系统的2/3超谐波共振的动力学响应。考虑了重力引起的预变形效应和裂纹呼吸行为，建立了由转子预变形引入的平方非线性和立方非线性的系统动力学方程。采用多尺度法推导出系统的演化方程，详细讨论了系统参数变化对系统动力学行为的影响规律，表明随着裂纹深度和横向阻尼系数的增大，系统频响曲线会出现“频率岛”现象；阐明了平方非线性对系统有软特性，立方非线性对系统有硬特性。对系统动力学方程采用Runge-Kutta法进行了数值积分来观察其跳跃现象，并对多尺度的近似解进行了验证。研究结果为Jeffcott转子系统裂纹故障的非线性动力学分析提供了理论指导。

关键词: Jeffcott裂纹转子, 预变形, 多尺度法, 动力学行为

Abstract:

Based on the theories of rotor dynamics and nonlinear dynamics， the dynamics response of 2/3 super-harmonic resonance of the system was studied for the rigidly supported horizontal Jeffcott cracked rotors under the condition of 1∶1 internal resonance. Considering the gravity-induced pre-deformation effect and crack respiration behavior， a system dynamical equation with quadratic nonlinearity introduced by pre-deformation and cubic nonlinearity was established. The multi-scale method was used to derive the evolution equation of the system， and the influences of the changes of system parameters on the dynamics behaviors of the system were discussed in detail， and it is shown that with the increasing of crack depths and lateral damping coefficients， the frequency response curves of the system exhibit “frequency island” phenomenon. It is clarified that the square nonlinearity exhibits a softening effect on the system， while the cubic nonlinearity exhibits a hardening effect. Numerical integration of the system's dynamics equation was conducted using the Runge-Kutta method to observe the jumping phenomenon， and the approximate solutions obtained through the multi-scale method were validated. The findings provide theoretical guidance for the nonlinear dynamics analysis of crack faults in Jeffcott rotor systems.

Key words: Jeffcott cracked rotor, pre-deformation, multiscale method, dynamics behavior

中图分类号:

TH113

张博, 程明霞, 史云帆, 陈丽. 预变形Jeffcott裂纹转子超谐波共振的动力学响应[J]. 中国机械工程, 2025, 36(11): 2554-2562.

Bo ZHANG, Mingxia CHENG, Yunfan SHI, Li CHEN. Dynamics Response of Super-harmonic Resonance of a Pre-deformed Jeffcott Cracked Rotor[J]. China Mechanical Engineering, 2025, 36(11): 2554-2562.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.11.010

https://www.cmemo.org.cn/CN/Y2025/V36/I11/2554

图/表 8

图1 Jeffcott裂纹转子

Fig.1 Jeffcott cracked rotor

图2 裂纹深度因子λ变化对振幅影响的频响曲线

Fig.2 Frequency response curve of the effect of crack depth factor λ change on amplitude

图3 横向阻尼cx 变化对振幅影响的频响曲线

Fig.3 Frequency response curve of the effect of lateral damping cxchange on amplitude

图4 竖向阻尼cy 变化对振幅影响的频响曲线

Fig.4 Frequency response curve of the effect of longitudinal damping cy change on amplitude

图5 不同σ2下稳态响应振幅随裂纹深度的演变曲线

Fig.5 Evolution curve of steady-state response amplitude with crack depth different σ2

图6 非线性项对振幅影响的频响曲线（λ=0.3）

Fig.6 Frequency response curve of the effect of nonlinear term on amplitude（λ=0.3）

图7 正反向扫频（λ=0.25，cx =0.017）

Fig. 7 Forward and backward sweep frequency （λ=0.25，cx =0.017）

图8 不同λ和σ2 时系统的动力学响应

Fig. 8 Dynamic response of system for different λ and σ2

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