不平衡力对裂纹转子动力学响应与稳定性的影响

Effect of unbalance force on the nonlinear dynamic response and stability of cracked rotors

摘要

研究裂纹转子系统的动力学行为与稳定性可为转子裂纹故障诊断和设计优化提供支撑，也是转子动力学领域的重要问题。现有文献大多基于重力占优假设构建裂纹模型，忽略了不平衡力的影响。在很多情况下，不平衡力与重力的比值较为可观，可能对裂纹呼吸效应产生影响。为揭示不平衡力对裂纹转子系统非线性动力学响应与稳定性的影响，本研究采用有限元法构建转子系统的动力学分析模型，结合考虑不平衡力影响的呼吸裂纹模型，获得具有周期时变系数的系统动力学方程；为实现对高维周期时变微分方程组的高效求解，基于Hill方法推导了系统动态响应与特征值的高效计算方法，并通过系统特征值的实部判定其稳定性；进而，研究了不平衡力对裂纹转子过1/3、1/2以及1倍临界转速处的动力学响应与稳定性的影响特征。分析表明：不平衡力会显著影响裂纹的呼吸行为，进而影响裂纹转子系统刚度特征与谐振频率，并导致系统不稳定区域产生明显变化。

Abstract

Studying the dynamic behavior and stability of cracked rotor systems can provide support for rotor crack fault diagnosis and design optimization，and is also an important issue in the field of rotor dynamics. Most of the existing literature constructs crack models based on the assumption of gravity dominance，ignoring unbalanced forces impact. In many cases，the ratio of unbalanced force to gravity is considerable and may have an impact on the crack breathing effect. In order to reveal the influence of unbalanced force on the nonlinear dynamic response and stability of the cracked rotor system，this study uses the finite element method to construct a dynamic analysis model of the rotor system. Combined with the breathing crack model that considers the influence of unbalanced force，the model with periodic time is obtained. System dynamics equations with variable coefficients；in order to achieve efficient solutions to high-dimensional periodic time-varying differential equations，an efficient calculation method for system dynamic response and eigenvalues is derived based on the Hill method，and its stability is determined by the real part of the system eigenvalues properties；further，the influence of unbalanced force on the dynamic response and stability of the cracked rotor at 1/3，1/2 and 1 times the critical speed was studied. The analysis shows that the unbalanced force will significantly affect the breathing behavior of the crack，thereby affecting the stiffness characteristics and resonant frequency of the cracked rotor system，and causing significant changes in the unstable region of the system.

关键词

裂纹转子 / 不平衡力 / 非线性动力学 / 稳定性 / Hill方法

Key words

cracked rotor / unbalance force / nonlinear dynamics / stability / Hill method

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基金资助

国家自然科学基金资助项目(12272117)

三峡工程后续专项科研资助项目(SXHXGZ-2021-2)