Fault diagnosis for gearboxes based on Fourier decomposition method and resonance demodulation

Condition monitoring and fault diagnosis of gearboxes play an important role in the maintenance of mechanical systems. The vibration signal of gearboxes is characterized by complex spectral structure and strong time variability, which brings challenges to fault feature extraction. To address this issue, a new demodulation technique, based on the Fourier decomposition method and resonance demodulation, is proposed to extract fault-related information. First, the Fourier decomposition method decomposes the vibration signal into Fourier intrinsic band functions (FIBFs) adaptively in the frequency domain. Then, the original signal is segmented into short-time vectors to construct double-row matrices and the maximum singular value ratio method is employed to estimate the resonance frequency. Then, the resonance frequency is used as a criterion to guide the selection of the most relevant FIBF for demodulation analysis. Finally, for the optimal FIBF, envelope demodulation is conducted to identify the fault characteristic frequency. The main contributions are that the proposed method describes how to obtain the resonance frequency effectively and how to select the optimal FIBF after decomposition in order to extract the fault characteristic frequency. Both numerical and experimental studies are conducted to investigate the performance of the proposed method. It is demonstrated that the proposed method can effectively demodulate the fault information from the original signal. 目 的 齿轮箱的振动信号频谱结构比较复杂, 难以提取其故障特征频率. 傅里叶分解方法可以将振动信号分解为多个单分量信号, 利用共振频率筛选出最优分量并进行包络解调, 识别特征频率以实现故障诊断. 创新点 1. 为了求解共振频率, 提出一种基于短时向量的最大奇异值比方法; 2. 将傅里叶分解方法引入到齿轮箱故障诊断中, 并利用共振频率选择最优分量进行包络解调以提取故障特征频率. 方 法 1. 分析奇异值比与冲击信号的关系, 提出求解共振频率的最大奇异值比方法; 2. 对比最大奇异值比方法与谱峭度方法在求解共振频率方面的表现, 从而验证最大奇异值比方法的有效性; 3. 对比分析所提方法与传统的总体经验模态分解 (EEMD) 和变分模态分解 (VMD) 方法在信号分解与故障特征提取方面的效果, 并通过仿真和实验进行验证. 结 论 1. 最大奇异值比方法能够准确计算出共振频率, 比谱峭度方法求解的频率值更加精确; 2. 基于傅里叶分解方法和最大奇异值比的共振解调方法能够有效提取故障特征频率, 其在故障诊断方面的表现优于EEMD和VMD方法.