Vibration analysis is an effective approach to evaluate hob wear status and diagnose hob faults. However, the extraction of vibration signal features is susceptible to noise interference. To solve this problem, a method combining grey relational analysis (GRA) and variational mode decomposition (VMD), named GVMD, is proposed in this paper. In our method, the mode number K, the most important parameter of VMD, can be adaptively determined by GRA. After VMD decomposition, GRA is again used to distinguish noise-dominant modes and signal-dominant modes, in which noise-dominant modes are processed by soft thresholding method. Then, the processed noise-dominant modes and signal-dominant modes are reconstructed to obtain the denoised signal, and signal features can be accurately extracted. In experiments, simulation signals, hob wear vibration signals and hob broken tooth vibration signals are used to evaluate performance of GVMD and other methods. The results demonstrate that GVMD achieves better results than other methods. GVMD can eliminate noise interference and effectively extract signal features.

振动分析是评估滚刀磨损状态和诊断滚刀故障的有效方法。然而，振动信号特征的提取容易受到噪声干扰。针对这一问题，本文提出了一种结合灰色关联分析（GRA）和变分模式分解（VMD）的方法，称为GVMD。在我们的方法中，模式数 K，VMD 最重要的参数，可以由 GRA 自适应地确定。VMD分解后，再次使用GRA区分噪声主导模式和信号主导模式，其中噪声主导模式采用软阈值法处理。然后对处理后的噪声主导模式和信号主导模式进行重构，得到去噪后的信号，准确提取信号特征。在实验中，模拟信号，滚刀磨损振动信号和滚刀断齿振动信号用于评估GVMD等方法的性能。结果表明，GVMD 比其他方法取得了更好的结果。GVMD可以消除噪声干扰，有效提取信号特征。