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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. [ABSTRACT FROM AUTHOR]

• The combination of grey theory and EEMD for signal denoising is a novel idea. • Grey relational analysis is used to evaluate noise levels of signal components. • Grey model is used to determine noise-dominant signal components. • The proposed method eliminates the interference of human factors. When the vibration analysis is used to evaluate the wear status of the hob cutter, the collection of vibration signals is inevitably contaminated by noise. To solve this problem, a novel denoising method for the vibration signal based on ensemble empirical mode decomposition (EEMD) and grey theory, named EEMD-Grey, is proposed in this paper. Grey relational analysis (GRA) and grey model (G-model), as two important techniques in grey theory, are adopted. In the EEMD-Grey method, the noisy signal is first decomposed into several intrinsic mode function (IMF) components by EEMD. Then, GRA is used to evaluate noise levels of IMF components. After that, noise-dominant IMF components are selected through G-model to remove noise. Finally, processed components and other components are reconstructed to obtain the denoised signal. Simulation experiments demonstrate the effectiveness of EEMD-Grey by comparison with other denoising methods. In addition, EEMD-Grey is applied to denoise the vibration signal of the hob spindle. The result shows that EEMD-Grey can effectively remove noise and retain useful information. [ABSTRACT FROM AUTHOR]