Meshing frequency-constrained variational mode decomposition for fault feature extraction of a worm reducer driven by DC motors

Linear-driven elements that convert rotary motion to linear output have attracted increasing attention. Most mechanical faults of rotating machinery are mainly detected as modulated harmonics near meshing frequencies, while most signal decomposition methods neglect the inherent meshing dynamics of mechanical components. This study proposes a meshing frequency-constrained variational mode decomposition (MFCVMD) method for fault feature extraction in DC motor-driven worm reducers. Unlike classical VMD, the proposed MFCVMD rigorously calibrates the center frequencies to the meshing frequencies inherent in the worm reducer. Thus, the targeted decomposition of vibration signals into intrinsic mode functions (IMFs) that preserve fault-related modulations is realized. The constrained optimization problem is then iteratively solved through a multiplier-splitting framework. The envelope spectrum analysis applied to the extracted IMFs demonstrates effective fault feature isolation, as empirically validated through t-NSE. Compared to VMD and EMD methods, experiments demonstrate the superior clustering separability and spectral fidelity of the proposed MFCVMD. The gear tooth damage and uneven meshing faults of the DC motor-driven worm reducers are effectively captured by the proposed MFCVMD. Thus, this approach provides significant value for fault diagnosis in linear-driven systems. These findings highlight the significance of frequency-constrained decomposition for fault diagnosis in linear-driven elements, particularly for industrial applications that require accurate condition monitoring.