Tooth spalling is one of the most destructive surface failure models of the gear faults. Previous studies have mainly concentrated on the spalling damage of a single gear tooth, but the spalling distributed over double teeth, which usually occurs in practical engineering problems, is rarely reported. To remedy this deficiency, this paper constructs a new dynamical model of a gear system with double-teeth spalling fault and validates this model with various experimental tests. The dynamic characteristics of gear systems are obtained by considering the excitations induced by the number of spalling teeth, and the relative position of two faulty teeth. Moreover, to ensure the accuracy of dynamic model verification results and reduce the difficulty of fault feature analysis, a novel parameter-adaptive variational mode decomposition (VMD) method based on the ant lion optimization (ALO) is proposed to eliminate the background noise from the experimental signal. First, the ALO is used for the self-selection of the decomposition number K and the penalty factor â of the VMD. Then, the raw signal is decomposed into a set of Intrinsic Mode Functions (IMFs) by applying the ALO-VMD, and the IMFs whose effective weight kurtosis (EWK) is greater than zero are selected as the reconstructed signal. Combined with envelope spectrum analysis, the de-nosing ability of the proposed method is compared with that of the method known as particle swarm optimization-based variational mode decomposition (PSO-VMD), the fixed-parameter VMD, the empirical mode decomposition (EMD), and the local mean decomposition (LMD), respectively. The results indicate that the proposed dynamic model and background elimination method can provide a theoretical basis for spalling defect diagnosis of gear systems.

Gear fault diagnosis has been a vital technology to enhance the reliability and reduce the maintenance cost of gear systems. Tooth spalling is one of the most destructive surface failure models of the gear faults. Revealing the dynamic characteristics of a gear system with spalling fault and extracting the fault feature are the premise and basis for effective fault diagnosis. Previous studies have mainly concentrated on the spalling damage on a single gear tooth, but the spalling distributed over double teeth which usually occurs in practical engineering problems is rarely reported. To remedy this deficiency, this paper constructs a new dynamical model of a gear system with double-teeth spalling fault and validates this model with various experimental tests. The dynamic characteristics of gear systems are obtained by considering the excitations induced by the number of spalling teeth, the relative position of two faulty teeth, and the rotational speed. The method based on the Variational Mode Decomposition (VMD) and the Fast Kurtogram (FK) is proposed to extract the features of the double-teeth spalling fault. First, the raw signal is decomposed into a set of Intrinsic Mode Functions (IMFs) by applying the VMD, and the IMFs with strong correlation are summed as a reconstructed signal. The reconstructed signal is then filtered by an optimal band-pass filter based on the FK. Combined with envelope spectrum analysis, the feature extraction ability of the proposed method is compared with that of the original FK method and the method based on the Empirical Mode Decomposition and the FK, respectively. The results indicate that the proposed dynamic model and fault feature extraction method can provide a theoretical basis for spalling defect diagnosis of gear systems.