Accurate separation of amplitude-modulation and phase-modulation signal and its application to gear fault diagnosis

Long-time service and intricate work situation of gearbox make it liable to fault. The vibration signal of fault gear generally includes amplitude-modulation (AM) and phase-modulation (PM) components, which are the manifestation of fault and have strong connection with fault diagnosis. The corresponding relationships of AM and PM with gear fault type still lack of clarity. This paper proposes an accurate separation method of AM and PM signal, which contains squared amplitude demodulation and phase demodulation based on Bessel function of the first kind. Discrete spectrum correction technique is employed to correct modulation frequency and amplitudes in amplitude spectrum, which are utilized to establish system of nonlinear equations of AM and PM parameters. Trust-region reflective least square algorithm is then applied to solve these parameters and extract AM and PM components in sequence. The accuracy of this method is proved by various simulation signal. Additionally, simulation signals with different SRNs are employed to verify the anti-noise performance of the proposed method, which is further compared to Hilbert demodulation and energy-operator-based demodulation. Comparison results manifest the superiority of the proposed method in anti-noise performance. Experimental analyses confirm the effectiveness of this method and show the visible differences of separated PM components under different gear fault conditions, which can be used as an accordance of broken-tooth fault diagnosis. The relationship of the size of broken-tooth and modulation intensity is researched by the proposed method, which indicates that more serious broken-tooth degree behaves stronger modulation. A novel diagnosis method for gear broken-tooth fault is finally generated.