A Novel Optimization Demodulation Method for Gear Fault Vibration Overmodulation Signal and Its Application to Fault Diagnosis

Many demodulation methods are devoted to obtain the gear fault modulation frequency as the fault diagnosis indicator instead of the precise amplitude and frequency demodulation. It is because the precise demodulation is a challenge, especially for the overmodulation signal potentially caused by the gear fault, which further hinders the gear fault degree diagnosis. This article proposes a novel optimization demodulation method for overmodulation signal. The Hilbert transform demodulation (HTD) and the Jacobi–Anger expansion form are, respectively, combined with the trust region reflection optimization algorithm to achieve the precise amplitude and frequency demodulation. The objective function about amplitude modulation (AM) parameters considers the zero-crossing feature of the time-domain AM in the overmodulation signal. The iterated HTD (IHTD) is innovatively applied to remove the singularity effect in the residual signal caused by the overmodulation. The simulations and experiments demonstrate that the proposed method has the advantages of high accuracy and strong antinoise performance in the demodulation of overmodulation signal. The quantitative frequency modulation (FM) and AM signals obtained by the proposed method can be applied to detect the gear fault degree, which provides an approach for establishing linkages between the modulation intensity and the fault degree.