Gear Fault Diagnosis Using Kalman Filtering and Vibration Spectral Analysis

This work presents a method based on the Kalman filter for detecting and characterising broken-tooth failures in gears, using vibration signals acquired with accelerometers. The approach employs an autoregressive (AR) model to estimate the healthy periodic gear mesh response and to generate a residual signal that contains the components not explained by the model, where the impulses caused by the defect become more prominent. Statistical and spectral analysis of the residual signal revealed a marked increase in kurtosis and crest factor and the emergence of high-frequency resonances associated with the impact of the broken tooth. Among the condition indicators extracted, the Amplitude Mesh Ratio (AMR) proved to be the most sensitive to failure severity. To quantify the damage, a calibration curve was developed using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), which ensures a strictly monotonic and physically consistent mapping between the AMR value and the percentage of damage. This calibration achieved an absolute error below 2 % and a coefficient of determination R 2 of 0.99 when estimating the percentage of tooth removal. The proposed methodology is computationally efficient, suitable for real-time implementation, and capable of enhancing predictive maintenance of critical mechanical transmissions by isolating the failure signature from the standard gear mesh response. Its robustness and accuracy make it a valuable tool for condition monitoring and early failure detection in industrial gear systems.