Early Hidden-Crack Detection in Circular Magnetic Encoder Rings Through FM-AM Signal Decoupling

Early hidden cracks in circular magnetic encoder rings induce only slight magnetic perturbations at the incipient stage, yet they may evolve into missing-pole, demagnetization, or severe waveform-distortion faults that degrade angular-displacement measurement and closed-loop control. This study establishes a physical mapping between crack-induced magnetization nonuniformity, pole-pitch deviation, and the amplitude-modulated and frequency-modulated components of the measured magnetic signal, and models the encoder output as a compound frequency-modulated–amplitude-modulated waveform. A precision-controlled experimental platform equipped with a self-developed tunnel magnetoresistance read head, a precision rotary stage, multi-axis positioning stages, and laser displacement sensing was built to suppress eccentricity-related disturbances and disturbances related to sensor lift-off distance. An analysis workflow combining fast Fourier transform-based band-pass filtering, Hilbert demodulation, sixth-order Butterworth low-pass filtering, and coefficient-of-variation analysis was used to extract the instantaneous amplitude and instantaneous angular frequency. Experiments on intact, hidden-crack, and visible-crack states show that the proposed normalized indicators sensitively capture weak crack-related fluctuations, reduce sensitivity to sensor lift-off distance after normalization, and increase monotonically with damage severity. The method does not require a high-accuracy external reference and shows promise for online monitoring of circular magnetic encoder rings and related electromagnetic sensing elements.