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

Early hidden cracks in 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. 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 measure the spatial magnetic field during shaft rotation. Fast Fourier transform-based band-pass filtering, Hilbert transform-based demodulation, and sixth-order Butterworth low-pass filtering were used to extract the instantaneous amplitude Ai and instantaneous angular frequency ωi; coefficient-of-variation analysis was then used to construct the diagnostic indicators. Experiments on intact, hidden-crack, and visible-crack states show that the CV of Ai and the CV of ωi sensitively capture weak crack-related fluctuations and increase monotonically with damage severity. The method does not require a high-accuracy external reference and shows promise for online monitoring of magnetic encoder rings and related electromagnetic sensing elements.