Modeling of AMR magnetic encoder signals for instantaneous angular speed and vibration separation

Magnetic encoder signals are susceptible to distortions caused by small transverse vibrations and dynamic misalignments, particularly in off-shaft configurations. A novel anisotropic magnetoresistive (AMR) encoder coupling model is established, capturing both torsional and transverse displacements to reveal how dynamic vibrations affect signal formation. Based on this model, a dual-sensor reconstruction method is developed to estimate instantaneous angular speed (IAS) and transverse vibration. Simulation and experimental validation under varying encoder resolutions and multi-source vibration conditions confirm the method’s robustness and high accuracy, achieving high correlation coefficients and low normalized root mean square error (NRMSE). The approach enables accurate IAS measurement with fewer sensors and facilitates its integration into practical condition monitoring systems.