Magnetization Model and Detection Mechanism of a Microparticle in a Harmonic Magnetic Field

Inductive particle sensors are widely used in online wear condition monitoring. Understanding the behavior of a particle magnetized in an alternating current (ac) magnetic field and the associated sensing mechanism is fundamental to identifying the particle size, improving the detection precision and enhancing the sensor performance. Here, we first establish a particle magnetization model related to particle conductivity, permeability, diameter, and field frequency. Next, an expression for particle detection using inductance is derived that consists of a product of the particle volume, complex particle susceptibility, and particle sensor sensitivity. The derived formulas and experiments reveal that the output of the inductive sensor is a complex number. Therefore, a vector analysis method is proposed for inductive particle detection. The sensitivities of various sensors are discussed. Experiments are conducted using milliparticles and microparticles in various positions relative to sensors. A comparison of the calculation results with the experimental results exhibits satisfactory agreement. Consequently, an optimized rectangular cross-section of coils is proposed. This study provides a theoretical basis for the design and optimization of particle sensors based on magnetic principles.