Demagnetizing-field computation becomes a feedback problem when magnetization is updated from the effective field generated by its own magnetic sources. This letter identifies the convergence boundary of the classical unrelaxed explicit update by combining a closed-form finite-sidewall model, geometric-series analysis, a general fixed point interpretation, and independent finite-element (FEM) benchmarks. For a finite vertical sidewall, the material-side return field reduces to Hd = −KM, where M is the sidewall magnetization and K is a dimensionless geometry coefficient. With applied field H0, susceptibility x, and feedback gain q= xK, the update follows M(k+1) = xH0 - qm(k) The exact recurrence gives attenuating corrections for q < 1, an equal-amplitude two-cycle at q = 1, and alternating amplification for q> 1; it also yields the critical susceptibility xc = 1/ k and the correction order required by a prescribed tolerance. For a distributed linear update, the corresponding condition is (D) < 1, where D is the discrete return-field matrix and ρ(D) its spectral radius. A prescribed-source FEM benchmark reproduces the finite-specimen analytical return coefficient with a maximum difference of 0.00532%, while self-consistent FEM solutions remain finite for nominal gains q= 0.70–1.30. The results identify unit gain as the convergence boundary of the explicit correction path and show that spatial magnetization redistribution becomes increasingly important as feedback strengthens.
A method for detecting magnetic particles based on nonlinear circumferential magnetization in amorphous Co69Fe4Cr4Si12B11 microwires is demonstrated. The circumferential magnetic flux generated by an excitation current, together with the corresponding harmonic spectrum of the induced voltage, is strongly affected by an axial magnetic field, providing the basis for magnetic particle detection. Both pure magnetite and natural iron ore particles were investigated. The particles located near the microwire were magnetized using an external magnetic field applied perpendicular to the wire axis. Applying the perpendicular field enhances the influence of the particles on the circumferential magnetization process while preserving the ability to detect changes in the harmonic spectrum. The response produced by the perpendicular field alone was used as a baseline and accounted for by normalizing the harmonic amplitudes to the corresponding baseline response. Higher-order harmonics exhibited greater sensitivity to the presence of magnetic particles. These results demonstrate the potential of nonlinear harmonic analysis in amorphous microwires as a robust and sensitive approach for detecting magnetic microparticles.
Capacitive pressure sensors offer high sensitivity and low power consumption but are fundamentally limited by membrane nonlinearity, restricted dynamic range, and pull-in risk at large deflection. This work presents a magnetically force-balanced capacitive pressure sensing architecture in which Lorentz-force electromagnetic actuation actively suppresses pressure-induced membrane displacement, maintaining the diaphragm near its equilibrium position to achieve linear readout with an extended dynamic range. A coupled electromechanical model is developed and validated on flexible polyimide sensors with membrane radii of 6–15 mm, demonstrating sensitivities up to 452 fF/kPa and open-loop force compensation of 81–88% across applied loads of 5, 10 and 20 g. A key architectural feature is a single shared coil serving simultaneously as the Lorentz-force actuator and the inductive element of a passive LC resonant circuit, eliminating the need for separate actuation and sensing coils. Wireless LC interrogation is demonstrated with a resonance frequency shift of approximately 2 MHz from a 135 MHz baseline across the full actuation range. These results demonstrate the potential of flexible magnetically force-balanced sensing for compact, pull-in-free pressure monitoring in flexible electronics, wearable devices, and soft robotic systems.
This paper presents a contactless sensor system for real-time monitoring of pressure and temperature in automotive brake systems using glass-coated magnetic microwires. Amorphous magnetic microwires were prepared by the Taylor-Ulitovsky method. A functional experimental setup simulating a real automobile brake system was constructed for testing. For contactless pressure sensing, an amorphous Fe76Si9B10P5 microwire was attached to the brake hose. It demonstrated a monotonic response up to 60 bars with an average switching time sensitivity of 0.7 μs per 1 bar and a theoretical resolution of 0.008 bar. For contactless temperature sensing, a nanocrystalline Fe76Cr2Mo6B9Cu1Su1P5 microwire was attached to a copper tube section. This sensor yielded a switching time sensitivity of 2 μs per 1°C and a theoretical resolution of 0.002°C within the measured range up to 65°C. The switching time (tsw) of the microwires was accurately evaluated using a custom 170 MHz microcontroller-based electronic system. The results confirm that glass-coated magnetic microwires offer a highly sensitive, stable, and non-invasive alternative for predictive maintenance and diagnostics in modern vehicles.
This letter presents a computationally efficient two-dimensional finite element (FE) framework for coaxial magnetic gears (MGs) that couples a fixed-mesh magnetostatic solver with a calibrated analytical stability model to evaluate combined thermal and vibration faults. The fixed-mesh approach employs a sub-element quadrature boundary smoothing technique to resolve material boundaries during eccentric rotor displacements without remeshing, enabling rapid parametric sweeps. Key FE results—stall torque, air-gap field decay length $L_{c}$, and worst-case demagnetizing field $H_{\mathrm{op,max}}$—calibrate a reduced-order analytical model that generates stability margin maps, demagnetization safety-factor contours, and dynamic pole-slip predictions. For an NdFeB-based MG with a 4:11 pole-pair combination and a 7 mm inner air gap, the FE solution (torque computation validated via an independent inner/outer-contour gear-ratio self-consistency check, agreeing with the theoretical ratio $p_{2}/p_{1}$ to within 4.0%) gives a stall torque of 1.169 N$\cdot$m/m and $H_{\mathrm{op,max}}=342.7$ kA/m, with a fitted air-gap decay length $L_{c}=9.44$ mm. The calibrated reduced-order model reproduces independent FE evaluations at ten combined temperature-eccentricity operating points to within 10.9% mean error (range 1.6–21.6%, growing with eccentricity). At 80% of stall torque, low static stability margin drives pole-slip in 9.8 s, whereas at 60% load the system survives 51.4 s before thermal degradation causes loss of synchronism. The methodology provides a rapid design-screening tool linking FE data with scaled operational stability assessments.
