Modeling and Verification of Lorentz Force to Electromagnetic Torque Conversion Mechanism Based on Discrete Matrix Geometry
Current analytical methods for motor electromagnetic torque mostly rely on continuous Riemannian geometry modeling, making it difficult to fundamentally explain the conversion law between Lorentz force and electromagnetic torque from a topological perspective. To address this gap, this paper establishes a new mechanism analysis framework using Discrete Matrix Geometry (DMG), reconstructing the unified representation of electromagnetic fields and electromechanical coupling with discrete matrices as the mathematical carrier. Matrix operators are derived to obtain the analytical expression for Lorentz force to electromagnetic torque conversion, and the model accuracy, parameter disturbance resistance, and dynamic stability are verified against multi-condition finite element method (FEM) simulation data. Simulation results show that compared with traditional continuous FEM schemes, the proposed discrete matrix model keeps the full-condition calculation error within 20%. It maintains convergence under parameter perturbation, magnetic saturation, and variable speed conditions, and can accurately quantify the intrinsic correlation between matrix topology disturbance and torque ripple. This discrete modeling approach avoids the inherent boundary approximation defects of continuous geometry, providing a novel theoretical path distinct from classical continuous field theory for high-performance motor torque analysis and loss optimization.
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