Semi-Analytical Lorentz Actuator Model for a superconductor-based 6-DoF Levitation System exploiting Magnetization Periodicity

Lorentz actuators use magnetic interactions between coils and magnets to create forces and torques for actuation. Especially for applications that enable actively controlled 6-DoF levitation it is necessary to model these Lorentz forces and torques and evaluate these models in real time. Generally, Lorentz forces are evaluated using numerical integration of the Lorentz force integrals. These calculations become computationally expensive for increasing number of magnets and, therefore, deriving analytical or semi-analytical models for the integrals are important to reduce computation time while maintaining model accuracy. For the studied superconductor-based 6-DoF levitation system a semi-analytical model of the Lorentz actuators forces/torques is derived by exploiting the periodicity of the actuator magnets magnetization. Using Fourier series an analytical expression of the magnetic flux density of the actuator magnets is found by solving the Maxwell's equations under magneto-static conditions. Using this analytical expression a semi-analytical formulation of the Lorentz force integrals is given. In this publication the model derivation is presented and the model is validated and discussed based on single coil experiments and compared to the fully numeric surface charge model. It was possible to show that the semianalytical model can closely match the measured forces and torques even with a reduced set of approximation elements to reduce computational effort by over 70% with respect to a fully numeric implementation.