Limitations of Reluctance Networks to Model the Frequency-Dependent Leakage and Fringing Fluxes in Active Magnetic Thrust Bearings

Previous works have demonstrated that analytical high-fidelity models of nonlaminated actuators and magnetic thrust bearings cannot just describe the magnetic skin effect inside the solid core, but also be applied directly within the control circuit. By an appropriate rational approximation a digital implementation on a microcontroller becomes possible. These approximated models generally do not consider frequency-dependent fringing and leakage fluxes, which may account for more than 7% of the total flux. Reluctance networks are a popular choice to address this discrepancy. When calculated carefully, they can highly improve the accuracy of static models. However, their limitations in real-world scenarios are usually not discussed, even though the magnetic skin effect significantly changes the flux distribution in the nonlaminated core at already very low frequencies. In this article we review the practicability of reluctance networks and their possible simplifications in the context of real-time control systems. Depending on the control's objective we find they may be even discouraged, while simple correction factors allow for consistent results over the entire frequency range.