Energy Storage Flywheel Magnetic Bearing System - Magnetic Linear Circuit Vs. 3-D Finite Element Model Plus Electrical and Thermal Modeling

A 1 kW-hr (3.6 MJ) energy storage flywheel with a design operating speed of 40,000 rpm and an inside-out flywheel has been designed and optimized. It is supported in two thrust and two radial active magnetic bearings. The purpose of this paper is to present the active magnetic bearing system modeling including the magnetic analysis. At the design stage, there are two ways to evaluate the magnetic bearing properties: linear circuit model or finite element model. The linear circuit models are simple lumped mass models. The finite element model discretizes the bearing geometry and the surrounding space and requires a great deal more work. There are not many full 3-D finite element magnetic bearing systems that have been fully compared to the equivalent linear circuit model. There are legitimate questions about accuracy of magnetic bearing modeling results. This paper considers these two approaches to compare the results for a realistic energy storage flywheel design. If the differences are large, it is expected that the 3-D finite element model is more likely to be accurate. This paper documents the differences for the flywheel magnetic bearing designs. The linear circuit model prediction of axial force capacity was 17% lower and the prediction of coil inductance was 8% lower than the predictions from 3-D finite element model. The linear circuit model of the radial bearing underestimated the force capacity by 14% and underestimated the inductance by 8.5% when compared to the 3D finite element model. Values were also compared for the open loop stiffness, current gain and force slew rate for both bearing designs. These relatively large differences in magnetic bearing performance parameters obtained between the linear circuit model and the 3-D finite element model, shows that the linear circuit model is not very accurate. Thus, the concern is that designing and optimizing a complex magnetic bearing supported device requires 3-D finite element modeling at the design stage. The flywheel has not been constructed and the magnetic bearings are thus not available for testing. It is hoped that this can be future work.