Dynamic Stiffnesses of Active Magnetic Thrust Bearing Including Eddy-Current Effects

The eddy currents induced in a thrust bearing result not only in a power loss of the system but also in phase lag and a decrease in magnitude of the magnetic force. Therefore, an accurate model including eddy-current effects would be highly beneficial at the design stage. We present a linear model including eddy-current effects for a typical active magnetic thrust bearing (AMTB). We define and calculate the dynamic current stiffness and displacement stiffness using both an analytical method and transient finite element (FE) analysis. We present a simple magnetic circuit model including eddy currents from which the two stiffnesses can be derived analytically. Furthermore, by using a transient analysis of the FE model, flux saturation, leakage, and fringing effects can all be taken into account. We show that the two stiffnesses have the same frequency response characteristics, both in the analytical model and from the results of the linear FE analysis, when the leakage and fringing effects are ignored. Even in the more practical case when the flux saturation, leakage and fringing effects are considered, the two stiffnesses can be considered to have the same frequency response characteristics within the 3 dB bandwidth without introducing much error. The open-loop frequency response of the two stiffnesses derived from the analytical model and the FE model agrees well with the experimental results.