Theoretical and Experimental Investigation of Force Estimation Errors Using Active Magnetic Bearings with Embedded Hall Sensors

This paper gives an original theoretical and experimental contribution to the issue of reducing force estimation errors,
which arise when applying Active Magnetic Bearings (AMBs) with pole embedded Hall sensors for force quantification purposes. Motivated by the prospect of increasing the usability of AMBs by embedding Hall sensors instead of mounting these directly on the pole surfaces, force estimation errors are investigated both numerically and experimentally. A linearized version of the conventionally applied quadratic correspondence between measured Hall voltage and applied AMB force is suggested and investigated. A finite element (FE) model is constructed to study force error behavior as a function of rotor offset. The investigation confirms that the magnitude of the force error is dependent on how well the rotor is centered in the AMB. Furthermore, below a rotor offset corresponding to ∼ 20% of the nominal air gap the force estimation error is found to be reduced by the linearized force equation as compared to the quadratic force equation,
which is supported by experimental results. Additionally the FE model is employed in a comparative study of the force estimation error behavior for pole embedded and pole surface mounted Hall sensors. It is shown that in a given range of bias currents and rotor offsets, pole embedded and surface mounted Hall sensors perform equally well for the four pole heteropolar flux-split radial AMB under investigation. Furthermore, frequency dependence of the Hall sensor sensitivity factors is investigated, and found to be non-existing, hence static calibration of Hall sensors is sufficient, even for dynamic testing purposes.