Fast Approximate Calculation of the Radial and Tilt Stiffness of Magnetic Bearings Using Magnetostatic 2D Finite Element Analysis

In order to calculate the dynamic behavior of magnetically levitated rotors (eigenfrequencies, rotor deflections…), the knowledge of the radial and tilt stiffness of the active and passive magnetic bearings is necessary. An optimization of the stability against external disturbances and internal excitations (unbalance, magnetic tolerances) requires a large number of calculations of these magnetic bearing parts. Therefore, a short calculation time of the reluctance forces is crucial. As an original rotational symmetry is lost in case of a radially deflected or tilted rotor, the tilt stiffness and the radial stiffness of magnetic bearing parts are usually calculated with a 3D-FE software. These time-consuming calculations prevent fast optimizations of the rotor dynamics. This paper shows a method for the approximate calculation of the radial and tilt stiffness of rotationally symmetric magnetostatic problems by using a 2D-FE program. The accuracy of the approximation method will be verified by comparing the results with the exact analytical solution of a pure permanent magnetic configuration.