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Numerical modeling of a MEMS actuator considering several magnetic force calculation methods

Thomas Preisner (Research Engineer and Teaching Assistant in the Institute of Electromagnetic Theory at the Leibniz University of Hannover)
Christian Bolzmacher (Research laboratories of European aeronautic defence and space company (EADS) Deutschland GmbH in Ottobrunn/Munich, Germany)
Andreas Gerber (Center of Advanced European Studies and Research (CAESAR) in Bonn, Germany)
Karin Bauer (Charge of the micro technology team in the central research entity of the European Aeronautic Defence and Space Company (EADS))
Eckhard Quandt (Full Professor and holds the Chair for Inorganic Functional Materials within the Institute for Materials Science at the Faculty of Engineering)
Wolfgang Mathis (Full Professor at the Leibniz University of Hannover)



The purpose of this paper is to investigate the accuracy of different force calculation methods and their impact on mechanical deformations. For this purpose, a micrometer scaled actuator is considered, which consists of a micro‐coil and of a permanent magnet (PM) embedded in a deformable elastomeric layer.


For the magnetic field evaluation a hybrid numerical approach (finite element method/boundary element method (FEM/BEM) coupling and a FEM/BEM/Biot‐Savart approach) is used, whereas FEM is implemented for the mechanical deformation analysis. Furthermore, for the magneto‐mechanical coupling several force calculation methods, namely the Maxwell stress tensor, the virtual work approach and the equivalent magnetic sources methods, are considered and compared to each other and to laboratory measurements.


The numerically evaluated magnetic forces and the measured ones are in good accordance with each other with respect to the normal force acting on the PM. Nevertheless, depending on the used method the tangential force components differ from each other, which leads to slightly different mechanical deformations.

Research limitations/implications

Since the force calculations are compared to measurement data, it is possible to give a suggestion about their applicability. The mechanical behavior of the actuator due to the acting forces is solely calculated and therefore only an assumption concerning the deformation can be given.


A new kind of micrometer scaled actuator is numerically investigated by using two different hybrid approaches for the magnetic field evaluation. Based on those, the results of several force calculation methods are compared to measurement data. Furthermore, a subsequent structural analysis is performed, which shows slightly different mechanical deformations depending on the used force calculation method.



Preisner, T., Bolzmacher, C., Gerber, A., Bauer, K., Quandt, E. and Mathis, W. (2011), "Numerical modeling of a MEMS actuator considering several magnetic force calculation methods", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 4, pp. 1176-1188.



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