Chapter2 Effects of Magneto-Mechanical Coupling on Structural Modal Parameters M. Kirschneck, D.J. Rixen, Henk Polinder, and Ron van Ostayen Abstract Structures that are exposed to a magnetic field experience magnetic forces. As these forces are geometry dependent they vary with the displacement of the structure that can result in an additional stiffness. Furthermore eddy currents induced by the movement of the structure can lead to an increased dissipation resulting in a higher damping value for the mechanical part of the system. This paper introduces calculation techniques for predicting these effects and validates them with measurements done on a simple set up in the lab. Keywords Modal parameter identification • Magneto-mechanical coupling • Monolithic eigenvalue problem 2.1 Introduction All ferro-magnetic objects, that are exposed to a magnetic field, experiences local forces. For an object at rest in a magnetic field these local forces cancel each other out and the net force on the object is zero. But when the magnetic field is such that the local forces do not balance each other out the object experiences a net force. In such a case the magnetic force has an effect on the mechanics of the system. At the same time the change of geometry due to movement will affect the magnetic field. These kind of systems are called two way magneto-mechanically coupled systems. In such as system the dynamical behavior of can be altered compared to its behavior without that coupling. This also has an impact on the modal parameters that the system displays under no coupling conditions. Certain configurations and geometries contribute to the impact of the effect of the magneto-mechanical coupling. In this paper such a system is introduced and it is shown how the change on modal parameters can be simulated and predicted. There has been extensive research on magneto-mechanical systems. In fact many transducer that transforms electric energy to mechanic energy or the other way around, i.e. electric machines, are magneto-mechanical coupled systems. Therefore the research on magneto-mechanical coupled systems began by the discovery of forces due to electric currents and their mentioning by Maxwell [7]. In light weight structures the opposing aims of making a structure as stiff as possible and as light as possible is commonly found. For these kind of structures that are exposed to magnetic fields, the exact knowledge of the dynamics of the structure might be crucial. The knowledge might allow to reduce the weight of the structure further. The same is true for electric machines that operate in places where weight reduction is essential. The rotors and stators of these machines are exposed to magnetic fields while being required to be as stiff and as light as possible. Applications can be found in electric cars or large off-shore direct-drive wind turbines. M. Kirschneck ( ) • R. van Ostayen Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands e-mail: m.kirschneck@tudelft.nl D.J. Rixen Faculty of Mechanical Engineering, Technical University of Munich, Boltzmannstr. 15, 85748 München, Germany H. Polinder Faculty of Electrical Engineering Mathematics and Computer Science, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands R. Allemang (ed.), Topics in Modal Analysis II, Volume 8: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04774-4__2, © The Society for Experimental Mechanics, Inc. 2014 11
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