Magnetoelasticity, magnetic forces and magnetostriction in electrical machines

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Doctoral thesis (monograph)
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Report / Helsinki University of Technology, Department of Electrical and Communications Engineering, Laboratory of Electromechanics, 72
This thesis deals with the computation of magnetic and magnetostrictive forces, as well as with the magnetoelastic coupling in rotating electrical machines. Magnetoelasticity means here the interaction between the magnetic and elastic fields in the iron parts of a machine. Magnetostriction is the phenomenon by which an iron part changes its dimensions under the effect of a magnetic field. The equations for magnetoelastic coupling are derived within the finite element time stepping analysis of rotating electrical machines. The elastic part of these equations is implemented into an existing program that handles the magnetic and circuit equations. Formulas for the calculation of magnetic and magnetostrictive forces are also derived. The implemented method is used to compute the vibrations of the stator core of rotating electrical machines under the effect of magnetic and magnetostrictive forces. The effect of coupling between the magnetic and elastic fields is also computed for these machines. Moreover, the effects of structural damping and of different approaches (quasi-static, dynamic, coupled and uncoupled) are illustrated. The magnetostriction, as well as the magnetisation of electrical steel sheets, is measured within this work. The measurements are carried out using a modified version of the standard Epstein frame. The data obtained show a strong dependence on the applied mechanical stress. These results can be used not only in simulation but also for the determination of magnetoelastic coupling coefficients in some models of magnetoelasticity using coupled constitutive equations. It is noticed that the quasi-static elastic approach is not accurate enough for the calculation of vibrations in these machines. The structural damping plays an important role in determining the amplitude of vibrations; however, within realistic values of damping, these vibrations are almost the same. The magnetostriction damps the vibrations at some frequencies and increases them at others. The velocities of vibrations at some frequencies are found to be 8 to 9 times larger when the magnetostriction is taken into account. The magnetoelastic coupling between the displacement and the magnetic fields in the stator core of electrical machines increases the amplitudes of vibrations by about 17 % at some frequencies for the large machine, while its effect on the vibrations of the small stator is less than 0.5 %.
magnetic force, magnetostriction, electrical machine, finite element analysis, vibration, magnetoelastic coupling
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