An Acoustic Model for a Permanent Magnet Machine: Modal Shapes and Magnetic Forces

The magnetic field inside a machine is to a large extent responsible for the mechanical excitation of the stator structure, generating vibrations and thus, audible noise. The current numerical techniques allow an easy calculation of the magnetic field. Unfortunately, the step to the mechanical excitation of the stator is difficult to make, because of the numerical errors occurring when calculating the forces acting on its inner surface. In this paper, it is shown that this problem can be overcome by using the concept of modal analysis. Using a modal base, the stators vibrational behavior can be described. This is under the assumption that the user knows the modal parameters of the machine. Apart from the analytical study, a practical finite element formulation for the calculation of the generalized force is derived. Only the most important part of the generalized force is considered. It is proven that this part can be found by calculating the elementary flux linkages in the stator coils.