End-winding vibrations caused by steady-state magnetic forces in an induction machine

We conducted a 3-D electromagnetic analysis coupled with a 3-D mechanical analysis to analyze end-winding vibrations and deformation in an induction machine caused by steady-state magnetic forces on the end winding. Both the analyses were based on the finite-element method. The electromagnetic analysis was used to calculate magnetic forces. During the mechanical analysis, complex support structures in the end region were simplified. We first updated and validated the mechanical model according to a modal model obtained from a modal test, and afterward analyzed deformation, vibrations, and stresses. According to the analysis, the shape of the rotary dynamic deformation of the end winding caused by dynamic forces is similar to the most excitable mode shape though the natural frequency of that mode is much higher than the excitation frequency. The static deformation caused by static forces tends to expand the coil ends outward. Under both types of deformation, the nose portion of the coil ends experiences larger displacement, but von Mises stresses are larger mainly in the knuckle portion.