[PhD Thesis] Numerical Methods Applied to the Computation of Electromagnetic Vibrations: Magnetic Force Projection and Model Reduction

AuthorRaphaël Pile
DateJanuary 20, 2021
KeywordsElectrical machines, Electromagnetic noise, Machines vibrations, Magnetic Force, Maxwell Stress, Virtual Work Principle, Magneto-mechanical coupling.


The presence of electromagnetic force harmonics in electrical machines is generally a source of acoustic noise and vibration (e-NVH). This phenomenon must be considered at early design stage to comply with acoustic and vibration standards, particularly in the automotive sector. The eNVH level is obtained from multi-physical simulations based on electromagnetic, mechanical and acoustic models. This industrial PhD thesis takes part in the internal research program of EOMYS ENGINEERING. This company develops and commercializes Manatee software, dedicated to the e-NVH simulation of electrical machines. In this modeling context, this thesis focuses on numerical methods for the calculation of electromagnetic forces as well as magneto-mechanical weak coupling. The validity of the air-gap forces based on Maxwell Stress Tensor (MST) method, as well as the mechanical modulation effect have been studied. In particular, this work focuses on the validity of one load vector per tooth tip to achieve the magneto-mechanical coupling. A test bench based on a Permanent Magnet Synchronous Machine (SPMSM) with 12 slots and 10 poles was characterized in order to compare different models for eNVH simulations. This PhD work contains several contributions. The first result proposes an analytical equation to improve air-gap force accuracy. The second result discusses how to reduce accurately the magneto-mechanical model by using normalized simulation and modulation effect. The third result deals with a complementary experimental protocol to mechanical finite element analysis. The interest of the method is demonstrated in a hybrid magneto-mechanical simulation. The last result highlights the contribution of the tooth tip bending moments to magnetic vibrations.

Manuscript and presentation

The manuscript is available here (in English):

The presentation is available here (in French):