[EVER] Analysis of radial force harmonics in PMSM responsible for electromagnetic noise

AuthorsPatricio La Delfa ; Michel Hecquet; Fréderic Gillon ; Jean Le Besnerais
StatusPublished in: Ecological Vehicles and Renewable Energies (EVER), 2015 Tenth International Conference
Date31 March-2 April 2015
KeywordsMaxwell forces, air gap radial pressure- space order frequency, finite element analysis, analytical tool, convolution analysis, magnetic noise


This paper presents an analysis of the air gap radial Maxwell forces in some three-phase, inner rotor Concentrated Winding surface Permanent Magnet Synchronous Machine (CW-PMSM). Two modular winding machines and one asymmetric, winding machine are considered and simulated by a Finite Element method (FE). The air gap Maxwell pressure results from multiplication of the flux density harmonics due to magnetomotive forces and permeance linked to the magnet, to the armature, to the stator slots and their interactions. An analytical prediction tool, (Analytical Calculation of Harmonic Force Orders -ACHFO) calculates the space and time orders of theses magnetic force harmonics while identifying their origin in terms of, interactions between magnet, armature and teeth effects. Additionally, an experimental Operational Deflection Shape measurement (ODS) is realised, for one modular machine prototype, to validate the electromagnetic model results. Finally the analytical prediction of ACHFO is compared with another method to obtain the origin of low orders radial pressure based on radial flux density convolution combination approach.

Preprint and full paper

The full paper can be found on IEEE.


A generalization of “ACHFO” tool is available in MANATEE software to automatically rank and identify permeance, mmf, flux density harmonic combination leading to a given force, vibration, and acoustic noise harmonic depending on load conditions (open circuit, partial load) and electric machine topology.

Some examples can be found in the article dedicated to noise mitigation tools in electrical machines.