Analytical study of air-gap surface force – application to electrical machines

Abstract

The Maxwell stress tensor (MST) method is commonly used to accurately compute the global efforts, such as electromagnetic torque ripple and unbalanced electromagnetic forces in electrical machines. The MST has been extended to the estimation of local magnetic surface force for the vibroacoustic design of electrical machines under electromagnetic excitation. In particular, one common air-gap surface force (AGSF) method based on MST is to compute magnetic surface forces on a cylindrical shell in the air gap. However, the AGSF distribution depends on the radius of the cylindrical shell. The main contribution of this study is to demonstrate an analytic transfer law of the AGSF between the air gap and the stator bore radius. It allows us to quantify the error between the magnetic surface force calculated in the middle of the air gap and the magnetic force computed on the stator teeth. This study shows the strong influence of the transfer law on the computed tangential surface force distribution through numerical applications with induction and synchronous electrical machines. Finally, the surface force density at stator bore radius is more accurately estimated when applying the new transfer law on the AGSF.

Stochastic assessment of electric powertrain whining noise under early-stage design uncertainties

“…Also, under magnetostatic assumption, eddy current and temperature dependent effects are not considered. The radial and tangential Maxwell pressure, also referred to as the Airgap Surface Force (AGSF) in N/m 2 applying on the stator core along the airgap δ, are given by ( [33,34]):…”

“…The EM-domain is validated by comparing the average EM torque (see, see [34] for more details on EM torque computation using Maxwell Stress Tensor method) from the simulated data using Pyleecan and the measured data used in the reference article by Yang et al [48], in which the measurement was done on the same e-machine configuration as used in this study (refer to the nominal parameters in Tab. ( 2)).…”

Noise in Electric Motors: A Comprehensive Review

“…According to [72], the magnetic field is poorly defined at the corner of the teeth because it comes off at an angle. Numerical errors increase near a discontinuity in the magnetic permeability, such as at the tip of the teeth when using analytical calculations.…”

Damper Winding for Noise and Vibration Reduction of a Permanent Magnet Synchronous Machine

“…The interaction between the magnetic field of permanent magnets and the stator winding creates forces in the air gap. With the Maxwell stress tensor approach, the articles [ 40 , 41 ] explain how to deduce and simplify the expression of Maxwell forces in the air gap, considering several hypotheses. In fact, the noise and vibrations are mainly related to the radial magnetic pressure in the air gap [ 36 ].…”