This paper derives the analytical characterization of Maxwell radial vibrations due to Pulse-Width Modulation (PWM) supply in induction machines, and especially in traction motors supplied with an asynchronous switching frequency. The number of nodes and the velocity of these particular force waves are experimentally validated by visualizing some operational deflection shapes of the stator. It is shown that according to the switching frequency, these forces can be responsible for high magnetic noise levels during starting and braking. A simple rule to avoid PWM noise is then proposed, and applied to an industrial traction motor. Experimental results show that the choice of the switching frequency can have a 15 dB impact on the sound power level emitted by the motor during starting, and that a lower switching frequency can sometimes lead to lower magnetic noise. In agreement with analytical predictions, the new proposed switching frequency that avoids resonances between PWM exciting forces and corresponding stator modes reduces magnetic noise of 5 dB during starting.

Purpose -The purpose of this paper is to apply a fast analytical model of the acoustic behaviour of pulse-width modulation (PWM) controlled induction machines to a fractional-slot winding machine, and to analytically clarify the interaction between space harmonics and time harmonics in audible electromagnetic noise spectrum. Design/methodology/approach -A multilayer single-phase equivalent circuit calculates the stator and rotor currents. Air-gap radial flux density, which is supposed to be the only source of acoustic noise, is then computed with winding functions formalism. Mechanical and acoustic models are based on a 2D ring stator model. A method to analytically derive the orders and frequencies of most important vibration lines is detailed. The results are totally independent of the supply strategy and winding type of the machine. Some variable-speed simulations and tests are run on a 700 W fractional-slot induction machine in sinusoidal case as a first validation of theoretical results. Findings -The influence of both winding space harmonics and PWM time harmonics on noise spectrum is exposed. Most dangerous orders and frequencies expressions are demonstrated in sinusoidal and PWM cases. For traditional integral windings, it is shown that vibration orders are necessarily even. When the stator slot number is not even, which is the case for fractional windings, some odd order deflections appear: the radial electromagnetic power can therefore dissipate as vibrations through all stator deformation modes, leading to a potentially lower noise level at resonance.Research limitations/implications -The analytical research does not consider saturation and eccentricity harmonics which can play a significant role in noise radiation. Practical implications -The analytical model and theoretical results presented help in designing low-noise induction machines, and diagnosing noise or vibration problems. Originality/value -The paper details a fully analytical acoustic and electromagnetic model of a PWM fed induction machine, and demonstrate the theoretical expression of main noise spectrum lines combining both time and space harmonics. For the first time, a direct comparison between simulated and experimental vibration spectra is made. NomenclatureElectrical notations f s ¼ fundamental stator supply frequency f r mn ¼ rotor current harmonic frequency linked to the n-th stator current time harmonic and m-th stator mmf space harmonic f s n ¼ stator current n-th time harmonic f mm ¼ magnetomotive force f R ¼ mechanical rotation frequency ð f R ¼ ð1 2 sÞf s =pÞ F r , F s ¼ rotor and stator mmf waves g ¼ air-gap width h r , h s ¼ integers involved in rotor and stator mmf space harmonics expression i r b ¼ b-th rotor bar current i s q ¼ q-th stator phase current k r , k s ¼ integers involved in rotor and stator slotting terms in permeance Fourier series l sd ¼ stator tooth width l se ¼ stator slot opening width l rd ¼ rotor tooth width l re ¼ rotor slot opening width L n ¼ force line number n m ¼ m-th space harmonic due to stato...

This paper reviews the recent developments of semi-analytical subdomains modeling techniques to compute the flux density distribution in electrical machines by the exact solving of Maxwell equations. It is shown that with an appropriate development methodology and numerical implementation, these harmonic models break the traditional compromise between accuracy and computation time that must be done using finite element or other analytical methods. Besides that, subdomains model development techniques have been improved to overcome its topological limitations This fact is demonstrated on three different subdomains models in comparison with finite element methods in terms of accuracy and processing time. The first one is a subdomains model of a surface permanent-magnet synchronous machine, the second one is for an inset permanentmagnet synchronous machine, and the third one is for a squirrelcage induction machine. Thanks to an efficient implementation method, a very low computation time is obtained. The robustness of the subdomains on the geometrical assumptions is also demonstrated.

This paper presents the full analysis of the vibration behaviour responsible for audible magnetic noise in a PWM-fed fractional-slot induction machine, including theoretical predictions, numerical simulations, and experimental validations (stator modal analysis and deflection shapes visualisation). Magnetic force waves due to slotting harmonics, pulse-width modulation (PWM) harmonics and their interactions are characterised in terms of nodes number, rotation speed, and propagation direction. It is shown in particular that some odd spatial order vibration waves appear due to fractional slotting, and that some combinations between slotting lines and PWM lines can be very noisy due to an elliptical mode natural frequency close from the switching frequency.