Acoustic noise of electromagnetic origin in a fractional‐slot induction machine

Jean Le Besnerais (L2EP – Ecole Centrale de Lille, Villeneuve d'Ascq, France)
Vincent Lanfranchi (LEC – UTC, Compiègne, France)
Michel Hecquet (L2EP – Ecole Centrale de Lille, Villeneuve d'Ascq, France)
Pascal Brochet (L2EP – Ecole Centrale de Lille, Villeneuve d'Ascq, France)
Guy Friedrich (LEC – UTC, Compiègne, France)



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.


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.


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.


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.



Le Besnerais, J., Lanfranchi, V., Hecquet, M., Brochet, P. and Friedrich, G. (2008), "Acoustic noise of electromagnetic origin in a fractional‐slot induction machine", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 5, pp. 1033-1052.

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