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

Abstract

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...

Mixed-variable optimal design of induction motors including efficiency, noise and thermal criteria

“…which either maximize or minimize one of the objectives. As predicted Le Besnerais et al (2006Besnerais et al ( , 2008d, best noise objectives are reached with large air- gaps, high heights of yoke, and small stator and rotor slot openings. The stator core diameter has small influence on noise because the total diameter of the machine, including frame, is fixed during the optimization.…”

“…Natural frequencies f m are computed assimilating the stator as a 2D ring. Natural frequencies computation has been validated with FEM and experiments (Hubert 2000;Le Besnerais et al 2007b, 2008d.…”

“…The acoustic model was favourably compared to noise measurements made on a water-cooled induction machine (Ait-Hammouda et al 2006). More details about this analytical model and its validations can be found in Le Besnerais (2008), Le Besnerais et al (2008aBesnerais et al ( , 2008cBesnerais et al ( , 2008d.…”

“…Indeed, many trade-offs have to be made: for example, a smaller air-gap improves the efficiency, but increases the magnetic sound power level; increasing the stator height of yoke to diameter ratio generally lowers magnetic vibrations (Le Besnerais et al 2008d), but it heightens material cost, and with a fixed motor size, it decreases the available output torque and highers rotor temperature (Amor et al 1995). Nevertheless, dealing with both noise and thermal criteria in an induction motor optimal design process has never been done.…”

Multi-objective optimization of the induction machine with minimization of audible electromagnetic noise

“…More details about these electromagnetic, mechanical and acoustic models and their validation can be found in [14,18].…”