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.
The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the frame stiffness influence ͑FSI͒, based on porous material properties. The critical values of FSI under which the limp model can be used are determined using a one-dimensional analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used for configurations that include vibrating plates.
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...
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