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The aim of this paper is to use an analytical multi‐physical model – electromagnetic, mechanic and acoustic – in order to predict the electromagnetic noise of a permanent magnet synchronous machine.

The aim of this work is to develop and use an analytical multi‐physical model – electromagnetic, mechanic and acoustic – of a synchronous machine with permanent magnets. The complete model is coded in order to predict acoustic noise. A study of sensitivity is presented in order to deduce the influential – or significant – factors on the noise. For that, the technique of the experimental designs is used. More particularly, the modeling of the noise will be achieved due to the new “trellis” designs.

Three models are presented: electromagnetic, mechanical of vibration and acoustic. For each of them, comparisons with finite element method and experiments have been made. Several response surfaces are given; they represent the noise according to influential factors, with respect to different speeds of the machine. These surfaces are useful to deduce the parts of the design space to avoid.

Different multi‐physical aspects are considered: electromagnetic, mechanic and acoustic phenomena are taken into account due to a single analytical model. The experimental design method is the privileged tool used to make the complex relationships between the main variables appear.

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.

The analytical research does not consider saturation and eccentricity harmonics which can play a significant role in noise radiation.

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.

The first purpose of this paper is to identify – by an inverse problem – the unknown material characteristics in a permanent magnet synchronous machine in order to obtain a numerical model that is a realistic representation of the machine. The second purpose is to optimize the machine geometrically – using the accurate numerical model – for a maximal torque to losses ratio. Using the optimized geometry, a new machine can be manufactured that is more efficient than the original.

A 2D finite element model of the machine is built, using a nonlinear material characteristic that contains three parameters. The parameters are identified by an inverse problem, starting from torque measurements. The validation is based on local BH‐measurements on the stator iron.

Geometrical parameters of the motor are optimized at small load (low‐stator currents) and at full load (high‐stator currents). If the optimization is carried out for a small load, the stator teeth are chosen wider in order to reduce iron loss. An optimization at full load results in a larger copper section so that the copper loss is reduced.

The identification of the material parameters is influenced by the tolerance on the air gap – shown by a sensitivity analysis in the paper – and by 3D effects, which are not taken into account in the 2D model.

The identification of the material parameters guarantees that the numerical model describes the real material properties in the machine, which may be different from the properties given by the manufacturer because of mechanical stress and material degradation.

The optimization is more accurate because the material properties, used in the numerical model, are determined by the solution of an inverse problem that uses measurements on the machine.