Electromagnetically-excited acoustic noise and vibration

Electromagnetically-excited acoustic noise describe audible sound directly produced by materials vibrating under the excitation of electromagnetic forces. Some examples of electromagnetically-excited acoustic noise include the hum of transformers or the whine of some rotating electric machines. The hissing of high voltage transmission lines is due to corona discharge, not magnetism.

The phenomenon is also called audible magnetic noise[1], electromagnetic acoustic noise or electromagnetically-induced acoustic noise [2], more rarely electrical noise [3], or coil noise depending on the application. The term electromagnetic noise is generally avoided as the term is used in the field of electromagnetic compatibility, dealing with radio frequencies. The term electrical noise describes electrical perturbations occurring in electronic circuits, not sound. The terms electromagnetic vibrations [4] or magnetic vibrations [5] focusing on the structural phenomenon are less ambiguous.

Acoustic noise and vibrations due to electromagnetic forces can be seen as the reciprocal of microphonics, which describes how a mechanical vibration or acoustic noise can induce an undesired electrical perturbation.

General explanation

Electromagnetic forces can be defined as forces arising from the presence of an electromagnetic field (electrical field only, magnetic field only, or both).

Electromagnetic forces in the presence of a magnetic field include equivalent forces due to Maxwell stress tensor, magnetostriction and Lorentz force (also called Laplace force)[6]. Maxwell forces, also called reluctances forces, are concentrated at the interface of high magnetic reluctivity changes, e.g. between air and a ferromagnetic material in electric machines ; they are also responsible of the attraction or repulsion of two magnets facing each other. Magnetostriction forces are concentrated inside the ferromagnetic material itself. Lorentz or Laplace forces act on conductors plunged in an external magnetic field.

Electromagnetic forces due to the presence of an electrical field are more precisely named electrostatic forces.

All these forces can potentially generate vibrations of the ferromagnetic, conductive parts, windings and permanent magnets of electrical, magnetic and electromechanical device, resulting in an audible sound if the frequency of vibrations is below 20 kHz and if the sound level is high enough to be heard (e.g. large surface of radiation and large vibration levels).

Electromagnetic noise and vibrations in electric machines

Electromagnetic torque, which can be calculated as the average value of the Maxwell stress tensor along the airgap, is one consequence of electromagnetic forces in electric machines. As a static force, it does not create vibrations nor acoustic noise. However torque ripple (also called cogging torque for permanent magnet synchronous machines in open circuit), which represents the harmonic variations of electromagnetic torque, is a dynamic force creating torsional vibrations of both rotor and stator. The torsional deflection of a simple cylinder cannot radiate efficiently acoustic noise, but with particular boundary conditions the stator can radiate acoustic noise under torque ripple excitation [7]. Structure-borne noise can also be generated by torque ripple when rotor shaft line vibrations propagate to the frame [8].

Some tangential magnetic force harmonics can directly create magnetic vibrations and acoustic noise when applied to the stator teeth: tangential forces create a bending moment of the stator teeth, resulting in radial vibrations of the yoke [9].

Besides tangential force harmonics, Maxwell stress also includes radial force harmonics responsible for radial vibrations of the yoke, which in turn can radiate acoustic noise.

Electromagnetic noise and vibrations in passive components

Inductors

In inductors, also called reactors or chokes, acoustic noise is generally due to Maxwell forces [10]

Transformers

In transformers magnetic noise and vibrations are generated by several phenomena depending on the load case which include Laplace force on the windings, Maxwell forces in the joints of the laminations, and magnetostriction inside the laminated core.

Capacitors

Capacitors are also subject to large electrostatic forces. When the capacitor voltage/current waveform is not constant and contains time harmonics, some harmonic electric forces appear and acoustic noise can be generated.[11] This phenomenon is known as the "singing capacitor" effect.

Resonance effect in electrical machines

When the exciting electromagnetic force frequency matches a natural frequency of the vibrating body, a resonance can occur. This resonance can be observed in rotating machines as well as in passive components, such as inductors or capacitors.

In radial flux rotating electric machines, the resonance occurs at two conditions: there must be a match between the exciting Maxwell force and the stator or rotor natural frequency, and between the stator or rotor modal shape and the exciting Maxwell harmonic wavenumber (periodicity of the force along the airgap)[12]

Example of modal shape number 2 of a stator
Example of a rotating magnetic force of wavenumber 2
Illustration of the match between electromagnetic excitation (blue) and modal shape (red) at resonance

As an example a resonance with the elliptical modal shape of the stator can occur if the force wavenumber is 2. Under resonance conditions, the maxima of the electromagnetic excitation along the airgap and the maxima of the modal shape displacement are in phase.

Numerical simulation

The simulation of electromagneticallty-induced noise and vibrations is a multiphysic modeling process carried in three steps:

It is generally considered as a weakly coupled problem: the deformation of the structure under electromagnetic forces is assumed not to change the electromagnetic field distribution and resulting the magnetic stress.

The assessment of audible magnetic noise in electrical machines can be done using three methods:

Examples of device subject to magnetic noise and vibrations

A varying electromagnetic force can be produced either by a moving source of DC magnetic field (e.g. rotating permanent magnet or rotating coil supplied with DC current), or by a steady source of AC magnetic field (e.g. a coil fed by a variable current).

Static device

Static device include electrical systems used in electric power storage or power conversion such as

Rotating device

Rotating device include radial and axial flux rotating electric machines used for electrical to mechanical power conversion such as

In such device, dynamic electromagnetic forces come from variations of magnetic field, which either comes from a steady AC winding or a rotating DC field source (permanent magnet or DC winding).

Sources of magnetic noise and vibrations in electric machines

The harmonic electromagnetic forces responsible for acoustic noise and vibrations can come from

Reduction of magnetic noise and vibrations in electric machines

Some common noise reduction techniques include

Experimental illustrations

Forced vibration by a rotating permanent magnet

This animation illustrates how a ferromagnetic sheet can be deformed due to the magnetic field of a rotating magnet. It corresponds to an ideal one pole pair permanent magnet synchronous machine with a slotless stator.

Deflection of a ferromagnetic cylinder due to a rotating permanent magnet excitation field

Acoustic resonance by a variable frequency coil

The resonance effect of magnetic vibration with a structural mode can be illustrated using a tuning fork made of iron. A prong of the tuning fork is wound with a coil fed by a variable frequency power supply. A variable flux density circulates between the two prongs and some dynamic magnetic forces appear between the two prongs at twice the supply frequency. When the exciting force frequency matches the fundamental mode of the tuning fork close to 400 Hz, a strong acoustic resonance occurs.

Set-up of the electromagnetically-excited tuning fork

References

  1. ↑ Le Besnerais, J., Lanfranchi, V., Hecquet, M., & Brochet, P. (2010). Characterization and Reduction of Audible Magnetic Noise Due to PWM Supply in Induction Machines. IEEE Transactions on Industrial Electronics. http://doi.org/10.1109/tie.2009.2029529
  2. ↑ van der Giet, M., (2011). Analysis of electromagnetic acoustic noise excitations - a contribution to low-noise design and to the auralization of electrical machines, RWTH Aachen University, Shaker Verlag.
  3. ↑ Finley, W. R., Hodowanec, M. M., & Holter, W. G. (1999). An Analytical Approach to Solving Motor Vibration Problems, 36(5), 1–16.
  4. ↑ Carmeli, M. S., Castelli Dezza, F., & Mauri, M. (2006). Electromagnetic vibration and noise analysis of an external rotor permanent magnet motor. International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM) , 1028–1033. http://doi.org/10.1109/SPEEDAM.2006.1649919
  5. ↑ Le Besnerais, J. (2015). Effect of lamination asymmetries on magnetic vibrations and acoustic noise in synchronous machines. In 2015 18th International Conference on Electrical Machines and Systems (ICEMS). http://doi.org/10.1109/icems.2015.7385319
  6. ↑ Belahcen, A. (2004). Magnetoelasticity, magnetic forces and magnetostriction in electrical machines. PhD thesis, Helsinki University of Technology, Finland.
  7. ↑ Tan Kim A. (2013). Contribution à l’étude du bruit acoustique d’origine magnétique en vue de la conception optimale de machines synchrones à griffes pour application automobile. PhD thesis, Université de Technologie de Compiègne, France.
  8. ↑ De Madinabeitia I. G, (2016). Analysis of force and torque harmonics spectrum in an induction machine for automotive NVH Purposes. Master's thesis, University of Technology of Chalmers, Sweden.
  9. ↑ Devillers E., Le Besnerais J., Regniez M. and Hecquet M., (2017). Tangential effects on magnetic vibrations of induction machines using subdomain method and electromagnetic vibration synthesis, Proceedings of IEMDC 2017 Conference, Miami, USA.
  10. ↑ Rossi, M., & Le Besnerais, J. (n.d.). Vibration Reduction of Inductors under Magnetostrictive and Maxwell Forces Excitation. IEEE Transactions on Magnetics, (99), 1–7.
  11. ↑ M. Hurkala, Noise analysis of high voltage capacitors and dry-type air-core reactors. Doctoral dissertation, Aalto University, Finland, 2013
  12. ↑ Le Besnerais, J. (2008). Reduction of magnetic noise in PWM-supplied induction machines − low-noise design rules and multi-objective optimization. PhD Thesis, Ecole Centrale de Lille, Lille, France.
  13. ↑ "Flux software official website".
  14. ↑ "Jmag software official website".
  15. ↑ "Maxwell software official website".
  16. ↑ "Opera software official website".
  17. ↑ "Comsol software official website".
  18. ↑ "Ansys software official website".
  19. ↑ "Manatee software official website".
  20. ↑ Rossi, M., & Le Besnerais, J. (n.d.). Vibration Reduction of Inductors under Magnetostrictive and Maxwell Forces Excitation. IEEE Transactions on Magnetics, (99), 1–7.
  21. ↑ Weiser, B., Pfützner, H., & Anger, J. (2000). Relevance of Magnetostriction and Forces for the Generation of Audible Noise of Transformer Cores, 36(5), 3759–3777.
  22. ↑ Le Besnerais, J. (2008). Reduction of magnetic noise in PWM-supplied induction machines − low-noise design rules and multi-objective optimization. PhD Thesis, Ecole Centrale de Lille, Lille, France.
  23. ↑ Le Besnerais, J., Lanfranchi, V., Hecquet, M., & Brochet, P. (2010). Characterization and Reduction of Audible Magnetic Noise Due to PWM Supply in Induction Machines. IEEE Transactions on Industrial Electronics. http://doi.org/10.1109/tie.2009.2029529
  24. ↑ Le Besnerais, J., Lanfranchi, V., Hecquet, M., & Brochet, P. (2009). Optimal Slot Numbers for Magnetic Noise Reduction in Variable-Speed Induction Motors. IEEE Transactions on Magnetics. http://doi.org/10.1109/tmag.2009.2020736
  25. ↑ Verez, G., Barakat, G., Amara, Y., Bennouna, O., & Hoblos, G. (n.d.). Impact of Pole and Slot Combination on Noise and Vibrations of Flux-Switching PM Machines, (1).
  26. ↑ Zhu, Z. Q., Xia, Z. P., Wu, L. J., & Jewell, G. W. (2009). Influence of slot and pole number combination on radial force and vibration modes in fractional slot PM brushless machines having single- and double-layer windings. 2009 IEEE Energy Conversion Congress and Exposition, ECCE 2009, 3443–3450. http://doi.org/10.1109/ECCE.2009.5316553
  27. ↑ Le Besnerais, J., Lanfranchi, V., Hecquet, M., Lemaire, G., Augis, E., & Brochet, P. (2009). Characterization and Reduction of Magnetic Noise Due to Saturation in Induction Machines. IEEE Transactions on Magnetics. http://doi.org/10.1109/tmag.2008.2012112
  28. ↑ Torregrossa, D., Khoobroo, A., & Fahimi, B. (2012). Prediction of acoustic noise and torque pulsation in PM synchronous machines with static eccentricity and partial demagnetization using field reconstruction method. IEEE Transactions on Industrial Electronics, 59(2), 934–944. http://doi.org/10.1109/TIE.2011.2151810
  29. ↑ Le Besnerais, J. (2015). Effect of lamination asymmetries on magnetic vibrations and acoustic noise in synchronous machines. In 2015 18th International Conference on Electrical Machines and Systems (ICEMS). http://doi.org/10.1109/icems.2015.7385319
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