Effect of magnetic wedges on electromagneticallyinduced acoustic noise and vibrations of electrical machines J. Le Besnerais, Q. Souron Φ Abstract This article studies the effect of stator magnetic wedges on the electromagnetically-induced acoustic noise and vibration of a squirrel cage induction machine. Firstly, a review of previous studies analysing the effects of magnetic wedges both on electromagnetics and vibro-acoustic domain is done. Then, simulations are performed with MANATEE software to quantify the reduction of noise and vibrations due to Maxwell forces with the use of magnetic wedges in a squirrel cage induction machine presenting a strong resonance due to slotting effect. A sensitivity study is carried on the magnetic permeability of the wedge and it is shown that the maximum sound pressure level and vibration reduction reaches 2 db with a relative magnetic wedge permeability of 20. Index Terms Acoustic noise, Vibration, Electromagnetic forces, Electrical machines, Magnetic wedges T I. INTRODUCTION he reduction of acoustic noise and vibration due to magnetic forces in electrical machines is increasingly important in a number of applications due to more stringent standards, increased power density and cost optimization which leads to thinner yoke designs. One main cause of electromagnetic noise and vibrations is the so-called slotting effect, the airgap reluctance variation due to rotor and stator slots. This slotting effect makes the magnetic noise level particularly sensitive to the slot and pole combination both in induction machines [1] and synchronous machines [2]. The use of magnetic wedges, also called semi-magnetic wedges, is a well-known technique to reduce parasitic slotting effect: as the magnetic wedge as a higher permeability than the air, it reduces the effective slot opening and the Carter coefficient. Firstly this article makes a short review of the works on the electromagnetic and vibroacoustic effect of magnetic wedges. It is shown that no work specifically studies the effect of magnetic wedge permeability on electromagnetically induced acoustic noise, although several wedge manufacturer claims that it reduces acoustic noise and vibration. Some electromagnetic and vibroacoustic calculations are therefore run within MANATEE [13] simulation environment to estimate the effect of magnetic wedges on a squirrel cage induction machine. II. A. Electromagnetic effect STATE OF THE ART In [3] the use of magnetic wedges with 2 and 10 relative permeability is studied on large induction machines. A reduction of nominal torque, rated current, starting torque and starting current is observed. The torque reduction is due to the slot leakage increase. It is concluded that small permeability (<10) has negligible effect on motor performances. In [4] the effect of magnetic wedges with 2 to 3 relative permeability is studied on high voltage induction machines with different pole numbers. It shows that the loss reduction with magnetic wedges depends on the pole number, although the Carter coefficient reduction is similar. In [5] it is shown that the harmonic content of electromagnetic torque and current is significantly reduced using magnetic wedges with a relative permeability of 10 (up to 13 db reduction of line current rotor slot-related harmonics amplitudes, and 23 db reduction of torque harmonics). As torque is related to 0 wavenumber radial forces, similar reduction is expected on zero-th wavenumber radial force harmonics. However, these are not necessarily responsible for the overall acoustic noise and vibration levels. The use of magnetic wedges in [5] leads to slightly lower output power at nominal speed and lower power factor, but higher efficiency and lower stator current at nominal speed. In [6] the influence of magnetic wedge magnetic permeability from 1 to 10 is studied. The use of wedges decreases starting current and starting torque. It is shown that the shape of the magnetic wedges has a strong influence on the reduction of flux harmonics. In [7] magnetic wedges with 8 relative permeability is studied on an induction machine. It is shown that magnetic wedges mainly affect airgap permeance and not stator mmf, and that the rotor bar current harmonics are also reduced with magnetic wedges. The no-load current decreases and the efficiency increases using magnetic wedges. In [8] some high permeability (100) stator wedges are modelled in an induction machine. It is shown that the starting current decreases as in [3], but that the starting torque increases contrary to [3]. In [9] the electromagnetic simulation of magnetic wedges with permeability of 4 (Magnoval product) and 20 in an induction machine is carried. It is shown that both load and J. Le Besnerais and Q. Souron are with EOMYS ENGINEERING, 121, rue de Chanzy, 59260 Lille-Hellemmes, FRANCE (website: www.eomys.com, email: contact@eomys.com)
no-load currents decrease, and that power factor and efficiency are improved using wedges. Simulations are validated with experiments. In conclusion the expected electromagnetic effect of stator magnetic wedges is: Reduction of airgap stator slotting harmonic magnitude Reduction of synchronous and asynchronous harmonic torques Reduction of harmonic magnetic losses on the rotor side and eddy currents on the stator side Reduction of the stator tooth losses due to lower flux pulsations Reduction of induced slotting harmonics in the stator currents Increase of efficiency Increase of the stator slot leakage inductance B. Vibro-acoustic effect In [10] it is shown that the use of rotor magnetic wedges can introduce fluctuations of the unbalanced magnetic pull (UMP) in a synchronous generator with damper winding. In [11] the effect of stator magnetic wedges on a synchronous reluctance machine is studied and up to -25% reduction of radial force harmonics is obtained (equivalent to -2.5 db). In [12] the effect of rotor slot iron wedge (open slot or closed slot) on electromagnetic noise and vibration is studied. It is shown that the full closure of rotor slot has a significant influence on noise and vibration levels above 1 khz. In [9] the effect of stator magnetic wedges on electromagnetic noise of a PWM-fed PMSM is studied and a 2 db reduction is obtained numerically using a relative permeability of 3. The vibro-acoustic effect of magnetic wedges has therefore not been studied a lot. Magnetic wedges reduce the magnitude of slotting flux density harmonics. It also reduces the saturation of the tooth tips and therefore the magnitude of the saturated flux density harmonics. The change of the flux harmonics magnitude change the magnitude of the Maxwell stress harmonics and resulting magnetic vibration and acoustic noise. Besides that the magnetic wedges have lower stiffness than normal wedges, which could therefore enhance the tooth rocking mode involved in magnetic vibrations. However, the tooth bending mode is mainly excited by tangential force waves which are much smaller than radial force waves in induction machines. The second important vibroacoustic effect of magnetic wedges is the effect on the current level through the change of the equivalent electrical circuit properties. As an example, magnetic wedges have the following effect on induction machine single phase equivalent circuit: Reduction of the iron loss resistance Increase of the stator slot leakage inductance Increase of the magnetizing inductance and due to lower Carter coefficient Magnetic forces are indeed proportional to square of the magnetizing current in induction machines, so the noise and vibration levels change with [19] L w =40log I ( 1) If the power is kept constant, the phase current decreases with magnetic wedges which further reduces the acoustic noise and vibration levels. There are therefore two different impacts that must be studied separately for more generality. III. A. Introduction SIMULATION ENVIRONMENT MANATEE software [13] (Magnetic Acoustic Noise Analysis Tool for Electrical Engineering) is dedicated to the fast optimal electromagnetic design of electrical machines including acoustic noise and vibration due to Maxwell forces. The evaluation of the airgap flux density can be based on analytical models (permeance/magnetomotive force and winding function approaches [14], [16]); semi-analytical subdomain models (e.g. Erreur! Source du renvoi introuvable.) or finite element models (based on a coupling with FEMM [18]). Some analytical models allow to calculate the radial vibration of the yoke, and the resulting acoustic noise following similar analytical models as presented in [19], [20]. The acoustic sound power level (SWL) at variable speed can be obtained in a few seconds on a standard laptop, which allows to make fast design iterations optimisations. B. Assumptions In MANATEE software environment, the following assumptions are made: Noise and vibrations are only due to Maxwell forces Magnetic materials are non-linear (M400-50A) Electromagnetic models are 2D (no skew) Sinusoidal-supply without strong circuit coupling (the slotting harmonics are not present in the currents) Vibroacoustic study is carried up to 3500 RPM C. Electrical machine data A MANATEE simulation of a squirrel cage induction machine with =28 rotor slots, =36 stator slots and =3 pole pairs is performed. The geometry of the studied machine is shown on Fig. 1. Design parameters are summarized in Table 1. Fig. 1 Lamination geometry
Table 1: Machine parameters Stator outer diameter 400 mm Stator bore diameter 265.1 mm Stator slot isthmus height 1 mm Stator wedge width 14 mm Stator wedge height 1.5 mm Stator slot height 30 mm Stator slot width 12 mm Stator slot number 36 Airgap width 1.5 mm Stack length 350 mm Rotor bore diameter 262.1 mm Rotor slot isthmus height 3 mm Rotor slot height 20 mm Rotor slot width 10 mm Rotor slot number 28 models without rotor slots and without stator slots, and by imposing an arbitrary mmf along the airgap. Fig. 4 Elementary FEMM model built by MANATEE to calculate the magnetic wedge effect on stator permeance The winding is a 3-phase double-layer overlapping integral distributed winding. A scheme of winding pattern distribution is shown on Fig. 2. Fig. 5 Elementary FEMM model built by MANATEE to calculate the magnetic wedge effect on rotor permeance Fig. 2 Winding distribution D. Simulation process The multiphysic simulation process of MANATEE is summarized in Fig. 3. The electromagnetic model that is used here is the permeance / magnetomotive force decomposition. The structural model is a 2D equivalent analytical model: as there is no skew, it is assumed that the longitudinal modes are not excited and do not contribute to noise and vibration levels. The acoustic model is an analytical model. This technique, also used in [21], can be applied to calculate the effect of asymmetries [22] (e.g. flux concentration lamination, non circular lamination due to weldings). IV. EFFECT OF MAGNETIC WEDGES ON NOISE AND VIBRATION A. Simulation Description First, the vibro-acoustic behaviour of the studied machine is studied without wedge (, =1). Then, a sensitivity study is performed by varying, from 1 to 20 within MANATEE. The monitored output values are the following ones: : Nominal vibration level, : Maximum of A-weighting Sound Power Level (SWL) on the whole speed range from 300 to 3500 RPM, : Magnitude of the highest radial force harmonic of wavenumber (can be negative) Fig. 3 MANATEE simulation process The electromagnetic model consists in calculating separately the rotor and stator airgap permeance functions, which are affected by saturation and magnetic wedge effects. This is automatically done in MANATEE by creating some FEMM The studied machine has a nominal speed = 1000!" and a constant value of current of # $%& = 64.2 ).
B. Vibroacoustic effect of wedges at constant current Without wedge The studied machine is described in III. C. In order to analyse the vibro-acoustic behaviour of this machine without wedge, MANATEE computes the SWL spectra at variable speed as well as a sonagram (Fig. 6). This representation is a 2D visualisation of 3 values: *+,*-.: Sound Power Level frequency [Hz] 0+,*-.: Rotating speed [rpm] 1+,*-.: Sound Power Level magnitude [dba] On the sonagram, the dotted vertical lines represent natural frequencies computed by MANATEE. Fig. 6 shows 2 acoustic resonances at 380 and 1170 RPM. They correspond with two slotting magnetic excitations which resonate with the elliptical mode of the lamination. The maximum A-weighting SWL is at the 1170 RPM resonance and its value is, 106 23) Fig. 7 radial Maxwell tensor harmonics of the studied machine at no-load (without wedge) The main force harmonics are characterized by the following wavenumber and frequencies: 4 4+.52 +2 at f=f s(z r/p+2)=566.7 Hz 4 4+.+8 f=f sz r/p=467 Hz 4 44+3.+4 at f=f s(4z r/p)=1866.7 Hz All these harmonics are linked to pure slotting effects and are not linked to the winding (stator mmf harmonics). The two first ones are linked to the first rank of stator permeance harmonic, whereas the third one is linked to the third stator permeance harmonic. The force waves due to second rank of stator permeance harmonic are close to zero because the slot width is close from the tooth width [23]. The origin of all these force harmonics are studied in detail in [24]. It is then interesting to monitor the magnitudes of those particular slotting harmonics (,67,8 and,69 ) when changing the wedge permeability. Wedges added with varying A sensitivity study is carried by varying the magnetic wedge permeability from 1 (no wedge) to 20. The phase current is first imposed to analyze the effect on the slotting harmonics independently of the effect on the current level. The effect on,67,8 and,69 is shown in Fig. 8. Fig. 6 Overall noise level (up) and sonagram (down) of the studied machine without wedge obtained with MANATEE Fig. 7 shows the 2D spectrum of magnetic forces obtained with MANATEE without wedge at nominal speed of 1000!". Fig. 8 Evolution of highest Maxwell tensor harmonics The two force harmonics linked to the first order of slotting have the same decreasing behaviour. The magnitude,69 goes from 5407 /= 7 for no wedge to 4319 /= 7 with wedges with magnetic permeability of 20 whereas,67 goes from 2700 /= 7 to 2156 / = 7. It can be noticed that,69 magnitude is twice,67
In order to analyse the vibro-acoustic behaviour of the machine regarding the variation of,,, and are plotted in function of, (Fig. 9). A maximum reduction of 2 db is found. Fig. 10 Evolution of Carter coefficient in function of, This is further studied by imposing constant power in MANATEE simulation environment. The effect is a variation from 93.1 to 87.0 Arms for the phase current, which leads to 1.2 db additional noise and vibration reduction. Fig. 9 Evolution of (at the top) and, (at the bottom) regarding to, variation As Maxwell forces are quadratic functions of flux density, the decreasing of Maxwell forces harmonics can be expressed as: Δ20 ABC DE F G HIJ,KL,MIN G HIJ,KL,MOP Q (2) After calculation, the decreasing of,67 as the one of,69 is 2 db. This value of decreasing is exactly the same that is observed on Fig. 9 on as well as on,. This last value goes from 106 dba without wedge (which is the resonance value already identified on III. B. ) to 104 dba with wedges with magnetic permeability of 20. If the resonance was created by the third order slotting harmonic, a reduction of 3.75 db would be expected. C. Vibroacoustic effect of current variation Fig. 10 shows the calculated numerical Carter coefficient in MANATEE. The magnetizing inductance therefore increases of 13% with magnetic wedges of permeability 20. This will lead to a current reduction. V. CONCLUSION AND FUTURE WORK This article shows that the use of stator magnetic wedges at constant current level can reduce the magnetic noise and vibration level due to first slotting harmonic of 2 db when going from 1 (no-wedge) to 20. The noise and vibration reduction could be higher (up to 3.75 db) if the force harmonic responsible for noise was linked to higher ranks of stator permeance harmonics. However, higher ranks of permeance harmonics have low magnitude and are generally not the root cause of magnetic noise and vibrations. A wedge magnetic permeability of 3 only gives 0.5 db reduction, which may not justify the additional cost of magnetic wedges compared to standard non magnetic wedges in this particular case. This shows that the efficiency of magnetic wedges for noise and vibration reduction strongly depends on the machine design (slot and pole combination) and wedge geometry. This effect can be quantified within MANATEE simulation environment. When working at constant power, the phase current level further decreases due to lower Carter coefficient, further improving the noise reduction due to magnetic wedges. For studied machine, the additional noise reduction reaches 1 db, so 3 db in total for a permeability of 20. However this does not include the effect of magnetic wedges on magnetic loss reduction (which should further reduce the phase current) nor the effect on leakage increase (which should increase the phase current). Future work aims at calculating in MANATEE the leakage inductance evolution of magnetic wedges permeability and check the overall impact on the phase current and resulting noise and vibration. The shape of the magnetic wedge (distance to airgap and wedge width) will be also studied. VI. REFERENCES [1] J. Le Besnerais, V. Lanfranchi, M. Hecquet and P. Brochet, "Optimal Slot Numbers for Magnetic Noise Reduction in Variable-Speed Induction Motors," in IEEE Transactions on Magnetics, vol. 45, no. 8, pp. 3131-3136, Aug. 2009. [2] G. Verez, G. Barakat, and Y. Amara, "Influence of slots and rotor poles combinations on noise and vibrations of magnetic origins in `u'-core flux-switching permanent magnet machines," Progress In Electromagnetics Research B, Vol. 61, 149-168, 2014.
[3] M. Dems et al., "Analysis of effects of magnetic slot wedges on characteristics of large induction motor", PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), 2012 [4] Jae-myung Cha, Rae-eun Kim, Jee-hun Choi and Jang-ho Yun, "A study of the characteristic of the high-voltage induction motor considering the magnetic wedge effect with poles," Electrical Machines and Systems (ICEMS), 2015 18th International Conference on, Pattaya, 2015, pp. 122-124. [5] K. N. Gyftakis, P. A. Panagiotou, and J. C. Kappatou, "Application of Wedges for the Reduction of the Space and Time-Dependent Harmonic Content in Squirrel-Cage Induction Motors," Journal of Computational Engineering Volume 2013, 2013. [6] W. Li et al., "Influence of magnetic wedge on electromagnetic field distribution of permanent magent traction motor," Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles (ESARS), 2015 International Conference on, Aachen, 2015, pp. 1-5. [7] H. Mikami, K. Ide, K. Arai, M. 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Serrano-Iribarnegaray, P. Cruz-Romero, and A. Gomez-Exposito, "Critical review of the modified winding function theory," Progress In Electromagnetics Research, vol. 133, 2013 [17] E. Devillers, J. Le Besnerais, T. Lubin, M. Hecquet and J.P. Lecointe, A review of subdomain modeling techniques in electrical machines: performances and applications, Proceedings of ICEM 2016 [18] D. Meeker, "Finite element method magnetics, version 4.0.1 (03dec2006build), " http://www.femm.info, 2003 [19] J. Le Besnerais, "Reduction of magnetic noise in PWM-supplied induction machines low-noise design rules and multi-objective optimisation, " Ph.D. dissertation, Ecole Centrale de Lille, France, Nov. 2008 [20] J. Le Besnerais, A. Fasquelle, J. Pelle, S. Harmand, M. Hecquet, V. Lanfranchi, P. Brochet, and A. Randria, "Multiphysics modeling: electro-vibro-acoustics and heat transfer of induction machines, " in Proc. of the International Conference on Electrical Machines (ICEM 08), Villamura, Portugual, Sep. 2008 [21] M. Fakam, M. Hecquet, V. Lanfranchi and A. Randria, "Improved method to compute air-gap magnetic pressure of the Interior Permanent Magnet Synchronous Machine," Ecological Vehicles and Renewable Energies (EVER), 2015 Tenth International Conference on, Monte Carlo, 2015, pp. 1-8. [22] J. Le Besnerais, M. Farmaz, "Effect of lamination asymmetries on magnetic vibrations and acoustic noise in synchronous machines," Electrical Machines and Systems (ICEMS), 2015 18th International Conference on, Pattaya, 2015, pp. 1729-1733. [23] J. Le Besnerais, V. Lanfranchi, M. Hecquet, R. Romary and P. Brochet, "Optimal Slot Opening Width for Magnetic Noise Reduction in Induction Motors," in IEEE Transactions on Energy Conversion, vol. 24, no. 4, pp. 869-874, Dec. 2009. [24] E. Devillers, J. Le Besnerais, Q. Souron and M. Hecquet, Characterization of acoustic noise and vibrations due to magnetic forces in induction machines for transport applications using MANATEE software, Proceedings of ISMA, 2016 VII. BIOGRAPHIES Jean Le Besnerais currently works in EOMYS ENGINEERING as an R&D engineer on the analysis and reduction of acoustic noise and vibrations in electrical systems. Following a M.Sc. specialized in Applied Mathematics (Ecole Centrale Paris, France) in 2005, he made an industrial PhD thesis in Electrical Engineering at the L2EP laboratory of the Ecole Centrale de Lille, North of France, on the reduction of electromagnetic noise and vibrations in traction induction machines with ALSTOM Transport. He worked from 2008 to 2013 as an engineer in the railway and wind industries (Alstom, Siemens Wind Power, Nenuphar Wind) on some multiphysic design and optimization tasks at system level (thermics, acoustic noise and vibrations, electromagnetics, structural mechanics and aerodynamics). In 2013, he founded EOMYS ENGINEERING, a company providing applied research and development services including modeling and simulation, scientific software development and experimental measurements. Quentin Souron graduated in 2013 from the University of Technology of Compiègne (UTC) in Mechanical Engineering, specialized in acoustics and industrial vibrations. After an experience in an acoustic engineering office where he was in charge of acoustics missions in several domains (environment, buildings, industry), he made a research project in an academic laboratory on new types of noise barriers made of phononic crystals. In 2014 he joined EOMYS ENGINEERING as an R&D engineer in charge of vibroacoustic aspects of electrical systems (rotating machines and passive components).