A Practical Solution to Mitigate Vibrations in Industrial ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 5, SEPTEMBER/OCTOBER 2012

A Practical Solution to Mitigate Vibrations in Industrial PM Motors Having Concentric Windings Alain Cassat, Christophe Espanet, Member, IEEE, Ralph Coleman, Luc Burdet, Emmanuel Leleu, Dimitri Torregrossa, Student Member, IEEE, Jérémie M’Boua, Student Member, IEEE, and Abdellatif Miraoui

Abstract—Industry applications involving torque brushless dc motors require high efficiency over a large speed range. In order to achieve such specifications, flux weakening is necessary, which could lead to relative high electromagnetically induced vibrations and consequently to audible noises. Furthermore, in order to decrease cogging torque and to satisfy motor manufacturing constraints, concentric windings are usually considered. Such motor configurations lead to harmonics of the electromagnetic forces being the sources of mechanical vibrations. This paper focuses on the electromagnetic forces created in surface-mounted permanent magnet and internal permanent magnet motors for two concentric windings: one and two coil sides per slot. These forces are determined using both lumped magnetic scheme and two-dimensional finite-element (FE) simulations. Then, three-dimensional FE simulations enable to predict the mechanical modes and the acoustic radiated power. Finally, the authors propose a simple method to mitigate the magnetic forces and their variations. This method deals with skewing the stator. The skewing angle is optimized differently as in the usual case of decreasing the cogging torque. This method is really interesting for industry applications, because does not require any important change in the motor construction. The acoustic measurements confirm the analysis and the proposed improvement technique (stator skewing). Index Terms—Brushless dc (BLDC) motors, concentric windings, forces, internal permanent magnet (IPM), surface-mounted permanent magnet (SMPM), vibrations.

N OMENCLATURE B Ls f Kw θ

Flux density [T]. Axial active length [m]. Frequency [Hz]. Winding factor [−]. MMF [A].

Manuscript received July 16, 2011; revised November 9, 2011 and February 6, 2012; accepted February 21, 2012. Date of publication July 24, 2012; date of current version September 14, 2012. Paper 2011-EMC-398.R2, presented at the 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, GA, September 12–16, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. A. Cassat is with the EPFL-STI-IMT-LAI, 2002 Neuchâtel, Switzerland (e-mail: [email protected]). C. Espanet is with the University of Franche-Comte, FEMTO-ST Institute, 90000 Belfort, France (e-mail: [email protected]). R. Coleman and L. Burdet are with ETEL SA, 2112 Môtiers, Switzerland (e-mail: [email protected]; [email protected]). E. Leleu is with the Converteam SAS, 90000 Belfort, France (e-mail: [email protected]). D. Torregrossa, J. M’Boua, and A. Miraoui are with University of Technology of Belfort-Montbéliard, SET Laboratory, 90010 Belfort Cedex, France (e-mail: [email protected]; [email protected]; abdellatif. [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2012.2210172

δ χ, υ M r I T ds i t α, β, γ, φ ω j p s

Air-gap [m]. Harmonic index. Number of phases [−]. Referred to rotor. Current (RMS) [A]. Tooth pitch [m]. Current (instantaneous value) [A]. Time [s]. Angles [rad]. Pulsation [rad/s]. Stator phase #j. Number of pole pairs [−]. Referred to stator. I. I NTRODUCTION

I

NDUSTRY applications, involving torque brushless dc (BLDC) motors, require high efficiency over a large speed range. In order to meet these constraints, the BLDC motors are designed in such a way that at low speed, they work at constant current and at maximum torque output. For surface mounted permanent magnet (SMPM) motors, the phase current is in phase with the corresponding phase back EMF for SMPM and for internal permanent magnet (IPM) motors, the phase current is in advance with the corresponding phase back EMF. However, to reach higher speeds, the control then reduces the total phase flux by applying the optimum switching lead angle [1], [2]. The voltage control is associated with a pulse width modulation (PWM) at a relatively high frequency. To minimize the mass and to decrease the production costs related to the winding, concentric windings are often the proposed designs [3]–[5]. Such a choice also enables to decrease the cogging torque. However, the previous design choices can lead to mechanical vibrations [6]–[13]. In particular, during flux weakening, for a given torque, the reduction of the flux needs an increase of the RMS value of the phase current, leading to an increase of the magnetic forces (both mean value and variations). In addition, if there are harmonics in the spatial flux distribution, the difference of phase between phase current and back EMF will produce torque ripple. This paper investigates two industrial torque motors in the framework of collaboration between ETEL Company and academics (UTBM and UFC in France, and EPFL in Switzerland) [14]: first a SMPM and second an IPM. Both motor configurations have the same number of slots and poles. Furthermore, two types of stator windings are considered: one coil side per slot and two coil sides per slot. The stator teeth geometry is characterized by having no tooth shoe leading to a large

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CASSAT et al.: MITIGATING VIBRATIONS IN INDUSTRIAL PM MOTORS HAVING CONCENTRIC WINDINGS

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slot opening. To analyze the complete electrical drive and its acoustic characteristics, the paper presents the following points. • Magnetic and mechanical analysis—Numerical methods: – The spectrum of the winding factors is determined. – The relative magnetic air gap and its fast Fourier transform (FFT) are presented. – The motor dynamic is simulated in order to determined the phase currents versus time and their corresponding FFT. – The spatial forces are determined on each stator tooth using a lumped model [15]–[17] and two-dimensional (2-D) finite element (FE) analysis. – The forces FFT are introduced in the mechanical threedimensional (3-D) FE model (FEM), then the vibration spectrum is determined.

Fig. 1. Two-dimensional FEM—SMPM and IPM torque motor parts: stator and rotor.

• Passive improvement to mitigate the vibrations: A skewed stator is investigated as a passive mitigation technique for audible noise and vibrations. In the case of the motors considered in this paper, this technique has the important advantage to lead to minimal modifications of the construction, so that it is really an interesting solution for industry applications. • Electrical and mechanical measurements: Measurements of the modal frequencies, the audible noise, and the vibrations are presented for the initial motors and for the motors with a skewed stator in order to validate the calculations and the proposed solution. • Conclusions: Conclusions are addressed in relation to the choice of the motor winding configurations and the rotor types. II. M OTOR S PECIFICATIONS AND M OTOR C ONFIGURATIONS Table AI, in the Appendix, describes the key technical characteristics of the SMPM and IPM motors. Other technical information can be found in the website of ETEL company (www. etel.ch). The surface-mounted permanent magnet (SMPM) is an assembly of 2p trapezoidal PM segments. A laminated back iron completes the rotor. IPM having a transverse magnetization permits to increase the flux density in the air gap versus the SMPM configuration. The IPM favors the decrease of the phase flux since the inductance in the direct axis will be of higher value than for the SMPM configuration. The torque is increased due to the reluctance effect: direct Ld and transverse Lq inductances are different. These are the three main advantages of the IPM configuration. A laminated back iron with a specific geometry shape assures the magnetic field concentration in the air gap. The SMPM and IPM motors have the same slot and pole numbers. Two concentric windings are considered: one coil side per slot and two coil sides per slot. One coil side per slot permits to obtain a better copper filling factor, a slight improved winding factor 0.958 versus 0.949 (Fig. 4), and a lower production cost. Both windings reduce the axial length of the machine. These two windings lead to different spectrums of the winding factors. Figs. 1 and 2 show a partial view of such motors and the test setup.

Fig. 2. Three-dimensional CAD mechanical model and tests setup: motor, torque meter, and motor load.

III. W INDING FACTORS AND R ESULTING MMF The winding factors are determined for all harmonics related to the geometrical harmonic modes. As the motor configurations have a fractional number of slots per pole and per phase, sub-harmonic orders appear. Figs. 3 and 4 show the coil distribution and the spectrum of the winding factors with a periodicity equal to the number of poles 2p. More precisely, the Fig. 3 presents only half of the machine, since the winding the latter half has exactly the same winding due to symmetry. In addition, the four groups of coils per phase are connected in parallel to fit with the electric specifications of the motors (in Fig. 3, only two groups are plotted for one half of the machines). The harmonics of order 6 + 2pk (k integer) are particularly present for the stator having one coil side per slot. Fig. 5 presents the resulting magnetomotive force (MMF), for a specific current distribution, emphasizing the effect of the harmonics. As previously mentioned, the analysis is based on numerical methods; however, some simple equations permit explaining the effect of each characteristic spectrum. The resulting stator MMF is expressed in (1), where i1 (t), i2 (t), i3 (t) are the phase

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Fig. 6.

Magnetic air gap and FFT (geometrical harmonic mode).

for low harmonic indexes due to the terms kw(υ)/υ, decreasing with υ. For the permanent magnet, (3) gives the resulting MMF ⎫ ∞ kw(υ) ⎪ ⎪ ·sin (υ·α +β (υ)) θj (t, αs ) =ij (t)·N · s j ⎬ υ υ=1 [A] (1) m ⎪ ⎪ θres (t, αs )= θj (t, αs ) j = 1, 2, 3 ⎭ j=1

∞ m ij (t)= Iˆj (i)·sin (ω(i)·t+γj (i)) and ij (t, α)=0 [A] (2) i=1

θPM (t, αr ) =

∞

j=1

θˆPM (χ)·sin (χ·αr +φ(χ))

[A] (3)

θres (t, αs ) θPM (t, αr ) + δ(αs ) δ(αs )

[T]. (4)

χ=1

Bradial (t, αs , αr ) =

Fig. 3. Phase winding: 48 slots, 44 poles, one and two coil sides per slot.

Fig. 4. Winding factors-geometrical harmonic mode.

Equation (4) expresses an approximation of the radial flux density in the air gap. The radial force density is proportional 2 to Bradial (t, αs , αr ). This component induces three different forces: the reluctance force due to the stator MMF only, the mutual force between the stator and the permanent magnet respective MMF, and the force due to the PM MMF only. Equations (2) and (4) indicate that the magnetic air gap has to be known, emphasizing the influence of the slot opening, and furthermore the spectrum of the current has to be determined. IV. M AGNETIC A IR G AP The ratio of the slot opening over the tooth pitch is 0.518, leading to a strong influence of the slot effect. A specific determination of the magnetic air gap δ(αs ) is required, since Carter’s method does not give valid values for such a ratio. Fig. 6 shows the FFT of the obtained magnetic air-gap. V. C URRENT D ETERMINATION

Fig. 5. Resulting stator MMF: one and two coil sides per slot.

currents defined in (2) and (3). Even if the winding factors kw(υ) satisfying υ = p · k are very close in value for the two windings, the effect of the others harmonics modify strongly the stator MMF, resulting in different electromagnetic forces. Equation (1) indicates that the spatial harmonics have an impact

The currents are simulated [Fig. 7(a)], knowing the threelevels converter, the motor, and the control. The simulation outputs are the phase currents expressed as a FFT [Fig. 7(b)], having the harmonics defined by the low orders of the electrical fundamentals and the higher orders depending on the PWM type and its frequency fPWM and on the motor speed frequency fs . The FFT of the power two of the current is also presented, as it will appear in the forces. The PWM current frequency spectrum is expressed as: k = 2, 4, 8, . . . fPWM ± k · fsyn [Hz]. (5) 2 · fPWM ± k · fsyn k = 1, 5, 7, . . . For a frequency of the PWM at 5 [kHZ], the PWM harmonics will be 10, 15, and 20 [kHz], for a zero motor speed, as drawn in Fig. 7(c). Considering different motor speeds (400, 600,


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Fig. 8. SMPM—IPM—Resulting radial and tangential forces on the tooth.

Fig. 7. One coil side per slot—Partial phase currents and FFT (electrical mode). (a) Phase 1: defined by the partial phases 1, 4, 7, 10—speed 800 [rpm]. (b) Harmonic: index 1 of current = 1 [pu]; index 2 of current∧ 2 = 1 [pu]). (c) SPM—FFT of the current measurements (blue lines).

Fig. 9. SMPM and IPM—Spatial forces on the tooth—No load case.

800, and 1000 [rpm]) and measuring the current FFT (blue lines) leads to the appearance of frequencies as defined in (5), where the influence of the PWM harmonics are clearly seen and emphasized by straight lines starting from the reference harmonics at zero speed. VI. E LECTROMAGNETIC F ORCES A. Force Determination The electromagnetic forces are determined using a lumped magnetic scheme DCRAD [15]–[17] and 2-D FE analysis. For the IPM motor, only 2-D FEM are used to calculate the forces. The forces are determined on the coils (Lorentz forces) and on the teeth (Maxwell forces). B. SMPM and IPM—No Load Case The effect of the permanent magnets on the forces can be determined in the no load case. As expected for the IPM configuration, the dc radial force and the ac force variations are higher than for the SMPM configuration. Fig. 8 corresponds to the resulting force on the tooth. Fig. 9 emphasizes the local forces on the tooth. The main components are near the air gap, on the tooth extremity.

Fig. 10. SMPM one coil side per slot—Spatial forces on the coils (zoom).

C. SMPM—Rated Load Case—Forces on the Coils The previous currents are introduced as sources in the magnetic models. Then, the rated load cases are simulated. Fig. 10 shows the forces (Lorentz forces) per unit of volume on the coil for a given rotor position. The maximum force on the whole coil is 36 [N], which is low versus the forces (Maxwell forces) on the teeth (> 250 [N]). As seen in Fig. 10, this maximal force only concerns few wires in the slots: Lorentz forces on the coils are not considered later on. D. SMPM—Rated Load Case—Forces on the Teeth Due to the spatial repartition of the coils, groups of teeth seeing the same forces appear, as defined in Table AI. The

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Fig. 11. SMPM—Radial forces and torque—FFT (geometrical mode).

Fig. 12.

SMPM—Radial forces and torque—FFT (geometrical mode).

Fig. 13.

SMPM—One coil side per slot—Radial forces and torque—FFT.

following paragraphs described the forces and their FFT, for all the previous configurations and also considering a skewed stator. The corresponding developments related to the skewed stator will be presented in Chapter VII. E. Presentation of the Results In order to compare the different results, they are presented in two adjacent columns. On the left side column, the SMPM and IPM—One Coil Side per Slot figures are presented. On the right side column, the SMPM and IPM-Two Coil Sides per Slot figures are shown. Furthermore, still to improve the comprehension, the same presentation is applied to the passive improvement such as the skewed stator. Finally, the same figure scales are considered to enable a direct visualization of the trends between the different configurations. Only, the radial forces are presented. However, the tangential forces are determined and included in the 3-D FE mechanical model, as excitations. F. Forces Figs. 11–16, presenting the forces and the torques, show clearly the effect of the coil configurations. Local linearization of the forces (see (8) in Paragraph VII-C) permits to better


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Fig. 14. SMPM—Two coil sides per slot—Radial forces and torque—FFT.

Fig. 16. IPM—One coil per slot—Radial forces and torque—FFT.

the resulting stator MMF being 15% of the PM MMF (3722 [A]) and the local reluctance variation are not negligible, thus indicating an apparent reluctance effect of the stator MMF. This effect appears more strongly on the IPM motor. For the IPM, due to higher flux density in the air gap, the force FFT presents stronger harmonics. Furthermore, as the inductances in the direct and transverse axis are different due to the rotor geometry (see Fig. 1), stronger reluctance torques due to the current alone and due to the PM alone appear [see (8) in Paragraph VII-C]. Equation (8) shows that acting on the rotor geometry to reduce the reluctance forces is very difficult in the case of IPM, since all component forces will be modified, including the torque. In industrial applications, often IPMs are used when flux weakness is necessary because of the difference in the direct and transverse inductances. Such a choice induces motor vibrations and audible noise. Previous analysis shows ways to reduce vibrations, which are to reduce the flux variation in the air gap (stator skew) or to increase the magnetic symmetries of the motor (number of teeth, number of poles) or to inject appropriate current harmonics.

Fig. 15. IPM—One coil per slot—Radial forces and torque—FFT.

G. Rated Torque

understand the effect of the different motor configurations. For both rotor configurations SMPM and IPM, low FFT harmonic indexes 4, 6, are due to the current fundamental only as reluctance forces. Higher harmonic indexes are due to effect of the PWM current harmonic (see Fig. 7) resulting in force harmonic indexes 14, 16, 18, 20, 22. The FFT of the forces indicates that

The rated torque is determined for the different motors. As the number of poles is 44 and the number of teeth 48, the smallest common multiple is 528, corresponding to the number of periods of the cogging torque, and its magnitude is consequently extremely low. According to the previous remark, the difference between the torques of the different motor configurations is not relevant.

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VII. PASSIVE I MPROVEMENT A. Eccentricities The forces and their variations depend on the rotor eccentricities. For these industrial motors, the ratio of the mechanical air gap over the air gap diameter is 0.52%: the eccentricity is non negligible for such motor designs. The mutual inductances are present in the one coil side per slot involving circulating currents in the different coils due to the appearance of dissymmetric mutual inductances, in case of eccentricity (see Fig. 3). The mutual inductances are zero for the two coil sides per slot or very low with eccentricities. The authors of [18] have already explained the effect of faults (demagnetization and eccentricity) on the emitted sound power for permanent magnet synchronous motors (PMSM). We will not address this topic in this paper. However, we can add few comments regarding the eccentricity effect. The effect of static and/or dynamic eccentricities and/or non-repetitive run-out is to cancel the magnetic and electrical symmetries and or periodicities of the system (here a motor). Consequently, the tooth forces for the stator and the torque for the rotor are directly affected. In reality, all motors are measured with their resulting eccentricities and consequently, it does not correspond to the nominal cases. Excellent motors, such as the eight poles, nine slots, three phases configuration at nominal, presents high cogging torque as soon as an eccentricity appears and consequently vibrations will appear. For this reason, this motor configuration is not considered in the industry. For this motor, the highest possible common divider of the number of poles and the number of slots is one. The motors with 10 poles, 12 slots, 3 phases, which is often mentioned in publications as a good motor, present also high tooth forces variations and cogging torque as soon as eccentricity appears. For these motors, the highest possible common divider of the number of poles and the number of slots is two. Usually, in order to minimize or to decrease the negative influences of eccentricities, the magnetic and electrical periodicities are increased. This means that there is a direct positive effect to have the highest possible common divider of the number of poles and the number of slots, which automatically leads to high numbers of poles and slots. The ratio between the stator MMF and the permanent magnet MMF, which defines the saturation level (flux density), has also a direct effect, since eccentricity will locally modify the spatial distribution of the flux density. B. Active Improvements Two major active improvements can be considered: • choosing the number of converter levels, here three levels; • having a dynamic current compensation by choosing the connections between the stator coils (parallel and series). This technique can helps due to the appearance of dissymmetric inductances (one coil side per slot). However, such improvement is not easy to implement in industry applications, because the motor supplier is not always the power electronic supplier, so that the use of a special control is not always possible.

Fig. 17.

SMPM—-Skewed stator—Peak phase back EMF.

C. Passive Improvements To minimize the force variations, choosing appropriately the number of teeth and poles with concentric windings requires increasing the magnetic and geometric symmetries of the motor (numbers of teeth and poles). This is necessary when the eccentricity is an issue. Here, as the SMPM and IPM motors have the same stator, it was considered to only act on the stator defining a passive improvement (same number of slots). Passive improvement such as skewing the stator teeth is considered, and a stator prototype was built. Skewing the stator requires a design optimization since: the copper filling factor, the resistance, the inductance, the back EMF will be affected. To define the skew angle α (Fig. 17), the possible decrease in the phase back EMF coefficient is minimized. Equation (6) gives the evolution of the magnetic air gap with respect to the skew angle. For the prototype, the ratio Kis, defined as in (7) and its influence of the peak phase back EMF given in Fig. 17, is chosen equal to 0.5. As seen in (6), skewing the stator permits decreasing the force variations. Furthermore, skewing the stator reinforces the stator yoke to mechanical distortions, thus the motor modes are shifted to lower frequencies. These two improvements cannot be obtained by skewing the rotor permanent magnet. For the IPM skewing, the rotor will almost be impossible mechanically 1 · δskew (αs ) = Ls

Ls δ (αs − z · cos(α)) · dz

[m] (6)

z=0

Bi Kis = T ds

[−]. (7)

As the length of the flux lines in the air gap are never equal to zero or obviously not negative, (6) indicates that the average value of δskew (αs ) on one tooth pitch can be either higher, lower or equal to that one of the average of δ(αs )over one tooth pitch for a straight tooth. This depends directly on the geometrical dimensions of the tooth and slot of the considered motor. Consequently, the results of Fig. 17 cannot be generalized due to the physical meaning of (6), the spatial distribution of the flux density in the air gap, and the saturation level of the magnetic parts of the motor. One key question is related to the fact that: does a skewed stator induce axial forces? A tentative of answer is based on the


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following developments considering the local linearization of the problem around the spatial distribution of the flux density in the complete motor, where all the currents and permanent magnet MMF are considered as state variables. Then, after the determination of the spatial distribution of the flux density in all motor parts (2-D or 3-D), a local linearization is applied. For incremental 2-D virtual displacements (dx, dy) of the stator, the incremental forces in the directions (Ox) (curvilinear direction related to the motor direction), and (Oy) (axial direction) are expressed as: Fx = Fy =

1 2

·

1 2

·

N N k0 =1 k1 =1 N N k0 =1 k1 =1

dλkp dx

⎫ ⎪ · Θ k0 · Θ k1 ⎪ ⎬

dλkp dy

⎪ ⎭ · Θ k0 · Θ k1 ⎪

[N]. (8)

Fig. 18. SMPM—3-D FEM Sound power level.

Each one of these incremental forces have three components: • the force produced by the permanent magnet MMF only; • the force produced by the stator currents only; • the mutual force produced by the currents and the PM MMF. Force Fy Component Produced by the Permanent Magnet MMF Only, for a Given Position x: The skewed stator will not have an influence on this force, since only the end effect in the axial direction of the magnetization of the permanent will affect this term and consequently its corresponding reluctant axial effect (force). However, this case is also present for a straight tooth. Force Fy Component Produced by the Stator Currents Only, for a Given Position x: If the stator winding follows exactly the skewed effect of the tooth, meaning that the winding is strictly parallel to the skewed angle, then an incremental displacement dy is similar to an curvilinear displacement dxy through the mathematical following relation: dxy = −dy · tgt(α)

[−]. (9)

As a consequence, the effect of an incremental displacement dy is equivalent to a curvilinear shift of the curvilinear force in direction (Ox). There is no appearance of a force in the axial direction. Of course, as for a straight tooth, the reluctant end axial effect is present. Mutual Force Fy Component Produced by the Currents and the PM MMF, for a Given Position x: Equation (6) indicates that the level of saturation (spatial distribution of the flux density) will be only slightly higher than one for a straight stator. Consequently, only local effect due to change in the flux density spatial distribution could have some effect. Of course, as for a straight tooth, the reluctant end axial effect is present. Reluctant end Axial Effect: The reluctant end axial effect is, of course, present as for a straight tooth. This force (mentioned as “bias” force in the industry field) is usually used to pre-load the motor in the axial direction, as in some applications, for example in the hard disc drive industry.

Fig. 19. SMPM—Measurement—Speed of vibrations; 800 [rpm];140 [Nm].

VIII. M ECHANICAL 3-D FEM For the motor configurations, a mechanical 3-D FEM was developed. Considering only the motor for 3-D FE (see Fig. 2), all FE simulations show very good correlations, and the complete method and the corresponding results were presented in [19], [20]. The stator is simulated without the winding coils. No major differences were seen between one coil side per slot and two coil sides per slot in terms of the motor measured modes. Figs. 18 and 19, and Table I summarizes the obtained 3-D FE simulations and measurements. The three major frequencies in terms of vibration speeds and acoustic pressure are found numerically (Fig. 18) and by measurements (Fig. 19) at 586, 1173, and 4120 [Hz]. IX. M EASUREMENTS A. Mechanical Modes To measure the vibrations and their speeds, a laser vibrometer was used, completed by a microphone. A spatial map of measurements is defined by an outside grid cage permitting to identify the measurement points in the motor environment, as presented in Fig. 20.

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TABLE I M ECHANICAL M ODE —SMPM

Fig. 20. SMPM—-Measurement setup and spatial cage. TABLE II ACOUSTIC AND V IBRATION M EASUREMENTS

B. Skewed Stator Table II and Fig. 21 give the acoustic pressure and vibration speeds for the starting structure and for those with skewed stator. In order to obtain accurate audible acoustic noise measurements, it is necessary to use a microphone having a frequency bandwidth of 20 kHz. The microphone used for this purpose is a Bruel&Kjaer type 4165. C. Instruments A survey of the literature suggests that high-performance instruments are needed to obtain accurate results for characterization of vibration and noise [21]. Although there are a big variety of instrument for acoustic and vibration characterization, in this paper, an experimental setup suitable for of noise and vibration analysis in PMSM is suggested.

For the vibration characterization, piezoelectric accelerometer allows to measure quickly the acceleration on the particular point of the structure (generally, they are placed on the stator of the electrical machine). This placement can change the amplitude of the acceleration in the point where it is located and consequently invalidate the measure: if high accurate results are required, other instruments have to be used. In this paper, we used a laser vibrometer Polytec OFV-505. This kind of instrument does not invalidate the measure, and it does not need any device on the examined surface, it is a so-called non-contact instrument. It just projects a light in a particular point and gives the amplitude of the displacement. The main advantage is the possibility to change the point of measurement quickly just by moving the light. The signal concerning the measured velocity vibration has to be conditioned before to be stored. The conditioner is a lowpass filter OSV-5000 with a cut frequency equals 20 kHz. In this way, all the vibrations able to produce acoustic noise emission are considered. Even if vibration and noise are two phenomena linked with each other, it is important to measure and quantify the acoustic noise emission of a rotating electric machine. In order to obtain accurate audible acoustic noise measurement, it is necessary to use a microphone having a frequency response until 20 kHz. In this paper, we used a condenser microphone Bruel&Kjaer type 4165. This kind of microphone has long-term stability and operational reliability. The type 4165 is specially recommended for standardized noise measurements in accordance with IEC and ISO standards. It needs an external polarization voltage equals 200 V. It gives a voltage proportional to the measured sound pressure. Its sensitivity is 50 mV/Pa. An accurate source of sound for calibrating the microphone before each measurement is welcomed. In this paper, a source of 94 dB sound pressure level (SPL) has been used for the calibration. The signal coming from the microphone, that is a low voltage, must be amplified before to be stored. Intensimetric measurement needs to perform simultaneously two measurements of sound pressure with two closely spaced microphones. Of course, it is also necessary to use a sound intensity calibrator before each measurement session. In the work presented in this paper, a probe composed by two microphones, spaced of 12 mm, has been used. With this distance, it is possible to measure all the sound pressure components between 200 Hz and 5 kHz; in this way, the most important sensitive area of human auditory system is considered. D. Location of Measurement Points The SPL around an electric machine varies with the distance from the machine and with the angular position around it. A literature survey suggests using imaginary measuring surfaces for optimal placement of acoustic instruments and then for optimal calculation of the space average SPL. That requires many time-consuming measurements. Reference [22] proposes three kinds of measurement surfaces, hemispherical, rectangular, and conformal surface. The electric machine was placed on a laboratory room, and the microphones were located on rectangular parallelepiped surfaces as suggested in [23]. One


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Fig. 21. SMPM—skewed rotor: Acoustic pressure [dB] and vibration speed [dB] versus the motor speed 0 to 1000 [rpm] over the frequency band.

plane of the measuring surface is through the shaft axis, the other one is on one plane perpendicular to the shaft axis: in this way, the two main radiating sound power directions of electrical machine are considered. Vibration measurement points should belong to different pieces of the structure understudy. If the stator is accessible, it is a good idea to measure the vibration on it. However, it is difficult to perform accurate vibration measurement on the stator because of the housing of the machine. In this paper, the vibration measuring points are on the surfaces of the external housing because they are the main responsible surfaces for the radiated sound power. E. Choice of Sample Frequency In order to perform a post-analysis of acoustic and vibration variables, all the measurements must be acquired and stored. Of course, to perform more measurements (noise and vibration) in the same time, it is necessary to use a high-speed data acquisition board. The sample frequency used for the acquisition plays a key role on the post-analysis. The Nyquist-Shannon’s theorem assures that it is possible to observe accurately all the components of a signal until a frequency component equal to the half sample frequency [24]. From this standpoint, it is important to observe at least the frequency components that belong to the good sensitive region of the human hearing system. In this paper, a sample frequency equal to 25 kHz, allows for observing until 12.5 kHz, has been employed.

F. Room Measurement Noise measurement can be more complex than vibration measurement. Several factors like size of source, surroundings, and measurement points may influence the noise measurement. An ordinary laboratory of an industrial workspace can be used for noise investigation if the placement of the devices into the room is the same for multi-measurements of several machines. In this way, it is possible to compare the measurements obtained with the same surrounding conditions. To obtain the most accurate measurements, it is necessary to eliminate the sound coming from the environment. The best solution that is also the most expensive is to perform the measurement in an anechoic chamber. In this paper, all the tests have been performed in an ordinary electric machine laboratory where the background noise has been measured and was found to be negligible (7–8 dB) in comparison to the sound emission at the operating condition (110–120 dB). G. Conclusions Regarding the Stator Skew Improvements due to the stator skew are seen, since the stator modes are shifted to lower frequencies and the force variations are decreased. It can be noticed a reduction in the peak acoustic and vibration emissions equals 10 dB. Improvement of more than 8 [dB] for the SMPM and 4 [dB] for IPM are measured (see Fig. 21).

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TABLE AI T ECHNICAL C HARACTERISTICS OF THE S TUDIED M ACHINES

TABLE AII G ROUP OF F ORCES

Skewing the stator enables, as detailed in [19], to shift the modal frequencies and then to reduce the resonance phenomena during the operating of the targeted motor. Indeed, the modification of the mechanical rigidity leads first to a reduction of the resonance frequency and second to a mitigation of the amplitude of the resonance. More experimental results proving, on the particular case of the motors considered in this study, the important effect of stator slots skewing can be found in [19].

X. C ONCLUSION This paper presents a full investigation of the forces for SMPM and IPM industrial motors having concentric windings. This paper introduced tangential forces usually not considered in previous studies. Indeed, some of their harmonic frequencies were found closed to mechanical resonance frequencies. In addition, it has been observed that for concentric winding machines, the tangential forces variations are not negligible in comparison with the normal forces variations, even if the mean value of the tangential forces equal to zero whereas the mean value of normal forces is high. As already mentioned in the literature, the results have confirmed that the choice of the number of coil sides per slot has a strong influence on the vibrations and noise. PWM strategy and its resulting current harmonic have an effect on the higher vibration frequencies. Due to the straight teeth and the large slot opening, the local reluctance effect of the stator MMF only is non negligible. For all rotor configurations (SMPM and IPM), the one coil side slot configuration leads to higher amplitudes of vibrations, due to the winding factor harmonics. This fact is valid even if the magnetic motor symmetry is already 4 (48 slots, 44 poles). Moreover, calculation results show that the IPM rotor configuration will lead to higher vibrations and acoustic noise that SMPM rotor, because the air-gap flux density is higher so that the magnetic forces (mean value and variations) are higher. Of course, it is also due to the fact that the mechanical response of the stator (which is the main location of vibrations causing the noise) is not affected a lot when changing the rotor topology. Then, if the source of noise (force variations) is increased and the mechanical response is not changed a lot, then the output of the system (the SPL) is increased.

The authors have proposed to use a skewed stator to mitigate the vibrations. This technique shows a drastic improvement, proved by deep 3-D FE simulations and complete measurements. This solution is clearly well known to mitigate the torque ripple due to reluctance effect. However, in this case, the skew angle equals to one slot pitch (2π divided by the teeth number). However, in the present case, such a choice will lead to cancel the back EMF. In fact, assuming that the vibrations are created by the magnetic forces variations, we have proposed a choice of the skew angle to reduce those variations. In the case of the considered motors, the construction of the motors was nearly not changed. Indeed, the skew pitch was so small in comparison with the axial length that ETEL was able to use the same elementary coils to achieve the winding. The ratio of skew pitch versus the motor length is clearly the key limitation of the proposed technique. If the motor length is too small, the skew angle will be high and the construction difficult. In conclusion, this simple passive solution has the following advantages clearly interesting in an industrial context: • no change of the PM magnetization and more generally no change of the rotor; • no change of the currents (no modification of the motor feed and control); • no change of the number of poles and teeth; • nearly no change of the performance; • nearly no change of the stator construction except the skew of the laminations. A PPENDIX The technical characteristics of the targeted machines are detailed in Table AI. Table AII presents the group of teeth that are submitted to the same magnetic forces due to symmetries.


R EFERENCES [1] A. M. El-Refaie and T. M. Jahns, “Optimal flux weakening in surface PM machines using concentrated windings,” IEEE Trans. Ind. Appl., vol. 41, no. 3, pp. 790–800, May/Jun. 2005. [2] A. M. El-Refaie, T. M. Jahns, P. J. McCleer, and J. W. McKeever, “Experimental verification of optimal flux weakening in surface PM machines using concentrated windings,” IEEE Trans. Ind. Appl., vol. 42, no. 2, pp. 443–453, Mar./Apr. 2006. [3] J. Cros and P. Viarouge, “Synthesis of high performance PM motors with concentrated windings,” IEEE Trans. Energy Convers., vol. 17, no. 2, pp. 248–253, Jun. 2002. [4] F. Magnussen and C. Sadarangani, “Winding factors and Joule losses of permanent magnet machines with concentrated windings,” in Proc. IEEE IEMDC, Madison, WI, Jun. 1–4, 2003, pp. 333–339. [5] A. M. EL-Refaie, “Fractional-slot concentrated-windings synchronous permanent magnet machines: Opportunities and challenges,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 107–121, Jan. 2010. [6] Z. Q. Zhu and D. Howe, “Electromagnetic noise radiated by brushless permanent magnet dc drives,” in Proc. ICEM, Sep. 8–10, 1993, pp. 606–611. [7] Z. Q. Zhu, Z. P. Xia, L. J. Wu, and G. W. Jewell, “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,” in Proc. IEEE ECCE, 2009, pp. 3443–3450. [8] Y. S. Chen, Z. Q. Zhu, and D. Howe, “Vibration of permanent magnet brushless machines having a fractional number of slots per pole,” IEEE Trans. Magn., vol. 42, no. 10, pp. 3395–3397, Oct. 2006. [9] Z. Q. Zhu, D. Ishak, D. Howe, and J. T. Chen, “Unbalanced magnetic forces in permanent magnet brushless machines with diametrically asymmetric disposition of phase windings,” IEEE Trans. Ind. Appl., vol. 43, no. 6, pp. 1544–1553, Nov./Dec. 2007. [10] N. Velly, N. Takorabet, F. Meibody-Tabar, and P.-Y. Liégeois, “Magnetic forces calculation in surface PM motors with asymmetric stator windings for avionic applications,” in Proc. IEEE IEMDC, Miami, FL, May 3–6, 2009, pp. 1134–1139. [11] F. Magnussen and H. Lendenmann, “Parasitic effects in PM machines with concentrated windings,” IEEE Trans. Ind. Appl., vol. 43, no. 5, pp. 1223–1232, Sep./Oct. 2007. [12] N. Bianchi, S. Bolognani, M. D. Pre, and G. Grezzani, “Design considerations for fractional-slot winding configurations of synchronous machines,” IEEE Trans. Ind. Appl., vol. 42, no. 4, pp. 997–1006, Jul./Aug. 2006. [13] T. Sun, J.-M. Kim, G.-H. Lee, J.-P. Hong, and M.-R. Choi, “Effect of pole and slot combination on noise and vibration in permanent magnet synchronous motor,” IEEE Trans. Magn., vol. 47, no. 5, pp. 1038–1041, May 2011. [14] A. Cassat and A. Miraoui, “Phénomènes vibratoires dans les moteurs synchrones à aimants permanents—Modélisation et recherche de méthodes de réduction des vibrations,” Vibrations in Permanent Magnets Synchronous Motors—Modeling and Vibrations Reduction Methods Research, 2007/2008, INTERREG IIIA Project, Swiss Reference: 101/AJ/ 9.37, French Reference, ref. 6784. [15] J. K. Tangudu, T. M. Jahns, A. EL-Refaie, and Z. Q. Zhu, “Lumped parameter magnetic circuit model for fractional-slot concentrated-winding interior permanent magnet machines,” in Proc. ECCE, San Jose, CA, Sep. 20–24, 2009, pp. 2423–2430. [16] J. P. Wang, D. K. Lieu, W. L. Lorimer, and A. Hartman, “Comparison of lumped parameter and finite element magnetic modeling in brushless DC motor,” IEEE Trans. Magn., vol. 33, no. 5, pp. 4092–4094, Sep. 1997. [17] DCRAD software designed for Seagate Technology Ltd. USA. [18] D. Torregrossa, A. Khoobroo, and B. Fahimi, “Prediction of acoustic noise and torque pulsation in PM synchronous machines with static eccentricity and partial demagnetization using field reconstruction method,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 934–944, Feb. 2012. [19] D. Torregrossa, F. Peyraut, M. Cirrincione, C. Espanet, A. Cassat, and A. Miraoui, “A new passive methodology for controlling the noise in electrical machines: Impact of some parameters on the modal analysis,” in Proc. IEEE IEMDC, 2010, pp. 233–238. [20] D. Torregrossa, F. Peyraut, C. Espanet, A. Cassat, and A. Miraoui, “A new estimation of electromagnetic sound power radiated by a PM machine: An active and passive control guideline,” in Conf. Rec. IEEE IAS Annu. Meeting, Houston, TX, Oct. 4–8, 2009, pp. 1–4. [21] S. P. Verma and W. Li, “Measurement of vibrations and radiated acoustic noise of electrical machines,” in Proc. 6th ICEMS, 2003, vol. 2, pp. 861–866.

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[22] A. Mozurasa and E. Podzharovb, “Measurement of large harmonic vibration amplitudes,” J. Sound Vib., vol. 271, no. 3–5, pp. 985–998, Apr. 6, 2004. [23] IEEE Test Procedure for Airborne Sound Measurements on Rotating Electric Machinery, IEEE Std. 85-1973, 1980. [24] A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.

Alain Cassat was born in Lausanne, Switzerland, in 1946. He received the M.Sc. degree in electrical engineering and the Ph.D. degree from the Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland, in 1970 and 1977, respectively. From 1981 to 1986, he was the Director of Engineering of Applied Motion Products, Scotts Valley, CA, at the European headquarters. From 1986 to 2011, he was a Research Associate in the Integrated Actuator Laboratory at EPFL-STI-IMT-LAI and also a Consultant for Seagate Technology Inc., Scotts Valley, CA. Since 2011, he has been the Chief R&D Officer at BCD Engineering, in Lausanne. His research activities are centered on computer-aided design (CAD) of brushless dc motors, sensorless controls, linear motors, and high-speed public MAGLEV and multi-mobile transportation systems.

Christophe Espanet (M’04) was born in Belfort, France, in 1972. From 1991 to 1995, he studied at the Ecole Normale Supérieure in Paris, France. He received the Ph.D. degree from the University of Franche-Comte, Belfort, in 1999. His doctoral research dealt with the design and optimization of PM high-torque in-wheel motors. From 1999 to 2007, he was an Associate Professor in the Laboratory of Electrical Engineering and Systems. Currently, he is a Full Professor at the University of Franche-Comte, Belfort, and the Head of the Team of Energy Conversion Systems Design in the FEMTO-ST Instiute. He is the author of more than 20 international Transactions papers and more than 60 international conference papers. His research interests include the modeling and design of electrical systems and, in particular, PM synchronous machines.

Ralph Coleman graduated in electrical engineering from the Federal Institute of Technology of Lausanne, Lausanne, Switzerland, in 1996. After two years working on dc and brushless motor controllers with a research team at Portescap, he joined Technosoft, where he was able to gain experience in the field of digital signal processors for motion control. Since 2000, he has been working for ETEL, Môtiers, France, first as a Project Leader for space applications, then as a Manager of a research team, and finally as a Senior Researcher since 2012. His main contributions are in the fields of system identification, innovative motion control algorithms, active vibration isolation systems, synchronous motor design, and hardware-in-the-loop test equipment.

Luc Burdet received the Master’s degree in microtechnics engineering and the Ph.D. degree from the Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland, in 2002 and 2006, respectively. From 2007 until 2011, he worked as a Researcher on electromechanical design, motor noise reduction, and insulation improvement at the company ETEL SA in Môtiers, Switzerland. Since 2011, he has been working on electrical motor and mechatronics systems development at SwissMeo SA in Peseux, Switzerland. Since 2012, he has also been a Lecturer at the HEIG-VD for mechatronics.

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Emmanuel Leleu is born in Ste Catherine, France, in 1979. From 1999 to 2003, he studied at the Polytechnic School of the University of Nantes, Nantes, France. He received the Ph.D. degree from the University of Technology of Belfort-Montbeliard, Belfort, France, in 2009. His doctoral research dealt with vibration minimization in electrical drives fed by large-power pulsewidth modulation inverters. Currently, he is an R&D Engineer with General Electric Conversion Power, Belfort, France. He is working on the design of power conversion systems, and he is an expert in the area of electromagnetic vibrations of electric machines

Dimitri Torregrossa (S’11) was born in Palermo, Italy, in 1982. He received the Laurea degree (summa cum laude) in electrical engineering from the Università degli studi di Palermo, Palermo, in 2007. He has been working toward the Ph.D. degree in electrical engineering (electrical machines and energy) at Belfort-Montbéliard University of Technology (UTBM), Belfort, France, since 2007. His special interests include vibration and noise in permanent-magnet synchronous motors, speed and torque control of rotating electric machines, and optimal control of wind generators.

Jérémie M’Boua (S’10) received the Master’s degree from the University of Technology of BelfortMontbeliard (UTBM), Belfort, France, in 2007. Since 2008, he has been working toward the Ph.D. degree at UTBM, where he also teaches in the Department of Electrical Engineering. His research concerns electric machine modeling.

Abdellatif Miraoui received the Ph.D. degree from the University of Franche-Comte, Belfort, France, in 1992. He has been a Full Professor of electrical engineering (electrical machines and energy) at BelfortMontbéliard University of Technology (UTBM), Belfort, France, since 2000. He is a Vice PresidentResearch Affairs at UTBM. He was the Director of the Electrical Engineering Department from 2001 to 2009, the Head of the “Energy Conversion and Command” Research Team (38 researchers in 2007), and the Editor of the International Journal of Electrical Engineering Transportation (IJEET). He is the author of over 60 journal and 80 international conference papers. He is the author of the first textbook in French about fuel cells: Pile à Combustible: Principes, Technologies Modélisation et Applications (Ellipses-Technosup, 2007). His special interests include fuel cell energy, and energy management (ultra capacitor, batteries). Prof. Miraoui is a member of several international journal and conferences committees. He is a member of the IEEE Power Electronics, IEEE Industrial Electronics, and IEEE Vehicular Technology Societies. He is a Doctor Honoris Causa of Cluj-Napoca Technical University, Romania. In 2007, he received a high distinction from the French Higher Education Ministry, the “Chevalier dans l’Ordre des Palmes Académiques.” He was also distinguished as an Honorary Professor by the University of Brasov, Romania.