Fast Computation of Electromagnetic Vibrations in ...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 2, FEBRUARY 2012

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Fast Computation of Electromagnetic Vibrations in Electrical Machines via Field Reconstruction Method and Knowledge of Mechanical Impulse Response Dimitri Torregrossa, Babak Fahimi, Senior Member, IEEE, François Peyraut, and Abdellatif Miraoui

Abstract—The main objective of this paper is to provide an efficient computational model for fast and accurate calculation of electromagnetically induced vibrations in electrical machines. Although a three-phase permanent-magnet synchronous machine has been used in this paper, the same methodology can be extended to other types of electric machinery. A brief comparison between the different methods for structural analysis in electrical machines is introduced. The method proposed in this paper uses finiteelement analysis in order to extract the impulse responses that are used in calculating the vibration. A field reconstruction method is used for the electromagnetic field analysis. Index Terms—Field reconstruction method (FRM), mechanical impulse response (MIR), vibration evaluation, 3-D finite-element method (FEM) mechanical analysis.

I. I NTRODUCTION

P

ERMANENT-MAGNET (PM) synchronous machines (PMSMs) have been the focus of many research studies over the past few decades [1]–[10]. Fault diagnosis, speed and torque control, and vibration and noise mitigation are among the main research areas that have witnessed significant improvement. There are three main sources of acoustic noise in an electrical machine, namely aerodynamic, mechanical, and electromagnetic sources. For electrical machines with a rated power lower than 15 kW and a rotational speed lower than 1500 r/min, the majority of acoustic noise stems from the electromagnetic origin [1]–[4]. Therefore, vibrations originated from electromagnetic forces are the main focus of this paper. As shown in Fig. 1, accurate assessment of vibration in electrical machines requires a multiphysics analysis encompassing electromagnetic and structural field problems. Furthermore, computation of acoustic noise will require an additional step in computation of the fluid dynamic field problem which is excited Manuscript received June 11, 2010; revised September 13, 2010 and November 19, 2010; accepted December 23, 2010. Date of publication April 21, 2011; date of current version October 18, 2011. D. Torregrossa is with the Département Génie Électrique et Systèmes de Commande, Université de Technologie de Belfort–Montbéliard, 90010 Belfort, France (e-mail: [email protected]). B. Fahimi is with the Department of Electrical Engineering, The University of Texas at Dallas, Richardson, TX 75080 USA (e-mail: [email protected]). F. Peyraut is with the Laboratoire Mécatronique, Méthodes, Modèles et Métiers, Université de technologie de Belfort–Montbéliard, 90010 Belfort, France (e-mail: [email protected]). A. Miraoui is with the Université de Technologie de Belfort–Montbéliard, 90010 Belfort, France (e-mail: [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/TIE.2011.2143375

Fig. 1. Multiphysics analysis of electric machines.

by the deformations of the vibrating parts of the electric machine. It must be noticed that calculation of the emitted acoustic noise will consist of development of an efficient acoustic model. The input to the latter is the vibration and acceleration of the machine structure. This evaluation step is possible only if the material properties of the structure and the loading forces are known. Calculation of the electromagnetically induced vibrations, along with material properties of the electric machine, is the key step in development of an accurate and fast acoustic model of an electrical machine. A review of the past works in the literature indicates that the majority of the work in this field can be classified into two categories, namely, finite-element (FE) method (FEM) computation or an abstract analytical calculation. The first group of techniques requires a structural model of the electrical machine under study [1], [2], [5]. To obtain precise results, this will require substantial computational resources. The most salient attribute of the FEM is that it allows for computation of the vibration at any point of the structure with a high level of precision. In the contrary, analytical methods allow for quick computation of the vibration at select points using empirical and simplified analytical formulas [3], [4]. However, these analytical models suffer from poor accuracy. Notably, the analytical methods also require certain electromagnetic information such as direct and quadrature axis inductances [9], [10]. As it appears, the existing methods suffer from either long computational time or low accuracy. In this paper, the authors use a field reconstruction method (FRM) [12] to quickly and precisely calculate the distribution of the electromagnetic forces acting on the stator and rotor of a PMSM. The method is accurately explained in [12], and it can be used for several types of electrical machines, namely PMSMs, synchronous reluctance machines, and induction machines. The

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 2, FEBRUARY 2012

analysis, saturation can be neglected [12]. Impact of magnetic saturation, hysteresis, and eddy currents on the flux and force densities may also be of interest only in high-speed applications (for example, in a compressor employed in fuel cell systems). Analytical calculation of the electromagnetic forces and classical FE calculation are detailed in [3] and [4] and in [1] and [2], respectively. Electromagnetic forces are necessary to perform a transient structural FE analysis. To save computation time, the transient structural analysis is performed using the modal superposition method. This method requires a modal analysis to estimate the natural frequencies of the structure. The free vibration equation of a linear undamped system is thus considered [13]   (3) [K] − ωi2 [M ] {φ}i = {0} Fig. 2. Block diagram for a conventional structural analysis.

limitations of the application of this method are invoked in [12] and in this paper as well. In this paper, the authors have chosen a PMSM with a surface-mounted PM configuration to demonstrate the time efficiency of the proposed method. The FE mechanical model of the electrical machine under study has been validated with experiments. In order to calculate the mechanical transfer function of the system, an impulse response has been applied to a FEM transient structural model of the machine. In this paper, the following results have been presented: 1) a new model for simulating the transient structural response of the system; 2) fast prediction of vibration at the targeted points in the structure for any arbitrary waveform of the stator currents; 3) a comparison between the computational times required by the existing and the proposed numerical methods.

n 

{di }

(5)

i=1

Fig. 2 shows the block diagram for a complete conventional FEM structural analysis of an electrical machine. As can be noticed from Fig. 1, there are three main computational steps, namely, stator current analysis, electromagnetic FE analysis, and structural analysis. Upon calculating the tangential and normal components of the flux density using the stator current waveform and by the virtue of the FRM technique, one can use the Maxwell stress method to compute the electromagnetic force components as shown in the following [12]: 1 Bn Bt μ0  1  2 fn = Bn − Bt2 2μ0

It should be noticed that the modal analysis is an important step because the main computational effort of the proposed method is related to the solution of (4). The last output of the block diagram (see Fig. 2) is the vibration at any points of interest on the structure that can be used for acoustic computation. The calculation of these vibrations can be done by the virtue of the superposition theorem [13] {d} =

II. F UNDAMENTALS

ft =

where {φ}i and ωi represent the ith mode shape and the ith natural circular frequency of the structure, respectively. [M ] and [K] are the mass matrix and the stiffness matrix, respectively. Equation (4) is satisfied if neither the eigenvector nor the determinant of the matrix part of (4) is zero. The first case corresponds to a trivial solution which is of no interest while the second case provides the natural circular frequencies by solving the eigenvalue problem   (4) det [K] − ωi2 [M ] = 0.

(1) (2)

where Bn and Bt are the normal and the tangential components of the magnetic flux density, respectively, and μ0 is the magnetic permeability of the air. The magnitude of the forces acting on the stator teeth is deduced from (1) and (2). Since PM machines usually have a relatively large effective air gap, for the purposes of radial electromagnetic force

where {d} is the displacement at each point of the system, di is the modal displacement resulting from the previous modal analysis (at the selected point of interest), and n is the highest order of the modes that has been taken into account. Active noise control directly uses the current waveforms feeding the electrical machine in order to mitigate the vibration. If the current waveform is modified, the magnetic field distribution (and, consequently, the electromagnetic forces) changes. For evaluating the vibration level with a different current waveform, it is necessary to perform at least two FE simulations: one for the evaluation of the electromagnetic forces and one for the vibration calculations. The time required for these two calculations can be considerable. From this standpoint, it is clear that FEM is not an effective way to improve and verify any active noise control. The new method proposed in this paper can be summarized by the following flowchart. One can detect three main computational blocks in Fig. 3. The first block has been explained in Fig. 2. The second computational block allows for calculating the magnetic field distribution and, consequently, the electromagnetic forces

TORREGROSSA et al.: FAST COMPUTATION OF ELECTROMAGNETIC VIBRATIONS IN ELECTRICAL MACHINES

Fig. 3.

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Block diagram of the proposed analysis.

Fig. 5. Setup rig test.

Fig. 4.

Linear system representation of the structural system.

(radial and tangential) acting on the stator teeth using FRM. The computational time required for this step is almost 1000 times less than that of the classical FEM while maintaining the same precision as that in the FEM technique. The last step is the mechanical computation which is directly obtained by the knowledge of the impulse response. The structural field problem considered in this paper is assumed to be linear. It should be noticed that the targeted machine is a PMSM with a low rated rotational speed (in this case, the hypothesis of linearity can be accepted). Displacement of a probing point due to a concentrated electromagnetic force acting on the stator tooth can be expressed as (in a polar system of coordinates) dSj = dSj,rar + dSj,φaφ + dSj,zaz

(6)

where ar is the radial distance unit vector, aφ is the azimuth unit vector, and az is the axial position unit vector. In this paper, only displacement in a direction normal to the probing surface has been considered, and axial displacement has not been considered. However, the proposed technique can be extended to cover more directions. Furthermore, the electromagnetic forces are considered as concentrated forces which are acting in the radial direction and are applied to the center of the stator tooth. The model can thus be expressed via the impulse responses hSj (t) (j and S represent the number of the stator teeth and the location of the probing point, respectively), as shown in Fig. 4. The response of a linear system [i.e., y(t)] to an input function [i.e., x(t)] is commonly described by convolution integral ∞ x(τ ) · h(t − τ ) dτ.

y(t) = −∞

(7)

If the input to the structure is a unitary impulse function, the answer of the system is the impulse response. By exciting the structural model of the machine using a unitary impulse force, one can extract the entire frequency domain information of the system. In this case, all of the structure’s natural frequencies can be excited. Forces and vibration can be viewed as the input and the output of the linear structural system. The transfer function of this system describes the link between the applied forces and the vibration level at particular points of interest. One of the main objectives of this paper is to find the link between the forces applied on the stator teeth and the vibration computation in three arbitrarily selected points on the exterior of the stator. Having captured the time evolution of the impulse response, it is possible to evaluate the vibration level of the electrical machine for any waveform of electromagnetic forces caused by any waveform of the stator current. This, in turn, circumvents repeating any time-consuming multiphysics FEM computation, particularly in an iterative optimization problem such as active noise control.

III. VALIDATION OF THE M ECHANICAL M ODEL In order to validate the mechanical model, a comparison between experimental setup and simulated results is necessary. Resonance phenomena occur only if any exerting force frequency matches (or very closely coincides) with any natural frequencies of the structure. In this case, it is possible to observe high levels of vibration and, consequently, higher acoustic noise. In order to estimate these resonance frequency values, it is needed to analyze the spectrum of the acceleration and search for the peak values. Frequencies corresponding to these crest values are the resonance frequencies or the modal frequencies. For accurate modeling of the stator structure, a 3-D FEM model of the stator has been realized.

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TABLE I C OMPARISON OF M ODAL F REQUENCIES

Fig. 6. Structural FE model of the stator.

occurring through the three directions of the Cartesian axis (i.e., x, y, and z) can be computed. In this paper, three impulse responses, for three different points located in the x-axis, yaxis, and z-axis, have been calculated. Given the 12-slot configuration of the stator, this will result in a total of 36 impulse responses. The first point is located on the right surface of the stator shown in Fig. 6. The second point is located on the top surface of the stator where the accelerometer is placed. The last point is located on the front surface of the stator tooth. Since tooth vibration is a good indicator of the vibration level in an electrical machine, the proposed selection of the probing points offers a realistic picture of the vibration. The importance of an impulse response simulation is underlined in [14]. In order to simulate the impulse response, a modal superposition transient analysis has been performed by using Ansys 11.0. The general dynamic equation of motion for a damped structural system has thus to be considered [M ]{a} + [C]{v} + [K]{d} = {F }

Fig. 7. Example of vibration spectrum.

Fig. 5 shows the setup rig test used for obtaining the acceleration measurements. The accelerometer used during the test is the 1000A Vibrametric. It allows for measuring acceleration in the frequency range between 3 and 15 kHz. Fig. 6 shows the stator modeled using Ansys 11.0. This program allows for precise modeling of the stator and its attachment to the rest of the system. Notably, the mounting arrangement of the machine can have a profound impact on its mechanical natural frequencies. The stator is mounted horizontally on the baseplate using four screws. The FEM mesh of the whole structure contains almost 112.500 nodes. Fig. 7 shows the vibration spectrum measured for a speed of 750 r/min. Table I summarizes some comparison between the FEM resonance frequencies and those measured from the experimental setup used in our investigation. IV. I MPULSE R ESPONSE S IMULATIONS Impulse responses obtained from this analysis are the link between the magnetic forces applied to the stator teeth and the vibration at the selected points. Using the 3-D model that has been developed, the modal deformation of the structure

(8)

where [M ], [K], and [C] represent the mass, the stiffness, and the damping matrices, respectively. {a}, {v}, and {d} are the acceleration, the velocity, and the displacement of each mesh point of the system, respectively, and {F } is the applied load vector. Equation (8) is a second-order evolution equation in time. This differential equation could be solved using a time integration method as the Newmark scheme [13]. However, this method is considered tedious. The modal superposition method was selected in order to obtain a significant decrease of computation time. This method uses the mode shapes as a vector basis to calculate the response of the system by uncoupling the matrix equations. The global displacement of a given point is computed by summing the displacements di caused by individual modes to achieve the global displacement, as shown in (5). The modal contribution is linked with the modal shape via the following equation [13]: {di } = yi {φi }

(9)

where yi is the modal coordinate. This coordinate is calculated by incorporating (9) into (8) [M ]

n  i=1

y¨i {φi } + [C]

n  i=1

y˙ i {φi } + [K]

n  i=1

yi {φi } = {F }. (10)

The classical orthogonal property of the natural mode shapes is used next to deduce from (10) the following uncoupled

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system of equations where the unknown quantities are the modal coordinates yi : y¨i + ci y˙ i + ωi2 yi = Fi ,

for i = 1, . . . , n

(11)

where ci and Fi are defined through the Euclidean scalar product ci = [C]{φi }, {φi }

Fi = {F }, {φi } .

(12)

The fraction ξi of critical damping for mode i is introduced by ξi =

ci , 2ωi

0 < ξi < 1.

(13)

Equation (11) can then be rewritten as follows: y¨i + 2ξi ωi y˙ i + ωi2 yi = Fi ,

i = 1, . . . , n.

(14) Fig. 8. Time evolution of the impulse response.

Equation (14) portrays a system of n uncoupled second-order linear differential equations with constant coefficients. As the time-consuming computation has been previously done in the eigensolver, each equation can be solved quickly and independently from each other. The general homogeneous solution yi1 is obtained by using the characteristic equation and a linear combination of solution basis yi1 (t) = αi exp(λi+ t) + βi exp(λi− t)    j 2 = −1. λi± = ωi −ξi ± j 1 − ξi2

(15) (16)

The constant coefficients αi and βi are determined by using initial conditions. The impulse response Ki is deduced from the solution basis by Ki (t) =

exp(λi+ t) − exp(λi− t) H(t) λi+ − λi−

(17)

where H represents the Heaviside function. The convolution product of Ki with the right-hand side of (14) provides a particular solution of (15) t yi2 (t) = 0

exp (λi+ (t − s)) − exp (λi− (t − s)) Fi (s) ds. λi+ − λi−

By using (15), (18) can be simplified to t Gi (t − s)Fi (s)ds

yi2 (t) = 0 ωi 1 − ξi2

t yi (t) = αi exp(λi+ t) + βi exp(λi− t) +

0

Gi (t − s)Fi (s) ds

. ωi 1 − ξi2 (21)

If the initial displacement and the initial velocity are assumed to be equal to zero, the constant coefficients αi and βi are null, and the corresponding terms in (21) vanish. It finally results from (5) and (21) that the displacement {d} is related to the applied load vector {F } by n t  0 Gi (t − s) {F (s)} , {φi } ds

φi . (22) d(t) = ωi 1 − ξi2 i=1 In this paper, the vibration due to electromagnetic forces needs to be computed. From this standpoint in (22), the applied load vector is a function of the spatial and time evolution of the magnetic flux in the air gap. The electromagnetic forces acting on the stator teeth depend on the magnetic flux density stemming from the PMs and the stator magnetomotive forces. Accordingly, (22) can be rewritten as n t  0 Gi (t − s) {B(s, I)} , {φi } ds

φi (23) d(t) = ωi 1 − ξi2 i=1

(18)

(19)

where the function Gi is defined by

  2 Gi (s) = exp[−ωi ξi s] sin ωi 1 − ξi s .

by (18) and (19)

(20)

The general solution of (14) is obtained by adding the general homogeneous solution (15) and the particular solution defined

where B(s, I) is a function of the magnetic induction depending on the stator currents, as introduced in (1) and (2). The number of modes taken into account is 50. The highest modal frequency is equal to 14 kHz. The sample frequency used for the transient analysis is 30 kHz. As described in [15], the magnitudes and the phases of the frequency impulse response function depend on the length of recording. If the duration time of the simulated impulse response is not longer than the time needed to reach the steady state, a truncation error due to finite record length can occur. From this standpoint, it is necessary to take into account a satisfactory time simulation. As an example, Fig. 8 shows the

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TABLE II PMSM S PECIFICATIONS

Fig. 9. Diagram block of performed model.

impulse response for the point located in the y-axis, when a single unitary impulse force is applied on one tooth. By analyzing Fig. 8, it can be observed that a damped sinusoidal impulse response exists. The time taken into account (0.03 s) is sufficient to reach the steady state (the amplitude is almost four orders of magnitude lower than that in the beginning). In addition, the use of mechanical impulse response depends on linearity of the partial differential equation describing the dynamics of the structural system. As long as the linearity condition holds, the use of the proposed method is permitted. Typical electric machines with a power of 15 kW and a rotational speed of less than 1500 r/min satisfy the linearity condition. It should be noticed that the electromagnetic vibration emissions are the main sources of vibration emissions in rotating electric machines only for low power (< 15 kW) and low speed (< 1500 r/min) [11]. A nonlinear phenomenon can limit the use of mechanical impulse response.

V. I DENTIFICATION OF THE T RANSFER F UNCTIONS The method summarized in Fig. 9 requires the simulation of 12 impulse response functions (transfer functions in the frequency domain). Since each transfer function is independent from others, it is noticed that these calculations could be accelerated in a further stage by using a parallel programming technique. The impulse response has been simulated for a duration of 0.03 s. Since the sampling frequency is equal to 30 kHz, 900 points are captured per impulse response. In order to obtain a fast computation of vibration, the convolution between input and transfer functions can be done in the discrete time domain. As such, (7) becomes

y(k) =

N 

x(n) · h(k − n)

(24)

n=1

where N is the number of the points comprising the two sequences h and x. In our case, N is equal to 900.

Fig. 10.

Electromagnetic radial force.

VI. V IBRATION C ALCULATION In order to illustrate the advantages of the developed model in terms of time simulation, some vibration simulations have been performed. For the electrical machine under study (for which key specifications are summarized in Table II), the vibration calculations for different current spectra have been done. The linear system shown in Fig. 3 becomes that in Fig. 9. By the knowledge of the rotational speed and the torque required by the drive, the stator current, fed by the inverter, has been measured. Consequently, a fast Fourier transformation of the stator current has been performed in order to evaluate the electromagnetic field distribution by the FRM. The 12 radial forces acting on the 12 stator teeth have been calculated. Furthermore, using the 12 impulse responses (H1 , H2 , . . . , H12 ), the vibration at the points under study has been evaluated. With the 12 impulse responses, it is possible to evaluate the contribution of each force acting on each stator tooth. The total displacement has been obtained by adding the 12 contributions using the superposition method. Different rotational speeds of the electrical machine with different brake torques have been tried, and the resulting current spectra have been measured. Fig. 10 shows the time evolution of the radial force applied on the center of a stator tooth. The operating conditions taken

TORREGROSSA et al.: FAST COMPUTATION OF ELECTROMAGNETIC VIBRATIONS IN ELECTRICAL MACHINES

Fig. 11. Electromagnetic spatial force distribution.

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Fig. 13. Vibration level on the second point.

Fig. 12. Vibration level on the first point.

Fig. 14. Vibration level on the third point.

into account are as follows: 833 r/min and 0.295 N · m of brake torque. For the same tooth in Fig. 10, Fig. 11 shows the spatial distribution of the electromagnetic force density acting on one stator tooth for the test motor. The tooth inner surface has been subdivided into 70 shares. For each one of those partitions, the calculation of the force density has been performed. It can be noticed that the radial force distribution on the different stator teeth is quite uniform. With this in mind, for performing the superposition analysis, each harmonic force has been applied on the center of each stator tooth. For each tooth, the average radial force over the tooth has been calculated. The same qualitative results are obtained for the other teeth and for other operating conditions. The same hypothesis has been already assumed in the literature [1], [2]. The radial electromagnetic forces calculated by the virtue of the FRM are the input to the mechanical model. Twelve convolutions among the 12 radial forces and the 12 impulse responses have been performed to obtain the time evolution of the displacement and vibration of the three probing points (as summarized in Fig. 9). Figs. 12–14 show the vibration of the

three points under study for a rotational speed of 833 r/min and a brake torque of 0.295 N · m. By analyzing the aforementioned results, one can determinate the most important probing point: The first point, i.e., the point on the cage, has a peak sinusoidal amplitude displacement of 5.5 × 10−8 m. This complete calculation with a Dell PC with an Intel Core Duo 1.86 GHz just needs 20 s of simulation. The most expensive computation is required by the electromagnetic calculations. The vibration calculation takes just a few tenths of a second. If the same vibration calculation had been performed by FEM, the time computation would have been 350 times larger. As explained in the literature [3], [4], [16]–[18] in the active mitigation, the harmonic current content plays a key role. Any modification of the power converter feeding the PMSM under study, for example, those proposed in [19] and [20], or the application or any passive filter can change the vibration and the emitted sound power. This efficient computational tool can be effectively used for design of optimal stator excitation used in preemptive noise cancellation technique in PMSM.

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VII. C ONCLUSION

Fig. 15. Vibration level on the first point for a different brake torque value.

A fast multiphysics computation of electromagnetic forces and vibration, using FRM and mechanical impulse response, has been presented in this paper. The experimental validation of a 3-D FEM of the PMSM under study has been performed, and the mechanical transfer functions have been simulated. The 3-D mechanical FEM has been validated by experimental results. Active mitigations of vibration in electric machines, like PMSM, require to modify the spectrum current feeding the electric machine in order to change the amplitude and the frequencies of the electromagnetic forces. This results in a different excitation of natural frequencies and, consequently, in a different vibration level and sound emission. Each modification of the spectrum current needs to verify the new value of vibration in order to establish if the modification is the right one. The method proposed in this paper allows for fast computation of the displacement of several key points of the structure under study in order to compare their resulting vibration. The described technique can be very useful for active mitigation of vibration of PMSM in real-time domain. The time required for reaching the steady-state value of displacement is small and allows to get the desired current profiles for improving the behavior of PMSM. The method described in this paper can also be applied to other types of rotating electrical machines. R EFERENCES

Fig. 16. Spectrum comparison of vibration for a different brake torque value.

To shed some light on this point, in this section, a comparison of the vibration in time and frequency domains for two different operating conditions is presented. The first operating condition is the same as that described for Fig. 12. The second one has a rotational speed equal to 833 r/min and a brake torque value of 0.378 N · m (28% higher). Fig. 15 shows the comparison of time evolution of the displacement for the two operating conditions. The case with a brake torque value equal to 0.378 N · m has a peak vibration magnitude (detected by the arrow) 30% higher than the starting case with a 0.295-N · m brake torque value (2.93 × 10−8 for the 0.378-N · m case and 2.31 × 10−8 for the 0.295-N · m case). This is due to the fact that different contents of current harmonic have resulted in amplified harmonic vibration. As can be noticed in the frequency domain (Fig. 16), a higher peak vibration magnitude involves a higher harmonic content in the spectrum comparison. For example, for the operating condition with a torque equal to 0.378 N · m, the harmonics at 55 and 111 Hz are 7% higher than those with a brake torque equal to 0.295 N · m. This will result in a bigger radiated sound power.

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TORREGROSSA et al.: FAST COMPUTATION OF ELECTROMAGNETIC VIBRATIONS IN ELECTRICAL MACHINES

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Dimitri Torregrossa was born in Palermo, Italy, in 1982. He received the Laurea degree (summa cum laude) in electric engineering from “Università Degli Studi Di Palermo,” Palermo, in 2007. Since 2007, he has been working toward the Ph.D. degree in electrical engineering (electrical machines and energy) in the Département Génie Électrique et Systèmes de Commande, Université de Technologie de Belfort–Montbéliard, Belfort, France. His special interests include vibration and noise in permanent-magnet synchronous machines, speed and torque control of rotating electric machines, and optimal control of wind generators. He is the author/coauthor of more than 15 international papers.

Babak Fahimi (S’96–M’00–SM’02) was born in Tehran, Iran. He received the B.S. and M.S. degrees (with highest distinction) in electrical engineering from the University of Tehran, Tehran, in 1991 and 1993, respectively, and the Ph.D. degree in electrical engineering from Texas A&M University, College Station, in 1999. During 1999–2002, he was a Research Scientist with Electro Standards Laboratories, Inc., Cranston, RI. He is currently a Professor of electrical engineering with the Department of Electrical Engineering, The University of Texas at Dallas, Richardson. He is the author or coauthor of more than 180 technical papers and 15 book chapters, including a chapter in John Wiley Encyclopedia on electrical and electronics engineering. He is the holder of three U.S. patents and has nine pending patents. His research interests include analysis of electromechanical energy conversion, digital control of adjustable speed motor drives, and design and development of power electronic converters. Dr. Fahimi was the General Chair of the IEEE Applied Power Electronics Conference and Exposition in 2010. He has been the Chairman of the Electric Machines Committee in the IEEE Industrial Electronics Society. He is an Associate Editor for the IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRONICS.

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François Peyraut was born in Bordeaux, France, in 1962. He received the Ph.D. degree from the Paris VI University, Paris, France, in 1991, under the supervision of Professor G. Duvaut in the field of the propagation of acoustic waves for submarine application. He defended his “Habilitation á Diriger les Recherches” in 2004 (graduated from the University of Franche-Comté, Belfort, France) in the field of the numerical modeling of hyperelastic materials. From 1992 to 1997, he was an Engineer with the private company Sciences Industries Conseils, Versailles, France, where he designed mechanical products by using the finite-element method. From 1997 to 2005, he was an Associate Professor in the Design and Mechanical Department, Université de Technologie de Belfort–Montbéliard (UTBM), Belfort, France. Since 2005, he has been a Full Professor in the field of computational mechanics and finite-element method with UTBM. He has been the Director of the Laboratoire Mécatronique, Méthodes, Modèles et Métie, UTBM, since 2010 and a Member of the UTBM Scientific Council since 2008. His major research interests include nonlinear mechanics and hyperelasticity. Dr. Peyraut is also a member of the Atelier Inter-établissements de Productique et Pôle de Ressources Informatiques pour la MÉCAnique institution, a French network organized in regional centers which provide more than one million hours of educational training per year. He has been the Codirector of the Franche-Comté Center since 2005.

Abdellatif Miraoui received the Ph.D. degree in electrical engineering. Since 2000, he has been a Full Professor of electrical engineering (electrical machines and energy) with Université de Technologie de Belfort–Montbéliard (UTBM), Belfort, France. He is the Vice President of Research Affairs with UTBM. From 2001 to 2009, he was the Director of the Electrical Engineering Department, UTBM, where he was the Head of the “Energy Conversion and Command” Research Team (38 researchers in 2007). His special interests include fuel cell energy, energy management (ultracapacitor, batteries, etc.) in transportation, design, and optimization of permanent-magnet synchronous machines, and electrical propulsion/traction. He is the Editor of the International Journal on Electrical Engineering Transportation. He is the author of over 60 journals and 80 international conference papers. He is the author of the first textbook in French about fuel cells: Pile á Combustible: Principes, Technologies Modélisation et Applications (Ellipses-Technosup, 2007). Prof. Miraoui is a member of several international journal and conference committees. He is a member of the IEEE Power Electronics Society, IEEE Industrial Electronics Society, and IEEE Vehicular Technology Society. He was recognized as Doctor Honoris Causa of Cluj-Napoca Technical University, Cluj-Napoca, Romania. He was also recognized as Honorary Professor of the Transylvania University of Bra¸sov, Bra¸sov, Romania. In 2007, he received a high distinction “Chevalier dans l’Ordre des Palmes Académiques” from the French Higher Education Ministry.