HAL Id: hal-02958308
https://hal.archives-ouvertes.fr/hal-02958308
Submitted on 5 Oct 2020
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Harmonic pressure optimization on numerical electric motor model
Jaafar Hallal, P. Pellerey, F. Marion, Frédéric Druesne, Vincent Lanfranchi
To cite this version:
Jaafar Hallal, P. Pellerey, F. Marion, Frédéric Druesne, Vincent Lanfranchi. Harmonic pressure op-
timization on numerical electric motor model. 19th International Conference on the Computation of
Electromagnetic Fields COMPUMAG 2013, 2013, Budapest, Hungary. �hal-02958308�
Abstract— Audible noise of electric machines has become an important criterion in their design. In this paper we used a multi- physics numerical model (electromagnetic-dynamic) in order to predict mechanical vibration caused by magnetic pressure in a wound rotor synchronous machine. The final objective is to reduce this vibration. The novelty of this paper is to use an optimization method applied to this multi-physics numerical model in order to reduce important vibration peaks thanks to magnetic pressure harmonics.
Index Terms— Electric machines, frequency response, harmonic analysis, magnetic forces, numerical models, optimization, vibrations.
I. I NTRODUCTION
As a result of increasing usage of electric machine especially in vehicles, and with respect to the European standards, it has become necessary to reduce noise damages emitted by such machines, while keeping a good proportion of benefits. In this paper we optimized the motor on magnetic pressure criteria, unlike most cases where optimization focus on loss energy or torque level and quality [1]-[2]. Analytical models have been developed in order to calculate magnetic pressure and vibrational behavior [3]. In this context, optimizations were done on discrete criteria (slot numbers) [4].
A new approach is to optimize the spectrum of the magnetic pressure, then by applying a transfer function enable us to observe their vibratory effect.
Two finite element models are used:
2D Electromagnetic model to calculate magnetic pressure applied on the stator.
3D Mechanical model to calculate the frequency response.
A coupling tool implemented in Matlab project magnetic pressure calculated by Flux 2D on the dynamic model, and calculates frequency response using MSC. Nastran. With good precision and acceptable computation time, this coupling seems to be a good way to calculate magnetic vibration [5]-[6].
II. M ODELING A. Presentation of machine
This study was done on a wound rotor synchronous machine, with 48 stator slots and 2 pairs of poles. The electromagnetic 2D model represents ¼ of the machine with 7062 elements T3, unlike the dynamic 3D model which represent the whole stator with 26400 elements H8. (Fig. 1)
Fig. 1. Electromagnetic and dynamic meshes of wound rotor synchronous machine
B. Magnetic pressure
The magnetic pressure is calculated on the stator inner surface thanks to a finite element solver (Flux 2D). It can be written as [7]:
{[ ( )] } (1) Where represent the radial flux density. , and represent angular position, time and the permeability of air respectively. The computation of magnetic pressure is detailed in the full paper.
C. Frequency response
This magnetic pressure can vibrate the stator causing a lot of problem. We projected this magnetic pressure on a dynamic mesh thanks to the coupling tool implemented in Matlab, in order to calculate the frequency response (MSC. Nastran).
̈( ) ̇( ) ( ) ( ) (2) Forced vibrations are described by (2); M, C and K are respectively mass, damping and stiffness matrixes, f is the load vector and u is the displacement vector. The frequency response computation is detailed in the full paper.
III. O PTIMIZATION METHOD
In this study, we proposed to optimize the electromagnetic finite element model with the software Got-It. In order to reduce computation time, while keeping good results, this software proposes to apply the sequential surrogate optimizer (SSO) as an optimization algorithm.
SSO build a response surface, then apply the genetic algorithm to it, and finally compare the value of the surrogate (response surface) to the real one (finite element). If the results are too different, the SSO automatically reiterates the process by refining the response surface and reducing the research domain arround the considered point [8].
Harmonic pressure optimization on numerical electric motor model
J. Hallal 1 , P. Pellerey 1 , F. Marion 2 , F. Druesne 1 , and V. Lanfranchi 1
1
Université de Technologie de Compiègne, Compiègne, France [email protected]
2
Cedrat, Meylan, France
Manuscript received January 1, 2008 (date on which paper was submitted for review). Corresponding author: F. A. Author (e-mail:
[email protected]).
Digital Object Identifier inserted by IEEE
IV. C OMPUTATION A. Design Parameters:
In order to reduce computation time and according to vibration results, we chose to optimize harmonics 4, 12, and 48 in the spectrum of magnetic pressure applied on the stator.
Screening study shows that the distance modifying the curvature of the rotor pole arc (PA), the slot opening (SO), and the slot corner radius (RS) are the most influent parameters on optimization criterions.
B. Torque optimization
First of all, we tried to optimize the torque level and quality. Fig. 2 shows that we can increase torque about 3.5%, or reduce the peak to peak amplitude about 16.8%, by varying design parameters.
Fig. 2. Torque optimized C. Harmonics optimization
In this part we tried to optimize the shape of the curve of magnetic pressure, by choosing different harmonics as objective function allowing a 2% as a maximal loss in torque level. The table I shows the different design models, optimized harmonics, optimized values of influent design parameters, the loss in torque level, and the gain in peak value. According to optimization results, an optimization of a precise harmonic can change the value of other harmonics by different level.
Table I Optimization results Model Principal harmonic
optimized
Influent
parameter Torque Peak
D4 H 4 PA (-28%)
SO (-20%) -1.8% -26%
D5 H 12
PA (-29%) SO (-20%) RS (+5%)
-1.7% -26.8%
D6 H 48 PA (-29%)
SO (-20%) -1.8% -27.8%
Fig. 3. Vibration results
From vibratory level in Fig. 3, we notice that peaks at 6 and 9 kHz reduced about 14 dB for D5 and D6. Peak at 2.4 kHz are reduced about 9 dB for D4, and the peak at 7.2 kHz are decreasing about 6 dB for all design model.
V. C ONCLUSION
This study proved the feasibility and the interest of this optimization method even on unusual criteria (magnetic pressure harmonics).
Mechanical vibration can be reduced by optimizing some magnetic pressure harmonics. With acceptable loss in torque level we can improve vibration results.
This optimization method, and the coupling tool implemented in Matlab, can be used to predict and optimize magnetic vibration on other type of motor, provided that his geometry is not skewed.
R EFERENCES
[1] D. Wang, X. Wang, M.K. Kim and S.Y. Jung, “integrated optimization of two design technique for cogging torque reduction combined with analytical method by a simple gradient descent method”, IEEE Trans. Magn., vol. 48, no. 8, Aug. 2012
[2] M. Ashabani and Y.A.R.I. Mohamed, “multiobjective shape optimization of segmented pole permanent-magnet synchronous machines with improved torque characteristics”
IEEE trans. Magn., vol. 47, no. 4, Apr. 2011
[3] J. Le Besnerais, V. Lanfranchi, M. Hecquet and P.
Brochet,” prediction of audible magnetic noise radiated by adjustable-speed drive induction machines”, IEEE Trans. Ind.
Appl. , vol. 46, no. 4, Jul./Aug. 2010
[4] J. Le Besnerais, V. Lanfranchi, M. Hecquet and P.
Brochet,” optimal slot numbers for magnetic noise reduction in variable-speed induction motors”, IEEE Trans. Magn., vol.
45, no. 8, Aug. 2009
[5] P. Pellerey, V. Lanfranchi, G. Friedrich, “Coupled numerical simulation between electromagnetic and structural models, influence of the supply harmonics for synchronous machine vibrations” IEEE trans. Magn., vol. 48, no. 2, Feb.
2012
[6] M. van der Giet, C. Schlensok, B. Schmülling, and K.
Hameyer, “Comparison of 2-D and 3-D coupled electromagnetic and structure-dynamic simulation of electrical machines”, IEEE trans. Magn., vol. 44, no. 6, Jun. 2008 [7] W. finley, M. Hodowanec, and W. Holter, “An analytical approach to solving motor vibration problems,” in Proc. 46
thAnnu. Petroleum Chem. Ind. Conf., 1999, pp. 217-232 [8] M.C. Costa, J.L. Coulomb, Y. Maréchal, and S. I. Nabeta,
“An adaptive Method Applied to the diffuse element approximation in optimization process” IEEE Trans. Magn., vol. 37 no. 5, Sept. 2001
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10-3 0.937
0.969 1 1.031 1.063 1.094
Time [sec]
Torque [pressure unit]
initial torque torque level optimized torque quality optimized
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-30 -25 -20 -15 -10 -5 0 5 10 15 20
frequency [kHz]
Acceleration [dB]
initial D4 D5 D6
