PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
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3D FEA of SMPM Accounting for Skew and End Windings
M. Hédi Gmiden and H. Trabelsi
Sfax Engineering School, University of Sfax, Tunisia
Abstract— This paper presents the use of the three dimensions finite element method for
analyzing the surface mounted permanent magnet motor. The saturation of the motor is taken
into account in determination of the flux distribution and the inductances. Skew and end windings
are also taken into account. The results are presented and compared to demonstrate the effect
of skew and end windings.
1. INTRODUCTION
Skew is applied to electrical machines in order to reduce undesirable effects such as cogging torques,
higher-harmonic air-gap fields, torque ripple, vibrations, and noise [1]. In permanent magnet
synchronous machines, generally, cogging torque is reduced by skewing the stator slots. The skewing
of a cylindrical machine induces an electrical field in the azimuthally direction. The skewing destroys
the typical translatory symmetry of a cylindrical machine. Different approaches for accounting skew
have been reported. Commonly, multiple slices, each of them represented by a two-dimensional
finite-element (FE) model, are connected in series in order to account for the skewing [2]. This
approach mainly increases the computational cost of finite element machine simulations.
End winding inductance is generally treated as a small negligible component of the winding
inductance in many motor applications [3]. However, the end winding inductance may actually be
a significant percentage of the phase inductance, particularly for motors with low length/diameter
ratio, small inherent phase inductances, or long-pitched windings. Some researchers have reported
that the end winding inductance has a substantial influence in axial air-gap flux machines [4].
Hence, for such cases, the accurate calculation of the end winding inductance is necessary. Different
methods for the calculation of end winding inductance have been reported [5, 6]. Of these, finite
element analysis (FEA) has been directly applied to calculate inductance or used in conjunction with
analytical methods. However, although the improved accuracy, FEA tends to be time-consuming,
particularly when 3-dimensional analysis is used. Care should be taken when working with FEA
modeling to ensure numerical accuracy. Therefore, an analytical technique is still attractive. Some
researchers have reported on the derivation of fast analytical techniques [7], but the accuracy may
be variable due to the simplifications made.
In the following, the three dimension finite element model of the study motor with the specific
meshing are presented. Next, the key issue of the procedure: how to account skew and end winding
of SMPM is discussed. Finally the obtained results are both presented and discussed achieving by
a conclusion.
2. 3-D FE MACHINE MODELS
Three phase SMPM with stator slots (Figure 1) having no skewing and with different angle of
skewing have been analyzed for two type of excitation, only permanent magnet (PM) excitation
Stator outer diameter
Stator inner diameter
rotor outer diameter
rotor inner diameter
Stator pole number
Stator slot number
Stack length
Airgap length
Slot area
120 mm
75 mm
74 mm
26 mm
4
24
65 mm
0.5 mm
65 mm2
Table 1: Motor data.
Figure 1: Three phase SMPM model.
Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 859
Figure 2: Stator slots having no skewing.
Figure 3: Stator slots with skew.
(a)
(b)
(c)
Figure 4: The flux distribution (a) by the magnet excitation, (b) by the stator current excitation and (c) by
the magnet and the stator current.
and combined PM excitation current excitation for windings. Table 1 gives the details of the motor
analyzed.
Figures 1 and 2 represent the stator slots having no skewing and with skew.
3. SIMULATION RESULTS
Figure 4(a) shows the flux distribution at different part of motor when only the magnet excitation
is applied. Figure 4(b) represents the flux distribution at different region of motor when only the
stator current excitation is applied. Figure 4(c) shows the flux distribution produced by the magnet
and the stator current.
The value of inductance and the flux are illustrated in the Table 2. The Figure 5 shows the
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PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
Table 2: Inductance and flux.
Inductance (mH)
Flux (mwb)
3.06
9.3
Figure 5: Torque at the rotor.
torque at the rotor.
4. CONCLUSIONS
In this paper, the effect skewed stator slots on the various performance parameter of a SMPM
motor for only permanent magnet excitation and appropriate winding excitation pattern has been
presented. It is observed that by skewing the cogging torque is reduced.
REFERENCES
1. Jaykumark, K., et al., “Three dimensional finite element analysis of doubly salient permanent
magnet motor with skewed rotor teeth,” Finite Differences, Finite Elements, Finite Volumes,
Boundary Elements (F-and-B’08), Malta, September 11–13, 2008.
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machine models,” IEEE Transactions on Magnetics, Vol. 39, No. 3, May 2003.
3. Tounzi, T., et al., “3-D approaches to determine the end winding inductances of a permanentmagnet linear synchronous motor,” IEEE Transactions on Magnetics, Vol. 40, No. 2, March
2004.
4. Bumby, J. R.,et al., “Electromagnetic design of axial-flux permanent magnet machines,” IEE
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pre- and post-processing facilities,” International Journal for Numerical Methods in Engineering, Vol. 79, No. 11, 1309–1331, September 10, 2009.
7. Hsieh, M. F., et al., “Investigation on end winding inductance in motor stator windings,” IEEE
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