FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS (F-and-B'08)
Malta, September 11-13, 2008
Three Dimensional Finite Element Analysis of Doubly Salient Permanent
Magnet Motor with Skewed Rotor Teeth
JAYKUMAR K. SOLANKI, NIMIT K. SHETH, MEMBER, IEEE, RAJAL H. PATEL MEMBER, IEEE
Electrical Department
Nirma University
Sarakhej Ghandhinagar Highway,
Nirma University of Science and Technology,
Ahmedabad- 382481, Gujarat, India.
INDIA
Abstract: - This paper presents the results of three dimensional (3-D) finite element (FE) analysis carried out to
minimize the torque ripple of doubly salient permanent magnet (DSPM) motor by skewing of rotor teeth. The effect
of skewing rotor teeth on the performance of various characteristics like detent torque, average torque, torque ripple,
stator pole flux density, magnet operating point have been presented. It is observed that by increasing skew angle of
rotor pole flux density in stator pole is reduces. Results of harmonic analysis of detent torque and average torque at
various skew angles have been presented from which it is observed that 3rd and 4th and its multiple torque harmonics
are predominant ones for both type of torque. It also is observed that by skewing rotor teeth 6o to 9o will give higher
average torque with reduced torque ripple.
Index Terms: - DSPM, FE Analysis, Permanent Magnet Motor, Skewing, Torque ripple
1.
effects of variation of rotor pole arc and rotor pole
shapes on the performances of a doubly salient
permanent magnet (DSPM) motor are reported [2].
Torque ripple can be minimizing from both design
side and control side. This paper presents the results
of three dimensional finite element analysis carried
out to minimize the torque ripple of 8/6 pole DSPM
motor by skewing of rotor teeth.
INTRODUCTION
The DSPM motor incorporates the merits of both the
PM brushless motor and the SR motor. First, the
corresponding PMs are located in the stator,
eliminating
the
problems
of
irreversible
demagnetization and mechanical instability, while
retaining the merits of high efficiency and high power
density. Second, the corresponding rotor is the same
as that of the SR motor, hence, adopting the
advantages of simple configuration and mechanical
robustness. Similar to the SR motor, the DSPM motor
exhibits severe torque ripples and that is due to the
nature of doubly salient operation. It is present even at
ideal conditions of operation. Although this DSPM
motor possesses simple configuration, it does not
imply any simplicity in design and analysis because of
the heavy magnetic saturation in pole tips, the fringe
effect of poles and slots, as well as the cross coupling
between PM flux and armature current flux [1]. The
ISSN:1790-2769
2. EFFECT OF SKEWED ROTOR
TEETH ON THE PERFORMANCE OF
DSPM MOTORS FOR ONLY PERMA NENT MAGNET EXCITATION
Three-dimensional finite FE model of a 1 hp, 8/6
DSPM motor with rotor poles having no skewing and
with different angle of skewing have been analyzed
for two type of excitation namely; (i) only permanent
magnet (PM) excitation and (ii) combined PM
excitation with appropriate polarity of rectangular
current excitation for windings. Fig. 1 show the three
91
ISBN: 978-960-474-004-8
FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS (F-and-B'08)
Malta, September 11-13, 2008
dimensional view of 8/6 DSPM motor when rotor is
align with phase A. Table I gives the details of the
motor analyzed. For the analyzed motor flux-linkage
characteristics for various phases have been obtained
for only PM excitation. Fig. 2 shows the flux linkage
characteristics for phase A, phase B, phase C, and
phase D. It is observed from the flux-linkage
characteristics that flux-linkage with phase A and
phase C are exactly opposite to each other and the
same way phase B and phase D are exactly opposite to
each other. Therefore it possible to connect phase A
and C and Phase B and D back to back to make
DSPM motor working as two phase motor drive.
about the center point and detent torque cycle is 2π/S,
where S is the least common multiple of Stator and
rotor pole numbers. The maximum value of detent
torque is reduces by increasing the skew angle. The
harmonic torque component of the detent torque
profiles are shown in fig. 4 from which it observed
that 3rd, 9th and 4th and its multiple of it harmonic
torques are the predominant harmonic torques. It is
also observed that by increasing the skew angle the
magnitude of harmonic torques is reduces. The fourth
harmonic torque is the minimum for the skew angle of
9o other harmonic torque are also small at the same
skew angle. Above 9o skew angle some of the
harmonic torques is start to increase.
TABLE I
MOTOR DATA
128
75
75
0.45
20
4
8
6
22
26
13
10
250
2×(6×37.5×75)
Flux-linkage (weber)
Stator outer diameter (mm)
Stator inner diameter (mm)
Stack length (mm)
Airgap length (mm)
Rotor inner diameter (mm)
Number of phases
Stator pole number
Rotor pole number
Stator pole arc (degree)
Rotor pole arc (degree)
Stator pole depth (mm)
Rotor pole depth (mm)
ampere turns/pole
Magnet volume (mm3)
0
D
20
C
B
40
60
80
Angle (Degree)
Fig. 2. Flux-linkage profiles for various phases with
0o skewed rotor teeth and for only PM excitation.
3. PERFORMANCE OF DSPM MOTORS FOR SKEWED ROTOR TEETH
AND COMBINED PERM ANENATMAGNET AND APPRO PRIATE
WINDING EXCITATION
To get the average torque windings are excited with
appropriate excitation pattern as shown in fig. 5. Here
positive and negative sign indicates that the flux
produced by the winding excitation supports or
opposes the magnet excitation respectively. It is
observed from the fig. 6 that with the increase in the
skew angle the peak flux density reduces and also the
flux density characteristics is getting shifted towards
one side this is because the unstable equilibrium point
for a particular phase is shifting by a half a skew angle
in the opposite direction of the skew and this must be
considered while designing the control circuit.
Fig. 1. Three dimensional view of 8/6 DSPM motor
when rotor is align with phase A.
Fig. 3 shows the variation of the detent torque at
various skew angles for the rotor poles, from which it
is observed that the detent torque is anti-symmetric
ISSN:1790-2769
A
0.450
0.400
0.350
0.300
0.250
0.200
0.150
0.100
0.050
0.000
92
ISBN: 978-960-474-004-8
FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS (F-and-B'08)
Malta, September 11-13, 2008
skew 0º
skew 6º
skew 7º
skew 8º
skew 9º
skew 10º
skew 15º
skew 20º
skew 25º
skew 30º
Figure 7 shows flux density plot when the rotor pole
at align with the pole of phase A for a given excitation
pattern at various skew angles of rotor poles from,
which it is observed from flux density is not constant
throughout the rotor core therefore three dimensional
finite element analysis is required when rotor is
skewed.
Torque (Nm)
2.000
1.000
0.000
-1.000 0
20
40
60
80
-2.000
skew 0º
skew 6º
skew 7º
skew 8º
skew 9º
skew 10º
skew 15º
skew 20º
Flux density (T)
Angle (Degree)
Fig. 3. Detent torque profiles at various skew angle
of rotor poles.
2.5
2
1.5
1
0.5
0
0
40
80
60
Angle (Degree)
0.6
Fundamental
0.5
4
Torque (Nm)
20
0.4
3
0.3
12
0.2
Fig. 6. Flux density profiles in the pole of phase A for
a given excitation pattern at various skew angles of
rotor poles.
th
rd
8
th
9
th
th
0.1
0
0
5
10
15
20
25
30
35
-0.1
Skew angle (Degree)
Fig. 4. Variation of harmonic torque of the detent
torque profiles at various skew angles of rotor poles.
Fig. 5. Excitation pattern for phase A, phase B, phase
C and phase D.
ISSN:1790-2769
93
(a)
(b)
(c)
(d)
(e)
(f)
ISBN: 978-960-474-004-8
FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS (F-and-B'08)
Malta, September 11-13, 2008
skew 0º
skew 10º
skew 6º
skew 15º
skew 7º
skew 20º
skew 9º
0.9
(g)
Flux density (T)
0.8
(h)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Fig. 7. Flux density plot for a given excitation pattern
when rotor is aligned with the phase A at various
skew angles: (a) = 0o (b) = 6o (c) = 7o (d) = 8o (e) = 9o
(f) = 10o (g) = 15o (h) = 20o.
0
0
10
20
30
40
50
60
70
Angle (Degree)
Fig. 8. Magnet operation point for a given excitation
pattern at various skew angles of rotor poles.
Magnet operation point for a given excitation
pattern at various skew angles of rotor pole is shown
in fig. 8. It is observed that up to 15o skew angle there
is no much variation in magnet operating point with
rotor position and its flux density is 0.821 T but above
20o skew angle magnet operating point is reduces to
0.606 T and this is because of the increase in effective
reluctance due to skewing. Fig. 9 shows the develop
torque profiles for various skew angles from which it
is observed that by increasing skew angle developed
torque is reduces. Fig. 10 shows that 3rd and 4th and its
multiple torque harmonics are predominant ones and
by increasing skew angle all the harmonic torques is
reduces. Torque ripple for the developed torque have
been calculated using (1). Table II gives values of the
average torque and torque ripple for motor with
different skew angles.
Skew 0º
Skew 9º
Skew 6º
Skew 10º
Skew 6º
Skew 15º
Skew 7º
Skew 20º
Skew 8º
10
Torque (Nm)
9
8
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
70
Angle (Degree)
Fig. 9. Developed torque profiles for various skew
angles.
Fundamental
2nd
3rd
4th
8th
9th
10th
2
1.8
1.6
(1)
Torque (Nm)
⎛ T max − T min ⎞
Tripple (%) = ⎜
⎟ x 100
Tavg
⎝
⎠
It is observed from the Table II that by increasing
skew angle the torque ripple is reduces and average
torque is also reduces. At 9o skew angle the reduction
in average torque is 9.53 % and reduction in torque
ripple is 18.30 %. Above 9o skew angle average
torque is reduces but torque ripple is increases so one
can skew the rotor pole up to 9o to get minimum
torque ripple with higher average torque.
ISSN:1790-2769
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
Angle (Degree)
Fig. 10. Variation of harmonic torques for developed
torque.
94
ISBN: 978-960-474-004-8
25
FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS (F-and-B'08)
Malta, September 11-13, 2008
[6] Frede Blaabjerg, Leif Christensen, Peter O.
Rasmussen, Leo Oestergaard, Peder Pedersen,“
New advanced control methods for doubly salient
permanent magnet motor” IEEE Conf. on Industry
Applications, vol.1, Oct 1995, pp. 222-230.
[7] Ming Cheng, K.T.Chau and C.C.Chan, “Static
characteristics of a new doubly salient permanent
magnet motor” IEEE Trans. on Energy
Conversion, vol. 16, pp. 20-25, Mar 2001.
Table II.
AVERAGE TORQUE AND TORQUE RIPPLE FOR
VARIOUS SKEW ANGLE OF ROTOR POLE
Skew
Average
Torque
Angle
Torque
0o
6o
7o
8o
9o
10o
15o
20o
5.35
5.29
5.15
5.00
4.84
4.67
3.64
1.61
Ripple
97.17
85.18
82.32
80.06
79.39
79.60
87.95
136.59
4. CONCLUSION
In this paper, the effect skewed rotor teeth on the
various performance parameter of an 8/6 DSPM motor
for only permanent magnet excitation and appropriate
winding excitation pattern has been presented. It is
observed that by skewing the rotor teeth flux density
in the stator pole is reduces. Skewing the rotor teeth
form 6o to 9o will result in to minimum detent torque.
It is also observed that skewing the rotor teeth form 6o
to 9o will give less torque ripple without much
reduction in average torque. The magnet operating
point is constant for at any the rotor position.
5. REFERENCES
[1] Ming Cheng, K. T. Chau and C. C. Chan,
“Design and analysis of a new doubly salient
permanent magnet motor” IEEE Trans. on
magnetics, vol. 37, No.4, July 2001.
[2] Nimit K. Sheth and K. R. Rajagopal,
“Performance of doubly
salient permanent
magnet motors for parallel and tapered rotor
poles” Conference on Asia-Pacific Magnetic,
Dec. 2006, pp.1-2.
[3] A. R C Sekhar babu, K. R. Rajagopal , “Effect of
shifted stator pole and flat rotor poles on the
static characteristics of the doubly salient permanent magnet motor” IEEE Conference on
Magnetics, April 2005, pp. 659-660.
[4] Ming Cheng ,K.T Chau and C.C.Chan “New splitwinding doubly salient permanent magnet motor
drive” IEEE Trans. on Aerospace and Electronic
Systems, vol. 39, pp. 202- 210 Jan. 2003.
[5] Yuefeng Liao, Feng Liang and Thomas A. Lipo,
“A novel permanent magnet motor with doubly
salient structure” IEEE Conf. Industry application
vol.1, Oct 1992, pp. 308-314.
ISSN:1790-2769
95
ISBN: 978-960-474-004-8