Effect of Armature Reaction and Skewing on

the Performance of Radial-flux Permanent

Magnet Brushless DC Motor
Parag Upadhyay, and K. R. Rajagopal, Senior Member, IEEE

motor for various armature MMF. The saturation in the

Abstract -In this paper the effect of armature reaction and magnetic circuit will increase the reluctance of the circuit
skewing on the performance of a 70 W, 24 V, 350-rpm surface and drive the PM to operate at a lower permeance
mounted radial-flux permanent magnet brushless dc (PM coefficient. That means, the armature reaction determines
BLDC) motor is presented. The net reduction in peak torque
of the motor due the effect of armature reaction is only 2.8%.
the movement of the PM operating point under dynamic
The rate of reduction in airgap flux density because of the conditions.
armature reaction is 5.59 mT/A from no-load to full-load. The
2D Finite element (FE) results are exploited for the analysis of
skewing. The percentage torque ripple is reduced from 24% to II. COMPUTER AIDED DESIGN
13.63% and 7.07% for the half and full slot pitch skewing
respectively. The computer aided design (CAD) program of PM
BLDC motor is a two-loop MATLAB-program with
Index Terms Motor, PM BLDC Motor, Armature different function call. The outer loop is to set and correct
reaction, Skewing, Permanent Magnet Motor, FE Analysis, the assumed efficiency. Initially, the efficiency of the motor
Brushless Motor. is assumed. The CAD program designs the motor and
calculates the actual efficiency. The correction loop reduces
the assumed efficiency and it is active till the error between
INTRODUCTION
I.
the assumed efficiency and the actual efficiency is within
the given limit. The inner loop is for reducing the
pERMANENT magnet brushless dc (PM BLDC) motors
difference between the assumed and actual airgap flux
have advantages such as high efficiency, high torque
densities by changing the length of the magnet in a similar
density, high power density, and high reliability[1],[2].
way. The magnet length is increased till the error between
These motors are inherently maintenance free because of
the two is less than given limit.
the absence of a mechanical commutator. These
The airgap flux density, slot electric loading, winding
advantages, combined with the ease of control had made
factor, stacking factor, stator current density, slot space
them very attractive candidates increasingly being used in
factor, magnet fraction, slot fraction, flux density in the
various domestic and industrial applications.
stator back iron, etc. are assumed as fixed input parameters
As per definition, the armature reaction refers to the
in the design. The phase current is decided by the power
magnetic field produced by currents in the stator coils and
requirement and induced EMF decides the number
their interaction with the magnetic field produced by the
conductors per slot. Motor specifications, type of
permanent magnets[3]. In some locations in the airgap, the
armature reaction may be adding the PM field and at some
configuration, material types, and other assumed data for
the design are provided as the input.
other locations in the airgap, it may be opposing the PM
Selection of standard wire gauge (SWG), material data
field. The presence of saturation phenomenon in soft
for selected material number, specific iron loss data for a
magnetic materials in the stator, obviously lead to
given material flux density and the frequency, etc. are also
nonlinearity; therefore, addition or deletion of fields for the
part of the developed program. Number of magnet poles,
same armature MMF need not be the same at all locations
Number of slots/pole/phase, type of permanent magnet
in the airgap, which leads to variation in performance of the
material and its grade, type of soft magnetic material,
airgap, current density, stator flux density, airgap flux
Prof. P. R. Upadhyay is with the Electrical Engineering Department, density, slot electric loading, magnet fraction, slot fraction,
Nirma University of Science and Technology, Ahmedabad, INDIA. (e- stacking factor, slot space factor, winding factor, flux
mail: pru nirmaayahoo.com). density in the rotor core are the parameters required for the
Prof. K.R.Rajagopal is with the Electrical Engineering Department,
Indian Institute of Technology Delhi, New Delhi, INDIA. (e-mail: design.
rgopal0 ee iitd.c
a i2)
0-7803-9771-1/06/$20.00 t)2006 IEEE.
 III. ARMATURE REACTION EFFECTS the motor is taken as positive. However, in Fig. 1, the CW
direction appears to be positive, which may be clearly
In the PM BLDC motor, when there is no armature understood as the actual rotation of the motor to the CCW
current, magnetic neutral axis (MNA) coincides with the direction.
geometrical neutral axis (GNA) of the PM poles; that For example, in the 70 W, 24 V, 350 rpm surface
means the interpolar axis. But when the armature field is mounted radial-flux PM BLDC motor designed using the
also present, MNA will shift from the GNA in a direction developed CAD program with the desired airgap flux
and by an angle, decided respectively by the polarity and density of 0.8 T, and with the Nd-Fe-B 35 PM for which
strength of the armature field. This deviation depends on the retentivity, coercive force, and recoil permeability are
the amount of magnetic loading and the slot electrical 1.23 T, 890 kA/m and 1.01 respectively, the no-load PM
loading. operating point is given by the CAD program as Hm = -579
The torque vs. rotor position characteristics as well as A/mm and Bm = 0.93 T, based on which the PM MMF/pole
the developed average torque will change with the MNA. (Helm) is worked out to be 2895 A. The armature MMF/pole
The net effect of the armature reaction is to reduce the is also worked out based on the slot electric loading and its
torque developed by the motor. value is 221 A. Knowing these two MMF values, resultant
Considering current to be constant through the coils, in airgap MMF for various rotor positions from -300 to 300
the two-phase excited condition, so as to have maximum electrical can be worked out based on which corresponding
torque, the armature field vector is always considered to be developed torques can be calculated.
perpendicular to the PM field vector as shown in Fig. 1. It
can also be seen that the resultant airgap MMF can be more --CAD-wfth AR 2.5
or less in magnitude than the PM field MMF depending on FE
I p--
.lk-
the angle at which the armature MMF acts. CAD-wthot AR
,-o 2
_ E
d?- z
hIl:, 1140f/ 1.5
A11atu1 e
NM / L-o

FieldNWNI i

-10 -8 -6 -4 -2 0 2 4 6 8 10
Fig. 1. Vector representation of the airgap MMF of the radial-flux surface Rotor Position (deg)
mounted PM BLDC motor.
Fig. 2. Torque profiles of the designed 70 W radial-flux surface mounted
A typical case of a 3-phase, bipolar PM BLDC motor, PM BLDC motor.
which will be excited in 2-phase in series configuration
changing the phase combinations at every 600 electrical can The calculated torque profiles with and without
be well explained using Fig. 1. Ideally, we would like to considering for the armature reaction are given in Fig. 2.
have the armature MMF as perpendicular to the PM field The rotor position in mechanical degrees is taken in the x-
MMF. But the phase combinations will have the currents in axis of this figure. It may be noted that -10° to 100
them for 600 electrical. That means, the phases must be mechanical shown in this figure corresponds to -300 to 300
excited 300 electrical prior to the perpendicular positionelectrical in the 6-pole motor. It can be observed that the
armature reaction reduces the developed torque and also
and up to 300 electrical beyond the perpendicular position.
Therefore, as shown in Fig.1, the resultant airgap MMF shifts the torque profile symmetry away from the polar axis
(MMFAG) vector can vary in magnitude and also in phase towards the direction of rotation of the motor, CCW. That
from ob to od. The mathematical expression for MMFAG is means, there is a forward shift of the MNA; in this case it is
given below: observed that the shift is 1.9° mechanical. Effectively, the
shifting of the MNA depends on the PM length (or the
magnetic loading) and the slot electric loading. Thus, the
MMFAG = (MMFpM +MMFA sin 0)2 +(MMFA Cos 0)2
important inference is that in motor if the slot electric
loading is more, then the shift of MNA is more, which will
where, MMFpM is the PM field MMF/pole in the airgap, result in reduced average developed torque and increased
MMFA is the armature MMF/pole in the airgap and 0 is the torque ripples. Instead, if we provide more magnetic
angle between the ideal armature MMF vector ac and the loading, then the shift in MNA will be less, but will result
actual armature MMF vector (which can vary from ab to in more cogging torques and increased cost.
ad). The counter clockwise (CCW) direction of rotation of Figure 3 shows the torque profiles for the 70 W PM
BLDC motor at full-load and also at half load conditions
from which it can be observed that the armature reaction Figure 4 gives the average airgap flux density at no-load
effects are more predominant at higher loads. as well as at full-load for the 70W PM BLDC motor
obtained from the FE analysis. It clearly indicates the
reduction in the airgap flux density and also the shifting of
Half Load the MNA. The average airgap flux density (effectively, this
~~~---Full Load
ov9l is the average of the average flux densities obtained for the
rotor positions varying from -300 to 300 electrical) in the
airgap changes from the no-load value of 0.785 T to 0.766
T at full-load; the decrease of about 2.4% is obviously due
2 to the armature reaction effects.
w:r
0 oi*^^*

4
-1 1n -3O -~e -4 - -4 e 3 4 1
Rotor Position (deg)
Fig. 3. Torque profiles of radial-flux surface mounted PM BLDC motor
obtained using the CAD program at full-load and half-load.

IV. VERIFICATION BY FE ANALYSIS

FE analysis helps in visualizing the effects of

armature reaction very clearly. Analysis is carried out on
the designed 70 W, 24 V, 350 rpm surface mounted radial-
flux PM BLDC motor for the no-load and the full-load Fig. 5. Flux density plot of the designed 70 W radial-flux surface mounted
PM BLDC motor at no-load.
conditions. The actual torque profile with the armature
reaction obtained from the FE analysis is also given in
Fig.2. Even though the FE based and CAD based torque
profiles are not that close, two observations are very clear;
(i) the MNA shifts towards the direction of rotation, and
(ii), the average torque decreases with the armature
reaction. The average torque worked out by the CAD
program and by the FE analysis are 1.90 Nm and 2.02 Nm,
which are fairly matching, but with the deviations caused
by the slotting, which will very effectively be considered in
the FE analysis.
0.0^
079
0. 19
,s

1- Fig. 6. Flux density plot of the designed 70 W radial-flux surface mounted

PM BLDC motor at full-load.
r_I
The flux density plots of the motor for no-load and full-
Full-load load conditions obtained from the FE analysis are shown in
-wNoLoadcl figures 5 and 6 respectively. From the Fig. 6, the actual
shift of the MNA is observed as 1.80 as against the CAD
I! ' based calculated value of 1.9°. Even though, it is not linear,
-10 - 0 110 the rate of reduction in the average airgap flux density
Rotor Position (deg) because of armature reaction from the no lad to full-load
condition of the motor is accounted to be 5.59 mT/A; this is
Fig. 4. Airgap flux density vs. rotor position plots of the designed 70 W an acceptable rate in majority of the motors used in
radial-flux surface mounted PM BLDC motor.
domestic and industrial applications - thanks to the large
airgap (contributed by the physical airgap and the PM density in the airgap. Larger airgap and high-energy
length and also the availability of high energy of the PM permanent magnet material with low permeability will
materials) which keeps the adverse effects of armature reduce the adverse effects of the armature reaction. In the
reaction to very low limits. typical 70 W radial-flux surface mounted PM BLDC motor
designed in this paper, the net reduction in peak torque of
V. SKEWING OF SURFACE MOUNTED MOTOR
the motor due the effect of armature reaction is only 2.8%.
The rate of reduction in airgap flux density because of the
The same 70 W, 24 Volt, 350 rpm, radial-flux surface armature reaction is 5.59 mT/A from no-load to full-load.
mounted PM BLDC motor is used in this analysis. In From the analysis it is observed that the torque ripple is
case of the radial-flux surface mounted PM BLDC motors, reduced from 24% to 13.63% and 7.07°O for the half and
skewing of stator slots is a viable and easy method for the full slot pitch skewing respectively. The effect of skewing
can be observed from the 2D FE analysis.
torque ripple minimization by design. Here, rather than
doing a 3-D FE analysis, 2-D FE parametric analysis is
carried out by rotating the stator to the required skew angle VII. REFERENCES
in small steps by maintaining the rotor to the initial position [1] D. C. Hanselman, Brushless permanent magnet design McGraw Hill
itself and obtaining the torque profile for each step and then Inc. Publ., 1994.
finally adding the torque profiles of all the steps to get the [2] Handershot J.R., Miller TJE, "Design of brushless Permanent magnet
torque profile of the motor with the stator slots skewing. motors", Oxford Sc. Publ., 1994.
[3] Parag R. Upadhyay, K. R. Rajagopal, "Effect of Armature Reaction
_
-T20 T18 -Tl(-)T | on the Performance of an Axial-Field Permanent Magnet Brushless
DC Motor Using FE Method" IEEE Trans. Magnetics Vol. 40, NO.
10, pp-2023-2025, July 2004.

z
a; 1.9 VIII. BIOGRAPHIES
0.
0
F- K. R. Rajagopal (M'1998, SM'2000) was born
0 95
in Alappuzha, Kerala, India in 1961. He received
Diploma in Electrical Engineering from Carmel
09
Polytechnic, Alappuzha, India in 1979, B. Tech.
0 5
I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

10 15 25 30 35 40 45 50 55 60
20
Degree in Electrical Engineering from the
College of Engineering, Trivandrum, India in
Rotor Position (deg) 1988, M. Tech. Degree in Power Electronics,
Fig. 7. Torque profiles of the designed 70 W radial-flux surface mounted Electrical Machines and Drives and Ph. D.
PM BLDC motor with skewing in stator slots. Degree in Electrical Engineering from the Indian
Institute of Technology Delhi, New Delhi, India during 1991 and 1998
TABLE I respectively.
AVERAGE TORQUE AND TORQUE RIPPLE FOR DIFFERENT SKEW ANGLES IN From 1980 to 1983, he was with Aluminum Industries Ltd. (ALIND),
A 70 W RADIAL-FLUX SURFACE MOUNTED PM BLDC MOTOR Trivandrum, India, as an Application Engineer (Relays), from 1983 to
1999, he was with the Indian Space Research Organization (ISRO),
Trivundrum, India, where he was engaged in Analysis, Design,
Skew angle (' mechanical) 20 0 10 Development and Testing of Special Electrical Machines/Devices used in
Average torque (Nm) 1.89 2.03 1.99 space applications. Since 1999, he is with the Indian Institute of
Percentage torque ripple 7.07 24.18 13.63 Technology Delhi, New Delhi, India, where currently he is a Professor in
Electrical Engineering Department.
He has published more than 30 papers in International Journals and
The torque profiles of the motor with two different skew more than 60 papers in International conference proceedings. He received
angles in stator slots, (i) with skew angle equal to a slot Indian National Academy of Engineering (INAE) award for most
Innovative Potential Project in Engineering during the year 1998. His
pitch (200) and (ii) with the skew angle equal to a half of fields of interest include Electrical Machines and Drives, Special Electrical
the slot pitch (10°) along with the torque profile of the Machines (Stepper Motors, Switched Reluctance Motors, PM BLDC
motor with no skewing are given in Fig. 7. The average Motors, Hysterisis Motors, etc.,), Magnetic Devices, Finite Element
Analysis and CAD of Electrical Machines and Design of Energy Efficient
torque and the ripple toque in each case is worked and Motors for Home Appliances.
given in table- 1.
It can be observed that the skewing reduces the torque
Parag Upadhyay was born in Bhavnagar,
ripple, but with a penalty of reduction in average torque. Gujarat, India in 1971. He received B.E. Degree
For a full slot pitch skewing, the torque ripple is the least, in Electrical Engineering from the L.E. College
but with a 6.7% reduction in the average torque. With half Morbi, Gujarat, India in 1992, M. Tech. Degree
a slot pitch skewing, the torque ripple is 13.63%, but the in Power Electronics, Electrical Machines and
Drives in Electrical Engineering from the Indian
reduction in the average torque is only 1.97%. Institute of Technology Delhi, New Delhi, India
during 2000 and he is pursuing Ph.D. from the
VI. CONCLUSIONS Indian Institute of Technology Delhi, New Delhi,
India since 2003.
The effect of armature reaction reduces the flux
 In the year 1993, he worked in Menpara Pumps (P) Ltd. as testing
and quality engineer and Coretech Int (P) Ltd. as Project Engieer. From
1993 to 1996, he was with L. D. Engineering Colege, Ahmedabad, Gujarat,
India as a lecturer. Since 1996, he is with the Institute of Technology,
Nirma University of Science and Technology, Ahmedabad, Gujarat, India,
where currently he is an Assistant Professor in Electrical Engineering
Department.
He has published about 9 papers in International Journals and about
12 papers in International conference proceedings. He received Prof. A. K.
Sinha award for securing the highest CGPA in the electrical engineering
department of IIT Delhi for the year 2000 and also received L&T, ISTE,
Best M.Tech thesis award in 2001. His fields of interest include Electrical
Machines and Drives, Special Electrical Machines (PM BLDC Motors,
Axial Flux Motors etc.), Finite Element Analysis and CAD of Electrical
Machines.