Microsoft Word - hairik-ed.doc
ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 1, 2013, 338-344 338
www.etasr.com Thejel et al: Simulation and Experimental Verification of a HB-Type Vernier Motor
Simulation and Experimental Verification
of a HB-Type Vernier Motor
Rabee' Hashim Thejel
Department of Electrical Engineering
University of Basrah
Basrah, Iraq
rabee_alabbasi@yahoo.com
Haroutuon A. Hairik
Department of Electrical Engineering
University of Basrah
Basrah, Iraq
haroutuonhairik@ymail.com
Mazin Abdulelah Alwan
Department of Electrical
Engineering
University of Basrah
Basrah, Iraq
mazin_alwan@yahoo.com
Abstract— Direct drive motors are used as actuators in
numerous applications in which they must rotate at low speeds
with high torque and low torque ripple. Various types of vernier
motors have been studied recently. The HB type vernier motor is
one of them. Its rotor structure is the same as in a HB type
stepping motor but has a field winding at the rotor and has
multiphase windings in the stator. In the present work, a Matlab
simulation of a HB type vernier motor is presented. To validate
the motor results and response, the authors fabricated the motor
and implemented its drive circuit. The motor was tested for
different load conditions. Experimental results are found
identical to simulation results and it is also shown that the motor
has low torque ripple.
Keywords-direct drive; actuator; HB-type; vernier; Matlab
LIST OF SYMBOLS
Eo Electromotive force (V).
f Frequency (Hz).
IF Field current (A).
�1 Number of turns of phase “a”.
�2 Number of rotor single coil turns.
�sp Synchronous speed (r.p.m).
p Differential operator (d/dt).
r1 Stator winding resistance per phase (Ω).
rF Rotor winding resistance (Ω).
Te Electric torque (Nm).
TL Load torque (Nm).
XS Synchronous reactance (Ω).
α Phase shift for three phase or in general =
m
2π .
δL Power angle (rad).
ω1 Supply angular frequency (rad/sec).
ωm Rotor Angular speed (rad/sec).
2θ1
Stator Coil Pitch =
SN
2π .
2θ2
Rotor Coil Pitch =
RN2
2π .
θ′
Angle between the rotor adjacent N-silent pole
and S-silent pole.
I. INTRODUCTION
Application of direct drive systems in robot and factory
automation is constantly increasing, due to their controllability
and high accuracy, requiring motors with high torque at low
speed. Stepping motors and DC brushless motors are used as
direct drive motors. A stepping motor has a concentrated stator
winding and is driven by a pulse-shaped exaction voltage.
Therefore, in principle, torque pulsation exists during rotation.
Meanwhile, various types of vernier motors have been
developed, such as variable reluctance vernier motors and
permanent magnet vernier motors. The latest is probably the
HB type vernier motor which has the advantage of low torque
ripple. The construction of the HB type vernier motor requires
a field winding in the rotor and multiphase distributed winding
in the stator. As a result, the HB type vernier motor is identical
to a general synchronous machine in regards of voltage
equation and torque formula [1, 2]. In this paper, the
mathematical model of the HB type vernier motor is described
and the Matlab/Simulink software package is used to study the
dynamic motor responses due to normal and sudden load
torque. To validate the simulation, the authors fabricated a
motor and implemented a drive circuit. A sudden load torque
was applied to the motor shaft by using a loading device and
motor torque response was recorded. Results are presented and
discussed.
II. STRUCTURE OF HB-TYPE VERNIER MOTOR AND
EXPERIMENTAL DESIGN
The motor is a vernier-synchronous type and is not self-
starting in the speed range of 50 to 150 rpm. It is started with a
special starting circuit at reduced frequency and then gradually
increased to the actual speed [3].
The stator of the HB-type vernier motor has �S slots. These
slots have ordinary three-phase windings [4] with �P number of
ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 1, 2013, 338-344 339
www.etasr.com Thejel et al: Simulation and Experimental Verification of a HB-Type Vernier Motor
poles. The rotor consists of two parts which pinches the field
windings that axially penetrate the flux in the rotor as shown in
Figure 1.
Each rotor part consists of a number of salient poles (�R). The
first part contains the N-magnetized salient poles and the
second part contains the S-magnetized salient poles which are
deviated by half a slot in the circumferential direction. Thus,
these poles are appears alternately. The rotating magnetic fields
in the gap are the basic wave fields generated by the three
winding of the stator and the (�S ± �P/2) degree harmonic (slot
harmonic) field by pulsation of the gap permeance distribution
attributable to the stator slots.
The rotor rotates in synchronization with the slot harmonic
rotating magnetic field. The main relationship to design the
HB-type vernier motor which is similar to the HB-type stepper
motor is given by [4]:
R
P
S
�
2
�
� =± (1)
The synchronous speed of the HB-type vernier motor is
expressed as shown below:
R�2
f120
R�2
P�
P�
f120
sp� ==
(2)
For the present motor, which has �S=36, �R=30, and
�P=12, if f=50 Hz, the synchronous speed is 100 rpm.
III. VOLTAGE EQUATION AND TORQUE FORMULA
The motor has three phase windings in the stator and a field
winding in the rotor. Thus, the inductance matrix of the present
HB-type vernier motor has 4×4 size and can be written as given
in (3) [5, 6]:
where, L1 is the self inductance of the stator winding per phase,
Lm is the mutual inductance between stator phases, MR is the
mutual inductance between the stator phase winding and the
rotor winding, and LF is the self inductance of the rotor
winding, θ′ is the angle between the rotor adjacent N-silent
pole and the S-silent pole, α is the stator winding phase shift for
three phase equal to (
3
2π ).
Fig. 1. Rotor of HB-type Vernier motor
The voltage equation of the HB-type vernier motor is
similar to those for a general synchronous machine and is given
by [1, 2]:
[ ] [ ] [ ]{ } [ ]i.Lpr v += (4)
where p=d/dt.
Substituting for the inductance matrix [L] from (3) into (4)
gives:
( )
−′′
−−
++−
−++
=
αθθ R�cosRMpR�cosRMp
2
mLp
2
mLp
)mL1L(p1r
2
mLp
2
mLp)mL1L(p1r
Fv
cv
bv
av
( )
( )
( )
+−′
−′++
−′−
′−
Fi
ci
bi
ai
.
FpLFr2R�cosRpM
2R�cosRpM)mL1L(p1r
R�cosRMp
2
mLp
R�cosRMp
2
mLp
αθ
αθ
αθ
θ
(5)
on the condition that a balanced three-phase voltage is applied
and a balanced three-phase current flows through the motor.
The synchronous torque of the HB-type vernier motor is
expressed as follows:
1
3
. . . sin( )
o
R R L
S
VE
T � �
X
δ
ω
= (6)
where Eo is the induced electromotive force and XS is the
synchronous reactance, expressed as follows:
1
3
o F F
E M i
ω
= (7)
1 1
3
( )
2
S m
X L L aω= + (8)
where,
3
2
F R
M M=
−′′
−−
+−
−+
=
)(R�cosRMR�cosRM
2
mL
2
mL
mL1L
2
mL
2
mL
mL1L
]L[
αθθ
−′
−′+
−′−
′−
FL)2(R�cosRM
)2(R�cosRMmL1L
)(R�cosRM
2
mL
R�cosRM
2
mL
αθ
αθ
αθ
θ
(3)
ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 1, 2013, 338-344 340
www.etasr.com Thejel et al: Simulation and Experimental Verification of a HB-Type Vernier Motor
The usefulness of transforming an abc-reference frame to a
dq-reference frame stems from the fact that although each of
the stator phases sees a time-varying inductance due to the
saliency of the rotor, the transformed quantities rotate with the
rotor and hence see constant magnetic paths [6].
The relationship between a set of dq variables and the
corresponding set of three-phase abc variables is provided by
the transformation matrix Tdq. Since the three-phase systems
studied in this research are balanced, no 0-axis components are
present, which allows using a simplified version of dq-
transformation [5]:
a
d
dq b
q
c
v
v
T v
v
v
=
(9)
where
2 2
cos cos( ) cos( )
2 3 3
2 23
sin sin( ) sin( )
3 3
m m m
dq
m m m
t t t
T
t t t
π π
ω ω ω
π π
ω ω ω
− +
=
− +
(10)
and
m
ω is the speed (rad/sec) of the rotating frame.
The inverse transformation from dq to abc currents is
defined as:
1
a
d
b
q
c
dq
i
i
i T
i
i
−
=
(11)
By applying (9) on the stator part of (5), simplifying and
then adding the rotor part, the dq-model of HB-type vernier
motor can be obtained as shown in (12):
1 1 1
1 1 1
3 3 3
( ) ( )
2 2 2
3 3 3
( ) ( ) .
2 2 2
3
0
2
m R m m R
d d
q R m m m R m R q
F F
R F F
r p L L � L L p M
v i
v � L L r p L L � M i
v i
p M r p L
ω
ω ω
+ + − +
= + + + −
+
(12)
The electromagnetic torque is approximately given by:
e R F F q
T � M i i= − (13)
The dynamic equation of the mechanical torque is given by:
m
e F m L
d
J T B T
dt
ω
ω= − − (14)
where, J is the motor moment of inertia (kg.m2),
F
B is the
motor viscous fraction factor (Nm/rad/sec), and TL is the
mechanical load torque in Nm.
IV. MATLAB SIMULATION
The first row of (12) can be rearranged as follows:
1
1
[ ]
d d d S R m q F F
S
pi v r i L � i M pi
L
ω= − + − (15)
where,
1
3
( )
2
S m
L L L= +
The Matlab simulink representation of (15) is given in
Figure 2. The second row of (12) is rewritten as:
1
1
[ ]
q q q S R m d R m F F
S
pi v r i L � i � M i
L
ω ω= − − + (16)
This equation is simulated as shown in Figure 3. The third
row of (12) is rearranged in (17) and simulated as shown in
Figure 4.
1
[ ]
F F F d F F
F
p i v M p i r i
L
= − + (17)
The overall mathematical model of the HB-type vernier
motor given in (13)-(17) is simulated using Matlab. Simulation
can be very useful in many scientific studies to formulate a
hypothesis or a mathematical model, to explain the
observations and to predict the behavior of a system from
solutions or properties of the model. The model used is shown
in Figure 5, where the “abc to dq” block is given by (9) and the
“dq to abc” block is given by (11). The parameters of the
present HB-type vernier motor are listed in Table I.
V. SIMULATION RESULTS
The motor drive circuit in this paper consists of a Space
Vector Pulse Width Modulation (SVPWM) and a three phase
Voltage Source Inverter (VSI). SVPWM is a more
sophisticated technique for generating a sine wave that
provides a higher voltage to the motor with lower total
harmonic distortion [7]. The rotor DC voltage is vF=28 V.
The Matlab simulation results of 'a' phase voltages of the
SVPWM VSI at f=50 Hz, E=220 V, and
*
sv =0.55 pu. are
shown in Figure 6.
The motor model shows that the steady state speed changes
linearly with frequency as shown in Figure 7.
The motor behavior due to sudden change of the shaft load
is also tested. The motor is first driven at no load, and then the
load is suddenly changed to 5 N.m at t = 2 sec. The test results
of the motor speed and torque are shown in Figures 8-9. The
motor three-phase currents are shown in Figure 10.
ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 1, 2013, 338-344 341
www.etasr.com Thejel et al: Simulation and Experimental Verification of a HB-Type Vernier Motor
Fig. 2. Implemented Simulink model of (15)
TABLE I. PARAMETERS OF THE MOTOR USED IN THIS PAPER.
r1 0.9 Ω
rF 2.8 Ω
L1 0.055 H
Lm 0.0557 H
MR 0.0196 H
LF 0.0178 H
J 0.01 kg.m2
B 0.05 Nm/rad/sec
Fig. 3. Implemented Simulink model of (16)
Fig. 4. Implemented Simulink model of (17)
Fig. 5. Implemented Simulink model of the complete motor dq-model
ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 1, 2013, 338-344 342
www.etasr.com Thejel et al: Simulation and Experimental Verification of a HB-Type Vernier Motor
Fig. 6. Inverter phases ‘a’ voltage when f=50 Hz,
*
sv =0.55 pu
Fig. 7. Steady state speed-frequency curve of HB type vernier motor
Fig. 8. Speed response of the HB type vernier motor
Fig. 9. Torque response of the HB type vernier motor
Fig. 10. Three phase currents of the HB type vernier motor.
VI. EXPERNIMTAL IMPLEMENTATION
The motor was fabricated in order to validate the motor
mathematical model simulation. The motor specifications are
given in Table II:
TABLE II. SPECIFICATION OF TEST MOTOR.
Outside diameter of rotor 110 mm
Inside diameter of stator 111 mm
Core length 89 mm
1umber of stator turns per phase 336
1umber of field turns 305
The stator of the motor has 36 slots and is wounded with
three phase windings with 12 poles as shown in Figure 11.
The rotor of the motor has 30 silent poles in each side. The
field winding is supplied with DC current through two slip
rings as shown in Figure 12.
ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 1, 2013, 338-344 343
www.etasr.com Thejel et al: Simulation and Experimental Verification of a HB-Type Vernier Motor
Fig. 11. Stator of test Vernier motor
Fig. 12. Rotor of test Vernier motor
The experimental motor drive circuit is based on the space
vector technique and is consisted of two main parts, three phase
inverters and a PC computer interface with an inverter to
generate six gates pluses based on SVPWM as shown in
Figure 13.
Fig. 13. Motor drive circuit
VII. EXPERIMENTAL RESULTS
The motor is not self-starting for a frequency range greater
than 20 Hz. It is started with low frequency increasing step by
step until it reaches 50 Hz. The speed of the motor is measured
by using a shaft encoder connected on the motor shaft. The
experimental motor speed profiles at starting and steady state
are shown in Figure 14.
The motor phase voltage and current are shown in Figure 15.
The motor is tested for sudden load changes by using a loading
device as shown in Figure 16.
The motor is tested for two cases. At first, the motor
operates with no load and then a sudden load of 5 Nm is
applied. In the second case, the load is suddenly removed from
the motor. The results show that the motor has a short period of
torque oscillation as shown in Figures 17 and 18.
Fig. 14. Experimental speed profile of the motor
Fig. 15. Motor phase voltage and current
ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 1, 2013, 338-344 344
www.etasr.com Thejel et al: Simulation and Experimental Verification of a HB-Type Vernier Motor
Fig. 16. Motor set for loading test
Fig. 17. Motor torque response for 5 Nm sudden load torque
Fig. 18. Motor torque response for no load
VIII. CONCLUSIONS
In this paper, the mathematical model of a HB-type vernier
motor was simulated using the Matlab/Simulink software
package. To validate the simulation, a test motor was
fabricated. Results showed that:
• The motor steady state speed changes linearly with
frequency.
• The motor phase voltage and current simulation results are
identical with the experimental results.
• The motor speed and torque profiles exhibit small amounts
of oscillation due to sudden changes in the shaft load.
REFERENCES:
[1] H. Suda, Y. Matsushima, L. Xu, and Y. Anazawa , “Analysis of HB-type
Vernier motor”, IEEJ Transactions on Industry Applications, Vol. 125,
No. 3, pp. 270-276, 2005.
[2] H. Suda, Y. Anazawa, “Torque analysis of HB-type Vernier motor”, The
IEEE International Electric Machines and Drives Conference, IEMDC
'07, pp. 709-714, Turkey, 2007.
[3] L Blaisdell, R Rubin, O Mahr, “ATS mechanically despun
communications satellite antenna”, IEEE Transaction on Antennas and
Propagation, Vol. 17, No. 4, pp. 415-528, 1969.
[4] C. H. Lee, “Vernier motor and its design”, IEEE Transactions on Power
Apparatus and Systems, Vol. 82, No. 66, pp. 343-349, 1963.
[5] A. E. Fitzgerald, C. Kingsley Jr., S. Umans, Electric Machinery, Sixth
Edition, McGraw-Hill Companies, Inc., 2003.
[6] C. M. Ong, Dynamic simulation of electric machinery: using
Matlab/Simulink, Prentice Hall PTR, 1998.
[7] A. Bonnet, T. Alukaiday, P. C. K. Luk, “A high performance space
vector motor drive controller”, IEE Colloquium on DSP Chips in Real
Time Measurement and Control (Digest No: 1997/301), United
Kingdom, 1997.