A Novel Brushless Synchro: Operation Principle and Experimental

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A Novel Brushless Synchro: Operation Principle and Experimental
Results
Davood Pazouki*, Mahdi Ghafarzadeh**, Rezvan Abedini***, Aliakbar Damaki Aliabad****, Ali Kamali E.*****
*Iran University of Science and Technology, Tehran, Iran, [email protected]
**Sharif University of Technology, Tehran, Iran, [email protected]
***Amirkabir University of Technology, Tehran, Iran, [email protected]
****Yazd University, Yazd, Iran, [email protected]
*****Amirkabir University of Technology, Tehran, Iran, [email protected]
Abstract- In synchroes and resolvers, brushes and slip-rings
produce a lot of noise in the output signal. Compared to encoders,
the application of such position sensors in precision control systems
are restricted because of their lower accuracy. In this research, a
novel scheme of a brushless synchro is introduced. In this scheme,
the secondary windings are mounted on the stator and the stator
magnetic flux passes a certain path in the rotor and induces voltage
in the secondary windings. The operation principle is clearly
described in the paper and by using 2D finite element method the
novel synchro is initially designed and analyzed. The stator winding’s
turns is calculated by a method based on desired harmonic
elimination to have a sinusoidal magneto motive force. A prototype
has been fabricated and tested. The experimental results are in good
agreement with simulations and verify the theoretical concepts.
Keywords— Three-phase brushless synchro, E-shaped
stator, harmonic elimination
1.
Introduction
Among the various absolute position sensors,
resolvers/synchroes and encoders are often utilized in many
industrial applications for precision control purposes [1]-[4].
Compared to the resolvers/synchroes, the absolute encoders
are much more complicated, of larger size, and expensive [5].
Conventional resolvers/synchroes are constructed with a
wound rotor that is excited with an ac voltage through slip
rings and brushes [6]-[7]. Slip rings and brushes produce noise
and reduce the accuracy of the sensor [8]. Using rotary
transformer, the brushes and slip rings can be eliminated [9].
However, compared to the brushed types, the
resolvers/synchroes with rotary transformers have higher
power consumption, lower impedance angle, higher phase
shift, and lower unit torque gradient [10], [11].
In this research, a novel brushless synchro is introduced.
Unlike the other counterparts, in this scheme both the primary
and secondary windings are mounted on the stator. The
magnetic flux is conducted in a certain path within the rotor
and induces voltage in the secondary windings. Compared to
the synchroes with rotary transformer, the induced voltage
directly appears in the output winding and therefore, the
loading effects are suppressed. Moreover, this scheme has a
simple structure with lower cost of fabrication as it consists of
one stator and one non-wound rotor, without any additional
devices like brushes and slip-rings existing in the traditional
brushed structures, or the coupling transformer in brushless
ones.
In this paper first we describe the operation principle of the
scheme. Then, the initial (non-optimal) design procedure of
the synchro together with 2D finite element results is
presented. Finally, in order to verify the theoretical concepts
the experimental results of the fabricated synchro are
exhibited.
2.
Principle of the Scheme
Figure 1 represents the principle of the proposed scheme.
As shown in the figure, the three-phase voltage applied to the
primary windings generates a magnetic flux in E-shaped cores
of the stator. The produced flux passes the air gap, enters to
the rotor, and then returns to the stator from up or down side
of the rotor cores. In this way, if the secondary windings are
mounted on the stator (according to Fig. 1) the magnetic flux
crosses it and without using brush and slip-ring the voltage is
induced in the secondary winding.
To this end, the rotor should be composed of two magnetic
parts isolated by a non-magnetic medium. The non-magnetic
part can be made of aluminum and the magnetic parts should
be made of perpendicular laminated cores. In addition, the
stator should be fabricated as E-shaped cores so that the flux
passes through the two upper/lower stator teeth. On the other
hand, one of the magnetic cores of the rotor should be placed
in front of two upper teeth of the stator cores, and the other
one in front of two lower teeth. Otherwise, no voltage is
induced in the secondary windings. Furthermore, the polarity
of the induced voltage of the upper and lower portions of
secondary windings should be considered when they are
connected to each other. The three-phase primary windings,
mounted between stator slots, are wound the same as those of
the common synchroes.
Fig. 2. Assembling process of E-cores on the body of the stator.
Fig. 1. Schematic view of proposed brushless synchro.
3.
Design Considerations
3.1. Stator
The stator is composed of several sets of E-shaped,
laminated magnetic core. As described in the next section, the
more the number of slots, the more winding space harmonics
could be eliminated. However, considering mechanical and
fabrication restrictions 18 core sets have been selected for the
stator. As shown in Fig. 2, teeth of E-shaped cores are
mounted on the perimeter of a polyamide cylinder in equal
distances. While the longitudinal positions of E-cores are
adjusted by the polyamide cylinder, two rings from up and
down fix the angular position of E-cores on a unique circle.
Note that the primary and the secondary windings will be
wound before placing the stator’s cores. Coil-winding in this
way is very easier than the coil-winding method implemented
for the traditional synchroes.
Fig. 3. Stator winding connections diagram for three phases, a, b, c
3.2. Windings
In order to have a sinusoidal magneto motive force (MMF)
with minimum harmonics, the primary windings have been
distributed sinusoidally and the coils are connected to each
other in a spiral form as illustrated in Fig. 3.
The number of turns of the primary windings is calculated
by a method founded on desired harmonic elimination. In this
method, the coefficients of Fourier expansion of the generated
MMF are equated to zero in order to obtain the each winding
turns. Thus, one can write the Fourier expansion of the
generated MMF in the following form
f (t ) =
∞
∑ S n sin(nωt )
(1)
n=0
in which
Sn =
2
T
T
∫ f (t ) sin(nωt ) dt
(2)
0
Note that in three-phase winding the harmonics of 3, 9, 15,
… as well as even harmonics are identically zero; therefore,
the other harmonics such as 5, 7, 11, 13, … can be arbitrarily
eliminated. In a 18-slot concentrated winding, there are three
unknowns,
as
N1 = a3a3′ = a4 a4′ ,
N 2 = a2 a2′ = a5 a5′ ,
and, N 3 = a1a1′ = a6 a6′ for phase (a) and so on for other
phases. Since the total number of windings is achieved from
FEM analysis, only two harmonics can be eliminated. Here,
one may vanish 5th and 7th harmonics which are the most
powerful terms, as follows:
⎛ 3π 18
⎜
⎜ N1 sin(5ωt ) dωt
⎜
⎜ π 18
⎜ 5π
⎜
18
8i
S5 = ⎜ + ( N1 + N 2 ) sin(5ωt ) dωt
T⎜
⎜ 3π 18
⎜
⎜ π2
⎜
( N1 + N 2 + N 3 ) sin(5ωt ) dωt
⎜+
⎜ 5π
18
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟= 0
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎛ 3π 18
⎜
⎜ N1 sin(7ωt ) dωt
⎜π
⎜ 18
⎜ 5π
⎜
18
8i
S 7 = ⎜ + ( N1 + N 2 ) sin(7ωt ) dωt
T⎜
⎜ 3π 18
⎜
⎜ π2
⎜
( N1 + N 2 + N 3 ) sin(7ωt ) dωt
⎜+
⎜ 5π
18
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟= 0
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
∫
∫
∫
∫
∫
∫
(3)
figure confirms the calculations of winding turns and shows
that the low-order harmonics have been eliminated. As shown
in the figure, only the slot harmonics (17th and 19th) have
little values.
Using FEM analysis, the number of secondary windings is
determined equal to 400 turns to generate an output voltage
with peak amplitude of about 6 volts.
3.3. Rotor
The laminated rotor cores are placed aligned with the flux
path. The angle of rotor sector should be a multiple of stator
pitch angle, 20 degrees, to have a uniform reluctance from
rotor point of view. Here, we select 80 degrees for rotor sector
considering mechanical aspects.
To eliminate the slot harmonics, the rotor should be skewed
20 degree, which is equal to one stator pitch. It should be
noted because the stator E-shaped cores are separated from
each other; the magnetic flux of each core should be closed by
itself. For this purpose, the rotor’s cores should be skewed in a
reverse form at the middle height such as Fig. (6).
(4)
Fig. 4. The MMF waveform based on the calculated primary windings
Carrying out the preceding integrations results in
0.6428N1 − 0.866 N 2 − 0.342 N3 = 0
0.342 N1 − 0.866 N 2 + 0.9848 N3 = 0
(5)
In addition, as discussed later in the paper, FEM yields the
total number of windings of each phase as
2 × ( N1 + N 2 + N3 ) = 480
(6)
Hence, solving the above equations, N1 , N 2 , and N 3 are
obtained
(7)
N1 = 128,
N 2 = 83,
N3 = 29
Using the above number of turns for primary windings and
considering the rotor skew, the MMF waveform is calculated
as Fig. 4. The Fourier series analysis depicted in Fig. 5 shows
that the resulted MMF is very close to a sinosuidal wave and
has a Total Harmonic Distortion (THD) of about 0.46%. This
Fig. 5. Fourier analysis of the MMF produced by primary windings
Table I: Designed data of the synchro
Fig. 6. Schematic view of the fabricated rotor and stator.
4.
Simulation
Finite element software is used for modeling of the
designed synchro. To simplify the calculations we have used
an equivalent two-dimensional model shown in Fig. (7). The
magnetic paths in this model is the same as the designed
synchro (in both of them the magnetic flux crosses two airgaps and then returns to stator cores) and therefore, it can be a
good approximation. Although in this model the rotor skew
has not been considered, it is precise for calculation of the
synchro parameters such as winding turns, input current, and
the induced output voltage. By this method, the designed data
of the synchro are summarized in Table I.
The output voltage of the synchro in this condition is about
6V (peak) that is shown in Fig. 8 and the magnetic flux
distribution is shown in Fig. 9. The calculated input current of
the synchro, depicted in Fig. 10, shows that in this condition
the amplitude of the input current is about 0.1 A (rms) and the
current density of wires is about 3.4 A/mm2.
Parameter
Value
Unit
Input voltage (peak)
12
V
Frequency
50
Hz
Output voltage (peak)
6
V
Total turns of primary windings
in each phase
480
-
Secondary winding’s turns
400
-
Stator and rotor wire thickness
0.2
mm
Stator outer diameter
40
mm
Rotor outer diameter
30
mm
Stator length
87
mm
Number of Stator E-cores
18
-
Stator E-core thickness
3.8
mm
Fig. 8. Simulated output voltage signal.
Figure 9. The distribution of magnetic flux density.
Fig. 7. Schematic view of the equivalent 2D synchro.
Figure 10. Simulated input current of the synchro.
5.
Fig. 11(b). Input line to line voltage and output signal at 90 degree difference
with respect to zero reference angle.
Experimental Results
Fig. 6 represents the fabricated synchro. The synchro has
been tested under two conditions: single and double
(transmitter- receiver) arrangements. In the single arrangement
the three phase input voltage is applied to primary windings
and the output voltage induced in the secondary winding is as
relation (8) [11]. The following relation shows that in this
arrangement the amplitude of output signal is constant and its
phase is proportional to the rotor angle with respect to the
reference angle.
Vˆ = k V Sin (ω t + θ − θ )
(8)
out
s in
r
ref
In this relation Vˆout , k s , Vin , ω , θ r , and θ ref
are
respectively the output instant voltage, transformer ratio of
synchro, the amplitude of the input voltage, the frequency of
input voltage in radian per second, the rotor angle, and the
reference angle.
To implement first test, we have used a three-phase 9V
(rms), 50Hz voltage signal. Fig. 11(a) shows the measured
input (line to line) and output voltages at zero reference angle.
Figs. 11(b) and 11(c) illustrate results of the test
corresponding to the rotor angle of 90 and 180 degrees with
respect to the reference angle. It can be seen that the phase of
output voltage is proportional to the rotor angle and confirms
the operation principle of the proposed synchro.
Fig. 11(a). Input line to line voltage and output signal at zero reference angle.
Fig. 11(c). Input line to line voltage and output signal at 180 degree
difference with respect to zero reference angle.
In the second test, two synchroes are connected to each
other by their three-phase terminals in a star arrangement, as
shown in Fig. 12. In this condition, the voltage induced in the
secondary winding of the receiver synchro follows the relation
(9) [11]. As deduced from this relation, the phase of the output
voltage is constant and its amplitude is cosine function of the
angle difference between the rotors of two synchroes.
Vˆ = k V Cos (θ − θ ) Sin (ω t + ϕ )
(9)
out
d in
rr
rt
In this relation k d , θ rr , θ rt , and ϕ are respectively the
transformer ratio of this arrangement, the transmitter rotor
angle, the receiver rotor angle, and the phase difference caused
by the inductances of synchroes.
For this test, A single-phase 9V (rms), 50Hz voltage is
applied to the secondary winding of transmitter synchro. The
results for various difference angles are presented in Figs. 13
(a) to (c). As seen from these figures, the maximum amplitude
of the output voltage is occurred if the difference angle is 0
degree. In addition, in case of 60 and 90 difference angles the
amplitude of output voltage become half and zero,
respectively. These results meet the desired conditions and
verify the theoretical concept of the presented scheme.
6.
Fig. 4. Synchroes connection for transformer/ receiver arrangement
Fig. 5(a). Transformer and receiver voltage in case of aligned synchroes.
Fig. 13(b). Transformer and receiver voltage in case of 45 degree angular
difference between synchroes.
Fig. 13(c)6. Transformer and receiver voltage in case of 90 degree angular
difference between synchroes.
Conclusion
In this research, a new brushless scheme for three-phase
synchroes is proposed. This scheme opens a new way to
eliminate the brush and slip rings’ noises and enhance the
accuracy of the synchroes and resolvers. The concept of the
scheme was described clearly in the paper. Then, using 2D
finite element method the synchro was designed and analyzed.
In order to validate the theoretical concepts, two prototypes
were fabricated based on the designed parameters. The test
was performed in two ways; single and double arrangement.
The results confirmed the employed concept and also were in
good agreement with simulations.
The research is going on and the authors are now dealing
with the optimal design of the synchro as well as making a
digital convertor to compare the accuracy of present scheme
with conventional synchroes. These researches will be present
at the next occasion.
References
[1] R. Setbacken, ‘‘System performance and Application Tradeoffs
Determine the Choice Between Encoders and Resolvers in Brushless Servos,’’
Power Convers. Intell. Motion, vol. 22, no. 5, pp. 69---76, 1996.
[2] L. Harnefors, H.-P. Nee, ‘‘A General Algorithm for Speed and Position
Estimation of AC Motors’’, IEEE Trans. On Industrial Electronics, Vol. 47,
No. 1, Page(s): 77 --- 83, February 2000
[3] Yokozuka, Tsutomu, ‘‘Velocity Errors of the Resolver Phase Shifter ’’,
IEEE Trans. On Industrial Electronics, Vol. IE-30, No.4, Page(s): 386 --- 389,
Nov. 1983
[4] R. Hoseinnezhad, A. Bab-Hadiashar, P. Harding, ‘‘Calibration of Resolver
Sensors in Electromechanical Braking Systems: A Modified Recursive
Weighted Least-Squares Approach ‘‘’’, IEEE Trans. On Industrial Electronics,
Vol. 54, No. 2, Page(s): 1052 --- 1060, April 2007.
[5] L. Sun, ‘‘Analysis and Improvement on the Structure of Variable
Reluctance Resolvers’’, IEEE Trans. Magn., Vol. 44, No. 8, Aug. 2008
[6] V. Del Toro, ‘‘Electric Machines and Power Systems’’, Englewd Cliffs,
NJ: Prentice-Hall, 1985.
[7] D.C. Hanselman, ‘‘Techniques for improving resolver-to-digital
conversion accuracy’’, IEEE Trans. On Industrial Electronics, Vol. 38, No. 6,
Page(s): 501 --- 504, December 1991
[8] D.C. Hanselman, ‘‘Resolver Signal Requirements for High Accuracy
Resolver-to-Digital Conversion’’, IEEE Trans. On Industrial Electronics, Vol.
37, No. 6, Page(s): 556 --- 561, December 1990.
[9] H. Martinez, ‘‘Measuring the Position of Mechanical Shafts,’’ Power
Conv. Znt., vol. 9, no. 9, pp. 39-42, Oct. 1983.
[10] J. Wan, X. Li, and G. Hong, ‘‘The analysis and design of high-speed
brushless resolver plus R/D converter shaft-angle measurement system,’’ in
Electr. Mach. Syst., ICEMS, 2001, pp. 289---292.
[11] Moog component group, ‘‘Synchro and Resolver Engineering
Handbook’’, available on www.moog.com, downloaded at June 1, 2011.
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