Effective Switched Reluctance Drive Train in
Unmanned Aerial Vehicles: Design Investigations
C. Laudensack, Y. Polonskiy and D. Gerling
Φ
Abstract — The purpose of this paper is the design of
different switched reluctance drives for an existing drive train of
an electromechanical actuation system of a small unmanned
aerial vehicle. Therefore, the outside dimensions of the switched
reluctance machine are determined by the used permanent
magnet synchronous motor size to allow the easy exchange of the
motor drives. Moreover, the switched reluctance machines
should fulfill the same control requirements as the reference
motor.
I. INTRODUCTION
Generally, often commercial off the shelf (COTS) hobby
components, like permanent magnet synchronous motors or
DC motors, are used to drive the electromechanical actuation
system of small sized unmanned aerial vehicles (UAV) [1].
Based on the development of motor control possibilities,
today’s market situation for materials and the maturity of new
technologies, the actual proven solutions should be compared
with new considerations for effective drive train concepts of
electromechanical actuation systems in mini UAV in the near
future. The new designed switched reluctance machine (SRM)
should be inserted in an existing electromechanical actuation
system in the power classes for small sized UAV’s. Therefore,
it is important to design the switched reluctance machine in
the way that it is possible to replace the permanent magnet
synchronous motors used at present easily. From the literature
it is known that from time to time SRM are used either as
starter generators [2] or as electromechanical actuators [3, 4]
for larger power classes in more electric aircrafts (MEA). Due
to the complexity of the systems increase their reliability
drastically gets worse, hence advanced fault tolerant electrical
components are absolutely necessary for safety-critical
operations especially in aerospace applications. Switched
reluctance drives (SRD) seem to be a good solution for such
applications. [5]
Various advantages of SRM and rapid developments in the
areas of power electronics make them attractive to existing DC
and AC engines in the filed of adjustable speed drives. The
switched reluctance machine produces torque by the tendency
to move its rotor to a position where the inductance of the
excited winding is maximized. The construction of the crosssection is very simple and robust because the machine has
salient teeth on both stator and rotor. Concentrated coils are
____________________________
C. Laudensack is with the Department of Electrical Drives and Actuators,
Universitaet der Bundeswehr Muenchen, Neubiberg, Germany (e-mail:
christian.laudensack@unibw.de).
Y. Polonskiy is with the Department of Electrical Drives and Actuators,
Universitaet der Bundeswehr Muenchen, Neubiberg, Germany (e-mail:
yevgen.polonskiy@unibw.de).
D. Gerling is Full Professor and Head of the Department of Electrical
Universitaet der Bundeswehr Muenchen, Neubiberg, Germany (e-mail:
dieter.gerling@unibw.de).
978-1-4799-4775-1/14/$31.00 ©2014 IEEE
placed only around the stator teeh, while there are no windings
and permanent magnets on the rotor, which results in a low
rotor inertia. Furthermore, the high power-to-weight and
torque-to-weight ratios of a switched reluctance machine lead
to excellent starting characteristics with a high starting torque,
a wide speed range as well as a high speed performance.
These reasons clearly show the project purpose to analyze
new high efficiency electromechanical actuation systems for
small UAV at low-cost applications. The permanent magnet
synchronous motor (PMSM) used in small UAV actuation
systems until now, should be replaced by a switched
reluctance drive. Thus, different configurations of switched
reluctance machines are designed in consideration of given
performance and control requirements as well as the thermal
behavior of the drive are analyzed.
The fact that the torque is produced by the interaction
between flux and current is the cornerstone of electrical
machine design and leads to the more advanced work of
machine and drive design. It is always important to minimize
power losses and temperature rise caused by heating of the
conductors, core losses caused by hysteresis and eddy-currents
in the magnetic steel, torque pulsations and acoustic noise and
to use materials economically. Therefore, the first rough
estimations of the switched reluctance machines are designed
with SPEED PC-SRD [6], an analytical computer-aided
software package developed at SPEED laboratory. Moreover,
the thermal behavior of the drive is analyzed with an improved
lumped
parameter
thermal
model,
modeled
in
MATLAB/SIMULINK. Finally, same special configurations
are selected and verified with an electromagnetic finiteelement simulation in WORKBENCH/MAXWELL.
II. DESIGN SPECIFICATION AND ASSUMPTIONS
It is important to design the SRM in the way that it is
possible to replace the PMSM used at present easily.
The analytical design procedure is also described in detail in
[7]. After a rough design estimation of the cross section
geometry, the design of the SRM is optimized due to a
parameter variation with SPEED PC-SRD. These output
parameters are used as input parameters for the thermal
analyses to achieve the thermal behaviour of the motors.
Finally, the electromagnetic parameters are evaluated with the
finite-element analyses.
A. Requirements and specifications
The following design requirements and specifications
(TABLE I) of the SRM are determined by the reference
permanent magnet synchronous motor and the application.
They should be kept to allow the easy exchange of the motor
drives.
1108
1) Phase number
The electromechanical actuation system will be designed
for low-cost applications; therefore, the manufacturing costs
should be reduced as far as possible. Normally, this results in a
simple design and construction of the switched reluctance
machine and the power electronics. This means that the
number of phases should be as small as it is allowed by the
application because a small number of phases forces a simple
layout of the machines cross-section and a small number of
semiconductors of the converter, which results in low
manufacturing costs because of savings in the connections,
transistors and switches. Single-phase or two-phase drives,
which need only one transistor and one diode or respectively
two transistors and two diodes in the controller, achieve this
requirement at best. But they produce undesirable torque
ripples and usually are specified for low-power simple drive
systems and hence not suitable for high-performance drive
systems. Regular three-phase machines or machines with a
higher number of phases are able to start from any rotor
position and can be used for motoring or generating in either
forward or reverse direction. The advantages of less torque
ripple and an improved resulting torque of the four-and fivephase motors arise from their ability to operate with two
phases (four-phase machine) or three phases (five-phase
machine) on the same time. With a rising phase number the
complexity of the cross-section geometry and of the inverter
system also raises, hence the increasing costs make a four- and
five-phase machine hardly suitable for low cost applications.
2) Pole number
Regular switched reluctance machines cannot have the same
number of stator and rotor poles because this would not allow
the self-starting capability. The stator and rotor numbers have
to be a multiple of 2 because the poles are spaced on each part
equally and symmetrical to their centerlines. The advantage of
a large number of rotor poles is a lower torque ripple, but
unfortunately with the consequence of a lower inductance
ratio between aligned and the unaligned phase, which may
increase the controller volt-amperes and decrease the specific
output.
3) Material
The material for the switched reluctance machine can
individually be chosen for the stator, rotor and shaft.
Typically, the standardized electrical steel “M 330-35AP” is
preferred for new switched reluctance machines. Generally, it
is necessary to use thin laminations for the stator and rotor
core to reduce the eddy-currents caused by the flux change in
the iron parts. For SRM the laminations have to be bonded
with bonding vanish because fixing them with bolts or
welding them would strongly influence the performance of the
machine.
4) Air gap length
Generally, the air gap length of switched reluctance
machines should range between 0.3mm and 0.4mm, which are
also possible values for manufacturing. This is true because
with rising the air gap length the efficiency and the shaft
power and hence the torque decreases. This is the fact because
the torque is proportional to the area described by the
coenergy, which is bordered by the flux linkage of the aligned
and unaligned position. Thus, with increasing the air gap the
TABLE I
DESIGN REQUIREMENTS AND SPECIFICATIONS
Stator outer diameter
26.67mm
Stator length
17.6mm
Overall length
25.9mm
Shaft diameter
4.8mm
Supply DC voltage
Average DC current
Maximum DC current
70V
4A
5.5A
Speed at operation point
7750rpm
Nominal torque at operation point
Maximum torque at operation point
(duration 5s)
Ambient temperature / initial temperature of
machine
Cooling method
0.049Nm
Maximum operation time
0.079Nm
20°C
air cooled / totally enclosed
30s
ψ − i characteristic for the aligned position is lowered and
hence the coenergy. Therefore, the air gap length should be
chosen as small as possible to get a good performance of the
machine. The air gap size is also limited by accuracy of the
rotor concentricity and by the thermal extension. Furthermore,
when the rotor diameter and the stator outside radius are set
constant, with an increasing air gap the total weight of the
machine and hence of the whole drive decreases, but in a
smoother way than the efficiency. It has to be noticed, when
the stator inside diameter is kept constant and the air gap
length is reduced, the rotor outside diameter and hence the
rotating mass rise. Experience of manufacturing companies’
show that for small SRM, like in the present case, the air gap
length can be set to 0.2mm. In some cases the air gap also
could be reduced to 0.15mm, but additional detailed
calculations, which consider the deformations forced from the
rotating speed and the thermal expansion, are necessary.
5) Thermal analyses
The thermal analyses is done with a stand-alone simulation
tool [8, 9] for SRM developed in MATLAB/SIMULINK with
the improved lumped thermal network method for transient
working conditions (detailed description in [10]) with the
material properties for an ambient temperature of 20°C and the
additional thermal parameters shown in Table II .[11, 12] The
thermal lumped parameter network design is based on the
hypothesis that the machine structure, under the thermal point
of view, can be divided into several parts having the same
behavior and connected one to the other by the means of
thermal resistors and capacitors. The temperature is assumed
as constant in each machine part and calculated in the
midpoint of the machine part. Radial heat flows are
independent from axial heat flows and circumferential heat
flows are not considered. It is assumed, that the thermal
capacity and the heat generations are uniformly distributed.
Furthermore, the machine is symmetric about the shaft.
Improved lumped thermal models are used to calculate the
temperature distribution and the transient thermal
characteristics because conventional lumped thermal model
often leads to inaccurate results for bodies with distributed
heat generation by overestimating the temperature on each
node. This is done by a systematic mistake assuming that the
1109
heat flow through a component remains constant for each
member element within, while in fact, the flow changes
linearly with dimensions.
TABLE II
ADDITIONAL USED THERMAL PARAMETERS
Parameter
Ideal coil side of winding to stator teeth
conductivity
Contact coefficient between frame and stator
yoke
Conductivity of the air in the air gap
Thermal resistance end-winding to frame
Thermal resitance rotor yoke to frame
Air cooled:
Natural convection from frame to ambient
Totally enclosed cooling condition:
Heat flux from frame to ambient
Value [W/(m²K]
400
11700
0.5
100
100
12
0
B. Comparison of switched reluctance machine
configurations
Different SRM configurations for the electromechanical
actuation drive for small UAV are designed with respect to the
specified requirements (see chapter II.A). Some important
electromagnetic parameters from the analytical design with
SPEED PC-SRD are outlined in TABLE III.
TABLE III
COMPARISON OF CONFIGURATIONS FROM THE ANALYTICAL DESIGN PROCESS
Topology
Air gap
Phase number [-]
Turns per teeth [-]
Length of endwindings [mm]
Phase resistance
[mΩ]
Ld/Lq unsat [10-6 H]
Maximum/minimu
m phase current [A]
Supply voltage [V]
Speed [rpm]
Turn-ON/turn-OFF
angle [°mech]
Average Torque
[mNm]
Copper losses [W]
Iron losses [W]
Efficiency [%]
Wire diameter
[mm]
Current density
[A/mm²]
Shaft inertia [10-7
kgm²]
Copper mass [mg]
Iron mass [mg]
6/4
3
35
8/6
8/4
0.3mm
4
2
25
20
12/8
3
25
6/4
12/8
0.2mm
3
3
35
25
TABLE IV
Comparison of the temperature distribution for the different configurations
25.97
25.99
23.38
21.27
25.97
21.6
344
258
310
750
344
665
744/
255
340/
188
397/
166
479/
341
1056/
258
732/
344
11/10
16/15
19/18
17/16
9/8
9/8
48
7750
48
7750
48
7750
48
7750
48
7750
48
7750
45/88
31/52
50/85
22/40
45/88
21/43
46
48
46
48
47
electronics, which increases costs. Moreover, the 8/4
configuration can utilize even higher inductance ratio than the
8/6 configuration, but the motor suffers from the lack of selfstart capability whenever the rotor aligns with a stator phase.
Hence a parking mechanism or some starting assistance like a
magnet is needed to stop the rotor in a defined position.
However, this also increases the production cost and weakens
the robustness of the drive. The 12/8 configuration provides
the required torque with the lowest torque ripple, but with the
drawback of the highest current density, which leads to the
highest losses and hence the highest temperature distribution
in the motor. Technically speaking, the 12/8 configuration is
effectively a 6/4 “multiplied” by 2. The flux-paths within the
rotor are kept short due to 4-pole magnetic field topology,
which compensates the higher switching frequency of the
stator field and hence reduces the iron losses dramatically.
Besides the electromagnetic characteristics also the thermal
behavior of the drive is important. Dependent on the mounting
assembly the drives can be cooled from the ambient or they
have to be treated as totally enclosed ones.
TABLE IV shows clearly the strong relationship between
the temperatures and the copper losses. It is obvious that the
temperatures dramatically increase, when the heat exchange
with the ambient is stopped. Comparing the temperature
distributions with the current densities, it can be said, that the
current densities are acceptable for this machine size and for
the short operation time (30s).
Topology
Air gap
Air cooled
Totally
enclosed
EndWinding
[°C]
Winding
[°C]
Stator teeth
[°C]
Stator yoke
[°C]
Rotor teeth
[°C]
Rotor yoke
[°C]
Frame [°C]
47
55.8
3.7
38.7
82.8
6.5
30.3
83.2
1.9
30.3
209.5
4.8
15.4
36.9
3.9
48.4
68.7
5.5
33.3
0.48
0.47
0.52
0.36
0.48
0.39
39.9
50.5
53.8
94.8
32.3
49.8
2.03
1.94
1.44
1.58
2.14
3.52
18
41
17
53
15
46
12
48
18
41
14
45
It can be seen that the 6/4 configuration achieves the highest
“torque constant” because of the highest ratio of the aligned to
unaligned inductance (Ld/Lq). This is a benefit of topology,
which have a low number of stator and rotor poles, but with
the disadvantage that the torque ripple performance is poor
compared to higher order topologies. In comparison, the 8/6
configuration is a good compromise to achieve a high
inductance ratio and a lower torque ripple than the 6/4
configuration, but this motor requires a 4-phase power
Heating
period [s]
Temperature
after 30s
[°C]
6/4
8/6
X
X
X
8/4
12/8
0.3mm
X
X
6/4
X
X
X
X
12/8
0.2mm
X
X
X
31
226
345
296
33
294
54
633
27
162
31
230
29
225
33
295
32
293
51
631
26
162
30
230
29
225
33
295
32
293
51
631
26
162
30
230
27
225
31
295
30
294
47
632
25
162
29
230
29
200
32
260
32
261
49
548
26
145
30
211
29
195
32
255
32
257
49
536
26
141
30
206
23
22
45
23
24
22
32
27
22
22
24
23
25
600
25
600
25
600
600
600
25
600
30
500
30
84
35
107
33
100
64
234
27
64
31
96
Consequently, considering the results of the analytical
electromagnetic design studies and the thermal analyses as
well as the drive complexity and hence the manufacturing
costs, the 3-phase 6/4 and 12/8 configurations are the most
suitable configurations for this application. Thus, a 6/4 and
12/8 configuration with an air gap length of 0.2mm are also
pre-designed with SPEED PC-SRD and thermally analysed.
This air gap length would also be possible for the machines
with respect to the given requirements, especially the
operation speed of 7750rpm (see chapter A.4)).
More detailed electromechanical analyses are required to
determine the main electromagnetic characteristics of the
motors more precisely. Therefore, these configurations are
1110
simulated and optimized with the finite-element software
MAXWELL (TABLE V).
TABLE V
PERFORMANCE ANALYSES FROM FINITE-ELEMENT ANALYSES FOR 3-PHASE
6/4 AND 12/8 CONFGURATION, AIR GAP 0.2MM, 7750RPM
Topology
Average torque
Mechanical power
Electrical power
Iron losses
Copper losses
Efficiency
Average DC supply current
RMS phase current
Minimal torque
Maximal torque
Torque ripple
Maximal flux density
(teeth/yoke)
6/4
0.132Nm
107.82W
174.17W
10.15W
56.20W
61%
2.8A
7.4A
0.080Nm
0.170Nm
68%
12/8
0.062Nm
50.64W
136.12W
18.37W
67.11W
37.2%
3.23A
6.08A
0.055Nm
0.065Nm
16%
2.2T
1.8T
Fig. 2: Cross-section design of a 4 pole/12 notches PMSM with surface
mounted (left) and buried / interior permanent magnets (right)
Table VI outlines the basic construction and design
characteristics of a classic SRM and PMSM.
TABLE VI
CONSTRUCTION AND DESIGN CHARACTERISTICS OF SRM AND PMSM
The comparisons of the results from SPEED PC-SRD with
the values from MAXWELL show that with the more accurate
FEM simulations an improvement of the designs are possible.
For the 6/4 configuration the average torque can be
increased up to more than the double, while the efficiency is
increased from 48% to 61%. The average torque of the 12/8
configuration can be increased about 30%, and the efficiency
about 11%.
C. Comparison between switched reluctance machines and
permanent-magnet synchronous machines
Both machine types, SRM and PMSM, belong to rotating
field machines, which run synchronously to the excitation
field. The basic constructions of typical inner-rotor SRM- and
PMSM-drives are compared briefly.
1) Constructional and design aspects
SRM are characterized by the number of stator and rotor
poles. Therefore, the presented cross section Fig. 1 has 12
stator poles and 8 rotor poles resulting in a 12/8 topology.
SRM
Saliency structure
Saliency structure
Stator windings
Single-tooth
winding
Approximate
excitation MMF
Desired air gap
Phase number
Trapezoidal
PMSM
Saliency structure
•
Round structure
•
Magnets
Distributed winding
(concentrated windings are
not regarded here)
Sinusoidal
< 0.4mm
3-5
< 1.5mm
3
Stator
Rotor
The general characteristics of the drives are compared
relative to each other in Table VII. This evaluation is based
on a qualitative investigation.
A comparison, [13], of a single-phase switched reluctance
actuator and two different single-phase permanent magnet
actuators for low-cost applications shows that the cost for the
SRM are lower than for the PMSM whereas the total weight is
lower for permanent magnet actuators. Both machines are
based on the same requirements and similar properties. The
permanent magnet actuators are either build with ferrite
magnets or Neodymium Iron Boron (NdFeB) magnets. This is
a rare-earth magnet material and currently the strongest type
of permanent magnets.
TABLE VII
COMPARISON OF SRM AND PMSM
Production costs
Fig. 1: Cross-section design of a 12/8 SRM
In comparison the PMSM is given by a number of rotor
poles and stator notches, which results in a 4 pole machine
with 12 notches for the displayed cross section in Fig. 2.
Torque ripple
Torque constant
Iron losses
Winding losses
Rotor position feedback
Power density
Redundancy/Reliability
Temperature sensitivity
SRM
Pros:
+ No magnets
+ Single-tooth
winding
Contras:
- Air gap
- Rotor lamination
material
High
Low
High
Low
Required
Low
High
Low
PMSM
Pros:
+ Rotor lamination
material
+ Air gap
Contras:
- Magnets
- Distributed
windings
Low
High
Low
High
Required
High
Low
High
In a switched reluctance machine the phase are energized
from a DC voltage supply, which results in a unidirectional
1111
phase current (Fig. 3). Beside the transitionn time from one
phase to the other (overlapping time) only onne phase is feeded
with current at once.
with the pole pair number p , the rottor flux linkage (produced
by magnets) ψ Mag , the d- and q-axiis inductances Ld , Lq and
the d- and q-axis currents id , iq .
i IHi
Table VIII outlines the charracteristics of the power
electronics for both drives.
TABLE VIII: COMPARISON OF POWER ELEC
CTRONICS FOR SRM AND PMSM
βA
βK
β
βE
Current wave form
Current direction
Power electronics
(typical)
Phase number
u +UDC
SRM
Trapezoidal
Unidirectionall
Asymmetric half-b
bridge
PMSM
Sinusoidal
Bidirectional
Symmetric half-bridge
3-5
3
Moreover, the common power electronics for the SRM and
PMSM are given in Fig. 5.
β
In a permanent magnet synchronous machine all phases are
-UDC
energized
at the same time. The current iis sinusoidal and
bidirectional (Fig. 4). Because of the rottor magnets and
energizing all of the phases, a PMSM providees a higher torque
Fig. 3: Phase
(top) and excitation voltage (bottoom) of the SRM
constant
thancurrent
a SRM.
Fig. 5: 3-phase asymmetric half-bridge for
f the SRM (left) and 3-phase
symmetric half-bridge for the PMSM (righ
ht)
The main application fields of PMSM are servo drives,
positioning, traction, high-power density application. SRM are
mostly found in fans, pumps, low-co
ost applications.
2) High-speed behavior
The high-speed operation behav
vior of both motor types
strongly relates either to mechanicall and electrical aspects.
a)
Mechanical aspects
On the one hand, the rotor of th
he machine is loaded by a
Fig. 4: Phase current of the PMSM
Both machines produce torque by the maagnetic attraction,
which forces the rotor to align with the stator field. The
centrifugal force FC , which is given
n by [15]
FC = mR ⋅ ω R2 ⋅ r1
(4)
mechanical torque TMEC of a SRM is calcculated from the
where mR is the rotor mass, ωR is the angular velocity of the
magnetic co-energy WCo, MAG and from the rootor position θ R :
[14]
rotor and r1 is the rotor outer radiuss.
On the other hand, the rotor is loaaded by the magnetic force
TMEC =
∂WCo, MAG
(1)
∂θ R
This Eq. can be simplified for the linear caase, which means
FMAG , which is applied to the rotor either through the
electromagnetic attraction between
n stator and rotor teeth or
indirectly through the permanent maagnets. The magnetic force
that the inductance L θ R only depends on tthe rotor position
can be factorized into a tangentiial component FMAG ,tan ,
which produces the shaft torque, and a radial component
and not on the phase current iPh :
FMAG , rad , which produces vibrational and accostical noise.
( )
TMEC
( )
1 dL θ R 2
iPh
=
2 dθ R
(2)
In contrast the torque in a PMSM is describbed as
3
TMEC = p ⋅ iq ⎡⎢ψ Mag + id Ld − Lq ⎤⎥
⎣
⎦
2
(
)
(3)
The calculation of this magnetic forcce is not as straightforward
as of the centrifugal force because it has a time varying and
non-linear charesteristic.
For the reference PMSM the load
d forces on the magnets can
be read out from the design sheet. Thus,
T
the centrifugal force
can be estimated as 4N and the radial
r
force as 7.6N. For
surface mounted permanent-magneet synchronous machines,
like the used reference machine, thee magnets are glued on the
rotor outer surface. Additinally, thee magnets can be protected
1112
and fixed by a bandage, which is applied on the outer magnet
surface.
Glue materials are often limited by their shear strength
because in permanent-magnet machines the tangential force is
higher than the radial force. Typical values for shear strength
are in the range of 20-30N/mm², while for the tensile strength
the value is about 26N/mm² [16, 17, 18].
The mounting plane of a rotor magnet can be estimated to
79.2mm². This leads to a tensile stress of about 0.05N/mm²
and a shear stress about 0.09N/mm². Hence, the values show a
negligible loading of the glue.
A SRM does not use any magnets so it is more reliable for
high speed applications. The forces, which load the rotor, are
the same as for PMSM. Considering the weight of a rotor
tooth and the nominal speed the radial magnetic force can be
calculated to about 4.9N for the 6/4 SRM, about 2.1N for the
12/8 SRM, about 84N for the 6/4 SRM (air gap 0.2mm) and
about 39.4N for the 12/8 SRM (air gap 0.2mm)
The deflection S of a rotor tooth can be approximated by
the formula from the beam theory [15]
3
4 ⎛l⎞
(5)
S=
⋅⎜ ⎟ ⋅ F
E ⋅b ⎝ h ⎠
with the elasticity module E (approx. 2.00·1011N/mm² for M
330-35AP electrical steel and 1.40·105N/mm² for Vacodym
872AP magnets) and the force F . For the calculation of the
tensile and shear stress the product of the tooth width and
stack length is considered.
Table IX: Dimensions and deflection of the different machine topologies
b
l
h
Fc
[mm]
PMSM
SRM 6/4
SRM
12/8
FMAG,rad
[N]
σ SMAX
σt
[Nmm²]
[nm]
2.0
2.9
4.5
3.6
4.0
4.9
7.6
84
0.05
0.08
0.09
1.31
1.1
49
17.6
1.7
2.4
2.1
39.4
0.05
0.94
17
(6)
with a typical EMF-constant K f and the speed n .
Fig. 6: Equivalent circuit of one phase of a PMSM (left) and SRM (right)
In contrast to a SRM, the induced voltage in a PMSM is
produced always whenever the rotor moves, independent
whether the phase is energized or not. This is the reason, why
engineers need to spend a lot of thoughts, if they want to
design a fail-safe motor – in case of short-circuits etc. UEMF is
still generated, what could cause a retarding torque.
The other characteristic of the induced voltage is common
for all types of electric drives – with increasing the speed the
induced voltage comes closer and closer to the supplying
voltage. This means, the phase current will decrease because it
is proportional to their difference. So the motor torque is also
reduced. The estimation of the maximum speed n MAX , where
no torque is produced (idealized no load run) is easy, because
the maximum line-to-line voltage U ll equals the DC bus
n MAX ≈
As it can be seen from Table IX, the tensile stress is similar
for all machines, but the SRM show a much higher shear
loading than PMSM. The reason is clear because SRM
produce the torque by a phase-by-phase switching while the
PMSM runs with the three phases at the same time.
Nevertheless the stress values are too low to have any
considerable effect on the rotor or magnets.
b)
)
voltage U DC and the phase voltage is related to it as:
,
1
1
MAX
MAX
U EMF
= U Ph
= K f ⋅ n MAX ≈
⋅ U ll =
⋅ U DC (7)
3
3
For the reference permanent-magnet synchronous drive the
maximum speed can be estimated as
S
17.6
17.6
(
U EMF = K f ⋅ n ⋅ sin ωR ⋅ t + ϕ
Electrical aspects
From the electrical point of view the drives also have a
noticeable difference. For a better understanding an equivalent
scheme for a motor phase is given below.
A scheme of the equivalent electric circuit for stator phase
of a PMSM (considering surface mounted magnets, so
LPh = Ld = Lq ) and of a SRM is presented in Fig. 6. The
scheme consists of the phase resistance RPh, the inductance LPh
and the induced voltage UEMF, which is linked to the magnet
movement. The supplying voltage UPh is applied at the
terminals causing a phase current IPh. The shape and amplitude
of the induced voltage UEMF depends on the motor design, but
in most cases it has either a sinusoidal or a trapezoidal form.
The amplitude and the frequency of UEMF depend on the
rotational speed, like
U DC
3⋅Kf
≈ 11024rpm
(8)
The approximated value from PC-SRD is 12825rpm. The
data sheet of the manufacturing company gives a value of
12000rpm for no-load speed.
To overcome this speed limit imposed by UEMF a method
known as field weakening is used. It means that the motor
phase currents are controlled in the way that the rotor magnet
field is reduced. This is achieved by splitting the phase current
into two components – iq for producing the torque and id for
imposing an opposite magnetic field to the rotor. An opposite
magnetic field also reduces the motor torque constant, but the
speed range can be increased maintaining the motor power.
Physically the behavior of the phase inductance in a
switched reluctance machine differs strongly from a
permanent-magnet synchronous machine because
• the phase inductance is not constant,
• no voltage is induced actively because of the absence
of magnets.
To understand the behavior more clearly the formula for the
phase voltage is cited [14]:
1113
U Ph = RPh ⋅ iPh +
∂ψ
∂iPh
⋅
diPh
∂ψ
+ ωR ⋅
dt
∂θ R
(9)
(
)
With the flux linkage ψ iPh , θ R dependent on the phase
current iPh and the rotor angle θ R . The third term depicts the
voltage, which can be related to the induced voltage UEMF
within a permanent-magnet synchronous motor. This voltage
depends on the angular speed ωR , but it is only present in
case of the energized phase provides a flux linkage Ψ. This
results in a better fail-safe behavior of a switched reluctance
machine, because winding short-circits etc. do not produce
any torque unless the phase is feeded with current. As already
mentioned, the drives characteristics are highly non-linear, so
a prediction of the maximum speed range without load can be
done only by simulation.
In contrast to a permanent-magnet synchronous machine,
there is no field weakening for switched reluctance machine.
The only way to increase the speed above the limiting point is
to boost the increase rate of phase current with increasing the
supply voltage.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
III. CONCLUSION AND FUTURE WORK
Different switched reluctance machines for an existing
electromechanical actuation system of a small sized unmanned
aerial vehicle are designed. To allow the easy exchange of the
motor drives the outside dimensions of the switched
reluctance machine are determined by the actual proven
permanent magnet synchronous motor.
One of the big disadvantages of a switched reluctance drive
is its inherent torque ripple, which often disturbs a control
loop and causes pulsation of speed or rotor position.
Especially for a position control in such safety-critical
applications a smooth torque characteristic is needed to obtain
a good tracking of a set position. Additionally, another
requirement for the drive is to provide a high starting torque to
overcome some possible stalls due to freezing mechanisms.
Therefore, an overview of the chosen countermeasures and
finite-element simulation results will be given in [19].
IV. REFERENCES
[1]
[2]
[3]
[4]
[5]
M. Lukátsi, I.Réti, B.Vanek, Á. Bakos, J. Bokor, I. Gözse: “Mini
Actuators for Safety Critical Unmanned Aerial Vehicles Avionics”;
Systems and Control Laboratory, Computer and Automation Research
Institute, Hungarian Academy of Sciences; Budapest, Hungary;
Research article, Transportation Engineering, periodica polytechnic;
2013.
S. Shoujun; L. Weiguo; D. Peitsch; U. Schaefer.: “Detailed Design of a
High Speed Switched Reluctance Starter/Generator for More/All
Electric Aircraft”; School of Automation, Northwestern Polytechnical
University; Xi’an, China; School of Electrical Engineering and
Computer Sciences and School of Mechanical Engineering and
Transport Systems, Technical University of Berlin; Berlin, Germany;
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U. Kreutzer: “Ein Beitrag zur Regelung elektrischer Maschinen mittels
Sliding-Mode-Methodik”; Ph.D. dissertation, EAA-Forschungsberichte
Band 9, Institute for Electrical Drives and Actuators, Universitaet der
Bundeswehr Muenchen,; Shaker Verlag, Aachen, Germany; 2011. (in
German)
A. Schramm: “Redundanzkonzepte für Geschaltete Reluktanzmotoren”;
Ph. D. dissertation, EAA-Forschungsberichte Band 2, Institute for
Electrical Drives and Actuators, Universitaet der Bundeswehr
Muenchen,; Shaker Verlag, Aachen, Germany; 2006. (in German)
M. Ruba, I. Bentja, L. Szabó: “Novel Modular Switched Reluctance
Machine for Safety-Critical Applications”; XIX International
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[14]
[15]
[16]
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[18]
[19]
V. BIOGRAPHIES
Christian Laudensack was born in Germany, 1981. He graduated in 2007 at
the Universitaet der Bundeswehr Muenchen, majoring in aerospace
engineering. His employment experience included the German Federal Armed
Force, the IAB GmbH, Ottobrunn Germany, the Systemzentrum für
Luftfahrzeugtechnik, Erding, Germany, and the Institute of Electrical Drives
and Actuators, Universitaet der Bundeswehr Muenchen, Neubiberg, Germany.
His special fields of interest include the design and analyses of switched
reluctance machines.
Yevgen Polonskiy was born in Dnepropetrowsk, Ukraine on March 24, 1982.
He graduated from the technical high school in Konstanz in 2002 and started
studying Electrical Engineering at the University of Applied Sciences,
Konstanz. He completed with M.Eng. in 2008 and worked from 2009 to 2011
as development engineer at Maccon GmbH, Munich, Germany. Since August
2011 he is with Institute of Electrical Drives and Actuators at the Universitaet
der Bundeswehr Muenchen, Neubiberg, Germany. His research interests are
control of switched reluctance drives and power electronics.
Dieter Gerling, born in 1961, got his diploma and Ph.D. degrees in Electrical
Engineering from the Technical University of Aachen, Germany in 1986 and
1992, respectively. From 1986 to 1999, he was with Philips Research
Laboratories in Aachen, Germany as Research Scientist and later as Senior
Scientist. In 1999, Dr. Gerling joined Robert Bosch GmbH in Bühl, Germany
as Director. Since 2001, he is Full Professor and Head of the Institute of
Electrical Drives and Actuators at the Universitaet der Bundeswehr
Muenchen, Neubiberg, Germany.
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Maccon: “User’s Manual for PC-SRD 8.0 – Switched Reluctance
Brushless Motor Design Simulation Software”; Department of
Electronics and Electrical Engineering, University of Glasgow; Maccon,
Munich, Germany; 2002.
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Parameters on the Performance of Switched Reluctance Machines”; XIX
International Conference on Electrical Machines (ICEM); Rome, Italy;
2010.
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switched reluctance machines”; XIV International Conference – System
Modelling and Control (SMC); Lodz, Poland; 2011.
C. Laudensack, Q. Yu, D. Gerling: “Dynamic design tool for canned
switched reluctance machines”; International Aegean Conference on
Electric Machines and Power Electronics & Electromotion Joint
Conference (ACEMP); Istanbul, Turkey; 2011.
Q. Yu, C. Laudensack, D. Gerling: “Improved lumped parameter
thermal model and sensitivity analysis for SR drives”; XIX International
Conference on Electrical Machines (ICEM); Rome, Italy, 2010.
H. Kuchling: “Taschenbuch der Physik”; 17th Edition, Fachbuchverlag
Leipzig; Leipzig, Germany; 2001. ISBN3-446-21760-6 (in German)
G. Dajaku: “Electromagnetic and Thermal Modeling of Highly Utilized
PM Machines“; Ph.D. dissertation, EAA-Forschungsberichte Band 2,
Institute for Electrical Drives and Actuators, Universitaet der
Bundeswehr Muenchen,; Shaker Verlag, Aachen, Germany; 2006.
D. Gerling, H. Hofmann: “Single-Phase Reluctance Actuator and SinglePhase Permanent Magnet Actuator Compared for Low-Cost
Applications”; IEEE International Conference on Electrical Machines
(ICEM); Brügge, Belgiun; 2002.
T.J.E. Miller: “Switched reluctance motors and their control”; 1993.
ISBN 1-881855-02-3
D. Gross, W. Hauger, J. Schröder; W.A. Wall, S. Govindjee:
“Engineering Mechanics 3 Dynamics”; Springer-Verlag; Berlin
Heidelberg, Germany; 2011. ISBN 978-3-642-14018-1
Huntsman: “Glue Araldite 2021”; datasheet, Huntsman Advanced
Materials; Basel, Switzerland; 2004.
Kisling: “Glue ERGO 7214”; datasheet; Kisling AG; Tagelswangen,
Austria; 2004.
3M Company: “3M Scotch-Weld - Low-Odor Acrylic Adhesives”;
datasheet; 3M Industrial Adhesives and Tapes Division; St. Paul, USA;
2011.
Y. Polonskiy, C. Laudensack, D. Gerling: “Effective Switched
Reluctance Drive Train in Unmanned Aerial Vehicles: Torque
Investigations”; (paper in press).