Universitätsverlag der TU Berlin
Elektrische Energietechnik an der TU Berlin Band 9
Rong Dong
Design and comparison of two brushless DC drives for
an electric propulsion system of solar-power unmanned
aerial vehicles
Rong Dong
Design and Comparison of two Brushless DC Drives for an
Electric Propulsion System of Solar-Power Unmanned
Aerial Vehicles
The scientific series Elektrische Energietechnik an der TU Berlin is edited by:
Prof. Dr. Sibylle Dieckerhoff,
Prof. Dr. Julia Kowal,
Prof. Dr. Ronald Plath,
Prof. Dr. Uwe Schäfer
Elektrische Energietechnik an der TU Berlin | 9
Rong Dong
Design and Comparison of two Brushless DC Drives for an
Electric Propulsion System of Solar-Power Unmanned
Aerial Vehicles
Universitätsverlag der TU Berlin
Bibliographic information published by the Deutsche Nationalbibliothek
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Universitätsverlag der TU Berlin, 2020
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E-Mail: [email protected]erlin.de
Zugl.: Berlin, Techn. Univ., Diss., 2019
Gutachter: Prof. Dr.-Ing. Uwe Schäfer
Gutachter: Prof. Dr.-Ing. Sibylle Dieckerhoff
Gutachter: Prof. Dr.-Ing. Sami Hlioui (ENS de Cachan, Frankreich)
Die Arbeit wurde am 08. November 2019 an der Fakultät IV unter
Vorsitz von Prof. Dr.-Ing. Julia Kowal erfolgreich verteidigt.
This work – except for quotes, figures and where otherwise noted – is licensed
under the Creatice Commons Licence CC BY 4.0
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Cover image: Rong Dong | CC BY-SA 4.0
https://creativecommons.org/licenses/by-sa/4.0
Print: docupoint GmbH
Layout/Typesetting: Rong Dong
ISBN 978-3-7983-3126-6 (print)
ISBN 978-3-7983-3127-3 (online)
ISSN 2367-3761 (print)
ISSN 2367-377X (online)
Published online on the institutional repository of the
Technische Universität Berlin:
DOI 10.14279/depositonce-9331
http://dx.doi.org/10.14279/depositonce-9331
ACKNOWLEDGEMENTS
The work of this dissertation was completed during the time I worked at the re-
search institute of Elektrische Antriebstechnik at Technical University of Berlin.
First of all, I would like to thank my doctoral supervisor, Prof. Dr.-Ing. Uwe
Schäfer. He provided me a great opportunity to study the scientific research and
practice work, which not only cultivated my ability to think independently, but
also inspired me to move forward. His experienced advice and guidance are the
prerequisites for my successful completion of the thesis today.
Without the master’s study under the supervision of Prof. Manfeng Dou at the
research institute of permanent rare earth magnetic machine at Northwesten
Polytechnical University, I would never have had the opportunity to contact
this aviation field and continue to carry out the corresponding work.
I especially thank the colleagues who helped me during my work. Mechanical
technician Mr. Jürgen Federspiel assembled the designed motor and helped
me to built up the test bench setup and our laboratory engineer Mr. Arno
Hellemann ordered the materials and components for my project. Special thanks
I would give to the students who worked with me on this project.
Finally, I am grateful to my family with unconditional support and encourage-
ment.
v
ZUSAMMENFASSUNG
Das elektrische Antriebssystem als Kernkomponente von unbemannten Solar
Flugzeugen(UAVs, Unmanned Aerial Vehicles) für Langzeitflüge erfordert eine
hohe Leistungsdichte und robuste Antriebstechnik. Bürstenlose Gleichstrom-
motoren (BLDCM) mit hoher Leistungs- und Drehmomentdichte sowie dafür
angepasste Regelalgorithmen werden daher bevorzugt in UAVs eingesetzt.
Diese Dissertation zielt darauf ab, einen verbesserten BLDCM mit nur 4 einge-
betteten Magnetblöcken zu entwerfen, um 8 Pole zu realisieren im Vergleich
zu der herkömmlichen Struktur mit 8 Magnetblöcken. Das Verhalten beider
BLDCM-Designs wurde analytisch ermittelt und die Motormodelle mit Hilfe
von Finite-Elemente-Software in ANSYS verifiziert. Design und Konstruktion
der Prototypen mit der vorgeschlagenen und der herkömmlichen Magnetstruk-
tur wurden durchgeführt und es wurde ein Prüfstand für einen umfassenden
Leistungsvergleich aufgebaut.
Da die vorgeschlagene Magnetstruktur zu einem Magnetkreis führt, bei dem die
entgegengesetzten Pole keine Spiegelsymmetrie aufweisen, wurden die Längs-
und Querinduktivität durch Finite-Elemente-Modellanalyse und Experimente
absolut und differentiell untersucht. Weiterhin wurden Wirkungsgradkennfelder
erstellt und das thermische Verhalten untersucht, um ein umfassendes Verständ-
nis der beiden Motoren zu erhalten.
Um das sensorbedingte Ausfallrisiko zu eliminieren, wurde eine schnelle analoge
Isolationsschaltung mit hoher Linearität und Stabilität zur Messung der gepul-
sten Spannungen bei 270 V Gleichspannung entwickelt, um eine sensorlose Steue-
rungsstrategie zu realisieren. Die Schaltung verwendet einen linearen Optokop-
pler mit integrierter Rückkopplungsfotodiode, sowie einen PI-Regler mit schnel-
len Operationsverstärkern im Rückkopplungspfad.
Ein 3D-Statormodell wurde erstellt, um die mechanischen Resonanzfrequen-
zen und die mögliche Anregung durch die elektromagnetische Radialkraft zu
analysieren, die zu Vibrationen und Geräuschen bei der vorgeschlagenen und
herkömmlichen Rotorstruktur führt. Es wurde auch eine analytische Modal-
analyse durchgeführt, um die Genauigkeit von FEM-Simulationen und exper-
imentellen Ergebnissen mit dem Impulshammer zu vergleichen und zu vali-
dieren.
vi
ABSTRACT
The electrical propulsion system as the core component of solar-power Un-
manned Aerial Vehicles (UAVs) for long duration flight requires high power
density and stable drive technology. Brushless DC motors (BLDCM) with high
power and torque density and control algorithms suitable for drive system are
given preference for the application in UAVs.
This dissertation is aimed at designing an improved BLDCM using only 4 interior
magnet blocks to realize 8 poles compared to the conventional 8 magnet blocks
structure. The performances of both BLDCM designs have been analytically
determined and the motor models were verified through finite element software
in ANSYS. Design and construction of the demonstrators of BLDCMs with the
proposed and the conventional magnet structure have been carried out and a
test bench for extensive performance comparison has been set up.
Since the proposed magnet structure leads to a particularity of the magnetic
circuit, the behavior of absolute and differential synchronous direct and quadra-
ture inductances have been investigated by finite element model analysis and
experiments. Efficiency maps were generated and thermal characteristics have
been measured to gain a comprehensive understanding of the two motors.
To reduce the uncertainty of sensor control for BLDCM, a high speed, good
linearity analog isolation circuit to measure the voltages of 270 V DC voltage
to realize sensorless control strategy has been designed. The circuit combines a
PI controller with fast operational amplifiers with a built-in linearizing feedback
photodiode loop of a linear optocoupler.
A 3D stator model was built to analyse the mechanical resonance frequencies and
possible excitation by the electromagnetic radial force leading to vibration and
noise for the proposed and conventional rotor structure. Analytical calculation
of natural mode frequencies has also been conducted to compare and validate
the accuracy of FEM simulations and impact hammer testing experimental re-
sults.
vii
Contents
1 Introduction 1
1.1 UAV specification . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Climate-Sailor Mechanical Structure . . . . . . . . . . . . . . . 3
1.3 Operating conditions . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Concept of the electrical propulsion system 5
2.1 Selection of electrical machine . . . . . . . . . . . . . . . . . . . 5
2.2 Converter technology . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Converter technology . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Sensorless technology . . . . . . . . . . . . . . . . . . . . 8
2.3 Mechanical behavior of BLDCM . . . . . . . . . . . . . . . . . . 8
2.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Electromagnetic design of the motor for the propulsion system 10
3.1 Motor specification . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Motor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.1 Slot/Pole selection . . . . . . . . . . . . . . . . . . . . . 11
3.2.2 Selection of interior vs. surface mounted magnets . . . . 11
3.2.3 Design of stator and rotor . . . . . . . . . . . . . . . . . 12
3.2.4 Design of stator teeth . . . . . . . . . . . . . . . . . . . . 13
3.2.5 Design of interior permanent magnetic structure . . . . . 14
3.2.6 Winding design . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.7 Design of the Hall effect sensor circuit . . . . . . . . . . 19
3.2.8 Structure of the motor . . . . . . . . . . . . . . . . . . . 21
3.3 Verification of the design by FEA and test . . . . . . . . . . . . 23
3.3.1 Flux density . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.2 Back-EMF waveform . . . . . . . . . . . . . . . . . . . . 24
3.3.3 Mechanical stress of the bridge . . . . . . . . . . . . . . 26
3.3.4 Inductance study . . . . . . . . . . . . . . . . . . . . . . 27
3.3.5 Demagnetization analysis . . . . . . . . . . . . . . . . . 33
3.4 Summary of the design . . . . . . . . . . . . . . . . . . . . . . . 36
4 Test and verification 37
4.1 Description of the test bench . . . . . . . . . . . . . . . . . . . . 37
4.2 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Cogging torque . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 No load test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.5 Load test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.6 Thermal test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 BLDC motor drive system: inverter and control 54
5.1 Design of voltage source inverter . . . . . . . . . . . . . . . . . . 54
5.1.1 Transistor selection . . . . . . . . . . . . . . . . . . . . . 55
ix
5.1.2 Switching frequency . . . . . . . . . . . . . . . . . . . . 55
5.1.3 Loss analysis . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1.4 Cooling system . . . . . . . . . . . . . . . . . . . . . . . 62
5.1.5 Isolation design of PCB . . . . . . . . . . . . . . . . . . 63
5.2 Sensorless control strategy . . . . . . . . . . . . . . . . . . . . . 64
5.2.1 Concept of the sensorless circuit . . . . . . . . . . . . . . 66
5.2.2 Verification of the sensorless circuit . . . . . . . . . . . . 70
5.2.3 Temperature drift behavior . . . . . . . . . . . . . . . . 72
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6 Analysis of acoustic noise 74
6.1 Electromagnetic source . . . . . . . . . . . . . . . . . . . . . . . 75
6.1.1 Calculation of the electromagnetic force . . . . . . . . . 75
6.1.2 Vibration analysis of the motor . . . . . . . . . . . . . . 79
6.1.3 Acoustic noise performance . . . . . . . . . . . . . . . . 84
6.2 Mechanical source . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.1 Rotor unbalancing . . . . . . . . . . . . . . . . . . . . . 89
6.2.2 Modal analysis . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.3 Resonance frequency measurement . . . . . . . . . . . . 92
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7 Summary and future works 97
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.1.1 Motor performance . . . . . . . . . . . . . . . . . . . . . 97
7.1.2 Acoustic behavior . . . . . . . . . . . . . . . . . . . . . . 98
7.1.3 Sensorless control strategy . . . . . . . . . . . . . . . . . 98
7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Appendices 100
A Abbreviations 100
B Symbols 101
Bibliography 108
x
1 Introduction
An aircraft capable of sustained flight, propelled by a zero emission renewable
energy source, is a very attractive aerial platform. The increasing application
of Unmanned Aerial Vehicles (UAVs) for science and civil purposes includes
monitoring forest fires, border surveillance, weather prediction, etc. [1]. Corre-
sponding research is comprehensively carried on.
In 1954, Daryl Chapin, Calvin Fuller, and Gerald Pearson invented the first
silicon photovoltaic cell [2] which could transfer the sun’s energy to electric
power. Further progress made solar technology usable for propulsion of electric
model airplanes become reality. Solar power driven UAV applications reduce the
need for UAVs returning back to ground for changing batteries or recharging.
The first flight of a solar-powered UAV, called Sunrise I, and an improved
version, Sunrise II, were built and tested on the 4th of November 1974 and 12th
of September 1975, respectively [3].
Short-endurance UAVs fail to accomplish long strategic missions due to their
power source limitations. Although the solar power is used for extension of
flight duration, current flight times are limited by the battery capacity. The
ability of the UAV to fly for an extended period of time has been a challenge
for the aeronautical organizations [4]. Recently, there has been great interest in
the development of advanced long-endurance UAV capable of executing missions
in higher altitude environments resulting in less power consumption and large
amount of solar energy [5]. The main issue in high altitude flight is generating
lift in the low density atmosphere. The majority of vehicles that operate at these
altitudes do so by flying fast [6].
Recent remarkable solar powered long-endurance UAVs are listed as follows:
Sky-Sailor with 3.2 m wing span and 2.4 kg weight is designed to cruise on Mars.
Sky-Sailor has demonstrated the possiblity of continuous flight. It flew nonstop
for 27 hours in June, 2008 [3]. Zephyr has been developed as a high altitude
long endurance platform [1]. On 11th July 2018, Zephyr 8 flew for 25 days, 23
hours and 57 minutes in summer weather conditions, and has also performed
successfully the high altitude pseudo-satellite program. Its wing span is 28 m
and the weight is 53 kg, as shown in Fig. 1.1.
The flight duration of UAV varies widely depending on the aircraft size and
its operation [7]. Due to lower effort for assembly, easier transportation and
reduced requirements for the taking off and landing site, a small solar powered
UAVs structure aiming for longer flight duration will be used as an application
object for this thesis.
1
Fig. 1.1: Mechanical structure of Zephyr [8]
1.1 UAV specification
The current thinking for an aircraft’s renewable energy system is to employ a
photovoltaic array coupled to an electrochemical energy storage system such
as fuel cells or battery. This construction provides the possibility of the long
duration operation mode. The solar-powered UAVs collect and consume solar
energy during the day and store the remaining part for the night flight.
16.24m
8.06m
1.65m
Fig. 1.2: Mechanical structure of Climate-Sailor [9]
The operational environment and mission requirements also have a significant
influence on an UAV’s capabilities. Take an airship as an example, operating the
airship under minimum aerodynamic drag conditions will produce the maximum
performance with the minimum size. For observation missions, the station-
keeping drag is a function of mean wind velocity, airship’s size, weight including
payload, and the air density at working altitude [6].
2
1.2. Climate-Sailor Mechanical Structure
As shown in Fig. 5 from [10], the gradient of the solar radiation increases slowly
above 20 km altitude but the wing span increases dramatically. The required
wing area for solar cells will increase at high altitudes. Moreover, increasing the
operational altitude can lead to a heavier aircraft. Therefore, 20 km is selected
as the working altitude for the UAV in this thesis.
1.2 Climate-Sailor Mechanical Structure
In this thesis, the case study called Climate-Sailor for harvesting weather data
serves as base for fixing requirements. According to the demands of the frequency
of the measurement and monitoring, Climate-Sailor has to proceed with 30 m/s
at 20 km operating height. Climate-Sailor is basically a machine supported glider
with a wingspan of 16.24 m and a wing surface of 14.62 m2. The structure of
Climate-Sailor is shown in Figure 1.2.
1.3 Operating conditions
At a cruising speed of 30m/s, Climate-Sailor works at a height of 20 km and ob-
serves and collects information about meteorological data. It can also be used for
scientific research and civilian applications. Climbing and cruise operation mode
of Climate-Sailor are necessary for working out the demands on the drive. The
first operation mode is climbing which covers the period when Climate-Sailor is
ascending from ground level to cruising height (20 km). In order to overcome the
strong wind in the troposphere, a stable weather period is necessary. Another
solution is to lift the UAV by an air balloon into the stratosphere and then the
UAV starts to work. The problem of peak power demand during climbing mode
after UAV launching and low power requirement while cruising in good weather
conditions is solved through utilization of battery modules. A Maximum Power
Point Tracker (MPPT) keeps tracking the maximum power output of the solar
cells regardless of varying working conditions such as incident solar radiation,
shading and temperature variations.
Compared to fuel-powered aircrafts, a solar-powered aircraft presents a different
design challenge; the surface area used for the photovoltaic arrays is directly
affected by the size and layout of the aircraft. Apart from the power system,
the heart of a renewable energy aircraft is its propulsion system. The design
of the propulsion system has to meet the requirements of the three operational
states during the full running mode which are take off, cruise and high winds
situation. The aircraft spends the majority of its flight time in steady flight
mode, i.e. constant velocity. Thus, the propulsion system should be optimized
at its required operation point for steady flight. The main parameters of the
electrical propulsion system for Climate-Sailor are shown in the following list.
– DC-link voltage: 270 V
– Take off speed: 10 m/s
– Climbing-up speed: 20 m/s
– Cruise altitude: 20 km
3
– Cruise speed: 30 m/s
– Rated output power of the electrical machine: 1.5 kW @ 8000 rpm
The conclusion of [11] certifies that in most case, high voltage DC will definitely
lead to low power loss and can save cable weight in the airplane. Moreover,
270 V can be obtained directly from DC/DC converter connected to a battery
as shown in [12].
High efficiency electrical motors and propellers as well as the availability of
lightweight photovoltaic film cells and components for a 270 V DC power supply
system greatly increases the realizability for constructing a UAV.
4
2 Concept of the electrical
propulsion system
The architecture of a UAV system is presented here as the interaction among
levels of the UAV system, including solar power supply and battery, MPPT and
power management system and electrical propulsion layer, mechanical structure,
high-level decision making and control of flight, user interface, physical and air-
to/from-air/ground communication data-link layers.
The electrical propulsion system in a solar UAV converts electrical power to me-
chanical power for driving a propeller. Components of the electrical propulsion
system include the power supply, motor converter, driving motor, gearbox, and
a propeller. Figure 2.1 depicts the structure of the electrical propulsion system.
The performance of the core parts of the energy system, i.e. the motor control
strategy and the motor itself as shown in the dashed box, are investigated in
this thesis.
Solar cell
Battery
Power
electronic systemMotor Gearbox
Propeller
Communicate host computer
U
DC
T
n
U
VW
Power
Management
System
Max.Power
Tracking
Fig. 2.1: Block diagram of the solar UAV electric propulsion system model
This thesis focuses on the development of electrical machines and power elec-
tronic system in the electrical propulsion system of Climate-Sailor UAV.
2.1 Selection of electrical machine
The efficiency and weight of the propulsion drive motor will directly affect the
size and weight of the aircraft itself, the battery capacity, and the cruise duration.
Therefore it is necessary to select an lightweight and efficient motor. Following
motor types were discussed:
The switched reluctance machine has been addressed as a possible magnet-free
alternative and offers controllable flux and zero-field coasting. Though both
5
the induction motor and switched reluctance motor offer the advantage of more
flexibility of flux control strategy [13], they cannot offer the same absolute ef-
ficiency at maximum torque at the extremities of the speed range [14][15] at
weight optimized design.
Compare to Induction Motor (IM), Permanent Magnet (PM) Motors can achieve
higher efficiency and torque density. Since the squirrel cage in is not needed
for PM motors, there is no rotor losses in IM. However, the current needed
to meet torque requirements will increase which leads to more losses in the
stator[16]. Due to small size, less maintenance and price competitiveness, PM
Motors are now becoming more important for automotive and civil applications.
In general, PM motors outperform conventional DC motors with better speed-
torque characteristics, efficiency, longer operating life, and increased reliability.
The small size reflects high torque-to-mass ratio and high power density which
is extremely important to aircraft markets [17].
In Permanent Magnet Synchronous Motors (PMSM), the magnets in the ro-
tor produce a rotating magnetic field in the stator. For the control system
commonly field oriented control is applied, which is based on a rotor fixed coor-
dinate system. Stator current is separated into direct (Id) and quadrature (Iq)
components. A common control strategy is the maximum-torque-per-ampere
(MTPA) aproach, which includes the case of Id= 0 for machines that have
equal Ldand Lqinductances [18]. PMSM offers good dynamic behaviour and
minimum torque ripple. Therefore, PMSM with its complex control strategy is
primarily applied for accurate servo systems and applications requiring smooth
torque generation, such as robotics or electric vehicle drives [19].
The common strategy of controlling BLDCM has two active phases during one
commutation period which is 60◦wide (electrical angle). Back electromotive
force (back EMF) is directly proportional to the motor speed and the developed
torque is almost directly proportional to the phase current, so BLDCM have
good speed regulation performance at low computational effort. Apparently, a
BLDCM is the best choice for the electric propulsion system.
The Surface Mounted non-salient Permanent-magnet configuration (SMP) has
been studied extensively due to its simple control strategy reasoned in equal
inductances along both d and q axes [20]. However, this structure will commonly
lead to larger air gaps. Further, the existence of a bandage fixing the surface
magnets increases the complexity of the mechanical processing [21]. Currently,
Interior Permanent Magnet configurations (IPM) feature high torque density
and easier manufacturing and have gradually gained recognition [22]. In [23],
one obvious benefit of utilizing an IPM rotor is that the magnets are located
inside the rotor and thus the permanent magnet eddy current losses may be
remarkably reduced as the flux pulsations attenuate before penetrating into the
magnet material. The usual structures of SMP and IPM motors with single
tooth windings are shown in Fig. 2.2.
IPM was selected in this thesis and a new IPM rotor structure with a different
arrangement of the magnetic field and reduced number of magnet blocks was
proposed. The comparison of the conventional structure and the proposed one
will be analyzed in the 3rd chapter.
6
2.2. Converter technology
N
S
(a) SMP rotor
N
S
(b) IPM rotor
Fig. 2.2: Structure of BLDC motors
2.2 Converter technology
2.2.1 Converter technology
A BLDC motor is using the electronic commutation instead of commutator and
brushes in conventional DC machines. The electronic control device will process
the feedback information of the rotor position and generate control signals for
the power electronic switches. This eliminates failures caused by the brush as
well as reduces maintenance cost.
Q1
D1
C
UDC
v
Q3
D3
Q5
D5
Q4
D4
Q6
D6
Q2
D2
U
WV
UL
L1
L2
L3
Fig. 2.3: Three phase converter topology
Compared with PMSM, a BLDC motor only requires a rotor position sensor
or device to indicate the rotor position at the commutation points to drive the
electronics while its starting and operating. In one 360◦electrical period, a
BLDC motor has 6 commutation states that last for 60◦electrical each. Hence,
the power devices are commutated sequentially every 60◦.
Considering the cost of power-electronics converters and the requirement for
the control strategy, the topology of 2-level 3-phase converter is used for this
thesis. The structure is shown in Fig. 2.3. The voltage source topology requires
a symmetric Pulse Width Modulation (PWM) scheme for switching control.
7
The turn-on and turn-off sequence is controlled through the gate signals of the
semiconductors and generated by a micro-controller stage. Through 3 phase
bridge semiconductor, DC power supply is transferred into AC current signals
flowing in the coils.
2.2.2 Sensorless technology
For the solar UVA, the environmental conditions comprise rapid change of tem-
perature, illumination intensity, wind force, and other uncertainties. To improve
drive system stability, a sensorless control strategy based on the EMF in the dis-
connected coil is applied.
In order to sample the 3 phase voltages and DC voltage and transmit these
signals to the micro-controller, an isolation circuit has to be applied. Galvanic
isolation circuits are widely used in traditional industry, home appliance, solar
renewable system, etc. Common methods are transformer, capacitive coupling
and optical coupling. However, transformer and capacitive coupling are only
applicable in AC circuits [24].
A commonly used isolation amplifier is the ISO122 to realize an analog trans-
mission. This kind of the components has excellent offset, gain, accuracy and
stability over time and temperature, but the bandwidth around 50 kHz can not
meet the speed requirement in the present application. On the other hand,
using a high stability isolated error amplifier ADUM3190 with faster transient
response, renders a low accuracy of linearity.
In the thesis, a high speed, good-linearity analog isolation circuit to sample the
voltages of a 270 V Brushless DC Motor to realize sensorless control strategy is
proposed. The proposed linear optocoupler consists of a Light-Emitting Diode
(LED) and photodiodes. [25] [26] describe the application of this analog isola-
tion circuit with good linearity. In [27] [28], the application of a feedback signal
controlling the optical flux is used to improve linearity. For increased voltage iso-
lation requirements, optocouplers with closed loop optical transmission ssytem
have been applied [27].
A fast response time of the circuit is necessary to obtain the position infor-
mation from voltages with PWM. Good linearity ensures the accuracy of the
voltage signals. The key concept is to combine a PI controller with fast oper-
ational amplifiers to the built-in linearizing feedback photodiode loop of linear
optocoupler.
2.3 Mechanical behavior of BLDCM
The mechanical behavior of electric machine has a greater impact on the avi-
ation application field. The vibration of the motor could lead to its structure
damage and failure. Comparing with traditional application, aircraft applica-
tion deserves closer attention. The vibration and noise of BLDCM with two
different IPM rotor structures caused by electromagnetic force are analyzed. An
analytical method was also applied and the results of modal analysis were ex-
perimentally verified to provide the hints of inherent characteristics of motor
stator.
8
2.4. Outline
2.4 Outline
Chapter 3 presents the design procedure of two BLDCM for electric propulsion
system applications.
Chapter 4 presents the comparison of simulated results and experiments of the
performance of the conventional and proposed structure BLDCMs.
Chapter 5 introduces the electrical converter for two BLDCM including the
proposed sensorless control strategy and the losses consumption of main elec-
tronics.
Chapter 6 mainly analyzes the acoustic behavior of BLDCM and modal analysis
of the stator.
9
3 Electromagnetic design of the
motor for the propulsion system
The main advantage of a BLDCM electric drive system is the high efficiency
reducing the weight of the power supply system and therefore increasing the
payload capacity of the UAV. A new structure for an IPM rotor is proposed.
Both conventional and proposed machines use the same stator, but the rotors
have two different IPM structures with the same rotor external diameter and
shaft diameter. Compared to the conventional IPM motor, the magnetic and
mechanical characteristics of the proposed IPM structure will be analyzed.
3.1 Motor specification
Based on the aircraft operation condition, both electrical and mechanical pa-
rameters should meet the following requirements:
– 270 V DC Link voltage
– Rated torque 1.8 Nm
– Rated speed 8,000 RPM
– Max. stator diameter 110 mm
– Max. motor length 120 mm
– Air cooling
– Winding isolation class H 180◦C (for lab test, in case of motor failure)
3.2 Motor design
A manual design process of the motor was executed first, then the results
were simulated in SPEED anaytical software and optimized and verified in
MAXWELL Finite Element Analysis (FEA) software.
10
3.2. Motor design
3.2.1 Slot/Pole selection
In order to meet the low mass requirement, a rather high pole number motor
is considered. However, the pole number is limited by a compromise between
reduced mass and increased iron loss for large pole numbers [29]. Considering
the complex manufacturing of high number of slots and its winding pitch of 120
degree electric angle and the fundamental winding factor kNm = 0.866 [30] [31],
the popular combination of 12 slots and 8 poles was selected.
The concentrated winding can be applied in the above configuration. Since short
end-windings inherently result in low copper losses and fractional slot windings
have low cogging torque than the integer slot motor with same slot/pole [32],
single tooth winding configuration was used. A three phase BLDCM was chosen
in this application due to reliability of the control algorithm and the cost of the
power electronics [33].
3.2.2 Selection of interior vs. surface mounted magnets
Surface-mounted permanent magnets and interior permanent magnets for the
rotor structure are investigated. The SPM structure is often used for the com-
mon control strategy of 2 simultaneously conducting phases and 6 commutation
states [34].
As shown in Fig. 3.1, FEM simulated back EMF waveform with similar RMS
values at 9,000 rpm are compared. Both, SPM and IPM motors use a conven-
tional magnet structure with 8 magnet blocks and 8 poles. It is verified that
the SPM structure has a more trapezoidal back EMF waveform. As it is stated
above, the SPM structure will bring more difficulties to mount the magnets sym-
metrically and tightly on the rotor surface. This increases the width of the air
gap and decreases the utilization of the permanent magnet.
0 40 80 120 160 200 240 280 320 360
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
180
elec. angle [°]
back EMF [V]
8−8IPM
8−8SPM
Fig. 3.1: FEM based comparison of back EMF waveforms with interior and surface-mounted
permanent magnets
Different from SPM, Ldis usually smaller than Lqin an IPM motor. During
phase advanced control, the average value of Idduring one 60◦(electrical) period
becomes negative, leading to an overall increase of the torque at a given current,
11
taking into account the negative difference of the inductance in equation (3.1)
for sinusoidal currents. Considering the simplified mechanical installation and
the higher torque produced by IPM structure during phase advanced control,
interior permanent magnet structure is adopted [35].
Tem =3
2p·[ψfiq+ (Ld−Lq)idiq] (3.1)
where Tem is the electromagnetic torque, pis the number of pole pairs, Idand
Iqare the respective stator current components in d-axis and q-axis direction,
Ldand Lqare the respective inductances, and ψfis the synthetic flux linkage in
the air gap.
3.2.3 Design of stator and rotor
Due to the limitation of the installation position and space in the solar aircraft,
the frame dimension of the motor is fixed. The preliminary selection of frame
size automatically fixes the outer diameter of the stator. The inner diameter of
the stator depends on the air gap and rotor diameter. Equation 3.2 shows the
analytical method to calculate the diameter of the rotor [36].
D′
i=3
⌜
⎷
P′
π2αi2
3A′
s
ˆB′
δλnN
(3.2)
where,
αi: pole arc coefficients
A′
s
ˆ: peek value of current loading (A/m)
B′
δ: flux density in the air gap (T)
D′
i: the rotor diameter
λ: the ratio of motor length Lstk and rotor diameter D′
i
P′: rated power/motor efficiency
nN: rated speed
In the equation, the size of the motor depends on A′
sand B′
δ. By increasing the
value of A′
sand B′
δ, the motor size can be reduced.
For PM motors, an important parameter for the B′
δvalue is the characteristic
of the magnetic material itself, e.g. NdFeB has typically a residual flux density
of 1.2 – 1.3 T at 20◦C and Ferrite magnets have smaller flux densities of 0.2 –
0.4 T. In order to obtain a larger flux density in the air gap, NdFeB is selected
but the cost will increase. However, higher B′
δwill increase the saturation in
the stator and rotor core, specially in the teeth area. Since the iron losses are
approximately proportional to the square of the flux density, a higher B′
δwill
lead to a temperature rise of the motor.
12
3.2. Motor design
The current loading A′
s
ˆis defined as in equation 3.3:
A′
s
ˆ=NcZI
ˆ
πD′
i
(3.3)
where
Nc: the number of turns per slot
Z: the number of slots
I
ˆ: peak value of the phase current.
The current loading describes the number of winding conductors along the rotor
circle. Higher A′
svalues will lead to a higher risk of irreversible demagnetization
of the rotor’s magnets resulting in deterioration of the working characteristics
of the motor. If the current density of the winding is kept constant, a higher A′
s
leads to an increase of the number of the wires in the slot resulting in increasing
copper consumption, copper loss and temperature rise. If the dimension of the
tooth width is constant, a higher B′
δwill lead to high tooth flex density B′
T. Since
the frequency of the motor is rather high, maximizing B′
δis not recommendable.
The winding insulation class H is selected, so higher A′
sis allowed to keep the
motor size small. Moreover based on the magnetic characteristic of NdFeB
magnet material, the values are chosen as follows:
A′
s
ˆ= 36 A/mm
B′
δ= 0.6T
Considering the cost, silicon-iron M270-35A was selected as the lamination ma-
terial of the stator and rotor [37]. The mechanical values of the stator and rotor
parameters are shown in Tab. 3.1.
Tab. 3.1: Dimensions of the stator and rotor design
stator radius air gap rotor radius motor length tooth width
RsδRLstk Tw
45 mm 0.5 mm 30 mm 59.85 mm 5.6 mm
3.2.4 Design of stator teeth
Theoretically the working point should be assumed to be operating at a flux
density above the knee value obtained from the B-H characteristics of the mag-
net. Considering the size and width of flux path, the values of the flux density
located in different parts of the stator are certainly different. It is obvious that
the greater flux density happens at the stator teeth and rotor bridge area. The
structure of the slots in the stator is shown in Fig. 3.2.
13
SO
SOAng
Tw
filSB filSO
TGD SD
RRs
Fig. 3.2: Stator dimensions
3.2.5 Design of interior permanent magnetic structure
In this part, the proposed magnet arrangement will be introduced. Both BLD-
CMs use the same stator, but the two rotors have different IPM structures with
the same rotor external diameter and shaft diameter. The conventional rotor
utilizes 8 magnet blocks for 8 poles and will be denoted ’8-8’ throughout this
document. In the proposed IPM structure, there are only 4 magnet blocks for 8
poles and therefore it will be referred to by ’4-8’. To achieve this behavior, the
magnetization direction ”South pole” of all magnets in the proposed structure
point to the rotor center. The aforementioned preliminary analysis results of
the two rotor structures are shown in Fig. 3.3.
3.2.5.1 Determination of magnet dimension
Compared to ferrite magnets, the rare earth magnets such as Samarium-Cobalt
(SmCo5) and NdFeB feature much higher specific energy. Vacodym 655 HR
NdFeB is selected due to its high specific energy and high temperature resistance
capability, and for economic reasons. The parameters of 655 HR NdFeB are
shown in Table 3.2.
Tab. 3.2: Parameters of magnet material Vacodym 655 HR
Remanence Coercitivity Temperature coefficient T K(Br)
BrHCB 20 −100◦C 20 −150◦C
1.28 T 990 kA/m −0.090 %/◦C−0.100 %/◦C
In order to compare the performance of the two motors, both shall generate the
same RMS value of the back EMF voltage in the stator winding. Since there is
14
3.2. Motor design
Ri
RsH
LM
Wmag
NotchAng
Wslot
Bridge
S
SS
S
(a) Proposed ’4-8’-rotor structure with 4 magnet blocks and
8 poles
Ri
RsH
LM
Wmag
NotchAng
Wslot
Bridge
(b) Reference ’8-8’-rotor structure with 8 magnet blocks and
8 poles
Fig. 3.3: Comparison of the two rotor geometries
15
only one magnet block per pole pair in the magnetic circuit of the proposed mag-
net structure, the magnet thickness increases to 2 times of the magnet thickness
of the conventional structure. From Tab. 3.3 can be seen, that the simple con-
struction with 4 magnets only leads to an increase of magnet volume by 11.4 %.
From the mechanical point of view, the proposed rotor structure has a simpler
installation procedure.
Tab. 3.3: Dimension of magnet design
magnet blocks pole pairs LM W_mag magnet length bridge
4 4 8 mm 19.5 mm 59.85 mm 1.2 mm
8 4 4 mm 17.5 mm 59.85 mm 1.0 mm
3.2.5.2 Demagnetization behavior
Irreversible demagnetization of permanent magnets has to be avoided. It is
ususally caused by armature overcurrent, excessive temperature or unexpected
operation conditions. When irreversible demagnetization occurs, the flux den-
sity of PM is permanently degraded. Output power and torque may not satisfy
the operation condition and can lead to serious problems [38]. Two reasons of ir-
reversible demagnetization are increases in temperature or armature reaction.
Many researchers investigate the influence of the internal characteristics of PM
synchronous motors on irreversible demagnetization. The main reason for irre-
versible demagnetization is an over current due to short circuit, locked state of
the motor, over load, or winding short fault [39].
Large short current caused by inverter faults, is one of the most common reason
for the demagnetization. If this situation is caused by the hardware failure, the
damage of the system is irreversible. The aircraft can not work back to the state
of cruise and will drop down. The software failure will produce large short circuit
current which will lead to irreversible demagnetization. Therefore, in this case
the short circuit situations are limited by the protection strategy of the power
electronics system. The other fault of the drive system, which causes air crash,
is a three phase short circuit.
The most challenging operation point occurs when the motor runs at overload
situation. Since the motor has to continue to cruise even when overload situation
occurs, the effect of demagnetization under overload situation will be analyzed
by FEA in section 3.3.5.
3.2.5.3 Bridge design
The bridge is the mechanical weak point in the rotor part due to interior per-
manent magnet structure. The thickness of the bridge determines the behavior
of the leakage flux, thus the magnetic performance is strongly affected [40]. A
thicker bridge will result in better ability to stand the centrifugal force which is
proportional to the square of the rotating speed, depicted in equation 3.4. At the
16
3.2. Motor design
B_w48
(a) 4 magnet blocks
B_w88
(b) 8 magnet blocks
Fig. 3.4: Bridge structure in the rotor
same time a thicker bridge will lead to an inferior electromagnetic characteristic
due to an increased leakage flux.
Fcen =mv2
r(3.4)
where Fcen is centrifugal force, mis mass, vis rotating speed and ris the radius
of the rotating mass. The maximum centrifugal force occurs at 120 % of the
highest speed in the application.
Different types of bridges have been studied recently, e.g. H-bar, dual bridge or
V-shape IPM [41] [42]. Although the dual bridge has less leakage flux, this type
increases the machining difficulty. In this thesis the simple I-bar bridges were
used for both rotors. The structures are shown in Fig. 3.4. It is very common
to arrange holes or cut-outs in the rotor yoke and in proximity to the bars, e.g.
in V-shape magnet arrangements, to increase the stiffness of the rotor core and
optimize flux leakage. Considering the rotor diameter and the available space
around the bridge in the design, holes or cut-outs are neglected for this thesis.
In the PM rotor, the centrifugal forces are generated in the radial direction
and the electromagnetic forces are dominantly also in the radial direction of the
rotor. But the attraction forces due to the permanent magnets have opposite
direction against these two forces, which are vertical to the boundary of the
magnets. Based on the different interaction forces, the FEA analysis of the
mechanical stress distributed on the different rotor structures will be presented
in the following section 3.3.3.
3.2.6 Winding design
The fractional slot winding with a non overlapping concentrated winding was
chosen due to its short endwindings and high efficiency [43] [44]. In this thesis
a 3 phase motor with single tooth winding is used. Fig. 3.5 shows the EMF
vector diagram of the slots which are 120◦apart from each other. Fig. 3.6
17
shows mechanical connection of coil sides for the 3 phases. The numbers (first
layer) and the number with apostrophe (′) (second layer) denoted at each phase
represent the slots to be used for the corresponding phase.
Slot No.
1,4,7,10
120°
Slot No.
2,5,8,11
Slot No.
3,6,9,12
240°
Fig. 3.5: Star of slots
The details about the harmonic orders in the stator’s MagnetoMotive Force
(MMF) are shown in Fig. 3.7. 4th order is equal to the numbers of pole pairs
and is the fundamental waveform. MMF has 2th,4th,5th,7th,8th,10th,and 11th
harmonics component.
1 1' 2 2' 3 3' 4 4' 5 5' 6 6' 7 7' 8 8' 9 9' 10 10' 11 11' 12 12'
W- U+ V+ W+ U- V-
Fig. 3.6: Winding layout
0
1
2
3
4
5
6
7
8
9
10
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
MMF Amplittude
Harmonic order
Fig. 3.7: Spatial harmonics due to winding distribution referred to rotational speed
A slot fill factor of 35 % is considered to allow for the winding’s mechanical
processing. For the rated electric current density JNa rather high value was
18
3.2. Motor design
chosen, considering forced air cooling. This high value is necessary to satisfy the
demanded small size of the motor.
JN= 13.5 A/mm2(3.5)
3.2.7 Design of the Hall effect sensor circuit
The method of rotor position detection of BLDCM to control the inverter tran-
sistors can be classified into two categories. One method is using Hall effect
sensors [45] [46] [38]. The other one is the sensorless approach which is com-
monly using the back - EMF zero - crossing method [47] [48] [49]. Considering
the dynamic states, especially start - up, and the simplicity of the implemen-
tation, Hall effect sensors were included in the design and the corresponding
method was used to verify the design of the motor. The isolation circuit for the
sensorless control strategy will be investigated in section 5.2.
3.2.7.1 Principle of commutation
The commutation signals for BLDCM are only required every 60◦electric angle.
Encoders can provide more precise position information for sinusoidal control
but come at a higher price. For the implemented 6 commutation state control
method encoders are not necessary. Therefore a Hall effect sensor circuit was
chosen for position sensing.
Two different Hall effect sensor circuit options will be described here. In order to
save the cost of additional magnets and the compactness of the motor structure,
one method is to sense the magnetic field of the rotor directly by the Hall effect
sensors. However, due to the armature effect, the distortion of the magnetic
field could reduce the accuracy of output signals of Hall sensors. On the other
hand, insufficient space between the stator stack and end-plate of the housing
limit the feasibility of this approach. As an alternative, an external magnet disc
was mounted to the shaft. For a correct angular placement of the individual
Hall effect sensors, a corresponding PCB has been designed.
3.2.7.2 Distribution of Hall effect sensors for fractional slot armature
windings
The output signals of 3 Hall effect sensors H1, H2 and H3 are used to indi-
cate which of the motor’s phases to use for generating torque in the current
rotor position. Thus, a change in one of the signals can be used to trigger the
commutation from one phase to the next by selecting a different set of active
transistors. The number and allocation of the Hall sensors should satisfy this
demand. According to equation 3.6, using p= 4 pole pairs, the mechanical angle
θmbetween each of the phases in the symmetric 3 phase system is 30◦, thus three
Hall sensors are selected and located at 30◦mechanical angle from each other.
θm=θe
p(3.6)
19
U
U’
W’
W
V’
V
H1
H2
H3
aliged with 1st slot
aliged with 2nd slotaliged with 3rd slot
=120°
e
u-axis
v-axis
w-axis
Fig. 3.8: Location of Hall sensors corresponding to stator slot
Where θeis the electric angle. The three Hall sensors are displaced by a mechani-
cal angle of 30◦from each other and are aligned to the center line of corresponding
slots, as shown in Fig. 3.9.
As it is shown in Fig. 3.9, the magnet ring plate should provide magnetic
fields which are perpendicular to the surface of the Hall sensors. The 4 North
and 4 South poles of the Ferrite magnets are arranged alternately to produce
an 8 - pole alternating perpendicular magnetic field around the circumference of
the magnetic ring. For the mechanical construction an iron plate for magnets
installation was used. Then 8 precut parts of rubber compound ferrite magnets
were glued into this groove. The iron plate also provides the return path for the
magnetic flux.
N
S
S
S
S
N
N
N
n
H2
Rotor shaft
H1
H3
30°
30°
Iron plate
Fig. 3.9: Mechanical installation location of Hall sensors and exciting magnetic field
The sensor’s output will become ’high’, when a North pole of sufficient strength
is placed above the sensor. Correspondingly a South pole will lead to a ’low’
output. From Hall sensor data sheet, the rise time and fall time of output
signals is 400 ns [50]. When the motor runs at 9000 rpm, the delayed electric
20
3.2. Motor design
angle caused by the these times is 0.0864◦. By rotating the magnet plate with
motor shaft, the combination of Hall signals will indicate the position of the
rotor from 0◦to 360◦electric angle in steps of 60◦. The output signals of the 3
Hall sensors according to the rotor position are shown in Fig. 3.10.
Hall sensor output voltage
[V]
5
180°120° 240° 300°
elec. angle [°]
60°0 360°
Hall sensor 1
Hall sensor 2
Hall sensor 3
0
0
5
5
001 011 010 110 100 101
Fig. 3.10: Output signals of Hall sensors for one electrical period
Rotor cap
Fixed bearing
Floating
bearing
Steel disc
Hall sensor PCB
Hall sensors
Hall sensor magnets
Steel seat for
Hall magnets
Rotor stack
Stator stack
Rotor cap
Aluminum ring
Housing
Fig. 3.11: Motor structure in cross sectional view
3.2.8 Structure of the motor
The cross section of the designed BLDCM is shown in Fig. 3.11. It contains
most mechanical parts of the motor which are stator and rotor stacks, shaft, two
bearings and the Hall sensor assembly for position sensing.
21
(a) 4 magnet blocks
(b) 8 magnet blocks
(c) material
Fig. 3.12: Geometry of the 2 motors for FEM analysis
(a) 4 magnet blocks (b) 8 magnet blocks
Fig. 3.13: Distribution of magnetic flux density(at 0◦elec. angle)
22
3.3. Verification of the design by FEA and test
3.3 Verification of the design by FEA and test
Once all the parameters have been determined, the motor has to be verified
by FEM analysis. This section presents the result of FEM analysis for the
basic parameters of the two BLDCMs. Particular attention was paid on the
comparison of the two motors’ performances; the influence of different factors
on the parameters were also analyzed.
The 2D machine geometry was built up and imported into FEA software and
all energetically active parts of the machines were assigned with the specific
material properties, as shown in Fig. 3.12.
3.3.1 Flux density
Fig. 3.13 shows the results of the static no-load magnetic field simulation of the
two motors. For the proposed 4-8 IPM structure, the rotor also produces 8 poles
as does the reference 8-8 design.
A comparison of the air-gap flux densities Bδ, calculated by SPEED and FEM
software, will be shown first to undermine the necessity for FEM calculations.
In Fig. 3.14, the distribution of |Bδ|along the air-gap is shown for one electrical
period. The calculation was performed in SPEED software based on analytical
formulae and in FEM software for the proposed 4-8 BLDCM with 4 magnet
blocks. It is obvious that the motor design software SPEED 9.1 using quasi
analytical calculations is not able to predict flux densities accurately. Therefore
simulated values to verify the design have been calculated by FEM software in
this thesis.
0 40 80 120 160 200 240 280 320 360
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
elec. angle [°]
flux density |B δ | [T]
4−8FEM
4−8SPEED
Fig. 3.14: Comparison of the absolute air-gap flux density |Bδ|, calculated by FEM and
SPEED software for the 4-8 BLDCM
After the dimensions of the motor were imported and the material properties
were assigned, static analysis was conducted in ANSYS. In Fig. 3.15 the distri-
bution of the absolute air-gap flux density |Bδ|is shown for the proposed and
the reference design.
23
0 40 80 120 160 200 240 280 320 360
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
elec. angle [°]
flux density |B δ | [T]
4 magnet blocks
8 magnet blocks
Fig. 3.15: Comparison of the absolute air-gap flux density |Bδ|, calculated by FEM software
for the proposed 4-8 and the reference 8-8 BLDCM
The average flux density in the air gap is 0.558 T and 0.533 T for BLDCM with
4 magnet blocks and 8 magnet blocks, respectively.
3.3.2 Back-EMF waveform
Both rotors are designed to induce the same RMS values of the back-EMF
voltage in order to make the performance of two motors comparable. The other
important consideration is to reduce the 2nd harmonics order for the proposed
motor structure. The simulated back-EMF waveforms at a speed of n= 9000 rpm
are shown in Fig. 3.16. Obviously, the two rotors have a similar back EMF
voltage form.
0 40 80 120 160 200 240 280 320 360
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
180
elec. angle [°]
back EMF [V]
4−8_simulated
8−8_simulated
Fig. 3.16: Simulated back-EMF at 9000 rpm
24
3.3. Verification of the design by FEA and test
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
80
100
120
140
f/ff
voltage amplitude [V]
4−8magnet blcoks
(a) 4 magnet blocks
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
80
100
120
140
f/ff
voltage amplitude [V]
8−8magnet blcoks
(b) 8 magnet blocks
Fig. 3.17: EMF harmonics at 9000 rpm
0 40 80 120 160 200 240 280 320 360
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
180
elec. angle [°]
back EMF [V]
4−8_simulated
4−8_measured
(a) 4 magnet blocks
0 40 80 120 160 200 240 280 320 360
−180
−150
−120
−90
−60
−30
0
30
60
90
120
150
180
elec. angle [°]
back EMF [V]
8−8_simulated
8−8_measured
(b) 8 magnet blocks
Fig. 3.18: Comparison of back-EMF voltage, simulated and measured waveform
Through FFT data processing, the harmonic orders contained in the back-EMF
waveform were calculated and are shown in Fig. 3.17. Both structures develop
a5th harmonic, but for the 8-8 design it is considerably higher. For the 4-8
BLDCM the 7th order harmonic is almost invisible but a 7th order harmonic is
introduced.
The experimental back-EMF waveforms of both IPM machines correspond well
to the simulation results shown in Fig. 3.18. According to Table 3.4, the mea-
sured RMS values of the back-EMF voltage for both structures are larger than
the simulated values: 1.4 % increase for the 4 magnet blocks design and 3.7 %
increase for the 8 magnet blocks design. This is assumed to be mainly due to the
different operating temperature of the magnets. In FEM simulation, the mag-
net temperature was set to 120◦C. However, during the experimental test, the
magnet temperature must be assumed to be close to the ambient temperature.
25
Tab. 3.4: Comparison of back-EMF voltage values for simulated and measured values
4 magnet blocks 8 magnet blocks
FEM simulated value 115.0 VRMS 115.4 VRMS
Experimental value 116.6 VRMS 119.9 VRMS
3.3.3 Mechanical stress of the bridge
The mechanical stress inside the two rotors, especially around the bridge parts,
was analyzed in FEM. In order to ensure that the magnets can be properly
inserted to the magnet slot in the rotor, a dimensional tolerance between per-
manent magnet and rotor core of 0.1 mm is reserved. Commonly, this space is
filled with industrial adhesive to increase the solidity between the magnet and
the rotor core. With time elapsing, the bonding strength could become weaker
though.
Many publications only studied the mechanical characteristic of a 2D rotor
model. It is common that the effect of shaft dynamical forces is neglected [51].
For this thesis 3D rotor models with shaft mechanical characteristics were set
up. Mechanical transient analysis was carried out in ANSYS Workbench. Two
boundary conditions were applied as follows: transient rotation velocity; cylin-
drical support for two bearings.
Since the centrifugal force is depending on speed, the maximum value of stress
occurs at the speed of 10800 rpm corresponding to the usual overspeed calcula-
tion of 120 % idle speed 9000 rpm. Fig. 3.19 and Fig. 3.20 show the simulated
mechanical stress distribution from the FEM analysis. In both rotor structures,
mechanical stress is concentrated on the corner around the bridge. The maxi-
mum values are 56.47 MPa and 66.66 Mpa for conventional and proposed rotor,
respectively.
Therefore, maximum stress in the bridge is much lower than the yield strength
(450 Mpa) of the rotor core material. From these numbers it can be seen that
the bridge design has enough allowance.
26
3.3. Verification of the design by FEA and test
Equivalent Stress (MPa)
66.66Max
38.31
22.02
12.66
7.27
4.18
2.40
1.38
0.79
0.46
0.26
0.15
0.086
0.028 Min
Fig. 3.19: Equivalent stress of rotor with 4 magnet blocks at 10800 rpm
Equivalent Stress (MPa)
56.47Max
33.34
19.68
11.62
6.86
4.05
2.39
1.41
0.83
0.49
0.29
0.17
0.05
0.035 Min
Fig. 3.20: Equivalent stress of rotor with 8 magnet blocks at 10800 rpm
3.3.4 Inductance study
The analysis of the inductance characteristics for the two motors is important
and necessary for the investigation of the control strategy. Several inductance
studies based on different rotor structures were analyzed, such as flat-shaped
IPM, V-shaped IPM [52] and U-shaped IPM [53].
27
3.3.4.1 Influence of rotor position on inductance
An AC inductance test at rated frequency is widely used for determination of
the inductance [54] [55] [56]. In order to realize this method, the rotor shaft is
locked to eliminate back EMF content and V and W phase armature windings
were connected in parallel and linked to the U winding in series. Through
above method, an inductance L can be derived from the voltage equation of the
BLDCM, as follows in equation (3.7):
L=2
3
√︃(︂U1
I)︂2−R2
2πf (3.7)
where U1and Iare RMS values of injected voltage and current, respectively.
Ris the total resistance of the windings in this connection. fis the frequency
of the injected voltage. The inductance Lcan be thought to be the stator-side
inductance of one phase, but taking the mutual inductances into account.
Fig. 3.21 shows the principle circuit connection of the AC standstill test. An
AC current is selected in relation to the rated current. This current is injected
at a fixed frequency and the voltage is measured. To measure the inductance
at different rotor angles, the locked rotor position can be varied by an indexing
head in steps of 1◦mechanical angle.
AC Voltage
Source
IPM machine
Rotor Positionθ
iu
iv
iw
1u
i
U
W
V
Fig. 3.21: Schematic diagram for inductance measurement
The test was done by applying the circuit setup as in Fig. 3.21. By changing
the position of the locked rotor, the inductance was calculated for each rotor
position. The AC-current of 2 ARMS is about 44 % of the rated current. It was
injected at rated frequency of 533 Hz.
Fig. 3.22 depicts the variation of the absolute inductance during one mechanical
revolution in the experiment. The inductance of the conventional IPM machine
has 45◦mechanical symmetry, as shown in Fig. 3.22(b). The maximum induc-
tances occur in the q-axis. Analogously, the minimum values correspond to the
28
3.3. Verification of the design by FEA and test
0 40 80 120 160 200 240 280 320 360
0.6
0.8
1
1.2
1.4
1.6
1.8
elec angle [dregee]
Inductance [mH]
(a) 4 magnet blocks
0 40 80 120 160 200 240 280 320 360
0.6
0.8
1
1.2
1.4
1.6
1.8
elec angle [dregee]
Inductance [mH]
(b) 8 magnet blocks
Fig. 3.22: Measured inductance with rotor position
d positions. For the conventional IPM machine, Ldand Lqare equal for all
poles.
The proposed IPM machine with 4 magnet blocks shows a 90◦mechanical sym-
metry as in Fig. 3.22(a). The q inductances is still equal for all poles, but in the
d axis 2 different values occur depending on the rotor position. The lower Ld
corresponds to a position, where the magnets are aligned with the stator teeth.
The higher Ldvalue occurs when the axes of the magnets are aligned with the
slot instead.
The value of the inductance is influenced by the current magnitude which flows
through the coils. In order to study the effect factors on the d and q inductance,
the following analysis was conducted.
3.3.4.2 Effect of the saturation on Ldand Lq
The voltage equation of the motor can be expressed as in equation (3.8). In
this equation, Ldepends on the rotor position. To remove this dependency,
unsymmetrical machines are best described in a rotor oriented dq-coordinate
system. The accuracy of Ldand Lqwill further affect control precision. The
voltage equations in the dq-coordinate system for a PM rotor with a locked
rotor are given in equation (3.9).
u =i
R+Ldi
dt +dψ
R
dt (3.8)
Where u is the phase voltage, i
is the phase current, and ψ
Ris the flux linkage
of the rotor.
ud=idR−ωLdiq
uq=iqR+ωLdid+ωψ (3.9)
29
AC Current Source
DC Current Source
BLDCM
u
i
v
i
w
i
AC
i
DC
i
(a) Lqmeasurement at aligned q-axis
AC Current Source
DC Current Source
BLDCM
DC
i
AC
i
u
i
v
i
w
i
(b) Ldmeasurement at aligned d-axis
Fig. 3.23: d and q inductance test setup
Where udand uqis the synchronous direct and quadrature voltage, respectively.
idand iqis the synchronous direct and quadrature current, respectively. Ldand
Lqis d- and q-inductance, respectively.
As the d and q voltage in equation (3.9) shows, the d-inductance can be easily
calculated when the q-axis current is 0, and therefore the voltage Uqalso becomes
0.
Ld=2
3
√︃(︂U1
I)︂2−R2
2πf
\︄\︄\︄\︄\︄\︄\︄\︄d-axis || phase U-axis
(3.10)
Likewise, the q-inductance can be calculated when the d-axis current becomes
0.
Lq=2
3
√︃(︂U1
I)︂2−R2
2πf
\︄\︄\︄\︄\︄\︄\︄\︄q-axis || phase U-axis
(3.11)
where U1is the RMS value of the AC voltage and Iis the RMS value of the AC
current.
After turning the rotor by an electrical angle of 90◦, the stator phase U axis is
aligned with the q-axis, therefore the d- axis current component of the current
will be 0. Since the stator system is aligned with d- and q-axis respectively, it
is sufficient to inject a simple AC current to the three-phase winding system.
In this section, the saturation effect on the inductance value will be investigated.
The saturation occurs because of the change of the flux in the direction of d-
and q-axis. The study of the differential and absolute inductances is essential
for a high performance control system [57].
By varying the current about a working point, the differential d- and q-axis
inductances Ldiff at different currents can be calculated from equation (3.12).
30
3.3. Verification of the design by FEA and test
The FEM simulated results of the influence of DC bias current on Ldand Lqare
shown in Fig. 3.26.
Ldiff|I=I1+I2
2
=∆Ψ
∆I=Ψ1−Ψ2
I1−I2
(3.12)
where ∆Ψ is the difference of flux linkage generated from two different currents
I1and I2in FEM.
In this section only the effect of saturation on the larger Ldvalue in the motor
with 4 magnet blocks was analysed for the proposed motor.
The simulated d-axis inductance of the machine with the 4 magnet blocks rotor
is larger compared to the conventional rotor structure, which is 1.11 mH and
0.80 mH respectively, as shown in Fig. 3.26(a). The possible reasons for the
significantly different behavior in d-axis direction may be explained as follows:
since in one magnetic circuit the thickness of the magnets are the same for both
rotor, it should have not effect. But the wider magnet span in the 4 magnet
blocks configuration increases the cross sectional area and therefore it reduces
the magnetic reluctance, thus a larger value of Ldis obtained. As it is observed
from Fig. 3.26(a), Lddecreases along with an increasing d-axis bias current. Fig.
3.26(b) shows that the characteristics of q-axis inductance Lqare symmetric to
q-axis bias current for both motors. With increasing absolute value of the q-
axis DC bias current, the q-inductances of both motors saturate softly when the
rated current of 7.5 A is exceeded.
AC+DC
Current supply
BLDCM
aligned d or q axis
Power Analyser
AC DC
i
U
V
W
f
u
f
i
Fig. 3.24: Schematic block for inductance measurement
IPM
Machine
Power
Meter
DC Source
Power Amplifier
Waveform Generator
Fig. 3.25: Test setup for differential inductance measurement
31
−8−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7 8
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
d − axis bias current [A]
d − axis Inductance [mH]
4−8Ld
8−8Ld
(a) d differential inductances
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
q - axis bias current [A]
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
q - axis Inductance [mH]
4-8Lq
8-8Lq
(b) q differential inductances
Fig. 3.26: Simulated d and q differential inductances
In order to verify the FEM results, a test setup to analyze the bias effect on
d- and q-axis inductance was built, as shown in Fig. 3.25. The functional
principle of the circuit is shown in Fig. 3.24. To eliminate the effect of AC
current component during the test, RMS value of AC current is set as 0.1 A.
The frequency is set to the rated frequency 533 Hz. Different d- and q-axis
DC-bias currents were applied to extract the characteristic of the differential
inductances. For this investigation the currents flowing into the stator coils do
not just contain an AC current component but also a DC current. Therefore an
AC current and a DC current supply were connected in parallel and connected
to the stator winding terminal of the machine. A power analyser was used to
measure the fundamental RMS terminal voltage U1and current I1across the
connected coils, the frequency of the AC signal, and also the resistance of the
circuit at different DC bias currents. Ldand Lqare consequently calculated from
these quantities.
Fig. 3.27 shows the measured results of the differential d- and q-axis inductance.
The simulation results and test results of Ldhave the same variation trend as
shown in Fig. 3.27(a), but the differences of the simulated and experimental
d inductance may be caused by the temperature difference of the magnets for
simulation and test.
Fig. 3.27(b) shows the measured results of the differential q-axis inductance.
The simulation results and test results have a similar variation trend. The
differences of the simulated q inductance are about 1.5 % from the experimental
values.
The comparison of simulated and measured values of Ldand Lqare shown in
Table 3.5. The difference may be caused by inaccurate extrapolation of the
magnetizing curve of the silicon steel sheets when B is exceeds 1.8 T which is
the maximum value given in the datasheet. Also, the the FEM simulation was
conducted in 2D and therefore the magnetic effects of the end windings were
neglected. In conclusion, the proposed rotor structure with 4 magnet blocks has
a larger Ld, but Lqvalues of both motors are comparable.
32
3.3. Verification of the design by FEA and test
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
d - axis bias current [A]
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
d - axis Inductance [mH]
4-8Ld
8-8Ld
(a) d differential inductances
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
q - axis bias current [A]
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
q - axis Inductance [mH]
4-8Lq
8-8Lq
(b) q differential inductances
Fig. 3.27: Measured d and q differential inductances
Tab. 3.5: Comparison of inductance
Inductance Rotor type FEM result Measurement Difference
Ld
4magnet blocks 1.12 mH 0.92 mH +22 %
8 magnet blocks 0.81 mH 0.78 mH +3.8 %
Lq
4 magnet blocks 1.44 mH 1.57 mH -8.3,%
8 magnet blocks 1.55 mH 1.49 mH -4 %
3.3.5 Demagnetization analysis
During the climbing stage of the solar powered UAV, the drive system should be
able to withstand overload situations when there are strong winds. Therefore,
the power electronics system was designed to work under this overload situation.
The other point necessary to consider is the demagnetizing effect of an overload
current on the permanent magnets. The current waveform during the overload
operation is shown in Fig. 3.28. The RMS value of the overload current is 15 A,
which is 2 times the rated current.
33
0 60 120 180 240 300 360 420 480 540 600 660 720
−35
−28
−21
−14
−7
0
7
14
21
28
35
elec angle [dregee]
Current [I]
Fig. 3.28: Phase current waveform at overload situation
When a 3 phase short circuit happens, the short current at d axis calculated
from the d-inductance, q-inductance and flux linkage is 38 A. It is larger than
the overload current, so the effect of the short circuit current on demagnetization
behavior was analysed.
Fig. 3.29 shows the influence of the temperature on the flux density and po-
larization for Vacodym 655 HR. When the value of the magnet field is below
-800 kA/m, the magnet will produce irreversible demagnetization working at
exactly 120◦C.
Fig. 3.29: Demagnetization curve of Vacodym 655 HR (Flux density and polarization at
different temperatures)
Under this situation, the magnet field of the magnet are shown in Fig. 3.30 and
Fig. 3.31 for the motor with 4 magnet and 8 magnet, respectively.
As it is shown, the irreversible demagnetization area only has small effect the
edge of the magnet marked as dark blue color for the short circuit situation.
Therefore, the overload current will not cause large scale of the irreversible
demagnetization. Both motors could sustain it and work back to normal oper-
ation.
34
3.3. Verification of the design by FEA and test
-2e+05
-3e+05
-4e+05
-5e+05
-8e+05
-7e+05
-6e+05
-9e+05
-1e+05
H [A/m]
Fig. 3.30: Demagnetization behavior in 4-8 motor short circuit situation
-2e+05
-3e+05
-4e+05
-5e+05
-8e+05
-7e+05
-6e+05
-9e+05
-1e+05
H [A/m]
Fig. 3.31: Demagnetization behavior in 8-8 motor short circuit situation
35
3.4 Summary of the design
In this chapter, the design of a 1.5 kW, 3 phase BLDC machine with two different
magnet structures for the rotor has been introduced. The magnet structures,
stator core, stator winding connection, and air gap were optimized by three prin-
ciples. The first requirement was a high torque density performance. Secondly
both motors should have the same back EMF voltage. The third one was to
reduce cost by rational use of permanent magnet material.
After the geometric design of the motor, FEA validation was conducted to an-
alyze the parameters of both BLDCMs. In this analysis the mechanical perfor-
mance of the bridge structure was verified in FEM analysis. Then the demag-
netization behavior of both IPM structures was analyzed. Finally, an AC+DC
standstill frequency test method was applied to both IPM structures, to deter-
mine values for Ldand Lq, and the influencing factors on the inductance values
were studied and tested.
36
4 Test and verification
This chapter describes the tests carried out and an evaluation of the performance
of both rotors. The basic characteristics of the motors were already shown in
preceding chapters, such as inductance behavior and mechanical properties. This
chapter focuses on the operating characteristics of the motors. Results of no load
tests, different load operating points, an efficiency analysis, and thermal tests
will be presented.
4.1 Description of the test bench
A test bench was built to carry out the static and dynamic tests, as shown in
Fig. 4.1.
Converter of DC load motor
Anemometer BLDCM
DC load motor
Draught fan
Fig. 4.1: Test bench setup
37
The test bench consists of the following parts:
•SIEMENS 1 GG5132-0KK10-6JA1-Z load machine
•EA/TU-BERLIN Converter for load machine
•LORENZ DR-2643 torque and speed sensors
−Accuracy class: ±(0.1 % ∗5N.m + 0.02 %∗of measured value)
•EFFEPIZETA s.r.l. D09184 - 2007 fan
•ZES Zimmer LMG 670 Power Analyzer :
−Accuracy frequency input: ±50 ppm
−Accuracy analog input: ±(0.05 % of reading+0.05 % of full scale value)
−Accuracy electric power: ±(0.024 % of measuring range limit + 0.03 %∗of
measured value)
•Labview interface platform
The Labview interface platform was developed to realize real-time observation
of currents, voltages and speed as well as transmitting and receiving of control
instructions. Through CAN bus communication, different operational parame-
ters of the BLDC machines were changed. These include speed setpoint, current
setpoint, phase advance angle and PWM duty cycle, depending on the opera-
tional state. In addition, with combination of controlling the SIEMENS load
machine through a DAQ USB-6356 device and the BLDC machine by CAN bus,
serial testing of different load points can be conducted also. The transient data
as well as calculated values obtained from power meter LMG670 are used to
analyze and evaluate the performance of both BLDC machines.
One stator and two rotors have been built. The proposed IPM rotor with 4
magnet blocks and a conventional one with 8 magnet blocks were shown in Fig.
4.2 and the stator structure was shown in Fig. 4.3.
4.2 Resistance
The resistance of the phase winding is calculated as:
R20 =ρ20NLav
2ma2nbrS(4.1)
where
ρ20: the specific resistivity of the wire’s material at 20◦C
N: the total number of wires in all slots
Lav: the length of wire for one single coil
m: the number of phases
a: the number of parallel branches
38
4.3. Cogging torque
(a) Rotor for BLDCM with 4 magnet blocks (b) Rotor for BLDCM with 8 magnet blocks
Fig. 4.2: Mechanical structure of proposed and conventional rotors
nbr: the number of parallel wires per strand
S: the cross sectional area of the wire
The calculated value is 516.22 mΩ. At 19.5◦C, the measured phase resistances
of U, V, and W are 473.4 mΩ, 481.9 mΩand 484.7 mΩ, respectively. The uncer-
tainty of resistor measurement is ±0.7mΩcalculated from equation 4.2. These
resistance values were also used in preceding FEM simulations.
Fig. 4.3: Stator of both BLDCM
4.3 Cogging torque
For cogging torque measurement, the motor shaft is connected with a torque in-
dexing head. In the process of turning the shaft in intervals of 1.875◦mechanical
angle, the torque value at each position was measured and recorded from the
torque sensor.
Fig. 4.4 shows the simulated and measured cogging torque. The IPM machine
with 4 magnet blocks has a lower cogging torque than the 8 poles structure. The
39
0 10 20 30 40 50 60 70 80 90
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
mechanical angle[degree]
cogging torque[Nm]
4 magnet blocks
8 magnet blocks
(a) Simulated curves
0 10 20 30 40 50 60 70 80 90
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
cogging torque [Nm]
mechanical angle [degree]
4 magnet blocks
8 magnet blocks
(b) Measured curves
Fig. 4.4: Cogging torque of both BLDCM
average peak value of the cogging torque is 45.4 % lower in the 4-8 than in the
8-8 design. The uncertainty of the measurement is 0.06 Nm.
For the magnet arrangement of 4 magnet blocks, the cogging torque has a 30◦
mechanical symmetry. However, for the motor with 8 magnet blocks 8 pole pairs
has a 15◦mechanical symmetry.
4.4 No load test
The simulation of no load and load test is conducted through the combination
of 2D motor FEM analysis and external circuit with DC power supply and
converter in MAXWELL. The external circuit is shown in Fig. 4.5.
A no load test on a BLDCM gives information about the idle speed and idle
losses. By applying an increasing phase voltage to the stator by adjusting the
duty cycle without mechanical load (TL= 0), the idle speed and idle loss for
both motors at rated 270 V DC were calculated in FEM simulations. Apart
from copper loss and core loss, the mechanical loss including bearing loss and
windage loss is also calculated in FEM simulation. The comparison of FEM and
experimental results are shown in Tab 4.1.
40
4.4. No load test
Fig. 4.5: External circuit connected with 2D motor FEA module 41
0 0.5 1 1.5 2 2.5
100
110
120
130
140
150
160
170
180
190
200
torque [Nm]
power losses [W]
FEM results@8009rpm
experimental results@8009rpm
7
56
14
15
15
14
10
(a) 4-8 magnet blocks
0 0.5 1 1.5 2 2.5
100
110
120
130
140
150
160
170
180
190
200
torque [Nm]
power losses [W]
FEM results@8005rpm
experimental results@8005rpm
15
24
4
4
6
8
9
19
(b) 8-8 magnet blocks
Fig. 4.6: Differences of power losses of the motor in FEM simulated and experimental at
rated speed. Numbers in the graphs indicate loss difference(W) from experimental
to simulated values.
Tab. 4.1: Simulated and experimental comparison of idle losses of 270 VDC
rotor structure idle speed (rpm) idle losses (W)
Simulation results 4-8 magnet blocks 8851 103.76
8-8 magnet blocks 8638 104.06
Experimental results 4-8 magnet blocks 8715 107.13
8-8 magnet blocks 8559 113.52
4.5 Load test
To verify the accuracy of the power losses and efficiency results from FEM
simulation, load operation was also conducted on the test bench. To conduct
the tests, the load machine is driven at fixed speed and the closed loop controller
for the phase current is used for the BLDCM.
The phase advance angle is applied to maximize the motor efficiency at each
measured point. It means that the speed is set to constant and adjusting the
current by advance angle to reach the maximum efficiency of BLDCM. However
the field-weakening control of BLDCM is difficult and has limitations. It can
realized through the effect of the Ldi/dt part in the phase voltage equation. The
advance angle is corresponding to the reference speed which can be calculated
and applied to the commutation strategy.
Fig. 4.6 shows the simulated and experimental results of different load torque
points at rated speed of about 8000 rpm. The numbers at the FEM curves show
the differences of power loss (W) of the motor from experimental to simulation
42
4.5. Load test
0 0.5 1 1.5 2 2.5
55
60
65
70
75
80
85
90
95
torque [Nm]
efficiency [%]
FEM results@8009rpm
experimental results@8009rpm
(a) 4-8 magnet blocks
0 0.5 1 1.5 2 2.5
55
60
65
70
75
80
85
90
95
torque [Nm]
efficiency [%]
FEM results@8005rpm
experimental results@8005rpm
(b) 8-8 magnet blocks
Fig. 4.7: Comparison of FEM simulated and experimental motor efficiency at rated speed
result for each load point. The power loss of the motor from FEA calculation
includes core, copper, bearing, and windage losses. The differences increase
along with the torque for both motors. Different reasons could account for
that difference: material parameters not accurate or extrapolation necessary,
parameters for calculation of friction and windage losses inaccurate.
Also the magnet temperature was not part of the simulation, so the magnet
temperature is different in simulation and experiment. Comparing both motor
efficiencies from the experimental values reveals only a small difference, which
is increasing with load up to 0.5 % at 2 Nm in Fig. 4.7.
Further it can be seen, that the motor with 8 magnet blocks generates higher
losses than the one with 4 magnet blocks. This can be explained by the higher
no-load flux density of the 8-8 design. With higher flux densities the core losses
increase, which has a larger effect than the corresponding reduction of copper
losses since the core losses dominate the losses according to Fig. 4.9.
From an efficiency perspective, the difference between FEM calculation and
experiment is almost constant around 0.8 % for the 4-8 rotor and continuously
increasing with load for the 8-8 rotor reaching a maximum difference of 1.2 % at
2 Nm.
By operating BLDCM at different speed levels, the characteristics of torque
and current of both motors can be derived. The results are shown in Fig. 4.8.
Except the working points at 8000 rpm, all T - I curves have good linearity for
both motors. For both BLDC machines the gradient decreases for currents larger
than 5 A at 8000 rpm. This is due to operation at the voltage limit with elevated
phase advance angles. The T - I curves are compared for for both BLDCM at
1000 rpm and 8000 rpm in Fig. 4.8(c). At low speed it can be seen that the
gradient for the 8-8 rotor is steeper due to the higher flux density in the airgap.
At 8000 rpm however, the curves become almost equal, which is supposedly due
to the necessity for a larger phase advance angle in the 8-8 design.
The experimental recording of power losses for both motors was completed. The
copper losses take a rather low percentage of the total power losses when motor
43
0 1 2 3 4 5 6 7
0
0.5
1
1.5
2
2.5
current [A]
torque [Nm]
1000rpm
2000rpm
3000rpm
4000rpm
5000rpm
6000rpm
7000rpm
8000rpm
(a) 4-8 magnet blocks
0 1 2 3 4 5 6 7
0
0.5
1
1.5
2
2.5
current [A]
torque [Nm]
1000rpm
2000rpm
3000rpm
4000rpm
5000rpm
6000rpm
7000rpm
8000rpm
(b) 8-8 magnet blocks
0 1 2 3 4 5 6 7
0
0.5
1
1.5
2
2.5
current [A]
torque [Nm]
4−81000rpm
8−81000rpm
4−88000rpm
8−88000rpm
(c) comparison of two motors
Fig. 4.8: Experimental comparison of torque and current characteristics
44
4.5. Load test
0
20
40
60
80
100
120
140
160
180
200
0,18 0,47 0,76 1,06 1,34 1,61 1,86 2,05
power loss [W]
T [Nm]
Pcore loss
Pmech
Pcu
(a) 4-8 magnet blocks
0
20
40
60
80
100
120
140
160
180
200
0,18 0,47 0,77 1,07 1,31 1,60 1,85 2,03
power loss [W]
T [Nm]
Pcoreloss
Pmech
Pcu
(b) 8-8 magnet blocks
Fig. 4.9: Percentage of losses in total power losses
runs at high speed. Fig. 4.9 shows the amount of the calculated copper loss
inside the total losses at 8000 rpm. At 2.05 Nm the copper losses make up about
1/3 of the total losses for both machines (4-8: 34 %; 8-8: 33 %).
Fig.4.10 shows that the total power losses have a good linear relationship with
the square of the phase current. The BLDCM with 8 magnet blocks produces
more power loss at high phase currents, as shown in Fig. 4.10(c). Due to the
almost equal ratio of torque to current for both motors (Fig. 4.8(c)), this is
equally true for high torque values. At the maximum load point, the BLDCM
with 8 magnet blocks generates around 7 W higher losses than the motor with
4 magnet blocks.
A contour plot can be used to examine the efficiency of the machines for all
operating points at once. These efficiency maps are shown in Fig. 4.11. As it is
shown in Fig. 4.11(c), the BLDCM with 8 magnet blocks has a higher efficiency
than the one with 4 magnet blocks for most of the working range, but 8000 rpm
there is a slight advantage for the 4-8 design.
Accuracy and Precision of the load test measurement:
For each load point, the measured data was recorded more than 100 times by
the Power Analyzer [58]. Fig. 4.12 shows the probability distribution of the
efficiency for one measured load point. As it is shown in the graph, the standard
deviation of the efficiency is 0.2696 %.
45
0 5 10 15 20 25 30 35 40 45
0
20
40
60
80
100
120
140
160
180
200
phase current2 [A2]
total losses [w]
1000rpm
2000rpm
3000rpm
4000rpm
5000rpm
6000rpm
7000rpm
8000rpm
(a) 4-8 magnet blocks
0 5 10 15 20 25 30 35 40 45
0
20
40
60
80
100
120
140
160
180
200
phase current2 [A2]
total losses [w]
1000rpm
2000rpm
3000rpm
4000rpm
5000rpm
6000rpm
7000rpm
8000rpm
(b) 8-8 magnet blocks
0 5 10 15 20 25 30 35 40
100
110
120
130
140
150
160
170
180
190
200
phase current2 [A2]
total losses [w]
@8009rpm 4−8
@8005rpm 8−8
(c) losses comparison at rated speed
Fig. 4.10: Experimental comparison of power losses
46
4.5. Load test
speed [rpm]
torque [Nm]
90
89.75
89.5
89.5
89
89
89
88
88
88
88
88
87
87
87
87
87
85
85
85
85
83
85
85
83
83
83 83 83
75
80
80
75 75
7070
1000 2000 3000 4000 5000 6000 7000 8000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
(a) efficiency map of 4-8 rotor
speed [rpm]
torque [Nm]
90
89.75
89.75
89.5
89.5
89
89
89
89
88
87
85
83
80
88
87
88
88
87
87
85
85
85
85
85
85
83
83
80
80
75 75
75
70
1000 2000 3000 4000 5000 6000 7000 8000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
(b) efficiency map of 8-8 rotor
−7
−7
−7
−7
−6
−6
−6
−6
−5
−5
−5
−5
−4
−4
−4
−3
−3
−3
−3
−3
−2
−2
−2
−2
−2
−1
−1
−1
−1
0
0
0
speed [rpm]
torque [Nm]
1000 2000 3000 4000 5000 6000 7000 8000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
(c) difference of efficiencies; negative numbers in-
dicate a higher efficiency for the 8-8 rotor
Fig. 4.11: Experimental map of motor efficiencies
47
88.9 89 89.1 89.2 89.3 89.4 89.5 89.6 89.7 89.8 89.9 90 90.1 90.2 90.3
0
1
2
3
4
5
6
7
8
9
10
Frequency
Efficiency [%]
ηmean−σ ηmean+σ
ηmean=89.56%
σ=0.2696%
Fig. 4.12: Histogram of one measured point
Based on the uncertainty of the torque sensor and the Power Analyzer, which
measures the value of the electric power, torque and speed, the uncertainty
calculation of the efficiency will be discussed. Assuming all the variables are
uncorrelated, the uncertainty ucof the calculated value according to ffrom the
measured resources can be expressed as in equation 4.2:
uc=⌜
⎷
N
∑︂
i=1
(∂f
∂xi
u(xi))2(4.2)
where u(xi)are the error limits of the variables and contribute to the total
uncertainty.
The uncertainty of the motor efficiency is calculated from the uncertainty of the
corresponding measured values. The uncertainties of these are: uTof the torque
sensor itself, uTZ of the AD-conversion of the torque value , unZ of the speed
measurement and uPZ of the electric power measurement. These are expressed
in equation 4.3 – 4.6:
uT=2π
60
n
Pe
(0.1% ·Tf.s.s + 0.02% ·Tmeasured) (4.3)
uTZ =2π
60
n
Pe
(0.05% ·Tf.s.z + 0.05% ·Tmeasured) (4.4)
unZ =2π
60
T
Pe
(0.005% ·n) (4.5)
uPZ =−2π
60
nT
P2
e
(0.024% ·If.s.z ·Uf.s.z + 0.03% ·Pe) (4.6)
48
4.6. Thermal test
where Tf.s.s is the full scale value of the torque sensor (5 Nm), Tf.s.z is the the-
oretical full scale value of the torque reading of the Power Analyzer (13 Nm).
The power measuring range is derived from the maximum instantaneous values
of the current If.s.z and voltage Uf.s.z.Peis the electric Power.
The standard uncertainty uSD is calculated from equation 4.7.
uSD =±√︂u2
T+u2
TZ +u2
nZ +u2
PZ (4.7)
The hereby calculated absolute value depends on the working point. For the
above measurement it is ±0.477%, so the efficiency for that point can be stated
as η= (89.6±0.477)%. Torque measurement contributes the most inaccuracy to
the measurement of the efficiency.
4.6 Thermal test
In order to get a better understanding of the capacity and limitation of these
motors, thermal characteristics of the winding are presented in this part. To
emulate cooling at working height, an EFFEPIZETA SCL K05 - MS FAN motor
with ventilating pipe is adopted as air cooling system. The pipe is connected to
the non- driven end cover of the tested BLDCM. The test bench setup for the
thermal test is shown in Fig. 4.1.
In this application, plate fin heat sinks is applied for the forced convection
cooling system. The effect of this cooling system is explained as follows [59].
Channel-Reynolds number is expressed as in equation 4.9:
Re′
b=Reb
b
Lh
(4.8)
where Reynolds number Reb=V b/v1, b is the width of the fin channel, Vis the
wind speed, v1is the kinematic viscosity, and Lhis the length of the fin.
Re′
b=Reb
b
Lh
(4.9)
The dimensionless average heat transfer rated Nubis expressed in terms of the
Nusselt number Nuidefined as:
Nub=tanh[√︂2Nui·λf
λ1·H1
b·H1
t·(t
Lh+ 1)]
√︂2Nui·λf
λ1·H1
b·H1
t·(t
Lh+ 1) Nui(4.10)
where:
tanh is Hyperbolic tangent, H1is the high of the fin, tis the width of the fin, λ1
is the thermal conductivity of the aluminum, λfis the thermal conductivity of
the air.
49
Nui= [(Re′
b·Pr
2)−3+ (0.664√︂Re′
bP
1
3
r⌜
⎷1 + 3.65
√︂Re′
b
)−3]−1
3(4.11)
Heat transfer coefficient of hthe fin heat sink can be derived:
h=Re′
bλf/b (4.12)
Thermal resistance of the housing with fin heat sink is defined by:
Rhs =1
hA (4.13)
where A is the total area of the housing considering the fin heat sink.
Before the thermal test in the laboratory, the winding resistance and the back
EMF are measured at a room temperature TAof 19.5◦C. Then the motors op-
erated as close as possible to rated working condition until the change of the
temperature in the winding was less than 1◦C per hour. The air speed at the air
outlet was 11.9 m/s at ground level by measurement. During the experiments,
the motor with 4 magnet blocks run at 8000 rpm and the output mechanical
torque was 1.89 Nm. The motor with 8 magnet blocks run at 8008 rpm and me-
chanical torque was 1.87 Nm. The fan motor was turned on at 13 min 20 s (4-8)
and 5 min 5 s (8-8) after the start of the measurement.
Since the change of the temperature of is less than 2 K per hour after running
for 2.5 hours, the temperature measurement can be carried out. After stop-
ping motor operation, the measured temperatures decay quickly. International
Standard IEC 60034-1 [60] allows to estimate the temperature by the resistance
method in machines of less than 50 kW if it is measured within 30 seconds from
the disconnection instant [61]. Fig. 4.14(a) and Fig. 4.13(a) show the recorded
temperatures time course from different parts of winding for both motors at
rated operation. Three temperatures are shown in the graphs:
TTC: the winding temperature inside the slot measured by an inbuilt thermo-
couple
TR: the winding temperature estimated by measuring the resistance of winding
after disconnect
Tend: the temperature of the end winding measured by an inbuilt thermocouple
As it is shown in Fig. 4.14(b) and Fig. 4.13(b), the first resistance measurement
for calculating the temperature were recorded 20 s after the disconnection and
further resistance points are measured in 10 s intervals. The temperature differ-
ence from slot and end winding is less than 0.5◦C for both motors at the time
of disconnection.
Since the value of temperature at the disconnection instant can be estimated
with an exponential decay function, the red line in the figures shows the fitting
curve and the extrapolated temperature at the time of disconnection. This
average winding temperatures calculated by winding resistance are 83.5◦C and
86.7◦C for the motor with 4 magnet blocks and 8 magnet blocks, respectively.
These temperatures are approximately 2◦C lower than the values measured by
thermocouple in the end winding.
50
4.6. Thermal test
0 2000 4000 6000 8000 10000
10
20
30
40
50
60
70
80
90
100
time [s]
temperature of phase U [°C]
TTC
TR
fit
Tend
13min20s
(a) 4-8 structure
8900 8920 8940 8960 8980 9000 9020 9040 9060 9080 9100
20
30
40
50
60
70
80
90
100
time [s]
temperature of phase U [°C]
TTC
TR
fit
Tend
TTC =85.9°C
Tend=85.53°C
TR =83.5°C
(b) the extrapolation of the max. temperature
Fig. 4.13: Temperature trend of 4-8 motor with 4 magnet blocks under long time test
0 2000 4000 6000 8000 10000
10
20
30
40
50
60
70
80
90
100
time [s]
temperature of phase U [°C]
TTC
TR
fit
Tend
5min5s
(a) 8-8 structure
9100 9120 9140 9160 9180 9200 9220 9240 9260 9280 9300
20
30
40
50
60
70
80
90
100
time [s]
temperature of phase U [°C]
TTC
TR
fit
Tend
TTC =88.9°C
Tend=88.5°C
TR =86.7°C
(b) the extrapolation of the max. temperature
Fig. 4.14: Temperature trend of 8-8 motor with 8 magnet blocks under long time test
Since the power loss of the motor with 8 magnet blocks motor is larger at rated
operation, the winding temperature of the motor with 4 magnet blocks is 3 K
lower.
Considering the parameters of the air at ground level, the temperature under
the housing TH, temperature of the winding TW, and the temperature rise ∆Tf-H
from the surrounding air of the fin to the surface of the housing are shown in
Tab. 4.2.
The test was conducted in the laboratory at an air speed of 11 m/s. The higher
temperature of the 8-8 design translates into 64◦C at a working altitude of 20 km,
taking into account the adapted properties of the air, ambient temperature and
wind speed. At low operating heights the airspeed is assumed to be similar to the
conditions in the laboratory. Therefore the maximum temperature occurs at low
operating heights, i.e. at start and during climbing. The obtained temperatures
are well below the isolation class temperature of the wire (180◦C) and also below
51
the maximum magnet temperature of 120◦C. This gives the possibility to run
at overload conditions.
Tab. 4.2: Temperature under different altitude
Flight
Altitude
Air
Tem-
perature
Air
Pressure
Flight
Speed TA∆Tf-H THTW
ground
level 288.15 K 101325 Pa 11 m/s 292.65 K 48 K 67.5◦C 89 ◦C
20 km 216.65 K 5529.31 Pa 30 m/s 216.65K 99 K 42.5◦C 64 ◦C
According to the IEC 60 584, the tolerance of the bedded thermocouple K is
±1.5◦C when the temperature is between 40 and 375◦C. Data Logger Thermome-
ter YC-747UD is used to measure the temperature of thermocouple K bedded
in the winding. The accuracy of the YC-747UD is ±(0.1% rdg + 0.7◦C)=±0.79
when the temperature is between -100◦C and 1300◦C. The possible deviation is
from 0.886 % to 0.889 %.
4.7 Summary
To compare the performance of both BLDCMs, a series of experiments was
conducted and presented in this chapter. The BLDCM with 4 magnet blocks
has a considerably lower cogging torque than the conventional BLDCM. Through
the power loss test, it is verified, that at rated operation, the proposed BLDCM
generates less power loss and has a comparable efficiency. Thermal tests were
carried out to prove that even with a less powerful cooling system, the magnets
are not in danger of running into demagnetization for thermal reasons.
Based on the experimental results of the thermal test, the temperature of the
winding is much lower than the designed temperature (180◦C). It is because
this design is for the laboratory test and security. And obviously, the motors
are oversized.
52
5 BLDC motor drive system:
inverter and control
In this chapter the important design parameter of the inverter driving the
BLDCM will be presented, which includes the system structure and perfor-
mance. Later in this chapter the description of the new analog isolation method
for the sensorless control is given.
5.1 Design of voltage source inverter
The basic topology of the inverter is shown in Fig. 2.3. The inverter consists of
three phase-legs with transistors paralleling a free-wheeling diode. The principle
of driving a BLDC motor is to let the current flow through two phases and keep
one of the phases floating. This commutation sequence makes up the six different
states available for BLDCM. The applied voltage during each state is commonly
modulated by a PWM. First, a prototype of the inverter was built up. This
converter includes the following protection and auxiliary functions:
– control sequence of electric relays
– charging and discharging design of DC link capacitor
– overcurrent protection
– overvoltage protection
– overtemperature protection
– sensor control
– sensorless control
The converter was constructed for testing the motor in the laboratory. Therefore
it must withstand all motor tests safely. Based on this requirement it was
oversized and not optimized for weight or size.
54
5.1. Design of voltage source inverter
5.1.1 Transistor selection
Based on the rated DC voltage of 270 V, either Metal Oxide Semiconductor Field
Effect Transistor (MOSFET) and Insulated−Gate Bipolar Transistors (IGBT)
were considered as active devices.
MOSFETs have been developed for high voltage high frequency converter ap-
plications due to low loss and high speed switching performance [62]. It has an
on-state current carrying capability and off-state blocking voltage capability [63]
[64].
Due to high voltage and current ratings, and low conduction loss of IGBT, it
has become more attractive in the high voltage and high current applications
than the MOSFET [65] [66].
Considering the price, efficiency, application requirement, and selectivity of the
available products on the current market, IGBTs are selected as the main power
devices for the 270 V propulsion drive system.
In order to protect IGBT chips and reduce the complexity of testing, it is more
reliable to chose an integrated IGBT module. Based on this, the Semikron SKiiP
module 28AC065V1 was chosen. It offers six 600 V ultrafast Non punch through
(NPT) IGBTs for a 3-phase system as well as robust and soft freewheeling diodes
in Controlled Axial Lifetime (CAL) technology [67]. NPT IGBTs is based on
n-substrate with a lightly doped player implanted. It has lower switching losses,
higher VCEsat, and robustness. By locally influencing the carrier lifetime along the
current path between anode and cathode, the softness and low reverse recovery
charge of the CAL diode is achieved, intentionally lowering it at the p-n junction,
shown in Fig. 5.1. This non-uniform behavior is reflected in the naming of the
diode: Controlled Axial Lifetime or CAL [68]. This module also integrates a
Positive Temperature Coefficient (PTC) temperature sensor to monitor the heat
sink temperature enabling an over temperature shut down. It is placed near the
IGBT chips for easy readout. All components integrated in one package greatly
reduce handling and the reduced number of parts increases the reliability.
5.1.2 Switching frequency
The switching frequency is an important control parameter for the motor in-
verter. For space vector Pulse-Width Modulation (PWM)and discontinuous
Pulse-Width Modulation control algorithms [69], in order to decrease electro-
magnetic interference through introducing specific-order current harmonics, ran-
dom PWM is introduced [70] [71]. Inverter loss, particularly switching loss,
varies directly with switching frequency. Therefore, the switching loss cannot be
predicted as the switching frequency is varied randomly, which makes efficiency
calculation difficult [72].
55
Fig. 5.1: Schematic of CAL diode principle [68](refer to D1, D3, D5 and D2, D4, D6 in Fig.
2.3)
For the six commutation states algorithm, a constant switching frequency fPWM
is used. The fixed frequency will reduce the complexity of the control strategy.
Fig. 5.2: The output characteristic of IGBT [67]
The torque ripple usually comes from three parts: the motor structure, the
contol strategy and the PWM of the inverter. The torque ripple caused by
motor structure occurs usually at fundamental frequency and its harmonics [73].
Through improving the motor structure inherently, the torque ripple can be
reduced to a certain extent which is discussed in the last chapter. It is clear
that higher switching frequencies will reduce the torque ripple caused by PWM
[74] but lead to an increase of the switching losses.
The other consideration for selecting the switching frequency for this application
is to assist in the realization of the sensorless control strategy. To detect the
zero-crossing point of the back EMF voltage, the voltage of the floating phase
is measured and compared to UDC/2. This voltage has to be measured during
the on-state of the PWM period, thus the measurement has to be synchronized
to the PWM and typically one value will be obtained during each PWM cycle.
56
5.1. Design of voltage source inverter
To accurately detect the point at which the value equals 50 % of the DC-link
voltage, a high fPWM needs to be selected.
Hence, a switching frequency of 25 kHz which is roughly 47 times of the electric
frequency at rated speed should be sufficient. The limitation of sensorless circuit
on switching frequency is described in the next part.
5.1.3 Loss analysis
The majority of the power losses is caused by the power semiconductors which
are generated inside the semiconductor chips. The loss model used in this thesis
takes into account the conduction losses and the switching losses for different
working states [75] [76] [77]. The estimated losses are based on the data sheet
parameters of the IGBT module which generally are temperature dependent
[78]. However, due to the lack of information about switching losses at differ-
ent temperatures from the data sheet, the worst case condition of the junction
temperature (of 125 ◦C) is assumed for calculating the losses and selecting the
cooling system.
5.1.3.1 Conduction Losses
During pulse-width modulation, the power losses can be derived from switching
losses, conduction losses, and off-state losses which are negligible and do not
need to be calculated [79].
In MOSFETs, the conduction losses Pcond occur only due to its on-state resis-
tance. However, different from MOSFETs, IGBTs’ conduction losses are cal-
culated using an approximation of a series connection of the on-state constant
voltage drop VCE(TO), which represents the IGBT’s collector-emitter voltage dur-
ing turn-on state at zero current, and the voltage across the turn-on resistance
rT,IGBT. For the selected module the on-state voltage drop has a slight positive
temperature coefficient, therefore the on-state voltage drop will get larger when
the temperature increases. For the inverse diode the same modeling of the losses
is possible using V(TO) and rT,D. For the diodes of the selected module the overall
forward voltage drop has a negative temperature coefficient for most of the op-
erating area, i.e. currents below 100 A. The average conduction losses of IGBT
and the anti-parallel diode during on-state are given in equation (5.1):
Pcond,IGBT =1
Tsw ∫︂Tsw
0p(t)dt
=1
Tsw ∫︂Tsw
0(VCE(TO) ·ic(t) + rT,IGBT ·ic2(t))dt
=VCE(TO) ·Icav +rT,IGBT ·I2
crms
and accordingly
Pcond,D =V(TO) ·Icav +rT,D ·I2
crms (5.1)
57
where icis the current flowing through IGBT, Tsw is switching period, Icav and
Icrms is the average and rms value of the current, respectively. And the parame-
ters of the IGBT are selected based on the data sheet. The output characteristic
of IGBT is shown in Fig. 5.2.
5.1.3.2 Switching Losses
The switching loss calculation is depicted in this part. Switching losses of semi-
conductor switches are linearly dependent on switching frequency. It is more
accurate to use the turn-on energy losses Eon,IGBT and switch-off energy losses
Eoff,IGBT of IGBT to calculate switching losses, as shown in (5.2). It also can be
used to calculate switching losses of the diodes based on the reverse recovery
energy of diode Err.
Psw,IGBT = (Eon,IGBT +Eoff,IGBT)·fsw
Psw,D =Err ·fsw
(5.2)
where Psw,IGBT and Psw,D are the switching losses of the IGBT and diode, respec-
tively.
Eon,IGBT and Eoff,IGBT are decided by gate resistor, current and voltage, tempera-
ture, as shown in Fig. 5.3. Considering the max. temperature working condition
and over load situation, the values are selected based on equation (5.3).
Eon,270V =270V
300V·35A
100A·Eon,300V (5.3)
Fig. 5.3: Turn on/off energy of IGBT [67]
58
5.1. Design of voltage source inverter
Gate drive signal
Electric angle [°]
Q4
Q5
Q6
Q1
Q2
Q3
Fig. 5.4: Control strategy of inverter
59
5.1.3.3 IGBT module Losses
The control strategy of inverter is shown in Fig. 5.4. Q1, Q3,and Q5 are only
used for phase transition. PWM control is applied for Q2, Q4,and Q6 for current
regulation. Tab. 5.1 represents the power losses of each component during one
120◦electric commutation period which includes two 60◦electric commutation
periods and three commutation moments. As it is shown, IGBT Q1 and diode
D2 have the most power losses during 120◦electric commutation period which
can be calculated from equation (5.4) and (5.5), respectively.
Ploss,Q2 =Pcon,IGBT +Psw,IGBT +f1·Eturnoff,IGBT (5.4)
Tab. 5.1: Power losses of components for each commutation state
Component Commutation
moment
60◦
elec.period
Commutation
moment
60◦
elec.period
Commutation
moment
conducting
IGBT Q1, Q6→Q2 Q1, Q2 Q2, Q1→Q3 Q2, Q3 Q2→Q4, Q3
Q2 Eon,IGBT =
0♣i=0
Pcon,IGBT, Psw,IGBT Eturnoff,IGBT
D3
Efw,D,
Eturn off,D =
0♣
di
dt≪kA
µs
————
Q6 Eturnoff,IGBT ————
D5 — Pcon,D, Psw,D
Efw,D,
Eturnoff,D = 0♣
di
dt≪kA
µs
Q1 — Pcon,IGBT Eturnoff,IGBT ——
D4 — —
Efw,D,
Eturn off,D =
0♣
di
dt≪kA
µs
——
Q3 — — Eturnon,IGBT =
0♣i=0 Pcon,IGBT —
Q4 — — — — Eturnon,IGBT =
0♣i=0
60
5.1. Design of voltage source inverter
Ploss,D5 =Pcon,D +Psw,D +f1·Efw,D (5.5)
where,
Efw,D is the free wheeling energy of the diode,
Eturnon,IGBT and Eturnon,IGBT is the energy of turn on and off of IGBT, respec-
tively,
Pcon,IGBT and Psw,IGBT is the conduction losses and switching losses of IGBT,
respectively,
Pcon,D and Psw,D is the conduction losses and switching losses of diode, respec-
tively.
Considering the complex of the control strategy of switching the switch IGBT
alternately from high voltage side to low voltage side, this control algorithm
is not adopted. This converter utilizes only one IGBT at the low voltage half
bridge as switching transistor. The total power losses of the integrated IGBT
module can be derived from equation (5.6) and is dependent on the duty cycle.
PIGBT_module =6 ·PCM +Ploss,60◦
= (6 ·f1(Efw,D +Eturnoff,IGBT)
+(δPcon,IGBT +Psw,IGBT + (1 −δ)Pcon,D +Psw,D +Pcon,IGBT))
(5.6)
Where, δis the duty cycle.
The total power losses of IGBT module at worst working condition is consid-
ered. Assuming that the value of the duty cycle nearly 100 % and the switching
frequency 25 kHz, and the maximum peak phase current 30 A were chosen. Efw,D
is negligible. Therefore, the total losses of IGBT module is 156.6 W. The largest
power losses of one IGBT is 103.03 W and 53.98 W for diode. Based on the ther-
mal resistance of IGBT and diode, the temperature rise from the junction point
to the case of the IGBT ∆Tj-c,IGBT and to the case of diode ∆Tj-c,D is 51.55 K and
37.786 K.
5.1.3.4 Gate drive resistor losses
High switching frequency is required and essential for sensorless control in this
application. In general, the gate resistance value should be selected based on
the range given in the IGBT data sheet. A smaller gate resistor Rgwill lead to
lower switching losses, but results in higher di/dtand dv/dtthat lead to larger
voltage overshoot and EMI emissions. Therefore, it offers less ruggedness and
requires thoughtful layout design. [80] suggests that twice of the gate resistance
value used inside the IGBT’s data sheet is selected as a good starting point for
optimization.
Further, the driver must be able to support the peak gate current Ig,max which
can be derived from the following equation (5.7).
Ig,max = (Uon −Uoff)/Rg(5.7)
61
where Uon,Uoff is IGBT turn on and turn off gate drive voltage, respectively. Ig
is the average current through the gate resistor for each polarity of the current
and calculated as given in (5.8):
Ig=Q·fsw (5.8)
where Qis the electric charge transfer during IGBT turn-on or turn-off. The
maximum value of drive current can be obtained from the driver manual [81].
Since a driver can only support a maximum average gate current, this will lead
to a limitation of the switching frequency for a given power device.
Considering the above discussion, the gate drive resistance is chosen Rg= 20 Ω
here which is twice of the minimum gate resistor value from the data sheet. The
power losses on Rgare independent on resistance value and can be calculated
from equation (5.9).
Pg,upper =Q(Uon −Uoff)(fsw +f1)
Pg,lower =Q(Uon −Uoff)f1
(5.9)
where Pg,upper and Pg,lower is the power losses of gate resistor with PWM and
without PWM, respectively, f1is the fundamental frequency. In this system,
Pg,upper is 0.339 W and Pg,lower is 7.1 mW.
5.1.4 Cooling system
In the power electronic system, semiconductor devices are one of the major loss
sources and the cooling system contributes to the total volume [82].
Several types of cooling methods and technologies (e.g. natural cooling and
forced convection cooling) have been developed in the past [83] [84]. Due to its
simple structure, mounting way and low cost, the finned aluminum cooling heat
sinks are the most commonly used heat sinks in power electronic converters and
also adopted in this application.
The size of the contact area of the power electronics module to the heat sink and
the power of the DC fan are two important factors to ensure that the cooling
system works under optimum condition.
The proper design is to guarantee the heat generated from IGBT module can be
dissipated through the temperature difference between the surface of the IGBT
module and aluminum contact of finned heat sink.
∆Theat_sink ≤Tjunction_max −∆TIGBT_module −TAmb (5.10)
where,
∆Theat_sink is the maximum temperature rise for the heat sink,
Tjunction_max is the maximum junction temperature in IGBT,
62
5.1. Design of voltage source inverter
∆TIGBT_module is the temperature rise of IGBT module,
TAmb is the ambient temperature.
The temperature rise of IGBT module should be calculated under the worst
working condition which produces the maximum power losses, as showed in
equation (5.11).
∆TIGBT_module =Rth(j - s)PIGBT_module (5.11)
Therefore, the thermal resistance of the heat sink can be calculated:
Rth(heat_sink) ≤∆Theat_sink/PIGBT_module (5.12)
where the temperatures are in Kelvin.
Based on equation (5.12), the thermal resistance (0.25 K/W) of the finned heat
sink Rth(heat_sink) is chosen for as the results of the combination of the area of
heat sink and the fan power [85].
Considering the lab environment, the ambient temperature 40◦C is selected, the
temperature rise of the IGBT module is 25.75 K. Based on the temperature rise
of IGBT and diode, the maximum junction temperature of IGBT and diode at
the worst working situation is 117.3◦C and 103.75◦C which are smaller than the
maximum temperature (125◦C) that component can withstand.
Although the converter and cooling system are designed for lab test, the thermal
resistance((0.25 K/W)) of heat sink for IGBT module is also calculated working
under 20 km altitude. It is based on the calculation method of the thermal
resistance of the heat fin in section 4.6. Obviously, the heat emission condition
of this converter is not feasible working at 20 km.
5.1.5 Isolation design of PCB
The main electronic Printed Circuit Board (PCB) has to include the following
functions: the sampling circuit of the three phase voltages and the DC-link
voltage for the sensorless control strategy, a Hall sensor sampling circuit for the
sensor based control, a detachable microcontroller board connection, the phase
current sensors sampling hardware for the control strategy, the driver for the
IGBT module, and over-current/over-temperature protection circuits.
Because of the comparatively high voltage of 270 V for the power circuit, a failure
occurring during operation can easily lead to serious consequences, which can
even be life−threatening. Therefore the isolation design of this power circuit
from the electronic circuit is critical.
According to IEC 60664, the clearance is achieved by keeping a minimum dis-
tance 0.5 mm and minimum creepage is 1.6 mm. In Fig. 5.6 the blue plane in
the center and the signals inside or on top of this plane (blue for bottom, red
for top layer on PCB) belong to the control system. All other signals are from
the 270 V power system. Any components connected across this gap incorpo-
rate isolation: the isolated DC/DC converter, optical isolators for analog signals
63
(as described in detail in the following section) and isolated current transducers
for phase currents and DC current measurement. The outer blue area near the
outside of the PCB provides ground for the primary side of the voltage isolation
circuit. These circuits are supplied by a dual output DC/DC converter.
5.2 Sensorless control strategy
The schematic control system is shown in Fig. 5.5. It has not only a Hall sensor
circuit, but also a sensorless control strategy to increase the reliability of the
control system.
Fig. 5.5: Schematic of control system
64
5.2. Sensorless control strategy
15.01.2019 18:41:09 D:\2_Doctoraldissertation\dissertation\dissertationrong\5inverter\20.04.2015.new.schematic lpf_2.brd
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4.7pF
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RG1
RG2
RG3
RG4
RG5
RG6
C5
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U-IN V-IN W-IN
DC-OUT
DC-IN
U-OUT
V-OUT
W-OUT
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R72
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R7
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U1
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D1
D2
D3
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R12
R33
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R81 R82
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C38 C20 C24 C28 C29 C33
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C42
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R14
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R16
R8
C47
C48
R15
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R13
R6
R59
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R79
C50
C52
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R4
R11 R49
RVCET1 RVCET2 RVCET3 RVCET4 RVCET5 RVCET6
R54
C54
R18
R61
R9
C4
R55
R17
C15
C16
R57
R58
C22
R62
C17
R63
C6 R26
R25
R24
R22
C1
C3
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R21
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R29
R30
R31
R34
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C26
C25
R36
R64
R37
C30
R38
C31
C39
R48R47
R51
R46
C34
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R45
R44
R43
R41
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C23
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C57
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LM311N
CNY17
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CNY17
5k
787k
10k
IL300 IL300 IL300 IL300
78.7k
1.15k
1.15k
78.7k
1.15k
5k
5k
5k
5k
LM317KCT
LM337KCT
1N4004
1N4004
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240
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240
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10uF
16nF
10k
4.7nF
47nF
10k
4.7nF
47nF
20k
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10k
4.7nF
47nF
20k
20k
47nF
4.7nF
10k
1uF
976
3.3k
3.3k
3.3k
3.3k
16nF
16nF
10k
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383
1.6k
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51
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4.99k
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3.3k
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330pF
22pF
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499
30k
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4.7pF
4.7pF
4.7pF
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4.7pF
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MKDSN1,5/3-5,08
NEWEASYKIT
1uF
383
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LTC6247IMSPBF
LTC6247IMSPBF
LTC6247IMSPBF LTC6247IMSPBF LTC6247IMSPBF
LTC6247IMSPBF
22uH
Fig. 5.6: PCB schematic of high and voltages isolation(scaled)
A high speed, good linearity analog isolation circuit was designed to sample
the phase voltages of the motor and the DC-link voltage, which are required to
realize the sensorless control strategy.
This sensorless control strategy is using the combination of hardware and soft-
ware methods to detect the rotor position. The circuit has to transmit the
isolated terminal voltages U1-,U2- and U3- as well as the DC-link voltage UDC
to corresponding ADC inputs of the micro-controller. These voltages are re-
65
lated to the negative rail of the DC-link. When the measured voltage of the
floating phase crosses UDC/2, this coincides with the zero crossing of the corre-
sponding phase EMF and it can be used to identify the current rotor position.
With increasing speed, more accuracy is achieved due to the steeper gradient of
the sensed voltage, but less sample points per 60◦electric period will limit the
maximum achievable accuracy.
The waveform of a phase voltage UL(from Fig. 2.3)(relative to the negative rail)
including PWM is shown in Fig. 5.7. The voltages have to be sampled while the
PWM is in its on-period, but a delay after turn-on has to be taken into account,
to avoid the turn-on transient behavior. Therefore a minimum turn-on time has
to be present.
1/fPWM
UL-
1/fPWM
t
Q1_turn on Q6_turn on
0
Fig. 5.7: Phase voltage waveform with duty cycle
5.2.1 Concept of the sensorless circuit
The circuit has to fulfill two tasks. The first is to realize the galvanic isolation
for the analog voltage signals. The second task is to minimize the response time
of the PWM voltages, i.e. a rather high bandwidth is required.
The simple usage of an optocoupler is only sufficient for the first task. Therefore,
in this part the design of a fast analog isolation circuit (FAIC) with improved
response time will be presented.
The working principle is based on the linear optocoupler IL300. It uses a Light
Emitting Diode (LED) that is coupled optically to a servo PhotoDiode (PD)
and an output photodiode [86]. The device was designed for both photocurrents
to be proportional with low temperature coefficient. Therefore the servo PD is
used in a primary side feedback loop to enhance linearity and reduce drifting or
aging effects.
The IL300’s 130 dB common mode rejection ratio (CMRR), ±50 ppm/◦C stabil-
ity, and ±0.01 % linearity provide a quality link from the voltage to the controller
input including galvanic isolation, hence the IL300 was chosen for the isolation
circuit.
Although the photovoltaic topology (PD at zero voltage) of the IL300 offers the
best linearity, lowest noise and drift performance, the photoconductive photodi-
ode operation (PD reverse biased) provides a larger frequency bandwidth which
is desired in the circuit.
66
5.2. Sensorless control strategy
A:Transmission stage
Light emitting diodes have a nonlinear current to light power characteristic. In
order to realize a linear analog optical transmission system using light emitting
diodes and photodiodes, a feedback control can be applied. If a nonlinear system
is operated around a working point in a quite linear section of its characteristic
and inserted in a feedback loop control scheme, it can be considered as a linear
system [87]. Hence, a feedback loop is applied to connect the LED and servo
photodiode.
The servo photodiode (pins 3, 4) on the input side of the IL300 is optically
coupled to the LED and produces a current directly proportional to the light
flux falling onto its junction. It provides a feedback signal for a control loop
which is driving the current to the LED emitter (pins 1, 2). This technique
compensates for non-linear, thermal or aging problems of the light emitting
diodes.
The solution to meet the bandwidth requirements of the sensorless control sys-
tem is to add a PI controller in the feedback photodiode loop to control IP1, as
shown in Fig. 5.8.
Vin R9
R10
1
2
3
4
6
5
Vcc
Primary side of IL 300
IF
IP1
IP2
U1 U2
IL300
PI
Vout
Second side of IL 300
Fig. 5.8: Working principle diagram of the proposed circuit
A value of 25 kHz for the switching frequency was chosen to balance the following
two requirements in this application. The sensorless control strategy will be
applied only if the duty cycle is higher than 15 % which means the minimal turn
on time of one PWM period ton,min ≥6 µs. Assuming that the isolation circuit
behaves like a first order low pass with a time constant τ, a time constant of
τ=ton,min/3will settle to less than 5 % error during ton,min.
The working principle is explained according to the block diagram in Fig. 5.9.
The voltage to be measured is transmitted through a voltage divider to the first
fast operational amplifier U1, which is used as a difference amplifier. A second
fast operational amplifier U2 is used as PI controller. The output voltage of U2 is
applied to R9and becomes the LED current IF. Then the feedback photodiode
captures a part of the light flux of the LED and generates a corresponding
photocurrent IP1. The indicated time lag behavior is caused by the capacitance
of the photodiode in conjunction with the output resistor R10. Finally, IP1
leads to the desired output voltage across resistor R10.
This closed loop control improves both, the linearity and the response time.
67
U2: -1* PI -1/R9CTR
0.7%
R10
in
V
out
V
F
I
1P
I
U1
Fig. 5.9: PI Control model of the circuit
B:Reception stage
On the secondary side, the LED flux is also coupled to a photodiode. The output
current IP2 of this photodiode is amplified to satisfy the needs of succeeding
circuits. The value of the isolated voltage is limited to the supply voltage of
U3. The ratio of IP1/IP2 varies from device to device, so for compensation an
adjustable amplifier gain was considered.
Based on the control model of the FAIC, the electrical circuit is shown in Fig.
5.10. By adjusting the resistance of R9, the primary LED current IF can be lim-
ited. The operational amplifiers U1 and U2 use a ±2.5V power supply. In the
reception stage, an adjustable resistance R11 is used to eliminate all gain vari-
ations throughout the circuit. The additional capacitors C1, C2 and C3 across
the input and output of the operational amplifiers are used for compensation to
avoid oscillations.
Fig. 5.10: Equivalent circuit diagram of fast analog isolation circuit
C:Transfer gain of circuit
At the transmission stage side, the relationship of LED drive to input voltage is
shown by combining equations (5.13),(5.14) and (5.15).
V1+ =V1−=V′
a(5.13)
where V1+ and V1−is the voltage of the inverting input and non-inverting input
of the amplifier U1, respectively.
IP1 =IFK1(5.14)
V1−=IP1
R10R5
R5+R7+R10
(5.15)
68
5.2. Sensorless control strategy
Equation (5.18) shows that the LED current is related to the input voltage V′
a. A
changing V1+ causes a modulation in the LED flux. The LED flux will change to
a level which generates the necessary servo photocurrent to balance the optical
feedback loop. The LED flux will be a linear representation of the input voltage,
V′
a. The servo photodiode’s linearity controls the linearity of the isolation IL300.
V1+ =IP1
R10R5
R5+R7+R10
(5.16)
V′
a=IFK1
R10R5
R5+R7+R10
(5.17)
IF=V′
a
K1R10R5
R5+R7+R10
(5.18)
At the secondary side, the output photodiode is also operated in the photo-
conductive mode. IP2 is derived from the same LED that irradiates the servo
photodetector. The output signal, VA, is proportional to the output photocur-
rent, IP2, times the resistance of parallel connections of R11 and R12 (R11,12).
VA=Ip2R11,12 (5.19)
Ip2 =IFK2(5.20)
Combining equations (5.19) and (5.20) and solving for IFresults in equation
(5.21).
IF=VA
K2R11,12
(5.21)
The voltage divider at the input gives:
V′
a=Va
R2R4
R1R2+ (R1+R2)(R3+R4)(5.22)
The input-output gain of the isolation circuit is determined by combining equa-
tions (5.18),(5.21), and voltage divider equation (5.22), as shown in (5.25).
VA
Va
=K2
K1
·R11,12
R10R5
R5+R7+R10
·R2R4
R1R2+ (R1+R2)(R3+R4)(5.23)
K3is the transfer gain of the IL300. It describes the relation of the input-
output photocurrents of the device. The transfer gain is calculated as the output
(forward) gain, K2, divided by servo gain, K1, as shown in equation (5.24). That
leads to the final equation for the transfer gain of the isolation circuit in equation
(5.25).
69
0 2 4 6 8 10 12 14 16 18 20
−10
−5
0
5
10
15
20
25
−IF [mA]
time [µs]
(a) full scale plot
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
12.5
12.6
12.7
12.8
12.9
13
13.1
13.2
−IF [mA]
time [µs]
13mA
(b) detailed plot
Fig. 5.11: Simulated step response curve for primary side current IF
K3=K2/K1(5.24)
VA
Va
=K3·R11,12
R10R5
R5+R7+R10
·R2R4
R1R2+ (R1+R2)(R3+R4)(5.25)
5.2.2 Verification of the sensorless circuit
The model of the circuit was build in LTspiceIV and is used to simulate the
performance and response behavior of the isolated circuit. For the amplifier
dual LTC6247 (Analog Devices), providing two high speed unity gain stable
rail-to-rail input/output operational amplifiers [88], were applied.
The emitting current IFat rated input voltage is chosen depending on the max-
imum current allowed through the emitting diode of IL300 and the maximum
output sinking current of the LTC6247. However, this current is further limited
to less than 20 mA because the best linearity of IL300 will be obtained at drive
currents between 5 mA to 20 mA.
Then, in order to ensure the servo photodiode is operated with negative voltage
bias, the voltage across R10 must be smaller than the power supply voltage of
the servo photodiode of +2.5 V.
The IL300 eliminates the problems of gain nonlinearity and drift induced by
time and temperature, by monitoring the LED’s output flux. A smaller IFcould
decrease the effect of above factors. Considering all factors, IFwas chosen to be
around 13 mA at rated input voltage.
70
5.2. Sensorless control strategy
0 1 2 3 4 5 6 7 8 9 1011121314151617181920
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
time [µs]
voltage [V]
V’
a
VIP1
VIP2
(a) voltage waveform
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
−20
0
20
40
60
80
100
120
140
160
180
200
220
time [µs]
voltage [mV]
V’
a
VIP2
205.5mV
(b) input and output voltage waveform
Fig. 5.13: Simulated voltage waveform in LTspiceIV
0 2 4 6 8 10 12 14 16 18 20
0
10
20
30
40
50
60
70
−IP1 [µA]
time [µs]
Fig. 5.12: Simulated servo current response waveform
The input voltage in the simulation has a voltage step up to the rated voltage
at 2 µs, the corresponding response curve of primary side IFis shown as in Fig.
5.11. Fig. 5.11(b) shows that the current response value 3 µs later at 5 µs is equal
to 13 mA , i.e. within 1 % error of the stable value of 13.12 mA and therefore it
meets the design time requirements.
The maximum voltage across R10 is 0.231 V, which makes sure, that the servo
diode is working in photoconductive mode. At the same time, the photocurrent
IP1 is roughly -63 µA, as shown in Fig. 5.12.
Fig. 5.13(a) shows the relationship between input voltage and the response
behavior of servo feedback and secondary output voltages. In Fig. 5.13(b) the
output voltage VIP2 at 5 µs is 205.5 mV which is 1 % error compared with the
final value of 207.66 mV.
71
The measured response curves of the input and output signals are shown in
Fig. 5.14. The yellow curve represents V′
aafter the voltage divider, which is
transmitted to the non-inverting input of operational amplifier U1. The green
signal VIP2 is the output of the operational amplifier U3. The response time is
roughly 3 µs and therefore meets the requirement. The output signal has the
desired response speed and also meets the requirement of the input signal range
of the ADC inside the microcontroller.
Fig. 5.14: Input and output voltage response waveform
5.2.3 Temperature drift behavior
The temperature drift behavior of the electronic devices affects the accuracy of
the control for sensorless strategy. The main components of the sensorless circuit
are the amplifier and optocoupler. Based on the information of the temperature
drift in the data sheet, the effect is discussed here.
The input offset voltage drift of this amplifier is −2µV/◦C. The non-inverting
input voltage VIP1 of the amplifier U1 is 206 mV shown in Fig. 5.13. When
the change of the temperature is 100 K, the temperature drift effect is 0.1 %.
The inverting input signal of the amplifier U1 is from the output of the surface
mounted voltage resistor divider. The temperature coefficient of the surface
mounted resistor is around ±50 ppm/K and has less effect of temperature.
The transfer gain stability K3 of the optocoupler is ±0.5 % at IF= 10 mA when
the change of the temperature is 100 K.
Therefore, the effect of temperature on the sensorless circuit can be neglected.
72
5.3. Summary
5.3 Summary
A 3 phase full bridge inverter for controlling the BLDCM was designed and
built up. It was configured to allow for 200 % of rated load at standstill. It
includes the BLDC control strategy of 6 commutation states based on Hall
sensor signals, and incorporates over-temperature, over-voltage and over-current
protection circuits.
For sensorless control, a fast isolation circuit for phase- and DC-voltages was
realized and characterized. By designing the working current of the primary side
in the most suitable linear working area of the optocoupler and implementation
of the feedback loop for the photodiode light flux, it improves the linearity
of the analog signal significantly. A PI controller is applied in the feedback
circuit to ensure a response time suitable to follow the PWM modulated voltage
sufficiently fast, to allow for the sensorless control method.
73
6 Analysis of acoustic noise
Vibration and noise of electric machines have been studied extensively [89][90].
Acoustic noise up to 20,000 Hz could be harmful to human hearing [91][92]. The
acoustic noise sources of an electrical machine are mainly classified as magnetic,
mechanical and aerodynamic sources [93][94][95], as shown in Figure 6.1.
Several researchers applied improved control strategies to avoid exciting and
reinforcing the mechanical resonances [96]. [97] proposes high-order sliding mode
(HOSM) controllers, combined with the vector control method to improve the
dynamic performance of the excitation current and the motor speed.
However, stator vibration due to electromagnetic force is the dominant noise
source of the acoustic noise sources [98]. [92] derived an analytical model to
study the radial displacement of the stator and verified that noise and vibration
is caused by the stator teeth due to the radial electromagnetic force rather than
torque ripple and cogging torque. The intensity of acoustic noise is related to
the circumferential mode shapes, frequencies, and the magnitude of magnetic
radial force [99]. [93] examines the effect of a stator frame on the acoustic noise
and vibration.
Noise
Sources
Magnetic
Radial
Harmonics
Magnetic
Unbalance
Mechanical
Auxiliaries
Load Induced
Aerodynamic
Air Flow, etc...
Radial
Slot
Harmonics
Magnetic
Unbalance
Self
Stator Modes of
Vibration
Rotor
Bearings
Balancing Dynamic
Eccentricity
Static
Eccentricity
Auxiliaries
Load Induced
Couplings
Foudation
Air Flow, etc...
Unbalanced
Rotor
Elliptical
Rotor Surface
Fig. 6.1: Classification of noise sources [100]
This chapter focuses on the vibration and noise of BLDCM with two different
IPM rotor structures, which will be mainly divided into two parts. The first part
is dealing with acoustic noise caused by the electromagnetic force. The other
important reason of acoustic noise is the amplification by dynamic response
74
6.1. Electromagnetic source
of the motor structure. Therefore, the natural mode analysis is essential for
predicting the mechanical noise and was studied in the second part.
6.1 Electromagnetic source
The electromagnetic force produced by magnetic flux exists between magnets
and stator teeth, including components in both tangential and radial directions.
However, the main source of electromagnetic vibration and noise is the radial
force from air gap magnetic field to the stator teeth which is transmitted to
the stator surface. This radial force is generated by both, the magnetic field
from the rotor and the armature reaction from the load current. The tangential
electromagnetic force will provide the torque to drive electric machine.
The electromagnetic radial force generated in the air-gap have an effect on both
the stator and rotor. Since the rotor has a regular shape which means more
stiffness and less susceptible to the force, the noise is mainly produced by stator.
The radial force is distributed on the stator teeth which have less mass and
stiffness. Furthermore, the vibrations are also transmitted to the whole yoke
and housing structure.
6.1.1 Calculation of the electromagnetic force
The radial electromagnetic force is determined by the magnetic flux density.
Different arrangements of the embedded magnets generate distinguishing wave-
forms along the air gap, as shown in Fig. 3.15. This section will analyze the
difference between the electromagnetic forces of the motor with 8 magnet blocks
and the motor with 4 magnet blocks.
6.1.1.1 Two calculation methods for the electromagnetic force
There are two common methods to calculate the electromagnetic force [101].
The electromagnetic force is always represented by using the Maxwell stress
tensor [102] or force density [103].
A: Stress tensor method
Since the electrical forces can be neglected in electrical machines: E=0, only the
magnetic force density
→
fmcomponents is calculated in cylindrical coordinates in
equation (6.1) [104].
→
fm=∇ · Tm−H2· ∇µ(6.1)
The calculation of the electromagnetic force uses Maxwell’s Stress Tensor Tm.
→
F=∏︁
∐︂
Fx
Fy
Fz∫︁
ˆ︁=∫︂∫︂∫︂Vdiv(Tm)dV =∫︂ATmd→
A(6.2)
75
Fig. 6.2: Integration paths of edge force density method on one tooth
where the magnetic tension tensor Tmis the non-dispersive part of
→
fm,
Tm=µ·⋃︁
⋁︁
⋁︁
⨄︁
H2
x−H2
2Hx·HyHx·Hz
Hy·HxH2
y−H2
2Hy·Hz
Hz·HxHz·HyH2
z−H2
2
⋂︁
⎥
⎥
⋀︁(6.3)
Since 2D stator modal is used to simulate the electromagnetic forces, the force
density fmis only available in Maxwell 2D FEM. It is available only on object
outlines adjacent to air vacuum space, as defined as:
fm=1
µ0
n·⎟B2
x−B2/2BxBy
BxByB2
y−B2/2⟨︂(6.4)
where nis the outward normal direction of the edge.
B: Force density method
Force density
→
fis defined as derivation of the electromagnetic force on the stator
volume V. The total electromagnetic force →
Fcan be expressed as in equation
(6.5).
→
F=∏︁
∐︂
Fx
Fy
Fz∫︁
ˆ︁=∫︂∫︂∫︂V
→
f dV (6.5)
Based on the x- and y-components of the electromagnetic force density, the
electromagnetic forces on the stator can be derived from equations (6.6) and (6.7).
These forces will result by integration of the force density over the stator.
The radial electromagnetic force Frad and the tangential electromagnetic force
Ftan on one tooth can be estimated from the magnetic field in the air gap along
the purple line, as shown in Fig. 6.2.
Frad =⌊︂(fxcos ϕ+fysin ϕ)dl(6.6)
Ftan =⌊︂(−fxsin ϕ+fycos ϕ)dl(6.7)
76
6.1. Electromagnetic source
(a) 4 magnet blocks
(b) 8 magnet blocks
Fig. 6.3: Meshing results
where ϕis the polar angle, fxand fyrepresent the x- and y-components of the
electromagnetic force density.
6.1.1.2 Comparison of FEM results
Since the edge force density is one of the default results from electromagnetic
field calculation in Maxwell and could be used to calculate a set of electromag-
netic forces of the motor, the edge force density method is used to calculate
electromagnetic force. The forces obtained by this method are imported to AN-
SYS Mechanical for subsequent analysis on frequency response, vibration, and
acoustic noise.
Assuming the magnetic flux does not change along the axial direction and the
electromagnetic forces are primarily distributed in radial and tangential direc-
tion, a 2D FEM model is sufficient for this study. Due to the symmetry of the
traditional and the proposed machine, 1/4of the motor structure has been built
to represent the whole BLDCM.
The quality of the mesh impacts the accuracy of the result. In order to get an
FEM force result of higher precision, the air-gap was divided into 3 layers to get
a sufficiently fine mesh and therefore more accurate results.
Since the electromagnetic forces act directly on the surface of the stator teeth, a
finer mesh with a maximum size of 0.25 mm has been selected at their surface, as
shown in Fig. 6.3. The maximum mesh size of stator, coil, rotor and permanent
magnet was defined as 5 mm, 1 mm, 5 mm and 2 mm, respectively.
Fig. 6.4 shows the distribution of the radial electromagnetic force on three ad-
jacent stator teeth when the motors run at rated load situation. The maximum
electromagnetic force occurs when the axis of the magnet is aligned with a stator
tooth.
During the rated load situation, FEM simulated electromagnetic force in radial
and tangential direction on a stator tooth for both motors is shown in Fig. 6.5.
The magnitude of radial and tangential force differ dramatically and the value
of the radial force is much larger than the tangential force. The radial force is
the main reason to cause the deformation of the stator, vibration and acoustic
noise and the tangential forces mainly cause torque ripple.
77
(a) 4 magnet blocks
(b) 8 magnet blocks
Fig. 6.4: Electromagnetic force density distribution along the stator teeth
0 60 120 180 240 300 360 420 480 540 600 660
−200
−180
−160
−140
−120
−100
−80
−60
−40
electrical angle [°]
radial electromagnetic force [N]
4 magnet blocks
8 magnet blocks
(a) radial force
0 60 120 180 240 300 360 420 480 540 600 660
−14
−12
−10
−8
−6
−4
−2
0
2
electrical angle [°]
tangential electromagnetic force [N]
4 magnet blocks
8 magnet blocks
(b) tangential force
Fig. 6.5: Comparison of electromagnetic force on a stator tooth vs. rotor position
78
6.1. Electromagnetic source
The comparison of the radial force on a stator tooth for the two different mag-
netic structures is shown in Fig. 6.5(a). The radial force of the conventional
8-8 structure has 180◦symmetry and equal minimum absolute values of 73.0 N.
However, due to the distribution of flux density, the proposed 4-8 rotor structure
has two different minimum values, which are 49.1 N and 59.5 N. Both machines
have a rather similar maximum radial force, which is 173.7 N for the 8 magnets
rotor and 181.6 N for the 4 magnets rotor. It is more important and shows that
the poles of electromagnetic force is 1 in the proposed motor and 2 for the con-
ventional rotor structure. The tangential electromagnetic force to produce the
output torque is shown as in Fig. 6.5(b) .
In conclusion, the force difference of the radial force is slightly larger in the
machine with the 4 magnets rotor. Therefore the vibration in the machine with
4 magnet blocks will be larger.
6.1.2 Vibration analysis of the motor
In the preceding part, it was discussed that the radial electromagnetic force is
the main reason to cause the vibration of the electrical machine. Despite the
deformation of the stator structure caused by the force will affect the magnetic
field, only weak coupling between the electromagnetic forces and mechanical
movement can be assumed without loosing precision. Noise emission into the
surrounding medium is the result of the vibration. In order to analyze the
acoustic behavior of the electrical motor, the vibration caused by force variations
on the teeth of the stator is analyzed in this section.
The forced vibration analysis is the essence to evaluate the vibration character-
istics of the machine. The acceleration and velocity of the vibration are caused
by the excitation through the node force F, as expressed in equation (6.8).
[M]¶x¨(t)♢+ [C]¶x˙(t)♢+ [K]¶x(t)♢=¶F(t)♢(6.8)
where [M],[C],[K]are the mass, damping and stiffness characteristics. x¨(t),
x˙ (t),x(t)are the acceleration vector, velocity vector and displacement vector of
each node. This equation is the basis for the 3-D FEA mechanical analysis, in
which the radial electromagnetic forces act on the stator teeth.
6.1.2.1 FEM procedure
As shown in Fig. 6.6, the first step of the FEM process for motor vibration
analysis is to derive the electromagnetic force density from MAXWELL. After-
wards the force density in frequency domain is applied to the teeth of 3D stator
stack model. With ANSYS MECHANICAL, the frequency response and defor-
mation of the stator of the electromagnetic force on each tooth can be extracted.
The last step is to use the above results and calculate the subsequent acoustic
behavior.
79
FEM Machine
Modelling
Electromagnetic
Forces Simulation
Harmonic Excitation
Force Calculation
Harmonic Response
Vibration Simulation
Acoustic
Pressures Extraction
Fig. 6.6: Flow chart for vibration and noise prediction
Owing to the inner interaction and processes in ANSYS Workbench (see Fig.
6.7), the solutions achieved in Maxwell are transformed from time domain to
frequency domain by FFT. Afterwards, a harmonic analysis can be conducted
which helps to determine the steady state response of a structure to harmonic
loads. As a result, harmonic displacements at each Degree Of Freedom (DOF)
are generated along with frequency responses. Additionally, sound pressure level
result at corresponding frequencies is obtained by applying the acoustic exten-
sion. During the simulation, the entire model is assumed to have constant stiff-
ness and mass.
Fig. 6.7: FEM Simulation steps
80
6.1. Electromagnetic source
6.1.2.2 Simulation results
The electromagnetic radial and tangential forces were simulated under the rated
load situation of both BLDCMs and the time characteristic of these forces are
shown for one tooth in Fig. 6.5. The force density distribution of the inner
surface of the stator in time domain is applied as the excitation. Fig. 6.8 and Fig.
6.9 show the harmonic components of the radial and tangential electromagnetic
excitation force of one tooth. The radial force dominantly leads to the vibration
of the motor. During the rated load working condition, the frequency of the
electromagnetic excitation force is mainly located in the range of 0-20 kHz.
0 1 2 3 4 5 6 7 8 9 1011 1213 1415 1617 1819 2021 2223 2425 2627 2829 30 31 3233 34 35 36 37 38 39 40
10−5
10−4
10−3
10−2
10−1
100
101
102
103
harmonics
log| Frad | [N]
4 magnet blocks
8 magnet blocks
Fig. 6.8: Radial electromagnetic excitation force in the frequency domain on one tooth
Furthermore, it is shown in Fig. 6.8 that the interaction of the rotating rotor and
the armature reaction of the stator winding leads to main components located
at even order harmonics. Due to the 8-8’s 180◦periodicity, odd order harmonics
are very small for this design. For the 4-8 design, odd order harmonics are
present at low amplitudes, that are roughly one order of magnitude smaller
than surrounding even order harmonics.
0 1 2 3 4 5 6 7 8 9 1011121314 1516171819 2021 22 23 24 25 26 27 28 29 30 31 32 3334 35 36 37 3839 40
10−4
10−3
10−2
10−1
100
101
102
harmonics
log| Ftan | [N]
4 magnet blocks
8 magnet blocks
Fig. 6.9: Tangential electromagnetic excitation force in the frequency domain on one tooth
81
The electromagnetic force simulations are based on a 2D machine model. The
calculation result of the electromagnetic force from last Maxwell FEM is coupled
to MECHANICAL for harmonic response analysis in the frequency domain and
applied to the surfaces of the teeth of the 3D stator model. Fig. 6.10 shows that
the direction of electromagnetic forces applied to the stator teeth.
Fig. 6.10: Application of electromagnetic forces to the 3D mechanical stator model
Total Deformation
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Fig. 6.11: Total deformation of the stator(mm) effected by 4 magnet blocks rotor at
11200 Hz
82
6.1. Electromagnetic source
The frequency response of the harmonic response analysis at the rated working
point is shown in Fig. 6.12 and Fig. 6.13 for both motors. The interaction under
the excitation of the radial and tangential forces, the maximum acceleration of
the stator occurs at a frequency of 11200 Hz for the motor with 4 magnet blocks,
which is the 21st harmonic.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
100
200
300
400
500
600
Amplitude [mm/s²]
frequency [kHz]
11200Hz
Fig. 6.12: Vibration spectrum on stator with 4 magnet blocks
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
100
200
300
400
500
600
Amplitude [mm/s²]
frequency [kHz]
11741Hz
10673Hz
Fig. 6.13: Vibration spectrum on stator with 8 magnet blocks
6.1.2.3 Resonance condition
Since the poles of the electromagnetic forces for the motor with 4 magnet blocks
is 4 in 360◦mechanical angle, the mode shape of 4k(k= 1,2,3· · · · · · · · · )may
cause the resonance. By that analogy, the mode shape of 8k(k= 1,2,3· · · · · · · · · )
for the motor with 8 magnet blocks may cause the resonance.
In order to avoid certain operating speeds at which could cause strong resonance,
the corresponding speeds for the harmonic orders at different mode shapes of
stator are given in Tab. 6.1.
83
Tab. 6.1: The relationship of speed and resonance frequency
Mode shape 0 2 3 4 5
Frequency of mode shape fr(Hz) 16,928 2,366 6,340 11,330 16,534
Harmonic order gSpeed(rpm) n=fr/p/g
1 253,920 35,490 95,100 169,950 248,010
2 126,960 17,745 47,550 84,975 124,005
3 84,640 11,830 31,700 56,650 82,670
4 63,480 8,873 23,775 42,488 62,003
5 50,784 7,098 19,020 33,990 49,602
6 42,320 5,915 15,850 28,325 41,335
7 36,274 5,070 13,586 24,279 35,430
8 31,740 4,436 11,888 21,244 31,001
9 28,213 3,943 10,567 18,883 27,557
10 25,392 3,549 9,510 16,995 24,801
· · ·
21 8,093
As it is shown, during the speed varies from 0–8000 rpm, the motor with 8
magnet blocks does not cause any resonance. However, the motor with 4 magnet
blocks cause the weak resonance under the rated working point (8000 rpm) at
21th harmonic order. Fig. 6.11 shows the deformation of the stator with 4
magnet blocks at 11,200 Hz. Apparently mode shape r=4 is excited.
6.1.3 Acoustic noise performance
The vibration of the stator caused by electromagnetic force was simulated in
the former section. This vibration transmits energy to the air and generates
acoustic noise.
84
6.1. Electromagnetic source
6.1.3.1 FEM analysis
In order to study the acoustic noise, an air model is necessary and has been set
up in ANSYS, as shown in Fig. 6.14(a).
(a) Air model
Radiation boundary
One way coupling
(b) Meshing results
Fig. 6.14: Acoustic performance in the air model
Fig. 6.14(b) shows that the inner contact area of the air model encircles an
empty cylinder which has the same outer diameter as the stator model. This
entire geometry is defined as ’acoustic body’.
As presented in Fig. 6.8, the electromagnetic radial forces have less impact for
frequencies beyond 5 kHz. The element size of the air model should be less than
a quarter of the sound wave length. Hence, with the purpose of analyzing the
acoustic frequency range below 5 kHz, the mesh size was set to 17 mm. This
geometry is divided into six parts to perform sweep method meshing of the
extended outside of the stator.
For the rated operation situation, the excitation obtained from FEM harmonic
response have been coupled to the interior of the air model for a ’one way
coupling analysis’.
85
Acoustic Pressure
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(a) 4 magnet blocks at 11200 Hz
Acoustic Pressure
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(b) 8 magnet blocks at 11740 Hz
Fig. 6.15: Acoustic performance in the air model
Since the fourth natural mode has been excited at the rated working point, the
maximum acoustic pressure of the motor with 4 magnet blocks and 8 magnet
blocks occurs at the frequency of 11.2 kHz and 11.7 kHz, respectively. These
points were analyzed in FEM, as shown in Fig. 6.15 for both rotor structures.
The acoustic pressure for the 8-8 structure is larger than the 4-8 structure,
which are 8.3·10−7MPa and 5.4·10−7MPa, respectively. There is also another
phenomenon, i.e. a vibration occurs also along the axial direction of the machine.
Here the SPL decreases from the contact surface of the stator cap to the end
edge of the air model. But the noise caused along the axial direction is much
smaller than the one based on the radial electromagnetic force.
An ’Acoustic far field microphone’ was placed at a 1 m distance from the center
of the air model to measure the sound pressure level, as shown in Fig. 6.16. Far
field is one of the boundary type in ANSYS which defines an open boundary
used to model free-stream compressible flow at infinity.
86
6.1. Electromagnetic source
Microphone(Test Point)
Fig. 6.16: SPL test setup
0 5 10 15 20 25 30 35 40 45 50
−20
−10
0
10
20
30
40
50
60
70
80
frequency [kHz]
SPL [dB]
4 magnet blocks
8 magnet blocks
Fig. 6.17: FEM SPL comparison of both magnet structures
Fig. 6.17 shows the simulated sound pressure level at 8000 rpm rated operation
for both motors. In general, the proposed machine has a larger noise level. The
loudest noise component of 58.6 dB occurs at f= 11.2kHz and is 9.1 dB larger
than the highest noise level of the conventional rotor. Because the amplitude
of harmonic response analysis for motor with 4 magnet blocks is 96.5 mm/s2
larger, it may produce higher noise. Moreover, the trend of the 8 magnet blocks
structure is smoother before it reaches its peak value.
87
0 5 10 15 20 25 30 35 40 45 50
−20
−10
0
10
20
30
40
50
60
70
80
f[kHz]
SPL[dB]
8715rpm
8002rpm
6002rpm
2001rpm
(a) 4 magnet blocks
0 5 10 15 20 25 30 35 40 45 50
−20
−10
0
10
20
30
40
50
60
70
80
f[kHz]
SPL[dB]
8598rpm
8002rpm
6002rpm
2004rpm
(b) 8 magnet blocks
Fig. 6.18: Experimental acoustic noise test of two motors at different speeds
0 5 10 15 20 25 30 35 40 45 50
−20
−10
0
10
20
30
40
50
60
70
80
f[kHz]
SPL[dB]
4−8
8−8
Fig. 6.19: Measured SPL comparison at rated working condition
88
6.2. Mechanical source
Under the rated working condition, the SPL of both motors were measured at a
distance of 1 m from the motor. The result is shown in Fig. 6.19. At frequencies
below 2 kHz the proposed 4-8 design has larger noise.
Fig. 6.18 shows the measured sound spectrum for each motor at different working
speeds. It can be seen that the sound of the surroundings in the lab has the
rather same sound level. Since the noise level of the motor is relatively low,
more accurate acoustic measurements were not conducted. Instead, some further
possible sources are investigated in the following paragraph.
6.2 Mechanical source
The mechanical source of noise and vibration is mainly caused by rotor eccen-
tricity and stator vibration. Due to a rotor unbalance, bearing or manufacturing
tolerances, eccentricity may occur. This will lead to a rotor displacement from
the center of the stator, which causes the air gap magnetic field to generate
destabilizing radial forces [105][106]. On the other hand, the electromagnetic
force applied to the stator may excite the circumferential mode shapes and nat-
ural frequencies of the stator, which cause additional acoustic noise.
6.2.1 Rotor unbalancing
During the manufacturing of the two rotors, one of the shafts became bent during
the press fitting process of the rotor lamination to the shaft. In order to reduce
the eccentricity, a rotor balancing test became necessary and was conducted.
Limited by the test speed , both rotors were tested at 4700 rpm. Based on this
balancing, operation up to about 10,500 rpm is covered. Since the rated speed is
about 8000 rpm, the result form the unbalancing measurement is adequate and
the hereby calculated mass removals were carried out on the rotor caps.
6.2.2 Modal analysis
The natural frequencies are one of the inherent characteristics of every particular
body at which the structure is excitable to vibrate. During the design process
of the machine, the natural frequency behavior needs to be considered. When
the harmonic frequencies of the electromagnetic force accord with some of the
natural frequencies, strong vibrations can be excited and thus noise emitted.
Therefore, it is necessary to analyze this characteristic.
6.2.2.1 Analytical calculation of natural frequencies
Since both BLDCM have the same stator, modal analysis is used to calculate
the natural frequency of this stator. In [107] an analytical method was used to
calculate the natural frequencies based on the natural vibration modes of the
stator yoke. The following assumptions are made in predicting the frequencies:
89
– the yoke part of the stator is a round rigid body
– the stator teeth and winding wound on them have no rigidity, which means
the mass is simply attached to the yoke
– the periodic magnetic force waves with rth order are symmetrically ex-
tended onto the stator yoke ring
– all defects and notches on the stator have only the effect of mass reduction.
The following equations are used to calculate the natural vibration frequencies
frfor the force wave with rth order:
fr=1
2π√︄kr
m(6.9)
where mis the equivalent mass per square meter (kg/m2)on the cylindrical
surface at the average yoke radius, which can be expressed by the following
formula:
m=Wt
2πRy,avLstk
(6.10)
and kris the equivalent spring stiffness coefficient per square meter on the cylin-
drical surface at the average yoke radius, expressed below:
kr=∏︂
⋁︂
⋁︂
⨄︂
⋁︂
⋁︂
⋃︂
Ehy
R2
y,av r= 0
kDr= 1
r2(r2−1)
r2+1
Eh3
y
12R4
y,av r≥2
(6.11)
where Eis the Young’s modulus, hyis the yoke height in the radial direction,
Ry,av is the average radius of yoke, kDis the spring stiffness coefficient of the
shock absorber under the motor (kD= 0 without absorber), Lstk is the effective
length of yoke in axial direction, ris mode number and Wtis the yoke mass.
The numerical parameters for the stator stack are shown in Table 6.2.
Tab. 6.2: Machine parameters
Parameter Value Unit
Average radius of yoke Ry,av 41.25 mm
Yoke height in radial direction hy7.5 mm
Length of yoke in axial direction Lstk 59.85 mm
Young’s modulus E1.85 ·1011 Pa
90
6.2. Mechanical source
The analytical results from the above simplified calculation are shown in Table
6.3.
Tab. 6.3: Analytical results of the resonance frequencies
Mode Natural frequency (Hz)
0 15,264.9
2 2,149.9
3 6,080.7
4 11,659
5 18,855
6.2.2.2 FEM calculation of natural frequencies
The stator is a more complex object which consists of complex functions of mass
and stiffness matrices that are not considered in the analytical model used in
the previous section.
With the aid of the structural finite element method, natural frequencies and
mode shapes of the stator lamination stack are calculated for a 3D finite element
model. In this modal analysis FEM simulation, no load constrain has been
added. [M]and [C]in the equation (6.8) are real symmetric matrices of the
linear system. Hence, the displacement vector of each node x(t)can be expressed
as:
¶x(t)♢=¶ϕ♢cos(ωt) (6.12)
where ¶ϕ♢is the eigenvector and ωis the corresponding frequency. From (6.8)
and (6.12), the motion equation for an undamped system can be expressed in
the following matrix notation when the free vibration is periodic:
([C]−ω2[M])¶φ♢= 0 (6.13)
As hexahedral elements can guarantee free deformation in all degrees of freedom,
the sweep meshing method has been used to achieve hexahedral elements which
are more accurate compared with a default tetrahedral meshing method. To get
a systematic meshing result, the whole stator structure has been divided into
substructures, as shown in Fig. 6.20.
91
Fig. 6.20: 3D Meshing of stator [100]
In Fig. 6.21 the skewness of mesh metrics after meshing is shown on the x-
axis. The skewness represents the evaluation of the meshing quality. A smaller
value of the skewness describes better meshing results. The final meshing metric
skewness has an average value of 0.139. The mesh metrics are shown below in
Fig. 6.21. ’Hex20’ and ’Wed15’ stand for hexahedral and prismy elements.
The hexahedron is the most regular shape and easy to accurately solve. Using
hexahedron for meshing, the number of units and nodes is reduced compared
to prismatic elements, thus it will save computing time and resources to use
hexahedrons dominantly.
Fig. 6.21: Skewness of mesh metrics [100]
The FEM simulation results for the dominant mode shapes and resonance fre-
quencies are shown in Fig. 6.22.
6.2.3 Resonance frequency measurement
To validate the computed results of the numerical models above, a resonance
frequency experiment was carried out. Several researchers used the electrical
92
6.2. Mechanical source
acceleration measurement with a certain frequency and sensitivity [108]. Since
the magnitude of the excitation does not effect the value of the natural frequency
and the procedure of the hammer excitation is much simpler compared to the
shaker excitation test, a simple impact hammer testing was conducted. The
impact produces an impulse force to excite the structure over a broad frequency
range.
6.2.3.1 Test setup
The Measured Object (MO) includes not only the stator stack, but also the coils,
housing and an additional aluminum ring placed between housing and stator.
A corresponding FEM model, shown in Fig. 6.23(a), was built to simulate the
actual structure shown in Fig. 6.23(b). Since the surface bodies that lie on top
of each other will have a gap between the midplanes, a setup to employ with
bonded contact across a gap between surface body midplanes was used in FEM
analysis.
During the test, the structure was hanging upside down on a thread attached
to the mounting feet of the housing. The hammer was used to apply a radial
direction impulse. The resonance sound was recorded by a microphone placed
at the opposite side of excitation side.
93
(a) mode=0, f=16,298 Hz
(b) mode=2, f=2,366 Hz
(c) mode=3, f=6,340 Hz
(d) mode=4, f=11,330 Hz
(e) mode=5, f=16,534 Hz
Fig. 6.22: 3D mode shapes and frequencies
94
6.2. Mechanical source
(a) Measured Object
(b) 3D FEM model[100]
Fig. 6.23: Test stator parts
AR
mode 2
1097Hz
MO
mode 2
1367Hz
SS
mode 2
2293Hz
MO
mode 4
2687Hz
Fig. 6.24: Sound spectrum of impact hammer testing [100]
6.2.3.2 Test results
Several tests have been performed to minimize the errors. The sound signal
spectrum after FFT transform is shown in Fig. 6.24. Some mode frequencies can
be identified from the spectrum. The ’mode=2’ of the Aluminum Ring (AR) and
Stator Stack (SS) are clearly showing as peak values. In Table 6.4 the analytic,
FEM simulation and test results are compared. As expected, the analytic results
show the largest deviation, which are 21.2 % and 10.2 %. The large deviation for
95
the 3D FEM and test results for the aluminum ring may be due to the damaged
stator housing which was repaired using resin glue between stator housing and
aluminum ring. The remaining 3D FEM results have relatively small deviation
to the test results.
The 2 and 4 mode of the measured object have also been detected in Fig. 6.24.
The whole measured object is a complex structure containing different parts,
that were modeled in a 3D FEM model. The natural frequency comparison of
this structure is also shown in Tab. 6.4.
Tab. 6.4: Natural frequency results comparison
Natural frequency(Hz)
Structure Part Mode Analytic method 3D FEM Test
Aluminum Ring (AR) 2 864.7 (21.2 %) 912 (16.9 %) 1097
Stator Stack (SS) 2 2,149.9 (10.2 %) 2,364 (1.2 %) 2,393
Measured Object (MO) 2 N 1,372.2 (0.38 %) 1,367
4 N 2,843.3 (2.7 %) 2,766.4
Comparing to 3D FEM results, the experimental values of the measured object
have 0.38 % and 2.7 % deviation for 2 mode and 4 mode, respectively. The
difference may come from the simplification of the model. The coils part were
just simplified as solid entity and the end coils were also considered. Further,
the connection box and the cooling fins on the housing were disregarded.
6.3 Summary
Acoustic performance of the BLDCM has been discussed in this chapter. 2D
FEM models were built to calculate electromagnetic forces of the proposed and
conventional BLDCM. Based on a 3D model of the stator, the difference of vibra-
tion behavior and noise level of the motors were analyzed. Analytic calculation
of natural mode frequencies has also been conducted to compare and validate
the accuracy of simulations. In addition, a hammer impact test has been per-
formed to compare the natural mode frequencies of different motor parts with
the performed calculations.
96
7 Summary and future works
7.1 Summary
This dissertation is aimed at designing and developing a high performance BLDC
machine and drive technology to improve the performance of electrical propulsion
system for solar-powered UAV applications.
A 8 pole BLDC motor with 12 stator slots with only 4 magnet blocks replacing
the conventional 8 magnet blocks structure is proposed to fulfill the require-
ments. Design and construction of prototypes of both proposed and conventional
magnet structure have been carried out. A test bench to study the performance
of the two motors was built. Hence, an extensive comparison between proposed
and conventional magnet structure of BLDC machines has been completed.
The important parameters of the two BLDCMs have been analytically deter-
mined and the motor models were verified through the finite element analysis
software ANSYS. The results showed good correlation between the simulation
and experimental results.
7.1.1 Motor performance
The proposed BLDC machine with 4 magnet blocks for 8 pole pairs has a cogging
torque, which is 45.4 % lower than in the conventional design.
The magnet volume only needed to be increased by 11.4 % for the machine using
4 magnet blocks to reach the same RMS value of the back EMF.
Attention was given to the calculation of d-axis inductance Ldand q-axis in-
ductance Lqand influence factors on absolute and differential inductance. The
change of the inductance value with rotor position is less sinusoidal for the pro-
posed design and shows two different minimal values. This leads to following
conclusions about d- and q-inductance: The Lqvalues of both motors are almost
equal. However, for the 4-8 motor the d-axis inductance has two different values
depending on the rotor position relative to the stator teeth. The higher Ldvalue
occurs when the center of each magnet is aligned with a slot, and the lower Ld
for alignment with a tooth. Both values are higher compared to the conventional
design, for the lower Ldit is +16 % and for the higher Ld+44 %. This leads to
an increase in reluctance torque and thus more torque in Maximum Torque Per
Ampere operation mode. In practical BLDC operation mode at rated working
point, the torque of the motor with 4 magnet blocks is increased by 1.083 %.
For Lqthere is only slight saturation visible, at ±8 A the inductance value de-
creases by 4.7 % for the 8-8 structure and 16.7 % for the 4-8 structure. For the
d-inductance the larger Ldvalue of the 4-8 structure was measured. For both
97
designs the trend is similar, but the absolute value of the 4-8 design is 21.9 %
higher at 0 A. But the relative change is almost identical for both motors.
Considering the uncertainty of 0.5 % of efficiency, the experimental efficiencies
of both motors are comparable at rated speed: for the proposed 4-8 design at
89.91 % and 89.56 % for the 8-8 design. At lower speeds the conventional 8-8
design has a higher efficiency: for rated torque the difference is about 1 % at
4000 rpm and 2 % at 2000 rpm. The accuracy of the efficiency measurement is
0.477 %.
A thermal test at rated load was carried out to verify the thermal behavior of
the two motors. The motors revealed a steady-state winding temperature of
88.9◦C for the 8-8 design and 85.9◦C for the 4-8 design. The test was conducted
in the laboratory at an air speed of 11 m/s. The higher temperature of the 8-8
design translates into 64◦C at a working altitude of 20 km, taking into account
the adapted properties of the air, ambient temperature and wind speed. At
low operating heights the airspeed is assumed to be similar to the conditions in
the laboratory. Therefore the maximum temperature occurs at low operating
heights, i.e. at start and during climbing. The obtained temperatures are well
below the isolation class temperature of the wire (180◦C) and also below the
maximum magnet temperature of 120◦C. This gives the possibility to run at
overload conditions.
7.1.2 Acoustic behavior
Acoustic performance of both motors has been studied in a FEM mechanical
analysis. A 3D model of the stator was used to analyze the different behavior of
the proposed and the conventional rotor structure regarding vibration and noise
level. The proposed machine with the 4 magnet blocks rotor produces higher
radial electromagnetic forces, leading to a stronger vibration and higher noise
levels.
Modal analysis of the stator was conducted through analytical calculation and
FEM. The natural frequency of the stator is around 30 times larger than the
fundamental frequency, so it can not be excited when the motors run at rated
working condition. The 4th mode frequency leads to the maximum resonance
and vibration in both motors under the rated working condition.
Modal analysis of the whole part which includes the stator, winding, aluminum
ring and housing was analyzed by FEM to verify the hammer impact test. The
modal frequencies of each part and the whole structure could be identified in
the spectrum of the sound from the hammer impact test.
7.1.3 Sensorless control strategy
For the sensorless control strategy, special attention was given to the isolation
of the voltages that need to be measured. A high speed, good linearity analog
optical isolation circuit was used to transfer the voltages of the 270 V system
to the microcontroller. The proposed circuit uses a PI controller using fast
operational amplifiers for the linearizing feedback loop of a linear optocoupler.
By this approach, the settling time of the output voltages is reduced to about
98
7.2. Future work
3µs, so the PWM modulated voltage can be accurately measured at low duty
cycles of 15 % at 25 kHz switching frequency.
7.2 Future work
Since the d-axis inductance of the proposed and conventional BLDCM have
different characteristics, the control behavior affected by inductance could have
theoretic and practical significance.
Considering the environment requirement, the lab design of the inverter must
be reviewed concerning its application in an aircraft flying in 20 km altitude
towards a more lightweight construction has higher challenges.
99
A Abbreviations
AR Aluminum Ring
BLDCM Brushless Direct Current Machine
CAL Controlled Axial Lifetime
DOF Degree of Freedom
EMF ElectroMotive Force
FEA Finite Element Analysis
IGBT Insulated−Gate Bipolar
IPM Interior Permanent Magnet
LED Light-Emitting Diode
Maximum-Torque-
Per-Ampere method MTPA
MMF MagnetoMotive Force
MO Measured Object
MOSFET Field Effect Transistor
MPPT Maximum Power Point Tracker
PM Permanent Magnet
PMSM Permanent Magnet Synchronous Motor
PTC Positive Temperature Coefficient
PWM Pulse Width Modulation
RMS Root mean square
SPM Surface-Mounted Permanent Magnet
SmCo2Samarium-Cobalt
SS Stator Stack
UAV Unmanned aerial vehicles
100
B Symbols
Greek and Other Symbols
αipole arc coefficients
ψfflux linkage in the air gap
ψRflux linkage of the rotor
ρair density
ρ20 resistivity
δair gap
θmMechanical angle
θeElectric angle
ωAngular frequency
ψFlux linkage
µ0Permeability of vacuum
λRatio of motor length and rotor diameter
λ1Thermal conductivity of the aluminum
λfThermal conductivity of the air
Latin
aumber of parallel branches
A′
s
ˆpeek value of current loading
AThe total area of the housing
bWidth of the fin channel
B′
δFlux density in the air gap
Bxx-component magnetic density
BrRemanence
Byy-component magnetic density
c Speed of sound
C Damping
D′
iRotor diameter
→
EElectric field
101
EYoung’s modulus
Eturnon,IGBT Switch-on energy of IGBT
Eturnoff,IGBT Switch-off energy of IGBT
Efw,D Free-wheeling energy of diode
Err Switch-off energy of diode
fdEdge force density
fsw Switching frequency
f1Fundamental Frequency
fLForce density
fmf Magnetic force density
frFrequency of mode shape
→
fmMagnetic force density
fmElectromagnetic force density
fxElectromagnetic force density on x-axis components
fyElectromagnetic force density on y-axis components
Fcen Centrifugal force
FElectromagnetic force
Frad Radial electromagnetic force
Ftan Tangential electromagnetic force
gHarmonic order
hHeat transfer coefficient
hyYoke height in the radial direction
HMagnetic field
HxMagnetic field on x-axis components
HyMagnetic field on y-axis components
HCB Coercitivity
102
H1High of the fin
→
iPhase current
icCurrent flowing through IGBT
idCurrent in direct axis
iqCurrent in quadrature axis
Icav Average value of current
Icrms RMS value of current
IFPrimary side current of IL300
Ip1 Secondary side feedback current of IL300
Ip2 Secondary side output current of IL300
IgCurrent through gate resistor
IuPhase U current
IvPhase V current
IwPhase W current
If.s.z Current range in the Power Analyzer measurement
JNElectric current density
kNm Winding factor
kDSpring stiffness coefficient
KStiffness
K1Servo gain of IL300
K2Output gain of IL300
K3Inout-output gain of IL300
kr(m3)Equivalent spring stiffness coefficient
LM Magnet thickness
Lstk Motor length
Ldif Differential inductance
103
LdSynchronous direct inductance
LqSynchronous quadrature inductance
LhLength of the fin
mMass
nNRated speed
NcNumber of turns per slot
NuiNusselt number
pMagnet pole pairs
P′Rated power/efficiency
psSound pressure
pref Reference of sound pressure
Pcond,IGBT Conduction losses of IGBT
Pcond,D Conduction losses of diode
Psw,IGBT Switching losses of IGBT
Psw,D Switching losses of diode
Ploss,D5 Power losses of the diode during 120◦electric angle
Ploss,Q2 Power losses of the IGBT during 120◦electric angle
PIGBT_module Power losses of the IGBT module
Pg,upper Power losses of the gate resistor with PWM
Pg,lower Power losses of the gate resistor without PWM
PeElectric Power
QElectric charge energy during IGBT turn-on or
turn-off
qElectric charge
r Mode number
rRadius of rotating mass
104
RuPhase U resistance
RvPhase V resistance
RwPhase W resistance
rcON-state resistance of IGBT
RgGate resistance
RgGate drive resistor
Rth(j-s) Thermal resistance of the heat sink
R10Feedback resistor of sensorless control circuit
R11,12 Output Parallel resistor of sensorless control circuit
Rs Stator radius
RRotor radius
Ry(av) Average radius of yoke
rTO on-state resistance of diode
Re′
bChannel-Reynolds number
RebReynolds number
SPL Sound pressure level
S Cross sectional area of wire
TwTeeth width
TK(Br)Temperature coefficient of remanence
Tem Magnetic torque
Tsw Switching period
∆Theat_sink Maximum temperature of the heat sink
Tjunction_max Maximum junction temperature in IGBT
TIGBT_module Temperature of IGBT module
TAmb Ambient temperature
Tf.s.z Full scale reading value of Power Analyzer
105
Tf.s.s Full scale value of torque sensor
Tmmagnetic tension tensor
tWidth of the fin
ucUncertainty of the measurement
u(xi)Error limit
UdSynchronous direct voltage
UTUncertainty of torque sensor
UTZ Uncertainty of AD-conversion of the torque value
UnZ Uncertainty of the speed measurement
UPZ Uncertainty of the electric power measurement
UqSynchronous quadrature voltage
uCE0Threshold voltage across IGBT collector-emitter
during ON-state
VCE(TO) on-state constant voltage drop of IGBT
VTO on-state constant voltage drop of diode
V1+ Voltage of the inverting input of the amplifier
V1−non-inverting input of the amplifier
V a Input voltage of sensorless control circuit
V a′Input voltage of sensorless control circuit after volt-
age divider
VAOutput voltage of sensorless control circuit
VWind velocity
vRotating speed
v1Kinematic viscosity
Wmag Magnet span
WtYoke mass
ZNumber of slots
106
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Schriftenreihe Elektrische Energietechnik an der TU Berlin
Hrsg.: Prof. Dr. Sibylle Dieckerhoff, Prof. Dr. Julia Kowal, Prof. Dr. Ronald Plath,
Prof. Dr. Uwe Schäfer
ISSN 2367-3761 (print)
ISSN 2367-377X (online)
1: Dinca, Christian: Motor design for maximum
material exploitation and magnetization
procedure with in-line quality check for mass
production. - 2017. - XV, 168 S.
ISBN 978-3-7983-2883-9 (print) EUR 13,00
ISBN 978-3-7983-2884-6 (online)
DOI 10.14279/depositonce-5630
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control strategies for inverter dominated
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Simulationsmodell für permanentmagnet-
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Design and comparison of two brushless DC drives for an electric propulsion
system of solar-power unmanned aerial vehicles
Universitätsverlag der TU Berlin
Universitätsverlag der TU Berlin
ISBN 978-3-7983-3126-6 (print)
ISBN 978-3-7983-3127-3 (online)
Elektrische Energietechnik an der TU Berlin Band 9
The electrical propulsion system as the core component of solar-power Unmanned Aerial Ve-
hicles (UAVs) for long duration flight requires high power density and stable drive technology.
Brushless DC motors (BLDCM) with high power and torque density and control algorithms sui-
table for drive system are given preference for the application in UAVs.
This dissertation is aimed at designing an improved BLDCM using only 4 interior magnet blocks
to realize 8 poles compared to the conventional 8 magnet blocks structure.
The performances of both BLDCM designs have been analytically determined and the motor
models were verified through finite element software in ANSYS. Design and construction of
the demonstrators of BLDCMs with the proposed and the conventional magnet structure have
been carried out and a test bench for extensive performance comparison has been set up.
Since the proposed magnet structure leads to a particularity of the magnetic circuit, the be-
havior of absolute and differential synchronous direct and quadrature inductances have been
investigated by finite element model analysis and experiments.
Rong Dong
9
Design and comparison of two brushless DC drives for an electric propul-
sion system of solar-power unmanned aerial vehicles
9 783798 331266
ISBN 978-3-7983-3126-6
http://verlag.tu-berlin.de
Rong Dong
Design and comparison of two brushless DC drives for
an electric propulsion system of solar-power unmanned
aerial vehicles
