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Virtual Prototyping of a Brushless Permanent Magnet AC Motor
Electromagnetic and Thermal Design using CAD Software
Bruno Ricardo da Fonseca Marques
Instituto Superior Técnico
Lisbon, Portugal
Abstract — This work’s aim is to describe the
electromagnetic and thermal design of a brushless permanent
magnet AC motor to be applied on a formula student
prototype car, FST05e, from Projecto FST Novabase. It´s a
Battery Electric Vehicle (BEV) designed to participate in
Formula Student events. The challenge is to create a machine
with high power density and fulfill the team goals. In all trials
of competition the motor is pushed to the limits, testing
acceleration, autocross, endurance, and fuel economy. The
main project goal is to achieve a lightweight motor with a
reduced moment of inertia, as well as keeping it cost efficient.
In an iterative way to achieve the power required with less
weight, it was used CAD software to make the machine´s
electromagnetic and thermal design. The first one was
developed with PC-BDC software from SPEED while the
second one was developed with MOTOR CAD software from
Motor Design Ltd©. To do FEA, PC-FEA software from
SPEED was used.
This work describes the electromagnetic and thermal
design process, both with the use of analytical formulations,
based on lumped circuit models, and numerical analysis using
FEA. The duty cycles for all trials in competition are analyzed
to verify the thermal machine behavior. Performance charts,
thermal limits and efficiency maps of the machine are also
studied using MOTOR LAB software.
At the end, the design obtained exceeds even the team
expectations.
Keywords— PM AC Machine; Design PM Machine; Radial
Flux PM Machine; Thermal Analysis BPM; SPEED PC-BDC
I. INTRODUCTION
In the passage from the XIX to the XX century most of
vehicles were electric. This was the natural consequence of
their superior reliability and cleanliness when compared
with the cars engaged with internal combustion engines.
However, since the last ones became more reliable and with
lower cost, their usage increased immensely which result in
the oblivion of these vehicles for almost a century.
Currently due to the increase of fuel price,
environmental issues and technological evolution of
electrical motoring techniques, it has been possible in the
last decades to create a “new life” concerning electrical
mobility. Electric sports cars have appeared with high
performance standards, which is possible due to the
electrical motors with high power densities and high
maximum torque per unit volume (TRV). To achieve this,
the use of high quality steel can be as important as the
magnets themselves.
This work focuses in the electric motor, in design
aspects that allow the vehicle to achieve the highest
performances.
A. Formula Student
This competition occurs every year in different
countries as individual events, each one with its own
character and challenges. Formula Student gives university
students from around the world the opportunity to design
and build a single-seat racing car, which is then put to the
test at various circuits in different competitions:
Acceleration; Autocross, Endurance and Fuel Economy.
The project focuses mainly in these dynamic events,
designed to test different aspects of a car’s performance. It’s
directed to a particular prototype vehicle, FST05e, built at
Instituto Superior Técnico by Projecto FST Novabase,
B. Team Requirements
The following list represents the team requirements for
the machine. The best and more economical choice has to
be made.
Dimensions and Others Related 1)
Total ideal diameter of 12 cm; total ideal axial length of
20 cm; less moment of inertia than Agni 95R [1] used in
FST04e; internal hub with 3 cm diameter; maximum weight
of 10kg.
Speed and Power Envelope 2)
Peak power of 42.5 kW at 6000 RPM. Field weakening
can be used until 9000 RPM.
Drive 3)
Sinewave current control. Battery is composed by 288
Li-Poly cells with nominal voltage of 533 V.
Cooling System 4)
The strategy to be employed has to be good enough to
handle all machine’s requirements at the four competitions
described. If water jacket is needed, the pump flow rate to
be considered is 50 cm3/s.
II. FIRST DESIGN
The first thing to decide was the machine type. Since
axial flux machine, Agni 95R, doesn’t fulfil the team needs
regarding moment of inertia, the selection passes to a radial
flux machine. The natural choice was a brushless permanent
magnet AC machine. It’s the preferred topology to electric
vehicle traction, due to their inherent high efficiencies and
excellent power densities. Interior magnet machines has the
advantage of saliency which enables using reluctance torque
and protect magnets from flux pulsation in the air gap due to
permeance harmonics. Between the several topologies
available, the selection fell in spoke rotor type. This
geometry hasn’t iron bridges and allows high air gap flux
density due to flux concentration principle.
Fig. 1 – Spoke rotor IPM machine [2]
To initiate the first design, initial assumptions were
made, and then an optimization process was applied. To
define poles number the first approach was choosing a good
frequency to easily find low loss iron. Based on recent
aerospace applications, it’s common to find 400 Hz in much
equipment. This defines 8 poles regarding the base speed of
6000 RPM. A silicon oriented grain iron was employed as
well as the strongest NdFeB magnets.
The optimization process taken was implemented by
means of Fmincon Matlab® routine. The objective function
was the machine weight, which had to be minimized.
Constrains were defined to guarantee the mechanical and
magnetic desired behaviours, expressed as function of
design variables. The nominal power and current density of
Agni 95R was tested to establish a comparison between two
motors.
TABLE I
OPTIMIZATION DESIGN RESULTS
Results Values
Length 12 cm
Total diameter 17 cm
Current Density 6 A/mm2
Slot fill gross 60 %
Rotor Diameter 10.2 cm
Lamination Weight 10.4 kg
The results indicate that machine obtained is out of
weight limit even without including mechanical parts.
Moreover the rotor diameter is close to Agni 95R which
means that moment of inertia is similar. Slot fill gross result
is too high for the standard overlapping winding considered
with 24 slots. In conclusion this design doesn’t fulfil the
team goals. However this experience highlighted important
topics to be considered in the future. This includes the
modulation of slot geometry to avail the effects on cogging
torque; viability of analytical models imposed that must take
into account the non-linearity of magnetic circuit; Epstein
data for BH iron curve; winding connection; skew
modulation; FEA methods non-dependent of mesh quality
to compute skewed and unskewed torque; iron losses
calculated by FEA and a transient solver to evaluate the
eddy currents in the rotor.
A. Cooling System
It’s possible to inset the machine desired in a certain
cooling category, in terms of maximum TRV. Considering
half value of total ideal diameter to calculate rotor volume
and the maximum torque corresponding to 42.5 kW at 6000
RPM, the calculation of TRV is defined by:
⁄
Comparing with the following table is possible to have
a rough estimative of cooling strategy to use.
Fig. 2 – Typical values for TRV [3]
Such results indicate that this machine needs an
intensive liquid cooling strategy, for example using housing
water jackets. This feature is crucial in a permanent magnet
machine that uses NdFeB magnets. As they lose flux with
temperature rise, this has the effect of increasing cooper
losses to achieve the same torque level.
III. PROTOTYPE MM03_V3: ELECTROMAGNETIC PROJECT
To fulfil team requirements it was necessary to change
the project paradigm. The natural solution was using
software CAD tools, enabling a more detailed description of
machine geometry. Moreover, software solutions turn
possible the iterative electromagnetic and thermal design by
co-simulation, taking advantage of Windows® Active X.
Using this procedure is possible to integrate the cooling
system into the electromagnetic project and get an accurate
loss prediction by means of temperature update in a steady
state or transient analysis. For the electromagnetic design
the software used was PC-BDC from SPEED lab. For the
thermal design the software used was Motor CAD from
Motor Design Ltd©.
A. Electromagnetic Basics
First design considerations were based on the analysis
of following key equations [4]:
{
√
To maximize the alignment torque and achieve a high
TRV it’s necessary to get a high EMF, in other words a high
flux linkage at open circuit. To perform it, the ideal is
maximizing flux per pole by using strong magnets and
avoiding the use of skew. However, since the machine has
small radial dimensions due to the required diameter, it’s
difficult to attain such goal because it implies a large least
common multiple between slots and poles. Taking into
account the number of poles defined it means that requires
many slots. As it´s expected a heavily loaded machine in
peak power working point, was decided to use few slots to
get wider teeth. The filtering effect of harmonic content in
air gap flux density can be done by means of stator skew.
Once a small air gap is used to increase the flux per pole,
it’s expected that a high cogging torque result and skew can
solve the two problems at same time. This reduces the EMF
and torque but it can be compensated by increasing the
number of turns, and at same time guaranteeing the variable
speed drive required.
The slots/pole combination selected was the Papst
design. It is characterized by 12 slots and 8 poles, allowing
the use of wide teeth and performing a low slotting passing
frequency. This combination that became very popular in
automotive industry has good symmetry properties and no
unbalanced magnetic pull is verified. It’s an expected result
because the greatest common divider between slots and pole
is superior to 1 [6].
B. Materials
The iron is the most important component in the
magnet circuit. Since it’s expected high saturation in the
machine and to explore strong magnets it’s advisable to use
iron cobalt alloy. The product selected was VACODUR® 49
[5] suited to maximum power density machines and low
losses, guaranteeing good mechanical properties.
The strongest magnet available in the market is sintered
NdFeB, available in standard shapes. Sm-Co could also be
considered but it’s heavier and with less coercivity field.
For shaft, the criterion was searching for a stainless
steel with the highest tensile strength possible, cheap and
with good machining properties. This was found with
stainless steel 455.
C. Geometry
Some variables describing radial and axial cross section
were defined based on project constrains, like shaft radius,
magnet inset, stator outer radius and cap thickness. Others
were defined by means of several FEA to understand the
important values to achieve in this design. Is the case of
rotor radius that was minimized to attain low moment of
inertia; air gap length and magnet width defined to achieve
1.4 T of peak air gap flux density at open circuit; iron pole
arc to minimize pole-to-pole leakage and at same time
maximize the flux lines gathered by tooth arc; tooth width to
deal with saturation at peak power; low slot opening to
minimize the cogging torque as well as a higher slot
opening angle and radial tooth tip length to avoid the
saturation in this areas. The axial stack length was defined
in the maximum possible to achieve the ideal length of 20
cm, increasing the flux per pole.
D. Winding
A balanced winding was developed to ensure equal
resistances and inductances in all 3 phases. Papst design was
selected and to guarantee a double layer winding in 12 slots,
the coil span defined was equal to 2. The non-overlapping
winding was not considered because it was difficult to find a
manufacturer in Portugal to make such configuration.
Considering a machine wound, the slot fill gross chosen was
54%, in the limit for an overlapping winding.
Fig. 3 – All phase’s layout
The winding MMF shows that it is difficult to get a
sinusoidal distribution, which means that high harmonic
content in MMF is expected.
Fig. 4 – 3 phases MMF and first electrical harmonic
Checking the winding factors bar chart is possible to
understand the filtering capability of this configuration.
Fig. 5 – Unskewed winding factors
As characteristic in Papst design, all winding factors
have the same value, which is 0.866. It’s low for first
harmonic and high for others. This suggests that is
necessary skew to filter the harmonic content in the air gap
flux density and achieve a sinewound machine. It’s
important to attain such characteristic in the design because
it makes it possible to use with more confidence the phasor
diagram to analyse the machine, as well as control
principles based on FOC.
E. FEA Open Circuit Calculations
This kind of operation is a good way to give the first
analytical model calibration, adjusting PC-BDC models
with FEA results.
Air Gap Flux Density 1)
Fig. 6 – FEA post-processor: open circuit calculation
The flux density values in rotor iron, tooth and stator
yoke are good when an iron cobalt ally is used. This states
that dimensions defined for this variables fulfil the design
goals.
Fig. 7 – Air gap flux density: PC-BDC results Vs FEA
It’s clearly seen the slot opening modulation in the flux
distribution. By adjusting the adequate calibration factors, is
possible to achieve good matching between the results.
Tooth flux Density 2)
Once the phase EMF is calculated under the tooth flux
method, is important to achieve good agreement here
between FEA and PC-BDC results.
Fig. 8 – Tooth flux density: PC-BDC results Vs FEA
In this waveform the slotting effect is not seen. The
good agreement between both results is attained by means
of calibration factors. The most important is in the effective
tooth arc for flux collection at stator surface, to define the
correct integration limits to apply Simpsons rule. In figure 6
is seen that about 98% of tooth head collect flux lines.
Phase EMF 3)
Fig. 9 – Phase EMF: PC-BDC results Vs FEA
Phase EMF is far from be sinusoidal which indicates
the necessity of stator skew. The adequate adjustments by
means of calibrations factors allow good agreement in
fundamental components.
Line-Line EMF 4)
Fig. 10 – Line-line EMF: PC-BDC results Vs FEA
This line-line EMF is near from a flat top waveform,
which may be bad for torque ripple. Its reduction is
important to improve machine life time, however in this
application a safe tolerance could be given on the basis that
car inertia filter much of this effects. It’s considered an
acceptable value if less than 5% of peak torque is achieved.
I-PSI Loop Unskewed 5)
Fig. 11 – FEA I-PSI loop unskewed: FEA results
The diagram is not perfectly elliptical, which means
that flux linkage has some harmonic content that has to be
filtered, while the current is always sinusoidal as required.
Cogging Torque 6)
Fig. 12 – Cogging Torque: Unskewed Vs Skewed (skew=0.5)
Special care was taken regarding the mesh density,
rotor steps and convergence tolerance to get reliable results.
The unskewed result based on co-energy calculation is 4.37
N.m peak-to-peak. It’s a high value, typical when small air
gap are used in conjugation with Papst design. When skew
is equal to halt of slot pitch, the cogging is eliminated.
I-PSI Loop Skewed 7)
Fig. 13 – FEA I-PSI loop skewed: Phase EMF and 1st harmonic
This result states the skew effect in air gap flux density
distribution. Phase EMF is practically sinusoidal and
identical to its fundamental component. Phasor diagram can
be used with accuracy to analyse the machine performance.
F. FEA On Load Calculations
The most critical working point is considered because
this is the worst case operation scenario. The necessary peak
phase current to achieve 42.5 kW at 6000 RPM is 267 Apk.
I-PSI Loop Skewed 1)
Fig. 14 – FEA post-processor: on load calculation
As expected, the machine is heavily saturated in this
working point attaining peak values of 2.4 T in tooth tips.
This is a little above of VACODUR®
49 saturation
polarization, therefore no special concern is need on that.
Fig. 15 – FEA I-PSI loop skewed: PC-BDC Vs FEA
Black result, which represents FEA calculation, is not
perfectly elliptical. Saliency, permeance harmonics and
mostly saturation distorts it. After calibration it was possible
to check the torque by means of following calculation:
The variable W represents the area under i-psi loop.
The value obtained was 67.63 N.m, which indicates that
after calibration the machine is developing the peak power
at rated speed, as it is required by the team.
Transient Solver 2)
Fig. 16 – FEA post-processor: transient solver
This result indicates a maximum eddy current density in
the magnet of 2.13 A/mm2 at peak power working point.
This corresponds to a total magnet loss of 84.8 W. It’s a
high value, mainly taking into account that NdFeB magnets
lose flux with the temperature increase. To minimize such
effect it’s considered that magnets are segmented in
circumferential direction. The number of segments
employed was 16 due to manufacturing constrains.
G. PC-BDC Results
Since analytical models were calibrated with numerical,
some preliminary results can be analysed for peak power
working point at 6000 RPM.
Phasor Diagram 1)
Fig. 17 – Phasor diagram: Blue-Voltage; Red-Current; Orange-Flux
Phasor diagram is inside of voltage limit circle for a six
step 180º operation.
Maximum voltage available from inverter is enough to
drive the machine until the base speed at peak power. The
safe margin given between the circle limit and phase voltage
is to guarantee the drive until 9000 RPM like required. This
was performed by connecting the winding in two parallel
paths, which has the effect of reducing machine reactance.
Current, EMF and Torque 2)
Fig. 18 – Graphs: Current, EMF and torque Vs Rotor position
Phase EMF is close to sinusoidal waveshape however
some torque ripple is observed.
Air Gap Flux Density 3)
Fig. 19 – Graphs: Air gap flux density unskewed Vs skewed
This graph gives good illustration about skew effect.
Dark line represents the air gap flux density after skewing
the stator. The filtering effect obtained in conjugation with
skewed winding factors, mainly those related to 5th
and 7th
harmonic, turn possible to achieve the phase EMF depicted.
Harmonic Analyses 4)
Fig. 20 – Harmonics: Alignment torque
Only the 6th
harmonic is relevant and justifies the
variation observed in figure 18. The torque ripple attained
was 4.4% of peak torque, which is within the limit defined.
Design Sheet Results 5)
TABLE II
MM03_V3 DESIGN RESULTS
Results Values
Motor Length 21,2 cm
Total diameter 11,6 cm
Current Density 28.9 A/mm2
Peak Power 42.5 kW
Corner Speed 6000 RPM
Lamination Weight 7.72 kg
Inertia Moment 8.56 E-4 kg.m2
The main team goals are accomplished. The most
important variables, regarding the weight, diameter and
inertia moment are achieved. In the last, the reduction when
comparing with Agni 95R is in the order of 1:28. The motor
length seems a little bit higher, however it takes into
account the end cap thickness which is not optimized.
IV. PROTOTYPE MM03_V3: THERMAL PROJECT
In order to know the real machine performance is
important to get the correct temperatures in all components.
This depends on the cooling strategy used as well as the
materials chosen.
A. Materials
For the housing and end caps a smooth material was
selected in order to minimize the contact resistances
between these two structures. A cheap material, compatible
with anodized treatment is the aluminium. It has resistance
to corrosion and can employ water jacket directly in the
housing.
Regarding the insulation and impregnation materials is
necessary to define the thermal class to be employed. It was
found materials with thermal class H at good price. The
maximum hot spot of 180ºC it’s an acceptable starting point.
The judgment has to be done in the thermal limit
exploration of the machine, if it handles or not the peak
power during the time required. A class H polyester film
based on PEN polymer was found. It has very low thickness
which improves the slot fill. The material chosen was
Teonex®. For the impregnation the selection passes for a
polyester resin, the typical material used, constrained to VPI
application. This process guarantees perfect impregnation
goodness, with almost no air pockets. After researching,
was found Dobeckan® LE 6500. It’s an unsaturated
polyester resin with 3 times the thermal conductivity of
common resins.
For groundwall insulation was selected an aramid fibre,
very tolerant to mechanical stresses and with good
absorption properties for impregnation. This allows
reducing the interface gap between stator lamination and
liner. The typical aromatic polyamide for this purpose is
Nomex®.
B. Cooling Strategy
Due to high TRV identified in section II, an intensive
cooling strategy is needed. Between the several strategies
available, the most simple and effective is housing water
jacket cooling. It’s standard in the manufacturing point of
view an guarantees a good dissipation of copper losses, as
they are the most significant. To achieve this it’s only
necessary to reduce the interface gap between stator
lamination and housing. This can be done by means of a
heat paste sink.
The most typical housing water jackets implementation
is with axial duct or spiral ducts. As can be seen on table II,
the machine perimeter is higher than motor length. This
means that for the same number of channels and geometry,
the axial ducts have more area available than spiral ducts.
This gives better balance in fluid flow, which allows
achieving the same temperature performance with lower
velocities and pressure drops. Therefore an axial water
jacket was implemented.
The duct geometry may be circular or rectangular and
same considerations can be taken here too. Selecting a
zigzag housing water jacket by connecting all the channels
in series, it’s possible to attain the same area with less
channels in rectangular form. Moreover, the extrusion
process to be applied in the aluminium housing removes
more material in this case. This means that this feature leads
to a lightweight machine.
Channel Dimensions 1)
To select the optimum channel dimension a sensitivity
analysis was performed to understand the impact of
parameter change in thermal model by variation of a single
parameter. The parameter selected was the fin
pitch/thickness ratio (Fpt). Since the fin thickness is defined,
increasing this variable allows increase channel width.
Fig. 21 – Sensitivity Analysis: Ph Vs Fpt
The pressure drop in the housing, Ph, decreases with
channel width. When Fpt is superior to 10, variation is less
pronounced. It’s important to check if the same thing
happens with fluid velocity in the channel, Vf.
Fig. 22 – Sensitivity Analysis: Vf Vs Fpt
The velocity in the channel decreases with area growth.
It’s important to have high values of velocity to get a better
heat transfer coefficient, however it’s good practice in
construction to keep values around 1 m/s. When Fpt is
superior to 10 the velocity decreases by steps, which
indicate that further increase don’t necessary represents a
great improvement in fluid flow. The temperature variations
in the critical components allow for final conclusions.
Fig. 23 – Sensitivity Analysis: Temperatures Vs Fpt
Magnet temperature in red is not too sensitive to Fpt as
the average and hot spot winding temperatures. When Fpt
is equal to 11 the temperature attained is in the middle of
maximum and minimum for each component. As this value
is in the range for the previous analysis, channel width can
be defined for Fpt equal to 11. This results in a zigzag water
jacket with 16 channels.
C. Interface Gaps
A sensitivity analysis can be performed to check
temperature dependence to tolerances and manufacturing
constrains. This analysis will fall in the most important
contact resistance for a housing water jacket cooling system:
interface gap between housing and stator laminations
(IG_sh). This will determine the capability of the cooling
system to extract the heat from the winding and iron.
Fig. 24 – Sensitivity Analysis: Temperature Vs IG_sh
The results on the graph consider an average
manufacturing process, defining IG_sh equal to 0.03 mm. If
a perfect contact is considered, temperature reduction in
winding hot spot and magnet is 30ºC and 20ºC respectively.
This justifies the great impact in the cooling and some
measures to reduce this interface include the use of heat
paste sink. It typically reduces IG_sh from 0.03 mm to 0.01
mm, allowing a temperature reduction in winding hot spot
and magnet of 18ºC and 14ºC respectively.
V. RESULTS
In machine design is important to appraise machine
performance across the entire torque-speed envelope. Such
solution was found with Motor LAB software from Motor
Design Ltd©. This tool takes advantage of Windows® Active
X to connect PC-BDC and Motor CAD, performing the
calculation of torque-speed characteristics, loss and
efficiency maps that can be used in an iterative design
process.
A. Saturation & Cross Coupling
The linear approximation used to describe flux linkage
doesn’t account for saturation and cross coupling effects
which do not fit the purpose when modelling at high
operating currents. It’s considered that flux linkage is
accurately described by second order polynomial functions
as given [7].
Fig. 25 – Saturation & Cross Coupling: Power Vs Speed
This characteristic confirms that peak power is attained
like required, independently of corner speed increase due to
saturation effect. The maximum power available, Pmax, is
62.5 kW at 10000 RPM which is the machine limit. This
defines a power density of 6.3 kW/kg.
B. Efficiency Maps
The proposed techniques also make it possible to plot
the efficiency characteristic over the full power-speed
envelope, performing an efficiency map. This is very useful
to understand where the ideal exploration regime of the
machine designed is.
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
10
20
30
40
50
60
70
X: 6000
Y: 42.48
Speed RPM
Sha
ft O
utpu
t P
ower
(kW
)
Speed Vs Shaft Output Power
Ismax
=267
Ismax
=201
Ismax
=136
Ismax
=70
Fig. 26 – Efficiency map: Power Vs Speed
Contour plot shows a big area between 90 and 95% of
efficiency. Peak power at 6000 RPM is attained
approximately with 91% of efficiency. In the autocross
competition the average power is 16 kW. Contour plot
shows that it’s possible to attain such result with efficiency
superior to 90% between 3000 RPM and 10000 RPM. It’s a
very comfortable margin and gives good perspective for the
fuel economy competition.
C. Limit Envelope
This study is directed to understand the machine limits
at steady state and transient operation. For steady state the
procedure was perform calculations with techniques
developed considering that winding hot spot is fixed in the
thermal class H limit, 180 ºC. Then the maximum power-
speed envelope is defined. For transient analysis the purpose
is different. The main goal is to understand how much time
machine can handle the peak power at 6000 RPM. Previous
studies on Motor CAD show that it’s 80 seconds. Now the
objective is to confirm it.
Steady State 1)
Fig. 27 – Steady state limit: Power Vs Speed
The limit power achieved at 6000 RPM is 28.25 kW.
This is an important result because the data obtained to the
different competitions with Matlab® simulations indicate
values below this. Therefore confirms that machine is good
enough to support all the performances demands in
autocross and endurance competition.
Fig. 28 – Steady state limit: Water jacket dissipation Vs Speed
This graph illustrates the cooling system capacity. This
machine has little area to dissipate the heat for such high
power densities involved. When the machine is operating at
42 kW at 10000 RPM, housing water jackets are dissipating
2.6 kW. This highlights cooling system performance for
such a high TRV machine.
Transient Operation 2)
Fig. 29 – Transient operation: Torque Vs Speed
Torque-speed characteristic indicates that the motor
develops 68.11 Nm at 6000 RPM continuously for 80
seconds. This is very close from peak torque, which
confirms the duty cycle results performed with Motor CAD.
The machine guarantees a large margin of safety in
exploration of peak power, mainly used in acceleration
competition as it has to be concluded before 4 seconds. The
80 seconds obtained are large enough to guarantee good
performance and not excessive overheating.
D. Thermal Maps
It´s also of interest to connect these analyses techniques
with thermal modelling using Motor CAD software. This
enables the generation of thermal maps, in a similar way to
creating efficiency maps.
0
0
0
0 0 0 0
80
80
80
80
80 80 80
81
81
81
81 81 8182
82
82
82
82 82 8283
83
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83
83 83 8384
84
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8484 84
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85 8586
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86 8687
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8989 90
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92 92
9293
93
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9394
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94 94
95
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95
9595
Efficiency
Speed (RPM)
Sha
ft O
utpu
t P
ower
(kW
)
0 2000 4000 6000 8000 100000
10
20
30
40
50
60
Eff
icie
ncy
(%)
80
82
84
86
88
90
92
94
96
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
5
10
15
20
25
30
35
40
45
X: 6000
Y: 28.25
Speed Vs Shaft Output Power
Speed RPM
Sha
ft O
utpu
t P
ower
(kW
)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100001900
2000
2100
2200
2300
2400
2500
2600
2700
X: 8600
Y: 2583
Speed Vs Water Jacket Dissipation
Speed RPM
Wat
er J
acke
t D
issi
patio
n W
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1000058
60
62
64
66
68
70
72
X: 6000
Y: 68.11
Speed Vs Shaft Torque
Speed RPM
Sha
ft T
orqu
e (N
m)
Fig. 30 – Winding hot spot thermal map: Torque Vs Speed
This thermal map shows that the winding hot spot
temperature increase with machine load. This is expectable
because torque is proportional to current and temperature
increase with current square. So every time that maximum
torque is achieved, the maximum hot spot will result
independently of speed value.
Fig. 31 – Magnet thermal map: Torque Vs Speed
Highest magnet temperature is verified at high speed
and load envelope. This is due to slotting passing frequency
(fsp), which means that higher speed leads to higher fsp and
consequently high flux pulsation in magnets. As the eddy
currents are resistance limited, an increase on them will
increase magnet losses and so the temperature.
VI. CONCLUSIONS
This prototype achieves all the specification
requirements given, in peak power and weight, as well as
the goals for all contests involved in the formula student
competition.
The torque ripple attained could be considered
acceptable for this application on the grounds that car inertia
filters most of these effects. The use of stator skew allows
achieving a sinewound machine, besides of cogging torque
cross off.
In the cooling system the adverse effects of interface
gap between housing and stator lamination can be mitigated
with heat paste sink. The water velocity and pressure drops
across the housing have very good values, which mean that
there is no problem with particles in coolant to wear away
the aluminium surface. The intensive cooling strategy, the
machine thermal class and VPI impregnation allows good
behaviour in thermal limit envelop. The maximum power
density for this machine is 6.3 kW/kg.
Improvements can be done to the future, namely:
checking the skew effects and magnet losses with 3D FEA
software; study the influence of proximity losses in the
design and explore a non-overlapping winding with a
different combination of slots per pole.
REFERENCES
[1] Agni Motors. 95 series datasheet. Agni Motors website. Accessed June 3, 2012, in www.agnimotors.com
[2] Hendershot, J.R. & Miller, T. J. E. (2010). Design of brushless
permanent-magnet machines. Florida: Motor Design Books LLC [3] Miller, T. J. E. (2011). SPEED’s electric machines. [S.I]:CD-
ADAPCO
[4] Miller, T. J. E. (2011). SPEED PC-BDC 9.1: user’s manual. [S. I]: Author
[5] Vacuumschmelze.(2012). VACODUR 49 datasheet. CWIEME 2012.
[S.I]: Author [6] Libert, F. (2004). Design, optimization and comparison of
permanent magnet motors for a low-speed direct-driven mixer.
Stockholm: KTH [7] Goss, J., Mellor, P. H., Wrobel, R., Staton, D. A., Popescu, M.
(2012). The design of AC permanent magnet motors for electric
vehicles: a computationally efficient model of the operational envelope. In 6th IET International Conference on Power Electronics,
Machines and Drives (PEMD 2012), Bristol, 27-29 March, 2012 (1-
6).
Winding Max
Speed (RPM)
Sha
ft T
orqu
e (N
m)
0 2000 4000 6000 8000 10000
5
10
15
20
25
30
35
40
45
50
Win
ding
Max
(oC
)
60
80
100
120
140
160
Magnet
Speed (RPM)
Sha
ft T
orqu
e (N
m)
0 2000 4000 6000 8000 10000
5
10
15
20
25
30
35
40
45
50
Mag
net
(o C)
60
80
100
120
140
160
