Design Methodology for Small Brush and Brushless DC
Motors
Jérôme Cros, Mehdi Taghizadeh Kakhki, Geraldo C.R. Sincero,
Carlos A. Martins, Philippe Viarouge
INTRODUCTION
Manufacturers of components and sub-systems for large scale applications are constantly
improving the quality of their products in order to ensure customer satisfaction. They are
facing severe competition constraints and this is particularly true for automotive industry.
The offer of new services and functionalities goes well together with the increasing use of
electronics and electrical actuators which provide auxiliary functions in a vehicle,
improving the functional performances.
Given this context, and the constant need for improving the electrical machines, the
present chapter focuses on the design methodology for brushed or brushless DC machines
as the two mostly used motor types in small accessories for vehicles. This methodology is
also applicable to many other machine types. We discuss various winding configurations
for the machine armature and the advantages of new motor designs using a concentrated
winding. We present a method for the selection of an efficient motor and an analytical
dimensioning process using a non-linear constrained optimization approach. Finally, we
discuss the application of finite element and time-simulation methods for the validation
of the optimal solution.
SMALL ELECTRIC MOTORS IN MODERN VEHICLES
An electrical actuator is a device designed for moving or controlling another mechanism
or system. Table 1 shows a list of automotive accessories using small power actuators,
(Cho and Johnston, 1999). Small rotating electric motors are an important part of the
electrical system and are used in several feature accessories in a modern car. Over 100
motors are used in a well equipped luxury vehicle (Thiemer, 2001). These machines have
very different requirements in terms of power, speed, torque, volume, form and size.
The energy conversion from electrical to mechanical in a rotating electrical motor is the
result of an interaction between two magnetic fields, one created by permanent magnets
(PM) or electromagnets and the other generated by current-carrying conductors (armature
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winding). The number of magnetic poles in the magnetic field is referred to as machine
poles. The current-carrying conductors are mounted in the armature core openings which
are referred to as armature slots.
Table 1. List of automotive accessories using small power actuators (Cho and Johnston,
1999).
starter motor, alternator, radiator motor-fan, air conditioning
Power train compressor drive, idle speed control, engine throttle control,
transmission shifter, electrically variable transmission, engine coolant
pump motor, electrical valve, and ECR actuators.
electric power steering system, electro-hydraulic power steering, ABS
systems, brake-by-wire actuators, active suspension actuator, and 2-4
Chassis
wheels drive actuator.
windshield wipers, window lifts, seat adjuster, seat vibrators, sunroof
actuators, sliding door closers, door lock mechanisms, headlamp
Body
adjuster, mirror adjusters, steering column adjuster, HVAC blower,
cruise control, headlight wiper motors, power antenna, headlight doors,
trunk closer, and auto-leveling system.
The two mostly used motor types in small accessories are PM brushed dc motor and PM
brushless dc motor. In a PM brushed dc machine, the permanent magnets are mounted on
the stationary part of the machine (stator) and the armature is the rotating part of the
machine (rotor). DC voltage is applied to the commutator copper segments through
carbon brushes pressing against these segments (Hamdi, 1994). The commutator
segments are mounted on a cylinder on the rotor shaft and are insulated from each other
and also from the rotor shaft. The commutator segments are wired to the ends of
the armature coils. In fact, the set formed by the commutator and the brush assembly acts
as a mechanical rotary switch. This allows reversing the coil current in the rotating
armature maintaining the torque production. Fig. 1 shows a brushed dc machine used as a
radiator cooling motor fan.
In a PM dc brushless machine, the permanent magnets are mounted on the rotor and the
armature is stationary. The armature coils are fed with a power electronic converter and
the coil current waveform must be synchronized with the rotor position. These motors are
often fed with square-wave currents or voltages when a simplified control system is
required. However, similar motors fed with sinusoidal currents and voltages are also
becoming increasingly popular since the cost of electronics (including microcontrollers)
is rapidly decreasing. Employing a sinusoidal current waveform is more advantageous
since it generates less noise and vibration. However, it requires several current sensors
and increases the complexity of the control system.
The power converter acts, therefore, as an electronic commutator and is generally
integrated inside the motor. It avoids the problems associated with a mechanical brushcommutator assembly including the mechanical wear and EMI compatibility (Torrey and
Kokernak, 2002) and results in a more efficient and reliable machine. The cost of
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production for PM brushless machine is higher compared to the brushed dc machine but
it allows for variable speed operation without an additional electronic converter. It is
usually used in more expensive luxury cars. Fig. 2 shows a 5-phase brushless dc machine
with an external rotor for a radiator cooling motor fan.
Fig.1. Brushed DC motor for a radiator cooling motor fan
Brush assembly
Armature
(rotor)
Permanent magnet poles
(stator)
Commutator
Fig.2. Brushless DC motor for a radiator cooling motor fan
Armature
(stator)
Permanent magnet poles
(rotor)
Power electronic
converter
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Table 2 and 3 show examples of PM brushed dc motors and PM brushless dc motors for
different applications in vehicles.
Table 2. Structure of PM dc motors applied on some of vehicle accessories
ElectroElectroHeater
Radiator
Wiper
Application
hydraulic
hydraulic
blower
Fan
ABS
Power
Fan
Poles
4
2
4
2
2
Slots
20
12
21
12
10
Brushes
4
2
4
2
2
2565
2000
1820
Speed
1000 rpm
2000 rpm
rpm
rpm
rpm
500 W
Power
150 W
500 W
120 W
120 W
1.5 kW
Input
12 V
12 V
12 V
12 V
12 V
Voltage
Starter
Motor
6
29
2
1800
rpm
1.2 kW
12 V
Table 3. Structure of PM brushless dc motors applied on some vehicle accessories
ElectroRadiator
Radiator
Heater
hydraulic Water
Application
Fan
Fan
blower
Power
Pump
Fan
Steering
Poles
4
6
4
6
4
Slots
20
9
8
9
12
Number of
5
3
2
3
3
Phases
1800
3500
5000
Speed
2500 rpm 2000 rpm
rpm
rpm
rpm
Power
250 W
350 W
120 W
1500 W
500 W
Dc Bus
12 V
12 V
12 V
42 V
42 V
Voltage
Trends in Small Motor Design for Automotive Applications
In the current economic context and due to severe competition, all kinds of electrical
machines should be constantly improved to reduce their costs and improve their
performance. This evolution has become possible thanks to more efficient and precise
calculation methods which allow the designer to further elaborate the optimization of the
structures. This is also due to technological advancements in materials, electronics,
manufacturing techniques and new technical specifications that lead to new developments
and new designs.
For instance, the 42V Powernet voltage modification has important consequences on
existing electrical equipment, mainly for brushed dc motors present in many systems and
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accessories. The higher input voltage may lead to current commutation problems,
electromagnetic interferences and, even, ring fire on brushed dc motors, among other
problems (Thiemer, 2001; Torrey and Kokernak, 2002; Hamdi, 1994). In this context,
many existing motors need to be improved. It is also interesting to evaluate new design
solutions that might be more appropriate for the new electrical system specifications.
Integration of the equipment in a new car design adds new constraints and should meet
new requirements. Designers will have to pay attention to a number of aspects such as
frame size, cost, noise, lifetime, ambient conditions, and quantities which vary from one
vehicle model to another.
New designs of electrical motors can benefit from new manufacturing techniques, for
example, new winding methods which reduce the copper volume and copper losses in
significant proportions.
The use of new materials may have important consequences on the machine structure.
For instance, the design of electromagnetic devices with soft magnet composite (SMC)
materials can offer several advantages over conventional laminated materials. It can
facilitate the implementation of new structures with fewer parts, reduced size and weight
(Hultman and Jack, 2003).
DESIGN METHODOLOGY
The design methodology allows the designer to find a compromise between material
properties, device dimensions, the cost of production and assembling processes, and
application constraints. It begins with the analysis of the application specifications and a
topological research to find a machine structure well-adapted for the given application.
The topological research is, in fact, the process of the pre-selection of machine structures
which have the best potential to meet the requirements of a given application. It allows
the designer to limit the number of solutions before proceeding to a dimensional and
geometrical optimization. Fig. 3 shows a general flowchart for this type of methodology.
Topological Research
This approach relies on the designers’ knowledge and experience (expert rules) and does
not need any particular Computer Aided Design (CAD) tools other than analytical
models. This approach enables the designer to find geometries of electrical machines
which take advantage of particular properties and performance of magnetic materials or
windings. This helps also in reducing the size of the optimization problem. For example,
Soft Magnetic Composite (SMC) materials may be an interesting choice for the type of
magnetic material, however, they may impose some specific constraints for the motor
geometry in regard to the pressing process. Nevertheless, compared to laminated
material, SMC materials have isotropic properties which allows the design of original
structures of magnetic circuits with different mechanical assemblies. This may improve
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the production process. This type of decision can not be easily formulated in an
optimization problem and all possible options should be studied individually. The
selection of a winding configuration, the choice of the number of poles and slots in a
machine, or brush and commutator segment numbers in the case of a brushed dc machine,
are also other examples of parameters to determine in a topological research before
proceeding to a dimensional and geometrical optimization.
Fig.3. Design optimization methodology
Topological Research
Analysis of
application
specifications
Selection of the structure
Axial or radial air-gap, number of poles,
number of slots, winding configuration,
etc.
Global optimization of a given structure
Dimensioning
Multi-physical modeling
Optimization
Prototypes and Tests
Classical Machine Dimensioning Method
In this classical approach, the main dimensions of the machine are derived directly from
the application specifications using simplified analytical formulas and expert factors
determined by experimental data from many years of design experience (Hamdi, 1994).
It may also employ Computer-Aided-Design (CAD) tools like Finite Element (FE)
magnetic field calculations to complete the analysis and to validate the structure. Fig. 4
shows the diagram of a complete CAD environment for electrical machine design. It
should bring together a multitude of coupled physical models to reproduce all the
physical phenomena typically appearing in an electrical machine. It is also possible to
perform several iterations with this CAD procedure. However, this is generally done by
the designer when comparing and analyzing different solutions without using a specific
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optimization method. In fact, this classical methodology is often confined to the
comparison of all the solutions resulting from a topological design approach.
Fig.4. Computer-AidedDesign (CAD)
Environment
with
of physical
models.
CAD Environment
with
coupling
ofcoupling
physical
models
Thermal Modeling
Heating transfer
Mechanical Modeling
Dilation,
dissipation
Assembly, parts movement
Iron Losses
Strength,
Vibration
Joule Losses
B(H) curve
Electrical Circuit Modeling
Current & voltage waveforms
Flux
densities
Magnetic Modeling
Magnetic flux
Global Optimization
The aim of global optimization is to find the optimal dimensions for a suggested structure
taking into account all kind of application constraints and material properties. The term
“Global” refers to the fact that this approach takes into account all different physical
phenomena and their interactions. A Global optimization approach needs also physical
models, but unlike the classical approach, it uses the dimensional parameters as design
variables and the application specifications are considered as constraints. The main
challenge is to define an optimization problem with a given objective, variables, and
linear and non-linear constraints (geometrical, electrical, thermal and mechanical). The
choice of an optimization tool and optimization method (such as gradient-based methods,
evolutionary algorithms, etc.) does not depend on the optimization problem. Any method
could be used as far as convergence towards a solution is possible and all constraints are
validated using modeling methods. Both analytical and finite element models could be
used to evaluate the performance of the electrical machine.
Optimization with Analytical Models
Analytical models are widely used in a global optimization process since they allow us to
take into account many physical phenomena and their mutual interactions. They are
simple to implement and fast in terms of simulation time. However, they need
simplifying assumptions which affect their accuracy and limit their utility in applications
with complex geometry and material non-linearities.
Optimization with Analytical Models Corrected with Finite Element Models
Finite Element (FE) models are used to analyze the performance of the electromagnetic
structures before their final realization. They are more precise than analytical models and
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are generally used as a reference for the validation of analytical models. Finite element
models are used for field calculation, thermal and mechanical modeling, etc.
Optimization schemes with analytical models corrected by finite element models are
becoming increasingly popular since they benefit from advantages associated with both
analytical models and field calculation tools. In this approach, for each intermediate
optimal design solution, the electrical parameters generated by the analytical model are
compared to those obtained by a 2D or 3D finite element computation (Cros et al., 2008).
If there is a significant difference between these two sets of parameters, correction factors
are applied to the analytical models to improve their accuracy. Figure 5 shows the
flowchart for a design methodology using this approach.
Optimization with Finite Element Models (Direct Method)
Two dimensional (2D) and three dimensional (3D) finite element based methods may
lead to more efficient tools for field calculation, allowing for a more precise evaluation of
the machine characteristics. Currently, however, an iterative optimization process using
finite element models may result in unpractical computation times in the case of electrical
machine design. With the new technological advancements in data processing and
computation speed increase, this approach will be progressively more interesting and will
become possibly predominant in the future.
Fig.5. Flowchart of the design methodology
Load and power specifications
Torque-speed characteristic
and energy requirements
Selection of motor main
parameters
Selection of
a winding
configuration
Iterative geometric
design calculation
Analytic electrical
equivalent model
Performance calculation and
validation
214
Slot and pole numbers
Brush and commutator segment numbers
Position of
phase coils in armature slots
2D FE magnetic computations
Correction factors for electrical
model
Commutator model for time
simulation
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ARMATURE WINDING CONFIGURATION
In conventional DC motors, three main types of rotor armature windings may be
identified: lap winding, wave winding, and frog-legs winding (Hamdi, 1994). These
windings are made with simple coil elements which are always interleaved. The ratio
between the axial length of the end-windings and the axial length of the armature
magnetic circuit is then relatively high. All these winding types differ primarily on the
method used to connect the terminals of the simple coils to the commutator. For a lap
winding, the number of parallel paths is equal to the number of poles. A wave winding
has only two paths in parallel, regardless of the number of poles. The frog-leg winding
method combines lap winding and a wave winding placed on the same armature, in the
same slots, and connected to the same commutator bars.
Figure 6 presents a conventional lap winding armature of a permanent magnet brush DC
motor used in an automotive application. One can notice that the yoke has a relatively
high number of slots and is made of laminations. The significant copper volume of the
end-windings is typical of a lap winding with a small axial motor length. To avoid the
interleaving of the coils, it is possible to directly wind the armature simple coils around
each tooth of the rotor magnetic circuit (Cros and Viarouge, 2002). This kind of winding
is called a concentrated winding but may be also called a non-superposed winding. As
shown in Fig. 6, this technique considerably reduces the copper volume of the endwinding, the total copper losses and the total axial length of the motor (Cros and
Viarouge, 2003). In small power applications using permanent magnet motors with
reduced axial length, concentrated windings are progressively replacing other types of
armature windings.
Fig.6. Comparison of armature end-windings
a) lap winding
b) concentrated winding
Armatures with concentrated windings have always a small number of slots with wide
openings and large tooth sections. They can be realized with a laminated material but
they are also well adapted to the use of soft magnetic composite (SMC) materials due to
the reduced mechanical constraints during the molding process. With such materials, it is
possible to insert the end-windings in the active part of the rotor magnetic circuit and
expand the tooth tips to perform an axial concentration of the air-gap magnetic flux into
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the teeth. Such modification takes advantages of the isotropic properties of magnetic
composite materials and partially compensates its low permeability. This axial insertion
of the end-windings reduces the volume of copper and the total axial length of the motor.
Concentrated Armature Windings of Brushed DC Motors
The concentrated winding technique is too often associated and restricted to windings
with a short pitch, i.e. windings with lower performances than those of classical winding
structures. The concentrated windings with a short pitch are then limited to sub-fractional
power applications with low voltage supply, where the performance in terms of torque to
current ratio is not critical.
In the case of the brushed DC motor, the simplest motor widely used for mirror
adjustment and door latch is using a concentrated winding armature because its
production cost is very low. This motor has 2 poles, 3 armature slots, 2 brushes, 3
commutator bars and a winding with a short pitch of 120 electrical degrees. Fig. 7(left)
shows the diagram of a developed surface of this drum armature. This developed diagram
is made by unrolling the periphery of the armature and commutator into a plane. This
motor, which is well adapted for low voltage and low power applications, presents
several drawbacks:



the current commutation is not efficient, because the number of segments on the
commutator and the number of coils per parallel path are very small (Fig.7, right).
The commutation voltage between two consecutive segments is relatively high r in
important Electro-Magnetic Interferences (EMI).
because the internal voltages in the parallel paths of the winding are unbalanced, the
path currents are different and there is a circulating current in the armature which is
generated by the third harmonic of the no-load emf in each coil. This current
decreases the motor efficiency and increases the noise and the torque ripple.
the winding coefficient associated to a short pitch of 120 electrical degrees is small
and equal to 0.866. The performance in terms of torque to weight ratio and torque
ripple is low.
Fig.7. Diagram of an armature with 3 slots, 2 poles and a single layer concentrated
winding with a short pitch of 120 electrical degrees (3 coils); Diagram of the parallel coil
paths (right)
2.1
3.1
1.1
1.1
3.1
V
S
N
3.1
1.1
2.1
1
2
2.1
3.1
3
V
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Fig. 8 (left) shows an evolution of the machine of Fig. 7 by using a multi-layer
concentrated winding. This new winding configuration increases the number of
commutator bars and of armature coils. In Fig. 8 (right), each coil has been identified by
2 numbers. The coils having the same first number (e.g., coils 1.1 and 1.2) are wound
around the same tooth and have the same no-load voltage. These coils are connected to
different bars of the commutator to get coil paths perfectly balanced. The current
commutation in the coils wound on a same tooth is achieved, simultaneously, by different
brushes. Consequently, the multi-layer winding improves the commutation when
compared to a single layer winding because the number of turns per coil and the coil
inductance are reduced for the same operating point (same values of DC supply voltage,
DC current and rated speed). Employing an armature with a multi-layer concentrated
winding is an interesting solution for applications which need more power and higher
voltages.
Fig.8. DC motor with 3 slots, 2 poles and a multi-layer concentrated winding using 6
coils (left); Diagram of the parallel coil paths (right).
2.1, 2.2
3.1, 3.2
1.1, 1.2
1.1
N
N
2.1
3.1
1
V
S
1.2
2
2.1
3.2
1
2
3
3
S
4
V
2.1
1.1
3.2
2.2
5
6
3.1
2.2
1.2
Comparison: Lap Winding versus Concentrated Winding
The drive of an automotive electrical motor fan, which is a typical application of the
permanent magnet brushed DC motor, is chosen to compare a conventional lap winding
armature with a multilayer concentrated winding one. The conventional motor has 20
armature slots with 20 simple coils, 4 stator poles and 4 brushes. This type of motor has
been adopted by a lot of manufacturers in the world. The winding of the rotor is
overlapped with a short pitch of 1 to 5. Fig. 9 shows the developed diagram of this
structure with coil connections on the 20 commutator segments. The coils having the
same first number (e.g., coils 1.1 and 1.2) have the same no-load emf and are in phase.
Fig. 10 shows the parallel coil paths for the same machine. Manufacturers sometimes
make simplifications to minimize the cost. For example, the number of brushes can be
reduced while adding equalizer connections on the commutator as shown in Fig. 11.
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Fig.9. Diagram of a lap winding machine having 20 rotor slots, 4 stator poles and a lap
winding and a short pitch from 1 to 5
3.1
4.1
5.1 1.2
2.2
3.2
4.2
5.2 1.3 2.3
N
1.1 2.1
5.4
1
2
4.3 5.3
4
5.1 1.2
5
6
8
4.4 5.4
3.4
1.1
N
2.2 3.2
7
2.4
1.4
S
3.1 4.1
3
3.3
4.2 5.2
9
10
1.3 2.3
11
12
3.1
S
3.3 4.3
13
2.1
14
5.3 1.4
15
16
2.4 3.4
17
18
4.4 5.4
19
20
V
Fig.10. Diagram of parallel coil path connections for the machine presented in Fig. 9
5.4
1.1
2.1
4.4
V
3.1
3.4
4.1
2.4
5.1
1.4
1.2
5.3
2.2
4.3
3.2
3.3
4.2
2.3
1.3
5.2
It is possible to design an equivalent motor using a multilayer concentrated winding
armature by using the same permanent magnet stator, the same commutator and the same
number of brushes (2 or 4 brushes). In fact, one avoids the interleaving of the endwindings by regrouping simple coils which have the same emf phase on the same tooth of
the armature. This leads to a new armature with only 5 big teeth and 4 simple coils
superposed on the same tooth (Fig. 12). The simple coils can be concentrated around the
tooth to minimize turn length and the copper volume in the end-winding. The connections
of the terminals of the simple coils to the commutator segments and the parallel coil paths
are always identical in both machines (i.e. machines in Fig. 9 and Fig. 12). The width of
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the tooth tip influences the electromotive force and can be modified to obtain the same
pattern of the no-load magnetic field in the air-gap.
Fig.11. Diagram of a machine with 20 rotor slots, 4 stator poles, 20 commutator
segments, 2 brushes with a lap winding and a short pitch from 1 to 5
3.1
4.1
N
5.4
5.1
1.2
2.2
3.2
4.2
N
1.1 2.1
1
3
5.1 1.2
4
5
2.3
1.3
3.3
4.3
S
S
3.1 4.1
2
5.2
2.2 3.2
6
7
8
N
4.2 5.2
9
10
11
5.3
2.4
1.4
3.4
N
1.3 2.3
12
5.3 1.4
14
15
16
1.1
3.1
2.1
S
S
3.3 4.3
13
5.4
4.4
2.4 3.4
17
18
4.4 5.4
19
20
V
Fig.12. Diagram of a multilayer concentrated winding machine with 5 rotor slots, 4 stator
poles, 20 commutator segments
5.1, 5.2
5.3, 5.4
4.1, 4.2
4.3, 4.4
3.1, 3.2
3.3, 3.4
4
5
1
2
3
4
2.2 3.2
5.1 1.2
5
6
2
1
N
S
3.1 4.1
1.1 2.1
1.1, 1.2
1.3, 1.4
3
N
5.4
2.1, 2.2
2.3, 2.4
7
8
1.3 2.3
4.2 5.2
9
10
11
12
S
13
14
2.4 3.4
5.3 1.4
3.3 4.3
15
16
17
18
4.4 5.4
19
20
V
It is also possible to make such a concentrated winding armature with only 2 brushes by
using equalized connections on the commutator as shown in the conventional armature of
Fig. 11. In this case, the number of coils can be also reduced to facilitate the
manufacturing process (Fig.13).
Fig. 14 (right) shows a new concentrated winding armature made of a soft magnetic
composite (SMC) material that can replace a 20 slots lap winding armature (Fig 14, left)
made of a stack of laminations in a 180 W/12V motor fan application. The stator, the
brushes and the commutator are the same for both motors. These machines have similar
performance (torque and efficiency) and Table 4 summarizes a comparative analysis on
the material weights. The use of a concentrated winding provides an important weight
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reduction of 58 % when compared to the lap winding armature. The armature winding
resistance and the overall armature weight are nearly equal. The magnetic material
weight of the soft magnetic composite armature is increased because the tooth tips are
axially expanded to concentrate the air-gap magnetic flux into the teeth.
Fig.13. Diagram of a machine with 5 rotor slots, 4 stator poles, 20 commutator segments
and 2 brushes with a rotor winding made of concentrated windings wound around the
teeth
5.1, 5.2
4.1, 4.2
5
4
3.1, 3.2
3
N
1
2
5.1
4.1
3
2
4
5
6
3.2
7
8
1
N
S
1.1
5.2
1.1, 1.2
2.1, 2.2
4.2
9
10
2.1
11
12
13
S
3.1
14
1.2
15
16
5.2
2.2
17
18
19
20
V
The superior performance of the multi-layer concentrated winding (for current
commutation) has also been confirmed in another study in the case of a 36V supply (Cros
and Viarouge, 2003). The long duration experimental tests at rated operation have shown
that there is no degradation of the commutator and brushes.
Fig 14: 180 W Motor fan with 4 stator poles: lap winding, 20 rotor slots (left);
concentrated winding, 5 rotor slots (right)
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Table 4. Comparative characteristics of 180W DC radiator cooling motor (Cros and
Viarouge, 2003)
Armature winding structure
Number of rotor slots
Number of stator poles
Number of brushes
Commutator segments
Brushes
Magnetic circuit material
Weight
Copper Weight
Total Weight without
Shaft and commutator
Lap winding
Concentrated
winding
20
4
2
5
4
2
20
2
Laminations
422 g
130 g
552 g
SMC
480 g
55 g
535 g
Synthesis of Efficient Brushed Dc Motor Structures with a Concentrated
Winding
The main requirement for an efficient winding armature is the maximization of the
winding coefficient kb which can be defined as the ratio between the fundamental
component of the magnetic flux embraced by a coil and the total magnetic flux per pole.
This coefficient must be near to unity to maximize the no-load emf amplitude with the
lowest number of turns (cros et al., 2002). Its value is less or equal to unity. Fig. 15
shows the winding coefficient value of several armatures versus the number of slots per
pole.
Fig.15. Variation of the winding coefficient for structures with a concentrated winding
1
0,95
winding coefficient (kb)
0,9
0,85
0,8
0,75
0,7
0,65
0,6
0,55
0,5
0,45
0,6
0,8
1
1,2
1,4
1,6
1,8
Number of slots per pole (s/2p)
One can see that the structures which offer the best winding coefficients are those which
have a number of slots nearly equal to the number of poles. It is always preferable to
choose a high number of stator poles to reduce the mass, however, this number should be
chosen based on a compromise considering the external diameter and the speed. The pole
AcademyPublish.org - Vehicle Engineering
221
number has an impact on the number of commutator segments and also on the number of
armature coils. To obtain an efficient brushed DC motor with concentrated winding, we
must select a machine of 2p stator poles and S rotor teeth which respects the following
condition:
S  2 p  a with a  1 or 1 or 2 or 3
(1)
With brushed DC motors with concentrated windings, the use a number of commutator
segments (Z) greater than the number of slots is better to minimize current commutation
problems. In this case, there is a plurality of simple coils wound around the same tooth.
The terminals of each coil are connected to different segments for simultaneous
commutation by different brushes. This type of coil arrangement will allow perfectly
balanced parallel paths and avoids any circulating current between these parallel circuits.
The number of segments (Z) is generally equal to the Least Common Multiple (LCM) of
S and 2p:
Z  LCM ( S , 2 p )
(2)
Generally, the number of brushes (2B) is equal to the number of stator poles (2p), as
shown by Eq. 3 and N of coils are wound around each tooth (Eq. 4). Consequently, the
number of coils per parallel path Npa is obtained by Eq. 5.
2B  2 p
N
Z
S
N pa 
(3)
(4)
Z
2p
(5)
In automotive applications the performance of the motor is sometimes compromised in
order to minimize the manufacturing costs. For example, it may be interesting to reduce
the number of brushes (2B) and the number of coils per tooth (N), particularly in cases of
higher number of stator poles. By employing equalizer connections, this simplification
could be easily realized and the winding would be always well balanced. However, this
modification will affect the life expectancy of the brushes because the current to be
commutated by each brush will increase.
Table 5 presents the main parameters of brushed DC machines for small power
applications which respect the former expressions. The possible simplifications for each
structure are shown in gray-colored cells.
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Table 5. Main parameters for DC motor structures with a well balanced concentrated
winding
2P Poles number
S slots
Z commutator segments
N coils per tooth
Npa coils/path
2B brushes
kb winding coefficient
2
3
6
2
3
2
0.87
4
5
20
2
6
5
30
4
2
6
7
42
6
2
6
8
24
6
2
6
5
5
7
4
2 4
0.95
2 6
0.95
2 6
0.97
2 6
0.92
8
10
40
2 4 8
5
2 4 8
0.95
Another possible simplification is to divide the number of commutator segments Z by
two (Eq. 6) and to reduce the number of coils per tooth. This simplification will result in
an unbalanced emf in the different coil paths between brushes but the level of this
unbalance is inversely proportional to the number of coils in each parallel path. The main
parameters of this kind of machine are presented in table 6.
Z
LCM ( S , 2 p )
2
(6)
Table 6. Main parameters for downgraded DC motor structures with concentrated
winding
2P Poles
number
S slots
Z=LCM(S,2P)/2
commutator
segments
N coils
per tooth
2B brushes
kb winding
coefficient
2
4
4
6
6
8
8
8
3
3
5
10
5
10
5
15
7
21
7
28
9
36
10
20
1
2
0.87
1
2
2 4
0.951
1
2
2 4
0.951
1
3
2 6
0.951
1
3
1
2 6
0.975
2
2
4
1
4 8
0.975
2
2
4
1
2
2
4 8
0.984
2
4 8
0.951
Synthesis of Efficient Brushless DC Motor Structures with Concentrated
Windings
The selection of a particular combination for the number of poles and the number of slots
in the armature of a brushless dc motor is done in the same manner. First, the number of
rotor poles 2p is chosen based on the operating speed and the rotor external diameter.
This number should be maximised to reduce the mass of the motor, however, it should be
chosen on the basis of a compromise with respect to the electric frequency in order to
limit the magnetic losses. According to the data shown in Fig. 15, the number of slots
should be close to the number of poles to maximize the winding factor and consequently
the motor performance.
The various combinations of slots and poles which allow for the realization of balanced
windings can be determined by Eq. 7 for the case of three-phase armatures. GCD(S,2p) is
the Greatest Common Divisor between the number of slots (S) and the number of poles
(2p) and k is an integer.
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223
S
 3k
GCD ( S , 2 p )
(7)
The number of slots per pole and per phase is defined by the following equation in the
case of a machine with mph phases.
S pp 
S
2 p  mph
(8)
Table 7 gives a list of the various structures of three-phase machines for which it is
possible to obtain balanced concentrated windings. The number of slots per pole and per
phase (Spp) and the winding coefficient kb are listed in each table cell. The winding
coefficient kb is the performance indicator for each solution. The gray-colored cells
indicate the most efficient structures which present a winding coefficient higher than 0.9.
There is an optimal value of Spp that allows for the maximization of the winding
coefficient kb, for each phase-number. These target values are respectively equal to 1/3
for a 3-phase motor, 1/5 for a 5-phase motor and 1/7 for a 7-phase motor. However, it is
not possible to realize a polyphase structure with a number of slots equal to the number of
poles (S=2p). We can choose however a structure with a number of slots nearly equal to
the number of poles, e.g., S=2p ±1 or S=2p ±2. These structures have the advantage of
minimizing the cogging torque without slot skewing (Cros et al., 2002). Indeed, the
number of pulsations of the cogging torque for a complete mechanical turn corresponds
to the Least Common Multiple between the number of slots and the number of poles.
Therefore, the frequency of the cogging torque is very high and its amplitude is low.
Table 7. Combinations of number of slots (S) and poles (2p) allowing for the realization
of three-phase machines with balanced concentrated windings
2p
S
3
6
2
4
1/2
0.866
1
0.5
1/4
0.866
1/2
0.866
3/4
0.617
1
0.5
9
12
2
0.259
6
1/2
0.866
15
18
1
0.5
21
24
27
30
224
2
0.259
8
10
1/8
0.866
1/4
0.866
3/8
0.945
1/2
0.866
5/8
0.711
3/4
0.617
7/8
0.538
1
0.5
9/8
0.423
5/4
0.389
1/10
0.866
1/5
0.5
3/10
0.945
2/5
0.966
1/2
0.866
3/5
0.735
7/10
0.650
4/5
0.588
9/10
0.525
1
0.5
12
1/4
0.866
1/2
0.866
3/4
0.617
14
16
1/14
0.866
1/7
0.5
3/14
0.617
2/7
0.966
5/14
0.951
3/7
0.902
1/2
0.866
4/7
0.760
9/14
0.695
5/7
0.640
1/16
0.866
1/8
0.866
3/16
0.328
1/4
0.866
5/16
0.951
3/8
0.945
7/16
0.870
1/2
0.866
9/16
0.767
5/8
0.711
18
1/2
0.866
20
22
1/20
0.866
1/10
0.866
3/20
0.328
1/5
0.5
1/4
0.866
3/10
0.945
7/20
0.953
2/5
0.966
9/20
0.878
1/2
0.866
1/22
0.866
1/11
0.5
3/22
0.617
2/11
0.259
5/22
0.711
3/11
0.902
7/22
0.953
8/22
0.958
9/22
0.915
3/22
0.874
24
1/8
0.866
1/4
0.866
3/8
0.945
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Method for the Determination of the Winding of a Three-Phase Machine
After the selection of the number of slots and poles, the next step is to determine the
winding configuration and the position of the coils in the slots. Generally, for a threephase machine, it is preferable to apply a method similar to the one used for the design of
large synchronous machines with a fractional number of slots per pole and per phase.
This method is based on the decomposition of the number of slots per pole and per phase
(Spp). For values below unity, Spp must be reduced to a fraction of two non divisible
integers b and c, as shown in Table 7.
Spp 
b
c
(9)
A repeatable winding sequence is a list of integer numbers which characterizes the
distribution of the larger and smaller pole-phase coil groups in the armature. This
repeatable sequence can be derived from Spp and Eq. 9. The list has c numbers made of 0
and 1. The number of “1”s in the repeatable sequence is equal to b and the number of
“0”s is equal to b-c. The initial repeatable sequence can then be described as follows:
c


0 0 0 . . . 0 111 . . . 1

 


c b
(10)
b
The configuration of the whole winding structure is derived from 3 consecutive
repeatable sequences under c rotor poles. If c is an even number, the same configuration
can be repeated as a periodic distribution of coils. If c is an odd number, this distribution
is antiperiodic and the direction of the conductors in the coils should be reversed. For a
given structure, one can determine an optimal sequence to find the winding that has the
highest performance (and the highest winding coefficient). This optimal sequence is
derived from the initial one and has the most regular distribution of the number ‘1’s
among the number ‘0’s.
To illustrate this winding determination method, we present an example with a threephase machine which has 18 slots and 16 poles. The configuration of the whole winding
can be determined in eight steps as shown in Fig. 16. In the first step, the Spp fraction is
reduced to 3/8 and the initial repeatable sequence of the winding is found to be composed
of five ‘0’s and three ‘1’s. Then, the repeatable sequence is reproduced three times (step
4). In the fifth step, the usual phase sequence AC'BA'CB' is associated to the whole
sequence (‘A’ characterizes the return conductor corresponding to conductor A). The
conductors associated to number ‘1’ in the sequence are selected to make the first layer of
winding (step 6). Generally, this layer of winding cannot be directly realized to form a
concentrated winding. In the seventh step, the second layer of the winding is obtained by
reproducing and shifting the initial layer by a tooth or a slot width. The direction of each
conductor must be also reversed. The final configuration of the winding of a three-phase
machine with 18 slots and 16 poles can be checked in the last step. The figure shows only
AcademyPublish.org - Vehicle Engineering
225
the winding for 8 rotor poles and this distribution repeats itself for the next 8 poles.
Fig. 16. Determination of the concentrated winding of a three-phase machine with 18
slots and 16 poles (periodic symmetry of the winding under 8 poles)
18
3
Step 1 :
S pp 

3  14 8
Step 2 : Initial repeatable sequence : 0 0 0 0 0 1 1 1
Step 3 : Optimal repeatable sequence for highest winding performance : 1 0 0 1 0 0 1 0
Step 4:
1 0 0 1 0 0 1 0
1 0 0 1 0 0 1 0
1 0 0 1 0 0 1 0
Step 5:
A C’ B A’ C B’ A C’
B A’ C B’ A C’ B A’
C B’ A C’ B A’ C B’
Step 6 :
A
A’
Step 7 :
Step 8 :
A’
A
A
B
A
A’
A’ A’
N
B’
A A
S
B
B’
A’ B
N
B
B’ B’
S
C
B’
C’
C
C’
C
C’
B B
B’ C
C’ C’
N
S
N
C’
C C
S
ANALYTICAL DESIGN AND FORMULATION OF AN OPTIMIZATION
PROBLEM
An iterative design process for brushed or brushless surface mount PM motors requires a
small computation time for estimation of steady state performances and constraint
evaluations in regard to the application requirements. Generally, the optimization
problem is formulated with a reduced number of variables, an analytical dimensioning
process, and several rapid modeling methods for comparison of different possible
solutions. Fig.17 presents a general flowchart of a design method based on the iterative
optimization process.
The main motor performance requirements impose several non-linear constraints for the
design method. These are the torque (Te), the motor speed (N), the supply voltage (UDC),
the operating temperature (Tw) and the minimal efficiency ( µ
8.
Other constraints for the maximal motor size are also added by using two parameters: the
maximum external diameter (Dext_max) and the maximum axial length of the motor
(Lmax).
Before beginning the optimization process, one selects the motor structural parameters
i.e. the number of slots (S) and the number of poles (2p), by taking account of the
winding type and the number of phases (mph). Such a decision should also consider the
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motor size and the winding performance, represented by the winding coefficient (kb), as
discussed in the preceding sections.
Table 8. Main specification parameters
Torque (N.m)
Te
Speed (rpm)
N
UDC
DC voltage (V)
Maximal external Diameter (m)
Dext-max
Maximal motor length (m)
Lmax
Working temperature (°C)
Tw

Minimal efficiency
Different kinds of permanent magnet, soft magnetic and conductive materials can be
selected and characterized by their respective parameters like the magnetic saturation
threshold for the laminations or the residual induction (Br) for the permanent magnets
(Hamdi, 1994). The residual induction and the copper resistivity (ρ) are adjusted
according to the motor operating temperature. The maximal flux density B sat in the softmagnetic material is fixed to avoid magnetic saturation. Several technological constraints
should also be considered. These parameters impose a limit for certain parameters like
the maximal copper filling factor kr and the minimal air-gap thickness. Generally, the
filling factor does not exceed 0.35 in a small motor and the air-gap thickness is around 1
mm. Table 9 summarizes main material characteristics and technological parameters.
Fig.17. Flowchart of the analytical design method of the motor structure
Motor structure parameters
Number of armature slots: S
Number of permanent magnet poles: 2p
Number of phases: mph
Winding performance coefficient: kb
Non-linear constrained optimization method
Iterative process
Design
Variables
Table 9
Specification and
realisation
Constraints
Tables 7 & 8
Analytical design
model
Table 10
Performance
Modelling
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A small number of variables including geometrical dimensions, current and magnetic flux
densities are computed by a non-linear constrained optimization procedure that takes
account of the performance criteria and the specifications constraints of the motor
application. These design variables are listed in Table 10. It should be noted that one may
use several similar variables (Bmag) to impose different flux densities in various parts of
the magnetic circuit. Fig. 18 illustrates a number of geometrical stator parameters and
Table 11 shows several equations which can be used to compute the main characteristics
of the motor during the iterative design process.
Table 9. Material parameters and technological constraints
Iron Maximal flux density (T)
Bsat
Lamination (< 1.8 T) and SMC (< 1.4T)
Residual induction (T)
Br
Ferrite < 0.4 T and NdFeB bonded (< 0.7 T)
Copper resistivity (Ω.m)
ρ
Air-gap thickness (m)
e
> 0.75 mm
Copper filling factor
kr
< 0.35
Table 10. Main design variables
Total copper section (m2)
Scu
2
Current density (A/m )
J
Armature (airgap) diameter (m)
D
Armature length (m)
L
Magnet thickness (m)
la
Permanent magnet arc ratio
ß
0  1
Bmag
Bmag  Bsat
Iron flux density (T)
Fig.18. Sectional view of a permanent magnet motor with external armature
eca
etb
t
De
ecr
e
Dint
Dext

la
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Table 11. Analytical design model for a brushless DC motor with concentrated winding
Parameter
Specific armature
loading (A/m)
Air-gap flux
density (T)
Analytical expression
Ba
Inner Rotor :
B r  la


D
D  ln 

 D  2  ( e  la ) 
2
External Rotor :
B r  la
 D  2  ( e  la ) 
D  ln 

D


2
Electromagnetic
Torque (Nm)
Tooth angular width
(rad)
T
Constraint relation
J  S cu
 D
A
k b  s in (β
θ

)
2
2  D 2  L  Ba  A
T  Te
Ba
2

Bm ag S
 
D
Ba
 2



 t 
4 B m ag  S

 D
Ba
 

4p
Bm ag
Tooth tips thickness
(m)
etb
Armature yoke
thickness (m)
eca
Permanent magnet
yoke thickness (m)
ecp
 
Slot diameter (m)
De
External armature :
D
 D
Ba

4p
Bm ag
 2  etb  
2
4  A   D  2  etb 
S
kr  J  (1   t 
)
2
Inner armature :
4  A   D  2  e tb 
S
k r  J  (1   t 
)
2
External armature : D e  2  eca
D
External diameter (m)
Dext
 2  e tb  
2
Inner diameter (m)
Dint
External armature : D
 2  ( e  la  e c p )
D e  2  eca
Inner armature :
One turn length per
coil for an external
armature
Lturn
Number of turns per
coil
Ns
Phase Resistance
Rph
RMS Phase current
Iph
RMS No-load flux
per phase
Total Copper losses
θ
Loss
2L 

S
Dext  Dext max
D  2 ( e  la  e c p )
Inner armature :
Ba

 1   
B sa t

 p  m ph 
D int  D int max


   D e  D  2 etb  
4

30
U
AD
 DC
S T  N
4 2
2 S2  Lturn
Ns2    
3
Scu
1 Scu  J

Ns
2S
T
Ns 
m ph  p  I
mph  Rph  Iph2
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229
PERFORMANCE ANALYSIS WITH FINITE ELEMENT AND TIMESIMULATION METHODS
The optimal solution must be evaluated by finite element analysis and time-simulation
methods to quantify the analytical model error or to validate the performances before
prototype realization. One can use a finite element model with step by step time
resolution of Maxwell equations. Such modeling method can compute magnetic losses
and takes account of magnetic saturation and rotor motion. When significant differences
on motor performances are observed between finite element and analytical methods,
several correction coefficients for analytical models are derived from these evaluations
and another optimization process is performed. With such a method, the convergence of
optimal analytical design process is achieved and all the constraints imposed by the
application specifications are validated by finite elements or time-simulations (Cros et al.,
2008).
In the case of the finite element calculation of a brushed DC machine, the collector
modeling is based on an equivalent circuit similar to a full bridge converter using a direct
coupling method with meshed armature coils (Fig. 19). Specific switches with an arc
model must be used to reproduce the conduction sequences between brush and collector
segments and to simulate the conduction by the electric arc (Sincero et al., 2010). This
approach is powerful for final solution analysis but it is very time consuming. It is
possible to estimate commutation phenomena more accurately and analyze influence of
some parameters such as the brush angle. To illustrate the performance of such finite
element simulation, the comparison of experimental and simulated armature current
waveforms for a 3 slots-2 poles DC motor with a concentrated winding is presented in
Fig. 20 (Sincero et al., 2010).
Fig.19. Simulation scheme for the finite element simulation of a 3 slots-2 poles DC motor
with a concentrated winding
Another method to model the brush and brushless motor variable speed operation is a
time-simulation method (Fig. 21) based on the matrix resolution of the differential
electrical equations of armature coils (Sincero et al., 2010). The armature winding coils
are modeled by their equivalent circuits composed of self and mutual inductances,
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resistances and electromotive forces. These equivalent circuits use constant inductance
values and neglect magnetic saturation. The commutator connects the armature coils to
the input DC source and by Eq. 11, we determine the armature coil current, which is
represented by vector [I]. The electromotive force [E], and the electromagnetic torque T o,
are determined by Eqs. 12 and 13:
[V ]  [ Rcoil ][ I ]  [ L]
d[ I ]
d [ ( )]
 p
dt
d
(11)
[ E ]  K flux p sin(2 f e  p ( ))
T0 
(12)
[ E ]T [ I ]
 Tironloss  Tmech

(13)
Where [V] is the matrix of coil voltages, [L] is the coil inductance matrix, R coil is the coil
resistance, [λ] is the armature flux vector, [θ] is the vector of the spatial phase angles of
the armature coils, p is the pole pair number and Ω is the mechanical angular speed.
Fig.20. Experimental & simulated waveforms for rotor coil voltage, armature current and
DC supply current.
40
Voltage (V)
Current (A)
15
30
10
20
10
5
0
0
-10
-20
Rotor coil voltage
DC Current
Rotor Coil current
-30
-40
0.025
0.03
0.035
-5
Times (s)
0.04
-10
0.045
The matrix resolution simulation is preferred since it speeds up the time spent on the
performance analysis of PM synchronous motors. Besides, it allows comparing different
structures by only changing the files that generate the parameter matrices. This approach
is more powerful and efficient during a design process where different motors have to be
compared.
The commutator and the control blocks are the systems that differ between a PMBLDC
motor and a PM dc motor in this simulation strategy, although their basic functionalities
AcademyPublish.org - Vehicle Engineering
231
are the same. Based on information about the rotor position, the gate signals are
generated to feed the armature coils with a current that is in phase with the emf. This is
necessary to maximize the output torque. However, it is also possible to simulate other
types of control strategies. The simulation method for the commutator of both the
brushless and brushed motors is detailed in (Sincero et al., 2008).
Fig.21. General flowchart of a time-simulation method for brushed and brushless
machines

t
0
dt
The inverter simulation model can neglect the PWM modulation by using the value of the
inverter output voltages averaged over one modulation period. The voltages applied to
the armature coils are positive or negative depending on the rotor position. During the
diode conduction, an amplified current error determines the voltage to be applied in order
to maintain a zero current in the phase (Figueroa et al., 2003). This simulation reproduces
accurately, among others, the waveforms of the machine coils voltages and currents, the
joule and inverter losses, and the torque ripple due to phase commutation effects
(Figueroa et al., 2003).
The average value over each modulation period can be also used to model the dc-dc
converter. This linear variable dc voltage source is connected to the collector model. The
real operation is similar to the inverter one: depending on the rotor position, the positive
or negative input voltage is applied to the armature coils, which is equivalent to the
collector segment contact with the positive or negative brush. The coil under
commutation is short-circuited in order to invert its current direction while maintaining
the output torque constant. If the current commutation is not completed at the end of the
short-circuit interval, an electric arc voltage is generated and applied to the armature coil
which generates an arc current until the complete coil current inversion (Sincero et al.,
2008). The advantage of this methodology is the accurate estimation of the machine
current waveforms, joule and commutation (arc and brush) losses, torque ripple and DC
input current . Fig. 22 shows the brushed dc motor model block diagram.
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Fig.22. Brush dc motor model block diagram.
Brush Machine
Input Stage
Coupling
Vs
Vb
Series
Impedance
Ib
I in
[U ]
Collector
Model
[T u]
[I]
[T i ]
[V ]
[J]
Supply
Voltage
[Seq]
Control
C em
Mechanical
Load
Ω
[J]
Electro Mechanical
Conversion
[E ]
Currents [J]
calculations
(Energy
storage
[V ]
circuits –
RL )
Armature Model
Figs. 23 and 24 show the armature coil current and the DC input current for a PMBLDC
motor and PM dc motor, respectively. The steady state waveforms show a good
agreement between experimental and simulation results for both motors.
Fig. 23: PMBLDC motor armature coil current.
15
Armature Coil Current (A)
10
5
0
-5
-10
-15
0.005
0.01
0.015
Time (s)
0.02
0.025
Experimental
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Simulated
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Fig. 24: PM DC motor input current.
18
16
Dc input current (A)
14
12
10
8
6
4
Simulated
Experimental
2
0
0.031
0.032
0.033
0.034
0.035
Time (s)
0.036
0.037
0.038
0.039
CONCLUSIONS
The constant need to replace mechanical actuated systems and the proposed
move toward a 42V platform, has led to rapid developments in the design of DC
machines for car accessories. The advantages associated with brushless
machines for variable speed applications have also motivated the manufactures
to reconsider the use of traditional brushed DC machines for such applications.
In this context, we have shown that machines with concentrated windings are
particularly efficient. This type of winding is an interesting economical solution
for the minimization of the copper volume or to improve motor efficiency.
The design methodology presented in the preceding sections has been well
validated using several commercial machines. This methodology is general and
all of the steps in the design process for a DC motor (brushed or brushless) have
been described. This process benefits from new calculation techniques
(optimization, modelling) which are increasingly powerful and efficient.
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Cho and Johnston (1999), "Electric motors in vehicle applications", Proceedings of the
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Cros, Radaorozandry, Figueroa and Viarouge (2008), "Influence of the magnetic model
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Cros, Viarouge, Chalifour and Gélinas (2003), "Small brush DC motors using Soft
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