DESIGN OF SURFACE-MOUNTED PERMANENT-MAGNET BRUSHLESS DC MOTORS
COMBINED WITH GEAR MECHANISMS
Yi-Chang Wu1 and Hong-Sen Yan2
1 Department
of Mechanical Engineering, National Yunlin University of Science & Technology, Taiwan
of Mechanical Engineering, National Cheng Kung University, Taiwan
E-mail: wuyc@yuntech.edu.tw; hsyan@mail.ncku.edu.tw
2 Department
ICETI 2012-J1115_SCI
No. 13-CSME-65, E.I.C. Accession 3523
ABSTRACT
This paper presents novel design concepts by integrating surface-mounted permanent-magnet brushless DC
(BLDC) motors with embedded planetary gear trains (PGTs) to form compact structure assemblies with
desired functions. The operational principles and configurations of surface-mounted permanent-magnet
BLDC motors are introduced. With the aid of fundamental circuits, kinematic characteristics of PGTs are
identified. For rationalizing integrated design concepts, design requirements and constraints are concluded.
Four feasible design concepts with interior and exterior configurations are successfully generated subject to
these design requirements and constraints. The features of the integrated devices are also indicated.
Keywords: integrated design; brushless DC motor; gear mechanism.
CONCEPTION DE MOTEURS CC SANS BALAIS À AIMANT PERMANENT EN APPLIQUE
COMBINÉ AVEC DES MÉCANISMES À ENGRENAGES
RÉSUMÉ
Cet article présente des concepts innovateurs en intégrant des moteurs CC sans balais à aimant permanent en
applique avec des mécanismes à engrenages intégrés pour former une structure compacte ayant les fonctions
souhaitées. Les principes opérationnelles et configurations des moteurs CC sans balais à aimant permanent
en applique sont présentés. Avec l’aide de circuits fondamentaux et les caractéristiques cinématiques, des
mécanismes à engrenages sont identifiés. Pour la rationalisation des concepts, des exigences de conception
et contraintes sont déterminées. Quatre concepts possibles avec des configurations intérieures et extérieures
sont générés avec succès. Les caractéristiques intégrées du dispositif sont indiquées.
Mots-clés : concept intégré ; moteur CC sans balais ; mécanisme à engrenages.
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439
NOMENCLATURE
BLDC
DOF
PGT
GKC
SR
Zi
brushless DC motor
degrees of freedom
planetary gear train
geared kinematic chain
speed ratio
number of gear-teeth of gear i (teeth)
Greek symbols
γ
ωi
gear ratio
angular speed of link i (rad/s)
1. INTRODUCTION
Electric motors and gear reducers/multipliers respectively provide required functions of power generation
and transmission, which are frequently adopted in present day machinery. In general, these two kinds of
devices are designed and manufactured independently. To meet the needed drive requirements, gear reducers/multipliers are connected to electric motors for transforming speed and torque. In fact, a general
examination of related patents [1–3] and existing products in the current market [4] reveals that most combinations of electric motors and gear reducers/multipliers focus merely on connecting casings of gearboxes
to stators of electric motors. Besides, intermediary mechanical components, such as couplings or powertransmitting elements, are further employed between their terminals to transmit motion and power from the
electric motor to the gear reducer/multiplier. The existing designs inherently suffer from three main disadvantages. The first one is the use of couplings or power-transmitting elements, which not only is the primary
source of failure, but also increases the maintenance complexity and manufacturing costs. The second one
is the additional mechanical losses caused by the friction of these intermediary mechanical elements, which
results in undesirable low efficiency. The last one is the incompact workspace arrangement due to individual
designs of the electric motor and the gear reducer/multiplier, which makes it difficult to reduce the overall
size. Therefore, the combination of the electric motor and the gear reducer/multiplier should be developed
from the perspective of system integration to overcome the above shortcomings. During recent years, an
increasing interest in the integrated design of power sources and corresponding driven devices [5, 6] has
evolved. Compared with traditional designs, they offer new opportunities to improve system performance,
reliability, safety, and/or reduce manufacturing costs.
The purpose of this paper is to integrate the surface-mounted permanent-magnet brushless DC (BLDC)
motor with the basic planetary gear train (PGT) to form a compact structure assembly with the desired
functions. The qualitative features of the integrated design required to overcome the drawbacks of traditional
products are addressed herein. The reduction of the cogging torque of the integrated device is verified by
finite-element analysis.
2. CONFIGURATIONS OF SURFACE-MOUNTED PERMANENT-MAGNET BRUSHLESS DC
MOTORS
The surface-mounted permanent-magnet BLDC motor is essentially configured as alternate magnet poles
rotating past stationary conductors that carry the current. Considering the magnetic circuit of such an electric
machine, permanent magnets initially drive the magnetic flux across the air gap and into the stator core.
The flux then travels circumferentially along the stator core, and finally returns across the air gap as well
as through the back iron of the rotor to form closed flux loops. The back-EMF of the electric motor is
induced by the magnetic flux, which is also coupled with the winding coils. Thus, the electromagnetic
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force is produced by mutual interaction between current-carrying coils and the magnetic flux generated
by permanent magnets. Based on the Lorentz force equation, the current should reverse the polarity in
synchronism with the rotor position to develop a unidirectional torque on the rotor, hence resulting in motion.
Hall sensors, encoders, or similar devices are fixed to the stator to monitor the position of the rotor so that
stator windings can be energized in a proper sequence by the power electronic controller. The BLDC motors
possess a variety of constructions for different industrial applications. The most typical configuration is
cylindrical in shape with radial-flux topology. Among these radial-flux BLDC motors, the surface-mounted
permanent-magnet BLDC motor has been used extensively for decades due to the excellent advantages of
simple rotor structure, high motor efficiency and low manufacturing cost. In this study, only the surfacemounted permanent-magnet configurations with interior-rotor and exterior-rotor types are of concern. For
the interior-rotor BLDC motor, permanent magnets in even numbers are mounted on the rotating rotor, while
the stator with fixed polyphase windings appears on the outside of the rotor. Both the rotor and stator are
typically comprised of a lamination of magnetic steel slices to reduce the eddy current loss. Figure 1a shows
a cross-sectional view of an interior-rotor BLDC motor. It has six stator slots around which coils are wound.
The rotor is constructed by placing four arc-shaped permanent magnets with opposite poles mounted on
the outer surface of a soft-iron cylinder to provide flux return paths. The permanent magnets are usually
magnetized in the radial or parallel direction. From the structural point of view, such a motor configuration
provides a natural shield to protect the rotor from its surroundings. Besides, an important characteristic is its
high torque/inertia ratio, which makes this configuration widely employed in servo systems for the purposes
of rapid acceleration and deceleration. Conversely, the exterior-rotor BLDC motor is structurally inverted
to the interior-rotor type. Figure 1b shows a 3-phase, 4-pole/6-slot, exterior-rotor BLDC motor used in
treadmills. According to its configuration, permanent magnets are affixed to the inner surface of the rotor
yoke, which prevents the magnets from flying apart, especially in high-speed applications. Since the crosssection of the exterior-rotor BLDC motor is identical to the DC commutator motor, DC armature winding
machines can easily be adopted to wind the stator. Therefore, the main features of the exterior-rotor design
are simple to wind and easy to manufacture, resulting in low production cost. In addition, the relatively
large rotor diameter increases the moments of inertia, which in turn helps to maintain constant rotational
speed. Such a configuration is frequently used in data storage hard-disk drives, cooling fans, blowers and
direct driven wheel motors for electric scooters and vehicles. In general, when a high-torque and lowspeed electric motor is required, the interior-rotor design would be appropriate by using a high number of
magnet poles because numerous magnet poles usually create greater torque for the same current level. If
a continuous speed or higher speed is required which is constant or varies only slightly, the exterior-rotor
design can be considered [7]. Both of these two motor configurations are employed to develop innovative
design concepts of integrated BLDC motors and PGTs.
3. KINEMATIC CHARACTERISTICS OF THE BASIC PLANETARY GEAR TRAIN
The kinematic characteristics of a PGT are mainly determined by its topological structure that always governs the performance of this mechanism. Hence, the analysis of the kinematic structure, which contains the
essential information about which link is connected to which other link by what type of joint, is a major task
for the study of PGTs [8]. A PGT is a geared mechanism that consists of a geared kinematic chain (GKC)
with its central axis supported by bearings housed in the casing. For example, Fig. 2a shows a five-link, twodegrees-of- freedom (DOF) basic PGT used in a 3-speed rear transmission hub of bicycles. It is the simplest
PGT in the PGT family. The corresponding functional schematic of the basic PGT is depicted in Fig. 2b. For
reasons of clarity and simplicity, only those functional elements that are essential to the structural topology
are shown in the functional schematic. It consists of a ground link (member 0), a sun gear (member 1), a
carrier (member 2), a ring gear (member 3) and a planet gear (member 4). Since the sun gear, carrier and
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Fig. 1. Typically configurations of surface-mounted permanent-magnet BLDC motors: (a) interior-rotor type;
(b) Exterior-rotor type.
Fig. 2. Basic planetary gear train: (a) schematic diagram of the PGT; (b) functional schematic of the PGT; and
(c) functional schematic of the GKC.
ring gear all rotate about the same central axis mounted on the ground link, they are called coaxial links.
The sun gear is adjacent to the planet gear with an external gear pair, while the planet gear is adjacent to
the ring gear with an internal gear pair. The carrier is adjacent to the sun gear and planet gear with revolute
pairs. By releasing the ground link of the PGT, the corresponding one-DOF GKC is obtained, as shown
in Fig. 2c. The dependent relation between the input and output links of a PGT can be evaluated through
kinematic analysis. In the study of kinematic analysis of PGTs, several methods have been developed over
a long period of time. One frequently used approach is the fundamental circuit method. According to the
definition, a fundamental circuit is made up of one gear pair, which consists of two meshing gears i and
j, and one carrier k to maintain a constant center distance between the two gears, which is symbolically
denoted as (i, j)(k) [9]. For a fundamental circuit, the corresponding fundamental circuit equation is
ωi − γ ji ω j + (γ ji − 1)ωk = 0
(1)
where ωi is the angular speed of link i, γ ji = ±Z j /Zi represents the gear ratio and Zi is the number of teeth
on gear i. The positive sign of the gear ratio is for an internal gear pair, and negative for an external gear
pair. According to the structural characteristics, the number of fundamental circuits is equal to the number
of gear pairs for a PGT. Besides, only the coaxial links connected to the casing can be used as the input,
output, or fixed links due to the engineering reality. As can be seen from Fig. 2, there are two gear pairs in
the basic PGT and two fundamental circuits, identified as (1, 4)(2) and (3, 4)(2), respectively. The related
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Table 1. Arrangements of the input, fixed, and output links for the basic PGT.
Case Fixed Input Output
Speed ratio
SR range
I
1
2
3
Z3 /(Z1 + Z3 )
SR < 1
II
1
3
2
(Z1 + Z3 )/Z3
SR > 1
III
2
1
3
−Z3 /Z1
|SR| > 1
IV
2
3
1
−Z1 /Z3
|SR| < 1
V
3
1
2
(Z1 + Z3 )/Z1
SR > 1
VI
3
2
1
Z1 /(Z1 + Z3 )
SR < 1
fundamental circuit equations can be written as follows:
ω1 − γ41 ω4 + (γ41 − 1)ω2 = 0
(2)
ω3 − γ43 ω4 + (γ43 − 1)ω2 = 0
(3)
By eliminating ω4 from Eqs. (2) and (3), the kinematic equation of the basic PGT can be obtained as
γ43 ω1 + (γ41 − γ43 )ω2 − γ41 ω3 = 0
(4)
where γ41 = −Z4 /Z1 and γ43 = Z4 /Z3 . Since it is a two-DOF gear mechanism, two independent inputs: one
input link and one fixed link are required to obtain a predictable output. By designating three coaxial links
as the input, fixed and output links, respectively, there are a total of P33 = 3! = 6 different arrangements, as
shown in Table 1. The speed ratio (SR), which is defined as the ratio of the input shaft speed to the output
shaft speed, can be obtained from Eq. (4). As depicted in Table 1, cases II, III and V provide the function of
speed reduction, whereas others can be used for speed multipliers. We further observe that cases V and VI,
where ring gears are fixed links, respectively possess the largest speed reduction and speed multiplier for
the basic PGT. Furthermore, the rotations of the input and output links for cases III and IV, where carriers
are fixed links, are in opposite directions.
4. NOVEL INTEGRATED DESIGNS
The conceptual phase is a creative process and the essential source of all novel devices. Conceptual design of
BLDC motors with integrated basic PGTs requires generating preliminary solutions with desired functions
that satisfy design requirements and constraints. According to the kinematic structural characteristics of
the basic PGT, three coaxial links are designated as the input, ground and output terminals, respectively,
to obtain a constant SR. These terminals must be respectively connected to the BLDC motor, frame and
output shaft for the purpose of transmission. For compactness, one admissible approach is to structurally
integrate the gear element within the motor component; it can be achieved by placing gear teeth on the
circumference of the stator to form a single structural assembly. From the functional perspective, gear teeth
integrated on the stator would not only serve for transmission, but also for improving the magnetic field
distribution of the BLDC motor. Besides, the integrated device composed of the BLDC motor and the
basic PGT should not contain any additional mechanism in order to simplify system components as well as
minimize manufacturing costs. From the above discussion, the desired requirements of the integrated device
are summarized as follows:
R1. The fixed link of the basic PGT must be connected to the stator of the BLDC motor.
R2. The input link of the basic PGT must be connected to the rotor of the BLDC motor.
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Fig. 3. Exploded view and detailed components of the design concept Re-I.
R3. The output link of the basic PGT must be combined with the output shaft of the integrated device or
directly formed the output cylindrical casing of the integrated device.
R4. The gear teeth must be integrated on the stator of the BLDC motor facing the permanent magnets.
R5. Except for the basic PGT and the BLDC motor, no additional mechanisms are employed in the integrated device.
The design requirements mentioned above are to guarantee the resultant desired functions. However, design
constraints are flexible, and can be varied according to engineers’ decisions. In accordance with further
topological examination, several design constraints for this integrated device are carefully defined and concluded as follows:
C1. As the ring gear of the basic PGT is the fixed link, it is more suitable to be integrated with the stator
of an interior-rotor BLDC motor.
C2. When the sun gear of the basic PGT is the fixed link, it can adequately be combined with the stator of
an exterior-rotor BLDC motor.
C3. For the sake of simplicity, the integrated device will preferably be an interior-rotor type as an interiorrotor BLDC motor is employed, and vice versa.
For example, when the BLDC motor with an integrated basic PGT for the purpose of speed reduction is
needed, cases II, III and V of the basic PGT shown in Table 1 are possible solutions. Since the rotations of
the input and output links for case III are in opposite directions, an additional mechanism for reversing the
direction of the output link should be employed in practical applications. According to design requirement
R5, case III must be weeded out in the conceptual deign stage due to its complex kinematic structure. Only
cases II and V are available solutions. We first take case V of the basic PGT as an example to explain
the integrated process. Since the ring gear (member 3) of case V is the fixed link, an interior-rotor BLDC
motor should be employed for integration with the basic PGT, based on design constraint C1. Such an
integrated device, namely concept Re-I, is constructed with interior-rotor type based on design constraint
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Fig. 4. Cross-section of the design concept Re-I.
C3. By applying design requirements R1–R3, the ring gear and sun gear (member 1) of the basic PGT are
respectively connected to the stator and rotor of the interior-rotor BLDC motor, while the carrier (member
2) of the PGT is directly combined with the output shaft of the integrated device. The internal gear teeth of
the ring gear are further integrated on the stator due to design requirement R4. Figure 3 shows the exploded
view and detailed components of the design concept Re-I, employing a 4-pole/6-slot, interior-rotor BLDC
motor integrated with the basic PGT. It is noted that two or more identical planet gears (member 4) are
used to engage with the ring gear and the sun gear for increasing load capacity as well as providing better
balancing of gear tooth loads and inertial forces. The sun gear and the rotor of the BLDC motor are fastened
together by means of a key. The front and rear covers are fixed to the stator to support the rotor by bearings.
The geometry has the internal spur gear teeth integrated on the surfaces of pole shoes facing the permanent
magnets, as shown in Fig. 4. The addendum circle of the ring gear is coincident with the inner edge of the
stator. Each slot opening of the stator is formed by removing the bottom land of the ring gear; it enables
the copper conductors to be set into the slot areas without affecting the conjugate relation for gear meshing.
Since the internal gear teeth are integrated on the stator, the punching process forms the slices of the ring gear
and the stator simultaneously with the same punching die. Moreover, unlike the traditional manufacturing
process of cut gears, the ring gear is made up of stacking identical laminations of punched steel slices. In
assembly, those slices engaged with planet gears have a 90◦ mechanical angle shift with respect to others
along the central axis, enabling end-turns of copper windings to be entirely accommodated inside the slot
areas.
Similarly, the proposed device with exterior-rotor configuration can also be generated subject to design
requirements and constraints. We further take case II of the basic PGT to explain this better. Since the
sun gear (member 1) is the fixed link, an exterior-rotor BLDC motor is used to integrate with the basic
PGT due to design constraint C2. Such an integrated device, namely concept Re-II, is constructed with
an exterior-rotor configuration based on design constraint C3. According to design requirement R2, the
ring gear (member 3) of the basic PGT is integrated with the exterior-rotor of the BLDC motor to form a
single structural assembly, where permanent magnets are affixed to its inner yoke surface. The sun gear
made by stacking punched laminations is further connected to the stator due to design requirement R1,
whereby the whole part is fixed to the frame of the integrated device by keys. The carrier (member 2) of
the PGT is directly formed the output cylindrical casing of the integrated device due to design requirement
R3. Additionally, based on design requirement R4, the external spur gear teeth of the sun gear are integrated
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Fig. 5. Exploded view of the design concept Re-II.
Table 2. Design concepts of BLDC motors with integrated basic PGTs.
Design concept
PGT
BLDC motor
Fixed Input Output
SR
Re-I
3
1
2
SR > 1 Interior-rotor
Re-II
1
3
2
SR > 1 Exterior-rotor
Mu-I
3
2
1
SR < 1 Interior-rotor
Mu-II
1
2
3
SR < 1 Exterior-rotor
on the outer circumference of the pole shoes to face the permanent magnets. The addendum circle of the
sun gear is coincident with the outer edge of the stator. Figure 5 shows the explored view of the design
concept Re-II by employing a 4-pole/6-slot, exterior-rotor BLDC motor integrated with the basic PGT. It is
noted that the frame and output casing of the integrated device use ventilation holes to easily dissipate the
heat from the stator. Like the design concept Re-I, the sun gear also has a 90◦ mechanical angle shift along
the central axis to fully accommodate end windings inside the slot areas. Table 2 indicates four feasible
design concepts of integrated BLDC motors and basic PGTs that meet the desired design requirements
and constraints. From the functional point of view, design concepts Re-I and Re-II provide the function
of speed reduction, whereas concepts Mu-I and Mu-II provide the function of speed multiplication. From
the structural viewpoint, design concepts Re-I and Mu-I are related to the interior-rotor configurations,
whereas concepts Re-II and Mu-II are of exterior-rotor types. Figure 6 presents the corresponding schematic
diagrams of these four integrated designs, which are suitable for further embodiment designs and detailed
designs to implement these innovative devices.
In contrast to conventional devices, the proposed design concepts have the following qualitative
features:
1. The BLDC motor integrated with an embedded PGT reduces the use of couplings, the casing of the
gearbox and corresponding bolts or fasteners. Fewer mechanical components decrease production
costs, improve reliability and make the whole device more compact, lightweight and easier for maintenance.
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Fig. 6. Cut-away view of design concepts for BLDC motors with integrated basic PGTs: (a) design concept Re-I;
(b) design concept Re-II; (c) Design concept Mu-I; and (d) design concept Mu-II.
Fig. 7. Cogging torque for the proposed integrated design and the existing BLDC motor.
2. The motor component combined with the gear element into a single part makes it attractive for simplifying the component mechanisms. Furthermore, it shrinks the length of the power transfer path from
the rotor to the output shaft, which also reduces the required space for installation, especially in the
axial direction of the integrated device.
3. The output shaft of the gear reducer and the rotational shaft of the electric motor usually are not
coaxial in traditional products. For the proposed design, however, the rotor and stator of the BLDC
motor and most rotary components of the PGT are all coaxial with the output shaft, while the balanced
planet gears are also employed. From the kinetics point of view, it may possess better characteristics
on dynamic balance for reducing possible vibration and noise.
4. The geometry of gear teeth integrated on the pole shoes of the stator enables functions for transmission, while also acting as dummy slots for reducing the cogging torque and torque ripple of the
BLDC motor by properly determining the number of teeth. The cogging torque may induce undesirable mechanical vibration, position inaccuracy and noise, it is detrimental to electric motors and
mechanical devices [10]. Figure 7 shows the distribution of cogging torque of the integrated design
and an existing BLDC motor by using a commercial finite-element analysis package Ansoft/Maxwell
2D Field Simulator. The simulation result shows that the peak value of the cogging torque for the
integrated design is greatly reduced: it is only 30% of the existing BLDC motor. Such a characteristic
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is of benefit to the wide applications concerning the accurate position and motion control for BLDC
motors.
5. CONCLUSIONS
The conceptual design phase is an important stage in realizing engineering devices that satisfy desired functions, especially in regard to coming up with innovative devices. The structural characteristics of surfacemounted permanent-magnet BLDC motors as well as kinematic characteristics of the basic PGT, which are
the bases for the development of BLDC motors integrated with embedded PGTs, are summarized herein.
Design requirements and constraints are further identified based on the topological structures and the engineering reality to weed out complicated and/or unreasonable design concepts. Four feasible design concepts,
namely two interior-rotor configurations and two exterior-rotor types, satisfy the desired requirements and
constraints. These devices with compact structure assemblies provide functions of power generation associated with transmission, while successfully overcoming the disadvantages of conventional designs. Although
the presented concepts focus on the integrated BLDC motors and basic PGTs, the results of this work can
be extended to other kinds of electric motors and/or multi-stage PGTs for further industrial applications.
ACKNOWLEDGEMENT
The authors are grateful to the National Science Council (Taiwan, R.O.C) for supporting this research under
grants NSC 99-2212-E-006-033-MY3 and NSC 101-2221-E-224-019.
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