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Optimal design of an in-wheel BLDC motor for a kick scooter

Conference Paper · October 2010

DOI: 10.1109/ECCE.2010.5618023 · Source: IEEE Xplore

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University of Zagreb École Polytechnique Fédérale de Lausanne
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 Optimal design of an in-wheel BLDC motor for a kick scooter

Miroslav Markovic, Vincent Muller, Andre Hodder and Yves Perriard

Integrated Actuators Laboratory (LAI), Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland

Abstract—The paper presents an optimization design of an and on a horizontal rough surface (asphalt), the measured value
in-wheel BLDC motor for a kick scooter. The optimization is of resistive force (opposing to the movement) is 12.9 N and
performed using a genetic optimization tool combined with a 17.2 N, respectively. It is shown that those two values can be
FEM commercial software. The new contributions of the paper
are: i) introduction of three operating modes for which the motor approximately considered independent of the speed (for the
is optimized with a reduced number of FEM simulations and speed range between 3 and 5 m/s).
ii) new approach to simultaneously maximize the energetic effi-
ciency, minimize the cogging and respect the thermal constraint. A. Operating mode 0
The operating mode 0 is defined as the movement on a
Index Terms—BLDC motor, genetic algorithm, optimization.
horizontal smooth surface. The resistive force in this mode
I. I NTRODUCTION (12.9 N) is sufficiently low so that the user can be left to ride
without the motor assistance.
The electrically assisted vehicles, from the bicycle to the
The measurements show that a typical user generates the
truck, are gaining more and more popularity [1]-[5]. In many
force of 136 N during 0.5 s of acceleration phase. The speed
cases, the electric motor is in-wheel (direct drive) which
increases from the initial 4.17 m/s (15 km/h, 69.4 rad/s) to 4.87
greatly reduces the space occupied by the drive and eliminates
m/s (17.5 km/h, 81.0 rad/s). During the deceleration phase
the need for a mechanical transmission [6],[7]. The problem
which lasts for 4.76 s, the speed drops back to 4.17 m/s,
is that the rotating speed is relatively low, which requires a
completing one period of the movement (Fig. 2 a) and b)).
high torque and current to supply the necessary power.
The ratio between the acceleration time and the period time
This paper presents the optimal design of the motor for
is D=0.095.
an electrically assisted kick scooter. The laboratory [8] has
already built a prototype of the scooter but with a motor off-
the-shelf and mechanical transmission (Fig. 1). The idea now
to design an in-wheel motor for this application.

Battery

Motor

Transmission

Fig. 2: a) Speed profile; b) Force profile in the mode 0; c)

Force profile in the mode 1 (u=user, r=resistance, m=motor)
Fig. 1: Electrically assisted kick scooter
B. Operating modes 1, 2 and 3
II. S PECIFICATIONS Three more difficult modes (with increased resistive force)
The motor which is to be optimized will assist the user to are now introduced, in which the motor will assist the user.
drive the scooter. The total mass is m=88 kg (user 80 kg and The basic goal is to keep the same speed profile as in the mode
scooter 8 kg). The wheel external diameter of 120 mm gives 0 (Fig. 2 a)). To do this, an additional necessary traction force
the ratio between torque and force, and between rotating and (with reference to the mode 0), equal to the additional resistive
linear speed. force, will be provided by the user during the acceleration
In the previous work [8], some important physical quantities phase, and by the motor during the deceleration one.
concerning the scooter dynamics were measured. When the As the motor will be BLDC, it will generate iron losses
user rides the scooter on a horizontal smooth surface (concrete) during the rotation. These losses will generate a resistive

978-1-4244-5287-3/10/$26.00 ©2010 IEEE 292

torque, but it can be shown that it is negligible compared to to optimize the motor for more than one operating mode, and
the mechanical resistive torque. can be generalized for any number of modes.
The operating modes (during which the motor should pro-
vide the additional force during the deceleration phase) are III. E LECTRIC MOTOR MODELING
defined as follows: The stator is chosen to be made of the cheap silicon steel
• Mode 1 is movement on a horizontal rough surface. The M270-35A with the 0.35 mm lamination. The rotor will be
additional force compared to the mode 0 is 4.3 N (torque made of a simple steel. Both iron materials are described by
M1 =0.26 Nm). It is estimated that the motor will work their non-linear B-H curves. The permanent magnet is N45,
in this mode with the participation of τ1 =50% of its total with the remanency of 1.32 T. The magnets have the simple
operating time. Fig. 2 c) shows the forces in this mode rectangular shape.
(they can be shown for the others as well). According to the motor mechanical speed, the number of
◦ slots Ns and number of poles Np are chosen: 12/9 and 14/12.
• Mode 2 is movement up a 1.25% (0.72 ) slope on a rough
surface, with the participation τ2 =30%. Using the law of Fig. 3 shows those two configurations with the corresponding
the inclined plane, the additional force compared to the concentrated phase windings.
mode 0 is 15.1 N (torque M2 =0.91 Nm).
◦
• Mode 3 is going up a 2.5% (1.43 ) slope on a rough
surface, with the participation τ3 =20%. The additional - + - -
- + -
force compared to the mode 0 is 25.8 N (torque M3 =1.55 + +
+ + + -
Nm). - - -
+
+ + +
It is assumed that, during the movement up a slope, the +
- - - -
friction remains the same as at the horizontal surface. Indeed, -
+ + +
the force normal to the surface (which creates the friction - -
+ -
- -
force) remains almost the same as the cosine of the two slope + - + + + - +
angles is close to 1.
C. Electric motor
Fig. 3: Motor configurations 12/9 and 14/12
The three-phase BLDC motor is in-wheel (with exterior
rotor), therefore its maximal dimensions are determined by
the space available in the wheel: 82 mm external diameter A. FEM model
and 40 mm axial length (end windings excluded).
The available DC voltage is determined by the batteries: 2 As it is difficult to generate the motor analytical model, the
packs of 5 cells in series of the batteries Thunder Power PC finite elements commercial software FEMM is used [10]. The
[9] are used. Taking the voltage level of the empty and full program code for the motor simulation is written in Matlab,
batteries, the DC voltage takes values between 30 and 41 V. so that the motor parameters can be easily modified during the
The conductor insulation class is A with the maximal optimization process. For the given motor configuration and
allowed temperature of 105◦ C, therefore in the worst case position-dependent injected sinusoidal phase currents (which
of the maximal ambient temperature of 35◦ C the maximal are to be in phase with the corresponding phase back emfs to
allowed overtemperature is 70◦ C. generate the maximal motor torque), the FEMM model returns
In addition to this condition, the maximal overtemperature the motor torque and the stator flux density.
of the scooter housing surface (which can be touched by the B. Copper and iron losses
user’s leg) is 15◦ C. The calculations show that the former
condition is always critical, so is chosen for the optimization. The copper losses are calculated using the Joule formula.
Therefore, the constraint T < Tc should be satisfied, with The iron losses in W are, for the chosen stator iron material,
T overtemperature of the scooter housing and Tc =15◦ C its calculated using
maximally allowed value.  1.33
f
Pf e = 1.02 B 2 mf e (2)
D. Criteria for the optimization 50
The final goal is to maximize the motor energetic efficiency: with f electrical frequency in Hz, B amplitude of the stator
M1 Ω τ1 + M2 Ω τ2 + M3 Ω τ3 flux density in T and mf e the stator mass in kg.
η=
M1 Ω τ1 + Pl1 τ1 + M2 Ω τ2 + Pl2 τ2 + M3 Ω τ3 + Pl3 τ3 C. Simulated rotor positions
(1)
with Ω=75.2 rad/s the mean speed during the cycle. Pl = The problem with the presented slotted motors is that the
Pf e + Pcu are the losses in three operating modes, composed motor torque varies with the rotor position, so that it is not
of iron and copper ones. Maximizing η means at the same time enough to simulate the motor for only one rotor position. In
minimizing the losses (as all the values in the nominator are addition, the cogging torque can be significant and the exact
known). The last formula is important as it gives a possibility rotor position corresponding to the maximal cogging is not

293
known in advance. All this means that the motor has to be A set of individuals (forming a generation) is created. Each
simulated for several rotor positions. individual is characterized by a set of parameters (called
In order to have a reasonable simulation time, 5 points over genes). For each individual, the fitness (objective) function is
one electrical quarter-period are simulated. The mean value of calculated. Then, the individuals with the best fitness crossover
the obtained set of torque values is the motor (useful) torque their genes to generate a new generation of individuals, and a
M ; the difference between the maximal and minimal values small part of the genes of the new individuals is modified
is the torque ripple. This ripple divided by 2 is the cogging randomly by mutation. The condition of the end is that a
torque Mc . limited number of generations is achieved.
D. Thermal model B. Application to this case
The most of the motor losses are generated in the stator In the analyzed case, it is chosen that each generation
windings and iron. The generated power is evacuated by the consists of 10 individuals. Each individual is a motor design,
(forced) convection over the kick scooter surface. characterized by the values of 6 free input motor parameters
It is important to point out that the mode 3 is critical for (stator yoke radius r2 , air gap e, rotor yoke thickness d,
the temperature, as the corresponding current is maximal. In magnet thickness md , magnet width mw and tooth width tw ,
addition, note that the copper losses are generated only during as shown in Fig. 5). Additional conditions should be checked
the deceleration phase whereas the iron losses are generated before starting simulations, in order to be sure that for example
during the whole period. It means that the losses generating adjacent magnets do not overlap.
the heat are given by Pf e3 + (1 − D)Pcu3 .
As the stator is interior, the heat transfer is significantly md
reduced by the presence of the rotor: the heat flows from mw
the stator to the rotor either through the air or by conduction
through the bearings, and both flows are weak. The conclusion tw
is that the heat is evacuated from the stator only by the motor
r2 d
shaft and scooter housing (Fig. 4).
r1 r6

Fig. 5: Motor geometrical parameters

The imposed limit values for the free input parameters,

which define the domain in which the optimum is searched,
are as follows (all in mm): 15 < r2 < 20, 0.5 < e < 1, 6
< d < 10, 1 < md < 5, 5 < mw < 20 and 3 < tw < 6.
The shaft radius is r1 =5 mm, and the rotor external radius
Fig. 4: Heat transfer from the motor stator to the scooter is r6 =41 mm. The motor should generate the torques M1 to
housing M3 in the three modes according to the specifications. Finally,
the temperature in the mode 3 should not exceed its maximal
The motor equivalent thermal circuit consists therefore of allowed value.
four thermal resistances in series: the winding, the stator yoke,
the shaft and the scooter housing. As the overtemperature of C. Reduction of the number of simulations
the housing is critical, it is sufficient to take into account only The FEMM simulation time is obviously critical for the
the fourth thermal resistance: according to the housing geom- total optimization time. Again, the modeling of each motor
etry, it is estimated to 1.34 K/W (corresponding to combined comprises 5 simulations, as the rotor position should vary.
effects of the conduction and forced air convection over the In order to minimize the number of simulations, it is chosen
housing surface). Finally, the scooter housing overtemperature to simulate the motor for a fixed value of the current density,
is given by the product of the losses in the mode 3 and this for example J=5 A/mm2 ; the densities J1 to J3 which generate
thermal resistance. the necessary torques M1 to M3 are then calculated supposing
a linear relation between the torque and current density. The
IV. O PTIMIZATION
necessary condition for this is that the iron stays linear, but it is
A. Principle of the genetic algorithm always satisfied as the optimization algorithm never saturates
The optimization design is performed using a genetic the motor iron.
optimization algorithm. It imitates the principles of genetic It finally means that the necessary conditions for the torques
evolution when creating a new generation from the previous M1 to M3 are satisfied; using the obtained J1 to J3 , the copper
one. losses Pcu1 to Pcu3 are calculated which enables to calculate

294
the efficiency using (1). The iron losses are calculated using cM =1. The coefficient cT should be chosen sufficiently high:
(2) as the FEMM returns the value of B. a suitable value is cT =100.
The cost functions are shown in Fig. 6. The dots present
D. Fitness function
the ideal cases.
The main problem with the genetic algorithm is how to
define the fitness function. A new approach to define it is 2 1.4
used in this paper: the fitness function F (which should be 1.3
minimized in this case) is given in the form of a product of

kM (−)
kη (−)
three cost functions in the form 1.5 1.2

1.1
F = kη kM kT (3)
1 1
The efficiency cost function is given by 0.9 0.95 1 0 0.05 0.1
η (−) Mc (Nm)
kη = 1 + cη (1 − η) (4) 60

It is used to impose that the efficiency (1) is to be maximized;

40
in the ideal case (which can never be achieved) η = 1 which

kT (−)
gives kη = 1. 20
The torque cost function is given by
Mc 0
10 15 20
k M = 1 + cM (5) T (C)
M1
It is used to impose that the ratio between the cogging torque Fig. 6: The cost functions kη , kM and kT (• ideal cases, N
and useful torque should be minimized; in the ideal case final values).
(which can never be achieved) the cogging is zero, which
gives kM = 1. (The useful torque in the mode 1 is taken
into account as it is lower than in the modes 2 and 3.) V. F INAL DESIGN
Finally, the temperature cost function is given by
( q The optimization procedure lasts for 3 hours on a PC with
cT T −T c
if T > Tc Intel Xeon processor 2.8 GHz. In spite of a partly random
kT = 1 + Tc (6) character of the algorithm, it always converges to one solution.
0 otherwise
The configuration 14/12 is better than 12/9, and is chosen for
It is used to impose the constraint that the overtemperature the final design. The final values of the parameters are: r2 =21.1
T should not exceed its maximally allowed value Tc . If this mm, e=0.54 mm, d=6.3 mm, md =2.9 mm, mw =11.7 mm and
condition is satisfied (which should always be the case), kT = tw =5.6 mm. According to the available DC voltage, 192 turns
1. per phase are wound. The phases are connected in triangle.
The whole system in exploded view is shown in Fig. 7. The
E. Cost functions
energetic efficiency is η=92.7%. The cogging torque is 0.012
Although the three cost functions are simply multiplied to Nm.
make the fitness function, they are obviously different. The
cost functions kη and kM are related to the optimization; they Wheel Rotor
can never take the value of 1, but the goal is to have them as
close to 1 as possible. Cover
The cost function kT is related to the constraint; its value
has to be 1. To do this, its first (right) derivative near the
point T = Tc should be as high as possible to heavily force
T to be less than Tc . The simplest way to do this is to use a
linear function of type c0T (T − Tc ) with a high value of c0T , Stator
but the problem with this function is that as T increases kT Shaft
would increase too much, so that we would lose insight into
the optimization process. Instead, the square root function is Fig. 7: Integration of the motor in the kick scooter wheel
suitable as the derivative at the point T = Tc is infinite, and (exploded view).
as T increases the derivative decreases, keeping numerically
acceptable values of kT . Concerning the fitness function, the final values of cost
The choice of numerical values for the coefficients cη and functions are kη =1.73, kM =1.05 and kT =1 (the corresponding
cM allows to choose importance of the efficiency and of the points are shown by triangles in Fig. 6), giving the fitness
ratio between the cogging and useful torques, respectively. function F =1.81. It is interesting to point out that the air gap
After several trials, suitable values are obtained: cη =10 and e does not necessarily take its minimal value, as the reduction

295
 of e means that the field and torque are increased but at the [6] C. Liu, K. Chau, ”A permanent-magnet hybrid in-wheel motor drive for
same time the cogging is increased as well. electric vehicles”, IEEE Vehicle Conference 2008, pp. 1–6
[7] C. Versele et al., ”Analytical design of an axial flux permanent magnet in-
As an illustration, in the mode 3 the necessary current wheel synchronous motor for electric vehicle”, 13th European Conference
density to generate the torque of 1.55 Nm is 5.67 A/mm2 , the on Power Electronics and Applications 2009, pp. 1–9
copper and iron losses are 10.65 W and 0.81 W, respectively. [8] A. Hodder, P. Jaquier, Y. Perriard, ”A new electrically assist scooter”, Int.
Conf. on Electrical Machines ICEM 2008, pp. 1–6
The overtemperature of scooter housing surface is 14◦ C. [9] Thunder Power website [Online]. Available: http://www.thunderpowerrc.
The motor prototype is fabricated according to the obtained com
final design. The photos of the stator and rotor are shown in [10] Finite Element Method Magnetics website [Online]. Available:
http://www.femm.info
Fig. 8.

Fig. 8: Photo of the motor stator and rotor (in wheel).

It is important to point out, that the eddy current losses in

the permanent magnets are neglected from the start. This is
assured by axially segmenting the magnets in 5 segments. It
required a special tool to safely insert the permanent magnets
at the stator surface.
VI. E XPERIMENTAL RESULTS
The motor prototype is tested at a test bench. Another DC
motor is used as a mechanical charge. The mechanical torque
is measured directly using a torquemeter. Unfortunately, due to
some mechanical problems and a fabrication delay, the motor
is not yet tested.
VII. C ONCLUSION
The motor for a kick scooter was optimized using a genetic
algorithm combined with a FEM commercial software. The
motor prototype is fabricated and tested at a test bench.
The next step is to integrate the motor and corresponding
electronics in a kick scooter and perform final tests.
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[1] C. Chen, M. Cheng, ”Implementation of a highly reliable hybrid electric
scooter drive”, IEEE Transations on Industrial Electronics, Vol. 54, No.
5, October 2007, pp. 387–391
[2] K. Rahman et al., ”Application of direct-drive wheel motor for fuel cell
electric and hybrid electric vehicle propulsion system”, IEEE Transactions
on Industry Applications, Vol. 42, No. 5, September/October 2006, pp.
1185–1192
[3] Y. Fan, K. Chau, ”Design, modeling and analysis of a brushless doubly
fed doubly salient machine for electric vehicles”, IEEE Transactions on
Industry Applications, Vol. 44, No. 3, May/June 2008, pp. 727–734
[4] K. Chau, C. Chan, ”Overview of permanent-magnet brushless drives for
electric and hybrid electric vehicles”, IEEE Transactions on Industrial
Electronics, Vol. 55, No. 6, June 2008, pp. 2246–2257
[5] I. Boldea, L. Tutelea, C. Pitic, ”PM-assisted reluctance synchronous
motor/generator (PM-RSM) for mild hybrid vehicles: electromagnetic
design”, IEEE Transactions on Industry Applications, Vol. 40, No. 2,
March/April 2004, pp. 492–498

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