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Comparative Analysis of Surface Mount PM Motors Structures for a Traction Application 529

1


Abstract This paper presents a comparative analysis of
several surface mount PM motor structures for a traction
application. A dedicated optimization CAD environment based on
the motor speed-cycle of the vehicle, including 2D FEA tools is
presented. It is demonstrated that a wide range of surface mount
PM motors structures in terms of number of slots, number of
poles and winding configurations can meet the same input-output
drive specifications. Their relative performances are compared
and discussed.

Index Terms Brushless DC motor, CAD, traction application

I.

I
NTRODUCTION

RACTION
applications are characterized by vehicle speed-
cycles. These speed-cycles are used to define the
specifications of the drive system. In this paper, we present a
design method of brushless DC motors based on vehicle
speed-cycles. This method uses an optimization CAD
environment
including
2D
FEA
tools.
The
motor
specifications and the control strategy for the drive
performance evaluation on the speed-cycle are presented in the
first part. The authors describe a design methodology using an
optimization process with analytical models corrected with FE
calculations. The methodology differs from other approach
that takes into account only the torque envelope of the drive
system like in [1]. This methodology is applied to compare
several motor structures for the same specifications. Finally, an
example of concentrated winding motor with external rotor is
detailed to illustrate the validation of the design methodology.
II.

VEHICLE CHARACTERISTICS AND SPEED
-
CYCLE

The objective is to design an electrical drive system that can
follow a typical vehicle speed-cycle with a high efficiency.
The main characteristics of this vehicle are presented in Table
I. Fig. 1 shows a combination of two typical vehicle speed-
cycles (EPA US06 and EPA UDDS) for aggressive highway

Manuscript received July 15, 2006.
J.R Figueroa is. with LEEPCI of Laval university, Quebec, G1K 7P4 ,
Canada; (e-mail: figueroa@gel.ulaval.ca).
L. Radaorozandry is with LEEPCI of Laval university, Quebec, G1K 7P4 ,
Canada; (e-mail: radaoro@gel.ulaval.ca)
J. Cros is with LEEPCI of Laval university, Quebec, G1K 7P4 , Canada ;
(e-mail: cros @gel.ulaval.ca)
P. Viarouge with LEEPCI of Laval university, Quebec, G1K 7P4 ,
Canada; (e-mail:
viarouge@gel.ulaval.ca
, phone : 418 656 7139 and fax :
418 656 3159)
and urban driving operation [2]. We have added a road slope
cycle (in blue on Fig. 1) to increase the load torque for harder
specifications of the drive system.
0
20
40
60
80
100
120
140
0
500
1000
1500
2000
2500
Time [s]
Speed [km/h]
0
0.05
0.1
0.15
0.2
0.25
0.3
Grade [pu]


Fig. 1 Vehicle speed and road grade slope cycles
T
ABLE
I.

V
EHICLE CHARACTERISTICS

Vehicle Mass
m
v
[kg]
1400
Wheel diameter
r
wheels
[m]
0.66
Rolling resistance
f
w

0.015
Air friction resistance
f
air
[Ns
2
/m
2
]
1.024


One can derive the operation points of each motor from the
vehicle characteristics and the imposed cycles. The traction
force of vehicle is evaluated by use of eq. (1):

4
3
42
1
4
3
42
1
4
4 3
4
4 2
1
4
3
42
1
Friction
Air
air
Friction
Wheels
w
force
Gravity
Tangential
v
force
on
Accelerati
v
t
v
f
t
v
f
t
g
m
dt
t
dv
m
t
F
))
(
(
))
(
(
))
(
sin(
)
(
)
(
+
+
+
=
(1)
We consider a fixed reduction gear between electrical
motors and wheels (Table II). Consequently, the speed of the
motor is determined with the wheels radius (r
wheels
) and the
gear reduction ratio (k
gear
):

wheels
gear
r
t
v
k
t
/
)
(
)
(
=
(2)
One can compute the motor torque by taking care of the
efficiency of the reduction ( gear
) and the number of motors
(n
motors
):
gear
motors
gear
wheels
load
n
k
r
t
F
t
T
=
)
(
)
(

(3)
Using a sampling of the torque-time function, with a
frequency of one Hertz, we can draw a torque-speed chart with
2475 points. Each point represents one second of the motors
Comparative Analysis of Surface Mount PM
Motors Structures for a Traction Application
J. Figueroa, L.Radaorozandry, J.Cros and P. Viarouge
T 529

2
operation cycle (Fig. 2). We have selected the four most
restrictive points in the chart to obtain four torque constraints
for the motor design specifications (in red on Fig. 2). If a drive
is able to operate in these four points, then it is able to operate
in every other point of the cycle. The efficiency is computed
considering all the points of this typical vehicle cycle speed.
T
ABLE
II.

E
LECTRIC DRIVE CHARACTERISTICS

Motor number
(n
motors
)
2
Reduction gear ratio
(k
gear
)
8:1
Maximal peak phase
voltage (V
max
)
144 V
Maximal peak phase
current (I
max
)
289 A

-40
-20
0
20
40
60
80
100
120
140
160
0
1500
3000
4500
6000
7500
9000
Speed (rpm)
Torque (N.m)


Fig. 2 Single motor torque-speed-cycle with the 4 most restrictive points
III.

T
ORQUE CONTROL STRATEGY AND EFFICIENCY

ON THE SPEED
-
CYCLE

It is necessary to determine an optimal torque control
strategy for each speed-cycle point that is defined by the direct
and quadrature axis currents in the motor. We have chosen to
minimize the copper losses of the machine for fixed values of
the maximum available voltage and current (V
max
) and (I
max
)
associated to the inverter limits. A three-step procedure is used
to compute the optimal currents by using a conventional
equivalent circuit model for the motor (stator resistance r
s
,
cyclic inductance L, maximal no-load flux ). In a first step,
for each operation point of the speed-cycle, we compute the
motor currents that minimize the copper losses only while
producing a reference torque (T
ref
) equal to the load torque
(T
load
) at the mechanical speed ( ). The following
optimization problem is solved to obtain the motor currents:

2
max
2
2
2
max
2
2
2
2
,
2
3
)
(
)
(
2
3
min
I
i
i
and
V
v
v
i
T
Li
p
i
r
v
Li
p
i
r
v
i
i
r
q
d
q
d
q
ref
d
q
s
q
q
d
s
d
q
d
s
i
i
q
d + + =
+
+
= =
+

(4)
It is sufficient to solve at most one quadratic equation to
determine the optimal values of the phase currents. The
computation of currents for the whole speed-cycle is fast
enough to be used in an iterative design process. During the
second step, the motor magnetic losses are evaluated. The
stator total flux s
can be derived from the current values
obtained in the first step by using the following equations:

q
q
d
d
q
d
s
Li
and
Li =
+
=
+
=
2
2
2

(5)
One can derive the magnetic flux densities B
l
in the motor
magnetic circuit from the cross section K
l
of the different
stator parts (back iron, tooth and tooth tips). The
corresponding magnetic losses are computed from an analytic
expression of the magnetic losses density and the weight of
each stator part. The coefficients (k
1
, k
2
) depend on the
magnetic material characteristics. An equivalent friction torque
(T
losses
) due to the magnetic losses can then be derived:

{
}
(
)
(
) =
+
=
= = )
(
)
(
)
(
,
,
2
2
2
1
l
P
T
l
Weight
B
p
k
B
p
k
l
P
tips
tooth
tooth
iron
back
l
with
K
B
losses
losses
l
l
losses
l
l
(6)
During the last step, the same procedure used in the first step
is performed to compute the final motor currents but with a
new value of the reference torque (T
ref
) that takes account of
the additional equivalent friction torque due to the magnetic
losses:

losses
load
ref
T
T
T
+
=

(7)
With such a method, the total losses of the motor are taken
into account for each operation point.
Finally, the drive efficiency on the whole speed-cycle can be
evaluated. First, we calculate the total mechanical energy (E
out
)
delivered to the vehicle with (8).

dt
T
dt
P
E
load
out
out =
=

(8)
This energy value is always equal to 18.22 MJ if the drive
system is effectively able to generate the load torque for all
points of the speed-cycle. In this case, the average output
power (P
out
) is equal to 7361 W.
The motor phase current and voltage can be also computed
for each point of the torque-speed-cycle and the total electrical
energy delivered to the motor by the power supply can be
derived from (9).

(
)
dt
i
v
i
v
dt
P
E
q
q
d
d
in
in
+
=
=
2
3

(9)
It must be noticed that, with the proposed procedure, this
energy takes account of both copper and magnetic losses.
The total drive efficiency on the vehicle speed-cycle is given
by:

= in
out
drive
E
E

(10)
IV.

D
ESIGN METHODOLOGY

An analytical design model for surface mounted PM motors
has been developed and associated to a global optimization
procedure. Fig. 3 presents a general flowchart of the design
method based on the iterative optimization process. The motor
structure (inner rotor or external rotor), the number of slots
and poles, the winding configuration and the material 529

3
parameters are selected at the initial step of the design
procedure. The influence of the number of slots and pole