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Application Note #3414 - 1 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com




Application Note #3414

Sinusoidal Commutation of Brushless Motors

Introduction
This application note includes a complete discussion of brushless motors. Part One is
devoted to an in-depth review of both brush- and brushless motor theory. Part Two
relates brushless commutation using a Galil Motion Controller. Part Three includes
some real-world cases of brushless motor examples, including tips and tricks to
maximize the performance of a brushless application.

Part One: Motor Technology

Brush-type motor theory

Basic principles of physics state that a force F is generated on a current I carrying wire
of length L when subject to a magnetic field B results in equation (1):





F = I L x B





(1)

When the magnetic field is always perpendicular to the current vector IL, equation (1)
becomes




F = I L B





(1a)

Consider Figure (1). As shown, a loop of wire with a torque arm R is free to rotate
about the z-axis. Rotational torque is defined as




T = F R



(2)
- 2 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

resultant force F
wire length L
current I
radius R
desired rotation
X
Y
Z
resultant force F
Y
Z
X
magnetic field B
magnetic field B



Figure (1) Current-carrying wire exposed to a magnetic field

The resulting torque at the axis of rotation is a function of the angle
with respect to the
magnetic field, or




T = F R sin





(3)


Substituting equation (1a) into equation (3),




T = I L B R sin





(4)

For a given system, the terms R, B, and L are constants. In terms of a DC motor, these
terms can be combined into a common motor constant K
t
. This results in equation (5):




T = I K
t
sin






(5)
As equation (5) shows, the applied torque will decrease as
approaches 0°. Figure (2)
shows the relationship at
= 45°. - 3 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

X
current I
Z
resultant force F
desired rotation
Y
Z
X
Y
magnetic field B
magnetic field B
resultant force F

Figure (2) Coil at 45°
At
= 0° the torque will be effectively 0. See Figure (3).
Z
Y
current I
Z
X
X
resultant force F
Y
magnetic field B
magnetic field B
resultant force F
desired rotation

Figure (3) Coil at 0°
If the system has inertia, the coil will drive past 0°, causing the torque to be supplied in
the direction opposite of desired. This will cause the system to oscillate around 0°. To
avoid this situation, a process known as commutation has been developed. Essentially, - 4 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

a commutator will reverse the direction of current in the coil, providing positive torque at
angles larger than 90°. Figures (4a) and (4b) illustrate the principle.
X
magnetic field B
Z
resultant force F
current I
Y
X
Z
Y
magnetic field B
resultant force F
desired rotation

Figure (4a)- Coil beyond 0° - Resultant force is reversed
current I
Z
resultant force F
Y
X
magnetic field B
resultant force F
X
Z
Y
magnetic field B
desired rotation

Figure (4b)- Coil beyond 0° - Reversed current; Resultant force OK
- 5 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

To produce any amount of useable rotational torque, the system design must rely on
multiple current carrying coils of wire to be exposed to the magnetic field B. Figure (5)
shows the physical design of a rotor.
current carrying wire
insulating material
wire length L
radius R

Figure (5)- Basic armature design
In addition to reversing direction of current in the coils, the commutator may also shut
off the current in the coil when they are at an angle near 90°, as the torque produced
may be too small and represent inefficient operation. To perform such a function, the
machine must switch the supply current to these multiple coils based on the rotor angle.
conductive material
insulating material
brush
connection to coil

Figure (6)- A simple commutator
- 6 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

Figure (6) shows the basic elements of a commutator. The machine conductors (which
constitute the windings on the armature) are connected in sequence to the segments of
the commutator. Figure (7) shows the flow of current through the commutator and
armature windings.
6'
7
A
6
5'
7'
Current in
I
1
1'
2
2'
5
B
4'
Current out
4
I
3'
3
Clockwise rotation

Figure (7)- Current flow through a motor armature
Current flows into the system at brush A and flows out at brush B. The small arrows
indicate current direction in the individual coil sides. If the motor rotation is clockwise, it
can be seen that 1/7 of a revolution after the instant shown, the current in coils 3-3 and
7-7 will have changed direction. As the commutator continues to turn, the brushes
pass over successive segments, causing the direction of current flow to change. At
some points in the armature rotation, the brush will be in contact with two segments. At
this condition, the coil connected to these two segments will be shorted through the
brush. As a result of this switching, the current flow in the armature occupies a fixed
position in space, independent of rotation.


Due to the action of the motor commutator, the armature can be thought of as a wound
core with an axis of magnetization fixed in space. The axis of magnetization is
determined by the rotary position of the brushes. For a motor to have equal
characteristics for both directions of rotation, the axis of magnetization, or brush axis, - 7 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

must be at an angle of 90° with respect to the magnetic field. Figure (8) shows the
resultant axis of magnetization.
I
Current out
Current in
I
S
S
Current into page
Current out of page
Coil shorted
Main field B
Axis of magnetization
determined by location of brushes
CCW torque

Figure (8)- Axis of magnetization
The major drawback of a brush-type motor design is the nature of the design itself. The
commutation brush, as a wear item, will eventually need to be replaced. As the brushes
begin to wear, microscopic particles are released, invalidating the motor for use in a
clean room environment. Also, due to the switching of the coils, some electrical arcing
will occur. This rules out brush motors for explosive environments. Otherwise, brush-
type motors are inexpensive, reliable, accurate machines that continue to play a role in
todays industrial workplace.
Brushless Motor Fundamentals
Many motor types can be considered brushless, including stepper and AC-induction
motors, but the term brushless is given to a group of motors that act similarly to DC-
brush type motors without the limitations of a physical commutator. To review, a DC-
brush motor consists of a wound rotor that can turn within the magnetic field as provided
by the stator, as shown in figure (9). By including the commutator and brushes, the
reversal of current is made automatically and the rotor continues to turn in the desired
direction. - 8 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

N
S
+
-
Commutator

Figure (9)- A Simple brush-type motor
To build a brushless motor, the current-carrying coils must be taken off the rotating
mechanism. In their place, the permanent magnet will be allowed to rotate within the
case. The current still needs to be switched based on rotary position; figure (10) shows
a reversing switch is activated by a cam.
N
S
Reversing Switch
+ -

Figure (10)- An inside-out DC motor
This orientation follows the same basic principle of rotary motors; the torque produced
by the rotor varies trapezoidally with respect to the angle of the field. As the angle

increases, the torque drops to an unusable level. Because of this, the reversible switch
could have three states: positive current flow, negative current flow, and open circuit. In
this configuration, the torque based on rotary position will vary as the current is switched
as shown in figure (11). - 9 -

Galil Motion Control, Inc.
3750 Atherton Road Rocklin, CA 95765 USA 800-377-6329 Ph: 916-626-0101 Fax: 916-626-0102 www.galilmc.com

0°
180°
360°
Torque T
Current I
Kt ( )

Figure (11)- Single-phase torque based on rotary position
In this model, the Torque T is the product of the theoretical motor const