Biomedical Engineering Reference
In-Depth Information
The friction torque can be calculated from the no-load current and the torque constant.
τ
f
=
K
m
I
o
=
10
−
3
19
.
6
×
4
.
91
×
=
0
.
096 mNm
The motor efficiency,
η
, describes the relationship between the mechanical power output
by the motor and the electrical power supplied.
V
i
I
=
ω
K
m
ωτ
η
=
(3.29)
V
i
It can be seen that the efficiency should increase with increasing speed (decreasing torque)
for a fixed supply voltage. However, at low torque (high speed), friction losses become
increasingly significant, and efficiency decreases rapidly. Maximum efficiency,
η
max
,is
calculated using the starting current and the no-load current and is dependent on the
supplied voltage
I
o
I
a
1
2
η
max
=
−
(3.30)
For the specified motor
1
I
o
I
a
2
η
max
=
−
2
4
91
281
.
=
1
−
75
which is close to the specified efficiency of 76%. As a rule of thumb, the maximum
efficiency occurs at roughly one-seventh of the stall torque. This means that maximum
efficiency and maximum output power do not occur at the same torque.
In addition to frictional losses (mechanical losses) there are copper losses due to the
resistance of the windings and in iron-core motors, there are losses due to magnetization
effects (electrical losses). Iron losses do not occur in modern coreless DC motors; therefore,
the power balance can be written as
=
0
.
P
el
=
P
mot
+
P
dis
(3.31)
where
P
dis
(W) is all of the electrical losses that do not contribute to the generation of a
torque.
This power balance can be expanded
V
i
I
I
2
R
=
ωτ
+
(3.32)
WORKED EXAMPLE
For the 2 W Maxon motor, the resistance of the coil windings is
R
, so the power
dissipated can be determined. This is a maximum at startup when the motor is still stalled
P
dis
=
=
53
.
3
I
a
R
10
−
3
=
281
×
×
53
.
3
=
4
.
2W
