Biomedical Engineering Reference
In-Depth Information
FIGURE 4-34
DC
motor block diagram
in time-constant
form.
which has the tabled solution
f
(
t
)
=
e
−
t
/τ
. Therefore, the electrical model of the motor
can be modified to conform as follows:
1
1
/
R
R
τ
1
+
1
/
R
=
R
s
+
1
=
L
Ls
+
1
so
R
is the electrical time constant of the motor.
Similarly,
τ
2
=
J
/
b
is the mechanical time constant for the motor and load.
The block diagram can be redrawn with the time constants for the electrical and
mechanical portions of the motor as shown in Figure 4-34.
Consider the Maxon motor selected to drive the turbine of a continuous positive
airway pressure (CPAP) air pump discussed in Chapter 3, whose specifications are listed
in Table 4-7.
A number of factors must be determined or scaled so that the model shown in
Figure 4-34 can be used. First, the electrical time constant
τ
1
=
L
/
τ
=
L
/
R
=
40
.
9
μ
s. The
1
mechanical time constant is given as
τ
2
=
5
.
28 ms; therefore, the damping,
b
,is
J
r
τ
2
b
=
10
−
7
1
.
22
×
=
10
−
3
=
2
.
31
×
10
−
5
.
×
5
28
Note that
J
r
has been converted from g.cm
2
to kg.m
2
for this calculation.
K
m
is converted to 31
.
4
×
10
−
3
Nm/A, and
K
e
is converted to 2903 rad/s per V. It
is also important to remember that in the feedback path the conversion is from speed to
voltage; therefore, the reciprocal of the constant is used in the model.
TABLE 4-7
Maxon RE 16 Motor Specifications
No-load speed @ 24 V
n
o
(rpm)
7250
No-load current
I
o
(mA)
3.11
Terminal resistance
R
()
42.8
Terminal inductance
L
(mH)
1.75
Torque constant
K
m
(mNm/A)
31.4
Speed constant
K
e
(rpm/V)
304
Output power
P
o
(W)
3.2
Mechanical time constant
τ
2
(ms)
5.28
Rotor inertia
J
r
(gcm
2
)
1.22
