Page 610 - Mechanical Engineers' Handbook (Volume 2)

10 Steady-State and Dynamic Behavior of Servoactuators and Servosystems 601

Numerical Example
A Magnetic Technology, Inc. dc servomotor (model 3069-237/045; see Ref. 14) is used to
rotate an inertia load. System parameters are as follows:
Motor:
B 1.9 in. oz s/rad (1.34 10 2 N m s/rad)
m
2
2
J 0.016 in. oz s /rad (1.13 10 4 N m s /rad)
m
K 0.236 V s/rad
E
K 33.4 in. oz/A (0.24 N m/A)
T
L 4.8 mH
a
R 4.5
a
Gearing:
n 3
Load:
B 35 in. oz s/rad (0.25 N m s/rad)
L
2
2
J 0.2 in. oz s /rad (1.41 10 3 N m s /rad)
L
Amplifier:
K 8 V/V
a
Substituting these parameters into Eqs. (78), (79), (82), and (83) gives the following gains
and performance factors:
K 7.87 rad/s V
1
K 0.044 rad/in. oz s (6.23 rad/N m s)
2
68.5 Hz
n
1.27
and from the definition for ,
e
L a 1.07 10 3 s
e
R a
Since the damping ratio ( ) is greater than 1, the system will have an overdamped dynamic
response. The transfer functions are as follows:
7.87
G (s) (87)
1
62
3
5.40 10 s 5.88 10 s 1
3
0.13(1.07 10 s 1)
G (s) (88)
2
3
62
5.40 10 s 5.88 10 s 1
Equations (87) and (88) can be used to determine the transient response or the frequency
response.