Page 571 - Mechanical Engineers' Handbook (Volume 2)

562 Servoactuators for Closed-Loop Control

Torque at 1000 rpm 5.4 in. oz (3.8 10 2 N m)
Voltages: v 110Vat 90 ; v 110Vat 0
c
m
Frequency 60 Hz
Synchronous speed 120ƒ/P 1800 rpm (188.3 rad/s)
s
Slip ratio at standstill S R1 1
Slip ratio at 1000 rpm S R2 ( )/ 0.44
s
m
s
Substituting T 9.5 in. oz at S 1 in Eq. (27) gives
R
1
9.5 (30)
C C 2
1
Similarly, substituting T 5.4 in. oz at S 0.44 gives
R
0.44
5.4 (31)
C C (0.44 )
2
2
1
Solving Eqs. (30) and (31) gives
C 0.076 1/in. oz (11 1/N m) C 0.029 1/in. oz (4.1 1/N m)
2
1
Substituting numerical values in Eqs. (28) and (29) gives
A 7.79 rad/V s
B 1.59 10 2 in. oz s/rad (1.12 10 4 N m s/rad)
From the definitions for the motor time constants
3 10 4 s 4.6 10 2 s
e
m
From Eq. (26), the motor transfer function is given as
7.79 V (s) 62.9 T (s)
(s) c m (32)
m
(3 10 4 s 1)(4.6 10 2 s 1)
Generally the mechanical time constant is much greater than the electrical time constant, as
is the case for this example. The term s 1 in the transfer function of Eq. (26) often may
e
be neglected without introducing significant error.

5 STEPPER MOTORS
Stepper motors (also called step motors) represent a significant breakthrough in the area of
electromechanical actuation. These are incremental motors that by their very nature are com-
patible with digital systems. A stepper motor converts an electrical pulse into an equivalent
rotary displacement. Since their introduction in the early 1930s, stepper motors have evolved
into sophisticated designs. 19–22
The stepper motor possesses some inherent advantages over a conventional servomotor:
(1) it is compatible with digital processors; (2) open-loop control is possible, which elimi-
nates stability problems associated with closed-loop servos; (3) the step error is non-
cumulative; and (4) the brushless design provides easy maintenance and ruggedness. As a
result of these advantages, stepper motors find widespread usage in industrial applications
such as drives for TV antennas, numerical control (NC) machines, computer drives, hydraulic
valve positioning, and other high-performance feedback control systems. The primary dis-