Page 560 - Mechanical Engineers' Handbook (Volume 2)

3 Direct-Current Servomotors 551

RJ
am (9)
RB KK E
am
T
Reference 9 discusses cases where the electrical time constant cannot be neglected.
The preceding mathematical models assume a voltage input. For applications where a
current amplifier is used, the following approximate model should be used:
(s) K m (10)
m
I(s) s 1
m
where I(s) is the Laplace transform of the current input i. The motor constant in this case
is

K K T (11)
m
B m
In principle, the models developed can be applied to all of the dc motors of the various
types with the appropriate input conditions. These models describe the open-loop response.
For closed-loop systems with velocity or position feedback, an appropriate closed-loop trans-
fer function can be derived easily by making use of the motor dynamic model. An example
of a closed-loop system is given in Section 10.2.

Numerical Example
For Motomatic PM servomotor model number E350-MG, 10 the following specifications are
given:
K 3.4 in. oz/A (0.024 N m/A)
T
K 2.5 V/krpm (0.024 V s/rad)
E
R 12.4
a
2
2
J 2.5 10 4 in. oz s /rad (1.8 10 6 N m s /rad)
m
B 0.015 in. oz/krpm (1.01 10 6 N m s/rad)
m
T ƒm 0.5 in. oz (3.5 10 3 N m)
T max 2.5 in. oz (1.8 10 2 N m)
I max 0.75 A
max 10,500 rpm at no load (1099 rad/s)
L 3.1 mH
a
0.25 10 3 s
e
R thermal resistance 13 C/W
th
The mechanical time constant can be computed as
J m 1.75 s (12)
m
B m
Since , Eq. (7) can be used to determine the dynamic response if the Coulomb friction
m
e
and load torque are neglected. In this case, the time constant is
RJ
am 0.037 s (13)
RB KK E
T
am
and the motor constant is
K K T 0.39 krpm/V (40.8 rad/V s) (14)
m
RB KK E
T
am
The transfer function of Eq. 7 becomes