Problems 97
referred to the motor shaft. When J 0 and are multiplied by 1/n^2 ,the inertia and
viscous-friction coefficient are expressed in terms of the output shaft. Introducing new parameters
defined by
moment of inertia referred to the output shaft
viscous-friction coefficient referred to the output shaft
the transfer function G(s)given by Equation (3–51) can be simplified, yielding
or
where
The block diagram of the system shown in Figure 3–29(b) can thus be simplified as shown in
Figure 3–29(c).
Km=
K
B
, Tm=
J
B
=
Ra J 0
Ra b 0 +K 2 K 3
G(s)=
Km
sATm s+ 1 B
G(s)=
K
Js^2 +Bs
K=K 0 K 1 K 2 nRa
B =Cb 0 +AK 2 K 3 RaBDn^2 =
J =J 0 n^2 =
b 0 +AK 2 K 3 RaB
Problems
B–3–1.Obtain the equivalent viscous-friction coefficient
beqof the system shown in Figure 3–30.
B–3–2.Obtain mathematical models of the mechanical sys-
tems shown in Figures 3–31(a) and (b).
x
b 3
y
b 2
b 1 k m
(a)
No friction
x (Output)
u(t)
(Input force)
m
(b)
No friction
x (Output)
u(t)
(Input force)
k 1 k 2
Figure 3–31
Mechanical systems.
Figure 3–30
Damper system.