Page 30 - Solutions Manual to accompany Electric Machinery Fundamentals


e  V  iR  120 V -  80 A 0.25    100 V
ind B
and the velocity of the bar will be
e 100 V
v  ind   400 m/s
Bl 0.5 T  0.5 m

(b) If the flux density drops to 0.45 T while the load on the bar remains the same, there will be a speed
transient until F app  F  ind 20 N again. The new steady state current will be

F app  F ind  ilB
F 20 N
i  app   88.9 A

 Bl 0.45 T 0.5 m 
The induced voltage in the bar will be

e ind  V  B iR  120 V - 88.9 A 0.25   97.8 V

and the velocity of the bar will be
e 97.8 V
v  ind   433 m/s

 Bl 0.45 T 0.5 m 
(c) If the battery voltage is decreased to 100 V while the load on the bar remains the same, there will be
a speed transient until F app  F  ind 20 N again. The new steady state current will be

F app  F ind  ilB
F 20 N
i  app   88.9 A

 Bl 0.45 T 0.5 m 
The induced voltage in the bar will be

e ind  V  B iR   100 V - 88.9 A 0.25   77.8 V
and the velocity of the bar will be
e 77.8 V
v  ind   344 m/s

 Bl 0.45 T 0.5 m 
(d) From the results of the two previous parts, we can see that there are two ways to control the speed of
a linear dc machine. Reducing the flux density B of the machine increases the steady-state speed, and
reducing the battery voltage V B decreases the stead-state speed of the machine. Both of these speed
control methods work for real dc machines as well as for linear machines.

24