Page 61 - Electric Machinery Fundamentals

lNTROOUCTION TO MACHlNERY PRlNClPLES 37

R B
~o i (I) X X X

+
v
-=- VB ejlld - _ Find

X X X

FIGURE 1-20
Starting a linear de machine.

3. Kirchhoff's voltage law for this machine. From Figure 1- 19 this law gives
VB - iR - eind = 0
(
I VB ~ e", + iR ~ 0 I (1-46)

4. Newton's law for the bar across the tracks:

I F nct - Ina I (1-7)

We will now explore the fundamental behavior of this simple de machine
using these four equations as tools.

Starting the Linear DC Machine
Figure 1-20 shows the linear de machine under starting conditions. To start this
machine, simply close the switch. Now a current flows in the bar, which is given
by Kirchhoff's voltage law:
VB - e ind
i ~ --"-"R-= (1-47)

Since the bar is initially at rest, e ind = 0, so i = V B/ R. The current flows down
through the bar across the tracks. But from Equation (1-43), a current flowing
through a wire in the presence of a magnetic field induces a force on the wire. Be-
cause of the geometry of the machine, this force is

Find = itB to the right (1- 48)
Therefore, the bar will accelerate to the right (by Newton's law). However,
when the velocity of the bar begins to increase, a voltage appears across the bar.
The voltage is given by Equation (1- 45), which reduces for this geometry to
eind = vBl positive upward (1-49)
The voltage now reduces the current flowing in the bar, since by Kirchhoff's
voltage law