Page 63 - Electric Machinery Fundamentals

INTRODUCTION TO MACHINERY PRINCIPLES 39

R
B
x x x

+
- Find
- V
x x x

FIGURE 1- 22
The linear de machine as a motor.

3. The bar accelerates to the right, producing an induced voltage einci as it
speeds up.
(
4. This induced voltage reduces the current flow i = (VB - e',d t)/ R.
S. The induced force is thus decreased (F = i l IB) until eventually F = O.
At that point, eind = VB. i = D, and the bar moves at a constant no-load speed
v.~s = VBI Bf.

This is precisely the behavior observed in real motors on statting.

The Linear DC Machine as a Motor
Assume that the linear machine is initially nmning at the no-load steady-state con-
ditions described above. What will happen to this machine if an external load is
applied to it? To find out, let's examine Figure 1-22. Here, a force F'OOd is applied
to the bar opposite the direction of motion. Since the bar was initially at steady
state, application of the force F 10ad will result in a net force on the bar in the direc-
tion opposite the direction of motion (F nct = F10l\d - Find) ' The effect of this force
will be to slow the bar. But just as soon as the bar begins to slow down, the in-
duced vohage on the bar drops (eind = v!BI). As the induced voltage decreases,
the current flow in the bar rises:

ii = VB - eind! (1-47)
R
Therefore, the induced force rises too (F,,,, = itIB). The overall result of this
chain of events is that the induced force rises until it is equal and opposite to the
load force, and the bar again travels in steady state, but at a lower speed. When a
load is attached to the bar. the velocity v, induced voltage e illd, current i. and in-
duced force F',d are as sketched in Figure 1-23.
There is now an induced force in the direction of motion of the bar, and
power is being converted from electrical form to mechanicalform to keep the bar
moving. The power being converted is