Dc Machine

2a.

i) Startup of a linear DC machine:

Startup of a linear DC machine: (See Fig 1.1)

1. The switch is closed which allows current to flow. The current flows thought the bar, which is given Kirhhoff's voltage law.

Note: The bar was at rest so eind = 0

I = VB-eind = VB/R

R R

2. While this current flows thu the there is a magnetic force, which induce a force on the wires.

Find = i/B

3. The bar will accelerate. When the the velocity of the bar increase, the voltage appears across the bar

find = vBl

4. Thus the increase voltage reduces the current flowing through the bar.

I = VB-eind

R

5. The result of this action is that eventually the bar will reach a constant steady state speed where the net force on the bar is zero. This happen when eind has risen all the way up to equal the voltage of VB & I=0. At that time the bar will be moving at a speed given by

Vss= VB

Bl

6. The bar will continue to move forever unless some external force disturbs it.

Linear DC Motor or Generator

ii) Motor Operation (See Fig 1.2)

Since the bar was initially at steady state, application of the force Fload motion will result in a force on the bar in the direction opposite the direction of motion.

Fnet = Fload - Find

The resulting acceleration a = Fed/m is negative, so the bar slows down the voltage eind=v Bl falls, and so I=(VB - eind)/R increase

The