linear dc machine

We are getting closer to the point! But first, you need to understand how a linear DC machine works since it is the easiest-to-understand version of a dc machine. Also, by understanding its operations, we can apply the t he same principles and visualize the same behavior when we go to DC generators and DC motors! A linear DC machine consists of 1. A battery 2. A resistance 3. A switch 4. Frictionless railroad track 5. A conducting metal bar !!!IMPORTANT!!! 4 basic equations to be used in explaining the operations! 1.  = ( × ) Force on a wire in the presence of a magnetic field 2.  = (  × ) ∙   Voltage induced on a wire moving in a magnetic field − 3.  =  +  Kirchhoff’s voltage law or law or  =  4.  =  Newton’s law for the bar across the tracks Starting the Linear DC Machine (no-load steady state as a result) 1. Switch closed − flows in the bar 2.  =  a. at t=0, e=0 3.  =  is then induced on the wire. The direction is to the right according to the example figure. 4. The bar accelerates to the right ( = ) according to Newton’s law. 5. Since the velocity of the bar increases,  =  voltage induced appears across the bar. 6. As e increases, i flowing in the bar decreases. And so,  =  reduces. 7. As a result, the velocity of the bar decreases and eventually  = 0. 8. This occurs when e rises to be equal to VB.

9. The bar moves at a constant speed given by  =  =  See the graphs of values with respect to time.

The Linear DC Machine as a Motor Assume that the linear machine is initially running at no-load steady state and so F = 0. 1. Fload is applied opposite to the motion of the bar. 2.

 =   . There is Fnet.

3. The bar slows down,  4.  =  drops and 

=

 

where a is negative.

−

=

 5.  =  ,  also increases.

increases. (e
6. The bar moves at a new lower steady-state velocity when  =

. 7. Note that  is in the same direction as that of the bar. See the graphs of values with respect to time. The Linear DC Machine as a Generator Assume that the linear machine is initially running at no-load steady state and so F = 0. 1. Fapp is applied in the direction of the motion of the bar. 2.

 =   . There is Fnet.

3. The bar speeds up, 

=

4.  =  increase and  (e>VB)

 

=

where a is positive. − 

increases in an opposite direction.

5.  =  ,  also increases in the opposite direction (use (use the righthand rule). rule). 6. The bar moves at a new higher steady-state velocity when  =

. 7. Note that  is in the opposite direction as that of the bar. The graphs of values with respect to time are similar to the one Starting the Linear DC Machine.

 =  =  Motor Power from electrical form to mechanical form

Generator Power from mechanical form to electrical form

  

  

In real dc motor… motor… In real dc motor… motor… A load is added to the shaft. A torque is applied to the shaft in the The motor begins to slow down. direction of motion. The internal voltage reduces. The speed of the shaft increases. The The current flow increase. internal voltage increases. The torque induced increases. The current flows out of the The induced torque will equal the generator to the loads. load torque of the motor at a new, slower speed. In rotating machines:

 =  Problem!! How much current would flow at the start in Figure 1-25, knowing that the supply is 250V and its internal resistance is 0.10Ω 0.10 Ω. Try calculate that. (Keep in mind that e = 0 at t = 0) So…i at So…i  at start would be 2500A. This is massive! It’s dangerous!!! It would damage the motor! Both real ac and dc machines suffer from similar high-current high-current problems on starting. How to prevent this happening? Take the easy way… … insert an extra resistance into the circuit during starting to limit the current flow until e builds up enough to limit it.