2 a. 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 end = 0 I = VB-end = 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 = v Bl 4. Thus the increase voltage reduces the current flowing through the bar. I = VB-end 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 end 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. Feet = Fload - Find The resulting acceleration a = Fed / m is negative, so the bar slows down the voltage end = v Bl falls, and so I = (VB - end) /R increase The induced force Find = I lB increase until Find = Fload at a lower speed v. An amount of electrical power equal to ein di is now being converted to mechanical power equal to Find and and the machine is acting as a motor iii) Generator Operation (See Fig 1. 2) The concept of a generator is similar to the motor. When (Fig 1.
2) moved rapidly it is a generator but when it move slowly it a motor. In a Generator a force is applied in direction of motion. Now the applied force will cause the bar to accelerate in the direction of motion and the velocity of the bar will increase as the velocity increase, end = v Bl will increase and will be larger than the battery voltage VB. end >Vb the current reverse direction is given in the equation below. I = VB-end The current flows up through the bar it induces a force in the bar. The direction of the induced force is given in the right-hand rule find = vB lSo when the induce force equal and to the applied force the bar will be moving at a higher speed than before.
Now the battery is charging. The linear machine is now converted to electric power Find v and the machine is acting as a generator.