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Lecture 2

# ENB205 Electrical and Computer Engineering Week 2.dotx.docx

5 Pages
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Course
ENB205
Professor
Negareh Ghasemi
Semester
Spring

Description
ENB205 Lecture Electrical and Computer Engineering Linear DC Machines/Motor Linear DC Machine Simplest type of DC machine As soon as the rod starts to move due to the F acting on it, the rod induces a voltage According to Lenz’s Law this voltage opposes the flow of current Once the rod accelerates to a velocity where induced EMF € is equal to input voltage (V), there will be no force on the rod. In a perfect world without friction the rod would continue at this velocity for ever Equivalent circuit of the linear DC machine KVL around the loop gives: At start up the rod is stationary, so At terminal velocity, Applying a load to the machine, slows the motor down (a) due to Floadin opposite direction of the rod motion. As the motor slow down the induced voltage reduces, increasing (b) the current in the rod. (a) Increase in current in the rod provides more force to (c) counter the load: (b) The induced force rises until (c) Then the rod travels in steady state but at lower speed Rotational DC Machines Consider single loop generator: Voltage induced on length dc: Voltage induced on length ab : Total Voltage induced: Where 1 Week 2 Tuesday, 27 August 2013 ENB205 Lecture Electrical and Computer Engineering Voltage waveform induced by rotating loop: To achieve single polarity (DC) output, commutation is used. As the output voltage crosses 0V, and the velocity of the loop wire is parallel to the field, the brushes switch commutator plates. The commutator rotates with the loop such that the brushes continue to alternate commutator plate, maintaining the polarity of the output voltage. The voltage in any real machine will depend on:  The flux in machine  Speed of rotation  A constant representing the construction of the machine 4 Loop DC Machine 4 single loops around a rotor Each loop can represent more than one turn, however for simplicity a single turn will be considered. Output waveform from 4 loop machine Voltage generated by 4 loop machine is higher, and has a smaller percent ripple (50%) compared to two loop (100%). Higher numbers of loops can provide even less ripple in the output voltage as only one coil (out of many) is deactivated and reactivated as the commutator switches. 2 Week 2 Tuesday, 27 August 2013 ENB205 Lecture Electrical and Computer Engineering The current in the windings creates a force on the rotor in reaction to the magnetic field Forces on the conductors contribute to torque at the axle. As the machine rotates, a voltage will be generated in the windings which oppose the flow of current. This Is called ‘Back EMF’: In a similar way to the linear machine, the rotational DC motor will reach a maximum velocity. Terminal Velocity (v) at: Torque on a 4 loop DC motor If an external load is applied to motor Force of the load is in the direction opposite the direction of the force supplied by the motor F Small resistance in the windings and back EMF work ind Finally ind Fload so: to limit the velocity of the motor A new maximum velocity These equations are only valid for a 4 loop, 2 pole motor. Realistic DC Machines Realisitc DC machines have many loops, to make calculators easier some terms are defined Z = number of conductors on rotor C = number of coils on rotor N c Number of turns per coil Some have more than one set of poles: P = number of poles Some machines, due to winding structure have multiple Voltage induced in Real DC Generators current paths Generation voltage depends on A=Number of
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