E283C8 - EEEB344 Electromechanical Devices Chapter 8...

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EEEB344 Electromechanical Devices Chapter 8 CHAPTER 8 – DC MACHINERY FUNDAMENTALS Summary: 1. A Simple Rotating Loop between Curved Pole Faces - The Voltage Induced in a Rotating Loop - Getting DC voltage out of the Rotating Loop - The Induced Torque in the Rotating Loop 2. Commutation in a Simple Four-Loop DC Machine 3. Problems with Commutation in Real Machine - Armature Reaction - L di/dt Voltages - Solutions to the Problems with Commutation 4. The Internal Generated Voltage and Induced Torque Equations of Real DC Machine 5. The Construction of DC Machine 6. Power Flow and Losses in DC Machines 1
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EEEB344 Electromechanical Devices Chapter 8 1. A Simple Rotating Loop between Curved Pole Faces The simplest rotating dc machine is shown below: The Voltage Induced in a Rotating Loop If the rotor is rotated, a voltage will be induced in the wire loop. To determine the magnitude and shape of the voltage, examine the figure below: To determine the total voltage e tot on the loop, examine each segment of the loop separately and sum all the resulting voltages. The voltage on each segment is given by e ind = ( v x B ) l Thus, the total induced voltage on the loop is: e ind = 2vBl When the loop rotates through 180°, segment ab is under the north pole face instead of the south pole face. At that time, the direction of the voltage on the segment reverses, but its magnitude remains constant. The resulting voltage e tot is shown below: 2 It consists of a single loop of wire rotating about a fixed axis. The rotating part is called rotor, and the stationary part is the stator. The magnetic field for the machine is supplied by the magnetic north and south poles. Since the air gap is of uniform width, the reluctance is the same everywhere under the pole faces.
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π B A e P ind 2 = φϖ 2 = ind e EEEB344 Electromechanical Devices Chapter 8 There is an alternative way to express the e ind equation, which clearly relates the behaviour of the single loop to the behaviour of larger, real dc machines. Examine the figure below: The tangential velocity v of the edges of the loop can be expressed as v = rω. Substituting this expressing into the e ind equation before gives: e ind = 2rωBl The rotor surface is a cylinder, so the area of the rotor surface A is equal to 2πrl. Since there are 2 poles, the area under each pole is A p = πrl. Thus, Since the flux density B is constant everywhere in the air gap under the pole faces, the total flux under each pole is φ = A P B. Thus, the final form of the voltage equation is: In general, the voltage in any real machine will depend on the same 3 factors: 1. the flux in the machine 2. The speed of rotation 3. A constant representing the construction of the machine. 3
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This note was uploaded on 03/03/2010 for the course POWER 332 taught by Professor Dr during the Spring '10 term at Ain Shams University.

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E283C8 - EEEB344 Electromechanical Devices Chapter 8...

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