# E283C4 - EEEB344 Electromechanical Devices Chapter 4...

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EEEB344 Electromechanical Devices Chapter 4 CHAPTER 4 – AC Machinery Fundamentals Summary: 1. A simple loop in a uniform magnetic field - The voltage induced in a simple rotating loop - The Torque induced in a current-carrying loop 2. The Rotating Magnetic Field - Proof of the rotating magnetic field concept - The relationship between Electrical Frequency and the Speed of Magnetic field rotation - Reversing the direction of magnetic field rotation 3. Magnetomotive Force and Flux Distribution on AC Machines 4. Induced Voltage in AC Machines - The induced voltage in a coil on a two-pole stator - The induced voltage in a three-phase set of coils - The RMS voltage in a Three-Phase Stator 5. Induced Torque in an AC Machines 1 Synchronous Machines Induction Machines Magnetic field current is supplied by a separate dc power source Field current is supplied by magnetic induction (transformer action) into their field windings. The field circuits are located on their rotors. AC Machines

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EEEB344 Electromechanical Devices Chapter 4 1. A simple loop in a uniform magnetic field The figure below shows a simple rotating loop in a uniform magnetic field. (a) is the front view and (b) is the view of the coil. The rotating part is called the rotor, and the stationary part is called the stator. This case in not representative of real ac machines (flux in real ac machines is not constant in either magnitude or direction). However, the factors that control the voltage and torque on the loop are the same as the factors that control the voltage and torque in real ac machines. The voltage induced in a simple rotating loop If the rotor (loop) is rotated, a voltage will be induced in the wire loop. To determine the magnitude and shape, examine the phasors below: To determine the total voltage induced 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 equation e ind = ( v x B ) . l ( remember that these ideas all revert back to the linear DC machine concepts in Chapter 1 ). 1. Segment ab The velocity of the wire is tangential to the path of rotation, while the magnetic field B points to the right. The quantity v x B points into the page, which is the same direction as segment ab . Thus, the induced voltage on this segment is: 2
AB = max φ t e ind ϖ sin max = EEEB344 Electromechanical Devices Chapter 4 e ba = ( v x B ) . l = vBl sin θ ab into the page 2. Segment bc In the first half of this segment, the quantity v x B points into the page, and in the second half of this segment, the quantity v x B points out of the page. Since the length l is in the plane of the page, v x B is perpendicular to l for both portions of the segment. Thus, e cb = 0 3. Segment cd The velocity of the wire is tangential to the path of rotation, while B points to the right. The quantity v x B points into the page, which is the same direction as segment cd . Thus, e cd = ( v x B ) . l = vBl sin θ cd out of the page 4.

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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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E283C4 - EEEB344 Electromechanical Devices Chapter 4...

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