Chapter_03 ECSE461 2014.pdf

Chapter_03 ECSE461 2014.pdf - Electric Machinery 2014 3...

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1 Electric Machinery 2014 3. Electromechanical-Energy-Conversion Principles Objectives: (1) to understand the energy conversion (2) to provide (1) to understand the energy conversion, (2) to provide methods for designing and optimizing devices, and (3) to develop models. Small energy conversion devices, transducers: linear input- output, small signals – microphones, pickups, sensors and loudspeakers. Force producing devices : solenoids, relays and l iv-1 / 75 I. Shih electromagnets. Continuous energy-conversion equipment: motors and generators. concentrate on machines with magnetic fields as the conversion medium Electric Machinery 2014 3.1 Forces and torques in magnetic field systems The Lorentz law: F = q( E + v x B ) (3.1) gives the force on a charge particle q in an electric field and magnetic field. The magnetic force is perpendicular to the velocity and magnetic field. For a system with large number of charged particles with a density ρ : F v = ρ ( E + v x B ) (3.2) iv-2 / 75 I. Shih Here F v is the force density in newtons per cubic meter. The product ρ v is the current density: J = ρ v (3.5) Electric Machinery 2014 The magnetic force equation is: F v = J x B (3.6) iv-3 / 75 I. Shih Electric Machinery 2014 Example 3.1 A nonmagnetic rotor with a single-turn coil is placed in a uniform magnetic field B 0 , as shown in Fig. 3.2. The coil sides are at radius R and each wire carries current I. Find the θ -directed torque as a function of rotor position α when I = 10 A, B o = 0.02 T and R = 0.05 m. Assume that the length of rotor is l = 0.3 m. Solution: Multiply by A the cross-sectional area of the conductor Eq 3 6 Multiply by A, the cross-sectional area of the conductor, Eq. 3.6 becomes: F = I x B (I = J A) For wire 1 carrying current I into the paper, the θ -directed force is: F 1 θ = - IB 0 l sin α For wire 2 with a current in opposite direction, F 1 θ F 2 T T max iv-4 / 75 I. Shih F 2 θ = -IB 0 l sin α , here l is the length of the rotor. The torque T on the rotor is the sum of the force- moment-arm products for each wire T = -2IB 0 Rl sin α = -2x10x0.02x0.05x0.3 sin α = -0.006 sin α N-m. θ
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2 Electric Machinery 2014 F 1 θ T max F 2 θ T min iv-5 / 75 I. Shih Torque = arm length x force (perpendicular) Is a tendency to rotate an object around a center. T = maximum when α = 90 o T = 0 at α = 0 o Electric Machinery 2014 A simple model may be used to describe the machines: The rotor and the stator can be viewed as a set of north and south magnetic poles. These two sets of fields attempt to align, and torque is produced with their displacement from alignment (pull or push - just like the compass needle). For a motor, the stator magnetic field rotates ahead of the rotor, pulling on it and performing work. F h i fi ld i hi i iv-6 / 75 I. Shih For a generator, the stator magnetic field is pushing against rotor so that the rotor mechanical energy is converted into electricity .
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