electric motors & generators andrew holliday. motors and generators simple devices that use...
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ELECTRIC MOTORS & GENERATORS
Andrew Holliday
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Motors and Generators
• Simple devices that use basic principles of electromagnetic theory
• Technologically important• Motors drive everything from hybrid cars to vibrating
phones. • Most electrical power is provided by generators
• Work on the same principles: converting between
mechanical and electrical energy using the magnetic force
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Electric and Magnetic Fields
• Electric and magnetic fields are vector fields• A vector has magnitude and direction• A vector field describes a vector for every point in space
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Electric Force
• An electric field exerts force on electric charge.
• The force is in the direction of the field - charges get pushed in the direction of the field.
• F = qE (q is magnitude of charge).
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Magnetic Force• Magnetic fields exert force on moving charges• Force is perpendicular to field and to velocity• Units of Gauss: 1 G = 1 N*s/C*m
• FB = qvBsin(ϴ) : ϴ is the angle between v and B.
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Electric Motors• In a motor, current passes through a coil of wire in a
magnetic field• Magnetic field exerts force on charges moving in the coil
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Electric Motors• Current, and thus force, is in opposite directions on
opposite ends of the coil• Creates torque on the coil
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Electric Motors• When the coil is pulled "flat" by the magnetic force, the
direction of the current must be reversed:
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Electric Motors• This reverses the direction of the force• Momentum continues the rotation, and the new force
accelerates the rotation
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Electric Generators• In a generator, we rotate the rotor from "outside"• Wire moves in opposite directions on either side of loop• Opposite forces on either side create voltage around loop
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Electric Generators• As the loop makes a rotation, the direction of current
reverses• This produces alternating current
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Electric Generators• In my generator, coil is the "stator", magnet is the "rotor"• Circuit demonstrates how the current alternates
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Motors and Generators
• Different designs: magnet can be either rotor or stator
• Some motors use an electromagnet instead of a permanent magnet
• All designs operate on the same principle described here
• Charges moving relative to a magnetic field are pushed perpendicular to their motion and the field
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Back-EMF and Symmetry
• Motors and generators are basically the same
• In some cases, a single device is used as both a motor and a generator
• Gas turbines, hybrid electric cars (regenerative breaking)
• This symmetry is important for a deeper reason...
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Back-EMF and Symmetry
• Guarantees conservation of energy
• Current through a motor's coil causes it to rotate
• A rotating coil in a magnetic field induces voltage!
• By the Right-Hand Rule, this voltage is always in the opposite direction as the supplied voltage
• This is called back-EMF (ElectroMotive Force)
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Back-EMF and Symmetry
• Likewise, current induced in a generator induces torque
• Torque opposes rotation of the generator
• These reaction forces always resist the applied forces
• This is required by the Maxwell-Faraday Equation:
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Back-EMF and Symmetry
• Back-EMF is how energy is extracted from a voltage source by a motor
• Without load, motor is allowed to accelerate
• Back-EMF increases with motor speed
• When back-EMF equals supplied voltage, there is no net voltage, no current over the motor - it stops accelerating
• Since no current flows, no energy leaves the battery
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Back-EMF and Symmetry
• Load on the motor extracts rotational energy
• Motor does not reach the same top speed, so back-EMF is always less than supply voltage
• Heavier load => lower top speed => more current flows
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Back-EMF for square coil
We will calculate the peak back-EMF of a square coil.
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Back-EMF for square coil
Assume B and v are perpendicular: • Force on charge: FB = qvB (v and B are perp.: drop sin(ϴ))
• Force per unit charge: FB/q = vB
• Work per unit charge over distance L: LFB/q = LvB
• This is the Back-EMF over a distance L
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Back-EMF for square coil
Over the top and bottom edges of square coil: • ϴ = 90 degrees, sin(90) = 1
• Speed of edge v = 2π*f*r = 2π*f*0.019 m
• 6 turns, so length L = 6*0.038 m
• B = 0 T over top edge, 0.083 T over bottom edge
• 6*2π*f*(0.019 m)*(0.038 m)*(0.083 T) = (0.0023 m2T)*f
• (0.0023 m2T)*f = Vback
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Back-EMF for square coil
• What about the 3 turn coil?
• 3*2π*f*(0.019 m)*(0.038 m)*(0.083 T) = (0.0012 m2T)*f = Vback
• At maximum speed, Vback should be equal for both coils• So 6*2πfrLB = 6*2πfrLB• 2f1 = f2
• Top speed of the 3 turn coil should be about twice that of the 6 turn coil. Is it?
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Other coils
• What about the rectangular coils? Circular coils? Will they be faster or slower?
• For rectangular coil, B = 0.047 T• (0.0013 m2T)*f = Vback
• For circular coil, B = 0.140 T• (0.0039 m2T)*f = Vback
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Efficiency
• Vin = 2.7 V, but only applied half the time, so 1.35 V
• These frequencies are much lower than we'd expect
• These motors have very low efficiencies
• Efficiency is defined in terms of power, energy-per-time
• Efficiency n = Pout/Pin: ratio of input power to output power
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Efficiency
• Ideally, mechanical power of a motor equals electrical input power
• Electrical power of a generator equals mechanical input power
• In reality, this never happens
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Sources of Inefficiency
• Friction between the rotor and its joint
• Resistance and between electrons and the wire (resistance)
• Geometry - magnetic field, coil shapes don't maximize torque on coil
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Design considerations
• Number of turns: more turns give more torque, but also more resistance
• Joints: sliding contacts have a lot of friction - some motors apply current to loop by induction
• Geometry: vast variation in designs to maximize magnetic force!o Iron cores in coilso Multiple coils, multiple magnets
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What loop shape is most efficient?
• Which loop shapes give most efficient conversion? Why?• To find the answer, need more physics: