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Chapter 15
DC Machines
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Objectives
State Faraday’s Law and Lenz’s Law
Calculate the voltage generated by
passing a wire through a magnetic
field.
Sketch a simple generator and
describe how it operates.
Describe a commutator and brush
assembly and state how it works.
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Objectives
 Find the force produced on a current-carrying
wire in a magnetic field.
 State the differences between a shunt and
compound dc generator and describe the
performance characteristics of each.
 Sketch a simple dc motor and describe how it
operates.
 State the differences among a shunt, series, and
compound dc motor, and describe the
performance characteristics and application
examples of each.
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15-1 Introduction
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15-2 Magnetic Induction and the DC
Generator
 Faraday’s Law e = N dΦ / dt
e = the induced voltage in volts (V)
N = the number of series-connected turns of wire in
turns (t)
dΦ/dt = rate of change in flux in Webers/second
(Wb/s)
 e=BLv
B = the flux density in teslas (T)
L = the length of the conductor that is in the magnetic
field in meters (m)
v = the relative velocity between the wire and the flux,
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in meters/second (m/s)
Magnetic induction in a wire moving in a
field.
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Right-hand rule for magnetic induction.
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Wire loop rotating in a magnetic field.
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AC generator with slip rings and brushes.
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DC generator with commutator and
brushes.
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DC generator output waveform.
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DC generator with field control.
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DC generator four-pole field.
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DC generator rotor with two coils.
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Coil and output waveforms for a twowinding rotor.
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Rotor with several rotor coils and
commutator segments.
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15-3 Shunt and Compound DC Generator
Shunt Generator Model
Compound Generator Model
Efficiency
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DC shunt generator model.
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More precise dc shunt generator model.
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Shunt dc generator with field rheostat.
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Separately excited shunt dc generator.
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Compound generator, (a) short shunt and
(b) long shunt.
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Generator Efficiency
Pin = T nr / 7.04
Pin = the input power in watts (W)
T = the input shaft torque in foot-pounds (ft-lbs)
nr = the rotation speed of the shaft in
revolutions per minute (rpm)
η = Pout / Pin = Vt It / (T nr / 7.04)
η = the efficiency (dimensionless)
Vt = the generator terminal voltage in volts (V)
It = the generator output current in amperes (A)
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Generator Losses
 Rotor Copper Loss
 This is the I2R loss in the rotor due to the resistance of the wire.
 This loss varies with the square of the rotor current.
 Rotor Core Loss
 Because the rotor core (the iron upon which the rotor windings
are wound) is rotating inside a magnetic field, there will be eddy
current and hysteresis losses in the rotor core.
 These losses vary with the field flux and the rotor speed.
 Field Copper Loss
 The I2R loss in the field windings due to the resistances of the
wire.
 This loss varies with the square of the field current.
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Generator Losses (continued)
 Brush Loss
 There is power loss in the brush-commutator interface.
 This loss is proportional to the rotor current and brush drop and
is VbIa.
 Friction
 These are losses due to mechanical friction.
 They include the friction of the shaft bearings and the friction
created by the commutator and brush assembly.
 Windage
 These are losses due to the wind resistance of the rotor.
 In most generators, cooling fins are attached to the rotor to
circulate air through the generator, thus promoting cooling and
allowing the generator to be operated at higher output currents.
 These cooling fins increase the windage loss.
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15-4 Motor Action and the DC Motor
 F=BLI
 F = the resulting mechanical force in newtons (N)
 B = the flux density in teslas (T)
 L = the effective length of the wire (meters) in the field multiplied
by the number of turns
 I = the current in the conductor in amperes (A)
 Ia(start) = (Vt – Vb) / Ra
 Ia(start) = the armature starting current in amperes (A)
 Vt = the applied voltage in volts (V)
 Vb = the brush drop in volts (V)
 Ra = the armature resistance in ohms (Ω)
 Ia = (Vt – Vb – Vcemf) / Ra
 Vcemf = the induced counter emf in the armature windings in volts
(V).
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Force on a current-carrying wire in a
magnetic field.
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Flux compression and resulting force.
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Simple dc motor.
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DC motor with electromagnetic field.
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15-5 Shunt, Series, and Compound DC
Motor
Shunt Motor
Series Motor
Compound Motor
Motor Efficiency
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Shunt dc motor.
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Series dc motor.
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Compound dc motor.
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Motor Efficiency
 η = Pout / Pin = (T nr / 7.04) / (Vt It)
η = the efficiency (dimensionless)
Pout = the output power in watts (W)
Pin = the input power in watts (W)
T = the shaft torque in foot pounds (ft-lb)
nr = the rotor speed in revolutions per minute (rpm)
Vt = the applied input voltage in volts (V)
It = the applied input current in amperes (A)
 For a separately excited motor:
η = (T nr / 7.04) / (Vt It + Vf If)
Vf = the field voltage in volts (V)
If = the field current in amperes (A)
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15-6 Dynamic Braking of DC Motors
 In dynamic braking the armature is connected
to a resistive load after removing power, the
energy stored in the rotor in the form of angular
momentum will be transferred to the resistive
load, rapidly decreasing the rotor speed.
 When plugging a motor, the motor is
momentarily reconnected in such a way as to
reverse the direction of rotation. This can cause
excessive line currents and excessive torque on
the rotor.
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