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Chapter 15DC Machines

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Objectives

State Faraday’s Law and Lenz’s LawCalculate 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 = B L v 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,

in meters/second (m/s)

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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 two-winding 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 ModelCompound Generator ModelEfficiency

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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 = B L I 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 MotorSeries MotorCompound MotorMotor 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.