Lecture 32 DC Motors Part II. Learning Objectives Analyze the circuit equivalent of a permanent magnetic DC motor that accounts for armature resistance,

Lecture 32DC Motors Part II

Learning Objectives Analyze the circuit equivalent of a permanent magnetic

DC motor that accounts for armature resistance, induced electromotive force (back EMF), developed electromagnetic torque, and applied (input) voltage.

Define the power output of a permanent magnetic DC motor in terms of developed electromagnetic torque and angular velocity. Relate power output in terms of horse power.

Determine the efficiency of a permanent magnetic DC motor using the given or calculated power in and power out.

Basic DC Motor Operations

Parts of a DC Motor

SOURCE: Gears Educational Systems.

Rotary DC Motor

Torque developed Td=Kv Ia

Power Developed Pd = Td ω = Kv Ia ω

Back EMF Ea = Kv ω

Angular velocity ω = 2 (RPM/60)

, LOADT

DC motor power flow

Pmech loss

Pin Pout

Pelec loss

Pdev = Pout + Pmech loss

Electrical Power losses Electrical loss occurs due to the armature

resistance and is expressed as

Pelec loss = Ia2 Ra. Pelec loss

Torque losses (Tloss)

Pmech loss represents losses due to the friction of mechanical parts, magnetic inefficiencies of the material, and losses coupling brushes and commutator and is expressed as

Pmech loss = Tloss m

Pmech loss

Pd represents the power developed by the motor which includes power out and mechanical losses (Ploss). It is expressed

Pd = Pmech loss + Pout = Tdev v IA m

Power out is the power that ultimately gets to the load and is expressed Pout = TLOADm

Output Power

Pout

Pd = Pout + Pmech loss

Power Conversion Diagram

Electrical Mechanical

d a a dP E I T

Motor Efficiency Developed power is:

If we Ignore rotational losses, Pd=Pout, and machine efficiency can be calculated as:

d a a out mech lossP E I P P

100 100 100

= ( 0)

out a aD

in in DC a

aloss

DC

P E IP

P P V I

ET

V

Magnetic field Instead of permanent magnet, we could raise

the field strength B with an electromagnet. The wires wrapped around a ferromagnetic core

are known as field windings. The field windings are stationary and are part of

the stator.

Magnetic field

2 poles

Magnetic poles

Increasing the number of poles will increase and smooth the output torque.

eight-pole dc machinefour-pole dc machine

A 24 V DC motor is rated for 15 A.

RA = 0.20 ΩAssumed no rotational losses.

Determine:a) The input powerb) The power loss due to the resistance of the armaturec) The power developed

d) The back EMF (EA)e) The efficiency assuming no mechanical power lossf) Draw a power conversion diagram and fill-in the values

for power in, electrical power loss, power developed, mechanical power loss and power out.

Example Problem 1

A permanent magnet DC motor is rated for 120V, 17A and 1200 rpm.

The machine is 90% efficient at rated conditions

Tloss = 0.0334 N·m

Find Ra and Kv and torque developed by the motor .

Example Problem 2

We wish to design a 1/4 hp, 28 V DC motor with an efficiency of 96%. What current can we expect to draw? If the machine constant is Kv= 0.2139 ν·s, determine Tout if we ignore mechanical losses. Calculate rated speed in rpm.

Example Problem 3

Why is there so much field wiring on the Practical Exercise?

FIELD

ARMATURE

PE 20 Diagram

FIELD ARMATURE

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