Lesson 8 - DC Motors_copy
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Transcript of Lesson 8 - DC Motors_copy
DIRECT CURRENT MOTORS
The Electric Motor- It is a machine that converts electrical energy (or power) into mechanical energy (or power).
DC electric motor works on the principle that whenever a current carrying conductor is placed in a magnetic field, a force acts on a conductor causing it to move.
Speed Characteristics of a DC Motor
where:N = speed (rpm)a = number of armature current pathsP = number of polesZ = number of conductorsΦ = flux per pole (weber)Eb = back emf or counter emf (volt)
PZ
aEN b60
After the machine has been assembled, “PZ and a” are constant
where:k = proportionality constantSubscript 1 = for condition 1Subscript 2 = for condition 2
bEkN
1
2
2
1
2
1
b
b
E
E
N
N
Torque developed in the Armature
where:T = torque developed (newton-meter)Ia = armature current (ampere)
N = speed of armature rotation (rpm)a = number of armature current pathsP = number of polesZ = number of conductorsΦ = flux per pole (weber)
a
IPZT a
283.6
After the machine has been assembled, “PZ and a” are constant
akIT2
1
2
1
2
1
a
a
I
I
T
T
Example:
A simplex lap wound armature has 600 conductors and carries a current of 50 amperes per armature current path. If the flux per pole is 30 mWb, determine the electromagnetic torque developed by the armature.
m
IZ
mP
IPZ
a
IPZT aaa
283.6283.6283.6
mN
xT
24.1431283.6
501030600 3
Power Developed in the Armature
where:Pd = power developed in the armature (watt)
Ia = armature current (ampere)
Eb = back emf or counter emf (volt)
abd IEP
Mechanical Power Output in the Shaft
where:Hp = mechanical power output in the shaft (horsepower)N = speed of shaft rotation (rpm)T = torque developed
mNTrpmNNT
Hp
ftlbTrpmNNT
Hp
;760,44
2
;000,33
2
Types of DC Motor
SHUNT MOTOR- The armature and the field coils are connected
in parallel.
Note:In a shunt motor, unless otherwise specified, the flux is assumed to be constant.
where:Vs = supply voltage (volt)
Eb = back emf (volt)
Ra = armature equivalent resistance (ohm)
Rsh = shunt field winding resistance (ohm)
Im = current drawn from supply (ampere)
Ia = armature current (ampere)
Ish = shunt field current (ampere)
aasb RIVE sham III
sh
ssh R
VI
Example 1:
A shunt motor is taking 72 A at 120 V while developing an output of 10 bhp. Armature resistance is 0.05 ohm and shunt field resistance of 60 ohms. Determine
a. counter emfb. total copper lossesc. iron and friction losses
wattsP
RIRIP
B
voltsRIVE
AIII
AR
VI
A
copperloss
shshaacopperloss
aasb
shma
sh
ssh
48560205.070
.
5.11605.070120
70272
260
120
.
22
22
wattsP
P
PPP
wattsPPP
wattsP
wattsIVP
C
frictioniron
frictioniron
frictionironcopperlosses
outputinputlosses
output
msinput
695
4851180
118074608640
746074610
864072120
.
&
&
&
Series Motor- The armature and the field coils are connected in
series.
where:Rse = series field winding resistance (ohm)
ma II seaasb RRIVE
Example:
A 200V series motor has a field resistance of 0.2 ohm and an armature resistance of 0.1 ohm. The motor takes 30A of current at 900 rpm while developing full load torque. What is the motor speed when this motor develops 70% of full load torque?
Note:In a series motor, since the flux is proportional to the armature current, therefore, the torque is directly proportional to the square of the armature current.
VE
RRIVE
VE
RRIVE
AT
TI
T
TII
I
I
T
T
b
seaasb
b
seaasb
a
aaa
a
47.192
2.01.01.25200
191
2.01.030200
1.257.0
30
2
22
1
11
2
12
2
1
1
1
1
2
2
2
1
rpm
IE
INEN
IN
IN
E
E
IkkNE
ab
ab
a
a
b
b
a
10841.25191
3090047.192
'
21
12
2
1
2
1
12
2
1
Thus, E = k”NIa
LONG SHUNT COMPOUND MOTOR- The series field coil is connected in series with the armature coil while the shunt field coil is connected across the series combination.
sh
ssh R
VI
sham III
seaasb RRIVE
Example:
A long shunt compound motor draws a line current of 42A from a 230V DC source. The armature resistance is 0.1 ohm while the series and shunt field resistances are 0.2 ohm and 50 ohm respectively. If the iron and friction losses amount to 500W, determine the overall efficiency of the machine.
WVIP
WRIP
WRIP
AIII
AR
VI
sshsh
sease
aaa
shma
sh
ssh
10582306.4
752.2792.04.37
876.1391.04.37
4.376.442
6.450
230
22
22
%53.79
%1009660
628.19779660
966042230
628.1977
5001058752.279876.139&
x
P
PP
P
P
WIVP
WP
P
PPPPP
input
lossesinput
input
output
msinput
losses
losses
frictionironshsealosses
SHORT SHUNT COMPOUND GENERATOR- The series field coil is connected in series with the supply voltage while the shunt field coil is connected in parallel with the armature coil.
aasemsb RIRIVE
sham III
sh
semssh R
RIVI
Example:
A 220V short shunt compound motor has an armature resistance of 0.4 ohm, a shunt field resistance of 110 ohms and a series field resistance of 0.6 ohms. If this motor draws an armature current of 50A at rated load, determine
a. the counter emfb. horsepower developed in the
armature
hp
IEP
B
VE
RIRIVE
AI
II
III
II
R
RIVI
A
abd
b
aasemsb
m
mm
sham
mm
sh
semssh
325.11746
5097.168
746
.
97.1684.0506.0718.51220
718.51
005454.0250
005454.02110
6.0220
.
PONY BRAKE TEST OF A MOTOR- This test is used to determine the output
horsepower of a motor.
where:T = torque exerted by the motor during the testN = speed of the motor shaft during the test (rpm)Hp = output horsepower of the motor
T = (scale reading – dead weight) (length of arm)
Example 1:
The pony brake test of an elevator door drive shunt motor, the ammeter and voltmeter measuring the input read 34A and 220V. The speed of the motor is found to be 910 rpm and the balance on a 2 ft brake arm read 27.2 pounds. The tare weight of the arm is found to be positive 2.3 pounds. Determine the efficiency of the motor at this load.
T = (scale reading – dead weight) (length of arm)
%056.86
%100026.10
628.8
026.10746
34220
746
628.833000
8.499102
33000
2
8.4923.22.27
xP
P
hpIV
HP
hpNT
HP
ftlbT
in
out
msinput
output
Example 2:
Calculate the force that will be exerted on the scale in a pony brake test when a 20 hp, 1400 rpm motor is operating at full load. The length of the brake arm is 3 ft and the tare weight of the brake is 3.75 lbs.
Let: F = force exerted on the scale
T = (scale reading – dead weight) (length of arm)
lbsF
F
NTHP
FT
76.28
000,33
375.31400220
000,33
2
375.3
Substitute:
Assignment:
1. The shaft power of a shunt motor is 7.8 hp. It draws 50 A from 120 V. The field winding draws 1.2 A. What is the efficiency of the motor? Ans: 96.98%
2. A shunt motor was tested by means of a pony brake having a length arm of 3.5 feet and a tare weight of 5.7 lbs. The current drawn by the machine from a 240 V line was 50.9 A when the scale reading was 24 lbs and the speed of the motor was 1215 rpm. Calculate the rotational losses of the motor. The armature and shunt field resistances of the machine are 0.25 Ω and 240Ω, respectively. Ans: 673.5 W