University of Sciences October 29, 2018

and Masuku Techniques

Polytechnic School
of the Mask

Department M I

DUT- GIM 2

DIRECTED WORKS DUT GIM 2

APPLICATION EXERCISES

Each of the 8 coils in figure 27-33 has 12 turns and an inductance of 270
μH. The diameter of the collector is 100 mm and the width of the brushes is 8 mm.
The rotor rotates at a speed of 1800 RPM.
a) Calculate the average value of the voltage ELinduced, due to inductance
b) We reduce the number of turns per coil to 4, while increasing the number of
coils at 24. Calculate the new value of EL

Exercise 1
1. A separately excited motor powered at 220 V has a
armature resistance of 0.8Ω. At nominal load, the armature consumes a current
From 15 A. Calculate the electromotive force E of the motor.
2. The machine is now used as a generator (dynamo). It outputs a
current of 10 A under 220 V. Deduce the e.m.f.

Exercise 2
The nameplate of a direct current generator with excitation
independent indicates:
 11.2 Nm 1500 rpm
induces 220 V 6.8 A
excitation 220 V 0.26 A
mass 38 kg

1. Calculate the mechanical power consumed at nominal operation.

2. Calculate the power consumed by the excitation.
3. Calculate the useful power.
4. Deduce the nominal yield.

Exercise 3
A separately excited generator has an open-circuit voltage of 115 V. What happens next?
does it happen so
the speed is increased by 20%
b) the direction of rotation is changed
the excitation current is increased by 10%
d) the polarity of the field is reversed

Exercise 4
A 100 kW, 250 V compound additive generator has a winding
shunt of 2000 turns and a series winding of 7 turns. Knowing that the resistance
The shunt winding is 100 Ω, calculate the resulting EMF when the machine
works
a) empty
at full load

Exercise 5
a) Name the three excitation modes of c.c. motors.
b) How can we vary the speed of a c c motor?
c) Explain why the current of a shunt motor decreases as
this one accelerates.

Exercise 6
A shunt motor connected to a 230 V line and the current drawn by the armature.
is 60 A. Knowing that the resistance of the armature is 0.15 Ω. Calculate:
the c f m in volts
b) the power supplied to the armature in kW.
c) The power dissipated by Joule effect in the armature in W
d) The mechanical power delivered by the engine in kW.
What would be the value of the starting current if the motor were connected
directly on the starting line?
f) What is the resistance of the rheostat that would limit this current to 115 A?

Exercise 7
A Ward-Leonard control system consists of a generator of
1000 kW driving an 800 kW rolling mill motor. During the rolling of a billet
In steel, we observe the speeds, tensions, and currents indicated in figure 28-35.
from this data calculate:
a) the power supplied to the armature at the following times: 2, 10, 25, and 40 s
b) the couple at the same moments in kN m
 c) the time required to lower the current Ixmfrom 280 A field to 160 A
d) the maximum field strength evaluated as a percentage of the power of the
motor, knowing that the excitation voltage is 200 V
the energy supplied to the engine during the interval of 0 to 40 s. What is the cost of
the energy spent if the steelworks pays 1.5 F per kWh.

Exercise 8
We want to stop a motor using the dynamic braking system.
represented by figure 28-18, the engine has a power of 90 kW, a current
rated current of 400 A and it runs at 400 rpm under a voltage of Es of 240 V.
Calculate:
a) the value of the braking resistance R if we want to limit the value of the current
braking I2at 125% of its nominal value.
b) The braking power in kW when the engine runs at 200, 50, and 0
rpm
c) We use reverse braking to stop the motor (it runs at 400
rpm, its power is 90 kW, the armature current is 400 A under a
The voltage is 240 V. What should be the value of R (fig. 28-20) so that the
maximum braking current should still be limited to 125% of its value
nominal?
d) What is the braking power in kW when the motor is running at 200
rpm? 50 rpm? and 0 rpm?
e) Compare the braking power with the instantaneous power dissipated
in the resistance R at the moment when the motor is running at 50 rpm
Exercise 9
The armature of a 225 kW 1200 rpm DC motor has a diameter
of 559 mm, and an axial length of 235 mm.
a) calculate its moment of inertia knowing that the density of iron is
79,000 kg/m3. Neglect the presence of teeth
b) calculate the kinetic energy of the rotor when it spins at a speed of 1200
rpm.
c) Assuming that the moment of inertia of the windings and the collector is
equal to that of the previously calculated armature, determine the kinetic energy
total rotor for a speed of 600 rpm.

Exercise 10
A paper machine includes a direct current motor that winds the paper onto a
large roller whose diameter gradually increases from 300 mm to 1000 mm.
the paper feed is constant and the sheet is maintained under a fixed tension. The
the engine develops a power of 50 kW and runs at 600 rpm when
start the roller. What should be its speed and power when the
the roll is finished.

Exercise 11
A subway train with its passengers has a mass of 30 tons.
What is its kinetic energy when it is moving at a speed of 120 km/h?
b) This train is equipped with four series motors, each with a power of
114 kW. How long does it take to go from 0 to 120 km/h assuming
that half of the power is available for acceleration?

Exercise 12
A separately excited and constant direct current motor is
powered under 240 V. The armature resistance is equal to 0.5Ω, the field circuit
absorbs 250 W and the collective losses amount to 625 W. At nominal operation,
The motor consumes 42 A and the rotational speed is 1200 rpm.
1. Calculate
the f. e. m
the absorbed power, the electromagnetic power, and the useful power
the useful couple and the yield
What is the speed of the motor when the armature current is 30?
What happens to the couple useful for this new speed (it is assumed that the
Collective losses are always equal to 625 W)? Calculate the efficiency.

Exercise 13
An extraction machine is driven by a direct current motor.
independent excitation. The inductor is powered by a voltage u = 600 V and
traversed by a constant intensity current: i = 30 A. The armature of
Resistance R = 12 mΩ is powered by a source providing an adjustable voltage U
from 0 V to its nominal value: UN= 600 V. The intensity I of the current in the armature has a
nominal value: IN= 1.50 kA. The rated rotational frequency is nN= 30 rpm.
Note: Parts 1, 2, 3 are independent.

1–Start
a. Noting Ω the angular velocity of the rotor, the emf of the motor is expressed as:
E = KΩavecΩin rad/s. What is the value of E at rest (n = 0)?
b. Draw the equivalent model of the rotor of this motor indicating on the diagram
the arrows associated with U and I.
c. Write the relationship between U, E, and I across the terminals of the armature, and deduce the voltage U.dà
apply at startup so that Id= 1,2 IN.
d. Name a speed control system for this motor.

2- Nominal operation during a load ascent

a. Express the power absorbed by the motor's armature and calculate its value.
digital.
b. Express the total power absorbed by the motor and calculate its value
digital.
c. Express the total power lost due to the Joule effect and calculate its value
digital.
d. Knowing that the other losses amount to 27 kW, express and calculate the power
useful and the engine's efficiency.
e. Express and calculate the useful torque moment Tu and the torque moment
electromagnetic Tem.

3- Operation during a dry lift

a. Show that the moment of the electromagnetic couple Tem of this motor is
proportional to the intensity I of the current in the armature: Tin= AI.
It is acknowledged that during the operation of a no-load ascent, the moment of
electromagnetic couple has a value Temequal to 10% of its nominal value and
keep this value throughout the ascent.
b. Calculate the intensity I' of the current in the armature during the ascent.
c. The voltage U remaining equal to UNExpress and then calculate the induced emf E' of the motor.
d. Express, in terms of E', I' and Tem, the new rotation frequency does not.
Calculate its numerical value.

Exercise 14
An independently excited generator delivers a constant voltage of 210 V for
an inducing current of 2 A.
The resistances of the induced and inductor windings are 0.6 Ω and 40 Ω respectively.
The 'constant' losses are 400 W.
For a flow of 45 A, calculate:
The induced voltage U
The useful power Pu
Joule losses induced and inductor
The absorbed power Pa
The yield h

Exercise 15
A separately excited motor is powered by a constant voltage of
200 V. It absorbs a current I = 22 A. The resistance of the inductor is Re = 100Ω,
the armature resistance Ra = 0.5Ω. The constant losses are 200W.
1. Calculate the excitation and armature currents.
2. Calculate the back electromotive force.
3.Calculate the losses due to Joule effect in the inductor and in the armature.
 4. Calculate the absorbed power, useful power, and overall efficiency.
5. We want to limit the intensity in the armature at startup to 30 A. Calculate the value.
of the resistance of the starting rheostat.
6. We equip the engine with a field rheostat. Indicate its role. In which
Where should the field rheostat be located at startup? Justify your answer.
response.

Exercise 16
Let it be a direct current machine with independent excitation perfectly
compensated. Its armature resistance is: Ra = 0.3Ω. The constant losses will be
assumed null. At 1200 rpm:

1. The machine is idle and the excitation current is 1.5 A, we supply it.
rotor by a voltage source, assumed ideal, of 400 V. Calculate the speed
the rotor in rpm.
2. The machine absorbs a current of 40 A, the inducing current is now
of 2.5 A and the supply voltage of 300 V. Calculate the speed of the rotor in
rpm
3. The rotor is driven by a thermal engine at a speed of 1000 rpm, the
The excitation current is 2 A. Calculate the open circuit voltage of machine no. 1.
The machine operates on a direct current machine number 2 perfectly.
identical and also excited by a current of 2 A. This second machine
operates empty. Calculate the current drawn by machine no. 1 and the speed
from machine no 2.

5. The excitation current is reduced to 1 A on machine no. 2. Calculate the new

rotor speed.
The excitation current of machines 1 and 2 is once again set to 2 A.
Machine number 2 drives a pump and in doing so absorbs a power of 2.
kW. We will assume the simplifying hypothesis according to which the efficiency of
The torque opposing machine no. 1 is calculated.
1 to the thermal engine whose speed is always 1000 rpm. Calculate the
current debited by machine number 1. Calculate the rotation speed of the machine
no 2.