DC Motors -- Review Questions

The first nine questions test general understanding; questions 10 to 18 are numerical problems based mainly on the equivalent circuit; questions 19 to 26 are discursive questions related to d.c. machines; and the remaining questions are more challenging, with an applications bias.

1) What is the primary (external) parameter that determines the speed of an unloaded d.c. motor?

2) What is the primary external factor that determines the steady-state running current of a d.c. motor, for any given armature voltage?

3) What determines the small current drawn by a d.c. motor when running without any applied mechanical load?

4) What determines how much the speed of a d.c. motor reduces when the load on its shaft is increased? Why do little motors slow down more than large ones?

5) What has to be done to reverse the direction of rotation of:

(a) a separately excited motor;

(b) a shunt motor;

(c) a series motor?

6) Most d.c. motors can produce much more than their continuously rated torque. Why is it necessary to limit continuous torque?

7) What is the basic difference between a d.c. motor and a d.c. generator?

8) From the point of view of supply, an unloaded d.c. motor running light looks like a high resistance, but when running at full load it looks like a much lower resistance. Why is this? 9) Why do d.c. motors run faster when their field flux is reduced?

10) A separately excited d.c. motor runs from a 220 V supply and draws an armature current of 15 A. The armature resistance is 0 : 8 V .Calculate the generated voltage (back e.m.f.).

If the field current is suddenly reduced by 10%,calculate (a)the value to which the armature current rises momentarily, and (b)the percentage increase in torque when the current reaches the value in (a).

Ignore armature inductance, neglect saturation, and assume that the field flux is directly proportional to the field current.

11) A shunt-connected d.c. machine driven by a diesel engine supplies a current of 25 A to a 110 V battery. The armature and field resistances are 0 : 5 V and 110 V respectively, and the friction, wind age and other losses total 220W. Calculate (a)the generated e.m.f, (b)the efficiency.

12) A 250 V d.c. motor with an armature resistance of 1 V is running unloaded at 1800 rev/min and drawing a current of 2 A. Estimate the friction torque.

13)What voltage would you expect across the armature terminals of the motor in question 12 immediately after it had suddenly been disconnected from the 250 V supply?

14) The full-load current of the motor in question 12 is 32 A. Estimate the full-load speed and the rated torque.

15) (a)When driven at 1500 rev/min the open-circuit armature volt age of a d.c. machine is 110 V. Calculate the e.m.f. constant in volts per radian/s. Calculate also the machine torque when the armature current is 10 A.

(b) Suppose the machine was at rest, and a weight of 5 kg was suspended from a horizontal bar of length 80 cm attached to the shaft, as shown in Ill. Q.15.

What current must be applied to the armature to keep the arm horizontal? Will the equilibrium be a stable one? (Neglect the mass of the bar; g = 9.81 m/ s^2.) (c)When the machine runs as a motor drawing 25 A from a 110 V supply, the speed is 1430 rev/min. Calculate the armature resistance. Hence find the voltage needed to keep the bar horizontal.

(d) At what speed must the machine be driven to supply 3.5 kW to a 110 V system? Calculate the corresponding torque. If the field circuit consumes 100 W and the friction losses are 200 W, calculate the efficiency of the generator.

16) The manufacturer of a 12 V toy motor with an armature resistance of 8 V claims that it can produce a torque of 20 mNm at 5000 rev = min. Show that this claim isn't justified.

17) The following test results were obtained for a small permanent magnet ironless-rotor d.c. motor for use in a print-head drive: Armature resistance = 2 : 9 V

Speed when running unloaded with 6 V applied = 8000 rev = min Current when running unloaded with 6 V applied = 70 mA. Rotor inertia = 0 : 138 10 6 kg m^2.

Calculate the induced e.m.f. and the friction torque when running light with 6 V applied, and estimate the initial acceleration from rest when the motor is switched directly onto a 6 V supply.

18) The equations expressing torque in terms of current ( T = kI ) and motional e.m.f. in terms of speed ( E = k v ) are central in understanding the operation of a d.c. machine. Using only these equations, show that the mechanical output power is given by W = EI .

19) A customer finds a 24 W, 5000 rev/min motor with an armature resistance of 0 : 8 V which suits his application, except that it's a 12 V motor and the only supply he has is 24 V. The motor vendor says that he can supply a 24 V version instead. How would the parameters of the 24V version differ from the 12 V one?

20) Explain briefly why:

(a) large d.c. motors cannot normally be started by applying full voltage; (b) the no-load speed of a permanent-magnet motor is almost proportional to the armature voltage; (c) a d.c. motor draws more current from the supply when the load on the shaft is increased;

(d) the field windings of a d.c. motor consume energy continuously even though they don't contribute to the mechanical output power; (e) the field poles of a d.c. machine are not always laminated.

21) A separately-excited d.c. motor is running light with a constant armature voltage. When the field current is suddenly reduced a little, the armature current increases substantially, and the speed rises to settle at a higher level. Explain these events with the aid of an equivalent circuit and discussion of the relevant equations.

22) A separately-excited motor used in traction has a field control circuit that ensures that the field flux is directly proportional to the armature current. Sketch a family of torque -speed curves for the motor when operating with a range of armature voltages.

23) A small permanent-magnet d.c. motor has an armature resistance of 1 V .What is the maximum possible mechanical output power when the armature is supplied at 12 V? Why is this maximum power condition only of theoretical interest for large motors?

24) Explain brie fly why a universal motor is able to operate on either a.c. or d.c.

25) It is claimed in this book that a motor of a given size and power can be made available for operation at any voltage. But it's clear that when it comes to battery-powered hand tools of a given size and speed, the higher-voltage versions are more powerful. What accounts for this contradiction?

26) Series motors will work on a.c. because field and armature currents reverse simultaneously, so the torque remains unidirectional. If a shunt-connected motor was supplied with a.c., the voltage on its armature and field would reverse together, so would it not also work satisfactorily?

27) This question relates to a permanent-magnet d.c. machine with an armature resistance of 0 : 5 V .

When the rotor is driven at 1500 rev/min by an external mechanical source, its open-circuit armature voltage is 220 V. All parts of the question relate to steady-state conditions, i.e. after all transients have died away.

The machine is to be used as a generator and act as a dynamic brake to restrain a lowering load, as shown in Ill. Q.27(a).The hanging mass of 14.27 kg is suspended by a rope from a 20 cm diameter winding drum on the motor shaft.

Ill. Q.27 The majority of the generated power is to be dissipated in an external resistor ( R ) connected across the armature, as shown in Ill. Q.27(b).

(a) Calculate the value of resistance required so that the mass descends at a steady speed of 15 m/s. (Take g = 9 : 81 m = s^2.) (b)What is the power dissipated in (i) the external resistor,(ii) the armature? Where does the energy dissipated in the resistors come from? 28) This question is about dynamic (transient) behavior during dynamic braking in which the machine acts as a generator to convert its kinetic energy to heat in a resistor. Familiarity with first-order differential equations is needed to answer the question fully.

A permanent-magnet d.c. motor with armature resistance of 1 V is running at 3000 rev/min and drawing a current of 10 A from a 200 V supply. Calculate the motor constant.

If the motor runs unloaded from a 100 V supply and the supply is then suddenly disconnected and the armature terminals are connected to a 4 V resistor, show that the speed decays exponentially with a time-constant of 2.73 s. Hence calculate the time taken for the speed to reduce to 100 rev/min. Take the effective inertia as 0 : 2kg m^2 and ignore friction.

29) When the armature of an unloaded permanent-magnet d.c. motor is supplied with a sinusoidally varying current at a frequency of 0.5 Hz, the speed varies from = 2000 rev/min to 2000 rev/min.

Estimate the speed range when the frequency is increased to 5 Hz, the peak current remaining the same.

30) Two new and identical 200 kW,520 V,420 A,1000 rev/min d.c. machines are to be tested at close to full load by coupling their shafts together, so that one will act as a generator to supply power to the other, which will act as a motor and drive the generator (no, this isn't perpetual motion.....read on).In this way it's hoped that there will be no need for the manufacturer to provide high power electrical supplies, nor heavy-duty mechanical loading rigs.

The two armatures are connected in parallel, as shown in Ill. Q.30; care being taken to ensure that when the duo rotate, the polarities of the motional e.m.f.s. in the two machines are such that there is no tendency for current to circulate between them (i.e. both are say upwards in Fig Q.30).

Both machines are separately excited, and their field currents can be adjusted manually. The field currents of both machines are first set at the normal (rated) level, and the output of the d.c. supply is gradually raised (to avoid excessive current surges)until the armature voltage is 520 V and the motors are running at a no load speed of 1040.2 rev/min. In this condition, assuming that there is perfect balance, both motors draw 18.5 A, making a total of 37 A from the d.c. source. This current reflects mainly the torque required to overcome windage, friction, and iron losses.

If the armature circuit resistance of each machine is 0 : 05 V ,and brush volt-drop is ignored, estimate for each machine:

(a) the motional e.m.f. at no load;

(b) the no-load armature circuit power loss;

(c) the mechanical (friction and windage)power loss;

(d) the no-load torque.

Now suppose that the field current (and hence the flux) of machine 1 is gradually reduced until the current in machine 1 reaches its rated value of 420 A.

Assuming that the d.c. supply acts as an ideal voltage source, set up the two armature equations and the torque balance equation and solve them to find:

(a) the speed of the machines;

(b) the current in machine 2;

(c) the net torque;

(d) the power supplied by the d.c. source, as a percentage of the rated power of each machine.

In the light of the answers above, comment on the extent to which it can be claimed that the machines have been tested at full-load, and on the economy in terms of the power supply that's required to carry out the test.