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Basics of electrical drives

Pillai, Sivan Kumaraswami

Chapter 3

Characteristics of dc Motors - all with Video Answers

Educators

Chapter Questions

05:08

Problem 1

A 220 V, 21 A, $1000 \mathrm{~mm}$ de shunt motor has an armature resistance of $0.05 \mathrm{ohm}$ and a field resistance of $220 \mathrm{ohms}$. The magnetization curve for the machine is given by the following table:
$\begin{array}{llllllll}\text { Field current (A) } & 0.2 & 0.4 & 0.6 & 0.8 & 1.0 & 1.2 & 1.4 \\ \text { EMF at } 1000 \mathrm{rpm}(\mathrm{V}) & 50 & 100 & 150 & 190 & 219 & 235 & 245\end{array}$
Plot the speed-torque curve for the motor when
(a) no external resistances are included,
(b) a resistance of $0.05 \mathrm{ohm}$ is connected in series with the amature, and
(c) a resistance of 110 ohms is included in series with the field winding.

Narayan Hari
Narayan Hari
Numerade Educator
06:45

Problem 2

The motor in Problem 1 drives a certain load at $1000 \mathrm{~mm}$ taking a current of $21 \mathrm{~A}$ from the line. If it is desired to raise its speed to $1500 \mathrm{rpm}$, what value of resistance must be included in the field circuit when the load is of such a nature that $(a)$ the electromagnetic torque required of the motor remains constant, regardless of speed and $(b)$ the electromagnetic power required of the motor remains constant, regardless of the speed.
[Ans. (a) 156.7 ohms (b) 156.7 ohms]

Jordan Vanevery
Jordan Vanevery
Numerade Educator
01:46

Problem 3

The motor in Problem 1 draws an armature current of $21 \mathrm{~A}$ on full load and runs at $1000 \mathrm{rpm}$. If a resistance of $0.5 \mathrm{ohm}$ is inserted in series with armature, determine.
(a) the speed at full load torque,
(b) the speed at 60 per cent of full load torque, and
(c) the ratio of starting torque to full load torque.
[Ans. (a) $951.82 \mathrm{rpm}(b) 972.92 \mathrm{rpm}(c)$ 19.48]

Narayan Hari
Narayan Hari
Numerade Educator
02:21

Problem 4

A $220 \mathrm{~V}$ de series motor has an armature resistance of $0.05 \mathrm{ohm}$ and a field resistance of $0.05 \mathrm{ohm}$. While running as a generator at $1400 \mathrm{rpm}$, it gave the following results:
Current (A)
Terminal voltage (V)
15
80
30
150
45
195
60
216
75
240
Plot the speed-torque curve of the motor, when
(a) no external resistance is included in the circuit,
(b) a series resistance of $0.6 \mathrm{ohm}$ is inserted,
(c) the field winding alone is shunted by a resistance of $0.05 \mathrm{ohm}$,
(d) a resistance of 5 ohms is connected in parallel with the motor and 1.5 ohms in series with the line, and
(e) a resistance of $1.5 \mathrm{ohms}$ is connected in parallel with the armature and 2 ohms in series with the field winding.

Ajay Singhal
Ajay Singhal
Numerade Educator
05:08

Problem 5

For the motor in problem 4 , determine the values of the resistances $R_D$ in parallel with the armature and $R$ in series with the field for the shunted armature connection to give a speed-torque characteristic with $(G)$ a speed of $\$ 00 \mathrm{rpm}$ at zero torque and $(i i)$ a torque of $100 \mathrm{~N}-\mathrm{m}$ at zero speed.
[Ans. (i) For $I_f=60 \mathrm{~A}, R_D=1.286 \mathrm{ohms}$ and $R=2.3 \mathrm{ohms}$.
(ii) For $I_f=75 \mathrm{~A}, R_D=0.219 \mathrm{ohms}$ and $R=2.66 \mathrm{ohms}$.]

Narayan Hari
Narayan Hari
Numerade Educator
03:50

Problem 6

Plot the speed-torque curves for the motor in Problem 4 when connected as a shunt motor as shown in Fig. 3.31 with
(a) $R_1=2.5$ ohms,
$R=1 \mathrm{ohm}$, and
(b) $R_1=2.5$ ohms,
$R=2.5$ ohms.

Narayan Hari
Narayan Hari
Numerade Educator
01:46

Problem 7

If a series motor were connected as shown in Fig. 3.32. Show that the starting torque has a maximum value, when
$$
R_2=\frac{R\left(R_1+R_f\right)}{R+R_1+R_f}-R_{\mathrm{a}}
$$
FIGURE CANT COPY
Fig. 3.31. Motor connections for Problem 6
Fig. 3.32. Motor connections for Problem 7
FIGURE CANT COPY

Narayan Hari
Narayan Hari
Numerade Educator
06:45

Problem 8

A $230 \mathrm{~V}$ de series motor used in lifts has a resistance of $0.2 \mathrm{ohm}$. At a speed of $1800 \mathrm{rpm}$ it takes $50 \mathrm{~A}$. Determine the resistance to be added in series with the motor
(a) to limit the speed to $3600 \mathrm{rpm}$ when the current is $12.5 \mathrm{~A}$, assuming that the magnetization curve is a straight line between zero and $50 \mathrm{~A}$;
(b) to make the speed 900 rpm when the current is $70 \mathrm{~A}$, taking the flux per pole at $70 \mathrm{~A}$ is 20 percent greater than that at $50 \mathrm{~A}$.
At what speed will the motor run, when directly connected to the $230 \mathrm{~V}$ mains and drawing a current of $70 \mathrm{~A}$ ?
[Ans. (a) 9.4 ohms, (b) 1.2 ohms, $1472.73 \mathrm{rpm}$ ]

Jordan Vanevery
Jordan Vanevery
Numerade Educator
05:08

Problem 9

^ $230 \mathrm{~V}$ de series motor having the magnetization curve given below, runs at $750 \mathrm{rpm}$ with a certain load and take a current of $60 \mathrm{~A}$ from the lines:
Current (A)
1020
$30 \quad 40$
50
$60 \quad 70$
80
90
Flux per pole $(\mathrm{mWb})$
$\begin{array}{lll}2.9 & 5.5 & 7.4\end{array}$
8.5
9.2
$9.7 \quad 10.1$
10.6
10.8
The resistances of the field and armature are 0.05 and $0.1 \mathrm{ohm}$ respectively. Determine the value of the resistance of the divertor connected in parallel with the field in order to increase the speed to $900 \mathrm{rpm}$, the load torque remaining the same as before.
(Hint: Adopt trial and error method. Assume a lower value of flux corresponding to increased speed. Then, both new values of $I_a$ and $E$ are known, from which the divertor resistance can be determined. Then, new value of field current cab be found. Check whether this ficld current corresponds to the assumed value of flux.)
[Ans. 0.05 ohm]

Narayan Hari
Narayan Hari
Numerade Educator
03:40

Problem 10

Two identical $5 \mathrm{~kW}, 220, \mathrm{~V}, 24 \mathrm{~A}$ de shunt machines are to be used as the generator and motor in a Ward-Leonard system. The armature resistance of each machine is $0.5 \mathrm{ohm}$ and the magnetization curve for each machine at $1500 \mathrm{rpm}$ is given below:
Field current, $A$
induced $\mathrm{cmf}, \mathrm{V}$
02
0.4
0.6
0.8
1.0
1.2
1.4
80
160
210
228
237
243
247
The generator is driven at a constant speed of $1500 \mathrm{rpm}$.
(a) Determine the maximum and minimum values of the generator field current required to give the motor a speed range of $100 \mathrm{rpm}$ to $1500 \mathrm{rpm}$ at full load armature current of $24 \mathrm{~A}$, with the motor field current held constant at $0.6 \mathrm{~A}$.
(b) Determine the maximum motor speed obtainable at full load armature current if the motor field current is reduced to $0.10 \mathrm{~A}$ and generator field current is not allowed to exceed $1.2 \mathrm{~A}$.
[Ans. (a) $0.98 \mathrm{~A}$ and $0.08 \mathrm{~A}$, (b) $8212.5 \mathrm{rpm}]$

Bruce Edelman
Bruce Edelman
Numerade Educator
01:46

Problem 11

A $250 \mathrm{~V}, 10 \mathrm{~kW}, 1200 \mathrm{rpm}$ de shunt motor has a full losd efficiency of 80 per cent. Its field and armature reistances are 110 ohms and 0.25 ohm respectively. Calculate the value of the resistance to be inserted in series with the armature and the power lost in the armature circuit to reduce the speed to 80 percent when
(a) the load torque is constant regardless of speed,
(b) the load torque is directly proportional to the speed,
(c) the load torque varies as the square of the speed.
[Ans. (a) $1 \mathrm{ohm}$ and $2.847 \mathrm{~kW},(b) 1.31$ ohms and $2.274 \mathrm{~kW}$,
(c) $1.70 \mathrm{ohm}$ and $1.818 \mathrm{~kW}$ ]

Narayan Hari
Narayan Hari
Numerade Educator
06:45

Problem 12

A $250 \mathrm{~V}$ de series motor having armature and field resistance $0.25 \mathrm{ohm}$ and 0.15 ohm respectively runs, at $800 \mathrm{rpm}$, while taking 50 . $\mathrm{A}$ from the supply. Assuming the magnetic circuit of the motor to be unsaturated, determine its speed, when a divertor of $0.3 \mathrm{ohm}$ resistance is connected in parallel with the field winding of the motor, which is subjected to a load torque whose torque
(a) remains constant regardless of speed,
(b) varies in direct proportion of the speed.
(c) varies as the square of the speed.
[Ans. (a) $973 \mathrm{rpm}$, (b) $912 \mathrm{rpm}$, (c) $879 \mathrm{rpm}$ ]

Jordan Vanevery
Jordan Vanevery
Numerade Educator
01:46

Problem 13

A de series motor on load operating at $250 \mathrm{~V}$ dc mains draws $25 \mathrm{~A}$ and runs at $1200 \mathrm{rpm}$. Armature and field resistances are $0.1 \mathrm{ohm}$ and $0.3 \mathrm{ohm}$ respectively. A resistance of 25 ohms is placed in parallel with the armature of the motor. Determine:
(a) the speed of the motor with the shunted ammature connection, if the magnetic circuit remains unsaturated and the load torque remains constant, and
(b) the no load speed of the motor with the shunted armature connection.
[Ans. (a) $986.37 \mathrm{rpm},(b) 3125.38 \mathrm{rpm}$ ]

Narayan Hari
Narayan Hari
Numerade Educator
05:08

Problem 14

An adjustable speed de shunt motor has a speed range of $3: 1$. If the motor draws an armature current of $50 \mathrm{~A}$ at $1000 \mathrm{rpm}$, calculate the current at the speed of $3000 \mathrm{rpm}$ when speed control is achieved by (i) field flux control, and (ii) armature voltage control, with the motor driving a load whose,
(a) load torque is constant, and
(b) load power is constant.
Neglect all losses and effect of armature reaction
[Ans, (a) (i) $150 \mathrm{~A}$, (i) $50 \mathrm{~A}$, (b) (i) $50 \mathrm{~A}$, (ii) $50 / 3 \mathrm{~A}$ ]

Narayan Hari
Narayan Hari
Numerade Educator