Download Document

Tutorial Sheet – 06
1. A 4-pole 50-Hz induction motor is driving a load at 1450 r/min.
a) What is the slip of the motor?
b) What is the frequency of the rotor currents?
c) What is the angular velocity of the stator field with respect to the stator? With respect to the rotor?
d) What is the angular velocity of the rotor field with respect to the rotor? With respect to the stator?
2. A 3-Φ induction motor runs at almost 1000r/min at no load and 950 r/min at full load when supplied with
power from a 50-Hz 3-Φ line.
a) How many poles does the motor have?
b) What is the % slip at full load?
c) What is the corresponding frequency of the rotor voltages?
d) What is the corresponding speed of the rotor field with respect to the rotor?
e) Of the rotor field with respect to the stator?
3. A 3-phase induction motor runs at almost 1,200 rpm at no load and 1,140rpm at full load when supplied
with power from a 60-cps 3-phase line.
a) How many poles does the motor have?
b) What is the per cent slip at full load?
c) What is the corresponding frequency of the rotor voltages?
d) What is the corresponding speed (i) of the rotor field with respect to the rotor? (ii) of the rotor field with
respect to the stator? (iii) of the rotor field with respect to the stator field?
e) What speed would the rotor have at a slip of 10 per cent?
f) What is the rotor frequency at this speed?
g) Repeat part d for a slip of 10 per cent.
4. Describe the effect on the normal torque-speed characteristics of an induction motor produced by
(a) halving the applied voltage with normal frequency?
(b) halving both the applied voltage and the frequency?
Sketch the associated torque-speed characteristics in their approximate relative positions with respect to the
normal one. Neglect the effects of stator resistance and leakage reactance.
5. A 460-V, four-pole, 50-hp, 60-Hz, Y-connected, three-phase induction motor develops its full-load induced
torque at 3.8 percent slip when operating at 60Hz and 460V, The per-phase impedances of the motor are
𝑟1 = 0.33Ω 𝑋𝑚 = 30Ω
𝑥1 = 0.42Ω 𝑥2/ = 0.42Ω
Mechanical, core, and stray losses may be neglected in this problem.
a) Find the value of the rotor resistance 𝑟2.
b) Find 𝑇𝑚𝑎𝑥, 𝑠𝑚𝑎𝑥, and the rotor speed at maximum torque for this motor.
c) Find the starting torque of this motor. [Ans: (a) 0.171 Ω, 0.0068 Ω, (b) 448 N-m, 0.191, (c) 198 N-m]
1|Page
6. A 460V, 100hp, four-pole, ∆-connected, 60-Hz, three-phase induction motor has a full-load slip of 5
percent, an efficiency of 92 percent, and a power factor of 0.87 lagging. At start-up the motor develops 1.9
times the full-load torque but draws 8.5 times the rated current at the rated voltage. This motor is to be
started with reduced-voltage.
(a) What should be the reduced supply voltage so that the starting torque is equal to the rated torque of the
motor?
(b) What will the motor starting current at this voltage?
[Ans: (a) 333 V, (b) 716 A]
7. An induction motor has an efficiency of 0.9 when the load is 50h.p. At this load, the stator copper and rotor
copper loss each equals the iron loss. The mechanical losses are one-third of the no load loss. Calculate the
slip.
[Ans: 0.03]
8. The power input to a 500V, 50-cycle, 6-pole, 3-phase induction motor running at 975 per min is 40KW. The
stator losses are 1KW and the friction and windage losses total 2KW. Calculate (a) the slip; (b) the rotor
copper loss; (c) the brake horse-power; (d) the efficiency.
[(a) 0.025; (b) 975W; (c) 48.4h.p. ; (d) 90%.]
9. A 3-phase induction motor has a 4-pole, star-connected stator winding. The motor runs on a 50-c/s supply
with 200V between lines. The rotor resistance and standstill reactance per phase are 0.1Ω and 0.9Ω
respectively. The ratio of rotor to stator turns is 0.67. Calculate: (a) total torque at 4% slip; (b) total
mechanical power at 4% slip; (c) maximum torque; (d) speed at maximum torque; (e) maximum mechanical
power. Neglect stator impedance.
[ (a) 40.48 N-m, (b) 6.1 kW, (c) 63 N-m, (d) 1333 rpm; (e) 8.9 kW]
10. A 200-h.p. 1000-V, 25-c/s, star-connected induction motor has a star-connected, slip-ring rotor with a
transformation ratio of 3.6 : 1. The rotor resistance per phase is 0.01Ω and inductance 0.64mH. The stator
losses may be neglected. Find:
a) the rotor starting current per phase on normal voltage with slip-rings short-circuited;
b) the rotor power factor at starting;
c) the rotor current at 3% slip;
d) the rotor power factor at 3% slip;
e) the necessary external resistance per phase to obtain a starting current of approximately 30 A in the
stator.
[ ans: (a) 160 A; (b) 0.1; (c) 46.1 A; (d) 0.96; (e) 0.1Ω.]
11. A 3-phase induction motor with star-connected rotor has an induced electromotive force of 60V between
slip-rings at standstill on open-circuit with normal voltage applied to the stator. The resistance and standstill
reactance of each rotor phase are 0.6 Ω and 4Ω respectively. Calculate the current per phase in the rotor
a) when at standstill and connected to a star-connected rheostat of resistance 5Ω and reactance 2Ω per
phase;
b) when running short-circuited with 4% slip.
[ans: (a) 4.22A; (b) 2.22A.]
12. The rotor of a 6-pole, 50c/s, slip-ring induction motor has a resistance of 0.2 Ω per phase, and runs at 960
rev per min on full load. Calculate the approximate resistance per phase of a rotor rheostat such that the
speed is reduced to 800rev per min for full-load torque.
[0.8Ω.]
2|Page
13. The normal full load slip and shaft torque of a 500-h.p. 50-c/s, 3-phase induction motor are respectively
1.9% and 7000lb-ft. The rotor winding has a resistance of 0.25Ω and a standstill reactance of 1.5Ω per
phase. Estimate the slip and power output for full-load stator current when external resistances of 2Ω per
phase are inserted in the rotor circuit. Neglect magnetizing current.
[17.1%; 422 h.p.]
14. The output of a 3-phase, 50-c/s, 6-pole induction motor is 5h.p., at 935 rev per min.
a) Calculate the input if the stator losses are 400W.
b) What starting torque will the machine develop when switched directly on to the supply if maximum
torque is developed at 800 rev per min? Allow 1% for windage and friction.
[4.436 kW, 24.7 N-m.]
1
15. An 8-pole, 50-c/s induction motor has a full-load slip of 2 2 % and a maximum torque of twice full-load
torque. Draw to scale the torque /speed curve, taking maximum torque as unity. At what value of the slip
does the maximum torque occur?
[0.093]
16. The resistance measured between each pair of slip rings of a 3-phase 60-cps 300-hp 16-pole induction motor
is 0.035 ohm. With the slip rings short circuited the full-load slip is 0.025, and it may be assumed that the
slip-torque curve is a straight line from no load to full load. This motor drives a fan which requires 300hp at
the full-load speed of the motor. The torque required to drive the fan varies as the square of the speed. What
resistances should be connected in series with each slip-ring so that the fan will run at 300rpm?
[Ans: 0.481 Ω]
17. When operated at rated voltage and frequency, a 3-ph squirrel cage induction motor delivers full load at a
slip of 5% and develops a maximum torque of 250% of full load torque at a slip of 25%. Neglecting core
loss and rotational losses and assuming that the resistances and inductances of the motor are constant,
determine the starting torque (at rated voltage and frequency) of the motor expressed as percentage of the
full load torque.
[Ans: 121.67%]
18. A 40,000-hp 60-cps 22-pole wound-rotor induction motor is used to drive a load whose power requirement
varies as the cube of its speed and is 40,000hp at 297rpm. The speed must be adjustable over a range from
297 to 37.5 rpm. If external rotor-resistance is used to vary the speed, plot curves of the following variables
as function of the speed in rpm:
a) Load power, in kilowatts.
b) Power input to the motor, in kilowatts. Neglect stator copper, rotational, and stray load losses.
c) Total rotor-circuit copper loss, in kilowatts.
19. A 500-hp wound rotor induction motor, with its slip rings short-circuited has the following properties:
Full load slip = 1.5%
Rotor I2R at full load torque = 5.69 kW
Slip at maximum torque = 6.0%
Rotor current at maximum torque = 2.82I2fl , where I2fl is the full load rotor current
Torque at 20% slip = 3.95I2fl
If the rotor-circuit resistance is increased to 5Rrotor by connecting non-inductive resistance in series with
each rotor slip-ring, determine:
a) the slip at which the motor will develop the same full-load torque,
b) the total rotor circuit I2R loss at full-load torque,
c) the horse power output at full-load torque,
d) the slip at maximum torque,
e) the rotor current at maximum torque,
f) the starting torque, and
g) the rotor current at starting. Express the torques and rotor currents in per unit based on the full-load
torque values.
3|Page