Problem 107-1    Source:   Adapted from example 6-1 - page 315 - CHAPMAN, Stephen J. -    Book: Fundamentals of Electric Machines - 5th edition - Ed. McGrawHill - 2013.

A three-phase induction motor of 208 V, 10 HP, 4 poles is connected to a network at 60 Hz na star setting. It has a full load slip of 5%. To determine:

a) the synchronous speed of the motor;

b) the speed of the rotor with rated load;

c) the rotor frequency at rated load;

d) the torque on the motor shaft, when at full load.

Problem 107-2    Source:  Problem prepared by the website author.

A three-phase induction motor of 220 V, 80 HP, 6 poles is connected to a network at 60 Hz and delivers rated power with 6% slip. Determine:

a) the speed of the rotating magnetic field;

b) the rotor frequency at rated load;

c) the speed of the rotor with rated load.

Problem 107-3    Source:   Example 5.2 - page 218 - SEN, P.C. -    Book: Principles of Electric Machines and Electronics - 3rd Edition - Ed. Wiley - 2014.

A three-phase induction motor, 4 poles, 15 HP, 60 Hz, rotates at a speed of 1,728 rpm and delivers full power to a load connected to its axis. It has friction losses and 750 W fan. It is requested:

a) the mechanical power developed by the engine, P_mec ;

b) the power in the air gap, P_gap ;

c) the rotor copper losses, P_jr .

Problem 107-4    Source:   Adapted from example 6-2 - page 322 - CHAPMAN, Stephen J. -    Book: Fundamentals of Electric Machines - 5th edition - Ed. McGrawHill - 2013.

A three-phase induction motor of 480 V, 60 Hz and 50 HP, consumes 60 A   from the mains with FP = 0.85  delayed. The stator copper losses are 2 kW and the rotor copper losses are 700 W. Friction and windage losses are 600 W, core losses are 1800 W. Find the following quantities:

a) The power in the air gap, P_gap ;

b) The converted power P_mec ;

c) The output power P_n ;

d) The efficiency, η, of the engine.

Problem 107-5    Source:  Problem prepared by the website author.

A 380 V three-phase induction motor, 6 poles, 60 Hz and 50 HP, develops full power with 4% slip. The mechanical losses are 900 W. Find the following quantities:

a) The power in the air gap, P_gap ;

b) The torque (torque) on the motor shaft, τ_ind ;

c) Rotor copper losses, P_jr.

Problem 107-6    Source:   Adapted from example 6-3 - page 326 - CHAPMAN, Stephen J. -    Book: Fundamentals of Electric Machines - 5th edition - Ed. McGrawHill - 2013.

A three-phase induction motor of 460 V, 4 poles, 60 Hz and 25 HP, connected in the Y configuration with 2.2% slip, it has the following impedances per phase referred to the stator circuit:

R₁ = 0.641 Ω    R₂ = 0.332 Ω

X₁ = 1.106 Ω    X₂ = 0.464 Ω    X_m = 26.3 Ω

Also, the total rotational losses are 1,100 W and are assumed to be constant. Core losses are included in rotational losses. Find the following quantities:

a) the speed of the rotor ;

b) the electric current in the stator, I₁ ;

c) motor power factor, PF.

Problem 107-7    Source:   Adapted from example 6-3 - page 326 - CHAPMAN, Stephen J. -    Book: Fundamentals of Electric Machines - 5th edition - Ed. McGrawHill - 2013.

Based on results from previous issue (Problem 107-6) get the following motor quantities:

a) the mechanical power, P_mec, and the nominal power, P_n ;

b) the induction torque, τ_ind, and the load torque, τ_load ;

c) the efficiency or yield, η, of the engine.

Problem 107-8    Source:  Problem prepared by the website author.

A 440 V, 6 pole and 60 Hz three-phase induction motor, connected in the Y configuration , supplies a constant load of 120 N . m at a speed of 1,180 rpm. Ventilation losses are 600 W and friction losses are 400 W. Determine:

a) the mechanical power, P_mec, and the nominal power, P_n ;

b) the rotor copper losses, P_jr ;

c) the induction torque, τ_ind ;

d) the new speed of the machine if we double the value of the load.

Problem 107-9    Source:   Problem 5.7 - page 272 - SEN, P.C. -    Book: Principles of Electric Machines and Electronics - 3rd Edition - Ed. Wiley - 2014.

A three-phase induction motor of 460 V, 60 Hz and PF = 0.9 delayed, consumes a current of 25 A. The ventilation and friction losses are 300 W, the rotor copper losses are 400 W and the stator copper losses are 1,100 W. Determine:

a) the power in the air gap, P_gap ;

b) the mechanical power developed by the engine, P_mec ;

c) the output power, P_n ;

d) the efficiency of the engine.

Problem 107-10    Source:   Problem 5.10 - page 272 - SEN, P.C. -    Book: Principles of Electric Machines and Electronics - 3rd Edition - Ed. Wiley - 2014.

A three-phase induction motor of 60 Hz and 6 poles, rotates at 1,140 rpm and consumes 90 kW from the power source. Ventilation and friction losses are 2,100 W and stator and core copper losses are 4,800 W. . Determine:

a) the power in the air gap, P_gap ;

b) the rotor copper losses, P_jr ;

c) the mechanical power delivered to the load, P_mec ;

d) the torque on the load, τ_load ;

e) the engine efficiency.