Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as e = wmt + d, where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance between the rotor and the stator is given by = 7cos0 H An AC current source i =8cos 50t A is applied to the stator winding and another AC current source i, = 9sin 40f A is applied to the rotor winding. (i) Derive the instantaneous developed torque, T. (ii) Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10, 50 and 90 rad/s. (iii) If the rotor is locked at 0=45°, determine the average torque developed by the machine. Rotor axis 0 = Omt + 8 Stator axis
Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as e = wmt + d, where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance between the rotor and the stator is given by = 7cos0 H An AC current source i =8cos 50t A is applied to the stator winding and another AC current source i, = 9sin 40f A is applied to the rotor winding. (i) Derive the instantaneous developed torque, T. (ii) Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10, 50 and 90 rad/s. (iii) If the rotor is locked at 0=45°, determine the average torque developed by the machine. Rotor axis 0 = Omt + 8 Stator axis
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure
Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as
0 = wmt + 8,
where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance
between the rotor and the stator is given by
L2
= 7cos0 H
An AC current source i =8cos 50t A is applied to the stator winding and another AC current source
i, = 9sin 401 A is applied to the rotor winding.
(i)
Derive the instantaneous developed torque, T.
(ii)
Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10,
50 and 90 rad/s.
(iii)
If the rotor is locked at 0=45°, determine the average torque developed by the machine.
Rotor
аxis
0 = Omt + 8
Stator
аxis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66b6ed25-22fe-489c-a0b2-1043d6bba07c%2F7e541762-d7d7-4030-b067-2bf672f31255%2Fqsuj3rb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure
Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as
0 = wmt + 8,
where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance
between the rotor and the stator is given by
L2
= 7cos0 H
An AC current source i =8cos 50t A is applied to the stator winding and another AC current source
i, = 9sin 401 A is applied to the rotor winding.
(i)
Derive the instantaneous developed torque, T.
(ii)
Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10,
50 and 90 rad/s.
(iii)
If the rotor is locked at 0=45°, determine the average torque developed by the machine.
Rotor
аxis
0 = Omt + 8
Stator
аxis
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