plunger actuator

Figure Q3(a) shows a plunger actuator. When there is no current supplied to the
coil, the plunger drops to position xmax=4.0mm When a current of sufficient value is
supplied to the coil, the plunger rises to position xmin=0.4m. The inductance is given
by
� � =
2�
�� + �
where A and B are constants dependent on system parameters. Figure Q3(a) Plunger and coil
(i) Determine an expression for the field coenergy, Wfld’(x) and from it find an
expression for the magnetic force. (ii) State any two assumptions made in expressing the field coenergy in a(i) above
(iii) Explain the variation of magnetic stored energy and the force as the plunger
moves upwards. Consider a 50 Hz, 6 pole, three phase synchronous machine with rotor length of
1.85m, rotor diameter of 0.45m, and an airgap of 0.72cm. The synchronous
machine has Nf =580 turns on the rotor and a winding factor, kf, of 0.910. (i) Explain the meaning of the following expression: “..synchronous machine has Nf =580 turns on the rotor and a winding factor, kf, of 0.910”
(ii) Determine the rated speed of the machine in rpm
(iii) Find an expression for the current in the rotor winding as a function of the
peak flux density, Bp , in the airgap. Hence, calculate the current in the rotor
winding that would give Bp = 1.40 T. (iv) For the machine given in Q3b, if the stator has a phase winding consisting of
a series connection of coils where each pole pair has a 10 turn full pitch coil, calculate its generated rms voltage per phas

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