0195136047.pdf

548 ELECTROMECHANICS

l

b

Air gap

N-turn coil

Nonmagnetic sleeve

g

a

c

μ = ∞

μ = ∞

Cylindrical core

Plunger Mean radius of sleeve

Figure P12.4.4

I

Nonmagnetic sleeve

Core thickness (into paper) a

Core

N

b

Air gap

Plunger

g

a

2 a

μ = •

μ = •

Figure P12.4.6

12.4.7Let the coil of the solenoid of Problem 12.4.6

have a resistanceRand be excited by a voltage

v=Vmsinωt. Consider a plunger displacement

ofg=g 0.

(a) Obtain the expression for the steady-state

coil current.

(b) Obtain the expression for the steady-state

electric force.

*12.4.8A two-pole rotating machine with a singly ex-
cited magnetic field system as its stator and a
rotor (that carries no coil) has a stator-coil in-
ductance that can be approximated byL(θ )=
( 0. 02 − 0 .04 cos 2θ− 0 .03 cos 4θ)H, where
θis the angle between the stator-pole axis and
the rotor axis. A current of 5 A (rms) at 60 Hz is
passed through the coil, and the rotor is driven at

a speed, which can be controlled, ofωmrad/s. See

Figure P12.4.8 for the machine configuration.

(a) Find the values ofωmat which the machine

can develop average torque.

(b) At each of the speeds obtained in part (a),

determine the maximum value of the average

torque and the maximum mechanical power

output.

Note: Te = ∂Wm′(i, θ)/∂θ = 1 / 2 i^2

∂L(θ )/∂θ.Letθ=ωmt−δ.

12.4.9Consider Example 12.4.1. With the assumed

current-source excitations of part (c), determine

the voltages induced in the stator and rotor wind-

ings at the corresponding angular velocityωmat

which an average torque results.