0195136047.pdf

12.4 FORCES AND TORQUES IN MAGNETIC-FIELD SYSTEMS 533

The machine operates as asingle-phase induction machine,and the instantaneous

torque is pulsating. The average value of the torque is

(Te)av=−

LIsIr

4

sin(α+θ 0 )

If the machine is brought up to a speed ofωm=ωs−ωr, an average unidirec-

tional torque is established, and continuous energy conversion takes place at the

asynchronousspeed ofωm. Again, note that the machine is not self-starting, since

an average unidirectional torque is not developed atωm=0 with the specified

electrical excitations.

The pulsating torque, which may be acceptable in small machines, is, in general,

an undesirable feature in a rotating machine working as either a generator or a

motor, since it may result in speed fluctuation, vibration, noise, and a waste of

energy. In magnetic-field systems excited by single-phase alternating sources, the

torque pulsates while the speed is relatively constant. Consequently, pulsating power

becomes a feature. This calls for improvement; in fact, by employing polyphase

windings and polyphase sources, constant power is developed in a balanced system.

EXAMPLE 12.4.2

Consider an electromagnet, as shown in Figure E12.4.2, which is used to support a solid piece of
steel and is excited by a coil ofN=1000 turns carrying a currenti= 1 .5 A. The cross-sectional
area of the fixed magnetic core isA= 0 .01 m^2. Assume magnetic linearity, infinite permeability
of the magnetic structure, and negligible fringing in the air gap.

(a) Develop a general expression for the forcefacting to pull the bar toward the fixed

magnetic core, in terms of the stored energy, from the basic principle of conservation of

energy.

(b) Determine the force that is required to support the weight from falling forx= 1 .5 mm.

fe

Movable steel

N turns

i v

x

+−

Fixed core

Figure E12.4.2Electromagnet.