0195136047.pdf

510 ELECTROMECHANICS

Ferromagnetic pieces

Magentic flux lines

F

F

Figure 12.1.6Principle of alignment.

and shows the direction of forces. The force is always in a direction that reduces the net magnetic

reluctance and shortens the magnetic flux path.

A mechanical force is exerted on ferromagnetic material, tending to align it with or bring it

into the position of the densest part of the magnetic field. This force is the familiar attraction of a

magnet for pieces of iron in its field. In magnetic circuits, for example, definite forces are exerted

on the iron at the air–iron boundary. Energy changes associated with a differential displacement of

the iron cause the mechanical force. This force is the essential operating mechanism of many elec-

tromagnetic devices, such as lifting magnets, magnetic clutches, chucks, brakes, switches (known

as contactors), and relays. Solenoid-operated (solenoid being another name for the operating coil)

valves are common elements in piping systems. Actuators used in control systems operate due to

the mechanical force or torque converted from the electric, pneumatic, or hydraulic inputs.

In motor and generator action, the magnetic fields tend to line up, pole to pole. When their

complete alignment is prevented by the need to furnish torque to a mechanical shaft load, motor

action results when electric to mechanical energy conversion takes place. On the other hand, when

the alignment is prevented by the application of a mechanical torque to the rotor from a source of

mechanical energy, generator action results when mechanical to electric energy conversion takes

place.

EXAMPLE 12.1.1

A magnetic crane used for lifting weights can be modeled and analyzed as a simple magnetic

circuit, as shown in Figure E12.1.1. Its configuration consists of two distinct pieces of the same

magnetic material with two air gaps. Obtain an expression for the total pulling force on the bar

in terms of the flux densityBin the air-gap region and the cross-sectional areaAperpendicular

to the plane of paper, while making reasonable approximations.

Solution

Reasonable approximations include infinite permeability of the magnetic material, as well as

neglecting leakage and fringing. The magnetic energy stored in an incremental volume of the

air-gap region is given by

dWm=

1

2

B

(

B

μ 0

)

dv

whereBandH(=B/μ 0 ) are in the same direction. Working with one pole of the magnetic circuit,

in view of the symmetry, the incremental change in volume isdv=Adg. Hence,