Page 37 - Electric Machinery Fundamentals

INTI{QDUCTlQN TO MACHINERY PI{ INCIPU::S l j

There is also a magnetic analog of conductance. Just as the conductance of
an electric circuit is the reciprocal of its resistance, the penneance cP of a magnetic
circuit is the reciprocal of its reluctance:

(1-29)

The relationship between magnetomotive force and flux can thus be expressed as
(1- 30)
Under some circumstances, it is easier to work with the permeance of a magnetic
circuit than with its reluctance.
What is the reluctance of the core in Figure 1-3? The resulting flux in this
core is given by Eguation (1- 26):

(1-26)

(1-3 1)

By comparing Equation (1-3 1) with Equation (1-28), we see that the reluctance
of the core is

(1-32)

Reluctances in a magnetic circuit obey the same rules as resistances in an electric
circuit. The equivalent reluctance of a number of reluctances in series is just the
sum of the individual reluctances:
<Roq ~ 'R, + 'R, + 'R, + ... (1-33)
Similarly, reluctances in parallel combine according to the equation

_l_ ~_t_ + _t_ +_t_ + . (1- 34)
'R,q 'R, 'R, 'R,

Permeances in series and parallel obey the same rules as electrical conductances.
Calculations of the flux in a core performed by using the magnetic circuit con-
cepts are always approximations- at best, they are accurate to within about 5 per-
cent of the real answer. There are a number of reasons for this inherent inaccuracy:
1. The magnetic circuit concept assumes that all flux is confined within a mag-
netic core. Unfortunately, this is not quite true. The permeability of a ferro-
magnetic core is 2000 to 6000 times that of air, but a small fraction of the flux
escapes from the core into the surrounding low-permeability air. This flux