Electrical Engineering ⇒ Topic : Magnetic leakage and fringing

Magnetic Leakage and Fringing

The flux that does not follow the desired path in a magnetic circuit is called a leakage flux.

        In most of practical magnetic circuits, a large part of flux path is through a magnetic material and the remainder part of flux path is through air. The flux in the air gap is known as useful flux because it can be utilised for various useful purposes. Fig. (a) shows an iron ring wound with a coil and having a narrow air gap. The total flux produced by the coil does not pass through the air gap as some of it **leaks through the air (path at 'a') surrounding the iron. These flux lines as at 'a' are called leakage flux.

                                                                           figure (a)

The value of leakage coefficients for electrical machines is usually about 1.15 to 1.25.Magnetic leakage is undesirable in electrical machines because it increases the weight as well as cost of the machine. Magnetic leakage can be greatly reduced by placing source of m.m.f. close to the air gap.

Fringing. When crossing an air gap, magnetic lines of force tend to bulge out such as lines of force at bb in Fig. (a). It is because lines of force repel each other when passing through non-magnetic material such as air. This effect is known as fringing. The result of bulging or fringing is to increase the effective area of air gap and thus decrease the flux density in the gap. The longer the air gap, the greater is the fringing and vice-versa.

Note. In a short air gap with large cross-sectional area, the fringing may be insignificant. In other situations, 10% is added to the air gap's cross-sectional area to allow for fringing.

MAGNETIC LEAKAGE AND FRINGING

Fig. shows a metal ring symmetrically situated relative to the air gap in the iron ring. Let the magnetising winding be concentrated over a short length of the core. The flux through the metal ring may be considered as useful flux and that which returns by such paths as 1,2 and 3 is the leakage flux. The useful flux passing across the gap tends to buidge outwards (this is because the lines of force repel each other when passing through a non-magnetic material) as shown roughly in Fig.(a), thereby reducing the effective area of the gap and reducing the flux density in the gap. This effect is referred to as fringing; and the longer the air gap, the greater is the fringing.

                                                                        Fig.(a) Magnetic leakage and fringing

It is seen that the effect of leakage flux is to increase the total flux through the exciting winding.

If                Φ_t = total flux produced (produced in the exciting winding)

                  Φ = useful flux available in the air gap.

Then, leakage co-efficient (or factor),λ = Φ_t/Φ

 The value of  λ for electrical machines is usually about 1.15 to 1.25.

Note. Magnetic leakage can be minimised by placing the exciting coils or windings as close as possible to the air gap or to the points in the magnetic circuit where the flux is to be utilised

MAGNETIC LEAKAGE FLUX, FRINGING FIELD AND

LEAKAGE COEFFICIENT

Consider a ring specimen of a conductor carrying a winding of N turns with an air gap as shown in Fig. (1). When the winding carries a current, flux will be established in the specimen. A small portion of this flux may cross the air gap and link with the search coil dd₁. This flux is called the useful flux. Some of the flux may not cross the air gap as useful flux and returns by paths a, b and c, and is known as leakage flux. The flux in the air gap bulges outwards

                            FIGURE (1) Magnetic leakage and fringing

shown in Fig. (1), because of the variation in reluctance. This is known as fringing. The affect of fringing is to reduce the flux density in the air gap. The effect is more pronounced for larger air gaps. The flux through the air gap is known as useful flux and can be used for practical purposes. From Fig. (1), it can be seen that the effect of the leakage flux is to increase the total flux through the existing winding, and

The value of leakage coefficient varies from 1.15 to 1.25 for electrical machines. Thus, in electrical machines, total flux being known, the useful flux can be determined by assuming a suitable value of the leakage coefficient