Air-Gap Flux Fringing

In Section 39, equation 38 was developed for inductance of a linear reactor with an air gap. It is assumed that 85 per cent of the core flux is confined to the cross section of core face adjoining the gap. The remaining 15 per cent of the core flux "fringes" or leaves the sides of the core, thus shunting the gap. Fringing flux decreases the total reluctance of the magnetic path and increases the inductance to a value greater than that calculated from equation 38. Fringing flux is a larger percentage of the total for larger gaps. Very large gaps are sometimes broken up into several smaller ones to reduce fringing.

If it is again assumed that the air gap is large compared to l_c/μ, the reluctance of the iron can be neglected in comparison with that of the air gap. For a square stack of punchings, the increase of inductance due to fringing is

[39]

Equation 39 is plotted in Fig. 72 with core shapeas abscissas and gap ratio l_g/S as parameter.⁽¹⁾

Fig. 72. Increase of reactor inductance with flux fringing at core gap.

If the air gap is enclosed by a coil, as at the top of Fig. 72, flux fringing is reduced because of the magnetizing force set up near the gap by the ampere-turns of the coil. A coil fitting tightly all around the core would produce no fringing at all. As the distance from inside of the coil to the core increases, so does the fringing. Fringing therefore depends upon the coil form thickness; if it materially exceeds the air gap per leg, fringing is nearly the same as it would be in a core gap which is not enclosed by a coil. Figure 72 is based on a thick coil form.

(1)	See G. F. Partridge, Phil. Mag., 22 (7th series), 675 (July-December, 1936)