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# Iron and Air

Many magnetic structures include one or more air gaps. There are air gaps between the rotor and stator of motors and generators. Relays depend upon a change in the length of air gap as do solenoids of the plunger and clapper types. In such circuits the exciting winding must develop sufficient mmf to overcome not only the reluctance of the iron but also that of the air gap.

Example 3-3: Consider the simple magnetic circuit shown in Fig. 3-19 which consists of a laminated core of U.S.S. Transformer 72, 29 Gage Steel with an air gap g and an exciting winding of 300 turns. If the air gap

 Figure 3-19. Laminated electromagnet with air gap

has a length g = 0.100 in., determine the current to produce a flux of 20,000 lines in the core. Neglect leakage and fringing. Assume a stacking factor of 0.95 for the core.

Solution: Net area of core = 0.50 x 0.50 x 0.95 = 0.238 sq in.
Length of iron circuit = 2(2| + 2) = 9.00 in.

H(for iron, from Fig. 3-11) = 18 amp turns per in. The mmf for the iron is

Firon = HironIiron = NIiron
NIiron = 18 x 9 = 162 amp turns
Length of air gap = 0.10 in.

The mmf for air is

The area of the air gap is 0,50 x 0.50 = 0.25 sq in.

It should be noted that the stacking factor applies only to laminated iron and not to the air gap.

The air gap is in series with the iron as the same amount of flux traverses both, hence the total mmf is

Air gaps are undesirable in magnetic circuits where low mmf are required for given values of flux. This is true of power transformers where a low value of exciting current is desirable. However, the cost of keeping air gaps short or entirely eliminated must not be so great as to outweigh other factors such as cost and difficulty of construction. Air gaps can be eliminated by using punchings in the form of hollow discs, as for example in the toroidal core of Fig. 3-9(a). This construction is practical for small cores, but the cost of dies becomes prohibitive beyond a certain limited size. Figure 3-15 shows a group of small magnetic cores in toroidal form. A construction frequently used for reasons of low cost has the core made up of E and I laminations as shown in Fig. 3-20.

 Figure 3-20. Core comprised of E and I laminations with overlapping butt joints

The least laborious method for assembling such a core is to stack all the I laminations together to the desired thickness and all the E laminations together and then pushing the two stacks together. This, however, produces three butt joints where the I stack meets the three legs of the E stack and a small air gap results at each joint. The effect of these joints can be minimized by going to lap joints and assembling the I pieces one at a time with the E pieces in such a fashion that for successive layers the position of the I pieces alternates between top position and bottom position, and the corresponding E pieces between bottom position and top position. Thus, the gap in each layer is bridged by a solid piece of lamination on each side of the gap, as shown in Fig. 3-20. Lap joints can also be achieved by using L-shaped laminations for making up a two-legged core. Some two-legged cores are constructed from straight I-shaped laminations and using lap joints.

There are applications, however, in which an air gap is desired in a core to give a smaller variation of inductance with current or to prevent saturation of transformer cores. An air gap is also desired in the cores of chokes when direct current is present.

Last Update: 2011-08-01