rials, there is an upper limit to the achievable air gap flux density in a motor. Later this will be shown to be a crucial factor in motor performance. Example
The preceding discussion embodies the basic concepts of magnetic circuit analysis. Application of these concepts requires making assumptions about magnetic field direction, flux path lengths, and flux uniformity over cross-sectional areas. To illustrate magnetic circuit analysis, consider the wound core shown in Fig. 2-13 and its corresponding magnetic circuit diagram. Assuming that the permeability of the core is much greater than that of the surrounding air, the magnetic field is essentially confined to the core, except at the air gap. Comparing the structure to the magnetic circuit, the coil is represented by the MMF source of value Ni. The reluctance of the core material is modeled by the reluctance Rc=lcllÂąA, where lc is the median length of the core from one side of the air gap around to the other, ji is the permeability of the core material, and A is the cross sectional area of the core. This modeling approximates the flux path length around bends as having median length. It also assumes that the flux density is uniform over the cross section. The reluctance of the air gap Rg is given by the inverse of the air gap permeance discussed earlier. The solution of this magnetic circuit follows Kirchhoff's laws for electric circuits where MMF corresponds to voltage, flux corresponds to current, and reluctance corresponds to resistance. Using each of the three air gap models shown in Fig. 2.8, the flux density B=(p/A flowing in the circuit is 0.91T, 1.08T, and 1.09T for Figs. 2.8a, b, c
Rc -M/V
0.5 mm
<b
1 cm
Figure 2-13. A simple magnetic structure and its magnetic circuit model.