Question 7.8: Figure 7.18a defines the dimensions of a permanent-magnet dc......
Figure 7.18a defines the dimensions of a permanent-magnet dc motor similar to that of Fig. 7.17. Assume the following values:
Rotor radius R_r = 1.2 ~cm
Gap length t_{\mathrm{g}} = 0.05 ~cm
Magnet thickness t_m = 0.35 ~cm
Also assume that both the rotor and outer shell are made of infinitely permeable magnetic material (μ → ∞) and that the magnet is neodymium-iron-boron (see Fig. 1.19).
Ignoring the effects of rotor slots, estimate the magnetic flux density B in the air gap of this motor.
Because the rotor and outer shell are assumed to be made of material with infinite magnetic permeability, the motor can be represented by a magnetic equivalent circuit consisting of an air gap of length 2t_{\mathrm{g}} in series with a section of neodymium-iron-boron of length 2t_{\mathrm{m}} (see Fig. 7.18b). Note that this equivalent circuit is approximate because the cross-sectional area of the flux path in the motor increases with increasing radius, whereas it is assumed to be constant in the equivalent circuit.
The solution can be written down by direct analogy with Example 1.9. Replacing the air-gap length g with 2t_{\mathrm{g}} and the magnet length l_{\mathrm{m}} with 2t_{\mathrm{m}}, the equation for the load line can be written as
B_m = – μ_0 \left( \frac{t_m}{t_{\mathrm{g}}} \right) H_m= -7 μ_0 H_m
This relationship can be plotted on Fig. 1.19 to find the operating point from its intersection with the dc magnetization curve for neodymium-iron-boron. Alternatively, recognizing that, in SI units, the dc magnetization curve for neodymium-iron-boron is a straight line of the form
B_m = 1.06μ_0H_m + 1.25
we find that
B_m= B_{\mathrm{g}} = 1.09 ~T