armature. Also, the magnetic flux carried by the leakage flux paths must be carried by a portion of the magnet poles. This causes the magnet pole material to reach the saturation flux limit sooner than expected. Therefore, the leakage flux paths cause a large decrease in the armature force. When a permanent magnet is placed near the working gap, the armature force is increased, because some of the leakage flux becomes fringing flux. This essentially minimizes the leakage flux. Conversely, the leakage flux paths are useful in permanent-magnet systems as a means of protecting the permanent magnet from large demagnetizing fields. In this case, some of the demagnetizing flux bypasses the permanent magnet through the leakage flux paths.
The leakage flux paths can be evaluated by using the following procedures.
Half Cylindrical Shell). This flux path is identical in shape to path SP4.
The diameter of the internal half cylindrical shell d1 is equal to 33 percent of the permanent-magnet length. The radius of the external half cylindrical shell r1 is equal to 50% of the permanent-magnet length. These permeance relationships are shown here,based on Eqs. (1.126) through (1.131).This flux path is valid only for alnico and earlier permanent magnets, which have effective poles at 70 percent of the magnet length. Ferrite and rare-earth permanent magnets have effective poles at 95 percent of the magnet length; therefore, no magnetic flux is generated in this path and the permeance is zero.
Total Permeance and Equivalent Reluctance Circuit. The total reluctance of the
FIGURE 1.15 Equivalent reluctance network for the permanent magnet leakage shown in Fig. 1.14.
The total reluctance of the circuit shown in Fig. 1.15 as seen from the permanent magnet can be written as follows:
The total reluctance can be obtained by substituting Eqs. (1.179) through (1.18: into Eq. (1.184).
Total circuit reluctance
Total circuit permeance
