**3.4. Levitating area and parameters of the magnets**

Figure 8 shows the magnetic force map for the test model shown in Table 1. The tilting angle of the rotor magnet is set as ±1°. This figure shows that a tilting magnetic top, located within the red dotted lines and named as the 'levitating area', will be guided by the magnetic force along the direction of vectors towards the restoring centre A (0, 0, 99.5). Although the levitating area is shown as a two-dimensional area in this figure, the real shape of the levitating area is conic.

The size and shape of the levitating area are closely related to the dimensions of the permanent magnets and the tilting angle of the rotor magnet. Figure 9 shows the relationship between the shape and size of the levitating area and the parameters of the permanent magnets. The effects of precession are considered to set the tilt angle *θ* to −1° in *x*  > 0 and to 1° in *x* < 0. The conical shape of the levitating area is approximated by the rectangular area bounded by the green coloured dotted line in Figure 8 [5].

Feasibility Study of a Passive Magnetic Bearing Using the Ring Shaped Permanent Magnets 147

**Figure 9.** Relationship between the shape and size of the levitating area and the parameters of the

Figure 9(b) shows the levitating areas and the restoring points in the case where the outer diameter of the rotor magnet *dro* changes. When the outer diameter of the rotor magnet

permanent magnets.

**Figure 8.** Levitating area of a magnetic top tilted by 1°.

Figure 9(a) shows the levitating areas and the restoring points for the various inner diameters of the rotor magnet *dri*. When the inner diameter of the rotor magnet increases, the restoring point becomes higher and the levitating area becomes narrower in the radial direction and wider in the thrust direction. These results indicate that relatively well radial bearing characteristics can be obtained by a rotor magnet with a large inner diameter. On the contrary, relatively well thrust bearing characteristics can be obtained by a rotor magnet with a smaller inner diameter.

**Figure 8.** Levitating area of a magnetic top tilted by 1°.

with a smaller inner diameter.

Figure 9(a) shows the levitating areas and the restoring points for the various inner diameters of the rotor magnet *dri*. When the inner diameter of the rotor magnet increases, the restoring point becomes higher and the levitating area becomes narrower in the radial direction and wider in the thrust direction. These results indicate that relatively well radial bearing characteristics can be obtained by a rotor magnet with a large inner diameter. On the contrary, relatively well thrust bearing characteristics can be obtained by a rotor magnet

**A**

**Figure 9.** Relationship between the shape and size of the levitating area and the parameters of the permanent magnets.

Figure 9(b) shows the levitating areas and the restoring points in the case where the outer diameter of the rotor magnet *dro* changes. When the outer diameter of the rotor magnet increases, the restoring point becomes higher and the levitating area becomes narrower in the radial direction and wider in the thrust direction. These results state that relatively well radial bearing characteristics can be obtained by a rotor magnet with a large outer diameter. On the contrary, relatively well thrust bearing characteristics can be obtained by a rotor magnet with a smaller outer diameter.

Feasibility Study of a Passive Magnetic Bearing Using the Ring Shaped Permanent Magnets 149

Figure 9(c) shows the levitating areas and the restoring points in case where the inner diameter of the stator magnet *dsi* changes. When the inner diameter of the stator magnet increases, the restoring point becomes lower and the levitating area becomes wider in the radial direction and narrower in the thrust direction. These results show that relatively well radial bearing characteristics can be obtained by a stator magnet with a smaller outer diameter. On the contrary, relatively well thrust bearing characteristics can be obtained by a stator magnet with a larger outer diameter.

Figure 9(d) shows the levitating areas and the restoring points in the case where the outer diameter of the stator magnet *dso* changes. When the outer diameter of the stator magnet increases, the restoring point becomes higher and the levitating area becomes narrower in the radial direction. The outer diameter of the stator magnet hardly affects the axial height of the levitating area. These results indicate that relatively well radial bearing characteristics can be obtained by a stator magnet with a large outer diameter. The thrust bearing characteristics are not changed by the outer diameter of the stator magnet.
