**Author details**

160 Performance Evaluation of Bearings

**5. Conclusions** 

characteristics of the magnetic top.

following results are obtained:

dimensional static analysis.

nutation mode is not observed.

angle and in a certain rotating speed range.

with the accuracy of several micrometres.

observed using a digital video camera.

Figure 21(b) shows the time dependence of the tilt angle of the rotor magnet with respect to *z*-axis. This figure shows that the tilt angle varies within 1.4° while the top is levitating and

Figure 22 shows the trajectories of the magnetic top at the last 15 s of its levitation. Figures 22(a) and (b) demonstrate the trajectories of the shaft head and the centre of the levitating rotor magnet in its final 15 s levitation. These figures show that the precession quickly

A magnetic top levitates by itself, without any active control system, so long as it rotates in a certain speed range. The authors propose a simple and intuitive analysing method to predict

The quasi-three-dimensional static analysis, considering shapes and layout of the ringshaped rotor and stator magnets, is used to explain the principle of levitation and obtain the preliminary design parameters of the rotor and stator magnets. The behaviour of the magnetic top is also investigated by dynamic simulations based on the three-dimensional equations of motion considering the moment of inertia for the rotating magnetic top. The

1. A magnetic top can levitate when it rotates in precession mode with a slight tilting

2. The effects of the parameters, such as outer and inner diameters of the rotor and stator magnets, to the behaviour of the magnetic top can be discussed by the quasi-three-

3. A magnetic top rotating at a low speed levitates in both precession and nutation modes. On the contrary, a magnetic top rotating at a high speed levitates with precession, and

4. The lowest rotation speed is determined to maintain the attitude of the rotating magnet using its mechanical inertia. The maximum rotation speed is limited by the centrifugal

5. A magnetic top starting its rotation at the restoring centre will maintain its position

6. It is difficult to repeat experiments of a magnetic top in the same conditions. However, the proposed analytical results showed good accordance with the experimental data

A magnetic top may be used as a rotating demonstration model in which some swaying motion can be permitted such as in toys or other relaxation items. When a magnetic top is used in commercial system, a rotor should be rotated by some non-contact drive mechanism such as electric motor or air turbine, etc. Furthermore, touch down bearing should be equipped to suspend a rotor while rotating speed is out of operating range. Fundamental requirements to design a magnetic bearing based on the principle of a magnetic top will be

force that increases the tilt angle of the shaft of the magnetic top.

indicates that precession is needed to maintain levitation for a magnetic top.

becomes larger once the magnetic top exits the levitating area.

Teruo Azukuzawa *Japan Transport Safety Board, Tokyo, Japan* 

Shigehiro Yamamoto *Graduate School of Maritime Sciences, Kobe University, Kobe, Japan* 
