problem23

Forces in Permanent Magnets

Team Workshop Problem 23

N. Ida* and J.P.A. Bastos**

* Department of Electrical Engineering

The University of Akron,

Akron, OH. 44325-3904, USA

** Universidade Federal de Santa Catarina

UFSC/CTC/EEL/GRUCAD

C.P. 476

88.040-900 Florianopolis, SC, Brazil

General:

This problem is intended to address the questions of force calculations as well as modeling of permanent magnets in axisymmetric and three dimensional geometries.

Measurements:

The measurements presented here were performed as part of a design process followed by computation of forces to confirm the design. The measurements consist of axial and restoring forces for two configurations, both involving small magnets and coils. One configuration uses Samarium-Cobalt the other, Neodymium-Iron-Boron magnets. Two sizes of magnets and coils are used in each configuration.

The magnet and coil are shown in Figure 1. The coil is wound on a nonmagnetic form (brass in this case) with dimensions given in Table 1 for both configurations. The only differences between the configurations is in dimensions and type of magnets.

Figure 1. Configuration for axial force measurement and dimension. δ varies between 0 and 0.6526mm, nominal is 0.33mm.

Notes:

Small magnet is a cylindrical magnet 0.8128mm long and 1.6mm in diameter.

Large magnet is a cylindrical magnet, 1.6mm long and 3mm in diameter

The small coil is 1.524mm long, cylindrical, with inner diameter 1.524mm. 280 turns of #47 wire is wound on the inner core to form a cylindrical coil.

The large coil is 1.524mm long, cylindrical, with inner diameter 3.048mm. 280 turns of #47 wire is wound on the inner core to form a cylindrical coil.

Configuration A:. Samarium-Cobalt magnet and larger coil.

In measuring axial forces, the coil and magnet remain co-axial. In measuring restoring force, the magnet and coil move sideways with their axes parallel (see Figure 2). There is no twisting. In both axial and restoring force measurements, the magnet and coil were in repulsion mode.

the coil.

The following forces were measured.

Table 2. Forces as a function of current in coil at fixed distance between magnet and coil. Axial force between magnet and as a function of current at δ=0.254mm, magnet and coil are coaxial.

of 50mA. Magnet and coil are coaxial.

current of 50mA. Displacement is measured between the axes of the coil and magnet.

Configuration B: Neodymium-Iron-Boron Magnet and smaller coil.

In measuring axial forces, the coil and magnet remain co-axial. In measuring restoring force, the magnet and coil move sideways with their axes parallel. There is no twisting. In both axial and restoring force measurements, the magnet and coil were in repulsion mode.

The following forces were obtained.

Table 5. Forces as a function of current in coil at fixed distance between magnet and coil. Axial force between magnet and as a function of current at δ=0.254mm, magnet and coil are coaxial.

of 50mA. Magnet and coil are coaxial.

current of 50mA. Displacement is measured between the axes of the coil and magnet.

For computation purposes, the demagnetization curves in Figures 3 and 4 were used. These are based on data obtained from manufacturers. Although the computations we performed are close to the measured results, the demagnetization curves are not exact and are not measured for the samples for which the forces were measured. They are however the best we can provide. Should measured demagnetization curves be available in the future these will be provided.

?820 kA/m

Figure 3. Demagnetization curve for Neodymium-Iron-Boron Magnets

?720 kA/m

Figure 4. Demagnetization curves for Samarium-Cobalt magnets.