TEAM Workshop Problem No. 23
Forces in Permanent Magnets



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 adress 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 sizez 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.
d varies between 0 and 0.6526 mm, nominal is 0.33 mm.


Table 1 - Dimensions for the two configurations studied.

Configuration d1 d2 d3 l coil res. wire length
A 3.048 3.9624 2.9972 1.6 57 ohms 3 m
B 1.524 3.175 1.6 0.8128 32 ohms 1.68 m

A - Samarium-Cobalt
B - Neodymium-Iron-Boron


Notes:
Small magnet is a cylindrical magnet, 0.8128 mm long and 1.6 mm in diameter. Large magnet is a cylindrical magnet, 1.6 mm long and 3 mm in diameter. The small coil is 1.524 mm long, cylindrical, with inner diameter 1.524 mm. 280 turns of #47 wire is wound on the inner core to form a cylindrical coil. The large coil is 1.524 mm long, cylindrical, with inner diameter 3.048 mm. 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.


Figure 2 - Restoring force: The magnet is moved sideways while keeping its axis parallel to that of 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 d=0.254 mm.
Magnet and coil are coaxial.

Table 3 - Axial force between magnet and coil as a function of axial
displacement at a fixed current of 50 mA.
Magnet and coil are coaxial.

Table 4 - Restoring force between magnet and coil as a function
of side displacement at a fixed current of 50 mA.
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 d=0.254 mm.
Magnet and coil are coaxial.

Table 6 - Axial force between magnet and coil as a function of axial displacement at a fixed current of 50 mA.
Magnet an coil coaxial.

Table 7 - Restoring force between magnet and coil as a function of side displacement at a fixed current of 50 mA.
Displacement is measured between the axes of coil and magnet.

For computation purposes, the demagnetization curves in Figures 3 and 4 were used. These are based on data obtained from manufactures. 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.




Figure 3 - Demagnetization curve for Neodymium-Iron-Boron magnets




Figure 4 - Demagnetization curve for Samarium-Cobalt magnets