<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Four types of magnets were used in this study: neodymium NdFeB (grade N35 and N52), ferrite (Y10), and samarium-cobalt SmCo (XG30 2:17). They were chosen to represent a wide range of volumes from 0.035 to 19 cm<sup>3</sup> (540 times), radius <italic>R</italic> from 1.5 to 12.5 mm (8 ×), length L from 0.5 to 40 mm (80 ×), aspect ratio L/R from 0.051 to 17 (330 ×), and contact forces from 0.2 to 250 N (over 1000 ×). The study shows that previously reported closed-form equations are valid only at large distances (small forces). At short distances (large forces) the calculated force diverges to infinity or the accuracy depends on the aspect ratio, and some equations fail more than others. A new equation is proposed as a small modification of a previously known function, which provides reasonable behaviour over the whole studied range. However, the accuracy is unknown in a general practical case, because theoretical calculations do not take into account imperfections of real magnets, so there is no single absolute reference.</p>
</abstract>

Four types of magnets were used in this study: neodymium NdFeB (grade N35 and N52), ferrite (Y10), and samarium-cobalt SmCo (XG30 2:17). They were chosen to represent a wide range of volumes from 0.035 to 19 cm3 (540 times), radius R from 1.5 to 12.5 mm (8 ×), length L from 0.5 to 40 mm (80 ×), aspect ratio L/R from 0.051 to 17 (330 ×), and contact forces from 0.2 to 250 N (over 1000 ×). The study shows that previously reported closed-form equations are valid only at large distances (small forces). At short distances (large forces) the calculated force diverges to infinity or the accuracy depends on the aspect ratio, and some equations fail more than others. A new equation is proposed as a small modification of a previously known function, which provides reasonable behaviour over the whole studied range. However, the accuracy is unknown in a general practical case, because theoretical calculations do not take into account imperfections of real magnets, so there is no single absolute reference.

Performance of closed-form equations for force between cylindrical magnets over wide range of volume, aspect ratio, and force

Journal of Electrical Engineering

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Four types of magnets were used in this study: neodymium NdFeB (grade N35 and N52), ferrite (Y10), and samarium-cobalt SmCo (XG30 2:17). They were chosen to...

Performance of closed-form equations for force between cylindrical magnets over wide range of volume, aspect ratio, and force

Published Online: Dec 24, 2022

Page range: 405 - 412

Received: Oct 17, 2022

DOI: https://doi.org/10.2478/jee-2022-0055

Keywords
closed-form equations, cylindrical magnets, forces between magnets, magnetic forces

© 2022 Stan Zurek, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Performance of closed-form equations for force between cylindrical magnets over wide range of volume, aspect ratio, and force

Published Online: Dec 24, 2022

Page range: 405 - 412

Received: Oct 17, 2022

DOI: https://doi.org/10.2478/jee-2022-0055

Keywordsclosed-form equations, cylindrical magnets, forces between magnets, magnetic forces

© 2022 Stan Zurek, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
closed-form equations, cylindrical magnets, forces between magnets, magnetic forces