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Understanding the L/D Ratio for Optimal Magnet Geometry

What’s L/D Ratio in magnetics?

The magnetic properties of a magnet depend significantly on its shape, which in turn affects the magnet’s ability to resist demagnetization from internal and external factors. The better the magnet’s shape suits the intended application, the stronger its resistance to self-demagnetization, elevated temperatures, and external demagnetizing fields.

The Magnetic Length / Effective Pole Diameter (L/D) ratio is a straightforward and valuable measure of a magnet’s shape. For NdFeB magnets, the L/D ratio is an essential reference point for initially assessing the magnet’s temperature resistance. The magnetic length represents the magnet’s size along its magnetic axis, while the effective pole diameter refers to the diameter of the pole region or its equivalent for non-circular poles.

Typically, an L/D ratio of over 0.5 (preferably ≥0.7) is recommended.

L/D ratio magnet

How to calculate L/D ratio?

(1) For example, for a cylinder with dimensions D20x15 and a magnetization direction of 5, the L/D ratio is 15/20=0.75. This L/D ratio is considered very good and has excellent high-temperature resistance.

(2) For example, for a square with dimensions 20x20x5 and a magnetization direction of 5, the L/D ratio is 5/(√(20x20x4)/π)=0.22. This L/D ratio is relatively small, resulting in poor high-temperature resistance that needs improvement.

The following formula can be utilized to convert the pole area of magnets with square or almost square poles to an equivalent circular area:

L/D ratio (square)

Optimizing L/D Ratio for Magnetic Performance and Cost

A higher L/D ratio indicates a stronger resistance to demagnetization. However, achieving such resistance often involves using a larger amount of magnet material, which increases the cost. Importantly, while a higher L/D ratio generally correlates with better magnetic performance, the relationship is not always linear. There is a point where the increase in L/D ratio does not result in a significant improvement in magnetic performance.

It is worth noting that for non-disc magnet shapes, the equivalent diameter or area of a circle can be used in the L/D ratio calculation. This involves determining the pole’s area and finding the equivalent diameter of a circle with the same area.

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Jonah Jin

Jonah Jin
Managing Director

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