Ι What Is L/D Ratio?
In magnet design, the L/D ratio (Length-to-Diameter ratio) is a key measure of a magnet’s geometry. It represents the ratio of the magnetic length to the effective pole diameter of the magnet.
- Magnetic Length: Refers to the physical dimension of the magnet in the direction of magnetization.
- Effective Pole Diameter: Refers to the diameter of the pole region or the equivalent diameter for non-circular poles.
The L/D ratio provides a straightforward and valuable metric for evaluating a magnet’s shape and dimensions. While some magnet insiders may argue that the L/D alone is not always sufficient for assessing a magnet’s design, it remains an essential reference for the preliminary judgment of the magnet’s temperature resistance and performance characteristics.
One important consideration is that the higher the L/D ratio, the better the magnet can resist demagnetization. This is because magnets with a higher L/D tend to have more stability in their magnetization direction, making them more resistant to external forces that could potentially cause the magnet to lose its magnetization.
How to Calculate L/D Ratio?
To calculate the L/D ratio for magnets, we divide the length (L) by the diameter (D) or width (D), depending on the magnet’s shape.
For cylindrical magnets, the L/D ratio is determined by dividing the length (L) by the diameter (D). For example, if a cylindrical magnet has dimensions D10x5 mm, the L/D ratio is calculated as 5/10 = 0.5.
If a magnet has square or almost square poles, its pole area can be converted into a circular area using the following formula:
For rectangular magnets, the L/D ratio is calculated by dividing the height (c) by the calculated diameter D. For instance, a rectangular magnet with dimensions a = 10 mm, b = 10 mm, and c = 5 mm results in an L/D ratio of
Under normal circumstances, we recommend an L/D ratio of over 0.5 (preferably ≥0.7) for Neodymium magnets. While for AlNiCo magnets, an L/D of at least 4 or 5 is a rule of thumb.
L/D Ratio and Permeance Coefficient: The Connection
The permeance coefficient (Pc) is a crucial concept in the design of magnetic circuits, and it is also heavily influenced by the magnet’s geometry. However, many people mistakenly equate the Pc value with the L/D ratio, especially when discussing the maximum operating temperature of permanent magnets.
The maximum operating temperature of a permanent magnet is the highest temperature at which the magnet can maintain its magnetic properties with a specific irreversible flux loss. For a saturated cylindrical magnet with an L/D of 0.7, this temperature is determined by heating the magnet from room temperature to a constant temperature in an open-circuit state, holding it for 2 hours, and then cooling it back to room temperature. The temperature at which the irreversible flux loss does not exceed 5% is considered the maximum operating temperature.
It’s important to note that this value is based on the L/D ratio, not the Pc value. For example, a cylindrical Neodymium magnet with an L/D of 0.7 can have a Pc value as high as 2.17.
In practice, calculating the Pc value is far more complex than working with the clearly defined L/D ratio. However, in simpler terms, it can be said that a higher L/D inevitably leads to a higher Pc value.
