What is the formula of the zigzag specific permeance?

The specific permeance (also referred to as the Carter coefficient in some contexts) in electric machines such as transformers and motors, especially with regard to the air gap in a magnetic circuit, is a key factor in calculating magnetic circuit parameters. However, the formula for specific permeance, particularly for configurations described as “zigzag” or involving complex geometries and flux paths, isn’t straightforward or universally recognized under a singular, concise formula. Instead, specific permeance calculations are typically tailored to the geometry and magnetic properties of the materials involved.

For a magnetic circuit, basic permeance ((P)) can be defined by the formula:

[P = frac{mu A}{l}]

Where:

– (P) is the permeance, measured in webers per ampere-turn (Wb/At),

– (mu) is the permeability of the material (comprised of (mu_0), the permeability of free space, and (mu_r), the relative permeability of the material),

– (A) is the cross-sectional area of the flux path, and

– (l) is the length of the path through the material.

However, for “zigzag” or complex flux paths, such as those encountered in certain electrical machine designs or in the presence of features like laminations and air gaps which act to reduce eddy currents, the calculation of specific permeance becomes more involved. Adjustments must be made to account for the