Reluctance calculation when the cross-sectional area is not constant.

[bpelec]

Generally, when performing basic reluctance calculations for E-cores or I-cores, the cross sectional area is always constant over the element considered and the following equation is used:

Reluctance = Length / mu * Area

I need to calaculate the reluctance of a 'cake slice', where the cross-sectional area A is a function of the length... If you imagine the 'cake slice', as you move away from the centre of the cake, the cross-sectional area increases...

I have tried forming an integral, but I have arrived at the suprising result that the reluctance of my 'cake slice' section is independent of its radius.

Given that I need to develop an explicit equation, does anyone have any advice on how I should perform this reluctance calculation?

Thank you for your help.

Best regards,

bpelec.

 

[itsmoked]

Doesn't the cake slice have infinite reluctance at the pointy end rendering the rest moot? (hence radius ignorant)

 

[bpelec]

Well, yes, that could well be true from a mathematical view point... However, in my case, we can assume that we are starting a little way in from the pointy end. If you like, by calling the pointy end of the 'cake slice' the origin, we could consider the reluctance between two 'cuts' on the radius, r1 and r2, where r2>r1>0...