effective_magnetic_permeability

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effective_magnetic_permeability [2020/12/06 23:15] (current) stan_zurek [Definition] |
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+ | ====== Effective magnetic permeability ====== | ||

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+ | | // | ||

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+ | **Effective magnetic permeability** (also **apparent magnetic permeability**[([[http:// | ||

+ | [([[http:// | ||

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+ | {{page> | ||

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+ | An [[air gap]] in a [[magnetic circuit]] | ||

+ | [[file/Air gap diagram.png|{{Air gap diagram.png}}]] | ||

+ | {{page> | ||

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+ | Air gap reduces the effective permeability | ||

+ | [[file/Air gap in BH loop.png|{{Air gap in BH loop.png}}]] | ||

+ | {{page> | ||

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+ | <box 30% left #f0f0f0> | ||

+ | Changes of effective permeability and linearisation of the [[B-H loop]] caused by increasing air gap[(Finke)] | ||

+ | [[file/ | ||

+ | {{page> | ||

+ | </ | ||

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+ | ===== Effect of air gap ===== | ||

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+ | [[Magnetic permeability]] of a [[magnetic material]] is linked to the slope of a [[B-H curve]] or (or [[B-H loop]]). With increasing [[air gap]] the slope is reduced, and changes caused by non-linearity of the material (due to variations in [[flux density]], temperature, | ||

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+ | With the gap present, higher [[magnetomotive force]] (excitation) is required to reach the same [[flux density]]. Similar behaviour could be obtained if the [[magnetic circuit]] was made not from a gapped core but from a non-gapped core made from material with proportionally lower permeability. A value of permeability required to obtain equivalent // | ||

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+ | ===== Equations and calculations | ||

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+ | <box 40% right #f0f0f0> | ||

+ | [[Gapped core]] with: total [[magnetic path length]] $l$ (orange), length of core $l_{core}$ (blue) and length of gap $l_g$ (red) | ||

+ | [[file/ | ||

+ | {{page> | ||

+ | </ | ||

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+ | It is possible to [[analytical calculations|analytically calculate]] the value of relative effective permeability for simple magnetic circuits, with a uniform gap.[(Finke> | ||

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+ | There are several assumptions: | ||

+ | * the cross section area of the [[magnetic circuit]] is constant at every point of the circuit, and is the same for the core and for the gap | ||

+ | * the length of the air gap is much shorter than the [[path length]] of the magnetic core | ||

+ | * the magnetisation is uniform and [[flux fringing|fringing effect]] is negligible | ||

+ | * permeability of the core material is much greater than the permeability of air gap | ||

+ | * [[relative permeability]] of the medium in the air gap is assumed to be unity (i.e. the same as [[permeability of free space|vacuum]]). | ||

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+ | The equation is derived by using the concept of [[magnetic reluctance]][(Finke)] and with the assumptions listed above. All values of permeability (input and output) are given as [[relative permeability]] (so the value of " | ||

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+ | Equations can also be derived for multi-path or non-uniform magnetic circuits, but these are obviously configuration-dependent and must be calculated for each specific structure.[(Finke)] For example, in a three-leg core (as shown in the image) the path length is considered to be only around one window (e.g. just the orange path). | ||

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+ | {{page> | ||

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+ | ===== Composite materials ===== | ||

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+ | <box 30% right #f0f0f0> | ||

+ | The ratio of air gap and the particles in a [[powder core]] dictate the value of effective permeability. The black lines illustrate distribution of [[magnetic flux]]. | ||

+ | [[file/ | ||

+ | {{page> | ||

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+ | The value of effective permeability is important for [[composite material|composite materials]], | ||

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+ | For instance, [[Ferrotron 119]] used for [[flux concentrator]]s in [[induction heating]] has a maximum [[relative permeability]] of 8.0 (despite being made from ferromagnetic particles), because it is designed to work at high frequency (up to 5 [[MHz]]) and high excitation (20 [[kA-m|kA/ | ||

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+ | However, because such a magnetic core does not have a concentrated air gap then the simple equation given above cannot be used. Depending on the complexity of given material the calculations can become very difficult to solve or even formulate.[([[http:// | ||

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+ | Hence, the end users of composite cores can rely on the effective permeability values given by the manufacturers of the materials or magnetic cores. If the product is a magnetic core, then the [[AL value]] (inductance per turn) is often more useful than the value effective permeability as such.[([[http:// | ||

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+ | Nevertheless, | ||

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+ | ===== See also ===== | ||

+ | * [[Magnetic permeability]] | ||

+ | * [[Air gap]] | ||

+ | * [[Magnetic core]] | ||

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+ | ===== References ===== | ||

+ | ~~REFNOTES~~ | ||

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+ | {{tag> | ||