# Encyclopedia Magnetica

Encyclopedia of magnetics and electromagnetics.

air_gap

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 air_gap [2016/02/13 23:51]Dr Stan Zurek grammar by JJ air_gap [2019/06/03 18:28] (current) Both sides previous revision Previous revision 2017/01/30 14:23 Dr Stan Zurek -review2016/07/01 17:31 Dr Stan Zurek title link2016/02/13 23:51 Dr Stan Zurek grammar by JJ2016/01/03 20:43 Dr Stan Zurek math2016/01/03 00:02 Dr Stan Zurek new math2015/11/16 16:47 Dr Stan Zurek [Influence on B-H loop] 2015/11/02 23:56 Dr Stan Zurek [Flux fringing] 2015/02/26 16:24 Dr Stan Zurek [Distributed air gap] 2014/12/02 23:53 Dr Stan Zurek img bkgrnd2014/08/30 23:35 Dr Stan Zurek format2014/08/30 23:32 Dr Stan Zurek B and H2014/08/30 23:24 Dr Stan Zurek [Distributed air gap] 2014/08/30 23:14 Dr Stan Zurek [Current sensors] 2014/08/30 23:13 Dr Stan Zurek [Current sensors] 2014/08/30 23:13 Dr Stan Zurek [Current sensors] 2014/08/30 23:08 Dr Stan Zurek [Solenoids and linear actuators] 2014/08/30 23:05 Dr Stan Zurek [Gapped and air-cored inductors] 2014/08/30 20:09 Dr Stan Zurek ready for review2014/08/30 19:50 Dr Stan Zurek all figures uploaded2014/08/30 18:12 Dr Stan Zurek temp save2014/08/30 17:23 Dr Stan Zurek temp save2014/08/30 00:06 Dr Stan Zurek temp save2014/08/19 14:51 Dr Stan Zurek refs2014/08/19 14:46 Dr Stan Zurek refs2014/08/15 22:14 Dr Stan Zurek +photo2014/08/07 14:54 Dr Stan Zurek [Energy stored in air gap] 2014/08/07 14:49 Dr Stan Zurek fix2014/08/06 14:48 Dr Stan Zurek [Electromagnets] Next revision Previous revision 2017/01/30 14:23 Dr Stan Zurek -review2016/07/01 17:31 Dr Stan Zurek title link2016/02/13 23:51 Dr Stan Zurek grammar by JJ2016/01/03 20:43 Dr Stan Zurek math2016/01/03 00:02 Dr Stan Zurek new math2015/11/16 16:47 Dr Stan Zurek [Influence on B-H loop] 2015/11/02 23:56 Dr Stan Zurek [Flux fringing] 2015/02/26 16:24 Dr Stan Zurek [Distributed air gap] 2014/12/02 23:53 Dr Stan Zurek img bkgrnd2014/08/30 23:35 Dr Stan Zurek format2014/08/30 23:32 Dr Stan Zurek B and H2014/08/30 23:24 Dr Stan Zurek [Distributed air gap] 2014/08/30 23:14 Dr Stan Zurek [Current sensors] 2014/08/30 23:13 Dr Stan Zurek [Current sensors] 2014/08/30 23:13 Dr Stan Zurek [Current sensors] 2014/08/30 23:08 Dr Stan Zurek [Solenoids and linear actuators] 2014/08/30 23:05 Dr Stan Zurek [Gapped and air-cored inductors] 2014/08/30 20:09 Dr Stan Zurek ready for review2014/08/30 19:50 Dr Stan Zurek all figures uploaded2014/08/30 18:12 Dr Stan Zurek temp save2014/08/30 17:23 Dr Stan Zurek temp save2014/08/30 00:06 Dr Stan Zurek temp save2014/08/19 14:51 Dr Stan Zurek refs2014/08/19 14:46 Dr Stan Zurek refs2014/08/15 22:14 Dr Stan Zurek +photo2014/08/07 14:54 Dr Stan Zurek [Energy stored in air gap] 2014/08/07 14:49 Dr Stan Zurek fix2014/08/06 14:48 Dr Stan Zurek [Electromagnets] 2014/08/06 14:46 Dr Stan Zurek [Electromagnets] ref2014/08/06 14:28 Dr Stan Zurek save2014/07/31 15:06 Dr Stan Zurek save2014/07/31 14:57 Dr Stan Zurek created Line 2: Line 2: |< 100% >| |< 100% >| - | //​[[user/​Stan Zurek]], Air gap, [[http://​Encyclopedia-Magnetica.com|Encyclopedia-Magnetica.com]],​ {accessed on @YEAR@-@MONTH@-@DAY@}// | + | //​[[user/​Stan Zurek]], ​**[[Air gap]]**, [[http://​Encyclopedia-Magnetica.com|Encyclopedia-Magnetica.com]],​ {accessed on @YEAR@-@MONTH@-@DAY@}//​ | - | //​[[/​wiki/​awaiting review]] ​// | + **Air gap**, also **airgap**[([[http://​books.google.com/​books?​isbn=9780471777700|John R. Brauer, Magnetic Actuators and Sensors, John Wiley & Sons, 2006, ISBN 9780471777700]])] or **air-gap**[([[http://​books.google.com/​books?​isbn=9780080522043|Austin Hughes, Electric Motors and Drives: Fundamentals,​ Types and Applications,​ 3rd edition, Newnes, 2005, ISBN 9780080522043]])] - is a [[non-magnetic]] part of a [[magnetic circuit]]. It is usually connected magnetically in series with the rest of the circuit, so that a substantial part of the magnetic flux flows through the gap. **Air gap**, also **airgap**[([[http://​books.google.com/​books?​isbn=9780471777700|John R. Brauer, Magnetic Actuators and Sensors, John Wiley & Sons, 2006, ISBN 9780471777700]])] or **air-gap**[([[http://​books.google.com/​books?​isbn=9780080522043|Austin Hughes, Electric Motors and Drives: Fundamentals,​ Types and Applications,​ 3rd edition, Newnes, 2005, ISBN 9780080522043]])] - is a [[non-magnetic]] part of a [[magnetic circuit]]. It is usually connected magnetically in series with the rest of the circuit, so that a substantial part of the magnetic flux flows through the gap. Line 34: Line 33: ​ - The [[B-H loop]] of a magnetic circuit is affected by the presence of an air gap. Permeability of non-magnetic material is low and therefore it requires greater values of //H// to obtain the same value of //B// as compared with [[magnetically soft materials]]. With the introduction of an air gap the //B-H// loop of a [[magnetic circuit]] gets [[shearing of B-H loop|"​sheared"​]] (slanted), hence the value of its slope proportional to the [[effective permeability]] is reduced. The amount of "​shearing"​ is proportional to the length of the air gap - the larger the air gap the lower the slope. For [[air core]] coil (no magnetic material present) the //B-H// characteristics become by definition the same as for the non-magnetic material encircled by the winding (e.g. air). + The [[B-H loop]] of a magnetic circuit is affected by the presence of an air gap. Permeability of non-magnetic material is low and therefore it requires greater values of $H$ to obtain the same value of $B$ as compared with [[magnetically soft materials]]. With the introduction of an air gap the B-H loop of a [[magnetic circuit]] gets [[shearing of B-H loop|"​sheared"​]] (slanted), hence the value of its slope proportional to the [[effective permeability]] is reduced. The amount of "​shearing"​ is proportional to the length of the air gap - the larger the air gap the lower the slope. For [[air core]] coil (no magnetic material present) the B-H characteristics become by definition the same as for the non-magnetic material encircled by the winding (e.g. air). - Changes of [[effective permeability]] and linearisation of the **//B-H//** loops caused by increasing air gap \\ + Changes of [[effective permeability]] and linearisation of the B-H loops caused by increasing air gap - [[/​file/​influence_of_air_gap_magnetica.png|{{/​influence_of_air_gap_magnetica.png}}]]\\ + [[/​file/​influence_of_air_gap_magnetica.png|{{/​influence_of_air_gap_magnetica.png}}]] ​ {{page>​insert/​by_SZ}} {{page>​insert/​by_SZ}} ​ - Conversely, if no air gap is present then the slope becomes as steep as possible, and the //B-H// loop will represent the closest approximation of the characteristic of the magnetic material (for a given shape of the magnetic circuit). For this reason international standards defining [[magnetic measurement|magnetic measurements]] specify procedures to ensure that the influence of non-magnetic parts of a magnetic circuit remain within negligible levels. This can be achieved for instance by careful [[polishing]] or [[lapping]] of the flat faces, in order to reduce the surface roughness and the amount of space between the magnetic surfaces. + Conversely, if no air gap is present then the slope becomes as steep as possible, and the B-H loop will represent the closest approximation of the characteristic of the magnetic material (for a given shape of the magnetic circuit). For this reason international standards defining [[magnetic measurement|magnetic measurements]] specify procedures to ensure that the influence of non-magnetic parts of a magnetic circuit remain within negligible levels. This can be achieved for instance by careful [[polishing]] or [[lapping]] of the flat faces, in order to reduce the surface roughness and the amount of space between the magnetic surfaces. [(SST>​International standard, IEC 60404-3, Magnetic materials - Part 3: Methods of measurement of the magnetic properties of magnetic sheet and strip by means of a single sheet tester)] [(SST>​International standard, IEC 60404-3, Magnetic materials - Part 3: Methods of measurement of the magnetic properties of magnetic sheet and strip by means of a single sheet tester)] Line 81: Line 80: - [[Short-circuit]] current limiting [[air-cored choke]] rated at 1 [[kA]] ​\\ + [[Short-circuit]] current limiting [[air-cored choke]] rated at 1 [[kA]] - [[/​file/​short-circuit_current_limiting_choke.jpg|{{/​short-circuit_current_limiting_choke.jpg}}]]\\ + [[/​file/​short-circuit_current_limiting_choke.jpg|{{/​short-circuit_current_limiting_choke.jpg}}]] <​sup>//​by Stahlkocher,​ [[http://​creativecommons.org/​licenses/​by-sa/​3.0/​|CC-BY-SA-3.0]]//​ <​sup>//​by Stahlkocher,​ [[http://​creativecommons.org/​licenses/​by-sa/​3.0/​|CC-BY-SA-3.0]]//​ Line 187: Line 186: Multiple approaches are used in [[current sensor|current sensors]]. The importance and influence of the gap depends on the given technology.[([[http://​www.lem.com/​hq/​en/​content/​view/​161/​153/​|Open Loop Hall Effect, Hall effect current transducers (O/L), LEM, {accessed 11 Dec 2012}]])] [([[http://​www.telcon.co.uk/​Product_Brochure.html|Hall effect current sensors, Current transformers & Toroidal cores, Telcon, {accessed 11 Dec 2012}]])][([[http://​sensing.honeywell.com/​products/​current_sensors?​Ne=2308&​N=3027|Current Sensors Line Guide, Honeywell, June 2008, {accessed 11 Dec 2012}]])] Multiple approaches are used in [[current sensor|current sensors]]. The importance and influence of the gap depends on the given technology.[([[http://​www.lem.com/​hq/​en/​content/​view/​161/​153/​|Open Loop Hall Effect, Hall effect current transducers (O/L), LEM, {accessed 11 Dec 2012}]])] [([[http://​www.telcon.co.uk/​Product_Brochure.html|Hall effect current sensors, Current transformers & Toroidal cores, Telcon, {accessed 11 Dec 2012}]])][([[http://​sensing.honeywell.com/​products/​current_sensors?​Ne=2308&​N=3027|Current Sensors Line Guide, Honeywell, June 2008, {accessed 11 Dec 2012}]])] - A common approach used by sensor manufacturers is the "​[[open loop sensing]]"​ principle. a magnetic core as means of concentrating the magnetic flux, which is forced to flow through the air gap. A sensor of flux density ​//**B**// (or magnetic field strength ​//**H**//) is placed in the gap. Since the gap [[non-magnetic]] (and hence there is a linear response) the measured value of //**B**// or //**H**// can be related to the value of the primary current. + A common approach used by sensor manufacturers is the "​[[open loop sensing]]"​ principle. a magnetic core as means of concentrating the magnetic flux, which is forced to flow through the air gap. A sensor of flux density ​$B$ (or magnetic field strength ​$H$) is placed in the gap. Since the gap [[non-magnetic]] (and hence there is a linear response) the measured value of $B$ or $H$ can be related to the value of the primary current. Another common approach is the "​[[closed loop sensing]]"​. This technique also uses a magnetic core, and an air gap with a sensor. ​ Another common approach is the "​[[closed loop sensing]]"​. This technique also uses a magnetic core, and an air gap with a sensor. ​ Line 241: Line 240: This energy storing property is utilised for instance in energy storing [[inductor|inductors]] and [[flyback transformer|flyback transformers]],​ in which air gap in a pivotal design parameter. On the one hand, the air gap is used for storing the actual energy, but on the other it changes operating characteristics of the [[B-H curve]] and allows driving the inductor at higher currents hence higher [[magnetic field strength]] thus extending the range before [[magnetic saturation]] occurs. This energy storing property is utilised for instance in energy storing [[inductor|inductors]] and [[flyback transformer|flyback transformers]],​ in which air gap in a pivotal design parameter. On the one hand, the air gap is used for storing the actual energy, but on the other it changes operating characteristics of the [[B-H curve]] and allows driving the inductor at higher currents hence higher [[magnetic field strength]] thus extending the range before [[magnetic saturation]] occurs. - For a simple magnetic circuit with a single air gap (see the first image at the top), for which the core is made out of high-permeability material such that **//μmaterial ​>> μ<​sub>​0//​**, with the air gap itself and the flux density in the air gap being uniform, and if the [[flux fringing]] can be neglected, it can be derived that the stored energy is: + For a simple magnetic circuit with a single air gap (see the first image at the top), for which the core is made out of high-permeability material such that $μ_{material} >> μ_0$, with the air gap itself and the flux density in the air gap being uniform, and if the [[flux fringing]] can be neglected, it can be derived that the stored energy is: [(Hurley>​[[http://​books.google.com/​books?​isbn=9781118544679|W.G. Hurley, W.H. Wolfle, Transformers and Inductors for Power Electronics:​ Theory, Design and Applications,​ John Wiley & Sons, 2013, ISBN 9781118544679,​ example 2.3]])] [(Hurley>​[[http://​books.google.com/​books?​isbn=9781118544679|W.G. Hurley, W.H. Wolfle, Transformers and Inductors for Power Electronics:​ Theory, Design and Applications,​ John Wiley & Sons, 2013, ISBN 9781118544679,​ example 2.3]])] |  <​html><​div style="​font-size:​ 200%;">​ $E \approx \frac{B^2 ⋅ V}{2 ⋅ \mu_0}$  ​ |  (J)  | |  <​html><​div style="​font-size:​ 200%;">​ $E \approx \frac{B^2 ⋅ V}{2 ⋅ \mu_0}$  ​ |  (J)  | - where: ​**//E//** - stored energy (J), **//B//** - [[flux density]] in the air gap (T), **//V//** - volume of the air gap (m<​sup>​3​), ​**//μ//<​sub>​0​** ​- [[permeability of free space]] (H/m). + where: ​$E$ - stored energy (J), $B$ - [[flux density]] in the air gap (T), $V$ - volume of the air gap (m<​sup>​3​), ​$μ_0$ - [[permeability of free space]] (H/m). ===== Flux fringing ===== ===== Flux fringing ===== Line 260: Line 259: In energy-storing inductors the inductance is related to the reluctance of the air gap. The fringing lowers the overall reluctance, so that the resulting inductance is somewhat higher. This needs to be taken into account so that the inductance value is appropriate for a given design. There are various [[empirical equation|empirical equations]] suggested in literature for calculating the correction of this effect. In energy-storing inductors the inductance is related to the reluctance of the air gap. The fringing lowers the overall reluctance, so that the resulting inductance is somewhat higher. This needs to be taken into account so that the inductance value is appropriate for a given design. There are various [[empirical equation|empirical equations]] suggested in literature for calculating the correction of this effect. - For instance McLyman suggest the following "​[[flux fringing factor]]"​ (//F//):​[(fluxfringing>​[[http://​books.google.com/​books?​isbn=9780824751159|Colonel William T. McLyman, Transformer and Inductor Design Handbook, CRC Press, 2004, ISBN 9780824751159,​ section "​Fringing flux" in chapter 8]])] + For instance McLyman suggest the following "​[[flux fringing factor]]"​ ($F$):​[(fluxfringing>​[[http://​books.google.com/​books?​isbn=9780824751159|Colonel William T. McLyman, Transformer and Inductor Design Handbook, CRC Press, 2004, ISBN 9780824751159,​ section "​Fringing flux" in chapter 8]])] |  <​html><​div style="​font-size:​ 200%;">​ $F = 1 + \frac{l_{gap}}{\sqrt{A}} ⋅ ln \left( \frac{2 ⋅ l_{window}}{l_{gap}} \right)$  ​ |  (unitless) ​ | |  <​html><​div style="​font-size:​ 200%;">​ $F = 1 + \frac{l_{gap}}{\sqrt{A}} ⋅ ln \left( \frac{2 ⋅ l_{window}}{l_{gap}} \right)$  ​ |  (unitless) ​ | - where: ​**//​Factor//​** ​- factor by which the inductance is increased (unitless), ​**//​l<​sub>​gap//​** ​- length of the air gap (m), **//A//** - cross-section area of the core (m<​sup>​2​), ​**//​l<​sub>​window//​** ​- length of the inside (in the window) of the core leg in which the gap is present (m). + where: ​$F$ - factor by which the inductance is increased (unitless), ​$l_{gap}$ - length of the air gap (m), $A$ - cross-section area of the core (m<​sup>​2​), ​$l_{window}$ - length of the inside (in the window) of the core leg in which the gap is present (m). Another example is when the area of the air gap is scaled according to its length. For instance if the magnetic core cross-section is a rectangle the following calculation can be used: [([[http://​books.google.com/​books?​isbn=1119964911|Marian K. Kazimierczuk,​ High-Frequency Magnetic Components, John Wiley & Sons, 2011, ISBN 9781119964919,​ p. 38]])] Another example is when the area of the air gap is scaled according to its length. For instance if the magnetic core cross-section is a rectangle the following calculation can be used: [([[http://​books.google.com/​books?​isbn=1119964911|Marian K. Kazimierczuk,​ High-Frequency Magnetic Components, John Wiley & Sons, 2011, ISBN 9781119964919,​ p. 38]])] Line 271: Line 270: |  <​html><​div style="​font-size:​ 200%;">​ $F = 1 + \frac{l_{gap} ⋅ (a + b + 2 ⋅ l_{gap})}{a ⋅ b}$  ​ |  (unitless) ​ | |  <​html><​div style="​font-size:​ 200%;">​ $F = 1 + \frac{l_{gap} ⋅ (a + b + 2 ⋅ l_{gap})}{a ⋅ b}$  ​ |  (unitless) ​ | - where: ​**//a//** and **//b//** are the lengths of each side of the rectangular cross-section of the magnetic core (m). + where: ​$a$ and $b$ are the lengths of each side of the rectangular cross-section of the magnetic core (m). Yet another approximating equation is given by Hurley and Wölfle[([[http://​google.com/​books?​isbn=9781118544679|W.G. Hurley, W.H. Wölfle, Transformers and Inductors for Power Electronics:​ Theory, Design and Applications,​ John Wiley & Sons, 2013, ISBN 9781118544679]])] Yet another approximating equation is given by Hurley and Wölfle[([[http://​google.com/​books?​isbn=9781118544679|W.G. Hurley, W.H. Wölfle, Transformers and Inductors for Power Electronics:​ Theory, Design and Applications,​ John Wiley & Sons, 2013, ISBN 9781118544679]])]