IEC 60205 ® Edition 3.1 2009-08 INTERNATIONAL STANDARD Calculation of the effective parameters of magnetic piece parts IEC 60205:2006+A1:2009 Calcul des paramètres effectifs des pièces magnétiques LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU NORME INTERNATIONALE THIS PUBLICATION IS COPYRIGHT PROTECTED Copyright © 2009 IEC, Geneva, Switzerland All rights reserved Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either IEC or IEC's member National Committee in the country of the requester If you have any questions about IEC copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or your local IEC member National Committee for further information Droits de reproduction réservés Sauf indication contraire, aucune partie de cette publication ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie et les microfilms, sans l'accord écrit de la CEI ou du Comité national de la CEI du pays du demandeur Si vous avez des questions sur le copyright de la CEI ou si vous désirez obtenir des droits supplémentaires sur cette publication, utilisez les coordonnées ci-après ou contactez le Comité national de la CEI de votre pays de résidence About the IEC The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes International Standards for all electrical, electronic and related technologies About IEC publications The technical content of IEC publications is kept under constant review by the IEC Please make sure that you have the latest edition, a corrigenda or an amendment might have been published Catalogue of IEC publications: www.iec.ch/searchpub The IEC on-line Catalogue enables you to search by a variety of criteria (reference number, text, technical committee,…) It also gives information on projects, withdrawn and replaced publications IEC Just Published: www.iec.ch/online_news/justpub Stay up to date on all new IEC publications Just Published details twice a month all new publications released Available on-line and also by email Electropedia: www.electropedia.org The world's leading online dictionary of electronic and electrical terms containing more than 20 000 terms and definitions in English and French, with equivalent terms in additional languages Also known as the International Electrotechnical Vocabulary online Customer Service Centre: www.iec.ch/webstore/custserv If you wish to give us your feedback on this publication or need further assistance, please visit the Customer Service Centre FAQ or contact us: Email: csc@iec.ch Tel.: +41 22 919 02 11 Fax: +41 22 919 03 00 A propos de la CEI La Commission Electrotechnique Internationale (CEI) est la première organisation mondiale qui élabore et publie des normes internationales pour tout ce qui a trait l'électricité, l'électronique et aux technologies apparentées A propos des publications CEI Le contenu technique des publications de la CEI est constamment revu Veuillez vous assurer que vous possédez l’édition la plus récente, un corrigendum ou amendement peut avoir été publié Catalogue des publications de la CEI: www.iec.ch/searchpub/cur_fut-f.htm Le Catalogue en-ligne de la CEI vous permet d’effectuer des recherches en utilisant différents critères (numéro de référence, texte, comité d’études,…) Il donne aussi des informations sur les projets et les publications retirées ou remplacées Just Published CEI: www.iec.ch/online_news/justpub Restez informé sur les nouvelles publications de la CEI Just Published détaille deux fois par mois les nouvelles publications parues Disponible en-ligne et aussi par email Electropedia: www.electropedia.org Le premier dictionnaire en ligne au monde de termes électroniques et électriques Il contient plus de 20 000 termes et définitions en anglais et en franỗais, ainsi que les termes ộquivalents dans les langues additionnelles Egalement appelé Vocabulaire Electrotechnique International en ligne Service Clients: www.iec.ch/webstore/custserv/custserv_entry-f.htm Si vous désirez nous donner des commentaires sur cette publication ou si vous avez des questions, visitez le FAQ du Service clients ou contactez-nous: Email: csc@iec.ch Tél.: +41 22 919 02 11 Fax: +41 22 919 03 00 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU IEC Central Office 3, rue de Varembé CH-1211 Geneva 20 Switzerland Email: inmail@iec.ch Web: www.iec.ch IEC 60205 ® Edition 3.1 2009-08 INTERNATIONAL STANDARD LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU NORME INTERNATIONALE Calculation of the effective parameters of magnetic piece parts Calcul des paramètres effectifs des pièces magnétiques INTERNATIONAL ELECTROTECHNICAL COMMISSION COMMISSION ELECTROTECHNIQUE INTERNATIONALE PRICE CODE CODE PRIX ICS 29.100.10 ® Registered trademark of the International Electrotechnical Commission Marque déposée de la Commission Electrotechnique Internationale CG ISBN 2-8318-1055-0 –2– 60205 © IEC:2006+A1:2009 CONTENTS FOREWORD Scope .5 Basic rules Formulae for the various types of cores Ring cores .6 Pair of U-cores of rectangular section Pair of U-cores of rounded section Pair of E-cores of rectangular section Pair of ETD/EER-cores 10 Pair of pot-cores 11 Pair of RM-cores 13 Pair of EP-cores 16 Pair of PM-cores 17 Pair of EL-cores 19 Pair of ER-cores (low profile) 21 Pair of PQ-cores 23 Pair of EFD-cores 26 Pair of E planar-cores 27 Annex A (informative) Purpose of revision 30 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 60205 © IEC:2006+A1:2009 –3– INTERNATIONAL ELECTROTECHNICAL COMMISSION _ CALCULATION OF THE EFFECTIVE PARAMETERS OF MAGNETIC PIECE PARTS FOREWORD 2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC National Committees 3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense While all reasonable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any misinterpretation by any end user 4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications transparently to the maximum extent possible in their national and regional publications Any divergence between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter 5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any equipment declared to be in conformity with an IEC Publication 6) All users should ensure that they have the latest edition of this publication 7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and members of its technical committees and IEC National Committees for any personal injury, property damage or other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC Publications 8) Attention is drawn to the Normative references cited in this publication Use of the referenced publications is indispensable for the correct application of this publication 9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent rights IEC shall not be held responsible for identifying any or all such patent rights International Standard IEC 60205 has been prepared by IEC technical committee 51: Magnetic components and ferrite materials This consolidated version of IEC 60205 consists of the third edition (2006) [documents 51/848/FDIS and 51/857/RVD] and its amendment (2009) [documents 51/928A/CDV and 51/940/RVC] The technical content is therefore identical to the base edition and its amendment and has been prepared for user convenience It bears the edition number 3.1 A vertical line in the margin shows where the base publication has been modified by amendment The French version of this standard has not been voted upon LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU 1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees) The object of the IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields To this end and in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)“) Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work International, governmental and nongovernmental organizations liaising with the IEC also participate in this preparation IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations –4– 60205 © IEC:2006+A1:2009 This edition includes the following significant technical changes with respect to the previous edition: a) unit of angles through the text are described by using “radian”; b) new words are added in 2.1 “All angles are in radians”; c) replacement, Clause 3.9, of the equation ln d g / d l2 ln d g / d l = by = ; A2 Dπ (h1 − h2 ) A2 Dπ (h1 − h2 ) / d) new cores “EL, ER, PQ, EFD and E planar” are added in this edition This publication has been drafted in accordance with the ISO/IEC Directives, Part • reconfirmed, • withdrawn, • replaced by a revised edition, or • amended LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU The committee has decided that the contents of the base publication and its amendments will remain unchanged until the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in the data related to the specific publication At this date, the publication will be 60205 © IEC:2006+A1:2009 –5– CALCULATION OF THE EFFECTIVE PARAMETERS OF MAGNETIC PIECE PARTS Scope This International Standard lays down uniform rules for the calculation of the effective parameters of closed circuits of ferromagnetic material Basic rules 2.1 All results shall be expressed in units based on the millimetre, shall be accurate to three significant figures, but to derive l e , A e , and V e the values of C and C shall be calculated to five significant figures All angles are in radians NOTE The purpose of specifying this degree of accuracy is only to ensure that parameters calculated at different establishments are identical and it is not intended to imply that the parameters are capable of being determined to this accuracy 2.2 A is the nominal value of the smallest cross-section All the dimensions used to calculate A shall be the mean values between the tolerance limits quoted on the appropriate piece part drawing 2.3 Calculations are only applicable to the component parts of a closed magnetic circuit 2.4 All dimensions used for the purpose of calculations shall be the mean value within the tolerance limits quoted on the appropriate piece part drawing 2.5 All irregularities in the outline of the core, such as small cut-outs, notches, chamfers, etc shall be ignored unless otherwise described 2.6 When the calculation involves the sharp corner of a piece part, then the mean length of flux path for that corner shall be taken as the mean circular path joining the centres of area of the two adjacent uniform sections, and the cross-sectional area associated with that length shall be taken as the average area of the two adjacent uniform sections Calculation of effective parameters l e , A e and V e The effective parameters can be defined as le = C1 /C2 Ae = C1 / C2 where le is the effective magnetic length of the core (mm); Ae is the effective cross-sectional area (mm 2); Ve is the effective volume (mm 3); C1 is the core constant (mm –1); C2 is the core constant (mm –3) Ve = le Ae = C1 / C2 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU The following basic rules are applicable to this standard –6– 60205 © IEC:2006+A1:2009 Formulae for the various types of cores 3.1 Ring cores X r0 r0 4× 4× h r ϕ h Section X-X IEC 584/06 C1 = C2 = 3.1.1 2π he ln (d / d ) 4π (1 / d − / d1 ) he ln (d1 / d ) For ring cores of rectangular cross-section with sharp corners he = h 3.1.2 For ring cores of rectangular cross-section with an appreciable average rounding radius r0 he = h(1 − k1 ) k1 = 3.1.3 For ring cores of trapezoidal cross-section with sharp corners he = h(1 − k2 ) k2 = 3.1.4 1,7168r0 h(d1 − d ) h(tan α + tan β ) d1 − d For ring cores of trapezoidal cross-section with an appreciable average rounding radius r0 he = (1 − k1 − k2 ) 3.1.5 For ring cores of cross-section with circular arc frontal sides he = h − d1 − d ⎛ ϕ sin ϕ ϕ ⎞ − ⎟ ⎜ sin − sin (ϕ / ) ⎝ 2 2⎠ LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU h X d1/2 d2/2 β d2/2 d1/2 α 60205 © IEC:2006+A1:2009 –7– ϕ = arcsin d1 − d 4r NOTE When the winding is uniformly distributed over a ring core, it may be expected that, at all points inside the ring core, the flux lines will be parallel to its surface No leakage flux will therefore leave or enter the ring core This justifies the use of a theoretically more correct derivation of the effective parameters which does not make use of the assumption that the flux is uniformly distributed over the cross-section 3.2 Pair of U-cores of rectangular section NOTE U + PLT (Plate)-cores use U core formulas q l1 p q A3 Area Y l′2 l″2 Y A1 Area s h l′4 X A2 Area l″5 l′5 X Section Y-Y l3 Section X-X IEC 585/06 Length of flux path associated with area A2 : l2 = l2′ + l2′′ Mean length of flux paths at corners: l4 = l4′ + l4′′ = l5 = l5′ + l5′′ = π π ( p + h) (s + h ) Mean areas associated with l and l : A4 = A1 + A2 A5 = A2 + A3 C1 = ∑ i=1 li Ai 3.3 Pair of U-cores of rounded section NOTE U + PLT (Plate)-cores use U core formulas C2 = ∑ i =1 li Ai LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU l″4 –8– 60205 © IEC:2006+A1:2009 l1 l″4 X l′4 p Area s Area Y Y l′2 l″2 h A1 A2 A3 Area Section Y-Y l″5 l′5 X s Section X-X IEC 586/06 In calculating A ignore any ridges introduced for the purpose of facilitating manufacture Length of flux path associated with area A2 : l2 = l2′ + l2′′ Mean length of flux path at corners: l4 = l4′ + l4′′ = l5 = l5′ + l5′′ = π π ( p + h) (s + h ) Mean areas associated with l and l : A +A A4 = 2 A5 = C1 = ∑ i =1 li Ai A2 + A3 C2 = ∑ i =1 li Ai LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU l3 – 48 – l = l 4′ + l 4′′ = γ = 60205 © CEI:2006+A1:2009 π ⎛ d h − h2 ⎞ ⎜γ − + ⎟ 2⎝ ⎠ (π − α )d12 + 2(ab − πd12 / − d1d / 2) 4(π − α ) où γ est un rayon hypothétique bissectant la surface de la section transversale de l'anneau: A4 = 1⎧ π d1d ⎛ h h ⎞⎫ + (π − α )d1 ⎜ − ⎟⎬ ⎨ab − d1 − 2⎩ ⎝ 2 ⎠⎭ A5 = π⎛ d h −h ⎞ ⎜ 0,29289 + ⎟ 2⎝ ⎠ ⎫ d + (h1 − h2 )⎬ ⎨ 2⎩ ⎭ π ⎧ d22 C1 = ∑ i =1 3.9 li Ai li C2 = ∑ i =1 Ai Paire de noyaux PM c l′4 b X l3 l′2 d1 lmin d2 lmax d3 d4 ƒ ϕ l″2 t e l″4 l1 l″5 l′5 β d1 A7 A8 X α h2 h1 Section X-X Surface totale de la branche: A1 = β (d 2 ) − d 22 − 2bt IEC 592/06 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU l5 = l5′ + l5′′ = 60205 © CEI:2006+A1:2009 ó β = α − arcsin – 49 – f d2 Facteurs de noyau associés l : l2 = l2′ + l2′′ d2 g l2 d3 = A2 Dπ (h1 − h2 )/ ln l min+ l max 2l D= A7 A8 ( ) 2 d + d − d d cos(α − β ) lmax = l2 (1 d3 − d )g = {Dπ (h1 − h2 ) 2}2 A2 A7 = β d2 + ϕ⎞ π 2 ⎛ f tan β − f tan ⎜α − ⎟ − d 8 ⎠ 16 ⎝ A8 = (d α − d3 − d4 2 ) Surface de la branche centrale: A3 = (d π ) Longueur moyenne des trajets du flux aux angles et surfaces moyennes associées ceux-ci: l4 = l4′ + l4′′ = A4 = l5 = l5′ + l5′′ = A5 = π (h1 − h2 + d1 − d ) {A1 + βd (h1 − h2 )} 2 ⎫ d3 + d4 ⎬ ⎨d3 + h1 − h2 − 4⎩ ⎭ π⎧ π (d ( ) − d + αd (h1 − h2 ) ) LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU où g = – 50 – C1 = ∑ i =1 li Ai 60205 © CEI:2006+A1:2009 C2 = ∑ i =1 li Ai 3.10 Paire de noyaux EL NOTE Les noyaux-(Plaques) EL + PLT utilisent les formules des noyaux EL C B D l1 l4 A E l5 R IEC 593/06 Surface de la branche extérieure: A1 = (A − E )C − 4⎜⎛ R − πR ⎞⎟ ⎝ ⎠ Longueur moyenne du trajet du flux au niveau de la branche extérieure: l1 = D Surface de la paroi de fond: A2 = (C + (F − F1 ) + πF1 /2 )(B − D ) Longueur moyenne du flux au niveau de la paroi de fond: ⎛E F ⎞ l2 = ⎜ − ⎟ ⎠ ⎝2 Surface de la branche centrale: A3 = 1⎧1 ⎫ ⎨ πF1 + (F2 − F1 )F1 ⎬ ⎩4 ⎭ Longueur moyenne du trajet du flux au niveau de la branche centrale: l3 = D Surface du coin extérieur: LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU F1 l3 l2 H F2 60205 © CEI:2006+A1:2009 – 51 – A4 = A1 + A21 où A 21 = (B – D)C Longueur moyenne du trajet du flux au niveau du coin extérieur: l4 = π ⎛⎛ A E⎞ ⎞ ⎜ ⎜ − ⎟ + (B − D )⎟ ⎝⎝ 2⎠ ⎠ Surface du coin intérieur: A23 + A3 où A23 = ((F − F1 ) + πF1 /2)(B − D ) Longueur moyenne du trajet du flux au niveau du coin intérieur: l5 = π ⎛ A3 ⎞ ⎜⎜ + (B − D )⎟⎟ ⎝ F2 ⎠ C1 = ∑ i =1 l e = C 12 /C li Ai C2 = ∑ Ae = C1/C2 i =1 li 2 Ai Ve = C13 /C22 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU A5 = – 52 – 60205 © CEI:2006+A1:2009 3.11 Paire de noyaux ER (profil bas) NOTE Les noyaux-(Plaques) ER + PLT utilisent les formules des noyaux ER B l1 D l4 A E F G l3 l2 C l5 A1 S1 A′3 A″3 α A3 IEC 594/06 Surface de la branche extérieure: ⎛ αE EG ⎞ − A1 = C (A − G ) − ⎜⎜ sin α ⎟⎟ ⎝ ⎠ où α = arc cos (G/E) Longueur moyenne du trajet du flux au niveau de la branche extérieure: l1 = D Surface de la paroi du fond: A = C(B – D) Longueur moyenne du trajet du flux au niveau de la paroi du fond: l2 = Surface de la branche centrale: ( E + G +C − 2F ) LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU β 60205 © CEI:2006+A1:2009 – 53 – 1⎛1 2⎞ ⎜ πF ⎟ 2⎝4 ⎠ A3 = Longueur moyenne du trajet du flux au niveau de la branche centrale: l3 = D Surface du coin extérieur: A1 + A2 A4 = l4 = π (p + h ) où h= B−D p= A E − 2 Surface du coin intérieur: A5 = A2 + A3 Longueur moyenne du trajet du flux au niveau du coin intérieur: l5 = π (2S + h ) La condition pour obtenir A ′ = A ″ est la suivante: S1 = F (1 − sin α ) = 0,2978 F C1 = ∑ i =1 l e = C 12 /C li Ai C2 = ∑ Ae = C1/C2 i=1 li Ai Ve = C13 /C22 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Longueur moyenne du trajet du flux au niveau du coin extérieur: – 54 – Paire de noyaux PQ NOTE Ce calcul ignore l’effet d’enfoncement du ressort NOTE Les noyaux (-plaques) PQ+PLT utilisent les formules des noyaux PQ NOTE Les équations ci-dessous sont cohérentes avec celles indiquées dans la CEI 62317-13 β l″2 lmin α l′4 l″4 A8 A7 l′2 3.12 60205 © CEI:2006+A1:2009 l3 E F J A G l′5 l″5 A3 A1/2 D C B l1 h IEC 014/09 Surface de la branche extérieure: A1 = C ( A − G ) − βE + GI 2 où ⎛G⎞ ⎟ ⎝E⎠ β = arccos⎜ I = E sin β Longueur moyenne du trajet du flux au niveau de la branche extérieure: l1 = D Facteurs de noyaux associés l : Pour l , A le rayon élémentaire dr illustré dans la Figure est la longueur élémentaire du trajet du flux dans l’intégrale ci-dessous Le vecteur du rayon s’étend de F/2 E/2 pour le cercle entier La longueur effective l i pour la section est multipliée par f La surface correspond la surface physique multipliée par K LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU lmax 60205 © CEI:2006+A1:2009 – 55 – r F E dr IEC 015/09 E F l2 i = A22 ∫ ⎛1 1⎞ ⎜ − ⎟ f F E⎠ dr = f ⎝ 2 [2πK (B − D )r ] 2[πK (B − D )] A est calculé de cette manière La longueur magnétique totale de cette section est 2l i pour les moitiés supérieure et inférieure réunies A2 = πKEF B−D ⎛E⎞ ln⎜ ⎟ E−F ⎝F⎠ EF ⎛ ⎛ E ⎞ ⎞ l2 = 2l2i = f ⎜ ln⎜ ⎟ ⎟ E − F ⎜⎝ ⎝ F ⎠ ⎟⎠ où A7 A7 = A8 π E − F 16 K= ( A7 = ) ( β ⋅ E −α ⋅ F + G ⋅ L − J ⋅ I ) ⎛ L⎞ ⎝J⎠ α = arctan⎜ ⎟ f = lmin + lmax 2lmin lmax = E + F − EF cos(α − β ) LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU E l2 i f f ⎛E⎞ dr = ln⎜ ⎟ = ∫F2 A2 K 2πr (B − D ) 2πK (B − D ) ⎝ F ⎠ – 56 – 60205 © CEI:2006+A1:2009 Définir les deux autres surfaces physiques dans le trajet du flux au niveau de la paroi du fond A9 = 2α ⋅ F (B − D ) A10 = 2β ⋅ E (B − D ) La surface mathématique A est donnée comme A 10 > A > A Surface de la branche centrale: A3 = πF l3 = D Surface du coin extérieur: A4 = (A1 + A10 ) = [A1 + E (B − D )β ] 2 Longueur moyenne du trajet du flux au niveau du coin extérieur: l4 = l4' + l4" = π⎛ 1 ⎞ ⎜ (B − D ) + A − E ⎟ 4⎝ 2 ⎠ Surface du coin intérieur: π ⎛F⎞ A5 = (A3 + A9 ) = ⎜ ⎟ + F (B − D )α 2⎝ 2⎠ Longueur moyenne du trajet du flux au niveau du coin intérieur: l5 = l5' + l5" = C1 = ∑ i =1 π⎛ ⎞ ⎞ ⎛ ⎜⎜ (B − D ) + ⎜1 − ⎟F ⎟ 4⎝ ⎠ ⎟⎠ ⎝ li Ai C2 = ∑ i =1 li Ai2 La surface de la section transversale physique minimale A est donnée comme suit: A = (A , A , A , A , A ) le = C12 C2 Ae = C1 C2 Ve = C13 C22 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Longueur moyenne du trajet du flux au niveau de la branche centrale: 60205 © CEI:2006+A1:2009 3.13 – 57 – Paire de noyaux EFD K C B F2 l1 D A E F1 l3 l2 q l4 l5 Surface de la branche extérieure: C (A − E ) A1 = Longueur moyenne du trajet du flux au niveau de la branche extérieure: l1 = D Surface de la paroi du fond: A2 = C (B − D ) Longueur moyenne du flux au niveau de la paroi du fond: l2 = E − F1 Surface de la branche centrale: A3 = F1 F2 − 2q 2 où q : chanfrein Longueur moyenne du trajet du flux au niveau de la branche centrale: l3 = D Surface du coin extérieur: A4 = (A1 + A2 ) LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU IEC 596/06 – 58 – 60205 © CEI:2006+A1:2009 Longueur moyenne du trajet du flux au niveau du coin extérieur: l4 = π ⎛A−E ⎜ 8⎝ ⎞ + (B − D )⎟ ⎠ Surface du coin intérieur: A5 = A2 + A3 Longueur moyenne du trajet du flux au niveau du coin intérieur: π ⎛⎜ F1 2 ⎛ C − F2 − K ⎞ ⎛ B − D ⎞ ⎞⎟ + ⎜ + ⎟ ⎜ ⎟ 4⎜ ⎝ ⎠ ⎟ ⎝ ⎠ ⎝ ⎠ C1 = ∑ i =1 le = C12 C2 li Ai C2 = ∑ i =1 Ae = C1 C2 li Ai2 Ve = C13 C22 3.14 Paire de noyaux planaires E NOTE Les noyaux-(Plaques) E planaires + PLT utilisent les formules de noyaux E planaires B C l1 D l4 l3 l2 R1 A E F R2 l5 IEC 597/06 Surface de la branche extérieure: A1 = C (A − E ) ⎛ π ⎞ − 4⎜ R − × R 12 ⎟ ⎝ ⎠ LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU l5 = 60205 © CEI:2006+A1:2009 – 59 – Longueur moyenne du trajet du flux au niveau de la branche extérieure: l1 = D Surface de la paroi du fond: A2 = C (B − D ) Longueur moyenne du flux au niveau de la paroi du fond: l2 = E −F π ⎛ ⎞ A3 = FC − 2⎜ R 22 − × R 22 ⎟ ⎝ ⎠ Longueur moyenne du trajet du flux au niveau de la branche centrale: l3 = D Surface du coin extérieur: A1 + A2 A4 = Longueur moyenne du trajet du flux au niveau du coin extérieur: l4 = π ⎛A−E ⎜ 8⎝ ⎞ + (B − D )⎟ ⎠ Surface du coin intérieur: A5 = (A2 + A3 ) Longueur moyenne du trajet du flux au niveau du coin intérieur: l5 = π ⎛F ⎞ × ⎜ + (B − D )⎟ ⎝2 ⎠ C1 = ∑ i =1 le = C 12 C2 li Ai Ae = C2 = ∑ li Ai C1 C2 Ve = i =1 C 13 C 22 LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU Surface de la branche centrale: – 60 – 60205 © CEI:2006+A1:2009 Annexe A (informative) Objet de la révision L'objet de cette révision est de fournir des formules grâce auxquelles tout le monde peut atteindre les mêmes valeurs de paramètres effectifs En premier lieu, il est nécessaire d'avoir un nombre suffisant de chiffres significatifs lorsque les chiffres sont arrondis dans le processus de calcul En outre, certaines formules de calcul ont été modifiées pour se rapprocher des formes réelles De plus, de nouveaux noyaux “EL, ER, PQ, EFD et E planaires” ont été ajoutés dans la présente édition Les paramètres contenus dans les normes CEI existantes seront révisés avec le résultat des formules de la présente norme _ LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU L'idée de base de calcul dans cette révision n'a pas été modifiée Récemment, l'analyse du champ magnétique dans le noyau a été considérablement améliorée; ainsi, on prévoit le développement de nouvelles approches et formules partir de cette nouvelle base LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU ELECTROTECHNICAL COMMISSION 3, rue de Varembé PO Box 131 CH-1211 Geneva 20 Switzerland Tel: + 41 22 919 02 11 Fax: + 41 22 919 03 00 info@iec.ch www.iec.ch LICENSED TO MECON Limited - RANCHI/BANGALORE, FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU INTERNATIONAL