IEC 61 400 23 Edition 1 0 201 4 04 INTERNATIONAL STANDARD Wind turbines – Part 23 Full scale structural testing of rotor blades IE C 6 1 4 0 0 2 3 2 0 1 4 0 4 (e n ) ® colour inside Copyright Internat[.]
I E C 61 40 -2 ® Edition 201 4-04 I N TE RN ATI ON AL S TAN D ARD colour i n sid e Wi n d tu rbi n es – IEC 61 400-23:201 4-04(en) P art 3: F u l l -s cal e s tru ctu ral te s ti n g of rotor bl ad es T H I S P U B L I C AT I O N I S C O P YRI G H T P RO T E C T E D C o p yri g h t © I E C , G e n e v a , S wi tz e rl a n d 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 I EC copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or your local I EC member National Committee for further information IEC Central Office 3, rue de Varembé CH-1 21 Geneva 20 Switzerland Tel.: +41 22 91 02 1 Fax: +41 22 91 03 00 info@iec.ch www.iec.ch Ab ou t th e I E C The I nternational Electrotechnical Commission (I EC) is the leading global organization that prepares and publishes I nternational Standards for all electrical, electronic and related technologies Ab o u t I E C p u b l i ca ti o n s 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 I E C Catal og u e - webstore i ec ch /catal og u e The stand-alone application for consulting the entire bibliographical information on IEC International Standards, Technical Specifications, Technical Reports and other documents Available for PC, Mac OS, Android Tablets and iPad I E C pu bl i cati on s s earch - www i ec ch /search pu b The advanced search enables to find IEC publications by a variety of criteria (reference number, text, technical committee,…) It also gives information on projects, replaced and withdrawn publications E l ectroped i a - www el ectroped i a org The world's leading online dictionary of electronic and electrical terms containing more than 30 000 terms and definitions in English and French, with equivalent terms in additional languages Also known as the International Electrotechnical Vocabulary (IEV) online I E C G l os sary - s td i ec ch /g l oss ary More than 55 000 electrotechnical terminology entries in English and French extracted from the Terms and Definitions clause of IEC publications issued since 2002 Some entries have been collected from earlier publications of IEC TC 37, 77, 86 and CISPR I E C J u st Pu bl i s h ed - webstore i ec ch /j u stpu bl i sh ed Stay up to date on all new IEC publications Just Published details all new publications released Available online and also once a month by email I E C C u stom er S ervi ce C en tre - webstore i ec ch /csc If you wish to give us your feedback on this publication or need further assistance, please contact the Customer Service Centre: csc@iec.ch I E C 61 40 -2 ® Edition 201 4-04 I N TE RN ATI ON AL S TAN D ARD colour i n sid e Wi n d tu rbi n es – P art 3: F u l l -s cal e s tru ctu ral tes ti n g of rotor bl ad es INTERNATIONAL ELECTROTECHNICAL COMMISSION ICS 27.1 80 PRICE CODE ISBN 978-2-8322-1 506-7 Warn i n g ! M ake su re th a t you obtai n ed th i s pu bl i cati on from an au th ori zed d i s tri bu tor ® Registered trademark of the International Electrotechnical Commission X –2– I EC 61 400-23:201 © I EC 201 CONTENTS FOREWORD I NTRODUCTI ON Scope Norm ative references Term s and definitions Notation Symbols Greek sym bols Subscripts 4 Coordinate system s General principles Purpose of tests Lim it states Practical constraints Results of test Docum entation and procedures for test blade Blade test program and test plans Areas to be tested Test program Test plans General Blade description 3 Loads and conditions 7 I nstrumentation 7 Expected test results Load factors for testing General Partial safety factors used in the design General 2 Partial factors on m aterials Partial factors for consequences of failure 8 Partial factors on loads 8 Test load factors 8 Blade to blade variation 8 Possible errors in the fatigue formulation 8 3 Environm ental conditions Application of load factors to obtain the target load 9 Test loading and test load evaluation 20 General 20 I nfluence of load introduction 20 Static load testing 20 Fatigue load testing 21 Test requirements 22 1 General 22 1 Test records 22 1 I nstrumentation calibration 22 I EC 61 400-23: 201 © I EC 201 –3– 1 Measurem ent uncertainties 22 1 Root fixture and test stand requirem ents 22 1 Environm ental conditions monitoring 22 1 Deterministic corrections 23 Static test 23 General 23 2 Static load test 23 Strain m easurem ent 24 Deflection measurem ent 24 Fatigue test 24 Other blade property tests 24 Blade mass and center of gravity 24 Natural frequencies 25 Optional blade property tests 25 1 Test results evaluation 25 1 General 25 1 Catastrophic failure 25 1 Permanent deformation, loss of stiffness or change in other blade properties 26 1 Superficial damage 26 1 Failure evaluation 26 Reporting 26 General 26 2 Test report content 27 Evaluation of test in relation to design requirem ents 27 Annex A (inform ative) Guidelin es for the necessity of renewed static and fatigue testing 28 Annex B (inform ative) Areas to be tested 29 Annex C (informative) Effects of large deflections and load direction 30 Annex D (informative) Form ulation of test load 31 D Static target load 31 D Fatigue target load 31 D Sequential single-axial, single location 34 D Multi axial single location 34 Annex E (inform ative) Differences between design and test load conditions 36 E General 36 E Load introduction 36 E Bending moments and shear 36 E Flapwise and lead-lag com binations 36 E Radial loads 37 E Torsion loads 37 E Environmental conditions 37 E Fatigue load spectrum and sequence 37 Annex F (informative) Determ ination of number of load cycles for fatigue tests 38 F General 38 F Background 38 F The approach used 38 Bibliograph y 43 –4– I EC 61 400-23:201 © I EC 201 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure – Chordwise (flatwise, edgewise) coordinate system – Rotor (flapwise, lead-lag) coordinate system C.1 – Applied loads effects d ue to blade deform ation and angulation 30 D.1 – Polar plot of the load envelope from a typical blade 31 D.2 – Design FSF 33 D.3 – Area where design FSF is sm aller than , (critical area) 33 D.4 – rFSF and critical areas, sequential single-axial test 34 D.5 – rFSF and critical area, m ulti axial test 35 E – Difference of m oment distribution for target and actual test load 36 F – Sim plified Goodman diagram 39 F – Test load factor γ ef for different number of load cycles in the test 42 Table Table Table Table – Recommended values for γ ef for different num ber of load cycles A – Exam ples of situations typicall y requiring or not requiring renewed testing 28 F – Recommended values for γef for different num ber of load cycles 38 F – Expanded recomm ended values for γ ef for different num ber of load cycles 41 I EC 61 400-23: 201 © I EC 201 –5– I NTERNATIONAL ELECTROTECHNICAL COMMI SSION WI N D T U RB I N E S – P a rt : F u l l -s c a l e s tru c tu l te s ti n g o f ro to r b l a d e s FOREWORD ) The I nternati on al Electrotechni cal Comm ission (I EC) is a worl d wid e organization for stand ardization com prisin g all nati on al el ectrotechnical comm ittees (I EC Nation al Comm ittees) The object of I EC is to prom ote internati onal co-operation on all q uestions concerni ng stand ardi zati on in the el ectrical and el ectronic fiel ds To this en d and in additi on to other acti vities, I EC pu blish es I nternational Stan dards, Techn ical Specificati ons, Technical Reports, Publicl y Avail abl e Specificati ons (PAS) an d Gu ides (hereafter referred to as “I EC Publication(s)”) Th eir preparation is entrusted to techn ical comm ittees; any I EC N ational Comm ittee interested in the subj ect dealt with m ay participate in th is preparatory work I nternational, governm ental an d n on governm ental organi zations l iaising with the I EC also partici pate i n this preparati on I EC col laborates cl osel y with the I ntern ational Organi zation for Stand ardization (I SO) in accordance with ditions determ ined by agreem ent between th e two organi zati ons 2) The form al decisions or ag reem ents of I EC on tech nical m atters express, as nearly as possible, an internati onal consensus of opi nion on the rel evant subjects since each technical com m ittee has representati on from all interested I EC N ational Com m ittees 3) I EC Publicati ons have the form of recom m endations for i nternational use an d are accepted by I EC National Com m ittees in that sense While all reasonable efforts are m ade to ensure that the tech nical content of I EC Publications is accurate, I EC cann ot be h eld responsible for the way in wh ich th ey are used or for an y m isinterpretation by an y en d u ser 4) I n ord er to prom ote internati onal u niform ity, I EC National Com m ittees undertake to apply I EC Publ i cations transparentl y to th e m axim um extent possible i n thei r national an d regi on al publicati ons Any d ivergence between an y I EC Publ ication and the correspondi ng n ational or regi on al pu blicati on shall be clearl y in dicated i n the latter 5) I EC itself d oes n ot provi de an y attestati on of conform ity I n depend ent certificati on bod ies provi de conform ity assessm ent services and, in som e areas, access to I EC m arks of conform ity I EC is not responsi ble for an y services carri ed out by ind ependent certification bodi es 6) All users shou ld ensure that th ey h ave the l atest editi on of thi s publicati on 7) No liability shall attach to I EC or its directors, em pl oyees, servants or ag ents inclu ding i n divi du al experts and m em bers of its tech nical comm ittees and I EC Nati on al Com m ittees for an y personal i nju ry, property d am age or other dam age of an y n ature whatsoever, wheth er di rect or indirect, or for costs (includi ng leg al fees) an d expenses arisi ng out of the publ ication, use of, or relian ce upon, this I EC Publicati on or an y other I EC Publications 8) Attention is drawn to th e Norm ative references cited in this publ ication Use of the referenced publ ications i s indispensable for the correct applicati on of this publication 9) Attention is drawn to the possibility that som e of the elem ents of this I EC Publication m ay be the su bject of patent rig hts I EC shal l not be held responsibl e for identifyi ng any or all such patent ri ghts I nternational Standard I EC 61 400-23 has been prepared by I EC technical committee 88: Wind turbines This first edition cancels and replaces I EC TS 61 400-23, published in 2001 I t constitutes a technical revision This edition includes the following significant technical changes with respect to I EC TS 61 400-23: a) description of load based testing onl y; b) condensation to describe the general principles and demands –6– I EC 61 400-23:201 © I EC 201 The text of this standard is based on the following docum ents: CDV Report on votin g 88/420/CDV 88/448/RVC Full inform ation on the voting for the approval of this standard can be found in the report on voting indicated in the above table This publication has been drafted in accordance with the I SO/I EC Directives, Part A list of all parts in the I EC 61 400 series, published under the general title be found on the I EC website Wind turbines, can The committee has decided that the contents of this publication will remain unchanged until the stability date indicated on the I EC web site under "http: //webstore iec.ch" in the data related to the specific publication At this date, the publication wi ll be • • • • reconfirm ed, withdrawn, replaced by a revised edition, or amended A bilingual version of this publication may be issued at a later date I M P O R T AN T th at it – Th e co n ta i n s u n d e rs t a n d i n g c o l o u r p ri n t e r of ' co l ou r c o l o u rs i ts in si d e' wh i ch c o n te n ts l og o a re U s e rs on th e cover c o n s i d e re d sh ou l d p ag e to t h e re fo re of th i s be p ri n t p u b l i cati on u s e fu l th i s fo r i n d i c ate s th e d ocu m e n t c o rre c t u si n g a I EC 61 400-23: 201 © I EC 201 –7– I NTRODUCTI ON The blades of a wind turbine rotor are generall y regarded as one of the m ost critical components of the wind turbine system I n this standard, the demands for full-scale structural testing related to certification are defined as well as the interpretation and evaluation of test results Specific testing m ethods or set-ups for testing are not demanded or included as full-scale blade testing methods historicall y have developed independently in different countries and laboratories Furtherm ore, demands for tests determining blade properties are included in this standard in order to validate some vital design assum ptions used as inputs for the design load calculations An y of the requirements of this standard m ay be altered if it can be suitabl y dem onstrated that the safety of the system is not compromised The standard is based on I EC TS 61 400-23 published in 2001 Compared to the TS, this standard onl y describes load based testing and is condensed to describe the general principles and dem ands –8– I EC 61 400-23:201 © I EC 201 WI N D T U RB I N E S – P a rt : F u l l -s c a l e s tru c tu l te s ti n g o f ro to r b l a d e s S cop e This part of I EC 61 400 defines the requirem ents for full-scale structural testing of wind turbine blades and for the interpretation and evaluation of achieved test results The standard focuses on aspects of testing related to an evaluation of the integrity of the blade, for use by m anufacturers and third party investigators The following tests are considered in this standard: • • • • static load tests; fatigue tests; static load tests after fatigue tests; tests determining other blade properties The purpose of the tests is to confirm to an acceptable level of probability that the whole population of a blade type fulfils the design assumptions I t is assumed that the data required to define the param eters of the tests are available and based on the standard for design requirem ents for win d turbines such as I EC 61 400-1 or equivalent Design loads and blade m aterial data are considered starting points for establishing and evaluating the test loads The evaluation of the design loads with respect to the actual loads on the wind turbines is ou tside the scope of this standard At the time this standard was written, full-scale tests were carried out on blades of horizontal axis wind turbines The blades were m ostl y made of fibre reinforced plastics and wood/epoxy However, most principles would be applicable to an y wind turbine configuration, size and material N o rm a t i ve re fe re n c e s The following documents, in whole or in part, are normativel y referenced in this document and are indispensable for its application For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including an y amendm ents) applies I EC 60050-41 5: 999, generator systems International Electrotechnical Vocabulary – Part 415: Wind turbine Wind turbines – Part 1: Design requirements I SO/I EC 7025: 2005, General requirements for the competence of testing and calibration laboratories I SO 2394: 998, General principles on reliability for structures I EC 61 400-1 : 2005, – 32 – I EC 61 400-23: 201 © I EC 201 I n order to determ ine the dam age due to a load system, the load has to be translated into strain or stress From these strain or stress cycles the dam age can be calculated using an appropriate method of cycle counting and an appropriate fatigue form ulation I n order to avoid stacking of inaccuracies, the dam age due to the test load and the damage due to the target load shall be evaluated using identical m ethods I n practice, all parts of a blade cannot be properly tested A criterion to determine the need to test a certain section of a blade can be the reserve against fatigue failure in that area This determination should be made i n accordance with the certifying bod y This reserve is generally expressed in the fatigue strain factor ( FSF) This is the factor by which the load has to be multiplied to obtain damage equal to unity Since the determ ination of the dam age is a non-linear process, FSF has to be determined iteratively For areas where this factor is high, a large reserve against fatigue dam age exists and hence the need for testing this area is less urgent I f this factor is close to unity, the area is critical with respect to fatigue and testing is required I n order for a given area to be properl y tested, the dam age due to the test load shall be equal or higher than the dam age due to the target load This m eans that the FSF for the fatigue test load shall be equal to or lower than the FSF for the fatigue target load The ratio between the FSF for the target load and the FSF for the test load can be defined as the relative FSF ( rFSF : ) rFSF = FSFtarget FSFtest where rFSF is the relative fatigue strain factor; FSFtarg et is the fatigue strain factor for the target load; FSFtest is the fatigue strain factor for the test load At all locations where the rFSF is bigger than unity the blade is properl y tested As an exam ple, the test load evaluation for a generic 62, m blade is given for two test m ethods The exam ples given are onl y dealing with the stresses in the blade longitudinal direction and no attention is given to possible critical details and stresses in other directions I n the first part, the test load evaluation is given for a sequential single axial test, where the blade is sequentiall y loaded in pure flat and pure lead-lag direction On the 62, m blade, strains are com puted every m of rotor diam eter and on 26 locations distributed over the circumference of the chord for each spanwise location From the resulting tim e series of strains in all these locations, together with the occurrences table and the fatigue life form ulation, the damage and FSF’s are determ ined The dam age in each material is com puted and at overlapping materials with different fatigue form ulation the m inim um FSF is considered All com putations are performed on the com plete load set specified by I EC guidelines using an integrated wind turbine design tool The dam age in the blade after 20 years of service has been determined The FSF’s are presented as contour plots in Figure D Although arbitrary, it has been chosen in this example to consider areas with an FSF lower than , as critical I EC 61 400-23: 201 © I EC 201 – 33 – IEC F i g u re D – D es i g n 04 /1 FSF The black line in Figure D connects the points where the FSF equals , The areas of the blade where this FSF is smaller than , 4, should be tested For clarity this area is represented as m arked in red in Figure D IEC F i g u re D – Are a wh ere d e s i g n 04 5/1 FSF i s s m al l e r th a n , (cri ti cal area) Areas where computation might underestim ate stresses should also be considered, for example areas of high stress concentration in the bolted root connection, bonded j oints of LE and TE and the area between the root and largest chord – 34 – D.3 I EC 61 400-23: 201 © I EC 201 Sequ ential singl e-axi al, singl e location At a single location two separate loads are applied successivel y in the main directions, the applied loads are periodic The load is applied at R = 40,0 m The load due to acceleration of the blade m ass is neglected The number of test cycles for each test load was fixed to m illion cycles Figure D shows the ratio of test and design FSF I n the graph the critical areas from Figure D are also indicated with a black contour line I t also shows which amount of the critical area is tested, while locall y in the critical area the blade is more than 30 % overloaded This example concerns onl y a single load introduction point – not taking into account inertia effects This can be im proved by a m ore realistic load distribution IEC Fig u re D – D.4 rFSF and 04 6/1 criti cal areas, sequ enti al si ng le-axi al test Multi axi al single location The second exam ple is from a bi-axial test where on a single location a flat load as well as a lead-lag load is applied with a phase offset of about 90° so that the load introduction point describes an ellipsoidal traj ectory in space The rFSF contours are given together with the aforementioned critical area in Figure D I EC 61 400-23: 201 © I EC 201 – 35 – IEC 04 7/1 Figure D.5 – rFSF and critical area, multi axial test I t can be seen that for this type of test, a much bigger part of the critical area is tested, while the overload in this area is lim ited to % I n this exam ple, and with the arbitraril y chosen FSF value of , to define the critical area, it appears that for both types of test, parts of the critical area are not satisfactorily tested H owever, as with the static test, it can be seen that with the fatigue test, combined loading (multi-axial) results in a considerably bigger part of the blade to be properl y tested – 36 – I EC 61 400-23: 201 © I EC 201 Annex E (informative) Differences between design and test load conditions E.1 General I deall y the testing performed on a wind turbine blade would recreate the design conditions of the blade H owever, in practice there are a range of lim itations on the tests that can be perform ed As a result of these lim itations som e m odifications and com prom ises are required in the static and fatigue testing undertaken on the blade The following highl ights some of the differences between design and test load conditions E.2 Load introduction During a test, the load introduction is usuall y concentrated at spanwise blade sections Due to the load concentration and possible reinforcem ent of the cross-section, expected deform ations of the cross-section might be prevented, which would alter the blade stresses and/or strength locall y These load introduction points should therefore be located away from the areas specified to be tested (see 9.2 and Annex B) E.3 Bending moments and shear I n a blade static test, loads are usually applied at a finite num ber of sections – whereas the ideal test load is distributed This results in different spanwise distributions of section mom ents (see Figure E ) and shear forces The distribution of section m om ents can be im proved by increasing the number of locations where load is applied; but this has the disadvantage of increasing the area of the blad e that is disturbed The objective is to replicate the target load as accuratel y as possible without com prom ising the validity of the test Areas disturbed by load introduction Moment Actual test load Target load Spanwise IEC 04 8/1 Figu re E.1 – Difference of moment distribution for target and actual test load E.4 Flapwise and lead-lag combinations I n static and fatigue tests, the results are most representative when combinations of flapwise and lead-lag loads are applied By appl ying only the flapwise bending m om ent or onl y the I EC 61 400-23: 201 © I EC 201 – 37 – lead lag mom ent, the resulting stresses and strains and/or dam age rates m ay be lower i n som e areas than the target values (see Annex D) E.5 Radial loads Radial loads on an operating wind turbine blade arise due to the gravitational and centrifugal forces Generall y, the stresses caused by the radial forces are low E.6 Torsion loads The magnitude of the torsion design loads shall be considered in the test loading I f torsion loads are significant in the structural design of the blade they should be included in the test (see 0.1 3) I n principle a representative m ulti-axial loading will result in a m ore realistic situation with respect to torsion loading than single axial-loading For a straight blade, the flapwise-loading and resulting flapwise displacement m eans that an y sim ultaneousl y acting lead-lag loading will introduce a torsion loading which increases toward the root This is true for the real operational situation as well as for the representative multi-axial test loading E.7 Environmental conditions The environmental and time conditions during testing are different from those in the design situation These conditions m ight include: • • • • • • hum idity; tem perature effects; UV radiation; aging (interaction of fatigue and tim e); salinity; chemical contamination Relevant effects have to be considered in the evaluation by using the appropriate strength and fatigue form ulation both for design and test conditions However, the validity of the different design formulations for the different conditions is not tested E.8 Fatigue load spectrum and sequence Fatigue testing is generall y accelerated com pared to in-service fatigue by appl ying a test load, which subj ects the blade to sufficient fatigue damage within a reasonable test period (see and Annex D) – 38 – I EC 61 400-23: 201 © I EC 201 An n ex F (informative) Determ i n ati on of n u m ber of l oad cycl es for fati g u e tes ts F G en eral This annex has been prepared in order to discuss the num ber of load cycles used by full -scale fatigue testing of rotor blades I t is assum ed that a test load factor covering errors in the fatigue form ulation γ ef of , 05 is appropriate for fatigue tests aim ing for a total of million load cycles On the basis hereof, it is found that a γef factor of ,035 should be used for full scale fatigue tests loading the structure with e g 2, million load cycles This result and others are summarized in Table F below Tabl e F – Re com m en d ed val u e s fo r γ e f for d i ffe re n t n u m b e r o f l oad cycl e s N u m b e r o f l o ad c yc l e s , 065 × 06 , 050 2, F γef × 05 × 06 , 035 × 06 , 025 × 07 , 01 Backg rou n d The num ber of loads cycles applied to a rotor blade during full scale fatigue testing is, of course, a decisive factor for the duration of the fatigue test Consequently, there will always be a wish to limit the number of load cycles as long as the test still fulfils its purpose with the intended trustworthiness On the basis of the coefficients historicall y used for calculating the test load factor, calculations are carried out in order to evaluate the influence of the number of load cycles in a full scale fatigue test on the test load factor F Th e ap proach u sed First of all consider the Goodm an diagram in Figure F , which has been reduced to a single sided diagram for the sake of simplicity I EC 61 400-23: 201 © I EC 201 – 39 – Cycle witdh Charac Reduced ° Mean value IEC 04 /1 F i g u re F – S i m p l i fi ed G ood m an d i ag ram The line denoted “Charac” is based upon the characteristic strength values with intersection of the horizontal axis in a value representing the static strength of the structure S and intersection with the vertical axis in the d ynam ic strength valid for one single load cycle D The line “Reduced” is valid for a certain number of cycles n This line also intersects the horizontal axis in the point S but the vertical axis is intersected in the point D r, which is given by Formula (F ) D Dr = ( ) n m where D r is D is n is m is the the the the (F.1 ) reduced d ynam ic strength valid for one load cycle; d ynamic strength valid for one load cycle; actual num ber of load cycles; fatigue damage exponent for the m aterial The dam age for a certain load width W and load m ean value M is given by the actual number of load cycles n divided by the allowed num ber of load cycles N, which is equal to the actual load width divided by the allowed load width to the power of m , Form ula (F.2) n W Damage = = Dr N ⋅ M + Dr − S where N is the allowed number of load cycles; W is the load width; S is the static strength of the structure; m (F.2) – 40 – M I EC 61 400-23: 201 © I EC 201 is the load mean value After inserting Formula (F ) in Formula (F 2) and re-arranging, Formula (F.3) is obtained Damage (1 ) W⋅ S⋅n m = D ⋅ (S − M ) m (F 3) The fatigue test is continued until the test damage, given by Formula (F.4) is equal to the target damage given by Form ula (F 5) where subscript “t” refers to the test and subscript “0” refers to the calculated loads and thereby the target dam age Test Damage Target Damage (1 ) Wt ⋅ S ⋅ n t m = D ⋅ (S − M ) t m (F 4) (1 ) W0 ⋅ S ⋅ n0 m = γ test ⋅ D ⋅ (S − M ) m m (F.5) where is a subscript referring to test values; t is a subscript referring to calculated values; γ test is the test load factor Setting the test damage equal to the target damage, Formula (F 6) is obtained after som e rearranging ( S − M t ) n0 ⋅ Wt = γ test ⋅ W0 ⋅ (S − M0 ) n t (1 m ) (F.6) I n order to investigate the sensitivity of Wt in relation to the fatigue dam age exponent m , the derivative of Wt with respect to m is calculated, Form ula (F 7) ∂Wt ∂m = − γ test ⋅ W0 ⋅ (S − Mt ) ⋅ ( S − M0 ) n0 n t m (1 m) n ⋅ ln nt (F.7) The effect of changing from one num ber of load cycles n t1 in the fatigue test to another num ber of load cycles n t2 can be illustrated by R defined by Form ula (F 8) ∂Wt R= ∂m ∂Wt ∂m (nt = (nt = n t1 ) n t2 ) = n0 n t1 n0 n t2 (1 m) (1 m) n ⋅ ln n t1 n ⋅ ln n t2 n = ( ) ln n n t2 m t1 ⋅ n t1 n0 ln n t2 (F.8) I EC 61 400-23: 201 © I EC 201 – 41 – where R is the relative effect of changing from one number of load cycles ( n t1 ) to another ( n t2 ); n t1 is the first (reference) number of load cycles; n t2 is the second (resulting) number of load cycles Suppose the total num ber of load cycles in the Markov m atrix n is 50 m illion and the fatigue damage exponent m is I f n t1 is 2, m illion and n t2 is m illion, Form ula (F.8) yields R = 0,7 I t should be noted that the sensitivity of R to changes in n and m is m inor The test load factor to be used for fatigue testing is the product of factors, where the γef equal to , 05 takes account of possible errors in the fatigue formulation, i e fatigue dam age exponents deviating from the assum ed values among others I f a value of γ ef of , 05 is appropriate for tests with m illion cycles, this % increase in loads should be reduced to 3, % in case the test is extended to 2,5 million cycles instead since 0, 05 × 0,7=0,035 The results for different values of the number of load cycles i n a fatigue test are stated in Table F Table F.2 – Expanded recommended valu es for γ ef for different number of load cycles n t1 R γ ef × 05 ,3 , 064 × 06 1 , 050 0, , 035 2, × 06 × 06 0, , 025 × 07 0, 32 , 01 The valu es are calculated on the basis of Form ula (F 8) usi n g n = 50 m illion, n t2 = m illion an d m = The results given in Table F are depicted graphicall y in Figure F – 42 – I EC 61 400-23: 201 © I EC 201 ,07 ,06 Test load factor ,05 ,04 ,03 ,02 ,01 ,0 × 2,5× 5,0 × Number of load cycles 7,5 × ,0 × IEC Fi g u re F – Test l oad factor γ ef for d i fferen t n u m ber of l oad cycl es i n th e test 05 0/1 I EC 61 400-23: 201 © I EC 201 – 43 – Bibliography I EC 61 400-22, Wind turbines – Part 22: Conformity testing and certification _ INTERNATIONAL ELECTROTECHNICAL COMMISSI ON 3, rue de Varembé PO Box 31 CH-1 21 Geneva 20 Switzerland Tel: + 41 22 91 02 1 Fax: + 41 22 91 03 00 info@iec.ch www.iec.ch