1、BSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06Paper and board Testing of coresPart 8: Determination of natural frequency and flexural modulus by experimental modal analysisBS ISO 110938:2017 ISO 2017Paper and board Testing of cores Part 8:Determination of natural f
2、requency and flexural modulus by experimental modal analysisPapier et carton Essais des mandrins Partie 8: Dtermination de la frquence propre et du module de flexion par analyse modale exprimentaleINTERNATIONALSTANDARDISO11093-8Third edition2017-06Reference numberISO 11093-8:2017(E)National foreword
3、This British Standard is the UK implementation of ISO 110938:2017. It supersedes BS ISO 11093-8:2012, which is withdrawn. The UK participation in its preparation was entrusted to Technical Committee PAI/11, Methods of test for paper, board and pulps.A list of organizations represented on this commit
4、tee can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2017 Published by BSI Standards Limited 2017ISBN 978 0 580 96002 4ICS 85.060Co
5、mpliance with a British Standard cannot confer immunity from legal obligations. This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 June 2017.Amendments/corrigenda issued since publicationDate Text affectedBRITISH STANDARDBS ISO 110938:2017 IS
6、O 2017Paper and board Testing of cores Part 8: Determination of natural frequency and flexural modulus by experimental modal analysisPapier et carton Essais des mandrins Partie 8: Dtermination de la frquence propre et du module de flexion par analyse modale exprimentaleINTERNATIONAL STANDARDISO11093
7、-8Third edition2017-06Reference numberISO 11093-8:2017(E)BS ISO 110938:2017ISO 11093-8:2017(E)ii ISO 2017 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2017, Published in SwitzerlandAll rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized other
8、wise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISOs member body in the country of the requester.ISO copyright officeCh
9、. de Blandonnet 8 CP 401CH-1214 Vernier, Geneva, SwitzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47copyrightiso.orgwww.iso.orgBS ISO 110938:2017ISO 11093-8:2017(E)Foreword iv1 Scope . 12 Normative references 13 Terms and definitions . 14 Principle 25 Apparatus . 26 Test piece 26.1 Sampling . 26.2
10、Test-piece size 36.3 Conditioning 37 Procedure. 58 Calculation 58.1 Calculation of the flexural modulus 58.2 Calculation of the rotational speed factor . 69 Test report . 6Bibliography 8 ISO 2017 All rights reserved iiiContents PageBS ISO 110938:2017ISO 11093-8:2017(E)ForewordISO (the International
11、Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been esta
12、blished has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardiza
13、tion.The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance wit
14、h the editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of an
15、y patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www .iso .org/ patents).Any trade name used in this document is information given for the convenience of users and does not constitute an endorsem
16、ent.For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL
17、: www .iso .org/ iso/ foreword .html.This document was prepared by Technical Committee ISO/TC 6, Paper, board and pulps.This third edition cancels and replaces the second edition (ISO 11093-8:2012), of which it constitutes a minor revision with the following changes: correction to 8.1, Formula (1);
18、editorial updates.It also incorporates the Technical Corrigendum ISO 11093-8:2012/Cor 1:2013, which included updates to Figure 1 and Figure 2.A list of all parts in the ISO 11093 series can be found on the ISO website.iv ISO 2017 All rights reservedBS ISO 110938:2017INTERNATIONAL STANDARD ISO 11093-
19、8:2017(E)Paper and board Testing of cores Part 8: Determination of natural frequency and flexural modulus by experimental modal analysis1 ScopeThis document specifies a method for the determination of the flexural modulus by using experimentally measured natural frequencies in the free-free mode of
20、transverse vibration of cylindrical paper and board cores, which meet the following criteria: internal diameter: 50 mm to 350 mm; minimum wall thickness: 0,02 internal diameter or not less than 2,0 mm; minimum length of core: 8 internal diameter.NOTE For the determination of the flexural modulus by
21、the three-point method, see ISO 11093-7.2 Normative referencesThe following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest editio
22、n of the referenced document (including any amendments) applies.ISO 11093-1, Paper and board Testing of cores Part 1: SamplingISO 11093-2, Paper and board Testing of cores Part 2: Conditioning of test samplesISO 11093-3, Paper and board Testing of cores Part 3: Determination of moisture content usin
23、g the oven drying method3 Terms and definitionsFor the purposes of this document, the following terms and definitions apply.ISO and IEC maintain terminological databases for use in standardization at the following addresses: ISO Online browsing platform: available at h t t p :/ www .iso .org/ obp IE
24、C Electropedia: available at h t t p :/ www .electropedia .org/ 3.1natural frequencyf1first frequency which is the lowest frequency a structure vibrates in, depending on its material, shape and supporting system, when an impulse is applied to it ISO 2017 All rights reserved 1BS ISO 110938:2017ISO 11
25、093-8:2017(E)3.2flexural modulusEmaterial property which, together with core dimensions, describes the resistance of the core to bending deflection3.3rotational speed factorSfcore E-modulus divided by its density (E/) which can be used to estimate vibration performance of coresNote 1 to entry: Cores
26、 with equal dimensions, eccentricity and speed factor deliver at identical chucking conditions an equal resonance frequency.Note 2 to entry: The higher the speed factor, the higher the resonance frequency.4 PrincipleIn the experimental modal analysis, the test piece is considered as a “beam” and Tim
27、oshenkos beam theory for isotropic materials is applied in evaluating transverse vibration. In this theory, the influence of rotary inertia and shear deformations on transverse vibrations are included. During the test, the test piece is suspended so that it is free to vibrate in the transverse direc
28、tion. The flexural modulus is calculated as described in 8.1.5 Apparatus5.1 Test-piece suspension.The basic idea is to measure the first natural frequency in the free-free mode of transverse vibration. To ensure free-free boundary conditions in the lateral direction, the test piece is supported by a
29、 wire and hanging with its axis in the vertical direction (see Figure 1). The minimum length of the support wire (1) is about 300 mm. The supporting system consists of two clamps and the wire. An example of attaching the clamps is shown in Figure 2. The mass of the clamps should be less than 0,01 ma
30、ss of the test piece. The angle, , (see Figure 2) should be more than 45. The distance of the fixing screw from the edge of the core should be 5 mm to 10 mm.5.2 Experimental modal analysis system.The first natural frequency is measured with a signal analyser. The test piece is impacted by a hammer i
31、n the direction (Z-direction) perpendicular to the plane of the support wires (XY-plane) (see Figure 1). The impulse response is measured by a piezoelectric accelerometer at one end of the test piece mounted with its axis in the Z-direction (see Figure 1). The sensitivity of the accelerometer shall
32、be 8 mV/g to 100 mV/g; the frequency range limit of the accelerometer shall be 0,1 Hz to 10 000 Hz. The measured signal is analysed using a signal analyser and the frequency of the lowest mode of bending vibrations is determined from the frequency response function.6 Test piece6.1 SamplingSamples sh
33、all be taken in accordance with ISO 11093-1, but it has to be ensured that the core is not damaged.2 ISO 2017 All rights reservedBS ISO 110938:2017ISO 11093-8:2017(E)6.2 Test-piece sizeThe minimum length of the test piece shall be 8 times the internal diameter of the core.NOTE 1 If the test piece is
34、 too short, it is not possible to read the response of the frequency analysis.NOTE 2 The calculated flexural modulus, E, is more accurate for long test pieces.Regarding the dimensions of the test piece, the following tolerances are specified: length of the core, L: 1 mm; outer diameter of the core,
35、D: 0,1 mm; internal diameter of the core, d: 0,1 mm.6.3 ConditioningThe test piece shall be conditioned in accordance with ISO 11093-2. The moisture content of the test piece shall be measured in accordance with ISO 11093-3.In practice, the test piece shall be conditioned and dried such that the moi
36、sture content shall be equal to that specified for the lot. ISO 2017 All rights reserved 3BS ISO 110938:2017ISO 11093-8:2017(E)Dimensions in millimetresKey1 support wire2 clamps3 test piece4 hammer5 accelerometerFigure 1 Schematic drawing of the test4 ISO 2017 All rights reservedBS ISO 110938:2017IS
37、O 11093-8:2017(E)Dimensions in millimetresKey1 support wire2 clamps3 test bolt4 test pieceFigure 2 Schematic drawing of the test-piece supension7 ProcedureCarry out the test under the same atmospheric conditions as those used to condition the test piece.Impact the test piece in the Z-direction in th
38、e middle of the length of the test piece by means of a hammer as shown in Figure 1. After the impact, the first natural frequency in bending shall be read from the frequency response of the analysis. The obtained value, f1, is used in Formula (1) to calculate the flexural modulus of each tested test
39、 piece.8 Calculation8.1 Calculation of the flexural modulusThe flexural modulus, E, in megapascals, is calculated by using Formula (1):EfmLQI=788108 124,L(1) ISO 2017 All rights reserved 5BS ISO 110938:2017ISO 11093-8:2017(E)wheref1is the natural frequency of the first order, expressed in hertz;mLis
40、 the length-related mass, expressed in kilograms per metre;L is the length of the core, in millimetres;Q is the dimensionless coefficient;I is the second moment of inertia, in mm4.The second moment of inertia, I (mm4), of the core cross section is calculated according to Formula (2):IDd= pi6444() (2
41、)whereD is the outer diameter of the core, in millimetres;d is the internal diameter of the core, in millimetres.The dimensionless coefficient, Q, is calculated according to Formula (3):QIAL=+82 6612,(3)where A is the area of the core cross-direction, in mm2, calculated according to Formula (4):ADd=
42、()pi224(4)8.2 Calculation of the rotational speed factorThe rotational speed factor, Sf, is calculated by using Formula (5):SEf=(5)whereE is the flexural modulus, expressed in megapascals (MPa); is the density, expressed in kilograms per cubic metre.NOTE can be calculated as mass divided by volume.9
43、 Test reportThe test report shall include the following information:a) a reference to this document, i.e. ISO 11093-8;b) the type and designation of the cores tested;c) the place and date of sampling;d) the place and date of testing;6 ISO 2017 All rights reservedBS ISO 110938:2017ISO 11093-8:2017(E)
44、e) the number of test pieces tested;f) the core dimensions;g) the measured moisture content;h) L and f;i) individual and mean values for E;j) the rotational speed factor;k) the date and signature;l) any deviation from this document that may have affected the results. ISO 2017 All rights reserved 7BS
45、 ISO 110938:2017ISO 11093-8:2017(E)Bibliography1 ISO 11093-7, Paper and board Testing of cores Part 7: Determination of flexural modulus by the three-point method8 ISO 2017 All rights reservedBS ISO 110938:2017This page deliberately left blank ISO 11093-8:2017(E)Bibliography1 ISO 11093-7, Paper and
46、board Testing of cores Part 7: Determination of flexural modulus by the three-point method8 ISO 2017 All rights reservedThis page deliberately left blankBSI is the national body responsible for preparing British Standards and other standards-related publications, information and services.BSI is inco
47、rporated by Royal Charter. British Standards and other standardization products are published by BSI Standards Limited.British Standards Institution (BSI)About usWe bring together business, industry, government, consumers, innovators and others to shape their combined experience and expertise into s
48、tandards -based solutions.The knowledge embodied in our standards has been carefully assembled in a dependable format and refined through our open consultation process. Organizations of all sizes and across all sectors choose standards to help them achieve their goals.Information on standardsWe can
49、provide you with the knowledge that your organization needs to succeed. Find out more about British Standards by visiting our website at or contacting our Customer Services team or Knowledge Centre.Buying standardsYou can buy and download PDF versions of BSI publications, including British and adopted European and international standards, through our website at where hard copies can also
