DIN ISO 11093-8-2016 Paper and board - Testing of cores - Part 8 Determination of natural frequency and flexural modulus by experimental modal analysis (ISO 11093-8 2012 + Cor 1 20.pdf

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1、August 2016 English price group 8No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS 85.080.30!%X?“2535628www.din.deDIN

2、 ISO 11093-8Paper and board Testing of cores Part 8: Determination of natural frequency and flexural modulus by experimental modal analysis (ISO 110938:2012 + Cor. 1:2012),English translation of DIN ISO 11093-8:2016-08Papier und Pappe Prfung von Wickelkernen aus Hlsenkarton Teil 8: Bestimmung der Ei

3、genfrequenz und des Elastizittsmoduls durch experimentelle Schwingungsanalyse (ISO 110938:2012 + Cor. 1:2012),Englische bersetzung von DIN ISO 11093-8:2016-08Papier et carton Essais des mandrins Partie 8: Dtermination de la frquence propre et du module de flexion par analyse modale exprimentale (ISO

4、 110938:2012 + Cor. 1:2012),Traduction anglaise de DIN ISO 11093-8:2016-08SupersedesDIN ISO 110938:201309www.beuth.deDocument comprises 11 pagesDTranslation by DIN-Sprachendienst.In case of doubt, the German-language original shall be considered authoritative.07.16 A comma is used as the decimal mar

5、ker. Contents PageNational foreword . 31 Scope . 52 Normative references 53 Terms and definitions . 54 Principle 65 Apparatus . 65.1 Test-piece suspension . 65.2 The experimental modal analysis system 66 Test piece 66.1 Sampling . 66.2 Test-piece size 66.3 Conditioning 77 Procedure. 98 Calculation 9

6、8.1 Calculation of the flexural modulus 98.2 Calculation of the rotational speed factor 109 Test report 10Bibliography .11National Annex NA (informative) Bibliography iv42DIN ISO 11093-8:2016-08 DIN ISO 11093-8:2016-08 3 National foreword This document (ISO 11093-8:2012 + Cor. 1:2012) has been prepa

7、red by Technical Committee ISO/TC 6 “Paper, board and pulps (Secretariat: SCC, Canada). The responsible German body involved in its preparation was DIN-Normenausschuss Papier, Pappe und Faserstoff (DIN Standards Committee Paper, Board and Pulps), Working Committee NA 074-01-41 AA Zylindrische Wickel

8、kerne aus Papier und Pappe fr Flchengebilde. ISO 11093-8:2012 + Cor. 1:2012 has been adopted without modifications. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. DIN and/or DKE shall not be held responsible for identifying any o

9、r all such patent rights. The DIN Standards corresponding to the International Standards referred to in this document are as follows: ISO 11093-1 DIN ISO 11093-1 ISO 11093-2 DIN ISO 11093-2 ISO 11093-3 DIN ISO 11093-3 ISO 11093-7 DIN ISO 11093-7 DIN ISO 11093 consists of the following parts, under t

10、he general title Paper and board Testing of cores: Part 1: Sampling Part 2: Conditioning of test samples Part 3: Determination of moisture content using the oven drying method Part 4: Measurement of dimensions Part 5: Determination of characteristics of concentric rotation Part 6: Determination of b

11、ending strength by the three-point method Part 7: Determination of flexural modulus by the three-point method Part 8: Determination of natural frequency and flexural modulus by experimental modal analysis Part 9: Determination of flat crush resistance Amendments This standard differs from DIN ISO 11

12、093-8:1998-03 as follows: a) the standard has been brought in line with the current rules of presentation; b) (German version only) in the main title, the word “Hlse” has been replaced by “Wickelkern” (core); c) the definition of “rotational speed factor“ has been added; d) tolerances for the test p

13、iece size have been included; e) formula (5) for the calculation of the rotational speed factor has been added; f) the standard has been adopted as a DIN ISO Standard without any modification. Compared with DIN ISO 11093-8:2013-09, the following corrections have been made: a) Figure 1 has been corre

14、cted; b) Figure 2 has been corrected. Previous editions DIN ISO 11093-8: 1998-03, 2013-09 National Annex NA (informative) Bibliography DIN ISO 11093-1, Paper and board Testing of cores Part 1: Sampling DIN ISO 11093-2, Paper and board Testing of cores Part 2: Conditioning of test samples DIN ISO 110

15、93-3, Paper and board Testing of cores Part 3: Determination of moisture content using the oven drying method DIN ISO 11093-7, Paper and board Testing of cores Part 7: Determination of flexural modulus by the three-point method 4DIN ISO 11093-8:2016-08 Paper and board Testing of cores Part 8: Determ

16、ination of natural frequency and flexural modulus by experimental modal analysis1 ScopeThis part of ISO 11093 specifies a method for the determination of the flexural modulus by using experimentally measured natural frequencies in the free-free mode of transverse vibration of cylindrical paper and b

17、oard 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 the three-point method, see ISO 11093-7.2 Norma

18、tive referencesThe following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 11093-1, Paper and board Testin

19、g 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 using the oven drying method3 Terms and definitionsFor the purposes of this document, the following ter

20、ms and definitions apply.3.1natural frequencyf1first frequency which is the lowest natural frequency a structure vibrates in, depending on its material, shape and supporting system, when an impulse is applied to it3.2flexural modulusEmaterial property which, together with core dimensions, describes

21、the resistance of the core to bending deflection5DIN ISO 11093-8:2016-08 3.3rotational speed factorSfcore E-modulus divided by its density (E/) which can be used to estimate vibration performance of coresNOTE 1 Cores with equal dimensions, eccentricity and speed factor deliver at identical chucking

22、conditions an equal resonance frequencyNOTE 2 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 Timoshenkos beam theory for isotropic materials is applied in evaluating transverse vibration. In t

23、his 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 direction. The flexural modulus is calculated as described in 8.1.5 Apparatus5.1 Test-piece suspension

24、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 wire and hanging with its axis in the vertical direction (see Figure 1). The minimum length of th

25、e 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 mass of the test piece. The angle (see Figure 2) should be more than 45. The distance of the fixing

26、screw from the edge of the core should be 5 mm to 10 mm.5.2 The experimental modal analysis systemThe first natural frequency is measured with a signal analyser. The test piece is impacted by a hammer in the direction (Z-direction) perpendicular to the plane of the support wires (XY-plane) (see Figu

27、re 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 be 8 mV/g to 100 mV/g; the frequency range limit of the accelerometer shall be 0,1 Hz to 10 000 Hz

28、. 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 shall be taken in accordance with ISO 11093-1, but it has to be ensured that the core is not damaged

29、.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 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.Regardin

30、g the dimensions of the test piece, the following tolerances are specified:6DIN ISO 11093-8:2016-08 length of the core L: 1 mm; outer diameter of the core 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 moistu

31、re 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 moisture content shall be equal to that specified for the lot.7DIN ISO 11093-8:2016-08 Dimensions in millimetresKey1 Support wire2 Clamps3 Test piece

32、4 Hammer5 AccelerometerFigure 1 Schematic drawing of the test8DIN ISO 11093-8:2016-08 Dimensions in millimetresKey1 Support wire2 Clamps3 Test boltFigure 2 Schematic drawing of the test-piece supension7 ProcedureCarry out the test under the same atmospheric conditions as those used to condition the

33、test piece.Impact the test piece in the Z-direction in the 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 f1is used in Formula (1)

34、 to calculate the flexural modulus of each tested test piece.8 Calculation8.1 Calculation of the flexural modulusThe flexural modulus E, in megapascals, is calculated by using Formula (1) :EfmLQL= 788108 124,L(1)wheref1is the natural frequency of the first order, expressed in hertz;mLis the length-r

35、elated mass, expressed in kilograms per metre;L is the length of the core, in millimetres;Q is the dimensionless coefficient.N1)National footnote: Formula (1) given in the original ISO document is incorrect. It should correctly read: = 7,88108 12L4N1)“ 9DIN ISO 11093-8:2016-08 The second moment of i

36、nertia, I (mm4), of the core cross section is calculated according to Formula (2):IDd= pi6444() (2)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)w

37、here A is the area of the core cross-direction, in mm2, calculated according to Formula (4).ADd=pi()224(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 den

38、sity, expressed in kilograms per cubic metre.NOTE can be calculated as mass divided by volume.9 Test reportThe test report shall include the following information:a) a reference to this part of ISO 11093;b) type and designation of the cores tested;c) place and date of sampling;d) place and date of t

39、esting;e) number of test pieces tested;f) core dimensions;g) measured moisture content;h) L and f;i) individual and mean values for E ;j) rotational speed factor;k) date and signature;l) any deviation from this part of ISO 11093 that may have affected the results.10DIN ISO 11093-8:2016-08 Bibliography1 ISO 11093-7, Paper and board Testing of cores Part 7: Determination of flexural modulus by the three-point method11DIN ISO 11093-8:2016-08