1、AMERICAN NATIONAL STANDARDRESONANCE METHODFOR MEASURINGTHE DYNAMIC MECHANICALPROPERTIES OF VISCOELASTICMATERIALSAccredited Standards Committee S2, Mechanical Vibration and ShockStandards SecretariatAcoustical Society of America120 Wall Street, 32nd FloorNew York, New York 10005-3993ANSI S2.22-1998AN
2、SIS2.22-1998Reaffirmed by ANSI July 31, 2002 Reaffirmed by ANSI July 5, 2007 Reaffirmed by ANSI August 27, 2012 The American National Standards Institute, Inc. (ANSI) is the na-tional coordinator of voluntary standards development and the clear-ing house in the U.S. for information on national and i
3、nternationalstandards.The Acoustical Society of America (ASA) is an organization of sci-entists and engineers formed in 1929 to increase and diffuse theknowledge of acoustics and to promote its practical applications.American National StandardResonance Method for Measuring theDynamic Mechanical Prop
4、erties ofViscoelastic MaterialsSecretariatAcoustical Society of AmericaApproved 22 June 1998American National Standards Institute, Inc.AbstractThis Standard defines a method for measuring the dynamic mechanical properties of viscoelastic materialsusing longitudinal resonance in a bar-shaped test sam
5、ple. The dynamic mechanical properties areexpressed in terms of the frequency dependence of Youngs modulus and loss factor at a given referencetemperature. The Standard provides information for constructing such equipment and analyzing the resultsobtained.ANSI S2.22-1998AMERICAN NATIONAL STANDARDS O
6、N ACOUSTICSThe Acoustical Society of America (ASA) provides the Secretariat for AccreditedStandards Committees S1 on Acoustics, S2 on Mechanical Vibration and Shock,S3 on Bioacoustics, and S12 on Noise. These committees have wide represen-tation from the technical community (manufacturers, consumers
7、, and general-interest representatives). The standards are published by the Acoustical Society ofAmerica through the American Institute of Physics as American National Stan-dards after approval by their respective standards committees and the AmericanNational Standards Institute.These standards are
8、developed and published as a public service to providestandards useful to the public, industry, and consumers, and to Federal, State,and local governments.Each of the Accredited Standards Committees operating in accordance with pro-cedures approved by American National Standards Institute (ANSI) is
9、responsiblefor developing, voting upon, and maintaining or revising its own standards. TheASA Standards Secretariat administers committee organization and activity andprovides liaison between the Accredited Standards Committees and ANSI. Afterthe standards have been produced and adopted by the Accre
10、dited StandardsCommittees, and approved as American National Standards by ANSI, the ASAStandards Secretariat arranges for their publication and distribution.An American National Standard implies a consensus of those substantially con-cerned with its scope and provisions. Consensus is established whe
11、n, in thejudgment of the ANSI Board of Standards Review, substantial agreement hasbeen reached by directly and materially affected interests. Substantial agreementmeans much more than a simple majority, but not necessarily unanimity. Consen-sus requires that all views and objections be considered an
12、d that a concertedeffort be made towards their resolution.The use of American National Standards is completely voluntary. Their existencedoes not in any respect preclude anyone, whether he or she has approved thestandards or not, from manufacturing, marketing, purchasing, or using products,processes
13、, or procedures not conforming to the standards.NOTICE: This American National Standard may be revised or withdrawn at anytime. The procedures of the American National Standards Institute require thataction be taken periodically to reaffirm, revise, or withdraw this Standard.Standards SecretariatAco
14、ustical Society of America120 Wall Street, 32nd FloorNew York, New York 10005-3993USATelephone: 11 212 248 0373Telefax: 11 212 248 0146E-mail: asastdsaip.orgInternet: http:/asa.aip.org 1998 by the Acoustical Society of America. This Standard may not be reproduced inwhole or in part in any form for s
15、ale, promotion, or any commercial purpose, or any purposenot falling within the provisions of the Copyright Act of 1976, without prior written permissionof the publisher. For permission, address a request to the Standards Secretariat of theAcoustical Society of America.ContentsPageForeword ii0 Intro
16、duction 11 Scope, purpose, and applications . 11.1 Scope . 11.2 Purpose . 11.3 Applications 12 Informative references . 13 Definitions . 13.1 Youngs modulus . 13.2 Loss factor . 13.3 Fast Fourier transform . 13.4 Frequency response function . 23.5 Time-temperature superposition 23.6 Shift factor . 2
17、3.7 Glass transition temperature . 24 Test equipment . 24.1 Electromagnetic shaker 24.2 Accelerometers . 24.3 Charge amplifiers . 24.4 Test stand . 24.5 Environmental chamber . 24.6 Dual channel spectrum analyzer 34.7 Computer 35 Operating procedures . 35.1 Sample preparation and mounting 35.2 Data
18、acquisition 35.3 Temperature cycle 46 Analysis of results 56.1 Modulus and loss factor . 56.2 Time-temperature superposition 56.3 Data presentation . 6Figures1 Schematic diagram of resonance apparatus . 22 Typical acceleration ratio (solid line) and phase (dashed line)vs. frequency . 4iForewordThis
19、Foreword is for information only, and is not a part of ANSI S2.22-1998 AmericanNational Standard Resonance Method for Measuring the Dynamic Mechanical Properties ofViscoelastic Materials.This Standard was developed under the jurisdiction of Accredited Standards Com-mittee S2, Mechanical Vibration an
20、d Shock, which has the following scope:Standards, specifications, methods of measurement and test terminology in thefields of mechanical vibration and shock and condition monitoring and diagnos-tics of machines, but excluding those aspects which pertain to biological safety,tolerance, and comfort.At
21、 the time this Standard was submitted to Accredited Standards Committee S2,Mechanical Vibration and Shock, for approval, the membership was as follows:D. J. Evans, ChairR. F. Taddeo, Vice ChairA. Brenig, SecretaryAcoustical Society of America D.J.EvansR. F. Taddeo (Alt.)Boyce Engineering Internation
22、al M.P.BoyceC. Meher-Homji (Alt.)Bruel Tele-phone: 11 212 248 0373; Fax 11 212 248 0146.iiiAmerican National StandardResonance Method forMeasuring the DynamicMechanical Properties ofViscoelastic Materials0 IntroductionViscoelastic materials are used extensively to re-duce vibration amplitudes in str
23、uctural systemsthrough dissipation of energy (damping) or isola-tion of components, and in acoustic applicationswhich require a modification of the reflection,transmission, or absorption of energy. Such sys-tems often require specific dynamic mechanicalproperties in order to function in an optimum m
24、an-ner. Energy dissipation is due to interactions onthe molecular scale and can be measured in termsof the lag between stress and strain in the mate-rial. The viscoelastic properties, modulus and lossfactor, of most materials depend on frequency,temperature, and strain amplitude. The choice of aspec
25、ific material for a given application determinesthe system performance. This Standard applies tothe linear behavior observed at small strain ampli-tudes.1 Scope, purpose, and applications1.1 ScopeThis Standard defines a procedure for measure-ment and analysis of the dynamic properties ofviscoelastic
26、 materials using a resonance method.The Standard applies to materials used in soundand vibration damping systems operating at fre-quencies from a fraction of a hertz to about 20kHz.1.2 PurposeThe purpose of this Standard is to assist users ofthis method in setting up the measurement equip-ment, perf
27、orming the measurements, and analyz-ing the resultant data. A further purpose is to pro-mote uniformity in the use of this method.1.3 ApplicationsThis Standard applies to the use of the resonancemethod to evaluate material characteristics for re-search, quality control, and materials selection.2 Inf
28、ormative references1 ASTM D 792-91, Standard Test Method forDensity and Specific Gravity (Relative Density) ofPlastics by Displacement.2 T. Pritz, Transfer Function Method for Investi-gating the Complex Modulus of Acoustic Materials:Rod-like Specimen, J. Sound and Vibration 81,359-376 (1982).3 W. M.
29、 Madigosky and G. F. Lee, Improvedresonance technique for material characteriza-tion, J. Acoust. Soc. Am. 73, 1374-1377 (1983).4 J. L. Buchanan, Numerical solution for the dy-namic moduli of a viscoelastic bar, J. Acoust.Soc. Am. 81, 1775-1786 (1987).5 J. D. Ferry, Viscoelastic Properties of Poly-me
30、rs, 3rd ed., Wiley, New York, 1980, pp 264-320.3 DefinitionsFor the purposes of this Standard, the followingdefinitions apply:3.1 Youngs modulus. Quotient of tensilestress, in pascals, to resulting tensile strain, orfractional change in length. Youngs modulus forviscoelastic materials is a complex q
31、uantity withsymbol E *, having a real part E 8 and an imaginarypart E 9. Unit, pascal (Pa).NOTE Physically, the real component of Youngsmodulus represents elastic stored mechanical en-ergy. The imaginary component is a measure ofmechanical energy loss. See 3.2.3.2 loss factor. Ratio of the imaginary
32、 part ofthe Youngs modulus of a material to the real partof the Youngs modulus (the tangent of the argu-ment of the complex Youngs modulus).NOTE When there is energy loss in a material, thestrain lags the stress by a phase angle, d. The lossfactor is equal to tan d.3.3 fast Fourier transform. An alg
33、orithm or cal-culation procedure for obtaining the discrete Fou-rier transform (DFT) with a greatly reduced num-ber of arithmetic operations compared with a directevaluation.AMERICAN NATIONAL STANDARD ANSI S2.22-19981 1998 Acoustical Society of America3.4 frequency response function. For the pur-pos
34、es of this Standard, the quotient of the crossspectrum of the signals produced by accelerom-eters at the output and input of a sample under testto the autospectrum of the signal produced by anaccelerometer at the input to the test sample.NOTE The frequency response function is some-times known as th
35、e transfer function. It is actually aspecial case of the transfer function.3.5 timetemperature superposition. Prin-ciple by which, for viscoelastic materials, time andtemperature are equivalent to the extent that dataat one temperature can be superimposed upondata taken at different temperature mere
36、ly by shift-ing the data curves along the frequency axis.3.6 shift factor. Measure of the amount of shiftalong the logarithmic axis of frequency for one setof constant temperature data to superimpose uponanother set of data.3.7 glass transition temperature. Tempera-ture at which a viscoelastic mater
37、ial changes statefrom glassy to rubbery. The glass transition tem-perature is typically determined from the inflectionpoint of a specific heat vs. temperature plot andrepresents an intrinsic material property. Symbol:Tg. Unit, degrees celsius (C).NOTE Tgis not the peak in the dynamic mechani-cal los
38、s factor. That peak occurs at a higher tempera-ture than Tgand varies with the measurement fre-quency, hence is not an intrinsic material property.4 Test equipmentA schematic diagram of the test equipment isshown in figure 1.4.1 Electromagnetic shakerAn electromagnetic shaker, with the followingspec
39、ifications, is required to provide a driving forcefor the test specimen:(1) frequency range: 25 Hz to 18 kHz;(2) force rating: .5N.4.2 AccelerometersPiezoelectric accelerometers, with the followingspecifications, are required to measure the inputand output acceleration of the test sample:(1) frequen
40、cy range: 25 Hz to 18 kHz;(2) charge sensitivity: .1 pC/gn;(3) mass: , 1g.NOTE The accelerometer mass limitation excludesits connecting electric cable.4.3 Charge amplifiersCharge amplifiers with a sensitivity of no less than1 mV/pC are required to amplify the output signalfrom the accelerometers.4.4
41、 Test standA test stand is required to suspend the shaker andthe test sample in a vertical position.4.5 Environmental chamberAn environmental chamber is required to cool thetest sample to a temperature below room tempera-ture, maintain this temperature until the samplehas reached equilibrium, then b
42、e capable of in-creasing the temperature of the sample in incre-ments of 5 C. The chamber shall be capable ofoperating over the temperature range from 260 Cto 70 C and be controllable within 0.5 C.NOTES1 The required temperature range is appropriate fora viscoelastic material having a glass transiti
43、on tem-perature greater than 245 C. Materials with lowerglass transition temperatures will require a lowerstarting temperature point.2 Some materials are sensitive to humidity and itmay be desirable to control or at least record therelative humidity in the chamber.Figure 1 Schematic diagram of reson
44、anceapparatus.ANSI S2.22-19982 1998 Acoustical Society of America4.6 Dual-channel spectrum analyzerA dual channel spectrum analyzer, with the follow-ing capabilities, is required to drive the shaker andanalyze the accelerometer output signals:(1) random noise source;(2) two input channels;(3) FFT, f
45、requency response function, and co-herence analysis;(4) rms signal averaging;(5) frequency range: 25 Hz to 18 kHz;(6) dynamic range: 32 dB;(7) band selectable zoom FFT resolution: 0.1Hz.4.7 ComputerA computer is required to automate the data ac-quisition and analyses. The computer should beeasy to p
46、rogram and operate.5 Operating procedures5.1 Sample preparation and mountingMold test specimens into the shape of a bar. Themold shall be at least 150 mm long, with squarelateral dimensions of 6.35 mm, 1 0 mm, 20.13mm. Trim the molded specimen of all flash and cutto a length of 102 mm 6 13 mm, using
47、 a razorblade. Square the ends of the bar by machining.After machining, the bar shall be able to stand up-right on either end without support. Square endsare required to obtain a good bond between thetest specimen and mounting blocks.NOTES1 A circular cross-section of about 6.35 mm diam-eter is also
48、 acceptable instead of a square bar.2 Lengths no less than one-half the 102 mm speci-fied or no more than twice that length are also ac-ceptable. Shorter lengths produce resonances athigher frequencies and can lead to fewer peaksbeing observed due to higher absorption at higherfrequencies. Longer le
49、ngths produce resonances atlower frequencies and can lead to problems due tobending of the longer specimen.Three properties of the specimen, required in theanalyses, shall be measured before bonding thespecimen to the mounting blocks. Determine, by amicrometer, the length in meters to four significantdigits. Determine, by a balance, the mass of thespecimen in kilograms to four significant digits. De-termine the density of the specimen in kg/m3by awater displacement technique.NOTE A method such as ASTM D 792, StandardTest Method for S
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