1、Designation: D5992 96 (Reapproved 2018)Standard Guide forDynamic Testing of Vulcanized Rubber and Rubber-LikeMaterials Using Vibratory Methods1This standard is issued under the fixed designation D5992; the number immediately following the designation indicates the year oforiginal adoption or, in the
2、 case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide covers dynamic testing of vulcanized rubberand rubber-like (both hereinafter
3、 termed “rubber” or “elasto-meric”) materials and products, leading from the definitions ofterms used, through the basic mathematics and symbols, to themeasurement of stiffness and damping, and finally through theuse of specimen geometry and flexing method, to the measure-ment of dynamic modulus.1.2
4、 This guide describes a variety of vibratory methods fordetermining dynamic properties, presenting them as options,not as requirements. The methods involve free resonantvibration, and forced resonant and nonresonant vibration. Inthe latter two cases the input is assumed to be sinusoidal.1.3 While th
5、e methods are primarily for the measurement ofmodulus, a material property, they may in many cases beapplied to measurements of the properties of full-scale prod-ucts.1.4 The methods described are primarily useful over therange of temperatures from 70C to +200C (100F to+400F) and for frequencies fro
6、m 0.01 to 100 Hz. Not allinstruments and methods will accommodate the entire ranges.1.5 When employed for the measurement of dynamicmodulus, the methods are intended for materials having com-plex moduli in the range from 100 to 100 000 kPa (15 to15 000 psi) and damping angles from 0 to 90. Not allin
7、struments and methods will accommodate the entire ranges.1.6 Both translational and rotational methods are described.To simplify generic descriptions, the terminology of translationis used. The subject matter applies equally to the rotationalmode, substituting “torque” and “angular deflection” for“f
8、orce” and “displacement.”1.7 This guide is divided into sections, some of whichinclude:SectionTerminology and Symbols 3Factors Influencing Dynamic Measurement 7Test Methods and Specimens 8Nonresonant Analysis Methods and Their Influence onResults9Report 10Mechanical and Instrumentation Factors Influ
9、encing DynamicMeasurementAnnex A1Guide to Further Reading Appendix X1Double-Shear SpecimensDerivation of Equations andDescriptions of SpecimensAppendix X2Torsion SpecimensDerivation of Equations andDescriptions of SpecimensAppendix X3Compression/Tension SpecimensDerivation of Equationsand Descriptio
10、ns of SpecimensAppendix X4Free Resonant VibrationEquations for Log Decrement andStiffnessAppendix X5Obtaining Loss Factor and Elastic Stiffness fromTransmissibility CurvesAppendix X61.8 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informati
11、ononly.1.9 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety, health, and environmental practices and deter-mine the applicability of regulatory limitations prior
12、 to use.1.10 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBa
13、rriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2D945 Test Methods for Rubber Properties in Compression orShear (Mechanical Oscillograph)D1566 Terminology Relating to Rubber1This guide is under the jurisdiction of ASTM Committee D11 on Rubber andRubber-like Materials and is
14、 the direct responsibility of Subcommittee D11.10 onPhysical Testing.Current edition approved Aug. 1, 2018. Published September 2018. Originallyapproved in 1996. Last previous edition approved in 2011 as D5992 96 (2011).DOI: 10.1520/D5992-96R18.2For referenced ASTM standards, visit the ASTM website,
15、 www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThi
16、s international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (T
17、BT) Committee.12.2 ISO Document:3ISO 2856 ElastomersGeneral Requirements for DynamicTesting2.3 DIN Document:4DIN 53 513 Determination of viscoelastic properties ofelastomers on exposure to forced vibration at non-resonant frequencies3. Terminology3.1 Definitions:3.1.1 Definitions The following terms
18、 are listed in relatedgroups rather than alphabetically (see also TerminologyD1566).3.1.2 delta, , n in the measurement of rubber properties,the symbol for the phase angle by which the dynamic forceleads the dynamic deflection; mathematically true only whenthe two dynamic waveforms are sine waves (S
19、ynonym lossangle).3.1.3 tandel, tan,nmathematical tangent of the phaseangle delta (); pure numeric; often written spaced: tan del;often written using “delta”: tandelta, tan delta (Synonymlossfactor).3.1.4 phase angle, nin general, the angle by which onesine wave leads another; units are either radia
20、ns or degrees.3.1.5 loss angle, nsynonym for delta ().3.1.6 loss factor, nsynonym for tandel (tan)().3.1.7 damping, nthat property of a material or system thatcauses it to convert mechanical energy to heat when subjectedto deflection; in rubber the property is caused by hysteresis; insome types of s
21、ystems it is caused by friction or viscousbehavior.3.1.8 hysteresis, nthe phenomenon taking place withinrubber undergoing strain that causes conversion of mechanicalenergy to heat, and which, in the “rubbery” region of behavior(as distinct from the glassy or transition regions), producesforces essen
22、tially independent of frequency. (See also hyster-etic and viscous.)3.1.9 hysteresis loss, nper cycle, the amount of mechani-cal energy converted to heat due to straining; mathematically,the area within the hysteresis loop, having units of the productof force and length.3.1.10 hysteresis loop, nthe
23、Lissajous figure, or closedcurve, formed by plotting dynamic force against dynamicdeflection for a complete cycle.3.1.11 hysteretic, adj as a modifier of damping, descrip-tive of that type of damping in which the damping force isproportional to the amplitude of motion across the dampingelement.3.1.1
24、2 viscous, adjas a modifier of damping, descriptiveof that type of damping in which the damping force isproportional to the velocity of motion across the dampingelement, so named because of its derivation from an oil-filleddashpot damper.3.1.13 equivalent viscous damping, c, nat a givenfrequency, th
25、e quotient of F“(1) divided by the velocity of theimposed deflection.c 5 F“1!/X*1! (1)3.1.13.1 DiscussionThe equivalent viscous damping isuseful when dealing with equations in many texts on vibration.It is an equivalent only at the frequency for which it iscalculated.3.1.14 dynamic, adjin testing, d
26、escriptive of a force ordeflection function characterized by an oscillatory or transientcondition, as contrasted to a static test.3.1.15 dynamic, adjas a modifier of stiffness or modulus,descriptive of the property measured in a test employing anoscillatory force or motion, usually sinusoidal.3.1.16
27、 static, adj (1)in testing, descriptive of a test inwhich force or deflection is caused to change at a slow constantrate, within or in imitation of tests performed in screw-operateduniversal test machines.3.1.17 static, adj (2)in testing, descriptive of a test inwhich force or deflection is applied
28、and then is truly unchang-ing over the duration of the test, often as the mean value of adynamic test condition.3.1.18 static, adj (3)as a modifier of stiffness or modulus,descriptive of the property measured in a test performed at aslow constant rate.3.1.19 stiffness, nthat property of a specimen t
29、hat deter-mines the force with which it resists deflection, or the deflec-tion with which it responds to an applied force; may be staticor dynamic (See also complex, elastic, damping.) (Synonymspring rate).3.1.20 modulus, nthe ratio of stress to strain; that propertyof a material which, together wit
30、h the geometry of a specimen,determines the stiffness of the specimen; may be static ordynamic, and if dynamic, is mathematically a vector quantity,the phase of which is determined by the phase of the complexforce relative to that of deflection. (See also complex, elastic,damping.)3.1.21 complex, ad
31、jas a modifier of dynamic force, de-scriptive of the total force; denoted by the asterisk (*) as asuperscript symbol (F*); F* can be resolved into elastic anddamping components using the phase of displacement asreference.3.1.22 elastic, adjas a modifier of dynamic force, descrip-tive of that compone
32、nt of complex force in phase with dynamicdeflection, that does not convert mechanical energy to heat, andthat can return energy to an oscillating mass-spring system;denoted by the single prime () as a superscript symbol, as F.3.1.23 damping, adjas a modifier of dynamic force, de-scriptive of that co
33、mponent of complex force leading dynamicdeflection by 90 degrees, and that is responsible for theconversion of mechanical energy to heat; denoted by thedouble prime (“) as a superscript symbol, as F“.3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY
34、 10036, http:/www.ansi.org.4Available from Beuth Verlag GmbH (DIN- DIN Deutsches Institut furNormung e.V.), Burggrafenstrasse 6, 10787, Berlin, Germany, http:/www.en.din.de.D5992 96 (2018)23.1.24 storage, adjas a modifier of energy, descriptive ofthat component of energy absorbed by a strained elast
35、omer thatis not converted to heat and is available for return to the overallmechanical system; by extension, descriptive of that compo-nent of modulus or stiffness that is elastic.3.1.25 Fourier analysis, nin mathematics, analysis of aperiodic time varying function that produces an infinite seriesof
36、 sines and cosines consisting of a fundamental and integerharmonics which, if added together, would recreate the originalfunction; named after the French mathematician JosephFourier, 17681830.3.1.26 shear, adjdescriptive of properties measured usinga specimen deformed in shear, for example, shear mo
37、dulus.3.1.27 bonded, adjin describing a test specimen, one inwhich the elastomer to be tested is permanently cemented tomembers of much higher modulus for two purposes: (1)toprovide convenient rigid attachment to the test machine, and(2) to define known areas for the application of forces to theelas
38、tomer.3.1.28 unbonded, adjin describing a test specimen, one inwhich the elastomer is molded or cut to shape, but thatotherwise demands that forces be applied directly to theelastomer.3.1.29 bond area, nin describing a bonded test specimen,the cemented area between elastomer and high-modulus attach-
39、ment member.3.1.30 contact area, n in an unbonded specimen, that areain contact with a high-modulus fixture, and through whichapplied forces pass; may or may not be constant, and iflubricated, may deliberately be allowed to change.3.1.31 lubricated, adj in describing an elastomeric testspecimen havi
40、ng at least two plane parallel faces and to betested in compression, one in which the plane parallel faces areseparated from plane parallel platens of the apparatus by alubricant, thereby eliminating, insofar as possible, frictionbetween the elastomer and platens, permitting the contactsurfaces of t
41、he specimen to expand in area as the platens aremoved closer together.3.1.32 Mullins Effect, nthe phenomenon occurring invulcanized rubber whereby the second and succeeding hyster-esis loops exhibit less area than the first, due to breaking ofphysical cross-links; may be permanent or temporary, depe
42、nd-ing on the nature of the material. (See also preflex effect.)3.1.33 preflex effect, nthe phenomenon occurring in vul-canized rubber, related to the Mullins effect, whereby thedynamic moduli at low strain amplitude are less after a historyto high strains than before. (See also Mullins effect.) (Al
43、socalled strain history effect.)3.1.34 undamped natural frequency, nin a single-degree-of-freedom resonant spring-mass-damper system, that naturalfrequency calculated using the following equation:fn5 SQRT K/M! (2)where:K = the elastic stiffness of the spring, andM = the mass.3.1.35 transmissibility,
44、 nin the measurement of forcedresonant vibration, the complex quotient of response dividedby input; may be absolute or relative.3.1.36 absolute, adjin the measurement of vibration,aquantity measured relative to the earth as reference.3.1.37 relative, adjin the measurement of vibration,aquantity meas
45、ured relative to another body as reference.3.1.38 LVDT, nabbreviation for “Linear Variable Differ-ential Transformer,” a type of displacement transducer charac-terized by having a primary and two secondary coils arrangedalong a common axis, the primary being in the center, and amovable magnetic core
46、 free to move along the axis that inducesa signal proportional to the distance from the center of itstravel, and of a polarity determined by the phase of the signalsfrom the two secondary coils. The rotary version is called aRotary Variable Differential Transformer (RVDT).3.1.39 mobility analysis, n
47、the science of analysis of me-chanical systems employing a vector quantity called“mobility,” characteristic of lumped constant mechanical ele-ments (mass, stiffness, damping), and equal in magnitude to theforce through the element divided by the velocity across theelement.3.1.40 impedance analysis,
48、nthe science of analysis ofmechanical systems employing a vector quantity called“impedance,” characteristic of lumped constant mechanicalelements (mass, stiffness, damping), and equal in magnitude tothe velocity across the element divided by the force through theelement.3.1.40.1 DiscussionMobility a
49、nalysis is sometimes easierto employ than impedance because mechanical circuit dia-grams are more intuitively constructed in the mobility system.Either will provide the understanding necessary in analyzingtest apparatus.3.2 Symbols:3.2.1 General Comments:3.2.1.1 Many symbols use parentheses. The (t) denotes afunction of time. When enclosing a number, such as (1) or (2),the reference is to the number or “order” of the harmonicobtained through Fourier analysis (see Appendix X2). Thus, allof the parameters indic
