1、Designation: D 5992 96 (Reapproved 2006)e1Standard Guide forDynamic Testing of Vulcanized Rubber and Rubber-LikeMaterials Using Vibratory Methods1This standard is issued under the fixed designation D 5992; the number immediately following the designation indicates the year oforiginal adoption or, in
2、 the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.e1NOTESection 3 editorially corrected in July 2007.1. Scope1.1 This guide covers dynamic testi
3、ng of vulcanized rubberand rubber-like (both hereinafter 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 fl
4、exing method, to the measure-ment of dynamic modulus.1.2 This guide describes a variety of vibratory methods fordetermining dynamic properties, presenting them as options,not as requirements. The methods involve free resonant vibra-tion, and forced resonant and nonresonant vibration. In thelatter tw
5、o cases the input is assumed to be sinusoidal.1.3 While the 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 temperature
6、s from 70C to +200C (100F to+400F) and for frequencies from 0.01 to 100 Hz. Not allinstruments and methods will accommodate the entire ranges.1.5 When employed for the measurement of dynamic modu-lus, the methods are intended for materials having complexmoduli in the range from 100 to 100 000 kPa (1
7、5 to 15 000 psi)and damping angles from 0 to 90. Not all instruments andmethods 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 rotational
8、mode, substituting “torque” and “angular deflection” for“force” 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 onRes
9、ults9Report 10Mechanical and Instrumentation Factors Influencing DynamicMeasurementAnnex A1Guide to Further Reading Appendix X1Double-Shear SpecimensDerivation of Equations and De-scriptions of SpecimensAppendix X2Torsion SpecimensDerivation of Equations and Descrip-tions of SpecimensAppendix X3Comp
10、ression/Tension SpecimensDerivation of Equationsand Descriptions of SpecimensAppendix X4Free Resonant VibrationEquations for Log Decrement andStiffnessAppendix X5Obtaining Loss Factor and Elastic Stiffness from Transmissi-bility CurvesAppendix X61.8 The values stated in SI units are to be regarded a
11、s thestandard. The values given in parentheses are for informationonly.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 and health practices and determine th
12、e applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 945 Test Methods for Rubber Properties in Compressionor Shear (Mechanical Oscillograph)D 1566 Terminology Relating to Rubber2.2 ISO Document:3ISO 2856 ElastomersGeneral Requirements for DynamicTestin
13、g1This guide is under the jurisdiction of ASTM Committee D11 on Rubber andis the direct responsibility of Subcommittee D11.14 on Time and Temperature-Dependent Physical Properties.Current edition approved July 1, 2006. Published September 2006. Originallyapproved in 1996. Last previous edition appro
14、ved in 2001 as D 5992 96 (2001)e1.2For referenced ASTM standards, visit the ASTM website, 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.3Available from American Na
15、tional Standards Institute, 25 W. 43rd St., 4thFloor, New York, NY 10036.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.2.3 DIN Document:4DIN 53 513 Determination of viscoelastic properties ofelastomers on exposure to forced vibrati
16、on at non-resonant frequencies3. Terminology3.1 DefinitionsThe following terms are listed in relatedgroups rather than alphabetically (see also TerminologyD 1566).3.1.1 delta, d, nin the measurement of rubber properties,the symbol for the phase angle by which the dynamic forceleads the dynamic defle
17、ction; mathematically true only whenthe two dynamic waveforms are sine waves (Synonym lossangle).3.1.2 tandel, tand, nmathematical tangent of the phaseangle delta (d); pure numeric; often written spaced: tan del;often written using “delta”: tandelta, tan delta (Synonymlossfactor).3.1.3 phase angle,
18、nin general, the angle by which onesine wave leads another; units are either radians or degrees.3.1.4 loss angle, nsynonym for delta (d).3.1.5 loss factor, nsynonym for tandel (tand)(h).3.1.6 damping, nthat property of a material or system thatcauses it to convert mechanical energy to heat when subj
19、ectedto deflection; in rubber the property is caused by hysteresis; insome types of systems it is caused by friction or viscousbehavior.3.1.7 hysteresis, nthe phenomenon taking place withinrubber undergoing strain that causes conversion of mechanicalenergy to heat, and which, in the “rubbery” region
20、 of behavior(as distinct from the glassy or transition regions), producesforces essentially independent of frequency. (See also hyster-etic and viscous.)3.1.8 hysteresis loss, nper cycle, the amount of mechani-cal energy converted to heat due to straining; mathematically,the area within the hysteres
21、is loop, having units of the productof force and length.3.1.9 hysteresis loop, nthe Lissajous figure, or closedcurve, formed by plotting dynamic force against dynamicdeflection for a complete cycle.3.1.10 hysteretic, adjas a modifier of damping, descrip-tive of that type of damping in which the damp
22、ing force isproportional to the amplitude of motion across the dampingelement.3.1.11 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-
23、filleddashpot damper.3.1.12 equivalent viscous damping, c, nat a given fre-quency, the quotient of F9(1) divided by the velocity of theimposed deflection.c 5 F91! / vX*1! (1)3.1.12.1 DiscussionThe equivalent viscous damping isuseful when dealing with equations in many texts on vibration.It is an equ
24、ivalent only at the frequency for which it iscalculated.3.1.13 dynamic, adjin testing, descriptive of a force ordeflection function characterized by an oscillatory or transientcondition, as contrasted to a static test.3.1.14 dynamic, adjas a modifier of stiffness or modulus,descriptive of the proper
25、ty measured in a test employing anoscillatory force or motion, usually sinusoidal.3.1.15 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.3.1.16
26、static, adj (2)in testing, descriptive of a test inwhich force or deflection is applied and then is truly unchang-ing over the duration of the test, often as the mean value of adynamic test condition.3.1.17 static, adj (3)as a modifier of stiffness or modulus,descriptive of the property measured in
27、a test performed at aslow constant rate.3.1.18 stiffness, nthat property of a specimen that 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).3.1.19
28、 modulus, nthe ratio of stress to strain; that propertyof a material which, together with 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 complexforc
29、e relative to that of deflection. (See also complex, elastic,damping.)3.1.20 complex, adjas 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 asr
30、eference.3.1.21 elastic, adjas a modifier of dynamic force, descrip-tive of that component 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 (8) as a superscrip
31、t symbol, as F8.3.1.22 damping, adjas a modifier of dynamic force, de-scriptive of that component of complex force leading dynamicdeflection by 90 degrees, and that is responsible for theconversion of mechanical energy to heat; denoted by thedouble prime (9) as a superscript symbol, as F9.3.1.23 sto
32、rage, adjas a modifier of energy, descriptive ofthat component of energy absorbed by a strained elastomer 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.3.1.24 Fourier anal
33、ysis, nin mathematics, analysis of aperiodic time varying function that produces an infinite seriesof sines and cosines consisting of a fundamental and integer4Available from Deutsches Institut fur Normung, Burggrafenstr 4-7, 1 Berlin 30,Germany.D 5992 96 (2006)e12harmonics which, if added together,
34、 would recreate the originalfunction; named after the French mathematician Joseph Fou-rier, 17681830.3.1.25 shear, adjdescriptive of properties measured usinga specimen deformed in shear, for example, shear modulus.3.1.26 bonded, adjin describing a test specimen, one inwhich the elastomer to be test
35、ed 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 theelastomer.3.1.27 unbonded, adjin describing a test specimen, one inwhich the elastomer is mold
36、ed or cut to shape, but thatotherwise demands that forces be applied directly to theelastomer.3.1.28 bond area, nin describing a bonded test specimen,the cemented area between elastomer and high-modulus attach-ment member.3.1.29 contact area, nin an unbonded specimen, that areain contact with a high
37、-modulus fixture, and through whichapplied forces pass; may or may not be constant, and iflubricated, may deliberately be allowed to change.3.1.30 lubricated, adjin describing an elastomeric testspecimen having at least two plane parallel faces and to betested in compression, one in which the plane
38、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 the specimen to expand in area as the platens aremoved closer together.3.1.31 Mullins Effect,
39、 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, depend-ing on the nature of the material. (See also preflex effect.)3.1.32 preflex effect, nthe
40、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.) (Alsocalled strain history effect.)3.1.33 undamped natural frequency, nin a single-degree-of-fr
41、eedom resonant spring-mass-damper system, that naturalfrequency calculated using the following equation:fn5 SQRT K8/M! (2)where:K8 = the elastic stiffness of the spring, andM = the mass.3.1.34 transmissibility, nin the measurement of forcedresonant vibration, the complex quotient of response divided
42、by input; may be absolute or relative.3.1.35 absolute, adjin the measurement of vibration,aquantity measured relative to the earth as reference.3.1.36 relative, adjin the measurement of vibration,aquantity measured relative to another body as reference.3.1.37 LVDT, nabbreviation for “Linear Variable
43、 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 free to move along the axis that inducesa signal proportional to the distance from the ce
44、nter 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).3.1.38 mobility analysis, nthe science of analysis ofmechanical systems employing a vector quantity called “mo-bility
45、,” characteristic of lumped constant mechanical elements(mass, stiffness, damping), and equal in magnitude to the forcethrough the element divided by the velocity across the element.3.1.39 impedance analysis, nthe science of analysis ofmechanical systems employing a vector quantity called “im-pedanc
46、e,” characteristic of lumped constant mechanical ele-ments (mass, stiffness, damping), and equal in magnitude to thevelocity across the element divided by the force through theelement.3.1.39.1 DiscussionMobility analysis is sometimes easierto employ than impedance because mechanical circuit dia-gram
47、s 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 i
48、s to the number or “order” of the harmonicobtained through Fourier analysis (seeAppendix X2). Thus, allof the parameters indicated as (1) are obtained from thefundamental, or first, harmonic. A second harmonic from thecomplex force would be denoted as F*(2), etc. It should benoted that each harmonic
49、 has a phase angle associated with it.In the case of the fundamental, it is the loss angle (d). Thephase angles become important for the higher harmonics if thereverse Fourier transform is employed to reconstitute data inthe time domain.3.2.1.2 Three superscripts are used: the asterisk (*), thesingle prime (8), and the double prime (9). This guide discussesdynamic motion and force. As raw data, each is a “complex”parameter, denoted by the asterisk. In this guide force isreferenced to motion for its phase. The component of
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