1、 ANSI/ASA S2.9-2008 (Revision of ANSI S2.9-1976)AMERICAN NATIONAL STANDARD Parameters for Specifying Damping Properties of Materials and System DampingAccredited Standards Committee S2, Mechanical Vibration and Shock Standards Secretariat Acoustical Society of America 35 Pinelawn Road, Suite 114E Me
2、lville, NY 11747-3177ANSI/ASA S2.9-2008 Reaffirmed by ANSI May 28, 2013 The American National Standards Institute, Inc. (ANSI) is the national coordinator of voluntary standards development and the clearinghouse in the U.S.A. for information on national and international standards. The Acoustical So
3、ciety of America (ASA) is an organization of scientists and engineers formed in 1929 to increase and diffuse the knowledge of acoustics and to promote its practical applications. ANSI/ASA S2.9-2008 (Revision of ANSI S2.9-1976) AMERICAN NATIONAL STANDARD Parameters for Specifying Damping Properties o
4、f Materials and System Damping Secretariat Acoustical Society of America Approved June 13, 2008 American National Standards Institute, Inc. Abstract This standard presents the required nomenclature to improve communications among the many technological fields concerned with material damping that are
5、 used for resilient mountings so there will be a clear understanding by both the user and the manufacturer. Since the intention of this standard is to encourage better communication between the manufacturer and the user, the material set forth herein should be regarded as a nomenclature for specifyi
6、ng damping properties of the resilient materials. It is intended to outline, in standardized form, what information should be presented to enable the experienced designer to apply them for selecting the resilient material for machine mountings correctly. Also, the standard defines terminology in a f
7、urther effort to ease the problem of communication between user and manufacturer. AMERICAN NATIONAL STANDARDS ON ACOUSTICS The Acoustical Society of America (ASA) provides the Secretariat for Accredited Standards Committees S1 on Acoustics, S2 on Mechanical Vibration and Shock, S3 on Bioacoustics, S
8、3/SC1 on Animal Bioacoustics, and S12 on Noise. These committees have wide representation from the technical community (manufacturers, consumers, trade associations, organizations with a general interest, and government representatives). The standards are published by the Acoustical Society of Ameri
9、ca as American National Standards after approval by their respective Standards Committees and the American National Standards Institute (ANSI). These standards are developed and published as a public service to provide standards useful to the public, industry, and consumers, and to Federal, State, a
10、nd local governments. Each of the accredited Standards Committees (operating in accordance with procedures approved by ANSI) is responsible for developing, voting upon, and maintaining or revising its own Standards. The ASA Standards Secretariat administers Committee organization and activity and pr
11、ovides liaison between the Accredited Standards Committees and ANSI. After the Standards have been produced and adopted by the Accredited Standards Committees, and approved as American National Standards by ANSI, the ASA Standards Secretariat arranges for their publication and distribution. An Ameri
12、can National Standard implies a consensus of those substantially concerned with its scope and provisions. Consensus is established when, in the judgment of the ANSI Board of Standards Review, substantial agreement has been reached by directly and materially affected interests. Substantial agreement
13、means much more than a simple majority, but not necessarily unanimity. Consensus requires that all views and objections be considered and that a concerted effort be made towards their resolution. The use of an American National Standard is completely voluntary. Their existence does not in any respec
14、t preclude anyone, whether he or she has approved the Standards or not, from manufacturing, marketing, purchasing, or using products, processes, or procedures not conforming to the Standards. NOTICE: This American National Standard may be revised or withdrawn at any time. The procedures of the Ameri
15、can National Standards Institute require that action be taken periodically to reaffirm, revise, or withdraw this Standard. Acoustical Society of America ASA Secretariat 35 Pinelawn Road, Suite 114E Melville, New York 11747-3177 Telephone: 1 (631) 390-0215 Fax: 1 (631) 390-0217 E-mail: asastdsaip.org
16、 2008 by Acoustical Society of America. This standard may not be reproduced in whole or in part in any form for sale, promotion, or any commercial purpose, or any purpose not falling within the provisions of the U.S. Copyright Act of 1976, without prior written permission of the publisher. For permi
17、ssion, address a request to the Standards Secretariat of the Acoustical Society of America. 2008 Acoustical Society of America iContents 1 Scope . 1 2 Standard nomenclature 1 3 Terms and definitions. 1 4 Engineering information of damping parameters for specifying damping properties of resilient mou
18、nting materials 6 4.1 Vibration suppression mounting nomenclature. 6 4.2 Damping mechanisms and magnitudes - Energy dissipation and transport. 9 5 Discussion of standard nomenclature 13 5.1 Classification of nomenclature 13 5.2 Standard nomenclature for unit damping properties of uniform materials 1
19、5 5.3 Standard nomenclature for linear materials 15 5.4 Standard nomenclature for linear and nonlinear materials. 15 5.5 Relations between unit properties of a uniform material and total properties of a uniform specimen . 16 Annex A (normative) Nonstandard damping parameters 17 Annex B (normative) C
20、lassification of system damping test parameters 19 Bibliography. 20 Tables Table 1 Vibration frequency ranges . 7 Table 2 Classification of types of damping phenomena (Adapted from 1) 12 Table 3 Classification of nomenclature for material and specimen damping (Adapted from 1). 14 Figures Figure 1 (a
21、) stress-strain plot for one cycle of harmonically loaded material for steady-state illustrating a hysteresis loop associated with internal damping. (b) elliptical hysteresis loop and its properties 6 Figure 2 Acceptable threshold of sinusoidal vibration for structural damage, machinery vibration, a
22、nd human perception 6. 8 Figure 3 Vibration isolation transmissibility formulas for both force and displacement 6. 9 Figure 4 Single-degree-of-freedom system 16 2008 Acoustical Society of America ii Foreword This Foreword is for information only, and is not a part of the American National Standard A
23、NSI/ASA S2.9-2008 American National Standard Parameters for Specifying Damping Properties of Materials and System Damping. This standard comprises a part of a group of definitions, standards, and specifications for use in mechanical vibration and shock. It was developed and approved by Accredited St
24、andards Committee S2 Mechanical Vibration and Shock, under its approved operating procedures. Those procedures have been accredited by the American National Standards Institute (ANSI). The Scope of Accredited Standards Committee S2 is as follows: Standards, specification, methods of measurement and
25、test, and terminology in the field of mechanical vibration and shock, and condition monitoring and diagnostics of machines, including the effects of exposure to mechanical vibration and shock on humans, including those aspects which pertain to biological safety, tolerance and comfort. This standard
26、is a revision of ANSI S2.9-1976, which has been technically revised. This edition has been restructured and some of the formulas, terms and definitions, and illustrations (figures) have been reviewed and corrected. Additional exhibits, illustrations, and a table have been added to this revision of t
27、he document. This standard is not comparable to any existing ISO Standard. At the time this Standard was submitted to Accredited Standards Committee S2, Mechanical Vibration and Shock for approval, the membership was as follows: R.L. Eshleman, Chair A.T. Herfat, Vice-Chair S.B. Blaeser, Secretary Ac
28、oustical Society of AmericaS.I. Hayek B.E. Douglas (Alt.) Acquip, Inc D. Josefsberg American Industrial Hygiene Association . J.J. Earshen D. Driscoll (Alt.) Association of American Railroads.J. Moller . N. Cooperrider (Alt.) CalnetixL. Hawkins . P. McMullen (Alt.) Caterpillar, Inc.D. Roley Charles
29、M. Salter AssociatesA. Nash Commercial Vehicle Group . L. Mullinix Emerson Electric Copeland Corporation.A.T. Herfat . M. Mezache (Alt.) EndevcoB. Yang 2008 Acoustical Society of America iiiGE Energy R. Bankert Infrared Training Center .G. Orlove R. Madding (Alt.) John Deere .L. DeVries Lord Corpora
30、tion .L. Miller . A. Crockett (Alt.) Mechanical Solutions, Inc. W.D. Marscher . M. Gaydon (Alt.) MIMOSA .K. Bever A. Johnston (Alt.) National Institute for Occupational Safety FAX: 631-390-0217; E-mail: asastdsaip.org. 2008 Acoustical Society of America vIntroduction The user of resilient mountings
31、sometimes cannot select appropriate mounting systems because insufficient technical information is provided by the manufacturer. Consequently, the user must conduct his own experimental evaluation of mountings and perhaps unknowingly duplicate work already performed by the manufacturer. Also, in mil
32、itary and confidential applications, the user cannot be allowed to disclose applicable information which might otherwise facilitate suggestions and recommendations by the mounting manufacturer. Hence, the user many times must acquire considerable proficiency in the art of applying resilient mounting
33、s, and in these instances, he needs appropriate technical information from the manufacturer. Alternatively, some manufacturers of resilient mountings have experience covering a wide variety of mounting applications. The manufacturers, in most instances, are willing to use their background informatio
34、n for solving the users mounting problems. However, it is frequently difficult for the manufacturer to provide this service, because the user has not furnished sufficient information to the manufacturer regarding the application. Meanwhile, communication among different engineering disciplines, whic
35、h often utilize different nomenclature, is generally quite difficult. This is due not only to the large variety of damping parameters used but also to the lack of unique definitions for many well-accepted parameters. AMERICAN NATIONAL STANDARD ANSI/ASA S2.9-2008 2008 Acoustical Society of America 1
36、American National Standard Parameters for Specifying Damping Properties of Materials and System Damping 1 Scope The term “damping“ as used in this Standard is restricted to those properties of a material that are related to the process of cyclic energy dissipation during harmonic vibration. This def
37、inition specifically excludes: energy transfer devices such as dynamic absorbers; external damping processes such as viscous damping, air-damping, or acoustic radiation; and energy dissipation during transient or random vibration. This standard presents the preferred nomenclature (parameters, symbol
38、s, definitions, and mathematical expressions) for specifying the damping properties of uniform materials and uniform specimens, where “uniform“ implies homogeneity on a macroscopic scale. For reference purposes, certain non-standard damping parameters are discussed in Annex A. Also included is a cla
39、ssification of damping test parameters (Annex B). The primary purpose for this standard is to improve communications among the many technological fields concerned with material damping. 2 Standard nomenclature The standard nomenclature for damping in terms of parameters, symbols, and definitions is
40、listed below. Dimensions and units in both SI (Systme International) and English units are given in brackets. Systme International units include force in newtons (N), length in meters (m), and time in seconds (sec), whereas English units include force in pounds (lb), length in inches (in), and time
41、in seconds (sec). For reference purposes, certain nonstandard damping parameters are discussed in Annex A. 3 Terms and definitions 3.1 bulk modulus K the ratio of the change in pressure acting on a volume to the fractional change in volume, or the ratio of the hydrostatic pressure to the volume stra
42、in NOTE 1 K is the bulk modulus of elasticity ML-1T-2 N/m2(lbf/ in2). NOTE 2 Complex bulk modulus of the damping material is defined as: K*= K+ iK“ (for harmonic time dependence), 1i = ML-1T-2 N/m2 (lbf / in2). K“is the dissipation modulus or imaginary part ML-1T-2 N/m2 (lbf / in2). K, K“, K*, | K*|
43、 are the various bulk moduli. | K*| is the absolute value of the complex bulk modulus and the magnitude equal to 221/2( ) ( “) +KK ML-1T-2 N/m2 (lbf / in2). ANSI/ASA S2.9-2008 2 2008 Acoustical Society of America 3.2 damping constant J is the damping constant in equationonDJ= (ML-1T-2)1-n, (N/m2)1-n
44、, (lbf / in2)1-n;n is the damping exponent for a material for which unit damping energy can be represented by onDJ= , where 2n . 3.3 damping energy total energy absorbed per cycle of loading by the entire part or structural assembly 3.4 damping energy density the energy dissipated by damping per uni
45、t volume of uniform material during one cycle of harmonic stress NOTE 1 Experiments performed on a large variety of materials show that energy loss per cycle due to internal friction is roughly proportional to the square of displacement. NOTE 2 D is the unit damping energy or damping energy density
46、proportional to the area within the dynamic stress-strain hysteresis loop mN/m3per cycle (in lbf / in3 per cycle) or N/m2per cycle (lbf / in2 per cycle). NOTE 3 In general = dEdD and, for harmonic vibration of angular frequency T-1 rad/sec, is also given by: = = 22/2/000( ) ( ) () () () ()/ Dtdt tdt
47、 tdtdt. NOTE 4 Subscript designation can be used to indicate normal, shear, and bulk stress. Recommended symbols are DE, DG, and DK, respectively. t is the time Tsec. 3.5 loss factor used in the sense that high loss means high ratio of energy dissipated to strain energy NOTE 1 It is proportional to
48、inverse of quality factor, Q. NOTE 2 is the loss factor of a material, equal to / 2DU Dimensionless. NOTE 3 For linear materials, “/ , “/ , and “/ EG KEE GG KK= = . NOTE 4 For low-damping materials (say 0.1 2) 5. Special cases and value of n in the equation 0DJn= ( n 2 ) (n = 2) MATERIALS STRUCTURES
49、 6. Characteristic shapes of hysteresis loop and typical values for n. Both materials and structures considered. Loop has many shapes but with rounded ends. For quadratic damping, n = 2 and loop is elliptical. For “plastic-strain“ and “magneto-plastic“ damping, n = 2 3 at intermediate stress, and n = 2 30 at high stress. A particular joined beam, n = 3. The term “linear damping“ is sometimes used for this case since these conditions also characterize line
