1、ANSI/AGMA 9004-B08(Revision of ANSI/AGMA 9004-A99)Reaffirmed May 2014American National StandardFlexible Couplings - MassElastic Properties and OtherCharacteristicsANSI/AGMA9004-B08iiFlexible Couplings - Mass Elastic Properties and Other CharacteristicsANSI/AGMA 9004-B08Revision of ANSI/AGMA 9004-A99
2、ApprovalofanAmericanNationalStandardrequiresverificationbyANSIthattherequire-ments for due process, consensus, and other criteria for approval have been met by thestandards developer.Consensusisestablishedwhen,inthejudgmentoftheANSIBoardofStandardsReview,substantial agreement has been reached by dir
3、ectly and materially affected interests.Substantialagreementmeansmuchmorethanasimplemajority,butnotnecessarilyuna-nimity. Consensus requires that all views and objections be considered, and that aconcerted effort be made toward their resolution.TheuseofAmericanNationalStandardsiscompletelyvoluntary;
4、theirexistencedoesnotin any respect preclude anyone, whether he has approved the standards or not, frommanufacturing, marketing, purchasing, or using products, processes, or procedures notconforming to the standards.The American National Standards Institute does not develop standards and will in noc
5、ircumstances give an interpretation of any American National Standard. Moreover, noperson shall have the right or authority to issue an interpretation ofan American NationalStandardinthenameoftheAmericanNationalStandardsInstitute. Requestsforinterpre-tation of this standard should be addressed to th
6、e American Gear ManufacturersAssociation.CAUTION NOTICE: AGMA technical publications are subject to constant improvement,revision, or withdrawal as dictated by experience. Any person who refers to any AGMAtechnical publication should be sure that the publication is the latest available from theAssoc
7、iation on the subject matter.Tablesorotherself-supportingsectionsmaybereferenced. Citationsshouldread: SeeANSI/AGMA9004-B08,FlexibleCouplings - MassElasticPropertiesandOtherCharac-teristics, published by the American Gear Manufacturers Association, 500 MontgomeryStreet, Suite 350, Alexandria, Virgin
8、ia 22314, http:/www.agma.org.Approved December 19, 2008ABSTRACTThis standard provides information and calculation methods related to mass elastic properties of flexiblecouplings. Properties discussed are coupling weight, polar weight moment of inertia (WR2), center of gravity,axial stiffness, axial
9、natural frequency, lateral stiffness, lateral natural frequency and torsional stiffness.Calculation examples are provided in informative annexes.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2008 by American Gear Manufacturer
10、s AssociationAll rights reserved.No part of this publication may be reproduced in any form, in an electronicretrieval system or otherwise, without prior written permission of the publisher.Printed in the United States of AmericaISBN: 978-1-55589-973-8AmericanNationalStandardANSI/AGMA 9004-B08AMERICA
11、N NATIONAL STANDARDiii AGMA 2008 - All rights reservedContentsForeword iv.1 Scope 1.2 Definitions and symbols 1.3 Responsibility 34 Coupling characteristics 3.5 Loads on connected equipment 8.Bibliography 34.AnnexesA Example of coupling component weight 9B Example of coupling component polar weight
12、moment of inertia, WR212.C Example of half coupling center of gravity 15.D Weight, WR2and center of gravity of homogeneous solids 19.E Torsional natural frequency calculation methods 21.F Example of calculation method for torsional stiffness 23G Derivation and example calculation for axial natural f
13、requency 26.H Derivation of equations for lateral natural frequency 28I Example calculations for lateral natural frequencies 30J Weight and mass units 32.Figures1 Coupling axial natural frequency model 62 Simply supported floating shaft on rigid supports 73 Simply supported floating shaft with centr
14、al weight on rigid supports 7.4 Schematic of a coupling as connected to a system (A) and its associatedfree body diagram (B) 7.Tables1 Symbols 2.2 Location of lumped mass 3ANSI/AGMA 9004-B08 AMERICAN NATIONAL STANDARDiv AGMA 2008 - All rights reservedForewordThe foreword, footnotes and annexes, if a
15、ny, in this document are provided forinformationalpurposesonlyandarenottobeconstruedasapartofANSI/AGMAStandard9004-B08, Flexible Couplings - Mass Elastic Properties and Other Characteristics.Thisstandardwasdevelopedthroughintensivestudyofexistingpractices,standards,textbooksandliterature. Theintento
16、fthisstandardistooffertorotatingequipmentdesigners,builders and users, a standard for design practice and methods of calculation of certainphysicalandmasselasticpropertiesofflexiblecouplings. Ingeneral,theinformationinthisstandardisaconsolidationofthemostcommonpracticesandcalculationscurrentlyinuseb
17、y the flexible coupling manufacturers, rotating equipment designers and users.This AGMA standard utilizes the physical dimensions and properties of the coupling orcouplingcomponentsforthecalculationmethodspresented. Thisstandarddoesnotcovercoupling characteristics that are covered in other AGMA flex
18、ible coupling standards, suchas coupling balance, which is covered in ANSI/AGMA 9000-C90, Flexible Couplings -Potential Unbalance Classification.Workwasstartedonthisstandardin1989atthesuggestionoftheAGMAFlexibleCouplingCommittee. Thepurposewastogainuniformityinthemethodsofcalculationofsomeofthemass
19、elastic properties of flexible couplings.This revision of ANSI/AGMA 9004-A99 corrects errors in equation 6 (axial naturalfrequency) and equation 8 (floating shaft coupling with central weight, lateral naturalfrequency). It also corrects equations E.3 and E.4 in Annex E; reworks Annex G to reflectthe
20、 changes made to equation 6 and adds a paragraph to Annex G that discusses thedamped response to external forced vibration that was added to ANSI/AGMA 9104-A06during its development. There were also minor editorial and clarification changes to theannexes.ThefirstdraftofANSI/AGMA9004-B08wasmadeinOcto
21、ber,2004. ItwasapprovedbytheAGMA Technical Division Executive Committee in August, 2008. ANSI/AGMA 9004-B08was approved as a standard by the AGMA membership on September 30, 2008, andapproved as an American National Standard on December 19, 2008.Suggestionsforimprovementofthisstandardwillbewelcome.
22、TheyshouldbesenttotheAmericanGearManufacturersAssociation,500MontgomeryStreet,Suite350,Alexandria,Virginia 22314.ANSI/AGMA 9004-B08AMERICAN NATIONAL STANDARDv AGMA 2008 - All rights reservedPERSONNEL of the AGMA Flexible Couplings CommitteeChairman: Glenn Pokrandt Rexnord Industries Coupling Operati
23、onsVice Chairman: Jim Paluh Ameridrives Coupling.ACTIVE MEMBERST. Hewitt Lord CorporationD. Hindman Rexnord Industries Coupling OperationsD. Lyle Ameridrives CouplingH.A. Lynn, III Rexnord Industries Coupling Operations.J.W. Mahan Lovejoy, Inc.J.R. Mancuso Kop-Flex/Emerson Power TransmissionG.E. Sau
24、nders Ameridrives Coupling.T. Schatzka Rexnord Industries, Inc.J. Sherred Ameridrives Coupling.J. Smihal T.B. Woods, Inc.R. Whitney Riverhawk CompanyANSI/AGMA 9004-B08 AMERICAN NATIONAL STANDARDvi AGMA 2008 - All rights reserved(This page is intentionally blank)1 AGMA 2008 - All rights reservedANSI/
25、AGMA 9004-B08AMERICAN GEAR MANUFACTURERS ASSOCIATIONAmerican National Standard -Flexible Couplings -Mass Elastic Propertiesand OtherCharacteristics1 ScopeThis standard presents information and calculationmethods for the mass elastic properties and othercharacteristics of flexible couplings. This dat
26、a is ofimportance to system designers for the selection ofsystem components and natural frequency calcula-tions. Calculation methods of the properties of thecoupling flexible elements are not included in thisstandard. Duetothediversityofcouplingtypes,thisstandard presents generally accepted practice
27、srather than rigorous engineering analysis. Somecharacteristicsarenotcoveredinthisstandard,suchascouplingbalancewhichiscoveredinANSI/AGMA9000-C90, Flexible Couplings - PotentialUnbalance Classification.2 Definitions and symbols2.1 Definitions2.1.1 Flexible elementThe part of a coupling which provide
28、s flexibility.Various flexible element designs utilize a number ofoperatingprinciplestoprovideflexibility. Thedesignof this element determines the character of thecoupling in terms of reaction forces, dynamics andreliability. For this standard, common flexibleelement types have been grouped into thr
29、ee majorcategories which are defined below. Note that thecharacter of a particular flexible element type maycross or fall outside the definitions below. Also notethe properties of flexible elements themselves arenot covered in this standard. The reader is directedto the appropriate coupling manufact
30、urers for in-formation on the properties of a particular type offlexible element.2.1.2 Metallic elementA form of flexible element which accommodatesmisalignment by material deflection of a metal orcompositemember. Theseelementsareverymuchlike springs in that they have a free form shape andwill resis
31、t a change in shape with a reaction force.Examplesofmetallicelementsaremetalorcompos-itecontoureddiaphragm,convoluteddiaphragmanddisc.2.1.3 Mechanical elementA form of flexible element which accommodatesmisalignment by sliding or rolling on matingsurfaces. These parts normally require lubrication.Th
32、ese elements do not have a free state position.They can be at rest at any combination of axial andangular positions within their flexible capability.Mechanical elements resist change in axial andangular position mainly as a function of shaft torqueand coefficient of friction between the mating sur-f
33、aces. Examples of mechanical elements are gear,grid and pin-bushing.2.1.4 Elastomeric elementTheseflexibleelementsarecharacterizedbytheuseofanelastomer. Therearemanytypesofelastomer-ic elements which accommodate misalignmentthrough varying degrees of material deflection andsliding motion. Reaction f
34、orces of these types offlexibleelementsaredeterminedbyelementconfig-uration, material stiffness, coefficient of friction andtorque. They can be categorized into two generaltypes, compression and shear, based upon the waytorque is transmitted through the flexible element.Because of the great variety
35、of designs someactually fit both categories in varying degrees.2.2 SymbolsThe symbols used in this standard are, whereverpossible, consistent with other approved AGMAdocuments. It is known, because of certain limita-tions, that some symbols, their titles and theirdefinitions, as used in this documen
36、t, are differentthan in similar literature.ANSI/AGMA 9004-B08 AMERICAN NATIONAL STANDARD2 AGMA 2008 - All rights reservedTable 1 is a list of the symbols used in this standard,along with the associated terms. The “Where firstused” column gives the clause or equation numberwhere the particular symbol
37、 is first used.NOTE: Some of the symbols and terminology con-tained in this document may differ from those used inother documents and AGMA standards. Users of thisstandardshouldassurethemselves thatthey areusingthe symbols, terminology and definitions in the mannerindicated herein. The unit “lb” is
38、a unit of force, “lbf”.See annex J.Table 1 - SymbolsSymbol Description Units First usedANF Axial natural frequency cpm 4.5.1DiInside diameter in Eq 4DoOutside diameter in Eq 4G Shear modulus lb/in2Eq 4g Local acceleration due to gravity in/s2Eq 2J Polar mass moment of inertia lb-in-s2Eq 2KBEquipment
39、 bearing lateral stiffness lb/in Eq 10KCCoupling tubular shaft or spacer tube portion lateral stiffness lb/in Eq 10Kd1Metallic element axial stiffness of end 1 of the coupling lb/in Eq 6Kd2Metallic element axial stiffness of end 2 of the coupling lb/in Eq 6KEEquivalent lateral stiffness of the syste
40、m lb/in Eq 9KLLateral stiffness of coupling flex element lb/in Eq 10KSConnected shaft lateral stiffness lb/in Eq 10KswCoupling suspended weight axial spring rate lb/in Eq 6KTTorsional stiffness for tube section lb in/rad Eq 4KDTorsional stiffness for disk section lb-in/rad Eq 5L Length in Eq 4l Dist
41、ance between flex/load points in Eq 7NcCoupling lateral natural frequency cpm Eq 7NsCoupling system lateral natural frequency cpm Eq 9N1Lateral natural frequency of coupling tubular section cpm Eq 11R Radius of gyration 4.2T Torque lb in 4.2t Section thickness in Eq 5V Volume in3Eq 1W Weight lb 4.1W
42、CTotal weight of coupling lb Eq 9WCWCentral weight lb Eq 8WcsSuspended coupling center weight lb Eq 6WnWeight of the nth component or section lb Eq 3WR2Polar weight moment of inertia lb-in24.2WtWeight of the tubular portion of the spacer lb Eq 11W1,W2Weight of the individual components or sections l
43、b Eq 3XcgLocation of the center of gravity of the complex shape (i.e., halfcouplings, hubs, etc.) from the shaft endin 4.3xncgDistance from shaft end to center of gravity location for the nthcomponent or sectionin Eq 3x1cg, x2cgDistance from shaft end to center of gravity location for theindividual
44、components or sectionsin Eq 3 Angular acceleration in/s24.2 Density lb/in3Eq 1ANSI/AGMA 9004-B08AMERICAN NATIONAL STANDARD3 AGMA 2008 - All rights reserved3 ResponsibilityThecouplingmanufacturerisresponsibleforprovid-ing accurate coupling data and information for thefollowing calculation methods. Th
45、e coupling masselasticpropertieswillaffectthesystemperformance.Thecustomerisresponsibleforsystemanalysisandactual response.4 Coupling characteristics4.1 Weight, WThe weight of a flexible coupling or component isused for the calculation of shaft stress, deflectionand bearing loading. See annex A for
46、the weightcalculation of a flanged coupling hub. See annex Dfor the equations for the weight calculation for somecommon shapes. For a discussion on units ofmassand weight, see annex J.W = V (1)whereW is weight, lb;V is volume, in3; is density, lb/in3.4.2 Polar weight moment of inertia, WR2The WR2of
47、a coupling is a useful characteristic forcalculating system torsional natural frequency androtational energy.The WR2of a coupling is a measure of the weightdistribution relative to the rotational axes. The polarmass moment of inertia, J, is a measure of a bodysresistancetorotationalaccelerationordec
48、eleration.The relationship between polar mass moment ofinertiaandpolarweightmomentofinertiaisgivenby:J =WR2g(2)whereJ is polar mass moment of inertia, lb-in-s2;WR2is polar weight moment of inertia, lb-in2;g is local acceleration due to gravity,= 386.4 in/s2.Coupling WR2is usually provided in (lb-in2
49、).However, the conversion to polar mass moment ofinertia, J, is needed so that it can be used in manyequations. For instance, the rotational analogy forNewtons second law relates torque, T, and angularacceleration, ,by: T = J,orT =(WR2/g).The polar mass moment of inertia, J, must not beconfusedwiththemomentofinertia,I. Themomentofinertiaisusedintorsionalwindupandshearstresscalculations, and does not consider mass.The WR2can be calculated by multiplying thecoupling weight, W, by the square of its radius
