1、ANSI/AGMA9104-A06ANSI/AGMA 9104-A06Reaffirmed May 2012AMERICAN NATIONAL STANDARDFlexible Couplings - Mass ElasticProperties and Other Characteristics(Metric Edition)iiFlexible Couplings - Mass Elastic Properties and Other Characteristics(Metric Edition)ANSI/AGMA 9104-A06Metric Edition of ANSI/AGMA 9
2、004-A99ApprovalofanAmericanNationalStandardrequiresverificationbyANSIthattherequire-ments for due process, consensus, and other criteria for approval have been met by thestandards developer.Consensusisestablishedwhen,inthejudgmentoftheANSIBoardofStandardsReview,substantial agreement has been reached
3、 by directly 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.TheuseofAmericanNationalStandardsiscompletelyvol
4、untary;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
5、 in nocircumstances 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 addresse
6、d to the 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 t
7、heAssociation on the subject matter.Tablesorotherself-supportingsectionsmaybereferenced. Citationsshouldread: SeeANSI/AGMA9104-A06,FlexibleCouplings - MassElasticPropertiesand OtherCharac-teristics(MetricEdition),publishedbytheAmericanGearManufacturersAssociation,500Montgomery Street, Suite 350, Ale
8、xandria, Virginia 22314, http:/www.agma.org.Approved: December 18, 2006ABSTRACTThisstandardprovidescalculationmethodsrelatedtomasselasticpropertiesofflexiblecouplings. Propertiesdiscussed include coupling mass, polar mass moment of inertia, center of gravity, axial stiffness, axial naturalfrequency,
9、 lateral stiffness, lateral natural frequency, and torsional stiffness. Calculation examples are pro-vided in informative annexes.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2006 by American Gear Manufacturers AssociationAl
10、l 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: 1-55589-900-5AmericanNationalStandardANSI/AGMA 9104-A06AMERICAN NATIONAL STANDARD
11、iii AGMA 2006 - All rights reservedContentsForeword iv.1 Scope 1.2 Definitions and symbols 1.3 Responsibility 24 Coupling characteristics 3.5 Loads on connected equipment 8.Bibliography 32.AnnexesA Example of coupling component mass 9.B Example of coupling component polar mass moment of inertia, JM1
12、2C Example of half coupling center of gravity 16.D Mass, polar mass moment of inertia, and center of gravity of homogeneoussolids 20E Torsional natural frequency calculation methods 21.F Example of calculation method for torsional stiffness 23G Derivation and example calculation for axial natural fr
13、equency 26.H Derivation of equations for lateral natural frequency 28I Example calculations for lateral natural frequencies 30Tables1 Symbols 2.2 Location of lumped mass 3Figures1 Coupling axial natural frequency model 62 Simply supported floating shaft on rigid supports 73 Simply supported floating
14、 shaft with central mass on rigid supports 74 Schematic of a coupling as connected to a system (A) and its associatedfree body diagram (B) 7.ANSI/AGMA 9104-A06 AMERICAN NATIONAL STANDARDiv AGMA 2006 - All rights reservedForewordThe foreword, footnotes and annexes, if any, in this document are provid
15、ed forinformational purposes only and are not to be construed as a part of AGMA Standard9104-A06,FlexibleCouplings - Mass ElasticProperties andOther Characteristics(MetricEdition.Thisstandardwasdevelopedthroughintensivestudyofexistingpractices,standards,textbooksandliterature. Theintentofthisstandar
16、distooffertorotatingequipmentdesigners,builders and users, a standard for design practice and methods of calculation of certainphysicalandmasselasticpropertiesofflexiblecouplings. Ingeneral,theinformationinthisstandardisaconsolidationofthemostcommonpracticesandcalculationscurrentlyinuseby flexible c
17、oupling manufacturers, rotating equipment designers and users.This AGMA standard utilizes the physical dimensions and properties of the coupling orcouplingcomponentsforthecalculationmethods. Itdoesnotcovercouplingcharacteristicsthat are included in other AGMA flexible coupling standards, such as cou
18、pling balance,which is addressed in ANSI/AGMA 9000-C90, Flexible Couplings - Potential UnbalanceClassification.Work was started on ANSI/AGMA 9004-A99 in 1989 at the suggestion of the AGMAFlexible Couplings Committee to achieve uniformity in the methods of calculation in inchunits of measure. ANSI/AG
19、MA 9004-A99 was approved as a standard by the AGMAmembershiponMarch4,1999,andasanAmericanNationalStandardonAugust3,1999.ThefirstdraftofANSI/AGMA9104-A06,inSIunitsofmeasure,was madein May2000. Itwas approved by the AGMA membership in July 2006. It was approved as an AmericanNational Standard on Decem
20、ber 18, 2006.Suggestionsforimprovementofthisstandardwillbewelcome. TheyshouldbesenttotheAmericanGearManufacturersAssociation,500MontgomeryStreet,Suite350,Alexandria,Virginia 22314.ANSI/AGMA 9104-A06AMERICAN NATIONAL STANDARDv AGMA 2006 - All rights reservedPERSONNEL of the AGMA Flexible Couplings Co
21、mmitteeChairman: Glenn Pokrandt Rexnord Industries Coupling Operations.Vice Chairman: Jim Paluh Ameridrives CouplingACTIVE MEMBERST. Hewitt Lord CorporationD. Hindman Rexnord Industries Coupling OperationsD. Lyle Ameridrives CouplingH.A. Lynn, III Rexnord Industries Coupling Operations.J.W. Mahan Lo
22、vejoy, Inc.J.R. Mancuso Kop-Flex/Emerson Power TransmissionG.E. Saunders Ameridrives Coupling.T. Schatzka Rexnord Industries, Inc.J. Sherred Ameridrives Coupling.J. Smihal T.B. Woods, Inc.R. Whitney Riverhawk CompanyANSI/AGMA 9104-A06 AMERICAN NATIONAL STANDARDvi AGMA 2006 - All rights reserved(This
23、 page is intentionally blank)1 AGMA 2006 - All rights reservedANSI/AGMA 9104-A06AMERICAN NATIONAL STANDARDAmerican National Standard -Flexible Couplings -Mass Elastic Propertiesand OtherCharacteristics (MetricEdition)1 ScopeThis standard presents information and calculationmethods for the mass elast
24、ic properties and othercharacteristics of flexible couplings. This data 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. Duetothedive
25、rsityofcouplingtypes,thisstandard presents generally accepted practicesrather than rigorous engineering analysis. Somecharacteristicsarenotcoveredinthisstandard,suchascouplingbalancewhichiscoveredinANSI/AGMA9000-C90, Flexible Couplings - Potential Unbal-ance Classification.2 Definitions and symbols2
26、.1 Definitions2.1.1 Flexible elementThe part of a coupling which provides flexibility.Various flexible element designs utilize a number ofoperatingprinciplestoprovideflexibility. Thedesignof this element determines the character of thecoupling in terms of reaction forces, dynamics andreliability. Fo
27、r this standard, common flexibleelement types have been grouped into three 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 t
28、his standard. The reader is directedto the appropriate coupling manufacturers for infor-mation 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. Theseelementsa
29、reverymuchlike springs in that they have a free form shape andwill resist a change in shape with a reaction force.Examplesofmetallicelementsaremetalorcompos-itecontoureddiaphragm,convoluteddiaphragmanddisc.2.1.3 Mechanical elementA form of flexible element which accommodatesmisalignment by sliding o
30、r rolling on mating sur-faces. These parts normally require lubrication.These 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 fu
31、nction of shaft torqueand coefficient of friction between the mating sur-faces. Examples of mechanical elements are gear,grid and pin-bushing.2.1.4 Elastomeric elementTheseflexibleelementsarecharacterizedbytheuseofanelastomer. Therearemanytypesofelastomer-ic elements which accommodate misalignmentth
32、rough varying degrees of material deflection andsliding motion. Reaction forces 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
33、 is transmitted through the flexible element.Because of the great variety 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-ANSI/AGMA
34、9104-A06 AMERICAN NATIONAL STANDARD2 AGMA 2006 - All rights reservedtions, that some symbols, their titles and theirdefinitions, as used in this document, are differentthan in similar literature.Table 1 is a list of the symbols used in this standard,along with the associated terms. The “Where firstu
35、sed” column gives the clause or equation numberwhere the particular symbol 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, te
36、rminology and definitions in the mannerindicated herein.3 ResponsibilityThecouplingmanufacturerisresponsibleforprovid-ing accurate coupling data and information for thefollowing calculation methods. The coupling masselasticpropertieswillaffectthesystemperformance.Thecustomerisresponsibleforsystemana
37、lysisandactual response.Table 1 - SymbolsSymbol Description UnitsWhere firstusedANFAxial natural frequency cpm 4.5.1DiInside diameter mm Eq 4DoOutside diameter mm Eq 4G Shear modulus N/mm2(MPa)Eq 4I Moment of inertia of shaft mm44.2JMPolar mass moment of inertia kg m2Eq 2KBEquipment bearing lateral
38、stiffness N/mm Figure 4KCCoupling tubular shaft or spacer tube portion lateral stiffness N/mm Eq 10KDTorsional stiffness for disk section Nm/rad Eq 5Kd1Metallic or composite element axial stiffness of end 1 of thecouplingN/mm Figure 1Kd2Metallic or composite element axial stiffness of end 2 of theco
39、uplingN/mm Figure 1KLLateral stiffness of coupling flex element N/mm Figure 4KSConnected shaft lateral stiffness N/mm Figure 4KsmCoupling suspended mass axial spring rate N/mm Eq 6KTTorsional stiffness for tube section Nm/rad Eq 4koRadius of gyration m Eq 2kEEquivalent lateral stiffness of the syste
40、m N/mm Eq 9L Length mm Eq 4l Distance between flex/load points mm Eq 7McTotal mass of coupling kg Figure 4m Mass kg 4.1mcCentral mass kg Eq 8mcsSuspended coupling center mass kg Figure 1mnMass of the nth component or section kg Eq 3mtMass of tubular portion of spacer kg Eq 11m1,m2Mass of the individ
41、ual components or sections kg Eq 3NcCoupling lateral natural frequency cpm Eq 7NsCoupling system lateral natural frequency cpm Eq 9N1Lateral natural frequency of coupling tubular section cpm Eq 11t Section thickness mm Eq 5(continued)ANSI/AGMA 9104-A06AMERICAN NATIONAL STANDARD3 AGMA 2006 - All righ
42、ts reservedTable 1 (concluded)Symbol Description UnitsWhere firstusedV Volume mm3Eq 1XcgLocation of the center of gravity of the complex shape (i.e.,half couplings, hubs, etc.) from the shaft endmm 4.3xncgDistance from shaft end to center of gravity location for the nthcomponent or sectionmm Eq 3x1c
43、g, x2cgDistance from shaft end to center of gravity location for theindividual components or sectionsmm Eq 3 Density kg/mm3Eq 14 Coupling characteristics4.1 Mass, mThemassofaflexiblecouplingorcomponentisusedfor the calculation of shaft stress, deflection andbearing loading. See annex A for the massc
44、alculation of a flanged coupling hub. See annex Dfor the equations for the mass calculation for somecommon shapes.m = V (1)wherem is mass, kg;V is volume, mm3; is density, kg/mm3.In engineering calculations involving couplings andcomponentsonthesurfaceofthe earth,the massinkilograms is multiplied by
45、 9.8 to obtain the approxi-mate force of gravity in newtons. (The force ofgravity acting on a mass of 1 kilogram varies fromabout9.77newtonsto9.83newtonsinvariouspartsof the world).4.2 Polar mass moment of inertia, JMThe polar mass moment of inertia, JM, is a measureof a bodys resistance to rotation
46、al acceleration ordeceleration. JMisacharacteristicusedforcalculat-ingsystemtorsionalnaturalfrequencyandrotationalenergy. JMis defined as:JM= mk2o(2)whereJMis polar mass moment of inertia, kg m2;m is mass, kg;kois radius of gyration, m.Theradiusofgyrationistheradiusatwhicharotatingbody mass can be s
47、aid to be concentrated in a thinring, and still have the same resistance to rotationalacceleration.The polar mass moment of inertia, JM, must not beconfusedwiththemomentofinertia,I. Themomentofinertiaisusedintorsionalwindupandshearstresscalculations, and does not consider mass.Annex B shows a sample
48、 calculation for the JMof aflanged coupling hub. This example uses themethod of adding or subtracting commonly knownshapes to make the hubs JMeasy to calculate.Annex D provides the equations for calculating theJMof common shapes.4.3 Half coupling center of gravity locationThehalfcouplingcenterofgrav
49、ity(effectivecenterofgravity)isthelocationrelativetotheshaftendwherehalf the coupling mass can be concentrated andprovide equivalent bearing and shaft deflectionloads. Knowingthisvalueallowscalculationofshaftdeflection,bearingloadsandsystemcriticalspeeds.Calculationofthecenterofgravityisdoneasshownin many text books in statics, with one exception.Halfthecentermembermassislumpedatthecenterof each flex element. Typical locations are given intable 2.Table 2 - Location of lumped massTypes LocationCovers Centerline of suppo
