1、AGMA 940-A09AGMA Information SheetDouble Helical Epicyclic GearUnitsAGMA940-A09iiDouble Helical Epicyclic Gear UnitsAGMA 940-A09CAUTION NOTICE: AGMA technical publications are subject to constant improvement,revision or withdrawal as dictated by experience. Any person who refers to any AGMAtechnical
2、publicationshouldbesurethatthepublicationisthelatestavailablefromtheAs-sociation on the subject matter.Tablesorotherself-supportingsectionsmaybereferenced. Citationsshouldread: SeeAGMA 940-A09, Double Helical Epicyclic Gear Units, published by the American GearManufacturersAssociation,1001N.FairfaxS
3、treet,5thFloor,Alexandria,Virginia 22314,http:/www.agma.org.Approved January 6, 2009ABSTRACTThisinformationsheetaddressesepicyclicgeardriveswhichutilizedoublehelicaltypegearingontheplanetaryelements. It is intended to be a supplement to and used in conjunction with ANSI/AGMA 6123-B06, DesignManualfo
4、rEnclosedEpicyclicGearDives. Itcoversonlythosetopicswhichareuniquetodoublehelicalgeararrangements in epicyclic gear drives.Notable features include the addition of a factor to account for load distribution between the helices of thedouble helical elements, KDH, and discussion of assembly considerati
5、ons.Published byAmerican Gear Manufacturers Association1001 N. Fairfax Street, 5thFloor, Alexandria, Virginia 22314Copyright 2009 by American Gear Manufacturers AssociationAll rights reserved.No part of this publication may be reproduced in any form, in an electronicretrieval system or otherwise, wi
6、thout prior written permission of the publisher.Printed in the United States of AmericaISBN: 978-1-55589-953-0AmericanGearManufacturersAssociationAGMA 940-A09AMERICAN GEAR MANUFACTURERS ASSOCIATIONiii AGMA 2009 - All rights reservedContentsForeword v1 Scope 1.2 Normative references 1.3 Symbols and t
7、erminology 14 Applications 14.1 Introduction to double helical gears 24.2 When to use double helical gears 44.3 Advantages 4.4.4 Disadvantages 44.5 Face to diameter ratio considerations 4.4.6 Configurations 54.7 System dynamics 54.7.1 Vibration analysis, dynamic loads 54.7.2 Natural frequencies 64.7
8、.3 System induced failure 6.4.7.4 Load sharing 64.7.5 Rotational speed 65 Epicyclic gearing arrangements 7.5.1 Fixed element 7.5.2 Types 75.2.1 Coupled epicyclics 7.5.2.2 Differential planetary 7.5.3 Epicyclic speed ratios 75.3.1 Coupled and compound-coupled planetaries 75.4 Relative speeds 8.6 Mesh
9、ing and assembly requirements 86.1 Assembly 8.6.2 Other meshing and assembly requirements 8.7 Tooth geometry 8.8 Circulating power 8.9 Load sharing 8.10 Double helical epicyclic drives 810.1 Mesh load share 8.10.1.1 Load sharing between planets 9.10.1.2 Load sharing between helices 9.10.1.3 Load dis
10、tribution factor, KH9.10.2 Special considerations for bearing selection and application 9.10.2.1 Bearing deformation 9.10.2.2 Dynamics in double helical epicyclic units 10.10.3 Special considerations for couplings and spline connections 10.10.3.1 Design and application of sliding, crowned splines 10
11、.10.3.2 Spline lubrication 1010.4 Special considerations for joining double helical components 1010.4.1 Ring gears 11.10.4.2 Sun pinion 11.10.4.3 Planet gears 11.10.4.4 Planet carrier design considerations 11.11 Thermal power rating 11.12 Lubrication 11Bibliography 22.AGMA 940-A09 AMERICAN GEAR MANU
12、FACTURERS ASSOCIATIONiv AGMA 2009 - All rights reservedAnnexesA Stoeckicht epicyclic drives 13.B Double helical epicyclic gear drive with minimum gap using assembled single helical components 17.C Double helical epicyclic with stationary carrier and bearing supported sun pinion 19D Double helical ep
13、icyclic gear drive 20Tables1 Symbols 2.Figures1 Double helical pinion 22 Double helical gear set 23 Examples of double helical epicyclic arrangements 34 Staggered tooth design 11.5 Non-staggered tooth design 116 Apex leading versus apex trailing 12.AGMA 940-A09AMERICAN GEAR MANUFACTURERS ASSOCIATION
14、v AGMA 2009 - All rights reservedForewordTheforeword,footnotesandannexes,ifany,inthisdocumentareprovidedforinformationalpurposesonlyandare not to be construed as a part of AGMA Information Sheet 940-A09, Double Helical Epicyclic Gear Units.Thepurposeofthisinformationsheetistoprovidespecification,com
15、parisonanddesigndatafordoublehelicalepicyclic gear units as a supplement to ANSI/AGMA 6123-B06, Design Manual for Enclosed Epicyclic GearDrives. While the scope of ANSI/AGMA 6123-B06 includes only spur and single helical epicyclic drives, asignificant portion of the material presented is applicable
16、to the double helical configuration and will bereferenced by this information sheet.Thedoublehelicalepicyclicconfigurationisgenerallyusedwhenitisdesiredtomaximizepowerdensity. Thisinformationsheetwilldiscusstheconsiderationsandcomplexitiesofthedoublehelicalepicyclicswhichincludeapplication, arrangem
17、ents, meshing/assembly, load sharing, lubrication and components (gearing, bearings,splines and carriers).The formulas presented or referenced in this information sheet contain numerous terms whose individualvaluescanvarysignificantlydependingonapplication,systemeffects,accuracyandmanufacturingmetho
18、ds.Proper evaluation of these terms is essential for realistic rating. The knowledge and judgment required toproperly evaluate the various rating factors comes primarily from years of accumulated experience indesigning,testing,manufacturingandoperatingsimilargearunits. Thedetailedtreatmentofthegener
19、alratingformulas for specific product applications is best accomplished by those experienced in the field.ThisinformationsheetisdedicatedtoDonMcVittie.Hisparticipationandinspirationledtothedevelopmentofthis information sheet. Mr. McVittie was the first Chairman of the Epicyclic Enclosed Drives Commi
20、ttee. Histhoroughnessandenthusiasmforgearing,alongwithhiscontributions,aswellasthecontributionsofhisfellowcommittee members brought out the best information from the committee as a whole.The first draft of AGMA 940-A09 was made in May, 2005. It was approved by the AGMA Technical DivisionExecutive Co
21、mmittee in January, 2009.Suggestions for improvement of this document will be welcome. They should be sent to the American GearManufacturers Association, 1001 N. Fairfax Street, 5thFloor, Alexandria, Virginia 22314.AGMA 940-A09 AMERICAN GEAR MANUFACTURERS ASSOCIATIONvi AGMA 2009 - All rights reserve
22、dPERSONNEL of the AGMA Epicyclic Enclosed Drives CommitteeChairman: Octave A. LaBath Gear Consulting Services of Cincinnati, LLCACTIVE MEMBERSJ.B. Amendola, Sr. Artec Machine SystemsM.R. Chaplin Consultant.J.R. Dammon Fairfield Manufacturing Co., Inc.R.L. Errichello GeartechR.A. Geary Comer Industri
23、es, Inc.U. Giger GDC Urs Giger GmbH.E.C. Hahlbeck Powertrain Engineers, IncJ.M. Hawkins Sikorsky Aircraft CorporationV. Kirov Merit Gear Corporation.T. Klaves Milwaukee Gear CompanyS.J. Matovic Horsburgh - apex runout, sometimes referred to as axial runout or apex wobble;- effects which influence ge
24、ar face load distribution;- special considerations for load sharing;- special considerations applicable to floating ring designs.Double helical epicyclic gear units with pitchline velocities in excess of 35 meters per second and aircraftpropulsion gears are excluded.This information sheet is a suppl
25、ement to ANSI/AGMA 6123-B06 covering design issues of double helicalepicyclic units which are not covered in that standard.2 Normative referencesThe following documents contain provisions which, through reference in this text, constitute provisions of thisinformationsheet. Atthetimeofpublication,the
26、editionswerevalid. Allpublicationsaresubjecttorevision,andthe users of this information sheet are encouraged to investigate the possibility of applying the most recenteditions of the publications listed.ANSI/AGMA 1012-G05, Gear Nomenclature, Definition of Terms with SymbolsANSI/AGMA 2101-D04,Fundame
27、ntalRatingFactorsandCalculationMethodsforInvoluteSpurandHelicalGear TeethANSI/AGMA 6123-B06, Design Manual for Enclosed Epicyclic Gear Drives3 Symbols and terminologyThe terms used, wherever applicable, conform to ANSI/AGMA 1012-G05. The symbols used in thisinformation sheet are shown in Table 1.NOT
28、E: Thesymbols andterms containedinthis documentmay varyfromthoseusedinotherAGMAstandards. Usersofthisinformationsheetshouldassurethemselvesthattheyareusingthesesymbolsandtermsinthemannerindicatedherein.4 ApplicationsIn addition to the following special design considerations for double helical epicyc
29、lic drives, clause 4 inANSI/AGMA 6123-B06 provides extensive information on drive selection, loading, and service factors that isapplicable for double helical drives as well.AGMA 940-A09 AMERICAN GEAR MANUFACTURERS ASSOCIATION2 AGMA 2009 - All rights reserved4.1 Introduction to double helical gearsA
30、nexternaldoublehelicalpinionhastwosetsofhelicalgearteethwithoppositehandhelices. Thehelicesareseparated by a distance, called the gap, where there are no teeth. The two sets of teeth form a V-shape or achevron shape. See Figure 1. If the teeth are projected into the gap, they intersect at the point
31、of the V. Thisimaginary point is the apex.Amatingexternalgeartothedoublehelicalpinionjustdescribedwouldalsohavetwosetsofteethseparatedbya gap and opposite helices. See Figure 2. A mating internal gear has the same hand as its mating gear.From these figures, one can see the two most important charact
32、eristics of double helical gearing:- Radial assembly - Double helical gears as described above, must be assembled/meshed radially, unlikespur or single helical gears that can be slid together axially into mesh.- Axial restraint - Once assembled (radially), the two members are not free to move in the
33、 axial directionindependently, i.e., one member of each mesh generally must be allowed to float allowing the apexes toalign.Table 1 - SymbolsSymbol Definition UnitsWherefirst usedd Diameter at half working depth mm 4.5F Effective facewidth (without gap) mm 4.5FtmTransmitted tangential load per helix
34、 N 10.1.2KDHHelix load sharing factor - - Eq 1KMesh load factor (takes into account the uneven distribution of loadbetween meshes for multiple transmission paths)- - 10.1.1KHLoad distribution factor - - 10.1.3KvDynamic factor - - 10.1.1NCPNumber of planets - - Eq 2ns/cSpeed of sun gear relative to c
35、arrier rpm Eq 3P Total transmitted power kW Eq 2PtmTransmitted power per helix kW Eq 3TsSun gear torque Nm Eq 3vtPitch line velocity at operating pitch diameter m/s Eq 2Figure 1 - Double helical pinionFigure 2 - Double helical gear setAGMA 940-A09AMERICAN GEAR MANUFACTURERS ASSOCIATION3 AGMA 2009 -
36、All rights reservedThese features create complex systems when double helical gearing is applied to an epicyclic drive. SeeFigure 3 for examples.Itisthegoalofthegeardesignertoarrangethegearing,bearings,couplings,andcarrierstousethesefeaturesadvantageously and compensate for the disadvantages.a) Rotat
37、ing carrier double helical epicyclicb) Fixed carrier double helical epicyclicFigure 3 - Examples of double helical epicyclic arrangements 1AGMA 940-A09 AMERICAN GEAR MANUFACTURERS ASSOCIATION4 AGMA 2009 - All rights reserved4.2 When to use double helical gearsSelectionofadoublehelicaldesigncanbebase
38、donmanyfactors,butthebasicreasonistomaximizegearboxcapacitywithaminimumdiameterduetothehighhelicaloverlapratiopotentialandlongerpermissiblelengthtodiameter ratios.4.3 AdvantagesDoublehelicalgearinginepicyclicdrivescanofferthefollowingadvantagesoverspurorsinglehelicalgearing:- The axial thrust forces
39、 generated at each helix, as a function of the tangential load and helix angle, areopposite and may cancel, possibly eliminating the need for a thrust bearing on all but one element.- For a fixed ring gear design, thrust bearings are not required. For a rotating ring gear design, an axiallylocating
40、bearing is required.- Large helix angles can be used (usually 25-30 degrees) resulting in very high helical overlap ratios.- As long as either the ring gears are fixed axially (most common) or the sun gear is fixed axially (leastcommon), the entire system is axially positioned automatically.- Since
41、the entire facewidth is shared by two helices, a longer effective face width for a given pitch diametercan be used (assuming that the planets are allowed to float axially to adjust themselves to the apex of thesun)comparedtospurorsinglehelicalgearingforthesameamountoftorsionaldeflection. Referto4.5f
42、oradditional information.- Since the net axial thrust force is minimized by the use of double helical gearing, the resulting overturningforces applied to the planets are reduced.- Theuseofawiderface(largerfacetodiameterratio),inconjunctionwithawiderbearingspreadundereachplanet, will reduce the angul
43、ar misalignment in the sun to planet and the planet to ring meshes.- Itiscommontoarrangeepicyclicgearsystemswithsungearsfreeofbearings. Thisallowsthesunto“float”radially between the planets to aid load sharing.4.4 DisadvantagesDouble helical gearing in epicyclic drives also have the following drawba
44、cks:- gearaccuracyvariationsfromonehelixtoanotherwillcauseapexrunout,possiblyresultinginundesirablevibrations and uneven load distribution;- external axial forces from couplings or thermal growth may be transmitted through the helices, having theeffect of increasing the tangential load on one helix;
45、- thegapbetweenthehelicesaddslengthtotheepicyclicdriveandisusuallyafunctionofthemanufacturingmethods used, possibly resulting in a larger and heavier gear unit;- provisions must be made to assemble the ring gears (or possibly the sun gear) axially in two pieces;- generally higher cost;- since the su
46、n and ring are tracking multiple planets, the axial motion variation of the sun and ring is acompromiseoftheapexrunoutofthematingplanets,andperfectloadsharingofthetwohelicescannotbeattained;- special attention to match marking may be required on the separate members (usually the ring gears) toestabl
47、ish the correct location of the apex, and facilitate assembly.4.5 Face to diameter ratio considerationsItiscommonlyacceptedthatdoublehelicalgearsallowlargerfacetodiameter(F/d)ratiosthanspurandhelicalgearsbecausetheaxialfloatingmembercanshiftaxiallyandcompensatesforsomeofthealignmenterrors. Ageneralr
48、ulehasbeenthattheF/dratioshouldbelessthanorequalto1.0forspurgearsandsinglehelicalgearsandlessthanorequalto2.0fordoublehelicalgears. Duetodeflection,gearsatorabovethese F/dratiolimitsprobably need helix modifications.SometimesthelimitationontheF/dratiofordoublehelicalgearingincludesthegapbetweenthetw
49、ohelicesinthevaluefor facewidth,F. Thismightbeappropriatefordoublehelicalgear setswithonlyonemesh. WiththeAGMA 940-A09AMERICAN GEAR MANUFACTURERS ASSOCIATION5 AGMA 2009 - All rights reservedmultiplemeshesonadoublehelicalepicyclicsunpinion,thetangentialandradialforcesarecounteractedandthebendingmomentacrossthedoublehelicalepicyclicgearingismuchlessthanthebendingmomentacrossthesinglemeshdoublehelicalgearing. Assumingperfectloadsharingonthemultipleplanets,therewouldbeazero net tangentia
