1、AGMAINFORMATIONSHEET(This Information Sheet is NOT an AGMA Standard)AGMA933-B03AGMA 933-B03AMERICAN GEAR MANUFACTURERS ASSOCIATIONBasic Gear GeometryiiBasic Gear GeometryAGMA 933-B03CAUTION NOTICE: AGMA technical publications are subject to constant improvement,revision or withdrawal as dictated by
2、experience. Any person who refers to any AGMAtechnicalpublicationshouldbesurethatthepublicationis thelatestavailablefromtheAs-sociation on the subject matter.Tables or other self-supporting sections may be quoted or extracted. Credit lines shouldread: Extracted from AGMA 933-B03, Basic Gear Geometry
3、, with the permission of thepublisher, the American Gear Manufacturers Association, 500 Montgomery Street, Suite350, Alexandria, Virginia 22314.Approved March 13, 2003ABSTRACTThis InformationSheetdescribes basic geometry relationships ofgearpitch,planeandangles. Itistheworkofone man, Alan H. Candee,
4、 originally documented in his paper for American Machinist of July 4 and 11, 1929.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2003 by American Gear Manufacturers AssociationAll rights reserved.No part of this publication ma
5、y 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: 1-55589-814-9AmericanGearManufacturersAssociationAGMA 933-B03AMERICAN GEAR MANUFACTURERS ASSOCIATIONiiiContentsPageForeword v.0 S
6、cope 11 Gears 12 Plane of rotation 1.3 Gear center 2.4 Line of centers 25 Center distance 2.6 Number of teeth 2.7 Gear ratio 3.8 Pitch point 39 Pitch circles 3.10 Pitch line 3.11 Circular pitch 412 Tooth profile 4.13 Point of contact 414 Line of action 415a Pressure angle 415b Profile angle 416 Base
7、 circle 417 Base pitch 418 Pitch element 4.19. Pitch plane 420 Transverse plane 421 Axial plane 622 Tangent plane 6.23 Plane of action 724 Normal plane 725 Axial plane of action 10.26 Pitch 11.27 Transverse pitch 1128 Axial pitch 11.29 Normal pitch 11.30 Center pitch 1131 Transverse base pitch 11.32
8、 Axial base pitch 1133 Normal base pitch 1134a Transverse pressure angle 11.35a Axial pressure angle 1136a Normal pressure angle 1134b Transverse profile angle 11.35b Axial profile angle 13.36b Normal profile angle 13.37 PItch helix angle 1438 Base helix angle 1439 Base helix angle 1440 PItch lead a
9、ngle 1441 Base lead angle 1442 Axial base lead angle 14AGMA 933-B03 AMERICAN GEAR MANUFACTURERS ASSOCIATIONivFigures1-4 Step-by-step development of some fundamental gear terms andrelationships 25-6 Some basic gear elements 37-8 Development from two parallel axes of the case of two intersectingaxes c
10、orresponding to bevel gears 5.9-10 The analogy between cylindrical and conical gears carried further, showingthe location of the transverse plane and the pitch plane in each case 511-14 A pitch cylinder and a pitch cone with their respective planes of rotation 6.15-18 Principal reference planes appl
11、ying to a pitch cylinder and a pitch cone 719-22 Use of space box to aid visualization of the tangent planes, plane of actionand normal plane 823 Charts showing that for every element in the plane of rotation, thereis a corresponding space element 924-27 Step by step development of the pitch figure
12、from oblique, involuterack elements 1028-35 Step by step breakdown of the pitch figure into various pitch triangles,each involving three pitches, or linear dimensions, and either a helix angleor a pressure angle. The relationships can all be expressed in a series ofsimple trigonometric formulas, col
13、lected in tabular form 13.36-37 Development of the pitch figure shown in perspective into a pitch diagramon which all lines and angles are shown in the true magnitude 14.Tables1 General classification of gears 1.2 Two given pitches determine angles and planes 15.3 One pitch determined by given secon
14、d pitch and angle 15.4 Angles determined by two given pitches 165 Two given pitches determine third pitch 176 Two given angles determine third angle 18AGMA 933-B03AMERICAN GEAR MANUFACTURERS ASSOCIATIONvForewordThe foreword, footnotes and annexes, if any, in this document are provided forinformation
15、al purposes only and are not to be construed as a part of AGMA InformationSheet 933-B03, Basic Gear Geometry.A paper entitled Gear Geometry, by Allan H. Candee, Mechanical Engineer, GleasonWorks, was presented at the Annual Meeting of the American Gear ManufacturersAssociation in May, 1929. The pape
16、r was an extension of the authors ideas presented inten blueprinted pages of diagrams, terms, and definitions to members of the AGMANomenclature Committee in April, 1928, under the title Universal Gear Geometry.Thepaperof1929was reproducedinAMERICANMACHINIST,July 4and11,1929. Later,in April, 1936, i
17、t was adopted by AGMA as a Recommended Practice, and reprints weredistributed to members. At that time, the letter symbols for angles were revised to conformto the standardization then under way in the Nomenclature Committee.The 1959 publication of AGMA 115.01, Basic Gear Geometry, was essentially a
18、 reissue ofthe 1929 paper by Allan H. Candee. The original wording was found to conform withoutneed of change to the terms and definitions in AGMA 112.03, Gear Nomenclature. Onlyminor editorial improvements were made, and a new term was introduced, profile angle,which is explained in the definitions
19、.This information serves as an introduction to and explanation of the geometricalrelationships in gear teeth, but it does not in any way modify or affect standard gearnomenclature which is the outcome of conscientious efforts by the AGMA NomenclatureCommittee which began more than seventy years ago.
20、The contents were reaffirmed by the AGMA Nomenclature Committee in 1988. It was thensubmitted to the American National Standards Institute (ANSI) as a proposed nationalstandard. ANSI approved AGMA 115.01 as a national standard on September 7, 1989.In2000,theTechnicalDivisionExecutiveCommitteevotedto
21、withdrawANSI/AGMA115.01as a national standard and to return its contents back as an AGMA information sheet,duplicating Candees original work. In a few instances, words have been deleted, , andadded (italic), in an effort to make the meaning clear to todays reader.The first draft of AGMA 933-B03 was
22、made in May, 2000. It was approved by the AGMATechnical Division Executive Committee on October 20, 2002.Suggestionsforimprovementofthisdocumentwillbewelcome. TheyshouldbesenttotheAmericanGearManufacturersAssociation,500MontgomeryStreet,Suite350,Alexandria,Virginia 22314.AGMA 933-B03 AMERICAN GEAR M
23、ANUFACTURERS ASSOCIATIONviPERSONNEL of the AGMA Nomenclature Committee, January 1959Chairman: Granger Davenport Gould butwith conical gears they are separate.AGMA 933-B03AMERICAN GEAR MANUFACTURERS ASSOCIATION5Axis no. 1Axis no. 2ShaftanglePitchanglePitchanglePitch radiusPitchradiusPitchpointFigure
24、8 - Intersecting axesAxis no. 1CenterdistancePitchpointPitchradiusPitchradiusAxis no. 2Figure 7 - Parallel axesFigures 7 and 8 - Development from twoparallel axes of the case of two intersectingaxes corresponding to bevel gearsInfigure10thepointsofintersectionofthegearaxesin the transverse plane are
25、 virtual centers, and thecircles struck fromthemarevirtualpitchcircles. Theprocess of laying-out gear teeth in the transverseplane, however, is the same for bevel gears as forspurgears. This similarity makes possibleageneralsystem of reference planes which can be adapted toall possible cases.Conical
26、 gearsTransverseplanePitchplanePitchradiusPitchradiusApexPitchelementFigure 10 - Intersecting axesPitch pointTransverse planePitchradiusPitch planePitchpointPitchelementCylindrical gearsPitchradiusFigure 9 - Parallel axesFigures 9 and 10 - The analogy betweencylindrical and conical gears carried fur
27、ther,showing the location of the transverse planeand the pitch plane in each caseAGMA 933-B03 AMERICAN GEAR MANUFACTURERS ASSOCIATION6Figures 11 to 14 illustrate a pitch cylinder and a pitchcone, with their respective planes of rotation, andrequire no explanation.Figures 15 to 18 show theimportant p
28、rincipalplanessuitable for application to any form of gear, and towhich all angles and directions are to be referred. Inaddition to the pitch plane and transverse planealready described, there is a third reference plane.21. THEAXIALPLANE(figures15and16)containsthe gear axis and is perpendicular to t
29、he pitch plane.These three planes are all mutually perpendicular,anditshouldbeobservedthattheycorrespondtothethree reference planes always used in mathematicsfor locating positions in space.22. THE TANGENT PLANE is tangent to the toothsurface at a point of contact with an engaging tooth.With involut
30、e teeth the tangent plane is actually thesideofatoothintherack,anditsintersectionwiththetransverseplaneisthelineformingthesideofatoothof the transverse rack section. The tangent planemay be parallel to the pitch element, correspondingto straight or spur teeth, as shown in figure 19, or itmay be obli
31、que to the pitch element as in figure 21,indicating helical or spiral teeth.Figure 11 - Pitch cylinder Figure 12 - Pitch coneFigure 13 - Plane of rotation Figure 14 - Plane of rotationFigures 11 - 14 - A pitch cylinder and a pitch cone with their respective planes of rotationAGMA 933-B03AMERICAN GEA
32、R MANUFACTURERS ASSOCIATION7TransverseplaneAxial planePitch planeFigure 15 - Reference planesPitch planeTransverseplaneAxial planeFigure 16 - Reference planesTransverseplaneAxial planePitchplaneFigure 17 - Reference solidTransverseplanePitchplaneAxial planeFigure 18 - Reference solidFigures 15 - 18
33、- Principal reference planes applying to a pitch cylinder and a pitch cone23. THE PLANE OF ACTION (figure 20) containsthelineofactioninthetransverseplaneandthepitchelementinthepitchplane. Itisperpendicularbothtothetransverseplaneandtothetangentplane. Inthecase of a cylindrical gear the plane of acti
34、on isparallel to the axis. It is tangent either to a basecylinder or a base cone.24. THENORMALPLANE(figure 22) is perpendic-ular to the pitch plane and to the tangent plane, thatAGMA 933-B03 AMERICAN GEAR MANUFACTURERS ASSOCIATION8is, it is normal to the tooth. In a cylindrical gear withhelical teet
35、h the normal plane is normal to the helixon the pitch cylinder, and in spiral bevel gears it isnormal to the tooth spiral on the pitch cone or in thepitch plane of the crown gear.Figure 19 - Tangent plane Figure 20 - Plane of actionFigure 21 - Tangent plane (oblique) Figure 22 - Normal planeFigures
36、19-22 - Use of space box to aid visualization of the tangent planes, plane of action andnormal planeAGMA 933-B03AMERICAN GEAR MANUFACTURERS ASSOCIATION9Itisnowtimetopointoutthatforeveryelementintheplane diagram of figure 6 there is a correspondingspace element. This is illustrated in detail in figur
37、e23. Forevery pointin thetransverse planethere is acorresponding line in space, and for every line orcurve in the plane there is a corresponding plane orsurface in space. In the case of a cylindrical spurgear all such planes and surfaces are parallel to theaxis,andalltransversesectionsareidentical,s
38、othatany one is sufficient to give all geometrical relation-ships. When, however, the tangent plane is obliqueto the axis, the case is not so simple.5577221433861111106Plane geometry Space geometryCenter 1AxisLine of centers 2 Axial planePitch point 3 Pitch elementPitch circle 4 Pitch surface (cylin
39、-der, cone)Pitch line 5 Pitch planeTangent line 6 Tangent planeLine of action 7 Plane of actionBase circle 8 Base cylinder (orcone)Involute curve 9 Involute surface(straight or helical)Tooth profile 10 Tooth surfacePoint of contact 11 Line of contactFigure 23 - Charts showing that for everyelement i
40、n the plane of rotation, there is acorresponding space elementIt should not be necessary to explain that thedimensions and angles for involute teeth can bedetermined most easily in the rack. These dimen-sions are the same in the rack as in a gear, and therack is composed entirely of planes, which ma
41、kes itcomparatively simple to diagram and calculate theelements.In figures 24 and 25 the three principal rack sectionsare illustrated. The transverse section is the oneusuallyconsideredforgears. Wormthreaddesignisusually based on the axial section. In any obliquetoothgearthenormalsectionisofimportan
42、tinterest.In all of the three principal planes, which are thetransverseaxialnormalthere are corresponding rack sections and ele-ments. For instance, in each plane there area pitch linea tangent linea line of actionpressure angle (and profile angle)pitchbase pitch, etc.All of the linear dimensions, w
43、hich, as is seen,consist of pitch values, and all ofthe angles involvedin the various involute rack sections can be com-bined into a single space figure which is here calledthe“pitchfigure”.Thepositionofthisfigureinrelationtothereferenceplaneswhichhavebeenestablishedis shown in figure 26, and in fig
44、ure 27 an enlargedview is given.A correct and complete mental picture of this pitchfigure can be obtained by giving attention to thefollowing facts. In the involute rack similar sides ofthe teeth consist of a series of equally spacedparallel lines. Each of the pitch values which havebeen referred to
45、 above is simply the distancebetween two of these parallel lines, or parallelplanes, taken in some definite direction. Thus, infigure 27, point O lies in one of the parallel planes ofthe rack, and points X, Y, Z, lie in the next parallelplane back of it. In the transverse section OY is thedistancein
46、thedirectionofthepitchlinebetweentwoof the parallel tangent lines, and is the pitch of therack teeth. Similarly OX is the distance between thesametwo parallelplanes takenin thedirection oftheAGMA 933-B03 AMERICAN GEAR MANUFACTURERS ASSOCIATION10pitchlineintheaxialsection,andsoistheaxialpitch.The pit
47、ch between the parallel planes indicated asOZ is in the direction of the line of centers and isperpendiculartothepitchplane. Itisherenamedthecenter pitch.It is possible now to complete our system of termsand definitions by reference tothe rack and thepitchfigure. There is one plane to be added to th
48、osealready defined.25. THEAXIALPLANEOFACTIONisperpendicu-lar to the side of a tooth in the axial plane and also isperpendicular to the axial plane. For instance, theplane of action of a wormgear is the axial plane ofaction of the mating worm.Figure 27 - Pitch figureAxialpitchCenterpitchPitch(transve
49、rse)YXZOAxialsectionTransversesectionFigure 24 - Helical rackNormalsectionAxialsectionFigure 25 - Helical rackXOZFigure 26 - Position of pitch figureFigures 24 - 27 - Step by step development of the pitch figure from oblique, involute rack elementsAGMA 933-B03AMERICAN GEAR MANUFACTURERS ASSOCIATION11This completes the list of eight planes, which are asfollows:Name of plane Definition1. Plane of rotation 22. Pitch plane 193. Transverse plane 204. Axial plane 215. Tangent plane 226. Plane of action (transverse) 237. Normal plane 248. Axial plane of action 25The plan
