1、AGMA913-A98AGMAINFORMATIONSHEET(This Information Sheet is NOT an AGMA Standard)AGMA 913-A98AMERICAN GEAR MANUFACTURERS ASSOCIATIONMethod for Specifying the Geometry ofSpur and Helical GearsiiMethod for Specifying the Geometry of Spur and Helical GearsAGMA 913-A98CAUTION NOTICE: AGMA technical public
2、ations 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 theAssociation on the subject matter.Tables or other self-supporting sections may be q
3、uoted or extracted. Credit lines shouldread: Extracted from AGMA 913-A98, Method for Specifying the Geometry of Spur andHelicalGears,withthepermissionofthepublisher,theAmericanGearManufacturersAs-sociation, 1500 King Street, Suite 201, Alexandria, Virginia 22314.Approved March 13, 1998ABSTRACTThis i
4、nformation sheet provides information to translate tooth thickness specifications which are expressed interms of tooth thickness, center distance or diameter into profile shift coefficients, as that term is used ininternational standards.Published byAmerican Gear Manufacturers Association1500 King S
5、treet, Suite 201, Alexandria, Virginia 22314Copyright 1998 by American Gear Manufacturers 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 S
6、tates of AmericaISBN: 1-55589-714-2AmericanGearManufacturersAssociationAGMA913-A98AMERICAN GEAR MANUFACTURERSASSOCIATIONiiiContentsPageForeword iv.1 Scope 12 Terms and symbols 1.3 Definitions 3.4 Profile shift 65 Internal gear pair calculations 11.Tables1 Symbols used in equations 12 Obsolete terms
7、3Figures1 The basic rack 3.2 Hypothetical tool 4.3 Profile shift of a helical gear 54 Effect of profile shift on involute tooth profiles 7.5 Distances along the line of action 9.6 Root radii cut with rack tool 10.7 Distances along the line of action for an internal gear pair 12.AnnexesA Tool proport
8、ions 15.B Calculation of profile shift 19.Bibliography 25.AGMA913-A98 AMERICAN GEAR MANUFACTURERSASSOCIATIONivForewordThe foreword, footnotes and annexes, if any, in this document are provided forinformational purposes only and are not to be construed as a part of AGMA InformationSheet 913-A98, Meth
9、od for Specifying the Geometry of Spur and Helical Gears.This information sheet is intended to provide sufficient information to allow its users to be ableto translate tooth thickness specifications which are expressed in terms of tooth thickness,center distance or diameter into profile shift coeffi
10、cients, as that term is used in internationalstandards.This AGMA information sheet and related publications are based on typical or average data,conditions or application.AGMA 913-A98 was approved by the AGMA membership on March 13, 1998.Suggestions for improvement of this standard will be welcome.
11、They should be sent to theAmerican Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria,Virginia 22314.AGMA913-A98AMERICAN GEAR MANUFACTURERSASSOCIATIONvPERSONNEL of the AGMA Nomenclature CommitteeChairman: John R. Colbourne University of Alberta.Vice Chairman: D. McCarroll Gleaso
12、n Works.ACTIVE MEMBERSW.A. Bradley III ConsultantR.L. Errichello GEARTECHD. Gonnella Texaco Lubricants CompanyD.R. McVittie Gear Engineers, IncO.A. LaBath Cincinnati Gear Company.I. Laskin Irving Laskin, P.EG.W. Nagorny Nagorny wtis the operating transverse pressure angle;tis the referencetransverse
13、 pressureangle.3.10 Addendum valuesThe gear addendum, measured from the referencecylinder, is usually chosen as (haP+ y). This valuedependsontheprofileshiftratherthantherackshiftandisthereforeindependentofthevaluechosenforbacklash. In certain designs, particularly when thecenter distance is signific
14、antly larger than thereference standard center distance, the gear ad-dendum may need to be reduced to allow adequateclearance at the roots of the meshing gear, see4.10.For internal gear pair equations which replaceequations 7 through 9, see 5.1.4 Profile shift4.1 Profile shift calculationProfile shi
15、ft is selected considering the followingcriteria:- avoiding undercut;- avoiding narrow top lands;- balanced specific sliding;- balanced flash temperature;- balanced bending fatigue life.The profile shift should be large enough to avoidundercut and small enough to avoid narrow toplands. The profile s
16、hifts required for balancedspecific sliding, balanced flash temperature andbalanced bending fatigue life are usually different.Therefore, the value used should be based on thecriterion that is judged to be the most important forthe particular application.Figure 4 illustrates how the shape of a gear
17、tooth isinfluenced by the number of teeth on the gear andthe value of the profile shift coefficient.The influence that the number of teeth has on toothform can be seen by viewing the teeth within anygiven column of figure 4. With small numbers ofteeth, thetoothhaslargercurvatureandtherelativethickne
18、ss of the teeth at the topland and at the formdiameter is smaller. As the number of teethincreases, the topland and tooth thicknesses in-crease and the curvature of the profiles decrease.Tooth thicknesses are maximum for a rack withstraight-sided profiles and theoretically infinitenumber of teeth.Vi
19、ewing figure 4 horizontally within any given rowshows how profile shift changes tooth form. Rowsnear the top of figure 4 show that gears with fewteethhaveatoothformthatdependsstronglyonthevalue of the profile shift coefficient. For gears withfew teeth, the sensitivity to profile shift narrows thecho
20、ice for profile shift coefficient because too littleprofile shift results in undercut teeth, whereas toomuch profile shift gives teeth with toplands that aretoo narrow. For example, the acceptable values ofprofileshiftcoefficientfora12toothgearrangefromx =0.4near undercut, to x =0.44for a toplandthi
21、ckness equal to 30% of the module. In contrast,rows near the bottom of figure 4 show that gearswithlargenumbersof teetharerelativelyinsensitiveto profile shift. This means that the gear designerhas wider latitude when choosing profile shift forgears with a large number of teeth. As a limitingcase, t
22、he shape of the teeth of a rack areindependent of profile shift.Generally, the performance of a gear is enhancedwith increasing numbers of teeth and the optimumvalue of profile shift. Fora fixedgear diameter, withthe exception of bending strength, load capacity isincreased when the number of teeth i
23、ncreases andthe profile shift is designed properly. Resistance tomacropitting, adhesive wear and scuffing is im-proved and the gears usually operate more quietly.Themaximumnumberof teethislimitedbybendingstrength because a large number of relatively smallteeth have high bending stresses. Therefore,
24、thegear designer must limit the number of teeth in thepinion based on maintaining adequate bendingstrength. Load capacity can be maximized bybalancing the pitting resistance and the bendingAGMA 913-A98AMERICAN GEAR MANUFACTURERS ASSOCIATION7strength of the gearset (see AGMA 901-A92). Abalanced desig
25、n has a relatively large number ofteeth in the pinion. This makes the gearsetrelatively insensitive to profile shift, and allows thedesigner to select the profile shift to minimizespecific sliding, minimize flash temperature orbalance the bending fatigue life of the pinion andgear.NumberofteethProfi
26、le shift coefficient1215203050100- 0.4 0.0 0.40.8Figure 4 - Effect of profile shift on involute tooth profilesAGMA 913-A98 AMERICAN GEAR MANUFACTURERS ASSOCIATION84.2 Basic gear geometry.(10)u=z2z1, where z2z1.(11)r1=z1mn2cos.(12)r2=z2mn2cos=r1u.(13)rb1=r1cos t.(14)rb2=r2cos t=rb1u.(15)t=arctanc5067
27、tan ncos c5072.(16)wt=arccosc5067arefcostawc5072.(17)inv t=tan t t.(18)inv wt=tan wt wt4.3 Sum of profile shift coefficients for zerobacklashNOTE: The equations to follow in this section are forexternalgearpairs only.The correspondingequationsfor internal gear pairs are given in 5.2.1.(19)x1+x2=aref
28、(inv wt inv t)mntan t4.4 Avoiding involute undercut teethThere are a number of design options to compen-sate for undercut teeth, including profile shift.Undercut is a condition in generated gear teethwhere any part of the fillet curve lies inside a linedrawn tangent to the working profile at its poi
29、nt ofjuncturewiththefillet.Forsuchgears, theendofthecutting tool has extended inside of the point oftangency of the base circle and the line of action,and removed an excessive amount of material.This removal of material can weaken the tooth andalso may reduce the length of contact, since gearaction
30、can only take place on the involute portion ofthe flank. Should a gear be made by anothermethod that would not undercut the flanks, theremay be interference of material and generally thegear would not mesh or roll with another gear. SeeAGMA 908-B89, Geometry Factors for Determin-ing the Pitting Resi
31、stance and Bending Strength ofSpur, Helical and Herringbone Gear Teeth.The minimum profile shift coefficient (to avoidundercut) for the pinion is given by:.(20)x1min=y1minmn.(21)y1min=haP0 r1sin2twherehaP0isthedistanceonthecuttingtooltoothfromthe reference line to the point near the tooltooth tip wh
32、ere the straight part of theprofile ends and the circular tip begins.(22)haP0=ha0 c19725a0+c19725a0sin nwhereha0is the addendum of the tool;a0is the radius of the circular tip of the tool.4.5 Avoiding narrow top landsThe maximum permissible profile shift coefficientsare obtained by iteratively varyi
33、ng the profile shiftcoefficientsof thepinionandgearuntiltheirtoplandthicknesses are equal to the minimum allowable.4.6 Balanced specific slidingSpecific sliding is defined as the ratio of the slidingvelocity to rolling velocity at a particular point ofcontact on the gear of interest.Maximumpittingan
34、dwearresistanceisobtainedbybalancingthespecificslidingateachendof thepathof contact. This is done by iteratively varying theprofile shift coefficients of the pinion and gear untilthe following equation is satisfied:.(23)c5067C6C1 1c5072c5067C6C5 1c5072=u2whereC6is the distance between interference p
35、oints(see figure 5);C1is the distance to SAP (see figure 5);C5is the distance to EAP (see figure 5).(24)C6=c5067rb1+rb2c5072tanwt=awsinwt.(25)C1=C6 r2a2 r2b2c5033.(26)C5= r2a1 r2b1c5033.(27)C2=C5 pbt.(28)C3=rb1tan wt.(29)C4=C1+pbtAGMA 913-A98AMERICAN GEAR MANUFACTURERS ASSOCIATION9HPSTCrb2wtpbtpbtC6
36、ra1C1C2C3C4C5rb1PawEAPLPSTCSAPra2Line ofactionFigure 5 - Distances along the line of action for external gear pair4.7 Balanced flash temperatureAccording to Bloks theory, the maximum scuffingresistance is obtained by minimizing the contacttemperature. This is done by iteratively varying theprofile s
37、hift coefficients of the pinionand gear, whilecalculatingtheflashtemperaturebyBloksequation(see annex A of ANSI/AGMA 2101-C95, Funda-mental Rating Factors andCalculation Methods forInvoluteSpurandHelicalGearTeeth),untiltheflashtemperature peaks in the approach and recessportions of the line of actio
38、n are equal. The flashtemperatureshouldbecalculatedatthepointsSAP,LPSTC, HPSTC, EAP and at several points in thetwo pair zones (between points SAP and LPSTCandbetweenpoints HPSTCand EAP, see figure5).4.8 Balanced bending strengthMaximum bending resistance is obtained by itera-tively varying the prof
39、ile shift coefficients of thepinion and gear until the ratio of the bendingstrength geometry factors equals the ratio ofallowable bending stresses, i.e.,.(30)YJ1YJ2=F2F1See ANSI/AGMA 2101-C95, clause 5.2 through5.2.3, for an explanation of YJ1,YJ2,F1and F2.AGMA 913-A98 AMERICAN GEAR MANUFACTURERS AS
40、SOCIATION104.9 Tooth thinning for backlashThe small adjustments of the position of the cuttingtool to thin the gear teeth for backlash areconsidered independently of the profile shift coeffi-cients (x1and x2) by specifying the amount thepinion and gear teeth are thinned for backlash,sn1and sn2. This
41、 way, the outside diameters areindependent of tooth thinning for backlash. Thetotal thinning coefficients are selected such that:.(31) sn1+ sn2=jnc5067arefawc5072wherejnis normal operating circular backlashA common convention among gear manufacturersis to reduce the normal tooth thickness of eachmem
42、berbythesameamount,whichmaybeavaluein greekmum or a function of the normal module, such as0.024mn. This maintains the same whole depth forboth members. However, for other directions oftooth thickness measurement, see ANSI/AGMA2002-B88.4.10 Tip-shortening coefficient for externalgearsetsForgearsopera
43、tingonextended centers(awaref),the outside radii of the gears may be shortened tomaintain adequate tip-to-root clearance. Theamount of adjustment of the outside radii isproportional to the tip-shortening coefficient, k:.(32)k =x1+x2 arefmnwhere.(33) aref=aw arefFor internal gear sets, see 5.2.3.4.10
44、.1 Tip-shortening optionsThree of the tip shortening options are as follows:4.10.1.1 Full length teeth - option 1.(34)ha1=c50671+x1c5072mn.(35)ha2=c50671+x2c5072mnCAUTION: Option1(fulllengthteeth)maygiveinsuffi-cient tip-to-root clearance if awC0038 aref. Check clear-ances or use option 3 (full tip-
45、to-root clearance).4.10.1.2 Full working depth - option 2.(36)ha1=c50671+x112kc5072mn.(37)ha2=c50671+x212kc5072mnCAUTION: Option 2 (full working depth) may give in-sufficient tip-to-root clearance if awC0038 aref. Checkclearances or use option 3 (full tip-to-root clearance)to be safe.4.10.1.3 Full t
46、ip-to-root clearance - option 3.(38)ha1=c50671+x1 kc5072mn.(39)ha2=c50671+x2 kc5072mn4.10.2 Root radius and clearanceRoot radii (cut with rack tool). See figure 6.(40)rf1=r1ha01+xE1mn.(41)rf2=r2ha02+xE2mnThe root clearances are:.(42)c1=awrf1ra2.(43)c2=awrf2ra1ha0yErrftool reference linetool pitch li
47、neyE=xEmnFigure 6 - Root radii cut with rack tool(refer to annex A for additional information)4.11 Addendum circle radii.(44)ra1=r1+ha1.(45)ra2=r2+ha2For internal gear sets, see 5.3.4.12 Generating rack shift coefficients.(46)xE1=x1 sn12 mntan n.(47)xE2=x2 sn22 mntan nAGMA 913-A98AMERICAN GEAR MANUF
48、ACTURERS ASSOCIATION11For internal gear sets, see 5.4.4.13 Normal circular tooth thickness.(48)sn1=c506712+2 xE1tan nc5072mn.(49)sn2=c506712+2 xE2tan nc5072mnFor internal gears, see 5.5.4.14 Determining profile shift coefficients ofexisting gear pairsIf the normal circular tooth thicknesses are know
49、n,the generating rackshift coefficientsare foundfromequations 50 and 51.(50)xE1=sn1mn22tann.(51)xE2=sn2mn22tannFor internal gear sets, see 5.6.4.14.1 Sumofgeneratingrackshiftcoefficients.(52) xE=xE2+xE1For internal gear sets, see 5.6.1.4.14.2 Normal operating circular backlash.(53)jn=c50672 awmntan narefc5072 c5067 x xEc5072For internal gear sets, see 5.6.2.4.14.3 Tooth thinning for backlashThe tooth thinning coefficients must satisfy equa-tion 31. However, it i
