AGMA 913-A98-1998 Method for Specifying the Geometry of Spur and Helical Gears《直齿轮和螺旋齿轮几何形状的确定方法》.pdf

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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: 1-55589-714-2AmericanGearManufacturersAssociationAGMA 913-A98AMERICAN GEAR MANUFACTURERS ASSOCIATIONiiiContentsPageForeword iv1 Scope 1.2 Terms and symbols 1.3 Definitions 3.4 Profile shift 6.5 Internal gear pair calculations 11.Tables1 Symbols used in equations 1.2 Obsolete te

7、rms 3.Figures1 The basic rack 32 Hypothetical tool 43 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 107 Distances along the line of action for an internal gear pair 12.AnnexesA Tool propo

8、rtions 15.B Calculation of profile shift 19.Bibliography 25AGMA 913-A98 AMERICAN GEAR MANUFACTURERS ASSOCIATIONivForewordThe 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, M

9、ethod for Specifying the Geometry of Spur and Helical Gears.Thisinformationsheetisintendedtoprovidesufficientinformationto allowitsusersto beableto translate tooth thickness specifications which are expressed in terms of tooth thickness,center distance or diameter into profile shift coefficients, as

10、 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. They shoul

11、d besent to theAmerican Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria,Virginia 22314.AGMA 913-A98AMERICAN GEAR MANUFACTURERS ASSOCIATIONvPERSONNEL of the AGMA Nomenclature CommitteeChairman: John R. Colbourne University of AlbertaVice Chairman: D. McCarroll Gleason WorksACT

12、IVE MEMBERSR.L. Errichello GEARTECH.D. Gonnella Texaco Lubricants Company.D.R. McVittie Gear Engineers, Inc.O.A. LaBath Cincinnati Gear Company.I. Laskin Irving Laskin, P.EG.W. Nagorny Nagorny wtis the operating transverse pressure angle;tis the referencetransverse pressureangle.3.10 Addendum values

13、The gear addendum, measured from the referencecylinder, is usually chosen as (haP+ y). This valuedependsontheprofileshiftratherthantherackshiftandisthereforeindependentofthevaluechosenforbacklash. In certain designs, particularly when thecenter distance is significantly larger than thereference stan

14、dard 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 shift is selected considering the foll

15、owingcriteria:- 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 shifts required for balancedspecific

16、 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 tooth isinfluenced by the number of

17、 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,thetoothhaslargercurvatureandtherelativethickness of the teeth at the topland and a

18、t 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.Viewing figure 4 horizontally within a

19、ny 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 thechoice for profile shift coefficient be

20、cause 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 toplandthickness equal to 30% of the module. I

21、n contrast,rows near the bottom of figure 4 show that gearswithlargenumbersofteetharerelativelyinsensitiveto profile shift. This means that the gear designerhas wider latitude when choosing profile shift forgears with a large number of teeth. As a limitingcase, the shape of the teeth of a rack arein

22、dependent 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 increases andthe profile shift is desig

23、ned properly. Resistance tomacropitting, adhesive wear and scuffing is im-proved and the gears usually operate more quietly.Themaximumnumberofteethislimitedbybendingstrength because a large number of relatively smallteeth have high bending stresses. Therefore, thegear designer must limit the number

24、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 design has a relatively large number ofteeth

25、 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.NumberofteethProfile shift coefficient1215203050100- 0.4

26、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 z2 z1.(11)r1=z1mn2cos.(12)r2=z2mn2cos= r1u.(13)rb1= r1cos t.(14)rb2= r2cos t= rb1u.(15)t= arctantan ncos .(16)wt= arccosarefcostaw.(1

27、7)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=arefinv wt inv tmntan t4.4 Avoiding involute undercu

28、t 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 point ofjuncturewiththefillet.Forsuchgears,theendofth

29、ecutting 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 can only take place on the involute portion ofthe f

30、lank. 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 Resistance and Bending Strength ofSpur, Helical and Her

31、ringbone 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 where the straight part of theprofile ends and the c

32、ircular tip begins.(22)haP0= ha0 a0+ a0sin 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 varying the profile shiftcoefficientsofthepinionandgearuntiltheir

33、toplandthicknesses 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.Maximumpittingandwearresistanceisobtainedbybalancingthespecificslidingateache

34、ndofthepathof contact. This is done by iteratively varying theprofile shift coefficients of the pinion and gear untilthe following equation is satisfied:.(23)C6C1 1C6C5 1= u2whereC6is the distance between interference points(see figure 5);C1is the distance to SAP (see figure 5);C5is the distance to

35、EAP (see figure 5).(24)C6=rb1+ rb2tanwt= awsinwt.(25)C1= C6 r2a2 r2b2.(26)C5= r2a1 r2b1.(27)C2= C5 pbt.(28)C3= rb1tan wt.(29)C4= C1+ pbtAGMA 913-A98AMERICAN GEAR MANUFACTURERS ASSOCIATION9HPSTCrb2wtpbtpbtC6ra1C1C2C3C4C5rb1PawEAPLPSTCSAPra2Line ofactionFigure 5 - Distances along the line of action fo

36、r 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 shift coefficients ofthe pinionand gear,whilecalculatingtheflashtemperaturebyBloksequation(see

37、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 action are equal. The flashtemperatureshouldbecalculatedatthepointsSAP,LPSTC, HPSTC, EAP and at sever

38、al 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 profile shift coefficients of thepinion and gear until the ratio of the bendingstrength geometry fact

39、ors 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 ASSOCIATION104.9 Tooth thinning for backlashThe small adjustments of the position of the cuttingtoo

40、l 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 way, the outside diameters areindependent of tooth thinning for backlash. Thetotal thinning coef

41、ficients are selected such that:.(31) sn1+ sn2= jnarefawwherejnis normal operating circular backlashA common convention among gear manufacturersis to reduce the normal tooth thickness of eachmemberbythesameamount,whichmaybeavaluein mm or a function of the normal module, such as0.024mn. This maintain

42、s the same whole depth forboth members. However, for other directions oftooth thickness measurement, see ANSI/AGMA2002-B88.4.10 Tip-shortening coefficient for externalgearsetsForgearsoperatingonextended centers(awaref),the outside radii of the gears may be shortened tomaintain adequate tip-to-root c

43、learance. 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 5.2.3.4.10.1 Tip-shortening optionsThree of the tip shortening options are as follows:4.10.1.1 Full length teeth - opti

44、on 1.(34)ha1=1 + x1mn.(35)ha2=1 + x2mnCAUTION: Option1(fulllengthteeth)maygiveinsuffi-cient tip-to-root clearance if awPndis the normal diametral pitch, in- 1;q is the finish stock allowance per flank, in(mm);nis the normal pressure angle at thereference diameter;hais the measured tool addendum (fro

45、m thetool tip to the tool measurement line), in(mm);t is the normal circulartooththicknessofroughing tool at the measurement line, in(mm);AMERICAN GEAR MANUFACTURERS ASSOCIATIONAGMA 913-A9816Materialallowance, q,for finishmachiningProfileangle,nqsin(n)Tool reference lineNormal circular pitch mnHypot

46、heticaltoolHypothetical tooladdendum, ha0Gear basic rackdedendum, hfPMeasuredtool (hob)addendum,haTool measurement lineHypotheticaltooldedendum,hf0Basic rackaddendum,haPHypothetical tool andbasic rack reference lineBasic rack “Zero Backlash” gear toothTool mn2 mn2Note the value for s is shownpositiv

47、e. It may have a negativevalue, which would change therelationships shown accordingly.s2tan(n)s2tFigure A.1 - Basic rack and hypothetical tool represented in rack forms is the adjustment if the roughing tool mea-surement line is not coincident with the toolreference line. When the measured tooladden

48、dum is taken from the tool referenceline, then s = 0. Otherwise, it may becalculated as:s =2Pnd t.(A.1).(A.1M)s = mn2 tha0is the hypothetical tool basic rack adden-dum,in(mm). Itismeasuredfromthetiptothe reference plane, where the hypotheticaltoolnormaltooththicknessis(mn)/2or/(2Pnd). The hypothetic

49、al tool basic rackaddendum is equal to hfP, the dedendum ofthe zero backlash tooth form basic rack.See figure A.1. Either SI or English unitsmay be used in the following equation:.(A.2)hfP= ha0= ha+s2tannqsinnA.3.3 Tool basic rack addendum coefficient(normalized)Tool basic rack addendum coefficient (normalized)is:.(A.3)ha0n= Pndha0.(A.3M)ha0n=ha0mnA.3.4 Additional tool data requiredpr istheprotuberance,asmeasuredontool,in(mm). Note that the 1996 relea