1、 g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58geometryICS 21.200Gears Cylindrical involute gears and gear pairs Concepts and BRITISH STANDARDBS I
2、SO 21771:2007BS ISO 21771:2007This British Standard was published under the authority of the Standards Policy and Strategy Committee on 28 September 2007 BSI 2007ISBN 978 0 580 54359 3Amendments issued since publicationAmd. No. Date CommentsCompliance with a British Standard cannot confer immunity f
3、rom legal obligations.National forewordThis British Standard is the UK implementation of ISO 21771:2007.The UK participation in its preparation was entrusted to Technical Committee MCE/5, Gears.A list of organizations represented on this committee can be obtained on request to its secretary.This pub
4、lication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application.Reference numberISO 21771:2007(E)INTERNATIONAL STANDARD ISO21771First edition2007-09-01Gears Cylindrical involute gears and gear pairs Concepts and geometry Engrenages R
5、oues et engrenages cylindriques dveloppante Concepts et gomtrie BS ISO 21771:2007ii iiiContents Page Foreword iv 1 Scope . 1 2 Normative references . 1 3 Symbols, subscripts and units 2 3.1 Symbols . 2 3.2 Subscripts . 8 3.3 Units . 9 4 Individual cylindrical gears 10 4.1 Concepts for an individual
6、gear 10 4.2 Reference surfaces, datum lines and reference quantities 12 4.3 Involute helicoids 17 4.4 Angular pitch and pitches 21 4.5 Diameters of gear teeth 24 4.6 Gear tooth height 24 4.7 Tooth thickness, space width 25 5 Cylindrical gear pairs . 27 5.1 Concepts for a gear pair 27 5.2 Mating quan
7、tities 28 5.3 Calculation of the sum of the profile shift coefficients. 31 5.4 Tooth engagement 32 5.5 Backlash 40 5.6 Sliding conditions at the tooth flanks. 41 6 Tooth flank modifications 44 6.1 Tooth flank modifications which restrict the usable flank . 44 6.2 Transverse profile modifications 45
8、6.3 Flank line (helix) modifications . 48 6.4 Flank face modifications 49 6.5 Descriptions of modifications by functions. 51 7 Geometrical limits. 52 7.1 Counterpart rack tooth profile. 53 7.2 Machining allowance 54 7.3 Deviations in tooth thickness 55 7.4 Generating profile shift, generating profil
9、e shift coefficient 56 7.5 Generated root diameter 57 7.6 Usable area of the tooth flank, tip and root form diameter 57 7.7 Undercut 59 7.8 Overcut 59 7.9 Minimum tooth thickness at the tip circle of a gear 59 Annex A (informative) Calculations related to tooth thickness. 60 Bibliography . 83 BS ISO
10、 21771:2007iv Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject
11、 for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC)
12、on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees
13、 are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be hel
14、d responsible for identifying any or all such patent rights. ISO 21771 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 1, Nomenclature and wormgearing. This first edition of ISO 21771 cancels and replaces ISO/TR 4467:1982, of which it constitutes a technical revision. BS ISO 21
15、771:20071Gears Cylindrical involute gears and gear pairs Concepts and geometry 1 Scope This International Standard specifies the geometric concepts and parameters for cylindrical gears with involute helicoid tooth flanks. Flank modifications are included. It also covers the concepts and parameters f
16、or cylindrical gear pairs with parallel axes and a constant gear ratio, which consist of cylindrical gears according to it. Gear and mating gear in these gear pairs have the same basic rack tooth profile. The equations given are not restricted to the pressure angle, 20 .P = The standard is structure
17、d as follows. Listing of symbols and nomenclature for a unique description of gears and gear pairs (see Clause 3). Equations and explanations of the relevant values for defining a cylindrical gear and its tooth system. The equations for determination of the nominal values for zero-deviation gear des
18、cription parameters are stated for radial tooth dimensions (gear tooth heights), the distance between flanks of the same hand, the distance between flanks of opposite hand, as well as the tooth flank characterizing parameters (see Clause 4). Equations and explanations of the relevant values for defi
19、ning cylindrical gear pairs. The equations for the essential parameters characterizing the engagement conditions of the unloaded gear pair are listed (see Clause 5). Equations and suggestions for desired flank modifications (see Clause 6). Concepts and recommendations needed for a unique geometrical
20、 definition of the intended results from manufacture (Clause 7). Equations for determination of the nominal values or the limiting values for the most used inspection methods for tooth thickness (see Annex A). 2 Normative references The following referenced documents are indispensable for the applic
21、ation of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 53:1998, Cylindrical gears for general and heavy engineering Standard basic rack tooth profile ISO 1328-1:1995,
22、Cylindrical gears ISO system of accuracy Part 1: Definitions and allowable values of deviations relevant to corresponding flanks of gear teeth ISO 1328-2:1997, Cylindrical gears ISO system of accuracy Part 2: Definitions and allowable values of deviations relevant to radial composite deviations and
23、runout information BS ISO 21771:20072 3 Symbols, subscripts and units 3.1 Symbols Symbol Description Used inawcentre distance of a cylindrical gear pair 5.2.3 a0centre distance in the generating gear unit 7.5 aLcentre distance for tooth flank engagement A.8 b facewidth 4.2.8 bFusable facewidth 4.2.8
24、 bMcontact line overlap (for measuring base tangent length) A.2.1 bwactive facewidth (the facewidth used) 5.4.7.2 c tip clearance 5.2.7 cFform over dimension 5.4.4 d reference diameter 4.2.4 datip diameter 4.5.3 da0tip diameter of tool 7.5 daMtip diameter of overcut cylindrical gears A.9 dbbase diam
25、eter 4.3.10 db0base diameter of the pinion-type cutter 7.6 dfroot diameter (nominal dimension) 4.5.4 dfEroot diameter produced 7.5 df0root diameter of the pinion-type cutter A.9 dvV-circle diameter 4.5.1 dwworking pitch diameter 5.2.5 dyY-circle diameter 4.3.3 dFatip form diameter 7.6 dFa0tip form d
26、iameter of the pinion-type cutter 7.6 dFfroot form diameter 7.6 dKdiameter of circle through centre of ball A.5 dMdiameter of a measuring circle A.2.1 dNaactive tip diameter 5.4.1 dNfstart of active profile diameter (SAP diameter, active root diameter) 5.4.1 etspace width on the reference cylinder 4
27、.7.3 eytspace width on the Y-cylinder 4.7.3 BS ISO 21771:20073Symbol Description Used inePspace width of the standard basic rack tooth profile 4.2.3 galength of addendum path of contact 5.4.5.2 gflength of dedendum path of contact 5.4.5.2 glength of path of contact 5.4.5.2 gydistance of a point Y fr
28、om pitch point C 5.6.1 garc of contact 5.4.7.4 h tooth depth (between tip line and root line) 4.6.1 haaddendum 4.6.2 haPaddendum of the standard basic rack tooth profile Figure 4 haP0addendum of the tool standard basic rack tooth profile 7.5 hfdedendum 4.6.2 hfPdedendum of the standard basic rack to
29、oth profile Figure 4 hfP0dedendum of the tool standard basic rack tooth profile A.9 hwworking depth of teeth in a gear pair 5.2.6 hFfPdepth of dedendum form of the standard basic rack tooth profile Figure 4 hKradius of the tip corner chamfering or tip corner rounding 6.1.2 hPtooth depth of standard
30、basic rack tooth profile Figure 4 inv involute function 4.3.9 jbncontact backlash 5.5 jrradial backlash 5.5 jtcircumferential backlash at the reference circle 5.5.2 jwtcircumferential backlash at the pitch circle 5.5 k number of teeth, spaces or pitches in a span (e.g. number of teeth spanned) A.2.1
31、 k addendum modification coefficient 4.5.2 lmaxpath of engagement 5.4.8 l sum of path of contact 5.4.8 mnnormal module 4.2.7 mttransverse module 4.2.7 mxaxial module 4.2.7 nanumber of revolutions of driving gear (rpm) 5.2.2 nbnumber of revolutions of driven gear (rpm) 5.2.2 p pitch, pitch on the ref
32、erence cylinder Figure 4 BS ISO 21771:20074 Symbol Description Used inpbnnormal pitch on the base cylinder 4.4.5 pbttransverse pitch on the base cylinder 4.4.5.1 pennormal base pitch on the path of contact 4.4.5.2 pettransverse base pitch on the path of contact 4.4.5.1 pnnormal pitch 4.4.2.2 pttrans
33、verse pitch 4.4.2.1 pxaxial pitch 4.4.4 pynnormal pitch on the Y-cylinder 4.4.3 pyttransverse pitch on the Y-cylinder 4.4.3 pzlead 4.3.2 q machining allowance on tooth flank 7.2 qFsundercut Figure 24 saKresidual tooth thickness at tip with tip corner chamfering or tip corner rounding 6.1.2 sbnnormal
34、 tooth thickness on the base circle A.2.2 snnormal tooth thickness on the reference circle 4.7.5 sniminimum normal tooth thickness on the reference circle 7.3 snsmaximum normal tooth thickness on the reference circle 7.3 sttransverse tooth thickness on the reference circle 4.7.1 synnormal tooth thic
35、kness on the Y-cylinder 4.7.5 syttransverse tooth thickness on the Y-cylinder 4.7.1 sPtooth thickness of the standard basic rack tooth profile 4.2.3 u gear ratio 5.2.1 vgsliding speed 5.6.1 vgasliding speed at the addendum 5.6.1 vgfsliding speed at the dedendum 5.6.1 vnnormal speed 5.6.1 x profile s
36、hift coefficient 4.2.9 xEgenerating profile shift coefficient 7.4 xEmingenerating profile shift coefficient at undercut limit 7.7 xLprofile shift coefficient of master gear A.8 z number of teeth 4.1.5 zanumber of teeth of driving gear 5.2.2 BS ISO 21771:20075Symbol Description Used inzbnumber of tee
37、th of driven gear 5.2.2 zLnumber of teeth of master gear A.8 z0number of teeth of pinion-type cutter 7.6 A starting point of meshing 5.4.3 B starting point of single tooth contact on driving gear 5.4.5.1 C pitch point, depth of relief for modifications 5.4.3 Caymodification of the profile 6.5 Cymodi
38、fication of the flank line 6.5 Cymodification of the flank surface 6.5 Caamount of tip relief 6.2.1 Cfamount of root relief 6.2.1 CEatip amount of triangular end relief modification 6.4.2 CEfroot amount of triangular end relief modification 6.4.2 Ci,jamount of modification at point (i,j) 6.4.1 CHamo
39、unt of transverse profile slope modification 6.2.2 Camount of profile crowning (barrelling) 6.2.3 CI, ClIamount of end relief 6.3.1 Camount of flank line crowning 6.3.3 CHamount of flank line slope modification 6.3.2 DMmeasuring ball or measuring cylinder diameter A.5 D end point of single tooth con
40、tact point on driving gear 5.4.5.1 E end point of meshing 5.4.3 Esnnormal tooth thickness deviation limit (or allowance) A.9 Esnilower deviation limit for tooth thickness 7.3 Esnsupper deviation limit for tooth thickness 7.3 Kgsliding factor 5.6.2 Kgasliding factor at tooth tip 5.6.2 Kgfsliding fact
41、or at tooth root 5.6.2 LAEroll length 6.2 LCatip relief roll length 6.2.1 LCfroot relief roll length 6.2.1 LCl, LClIlength of end relief 6.3.1 LEatip roll length of triangular end relief modification 6.4.2 BS ISO 21771:20076 Symbol Description Used inLEfroot roll length of triangular end relief modi
42、fication 6.4.2 MdKdimension over balls A.7 MdZdimension over cylinders A.7.1 MrKradial single-ball dimension A.5 MrZradial single-cylinder dimension A.6 N number of tooth or pitch 4.1.6 O centre of a circle Figure 10 Stwist of the transverse profile 6.4.3 Stwist of the flank line 6.4.3 Tsntooth thic
43、kness tolerance Figure 37 T contact point of tangent (lines of engagement) at base circle Figure 10 U involute point of origin 4.3.7 Wkbase tangent length over k measured teeth or measured spaces A.2.1 Y any point on a tooth flank or involute 4.3.5 nnormal pressure angle 4.3.6 ttransverse pressure a
44、ngle 4.3.5 wtworking transverse pressure angle of gear pair 5.2.4 wt0working transverse pressure angle in the generating gear unit 7.6 ynnormal pressure angle at the Y-cylinder 4.3.6 yttransverse pressure angle at the Y-cylinder 4.3.5 Ffpressure angle at root form circle 7.6 Kpressure angle at circl
45、e through centre of ball A.5 Kttransverse pressure angle at a point at circle through centre of ball A.5 Mttransverse pressure angle at a point at measuring circle A.5 Ppressure angle of the standard basic rack tooth profile 4.3.6 P0pressure angle of the tool basic rack tooth profile 7 Lworking tran
46、sverse pressure angle for double-flank engagement A.8 vttransverse pressure angle at the V-cylinder A.5 helix angle 4.3.3 bbase helix angle 4.3.3 yhelix angle at Y-cylinder 4.3.3 wangle of rocking for span measurement A.2.1 BS ISO 21771:20077Symbol Description Used in lead angle at reference cylinde
47、r 4.3.3 ylead angle at Y-cylinder 4.3.3 transverse contact ratio 5.4.7.1 overlap ratio 5.4.7.3 total contact ratio 5.4.7.5 specific sliding 5.6.3 fspecific sliding at end points of path of contact 5.6.3 space width half angle at reference circle 4.7.4 bbase space width half angle 4.7.4 yspace width
48、half angle at Y-circle 4.7.4 yrolling angle of the involute at point Y 4.3.7 Fa0rolling angle at tip form circle of pinion-type cutter 7.6 Ffrolling angle at root form circle 7.6 Narolling angle at active tip circle 5.4.1 Nfrolling angle at active root circle 5.4.1 fProot radius on the standard basi
49、c rack tooth profile Figure 4 yradius of curvature of the involute at point Y 4.3.8 angular pitch 4.4.2 jbacklash angle 5.5.2 transverse angle of transmission 5.4.7.1 overlap angle 5.4.7.3 total angle of transmission 5.4.7.5 tooth thickness half angle at reference circle 4.7.2 bbase tooth thickness half angle 4.7.2 ytooth thickness half angle at Y-circle 4.7.2 aangular velocity of driving gear 5.2.2 bangular velocity of driven gear 5.2.2
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