1、August 2014 Translation by DIN-Sprachendienst.English price group 30No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS
2、 21.200!%:=;“2232624www.din.deDDIN ISO 21771Gears Cylindrical involute gears and gear pairs Concepts and geometry (ISO 21771:2007),English translation of DIN ISO 21771:2014-08Zahnrder Zylinderrder und Zylinderradpaare mit Evolventenverzahnung Begriffe und Geometrie (ISO 21771:2007),Englische bersetz
3、ung von DIN ISO 21771:2014-08Engrenages Roues et engrenages cylindriques dveloppante Concepts et gomtrie (ISO 21771:2007),Traduction anglaise de DIN ISO 21771:2014-08Together withDIN21772:2012-07 andDIN 21773:2014-08supersedesDIN 3960:1987-03www.beuth.deDocument comprises 91 pagesIn case of doubt, t
4、he German-language original shall be considered authoritative.07.14 A comma is used as the decimal marker. Contents Page 1 Scope . 9 2 Normative references . 9 3 Symbols, subscripts and units 10 3.1 Symbols . 10 3.2 Subscripts . 16 3.3 Units . 17 4 Individual cylindrical gears 18 4.1 Concepts for an
5、 individual gear 18 4.2 Reference surfaces, datum lines and reference quantities 20 4.3 Involute helicoids 25 4.4 Angular pitch and pitches 29 4.5 Diameters of gear teeth 32 4.6 Gear tooth height 32 4.7 Tooth thickness, space width 33 5 Cylindrical gear pairs . 35 5.1 Concepts for a gear pair 35 5.2
6、 Mating quantities 36 5.3 Calculation of the sum of the profile shift coefficients. 39 5.4 Tooth engagement 40 5.5 Backlash 48 5.6 Sliding conditions at the tooth flanks. 49 6 Tooth flank modifications 52 6.1 Tooth flank modifications which restrict the usable flank . 52 6.2 Transverse profile modif
7、ications 53 6.3 Flank line (helix) modifications . 56 6.4 Flank face modifications 57 6.5 Descriptions of modifications by functions. 59 7 Geometrical limits. 60 7.1 Counterpart rack tooth profile. 61 7.2 Machining allowance 62 7.3 Deviations in tooth thickness 63 7.4 Generating profile shift, gener
8、ating profile shift coefficient 64 7.5 Generated root diameter 65 7.6 Usable area of the tooth flank, tip and root form diameter 65 7.7 Undercut 67 7.8 Overcut 67 7.9 Minimum tooth thickness at the tip circle of a gear 67 Annex A (informative) Calculations related to tooth thickness. 68 Bibliography
9、 . 91 National foreword . 3 National Annex NA (informative) Bibliography 4 National Annex NB (normative) Corrections 5 DIN ISO 21771:2014-08 2 National foreword This standard has been prepared by Technical Committee ISO/TC 60 “Gears”, Subcommittee SC 1 “Nomenclature and wormgearing”. The responsible
10、 German body involved in its preparation was the Normenausschuss Maschinenbau (DIN Standards Committee Mechanical Engineering), Working Committee NA 060-34-11 AA Zylinderrder Terminologie und Toleranzen of Section Antriebstechnik. Application of the present informative Annex A “Calculations related
11、to tooth thickness” is not recommended. The reason is the mixing of the “nominal tooth thickness system” (Germany) and the “functional tooth thickness system” (USA). This involves the risk of using wrong equations or quantities. Therefore, the informative Annex A of this standard cannot replace the
12、normative content of DIN 3960. In order to solve this problem, those parts describing the “nominal tooth thickness system” have been transferred to a separate standard, DIN 21773. Users of this standard should take note of the following: When preparing the German translation of ISO 21771, errors wer
13、e discovered in some of the figures and equations. The corrections are given in DIN ISO 21771, National Annex NB. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. This first edition of ISO 21771 cancels and replaces ISO/TR 4467:1982, of which
14、it constitutes a technical revision. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. DIN and/or DKE shall not be held responsible for identifying any or all such patent rights. The European Standards referred to in this document h
15、ave been published as the corresponding DIN EN or DIN EN ISO Standards, except for those below, which correspond as follows: ISO 53 DIN 867 ISO 54 DIN 780-1 ISO 1328-1 DIN 3961, DIN 3962-1, DIN 3962-2, DIN 3963 ISO 1328-2 DIN 3962-1, DIN 3963 ISO 4156 DIN 5480 (all parts) Amendments This standard di
16、ffers from DIN 3960:1987-03 as follows: a) the standard has been editorially revised; b) equations and calculations in Clauses 3, 4 and 9 and in Annex A have been revised. Previous editions DIN 3960: 1951-06, 1953-10, 1957-10, 1960-08, 1976-10, 1980-07, 1987-03 DIN ISO 21771:2014-08 3 National Annex
17、 NA (informative) Bibliography DIN 780-1, Series of Modules for Gears Modules for Spur Gears DIN 867, Basic rack tooth profiles for involute teeth of cylindrical gears for general engineering and heavy engineering DIN 3961, Tolerances for Cylindrical Gear Teeth Bases DIN 3962-1, Tolerances for Cylin
18、drical Gear Teeth Tolerances for Deviations of Individual Parameters DIN 3962-2, Tolerances for Cylindrical Gear Teeth Tolerances for Tooth Trace Deviations DIN 3963, Tolerances for Cylindrical Gear Teeth Tolerances for Working Deviations DIN 5480 (all parts), Involute splines based on reference dia
19、meters DIN ISO 21771:2014-08 4 National Annex NB (normative) Corrections In Subclause 3.2 “Subscripts”, the following subscripts have been corrected: Subscript Description Used in 2 for quantities associated with the wheel (larger gear) or internal gear 5.1.3 * used for designating a coefficient rel
20、ating to the module A.5 Equation (56) has been corrected to read: wtb1wtt11222ww1coscoscos2 dzzzzzad =+= Equation (57) has been corrected to read: wtb2wtt21222ww2coscoscos2 dzzzzzad =+= Equation (128) has been corrected to read: ( ) ( ) ( )t22naP0nEaP02naP0nEaP02b2naP0nEaP0tFfcotsin14sin12sinsin12si
21、n+=+=mxhmxhddmxhddtDIN ISO 21771:2014-08 5 Figure A.3 has been corrected as follows: Figure A.3 Diagram of portion of transverse section available for span measurement on external spur gear with number of teeth spanned k = 3 for a secure measuring surface contact (corrected) DIN ISO 21771:2014-08 6
22、Figure A.4 has been corrected as follows: Key 1 gear axis Figure A.4 Tooth thicknesses, normal chordal tooth thicknesses and height above normal chordal tooth thickness on tooth at Y-cylinder of right-hand helical cylindrical gear (corrected) DIN ISO 21771:2014-08 7 Figure A.11 has been corrected as
23、 follows: Key Y1 measuring ball diameter coefficient, MD for internal gearsY2 measuring ball diameter coefficient, MD for external gears Y3 amount of teeth z aInternal gear bExternal gear Figure A.11 Nomogram for determining measuring ball diameter coefficient MD for radial single-ball dimension or
24、dimension over balls for = 20n (corrected) DIN ISO 21771:2014-08 8 Gears 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
25、are included. It also covers the concepts and parameters for 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 restricte
26、d to the pressure angle, 20 .P = The standard is structured 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 deter
27、mination of the nominal values for zero-deviation gear description 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).
28、Equations and explanations of the relevant values for defining 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). Co
29、ncepts and recommendations needed for a unique geometrical 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 follo
30、wing referenced documents are indispensable for the application 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 engin
31、eering Standard basic rack tooth profile ISO 1328-1:1995, 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
32、of deviations relevant to radial composite deviations and runout information DIN ISO 21771:2014-08 9 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
33、flank engagement A.8 b facewidth 4.2.8 bFusable facewidth 4.2.8 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
34、.5 daMtip diameter of overcut cylindrical gears A.9 dbbase diameter 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 dy
35、Y-circle diameter 4.3.3 dFatip form diameter 7.6 dFa0tip form diameter 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
36、 root diameter) 5.4.1 etspace width on the reference cylinder 4.7.3 eytspace width on the Y-cylinder 4.7.3 DIN ISO 21771:2014-08 10 Symbol 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
37、 5.4.5.2 glength of path of contact 5.4.5.2 gydistance of a point Y from 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
38、profile 7.5 hfdedendum 4.6.2 hfPdedendum of the standard basic rack tooth 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 cor
39、ner chamfering or tip corner rounding 6.1.2 hPtooth depth of standard 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 t
40、eeth, spaces or pitches in a span (e.g. number of teeth spanned) A.2.1 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 nbnumb
41、er of revolutions of driven gear (rpm) 5.2.2 p pitch, pitch on the reference cylinder Figure 4 DIN ISO 21771:2014-08 11 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 pettransve
42、rse base pitch on the path of contact 4.4.5.1 pnnormal pitch 4.4.2.2 pttransverse 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 thickn
43、ess at tip with tip corner chamfering or tip corner rounding 6.1.2 sbnnormal 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 stt
44、ransverse tooth thickness on the reference circle 4.7.1 synnormal tooth thickness 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
45、.6.1 vgfsliding speed at the dedendum 5.6.1 vnnormal speed 5.6.1 x profile shift 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 DIN ISO 21771:2014-08 12 Symbol Description Used inzbnumber of teeth of driven gear 5.2.2 zLnumber of teeth of master gear A.8 z0number of teeth of pinion-type cutter 7.6 A sta
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