1、BS ISO 23509:2016Bevel and hypoid geargeometryBSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06BS ISO 23509:2016 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 23509:2016. It supersedes BS ISO 23509:2006 which is withdrawn.The U
2、K participation in its preparation was entrusted to Technical Committee MCE/5/-/13, Bevel gears.A list of organizations represented on this committee can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are respons
3、ible for its correct application. The British Standards Institution 2016.Published by BSI Standards Limited 2016ISBN 978 0 580 86045 4 ICS 21.200 Compliance with a British Standard cannot confer immunity from legal obligations.This British Standard was published under the authority of the Standards
4、Policy and Strategy Committee on 30 November 2016.Amendments/corrigenda issued since publicationDate T e x t a f f e c t e dBS ISO 23509:2016 ISO 2016Bevel and hypoid gear geometryGomtrie des engrenages coniques et hypodesINTERNATIONAL STANDARDISO23509Second edition2016-11-15Reference numberISO 2350
5、9:2016(E)BS ISO 23509:2016ISO 23509:2016(E)ii ISO 2016 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2016, Published in SwitzerlandAll rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mec
6、hanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISOs member body in the country of the requester.ISO copyright officeCh. de Blandonnet 8 CP 401CH-1214 Vernier, Geneva, Sw
7、itzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47copyrightiso.orgwww.iso.orgBS ISO 23509:2016ISO 23509:2016(E)Foreword vIntroduction vi1 Scope . 12 Normative references 13 Terms, definitions and symbols 13.1 Terms and definitions . 53.2 Symbols . 74 Design considerations 94.1 General . 94.2 Types o
8、f bevel gears 104.2.1 General. 104.2.2 Straight bevels .104.2.3 Spiral bevels 104.2.4 Zerol bevels 104.2.5 Hypoids . 114.3 Ratios 114.4 Hand of spiral 114.5 Preliminary gear size 125 Tooth geometry and cutting considerations.125.1 Manufacturing considerations . 125.2 Tooth taper 125.3 Tooth depth co
9、nfigurations . 145.3.1 Taper depth . 145.3.2 Uniform depth .155.4 Dedendum angle modifications . 175.5 Cutter radius 175.6 Mean radius of curvature 175.7 Hypoid design . 185.8 Most general type of gearing 185.9 Hypoid geometry . 195.9.1 Basics 195.9.2 Crossing point .216 Pitch cone parameters .216.1
10、 Initial data for pitch cone parameters . 216.2 Determination of pitch cone parameters for bevel and hypoid gears 226.2.1 Method 0 226.2.2 Method 1 226.2.3 Method 2 266.2.4 Method 3 317 Gear dimensions 337.1 Initial data for tooth profile parameters 337.2 Determination of basic data . 367.3 Determin
11、ation of tooth depth at calculation point .387.4 Determination of root angles and face angles .387.5 Determination of pinion face width, b1.407.6 Determination of inner and outer spiral angles 427.6.1 Pinion 427.6.2 Wheel 437.7 Determination of tooth depth . 447.8 Determination of tooth thickness 44
12、7.9 Determination of remaining dimensions 46 ISO 2016 All rights reserved iiiContents PageBS ISO 23509:2016ISO 23509:2016(E)8 Undercut check .478.1 Pinion . 478.2 Wheel . 49Annex A (informative) Structure of ISO formula set for calculation of geometry data of bevel and hypoid gears .51Annex B (infor
13、mative) Pitch cone parameters 57Annex C (informative) Gear dimensions 68Annex D (informative) Analysis of forces 75Annex E (informative) Machine tool data .78Annex F (informative) Sample calculations79Bibliography . 138iv ISO 2016 All rights reservedBS ISO 23509:2016ISO 23509:2016(E)ForewordISO (the
14、 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 for which a technical committe
15、e 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) on all matters of electrotechni
16、cal standardization.The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in
17、 accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).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 held responsible for identifying any or all such patent rights. D
18、etails of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not constitute an
19、 endorsement.For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword
20、.html.The committee responsible for this document is ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity calculation.This second edition cancels and replaces the first edition (ISO 23509:2006), which has been technically revised with the following changes: minor corrections of several formulae; the f
21、igures have been reworked; explanations have been added in 4.4; the structure of Formula (129) has been changed to cover the case m=0 ; a formula for the calculation of cbe2has been added as Formula (F.160); the values for nCand nDin Formulae (F.318) and (F.319) have been extended to three decimal d
22、igits to prevent rounding errors. ISO 2016 All rights reserved vBS ISO 23509:2016ISO 23509:2016(E)IntroductionFor many decades, information on bevel, and especially hypoid, gear geometry has been developed and published by the gear machine manufacturers. It is clear that the specific formulae for th
23、eir respective geometries were developed for the mechanical generation methods of their particular machines and tools. In many cases, these formulae could not be used in general for all bevel gear types. This situation changed with the introduction of universal, multi-axis, CNC-machines, which in pr
24、inciple are able to produce nearly all types of gearing. The manufacturers were, therefore, asked to provide CNC programs for the geometries of different bevel gear generation methods on their machines.This document integrates straight bevel gears and the three major design generation methods for sp
25、iral bevel gears into one complete set of formulae. In only a few places do specific formulae for each method have to be applied. The structure of the formulae is such that they can be programmed directly, allowing the user to compare the different designs.The formulae of the three methods are devel
26、oped for the general case of hypoid gears and to calculate the specific case of spiral bevel gears by entering zero for the hypoid offset. Additionally, the geometries correspond such that each gear set consists of a generated or non-generated wheel without offset and a pinion which is generated and
27、 provided with the total hypoid offset.An additional objective of this document is that, on the basis of the combined bevel gear geometries, an ISO hypoid gear rating system can be established in the future.vi ISO 2016 All rights reservedBS ISO 23509:2016Bevel and hypoid gear geometry1 ScopeThis doc
28、ument specifies the geometry of bevel gears.The term bevel gears is used to mean straight, spiral, zerol bevel and hypoid gear designs. If the text pertains to one or more, but not all, of these, the specific forms are identified.The manufacturing process of forming the desired tooth form is not int
29、ended to imply any specific process, but rather to be general in nature and applicable to all methods of manufacture.The geometry for the calculation of factors used in bevel gear rating, such as ISO 10300 (all parts), is also included.This document is intended for use by an experienced gear designe
30、r capable of selecting reasonable values for the factors based on his/her knowledge and background. It is not intended for use by the engineering public at large.Annex A provides a structure for the calculation of the methods provided in this document.2 Normative referencesThere are no normative ref
31、erences in this document.3 Terms, definitions and symbolsFor the purposes of this document, the terms and definitions given in ISO 1122-1 and the following apply.ISO and IEC maintain terminological databases for use in standardization at the following addresses: IEC Electropedia: available at http:/
32、www.electropedia.org/ ISO Online browsing platform: available at http:/www.iso.org/obpNOTE 1 The symbols, terms and definitions used in this document are, wherever possible, consistent with other International Standards. It is known, because of certain limitations, that some symbols, their terms and
33、 definitions, as used in this document, are different from those used in similar literature pertaining to spur and helical gearing.NOTE 2 Bevel gear nomenclature used throughout this document is illustrated in Figure 1, the axial section of a bevel gear, and in Figure 2, the mean transverse section.
34、 Hypoid nomenclature is illustrated in Figure 3.Subscript 1 refers to the pinion and subscript 2 to the wheel.INTERNATIONAL STANDARD ISO 23509:2016(E) ISO 2016 All rights reserved 1BS ISO 23509:2016ISO 23509:2016(E)Key1 back angle 10 front angle 19 outer pitch diameter, de1, de22 back cone angle 11
35、mean cone distance, Rm20 root angle, f1, f23 back cone distance 12 mean point 21 shaft angle, 4 clearance, c 13 mounting distance 22 equivalent pitch radius5 crown point 14 outer cone distance, Re23 mean pitch diameter, dm1, dm26 crown to back 15 outside diameter, dae1, dae224 pinion7 dedendum angle
36、, f1, f216 pitch angle, 1, 225 wheel8 face angle a1, a217 pitch cone apex9 face width, b 18 crown to crossing point, txo1, txo2NOTE See Figure 2 for mean transverse section, A-A.Figure 1 Bevel gear nomenclature Axial plane2 ISO 2016 All rights reservedBS ISO 23509:2016ISO 23509:2016(E)Key1 whole dep
37、th, hm5 circular pitch 9 working depth, hmw2 pitch point 6 chordal addendum 10 addendum, ham3 clearance, c 7 chordal thickness 11 dedendum, hfm4 circular thickness 8 backlash 12 equivalent pitch radiusNOTE See A-A in Figure 1.Figure 2 Bevel gear nomenclature Mean transverse section ISO 2016 All righ
38、ts reserved 3BS ISO 23509:2016ISO 23509:2016(E)Key1 face apex beyond crossing point, tzF17 outer pitch diameter, de1, de213 mounting distance2 root apex beyond crossing point, tzR18 shaft angle, 14 pitch angle, 23 pitch apex beyond crossing point, tz19 root angle, f1, f215 outer cone distance, Re4 c
39、rown to crossing point, txo1, txo210 face angle of blank, a1, a216 pinion face width, b15 front crown to crossing point, txi111 wheel face width, b26 outside diameter, dae1, dae212 hypoid offset, aNOTE Apex beyond crossing point values are positive when crossing point lies inside the respective cone
40、.Figure 3 Hypoid nomenclature4 ISO 2016 All rights reservedBS ISO 23509:2016ISO 23509:2016(E)3.1 Terms and definitions3.1.1mean chordal addendumhamc1, hamc2height from the top of the gear tooth to the chord subtending the circular thickness arc at the mean cone distance in a plane normal to the toot
41、h face3.1.2mean addendumham1, ham2height by which the gear tooth projects above the pitch cone at the mean cone distance3.1.3outer normal backlash allowancejenamount by which the tooth thicknesses are reduced to provide the necessary backlash in assemblyNote 1 to entry: It is specified at the outer
42、cone distance.3.1.4coast sideconvex pinion flank in mesh with the concave wheel flank3.1.5cutter radiusrc0nominal radius of the face type cutter or cup-shaped grinding wheel that is used to cut or grind the spiral bevel teeth3.1.6sum of dedendum anglesfsum of the pinion and wheel dedendum angles3.1.
43、7sum of constant slot width dedendum anglesfCsum of dedendum angles for constant slot width3.1.8sum of modified slot width dedendum anglesfMsum of dedendum angles for modified slot width taper3.1.9sum of standard depth dedendum anglesfSsum of dedendum angles for standard depth taper3.1.10sum of unif
44、orm depth dedendum anglesfUsum of dedendum angles for uniform depth3.1.11mean dedendumhfm1, hfm2depth of the tooth space below the pitch cone at the mean cone distance ISO 2016 All rights reserved 5BS ISO 23509:2016ISO 23509:2016(E)3.1.12mean whole depthhmtooth depth at mean cone distance3.1.13mean
45、working depthhmwdepth of engagement of two gears at mean cone distance3.1.14direction of rotationdirection determined by an observer viewing the gear from the back looking towards the pitch apex3.1.15drive sideby normal convention, concave pinion flank in mesh with the convex wheel flank3.1.16face w
46、idthblength of the teeth measured along a pitch cone element3.1.17mean addendum factorchamapportions the mean working depth between wheel and pinion mean addendumsNote 1 to entry: The gear mean addendum is equal to chamtimes the mean working depth.3.1.18mean radius of curvaturemradius of curvature o
47、f the tooth surface in the lengthwise direction at the mean cone distance3.1.19number of blade groupsz0number of blade groups contained in the circumference of the cutting tool3.1.20number of teethz1, z2number of teeth contained in the whole circumference of the pitch cone3.1.21number of crown gear
48、teethzpnumber of teeth in the whole circumference of the crown gearNote 1 to entry: The number may not be an integer.3.1.22mean normal chordal tooth thicknesssmnc1, smnc2chordal thickness of the gear tooth at the mean cone distance in a plane normal to the tooth trace6 ISO 2016 All rights reservedBS
49、 ISO 23509:2016ISO 23509:2016(E)3.1.23mean normal circular tooth thicknesssmn1, smn2length of arc on the pitch cone between the two sides of the gear tooth at the mean cone distance in the plane normal to the tooth trace3.1.24tooth tracecurve of the tooth on the pitch surface3.1.25mean pointpoint where the calculation of basic geometry is executedNote 1 to entry: Mean point does not necessarily coincide with middle point of face width.Note 2 to entry: In all the methods listed in this docume
