1、BSI Standards Publication PD ISO/TR 10828:2015 Worm gears Worm profiles and gear mesh geometryPD ISO/TR 10828:2015 PUBLISHED DOCUMENT National foreword This Published Document is the UK implementation of ISO/TR 10828:2015. It supersedes BS ISO TR 10828:1997 which is withdrawn. The UK participation i
2、n its preparation was entrusted to Technical Committee MCE/5/-/7, Worm 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 responsible for its corr
3、ect application. The British Standards Institution 2015. Published by BSI Standards Limited 2015 ISBN 978 0 580 85447 7 ICS 21.200 Compliance with a British Standard cannot confer immunity from legal obligations. This Published Document was published under the authority of the Standards Policy and S
4、trategy Committee on 30 September 2015. Amendments issued since publication Date Text affectedPD ISO/TR 10828:2015 ISO 2015 Worm gears Worm profiles and gear mesh geometry Engrenages vis cylindriques Gomtrique des profils de vis et des engrnements TECHNICAL REPORT ISO/TR 10828 Reference number ISO/T
5、R 10828:2015(E) Second edition 2015-08-15PD ISO/TR 10828:2015ISO/TR 10828:2015(E)ii ISO 2015 All rights reserved COPYRIGHT PROTECTED DOCUMENT ISO 2015, Published in Switzerland All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any
6、 form or by any means, electronic or mechanical, 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 office Ch. de Blan
7、donnet 8 CP 401 CH-1214 Vernier, Geneva, Switzerland Tel. +41 22 749 01 11 Fax +41 22 749 09 47 copyrightiso.org www.iso.orgPD ISO/TR 10828:2015 ISO/TR 10828:2015(E) ISO 2015 All rights reserved iiiContents Page Foreword . v Introduction vi 1 Scope 1 2 Normative references 1 3 Symbols and abbreviate
8、d terms 1 4 Formulae for calculation of dimensions . 5 4.1 Parameters for a cylindrical worm . 5 4.2 Parameters for a worm wheel 8 4.3 Meshing parameters 11 5 Generalities on worm profiles 12 5.1 Definitions 12 5.2 Conventions relative to the formulae of this document 12 6 Definition of profiles 13
9、6.1 Introduction 13 6.2 Type A . 14 6.3 Type I 15 6.4 Type N . 20 6.5 General formulae for A, I and N profiles . 21 6.6 Type K . 22 6.7 Type C . 25 6.8 Algorithm to initialize the calculation 30 7 Section planes . 31 7.1 Introduction 31 7.2 Axial plane 31 7.3 Offset plane 31 7.4 Transverse plane . 3
10、1 7.5 Normal plane 31 7.6 Point of the worm surface in an offset plane: offset profile of worm 32 8 Pitch surfaces 34 9 Conjugate worm wheel profile . 36 9.1 Introduction 36 9.2 Path of contact . 36 9.3 Worm wheel profile conjugate with worm profile 38 9.4 Trochoid (or fillet) at root of the worm wh
11、eel . 40 9.5 Equivalent radius of curvature in an offset plane 4 2 9.6 Singularities of worm gear mesh . 44 10 Geometry of contact 48 10.1 General . 48 10.2 Tangent plane at point of contact 49 10.3 Normal plane at point of contact . 49 10.4 Zone of contact 50 10.5 Lines of contact . 53 10.6 Contact
12、 ratio 56 10.7 Tangent vector to the line of contact 57 10.8 Normal plane at point of contact . 58 10.9 Principal equivalent radius of curvature . 59 10.10 Calculation of path of contact and zone of contact . 60 PD ISO/TR 10828:2015 ISO/TR 10828:2015(E) iv ISO 2015 All rights reserved10.11 Calculati
13、on of line of contact 60 11 Velocities at contact point 61 11.1 Velocity of a point of worm .61 11.2 Relative velocity between 2 conjugate flanks .61 11.3 Tangent to the path of contact .62 11.4 Velocity of the contact point along the path of contact.62 11.5 Velocity at the point of contact 63 Annex
14、 A (informative) Settings and derivatives of formulae for A, I, N profiles .64 Annex B (informative) Settings and derivatives of formulae for K and C profiles .70 Annex C (informative) Algorithm to determine the point of generations of worm and worm wheel 76 Annex D (informative) Comparison of diffe
15、rent worm profiles.78 Annex E (informative) Comparison of singularities for different worm profiles.82 Annex F (informative) Comparison of gear mesh for different worm profiles 84 Annex G (informative) The utilisation of existing tooling for machining of worm wheel teeth .92 Bibliography 95 PD ISO/T
16、R 10828:2015 ISO/TR 10828:2015(E) ISO 2015 All rights reserved vForeword 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 co
17、mmittees. Each member body interested in a subject 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 th
18、e International Electrotechnical Commission (IEC) on all matters of electrotechnical 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
19、the different types of ISO documents should be noted. This document was drafted in 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.
20、 ISO shall not be held responsible for identifying any or all such patent rights. Details 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 d
21、ocument is information given for the convenience of users and does not constitute an 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 WTO principles in the Technical Barriers to T
22、rade (TBT) see the following URL: Foreword - Supplementary information The c o m m it tee respo n si ble for this d ocument is I SO/TC 60, Gears, Subcommittee SC 1, Nomenclature and wormgearing. This second edition cancels and replaces the first edition (ISO/TR 10828:1997), which has been technicall
23、y revised. This edition includes the formulation for the geometrical dimensions of the worm and worm wheel, and that for the determination of gear mesh geometry (path of contact, zone and lines of contact) with the details to determine the non-dimensional parameters used to apply load capacity calcu
24、lations (radius of curvature, sliding velocities). PD ISO/TR 10828:2015 ISO/TR 10828:2015(E) vi ISO 2015 All rights reservedIntroduction Thread forms of the worms of worm gear pairs are commonly related to the following machining processes: the type of machining process (turning, milling, grinding);
25、 the shapes of edges or surfaces of the cutting tools used; the tool position relative to an axial plane of the worm; where relevant, the diameters of disc type tools (grinding wheel diameter). This Technical Report introduces all the aspects concerning the gear mesh geometry to define conjugate wor
26、m wheel, path of contact, lines of contact and other associated geometrical characteristics. PD ISO/TR 10828:2015 TECHNICAL REPORT ISO/TR 10828:2015(E) ISO 2015 All rights reserved 1Worm gears Worm profiles and gear mesh geometry 1 Scope In this Technical Report, thread profiles of the five most com
27、mon types of worms at the date of publication are described and formulae of their axial profiles are given. The five worm types covered in this technical report are designated by the letters A, C, I, K and N. The formulae to calculate the path of contact, the conjugate profile of the worm wheel, the
28、 lines of contact, the radius of curvature and the velocities at points of contact are provided. At the end the application of those formulae to calculate parameters used in load capacity calculations are provided. 2 Normative references The following documents, in whole or in part, are normatively
29、referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 1122-2, Vocabulary Worm gears ISO 701, International gear notatio
30、ns Symbols for geometrical data ISO/TR 14521, Worm gears Load capacity of worm gears 3 Symbols and abbreviated terms For the purposes of this document, Tables 1 to 3 give the symbols the indices and the description. Table 1 Symbols for worm gears from Clause 4 of this document Symbols Description Un
31、its Figures Formula number A distance from the worm axis to virtual point of the cutter (see ref.1) mm Fig. A.4 a centre distance mm Fig. 3 41/42 a0 refers to the worm/tool centre distance (length of the common perpendicular to the worm/tool axes) mm Fig. 18 54 a1 to a4 coefficient for A, I and N pr
32、ofile b1 facewidth of worm mm 24 b2H effective wheel facewidth mm Fig. 4 39 b2R wheel rim width mm Fig. 4 c1,c2 tip clearance mm 46/47 PD ISO/TR 10828:2015 ISO/TR 10828:2015(E) 2 ISO 2015 All rights reservedSymbols Description Units Figures Formula number da1 worm tip diameter mm 14 da2 worm wheel t
33、hroat diameter mm 35 db1 base diameter of involute helicoid (for I profile) mm 22 de2 worm wheel outside diameter mm 36 df1 worm root diameter mm 15 df2 worm wheel root diameter mm 34 dm1 worm reference diameter mm Fig. 1/3 10 dm2 worm wheel reference diameter mm Fig 2/3 25 dw1 worm pitch diameter m
34、m 43 dw2 worm wheel pitch diameter mm Fig 5 44 emx 1 worm reference tooth space width in axial section mm Fig. 1 17 en1 worm normal tooth space width in normal section mm 19 em2 worm wheel tooth space width in mid-plane section mm 28 h1 worm tooth depth mm 11 h2 worm wheel tooth depth mm 32 ham1 wor
35、m tooth reference addendum in axial section mm Fig. 3 12 ham2 worm wheel tooth reference addendum in mid-plane section mm Fig. 3 30 * 1 am h worm tooth reference addendum coefficient in axial section - * 2 am h worm wheel tooth reference addendum coefficient in mid- plane section - he2 worm wheel to
36、oth external addendum mm 33 hfm1 worm tooth reference dedendum in axial section mm 13 hfm2 worm wheel tooth reference dedendum in mid-plane section mm 31 * 1 fm h worm tooth reference dedendum coefficient in axial section - * 2 fm h worm wheel tooth reference dedendum coefficient in mid- plane secti
37、on - jx axial backlash mm mn normal module mm 9 mx1 axial module mm 2/G.1 pbn1 normal pitch on base cylinder mm 23 pn1 normal pitch mm 8 pt2 transverse pitch mm 26 px1 axial pitch mm Fig. 1 1 pz1 lead (of worm) mm 3 pzu1 unit lead (lead of worm per radian) mm/rd 4 q1 diameter quotient mm 5 rg2 worm
38、wheel throat form radius mm 40 PD ISO/TR 10828:2015 ISO/TR 10828:2015(E) ISO 2015 All rights reserved 3Symbols Description Units Figures Formula number rb1 base radius for involute profile mm Fig. A.4 and A.5rb1 base radius of a notional base circle mm Fig. A.4 and A.5r tradius at cusp mm Fig. 29 sm
39、2 tooth thickness at the reference diameter of the worm wheel mm Fig. 2 27 sK rim thickness mm Fig. 12 smx1 worm thread thickness in axial section mm Fig. 1 16 * mx1 sworm thread thickness in axial section coefficient - sn1 normal worm thread thickness in normal section mm 18 u gear ratio 45 x2 worm
40、 wheel profile shift coefficient - 29 z1 number of threads in worm - z2 number of teeth in worm wheel - 0n tool normal pressure angle 0t tool transverse pressure angle for A and I profiles Fig. 7 n normal pressure angle 20 m1 reference helix angle of worm 7 m1 reference lead angle of worm 6 b1 base
41、lead angle of worm thread (for I profile) Fig. A.1 21 b1 base lead angle of the notional base helix Fig. A.4 and A.5Gm Radius of curvature of grinding wheel (C profile) In calculation, when a radius is derived, the symbol d for diameter shall be replaced by r for radius. Table 2 Subscripts for worm
42、gears Symbols Description 0 cutting tool 1 worm 2 Wheel G grinding wheel Table 3 Coordinate of remarkable points Symbols Description G G y x , G y , G G y Coordinates of a point on the tool flank when the origin is at the point of intersection of the tool axis and the tool median plane, with the x-a
43、xis as the tool spindle axis and the PD ISO/TR 10828:2015 ISO/TR 10828:2015(E) 4 ISO 2015 All rights reservedabscissa on the trace of the median plane; r x y x , r x y y , r x y Coordinates of axial profile and axial pressure angle for A, I, N worm profiles G x y x , G x y y , G x y Coordinates of a
44、xial profile and axial pressure angle for K and C worm profiles D y x , p D , D y y , p D , D y , p D Coordinates of worm profile and pressure angle of worm profile in an offset plane D y x D , p , D y y , p D , D y , p D Coordinates of worm profile and pressure angle of worm profile in an offset pl
45、ane with origin on pitch axis D y x , p lD , D y y , p lDCoordinates of path of contact in an offset plane with origin on pitch axis D y xR , p D , D y R y , p DCoordinates of conjugate worm wheel profile of the worm in an offset plane with origin on worm wheel axis D r xT , t2D D , D r T y , t2D DC
46、oordinates of trochoid profile of the worm wheel profile in an offset plane with origin on worm wheel axis D ycusp x , D, D ycusp y , DCoordinates of cusp point in an offset plane with origin on pitch axis D y C , p eq1DCurvature for the worm at a point in an offset plane D y C , p eq2DCurvature for
47、 the worm wheel at a point in an offset plane D y R , p eqDEquivalent radius of curvature in an offset plane D r e2Doutside radius of the worm wheel in the offset plane D t2D r root radius of the worm wheel in the offset plane D D y M , p 1Coordinate of a point of contact for the worm (Eq 118) D y M
48、 , p 2Coordinate of a point of contact for the worm wheel (Eq 119) D y TN , 1 p contTangent unit vector to a line of contact (Eq 128) D y Nxy , Normal pNormal unit vector to the lines of contact (Eq 114) D y , NORMAL pNormal unit vector to the lines of contact (Eq 116) D y , q Re pRadius of curvatur
49、e along the line the contact (Eq 135) D y V , p 1Velocity of a point of the thread of the worm (Eq 138) D y V , p 2Velocity of a point of the tooth flank of the worm (Eq 140) D y V , p cDnVelocity at the contact point along the path of contact (Eq 150) D y V , p SUMnSum of velocities at the point of contact (Eq 153) for method B in ISO/TR 14521
