BS 978-2-1952 Specification for fine pitch gears Cycloidal type gears《小节距齿轮 第2部分 摆线齿轮》.pdf

1、BRITISH STANDARD CONFIRMED AUGUST1990 BS978-2:1952 Incorporating Amendment Nos. 1 and2 Gears for instruments and clockwork mechanisms Part2: Cycloidal type gears UDC621.833:6812BS978-2:1952 This BritishStandard, having been approved by the MechanicalEngineering IndustryStandards Committee and endors

2、ed by the Chairman ofthe Engineering Divisional Council, was published under theauthority of the General Council on 24 January1952 BSI 02-2000 First published in October1941 First revision January1952 ISBN 0 580 34084 8 Co-operating organizations The Mechanical Engineering Industry Standards Committ

3、ee under whose supervision this BritishStandard was prepared consists of representatives from the following Government departments and scientific and industrial organizations: The Government departments and the industrial organization marked with anasterisk in the above list, together with the follo

4、wing, were directly represented on the committee entrusted with the preparation of this standard: Admiralty* Institute of Petroleum Air Ministry Institution of Civil Engineers Associated Offices Technical Committee Institution of Gas Engineers Association of Consulting Engineers Institution of Heati

5、ng and Ventilating (Incorporated)* Engineers British Chemical Plant Manufacturers Institution of Mechanical Engineers* Association Institution of Mechanical Engineers British Compressed Air Society (Automobile Division) British Electrical and Allied Manufacturers Institution of Production Engineers*

6、 Association* Locomotive Manufacturers Association British Engineers Association* Machine Tool Trades Association* British Internal Combustion Engine Ministry of Fuel and Power Manufacturers Association Ministry of Labour and National Service British Iron and Steel Federation (Factory Department) Br

7、itish Railways, The Railway Executive* Ministry of Supply* Crown Agents for the Colonies Ministry of Transport* Department of Scientific and Industrial Ministry of Works Research Office of the High Commissioner for India Engineering Equipment Users Association War Office Institute of Marine Engineer

8、s Association of Mining Electrical and National Association of Lift Makers Mechanical Engineers National Federation of Engineers Tool British Clock and Watch Manufacturers Manufacturers Association National Physical Laboratory British Gear Manufacturers Association North East Coast Institution of En

9、gineers and British Horological Institute Shipbuilders Institution of Engineering Inspection Society of Motor Manufacturers and Traders Manufacturers of Instrument Gears Ltd. Milling Cutter and Reamer Trade Association National Association of Drop Forgers and Stampers Amendments issued since publica

10、tion Amd. No. Date of issue Comments 2407 March1956 4569 May1962 Indicated by a sideline in the marginBS978-2:1952 BSI 02-2000 i Contents Page Co-operating organizations Inside front cover Foreword ii Section 1. General 1 Scope 1 2 Terminology and notation 1 3 Range of standard modules 1 Section 2.

11、Tooth form and proportions 4 Wheels driving pinions 1 5 Driven pinions 3 6 Wheels and pinions for trains in which the pinion may act sometimes asthedriver and sometimes as the driven member 3 7 Contrate gears 5 Section 3. Tolerances (in millimetres) Appendix A Notes on the derivation of cycloidal ge

12、ars where the wheel drives the pinion 6 Appendix B Notation 6 Chart 1 Addendum factor 7 Chart 2 Addendum radius factor 8 Figure 1 Tooth proportions for wheels driving pinions in accordance with Clause4 1 Figure 2 Construction for position of centre of curvature of addendum 2 Figure 3 Proportions for

13、 driven pinions with alternative addendum profiles 2 Figure 4 Pinion addendum profiles 2 Figure 5 Tooth proportions for gears in accordance with Clause5 3 Figure 6 Contrate gears 4 Table 1 Range of modules 1 Table 2 Proportions of driving wheels 1 Table 3 Values of addendum factor (f) and addendum r

14、adius factor (f r ) 2 Table 4 Proportions of driven pinions 3 Table 5 Proportions of wheels and pinions for trains in which the pinion mayact sometimes as the driver and sometimes as the driven member 4 Table 6 Values of addendum factor (f) and addendum radius factor (f r ) fornominal drives 4BS978-

15、2:1952 ii BSI 02-2000 Foreword This standard makes reference to the following BritishStandards: BS978-1, Involute spur, helical and crossed helical gears. BS2519, Glossary of terms and notation for gearing. This BritishStandard supersedes BS978, “Gears for clockwork mechanisms”, which was published

16、in1941 as a war emergency measure to assist in the reduction of types and sizes of both gears and cutters. As a result of experience gained in its use it became evident that a revision was necessary and it was considered desirable to divide the standard into four separate parts as follows: Part1: In

17、volute spur, helical and crossed helical gears; Part2: Cycloidal type spur gears; Part3: Bevel gears; Part4: Worm gears. Part4 will be published as it becomes available. Suitable hobs and cutters will be dealt with in a later BritishStandard. The provisions of this part differ substantially from tho

18、se of the original BS978, as a cycloidal type of gear has been substituted for the circular arc form. The standards of the Swiss and Black Forest watch and clock industries, particularly the former, have been used as a basis; this was considered desirable because of the prevalent use of those standa

19、rds for horological work and other applications where a cycloidal form is preferred. An explanation of this type of gearing, as applied to wheels driving pinions, is included in Appendix A. Arising out of discussions which have taken place in connection with the work undertaken by the International

20、Organization for Standardization on gears, there are indications that it may be possible to simplify the provisions of the standard in regard to tooth form and proportions. It is intended to give further attention to this subject when more evidence is available. A British Standard does not purport t

21、o include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover,

22、 pagesi andii, pages1 to8 and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover.BS978-2:1952 BSI 02-2000 1 Section 1. General 1 Scope This part applies to cycloidal type

23、spur gears for spring or weight-driven mechanisms in which: a) the pinion is the driven member, or b) the pinion is required to act sometimes as the driver and sometimes as the driven member. For integrating electricity meters the particular form of gear specified herein is not necessary and it is r

24、ecognised that other existing forms of gear will continue to be used. 2 Terminology and notation The terms and notation shall be as defined in BS2519 “Glossary of terms and notation for gearing.” For the convenience of users of the standard, an abbreviated list of symbols is given in Appendix B. 3 R

25、ange of standard modules The standard modules shall be as set out in Table 1, preferred sizes being shown in bold type. Table 1 Range of modules Section 2. Tooth form and proportions 4 Wheels driving pinions a) General. The teeth of wheels driving pinions designed in accordance with Clause5 shall ha

26、ve the proportions given in Table 2 and Figure 1. Values for f and f r , appropriate to the gear ratio and the number of teeth in the pinion, shall be obtained from Table 3, or Chart 1andChart 2. The addendum height and the radius of curvature of the addendum shall be in accordance with Table 2. The

27、 centre of curvature for the addendum curve shall be chosen so that the curve and the centre line of the tooth intersect on the addendum circle; the radial flank is tangential to this curve (seeFigure 2). The bottom of the tooth spaces shall be approximately semi-circular (seeFigure 1). Wheels desig

28、ned in accordance with the provisions of this clause are only suitable to drive pinions designed in accordance with Clause5. Table 2 Proportions of driving wheels (dimensions in millimetres) Modules 0.070 0.0725 0.075 0.0775 0.080 0.0825 0.085 0.0875 0.090 0.0925 0.095 0.0975 0.100 0.105 0.110 0.115

29、 0.120 0.125 0.130 0.135 0.140 0.145 0.150 0.155 0.160 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.210 0.220 0.230 0.240 0.250 0.260 0.270 0.280 0.290 0.300 0.320 0.340 0.360 0.380 0.400 0.420 0.440 0.460 0.480 0.500 0.550 0.600 0.650 0.700 0.750 0.800 0.850 0.900 0.950 1.000 Tooth thickness a

30、long pitch circle 1.57m Addendum A fm Dedendum B 1.57m Radius of curvature of addendum r A mf r Pitch diameter D Tm Outside diameter D a D+2fm Root diameter D r D3.14m Figure 1 Tooth proportions for wheels driving pinions in accordance with Clause4BS978-2:1952 2 BSI 02-2000 Table 3 Values of addendu

31、m factor (f) and addendum radius factor (f r ) Ratio T/t 6Teeth 7Teeth 8Teeth 9Teeth 10Teeth 12Teeth 14Teeth 15Teeth 16Teeth f f r f f r f f r f f r f f r f f r f f r f f r f f r 3 4 5 6 6“ 7 7“ 8 8“ 9 9“ 10 11 12 1.259 1.280 1.293 1.303 1.307 1.310 1.313 1.315 1.318 1.320 1.321 1.323 1.326 1.328 1.

32、855 1.886 1.906 1.920 1.926 1.930 1.934 1.938 1.942 1.944 1.947 1.949 1.954 1.957 1.335 1.359 1.374 1.385 1.389 1.393 1.396 1.399 1.402 1.404 1.406 1.408 1.411 1.414 1.968 2.003 2.025 2.041 2.048 2.053 2.058 2.062 2.066 2.069 2.072 2.075 2.080 2.084 1.403 1.430 1.447 1.459 1.464 1.468 1.471 1.475 1.

33、478 1.480 1.482 1.484 1.488 1.491 2.068 2.107 2.132 2.150 2.157 2.163 2.169 2.173 2.177 2.181 2.184 2.187 2.193 2.197 1.465 1.494 1.513 1.526 1.531 1.536 1.540 1.543 1.547 1.549 1.552 1.554 1.558 1.561 2.160 2.202 2.230 2.249 2.257 2.263 2.269 2.274 2.279 2.283 2.287 2.290 2.296 2.301 1.523 1.554 1.

34、574 1.588 1.594 1.599 1.603 1.607 1.610 1.613 1.616 1.618 1.623 1.626 2.244 2.290 2.320 2.341 2.349 2.356 2.363 2.368 2.373 2.377 2.381 2.385 2.391 2.397 1.626 1.661 1.684 1.700 1.707 1.712 1.717 1.721 1.725 1.728 1.731 1.734 1.739 1.743 2.396 2.448 2.482 2.505 2.516 2.523 2.530 2.536 2.542 2.547 2.

35、552 2.556 2.563 2.569 1.718 1.756 1.782 1.799 1.807 1.812 1.818 1.822 1.827 1.830 1.834 1.837 1.842 1.847 2.532 2.589 2.626 2.652 2.662 2.671 2.679 2.686 2.692 2.697 2.703 2.707 2.715 2.722 1.760 1.801 1.827 1.845 1.853 1.859 1.864 1.869 1.874 1.878 1.881 1.884 1.890 1.895 2.594 2.654 2.692 2.719 2.

36、730 2.739 2.748 2.755 2.761 2.767 2.773 2.777 2.785 2.792 1.801 1.843 1.870 1.889 1.897 1.903 1.909 1.914 1.919 1.923 1.926 1.929 1.935 1.940 2.654 2.715 2.756 2.784 2.795 2.804 2.813 2.820 2.827 2.833 2.839 2.844 2.852 2.859 The two addendum curves intersect at the addendum circle Figure 2 Construc

37、tion for position of centreof curvature of addendum Figure 3 Proportions for driven pinions with alternative addendum profiles Figure 4 Pinion addendum profilesBS978-2:1952 BSI 02-2000 3 5 Driven pinions The teeth of pinions to be driven by wheels designed in accordance with Clause4 shall have the p

38、roportions given in Table 4, appropriate to the number of teeth. The centres of curvature for the addendum curves shall be chosen so that the curves and the centre line of the tooth intersect in the addendum circle; the radial flank is tangential to this curve (seeFigure 2). The bottom of the tooth

39、spaces shall be approximately semi-circular. (seeFigure 3). Three different addendum profiles are given, with different values for the addendum and the radius of curvature (seeFigure 4). In general these profiles are used under the following conditions: It should be noted, however, that profiles A a

40、nd B may, in certain circumstances, be used with advantage for pinions with smaller numbers of teeth than those given above. Table 4 Proportions of driven pinions (seeFigure 3) 6 Wheels and pinions for trains in which the pinion may act sometimes as the driver and sometimes as the driven member The

41、proportions for wheels and pinions for trains in which the pinion may act sometimes as the driver and sometimes as the driven member shall be in accordance with Table 5 and Figure 5. The centres of curvature for the addendum curves shall be chosen so that the curves and the centre line of the tooth

42、intersect on the addendum circle; the radial flank is tangential to this curve (seeFigure 2). The roots of the teeth shall be approximately semi-circular. For minute to hour reduction trains, winding trains and hand setting trains, involute teeth in accordance with Part1 of this standard, “Involute

43、spur, helical and crossed helical gears,” should be used. Profile A 10teeth and over Profile B 8 and9teeth Profile C 6and7teeth Number of teeth (t) 610 11 and over Tooth thickness along pitch circle Pitch diameter Outside diameter Root diameter Dedendum Bottom clearance Minimum backlash d d a d r b

44、c 1.05m. tm d+2a d2b (f+0.4)m 0.4m. 0.52m. 1.25m. tm d+2a d2b (f+0.4)m 0.4m. 0.32m. a Addendum Profile A Profile B Profile C a 0.525m. 0.67m. 0.855m. 0.625m. 0.805m. 1.05m. a Radius of curvature of addendum Profile A Profile B Profile C r a 0.525m. 0.70m. 1.05m. 0.625m. 0.84m 1.25m. a SeeClause5,3rd

45、 and4th paragraphs. Figure 5 Tooth proportions for gears in accordance with Clause5BS978-2:1952 4 BSI 02-2000 Table 5 Proportions of wheels and pinions for trains in which the pinion may act sometimes as the driver and sometimes as the driven member The values of f and f rappropriate to the number o

46、f teeth in the gear shall be obtained from Table 6. Table 6 Values of addendum factor (f) and addendum radius factor (f r ) for normal drives Tooth thickness along pitch circle 1.41m. Pitch diameter D or d Tmor tm Addendum A or a fm Dedendum B or b 1.75m. Radius of curvature of addendum r A or r a f

47、 rm Bottom clearance c B a or b A Minimum backlash 0.32m. Number of teeth in gear (T or t) Addendum factor (f) Addendum radius factor (f r ) 8 9 10,11 12,13 14 to16 17 to20 21 to25 26 to34 35 to54 55 to134 135 1.16 1.17 1.19 1.20 1.22 1.24 1.26 1.27 1.29 1.31 1.32 1.85 1.87 1.90 1.92 1.95 1.98 2.01

48、2.03 2.06 2.09 2.11 a) Section on pitch plane of a contrate gear cut with a single track milling cutter. b) Section on pitch plane of a hobbed contrate wheel. Figure 6 Contrate gearsBS978-2:1952 BSI 02-2000 5 7 Contrate gears (SeeFigure 6) a) Tooth proportions These shall be obtained by regarding th

49、e gear as the wheel in a pair having a ratio of12:1. b) Pitch. For contrate gears having teeth formed by rotary cutters the pitch diameter shall be taken as coincident with the outside diameter, i.e.,D a =D. For contrate gears having hobbed teeth the pitch diameter shall be taken as equal to the outside diameter minus the face width, i.e.,D a F=D. c) Face width. For contrate wheels with teeth formed by single track milling cutters the face width should not exceed1.57m. For contrate wheels having