fine pitch gears

BRITISH STANDARD

CONFIRMED AUGUST 1990

BS 978-1:1968Incorporating Amendment No. 1

Specification for

Fine pitch gears —

Part 1: Involute Spur and Helical Gears

UDC 621.833.1

BS 978-1:1968

This British Standard, having been approved by the Mechanical Engineering Industry Standards Committee and endorsed by the Chairman of the Engineering Divisional Council, was published under the authority of the General Council on 31 January 1968

© BSI 10-1999

First published October 1941First revision January 1952Second revision November 1962Third revision January 1968

The following BSI references relate to the work on this standard:Committee reference MEE/17, MEE/17/4Draft for comment 66/14936

ISBN 580 00028 1

Co-operating organizations

The Mechanical Engineering Industry Standards Committee, under whose supervision this British Standard was prepared, consists of representatives from the following Government departments and scientific and industrial organizations:

The Government department and scientific and industrial organizations marked with an asterisk in the above list, together with the following, were directly represented on the committee entrusted with the preparation of this standard:

Associated Offices’ Technical Committee Institution of Civil EngineersAssociation of Consulting Engineers* Institution of Gas EngineersAssociation of Mining Electrical and Institution of Heating and Ventilating

Mechanical Engineers* EngineersBoard of Trade Institution of Mechanical EngineersBritish Chemical Plant Manufacturers’ Institution of Mechanical Engineers

Association (Automobile Division)British Compressed Air Society Institution of Production Engineers*British Electrical and Allied Manufacturers’ Locomotive and Allied Manufacturers’

Association* Association of Great BritainBritish Gear Manufacturers’ Association* London Transport BoardBritish Internal Combustion Engine Machine Tool Trades Association*

Manufacturers’ Association Ministry of DefenceBritish Iron and Steel Federation Ministry of Labour (H.M. Factory Inspectorate)British Mechanical Engineering Federation Ministry of PowerBritish Pump Manufacturers’ Association Ministry of Public Building and WorksCrown Agents for Oversea Governments and Ministry of Technology — National

Administrations Engineering Laboratory*Electricity Council, the Central Electricity Ministry of Transport

Generating Board and the Area Boards National Coal Boardin England and Wales National Physical Laboratory (Ministry of

Engineering Equipment Users’ Association Technology)Gas Council Radio Industry CouncilInstitute of Marine Engineers* Royal Institute of British Architects

British Horological Institute Ministry of TechnologyElectronic Engineering Association Navy and Vickers Gearing Research Institute of British Foundrymen AssociationInstitution of Engineering Inspection North-East Coast Institution of EngineersInstitution of Engineers and Shipbuilders in and Shipbuilders

Scotland Society of Motor Manufacturers and TradersMilling Cutter and Reamer Association Ltd.Ministry of Defence, Army Department University of SheffieldMinistry of Defence, Navy Department Manufacturers of fine pitch gears

Amendments issued since publication

Amd. No. Date of issue Comments

3305 May 1980 Indicated by a sideline in the margin

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Contents

PageCo-operating organizations Inside front coverForeword iii1 General1.1 Scope 11.2 Terminology and notation 11.3 Preferred range of normal diametral pitches 21.4 Basic rack tooth profile 22 Design details2.1 Outside diameter and centre distance 32.2 Modification of addendum and centre distance 33 Accuracy of gear blanks and gears3.1 General 133.2 Dual flank composite testing 143.3 Limits of tolerance on blanks and gear elements 154 Limits and tolerances of assembly4.1 Centre distance 174.2 Depth of engagement 185 Information to be given on drawingsAppendix A Centre distance and addendum modification 21Appendix B Examples of calculations 23Appendix C Comparable diametral pitches and metric modules 29Appendix D Single flank composite testing: Limits of tolerance 29Appendix E Calculation of measuring pin dimensions for external and internal spur gears 29Figure 1 — Basic rack tooth profile for unit normal diametral pitch 2Figure 2 — Basic rack tooth profile for unit normal diametral pitch with backlash allowance 2Figure 3 — Limiting values of addendum modification coefficient 5Figure 4 — Minimum permissible addendum modification coefficient for helical pinions (!n = 20°) 6Figure 5 — Tolerance zone for profile error 15Figure 6 — Example of information to be given on drawings 20Figure 7 — Chart for normal backlash when x1 + x2 = y 28Table 1 — Normal diametral pitch Pn (inch units) 2Table 2 — Data for spur pinions of unit diametral pitch having fewer than 17 teeth 4Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4 7Table 4 — Forces appropriate to the pitch suitable for brass and steel product gears 14Table 5 — Limits of tolerance 14Table 6 — Limits of tolerance on gear blanks 15Table 7 — Limits of tolerance on tooth profile 16Table 8 — Limits of tolerance on pitch 16Table 9 — Limits of tolerance on tooth alignment 16

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PageTable 10 — Limits of tolerance on radial run-out of teeth 17Table 11 — Limits of tolerance on tooth thickness 17Table 12 — Limits of tolerance on centre distance of mounting 17Table 13 — Minimum depth of engagement for spur gear pairs with 28 to 33 teeth (z2 + z1) 18Table 14 — Minimum depth of engagement for spur gear pairs with more than 33 teeth (z2 + z1) 18

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Foreword

This standard makes reference to the following British Standards:BS 978, Fine pitch gears. BS 978-2, Cycloidal type gears. BS 978-PD 3376, Addendum No. 1 to BS 978-2, Double circular arc type gears. BS 978-3, Bevel gears. BS 978-5, Hobs and cutters. First published in 1952 and revised in 1962, this British Standard has been further revised under the authority of the Mechanical Engineering Industry Standards Committee.In the 1962 edition, dual flank composite testing was introduced in the form of an appendix to the specification. As this method of test became more widespread, users of the standard were becoming confused between the application of the composite tolerances and application of the individual elemental tolerances. The prime reason for revision, therefore, has been to give dual flank testing the importance it now deserves by placing it in the mandatory part of the standard as the main accuracy testing procedure. Also care has been taken to ensure that the user is not misled by attempting to reconcile composite errors with elemental errors. It is necessary to retain the elemental tolerances because these will continue to be used in some fields as acceptance criteria and because they are essential as the basis for manufacturing gears and cutting tools1). Recognizing also that single flank testing is used reference to this is made in an appendix.Opportunity has been taken to effect improvements in presentation and in the examples of calculations, and the terminology and notation is in accordance with that agreed within the International Organization for Standardization (ISO).This standard is a companion work to BS 978, “Fine pitch gears”, Part 2, “Cycloidal type gears” (including addendum PD 3376, “Double circular arc type gears”), Part 3, “Bevel gears”, and Part 5, “Hobs and cutters”.A British Standard does not purport to 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 pagesThis document comprises a front cover, an inside front cover, pages i to iv,pages 1 to 29 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.

1) BS 978, “Fine pitch gears”, Part 5, “Hobs and cutters”.

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1 General

1.1 ScopeThis British Standard relates to involute spur, helical and crossed helical gears, having diametral pitches finer than 20, in four accuracy grades. Examples of application are:Class A. Astronomical apparatus and scientific instruments; colour printing machinery; control systems (when multiple trains of gears are involved this grade would generally be used for low speed components where the effect of positional accuracy is important).Class B. Navigational instruments; high speed components of control systems where quietness and smooth running are essential; machine tool speed control; photographic instruments.Class C. General purpose instruments; accounting and calculating machinery; counters; clockwork mechanisms.Class D. Textile machinery; switch operating gear; clockwork mechanisms where accuracy is not the primary consideration.It is recommended that all spur, helical and crossed helical gears for use in horology should be produced to this British Standard with the possible exception of gears for weight or spring-driven mechanisms in which the pinion is the driven member and has 12 or fewer teeth. In such cases it may be preferable to use gears conforming to BS 978-22).

1.2 Terminology and notationAs the first step towards achieving international understanding of gears terminology, the terms and definitions of Draft ISO Recommendation No. 8883), “International vocabulary of gears”, have been applied, together with corresponding notation derived from Draft ISO Recommendation No. 889, “International gear notation, symbols for geometrical data”3).The notation used is as follows:

2) BS 978, “Fine pitch gears”, Part 2, “Cycloidal type spur gears”.3) To be incorporated in BS 2519, “Glossary of terms for toothed gearing”.

a Centre distanceav Virtual centre distanced Reference circle diameterd1 Reference circle diameter: piniond2 Reference circle diameter: wheelda Tip diameterda1 Tip diameter: pinionda2 Tip diameter: wheeldR Measuring pin diameterdb Base circle diameterjn Normal backlashja Coefficient for calculation of backlashl Length of arcPn Normal diametral pitchs Arc tooth thicknesss1 Arc tooth thickness: pinions2 Arc tooth thickness: wheelx Addendum modification coefficientx1 Addendum modification coefficient: pinionx2 Addendum modification coefficient: wheel%x1 Secondary addendum modification coefficient: pinion%x2 Secondary addendum modification coefficient: wheely Centre distance modification coefficient

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1.3 Preferred range of normal diametral pitchesThe pitch shall be selected from the following preferred range.

Table 1 — Normal diametral pitch Pn (inch units)

1.4 Basic rack tooth profileThe shape and proportions of the basic rack tooth for spur helical and crossed helical gears shall be as shown either in Figure 1 or Figure 2. In the case of helical and crossed helical gears, the shape and proportions of the tooth are on a section at right angles to the pitch cylinder helix.

Figure 1 shows the basic rack usually employed where it is desired to have minimum backlash, as in servomechanisms.

z Number of teethz1 Number of teeth: pinionz2 Number of teeth: wheelzv Virtual number of teeth!n Normal pressure angle!nw Normal pressure angle, operating!t Transverse pressure angle!tw Transverse pressure angle, operating" Helix angle at reference cylinder"b Helix angle at base cylindera BS 978, “Fine pitch gears”, Part 5, “Hobs and cutters”.

32 48 100 16024 36 64 120 18028 40 80 140 200

Figure 1 — Basic rack tooth profile for unit normal diametral pitch

Figure 2 — Basic rack tooth profile for unit normal diametral pitch with backlash allowance

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Figure 2 is used where it is desired to have backlash to avoid any risk of jamming and where the load is usually uni-directional, for example, in clockwork mechanisms. When non-topping hobs are used it is permissible to use a hob conforming to Figure 1 basic rack and to cut at greater depth than normal to obtain the required tooth thickness.For internal gears (Figure 1 and Figure 2 basic racks) the addendum shall normally be 0.850 instead of 1.000. In cases when the tips of the teeth have a radius of 0.25 or greater (up to 0.3 max. as shown) the 1.000 addendum may be applied.

2 Design details

2.1 Outside diameter and centre distanceFor the normal case when both z1 sec3" and z2 sec3" are greater than 17 the dimensions are as follows:

2.2 Modification of addendum and centre distance2.2.1 For an explanation of the principles followed in connection with addendum modification see Appendix A.2.2.2 Where no limitations are imposed, the value of x for any gear whose virtual number of teeth zv is less than 17 is given by the formulae:

This gives values in accordance with the lower limiting line XX in Figure 3 and a small and normally negligible amount of undercutting is thereby permitted.The addendum modification coefficient for helical pinions from 6 to 16 teeth and helix angles up to 45° is shown in Figure 4.2.2.3 When the pinion is modified as above and there are no other limitations, the wheel is unmodified and its dimensions are obtained from the formulae in 2.1; but the dimensions of the pinion and centre distance are as follows:

Parallel axis external gear pairs designed as above have backlash at this centre distance. (See Appendix A.)

(1) (2)

(3) (4)

(5)

(For spur gears, sec" = 1)

(See Table 2 and Figure 3 and Figure 4) (6)

where zv = z sec" sec2"b . z sec3" (7)

(8)

(Figure 1 type gears) (9)


(11)

x 1zv sin2 µ

2-------------------------n–=

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Table 2 — Data for spur pinions of unit diametral pitch having fewer than 17 teeth

2.2.4 Enlarged spur pinions with minimum backlash. Spur pinions enlarged according to Table 2 may be engaged with wheels in which x2 is zero, at centre distance derived from Table 3. Gears derived from Figure 1 basic rack will have no backlash at this centre distance. A small and negligible reduction of tip-to-root clearance is obtained at this centre distance.Table 2 is not applicable to helical gears, for which the formulae in Appendix A are required.Alternatively, spur pinions enlarged according to Table 2 or helical pinions enlarged according to Figure 4 may be engaged with wheels in which x2 = – x1, in which case the centre distance is as obtained in 2.1, and

Such gears derived from Figure 1 basic rack will have zero backlash at nominal dimensions.

No. of teeth

z1

Addendum modification

coefficient x1

Tip diameter

da1

Increase in circular tooth thickness at

standard pitch dia.

Recommended minimum number

of teeth in mating wheel

z2

8a

9a

10

0.53210.47360.4151

11.064211.947212.8302

0.38740.34480.3022

262524

111213

0.35660.29820.2397

13.713214.596315.4793

0.25960.21700.1744

232221

141516

0.18120.12270.0642

16.362317.245318.1284

0.13190.08930.0467

201918

a Pinions having 8 or 9 teeth generated from basic rack Figure 1 have narrow crest width, as also have pinions of 10 and 11 teeth generated from basic rack Figure 2. 10 is the smallest number of teeth that can be generated at full depth from basic rack Figure 2.



(14)

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SI 10-1999

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Figure 3 — Limiting values of addendum modification coefficient

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I 10-1999

Figure 4 — Minimum permissible addendum modification coefficient for helical pinions (!n = 20°)

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Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4

z1 = 10; x1 = 0.4151

z2 10 20 30 40 50 60 70 80 90 100

01234

10.684511.146011.606012.064412.5213

15.381415.882216.385116.883917.3846

20.388720.889321.389821.890422.3909

25.393425.893826.394126.894427.3947

30.396330.896631.396831.897132.3974

35.398735.898036.399136.899337.3994

40.400440.900541.400741.900842.4010

45.401945.902046.402246.902247.4024

50.403250.903351.403451.903552.4036

55.404355.904456.404556.904657.4046

56789

12.976713.430713.883314.379514.8804

17.885418.386118.886819.387519.8881

22.891323.391823.892224.392724.8931

27.895028.395328.895629.395829.8961

32.897633.397833.898134.398234.8985

37.899638.399838.900039.400039.9002

42.901243.401343.901444.401644.9017

47.902648.402748.902849.402949.9031

52.903853.403953.904054.404154.9042

57.904758.404858.904959.405059.9051

z2 110 120 130 140 150 160 170 180 190 200

01234

60.405260.905261.405361.905462.4055

65.405965.906066.406066.906267.4062

70.406670.906671.406771.906772.4068

75.407175.907176.407276.907277.4073

80.407680.907681.407681.907782.4077

85.408085.908086.408086.908187.4081

90.408390.908491.408491.908492.4085

95.408695.908796.408796.908797.4088

100.4089100.9090101.4090101.9090102.4091

105.4092105.9092106.4092106.9093107.4093

56789

62.905663.405663.905764.405864.9058

67.906268.406468.906369.406469.9065

72.906873.406973.906974.407074.9070

77.907378.407478.907479.407579.9075

82.907883.407883.907884.407984.9079

87.908288.408288.908289.408389.9083

92.908593.408593.908694.408694.9086

97.908898.408898.908899.408999.9089

102.9091103.4091103.9091104.4092104.9092

107.9093108.4093108.9093109.4094109.9094

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8 © BSI 10-1999


z1 = 11; x1 = 0.3566

z2 10 20 30 40 50 60 70 80 90 100

01234

11.146111.606012.064412.521312.9767

15.831516.332116.832717.333317.8338

20.836621.337021.837422.337822.8382

25.840226.340526.840827.341027.8413

30.842731.342931.843132.343332.8435

35.844536.344736.844837.345037.8451

40.846041.346141.846242.346342.8464

45.847146.347246.847347.347447.8474

50.848051.348151.848252.348352.8483

55.848856.348856.848957.349057.8490

56789

13.430713.883314.334414.830215.3309

18.334318.834819.335319.835820.3362

23.338523.838924.339224.839525.3399

28.341628.841829.342129.842330.3425

33.343733.843834.344034.844235.3444

38.345338.845439.345639.845740.3458

43.346543.846644.346844.846945.3470

48.347548.847649.347749.847850.3479

53.348453.848554.348654.848655.3487

58.349158.849259.349259.849360.3493

z2 110 120 130 140 150 160 170 180 190 200

01234

60.849461.349561.849562.349662.8496

65.850066.350066.850067.350167.8502

70.850471.350571.850572.350672.8506

75.850876.350976.850977.351077.8510

80.851281.351281.851382.351382.8513

85.851586.351586.851687.351687.8516

90.851891.351891.851892.351892.8518

95.852096.352096.852097.352097.8520

100.8522101.3522101.8522102.3522102.8522

105.8523106.3523106.8523107.3523107.8524

56789

63.349763.849864.349864.849865.3499

68.350268.850269.350369.850470.3504

73.350673.850774.350774.850875.3508

78.351078.851179.351179.851280.3512

83.351483.851484.351484.851485.3515

88.351688.851789.351789.851790.3518

93.351893.851994.351994.851995.3519

98.352098.852199.352199.8521

100.3521

103.3522103.8523104.3523104.8523105.3523

108.3524108.8524109.3524109.8524110.3524

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© BSI 10-1999 9


z1 = 12; x1 = 0.2982

z2 10 20 30 40 50 60 70 80 90 100

01234

11.606012.064412.521312.976713.4307

16.280616.781117.281517.782618.2827

21.284421.784722.285022.785223.2855

26.286826.787027.287227.787428.2876

31.288431.788532.288632.788833.2889

36.289636.789737.289837.789938.2900

41.290541.790642.290742.790843.2909

46.291346.791447.291447.791547.2916

51.291951.792052.292152.792153.2922

56.292556.792557.292657.792658.2927

56789

13.883314.334414.784115.279615.7801

18.782819.283119.783520.283820.7841

23.785824.286024.786225.286425.7866

28.787729.287929.788030.288230.7883

33.789034.289134.789235.289335.7894

38.790139.290239.790340.290440.7905

43.790944.291044.791145.291245.7912

48.791649.291749.791850.291850.7919

53.792254.292354.792355.292455.7924

58.792759.292859.792860.292860.7929

z2 110 120 130 140 150 160 170 180 190 200

01234

61.292961.793062.293062.793063.2931

66.293366.793467.293467.793468.2934

71.293671.793772.293772.793773.2938

76.293976.794077.294077.794078.2940

81.294281.794282.294282.794283.2942

86.294486.794487.294487.794488.2944

91.294691.794692.294692.794693.2946

96.294896.794897.294897.794898.2948

101.2949101.7949102.2949102.7949103.2950

106.2950106.7950107.2950107.7950108.2950

56789

63.793164.293264.793265.293265.7933

68.793569.293569.793570.293670.7936

73.793874.293874.793875.293975.7939

78.794179.294179.794180.294180.7942

85.794384.294384.794385.294385.7944

88.794589.294589.794590.294590.7946

93.794794.294794.794795.294795.7948

98.794999.294999.7949

100.2949100.7949

103.7950104.2950104.7950105.2950105.7950

108.7951109.2951109.7951110.2951110.7951

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10 © BSI 10-1999


z1 = 13; x1 = 0.2397

z2 10 20 30 40 50 60 70 80 90 100

01234

12.064412.521312.976713.430713.8833

16.728217.228517.728818.229118.7293

21.730622.230822.731023.231223.7314

26.732227.232327.732528.232628.7327

31.733332.233432.733533.233633.7337

36.734137.234237.734338.234438.7344

41.734742.234842.734843.234943.7349

46.735247.235347.735348.235348.7354

51.735652.235752.735753.235753.7358

56.735957.236057.736058.236058.7361

56789

14.334414.784115.232415.727616.2280

19.229619.729820.230020.730221.2304

24.231624.731725.231825.732026.2321

29.232829.732930.233030.733131.2332

34.233834.733835.233935.734036.2340

39.234439.734540.234640.734641.2347

44.235044.735045.235145.735146.2352

49.235449.735550.235550.735551.2356

54.235854.735855.235855.735956.2359

59.236159.736160.236260.736261.2362

z2 110 120 130 140 150 160 170 180 190 200

01234

61.736262.236362.736363.236363.7364

66.736567.236667.736668.236668.7366

71.736772.236872.736873.236873.7368

76.736977.237077.737078.237078.7370

81.737182.237182.737183.237183.7372

86.737287.237287.737288.237288.7372

91.737392.237392.737393.237393.7374

96.737497.237497.737498.237498.7374

101.7375102.2375102.7375103.2375103.7376

106.7376107.2376107.7376108.2376108.7376

56789

64.236464.736465.236465.736566.2365

69.236669.736670.236770.736771.2367

74.236874.736875.236975.736976.2369

79.237079.737080.237180.737181.2371

84.237284.737285.237285.737286.2372

89.237389.737390.237390.737391.2373

94.237494.737495.237495.737496.2374

99.237599.7375

100.2375100.7375101.2375

104.2376104.7376105.2376105.7376106.2376

109.2376109.7376110.2376110.7377111.2377

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© BSI 10-1999 11


z1 = 14; x1 = 0.1812

z2 10 20 30 40 50 60 70 80 90 100

01234

12.521312.976713.430713.883314.3344

17.174617.674818.174918.675119.1752

22.176022.676123.176223.676324.1764

27.176927.677028.177028.677129.1772

32.177532.677633.177633.677734.1777

37.178037.678138.178138.678139.1782

42.178442.678443.178545.678544.1785

47.178747.678748.178748.678849.1788

52.178952.678953.178953.679054.1790

57.179157.679158.179158.679259.1792

56789

14.784115.232415.679316.174016.6744

19.675420.175520.675621.175821.6759

24.676525.176625.676626.176726.6768

29.677330.177330.677431.177431.6775

34.677835.177835.677936.177936.6780

39.678240.178240.678341.178341.6784

44.678645.178645.678646.178746.6787

49.678850.178850.678851.178951.6789

54.679055.179055.679056.179156.6791

59.679260.179260.679261.279261.6792

z2 110 120 130 140 150 160 170 180 190 200

01234

62.179262.679363.179363.679364.1793

67.179467.679468.179468.679469.1794

72.179472.679573.179573.679574.1795

77.179677.679678.179678.679679.1796

82.179782.679783.179783.679784.1797

87.179887.679888.179888.679889.1798

92.179992.679993.179993.679994.1799

97.179997.679998.179998.679999.1799

102.1800102.6800103.1800103.6800104.1800

107.1800107.6800108.1800108.6800109.1800

56789

64.679365.179365.679366.179366.6793

69.679470.179470.679471.179471.6794

74.679575.179575.679576.179576.6795

79.679680.179680.679681.179681.6796

84.679785.179785.679786.179886.6798

89.679890.179890.679891.179891.6799

94.679995.179995.679996.179996.6799

99.6799100.1800100.6800101.1800101.6800

104.6800105.1800105.6800106.1800106.6800

109.6800110.1801110.6801111.1801111.6801

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z1 = 15; x1 = 0.1227

z2 10 20 30 40 50 60 70 80 90 100

01234

12.976713.430713.883314.334414.7841

17.619518.119618.619719.119819.6199

22.620223.120323.620324.120424.6204

27.620728.120728.620729.120829.6208

32.621033.121033.621034.121034.6211

37.621238.121238.621239.121239.6213

42.621443.121443.621444.121444.6214

47.621548.121548.621549.121549.6215

52.621653.121653.621654.121654.6216

57.621758.121758.621759.121759.6217

56789

15.232415.679316.124816.619217.1193

20.120020.620021.120121.620122.1202

25.120525.620526.120526.620627.1206

30.120830.620831.120931.620932.1209

35.121135.621136.121136.621237.1212

40.121340.621341.121341.621442.1214

45.121445.621546.121546.621547.1215

50.121650.621651.121651.621652.1216

55.121655.621756.121756.621757.1217

60.121860.621861.121861.621862.1218

z2 110 120 130 140 150 160 170 180 190 200

01234

62.621863.121863.621864.121864.6218

67.621868.121968.621969.121969.6219

72.621973.121973.621974.121974.6219

77.622078.122078.622079.122079.6220

82.622083.122083.622084.122084.6220

87.622088.122088.622089.122089.6220

92.622193.122193.622194.122194.6221

97.622198.122198.622199.122199.6221

102.6221103.1221103.6221104.1221104.6221

107.6222108.1222108.6222109.1222109.6222

56789

65.121865.621866.121866.621867.1218

70.121970.621971.121971.621972.1219

75.121975.621976.122076.622077.1220

80.122080.622081.122081.622082.1220

85.122085.622086.122086.622087.1220

90.122090.622191.122191.622192.1221

95.122195.622196.122196.622197.1221

100.1221100.6221101.1221101.6221102.1221

105.1222105.6222106.1222106.6222107.1222

110.1222110.6222111.1222111.6222112.1222

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3 Accuracy of gear blanks and gears

3.1 GeneralThe measurement of individual elemental errors in fine pitch gears is sometimes difficult and often involves the use of equipment which may not readily be available. Furthermore, the individual limits of tolerance may be so very minute as to render them unrealistic as inspection criteria.The acceptance criteria of this British Standard are therefore based on dual flank composite error testing, by which product gears are rotated in close mesh with master gears of known error, and the results given in terms of the measured variations in centre distance appropriate to the combination of master gear and product gear.It is necessary, however, to appreciate that the variation in centre distance so measured, may include the combined effects of profile, tooth thickness, adjacent pitch and tooth alignment errors but will not necessarily be the sum of such errors. Under some circumstances, therefore, it may be necessary to control and assess elemental errors and, for this reason, coupled with the need to provide an adequate basis for accurate manufacture of the related hobs and cutters, the limits of tolerance for each possible contributing source of error are also given.Therefore, the test methods embraced within this British Standard are:

However, recognizing the development of the single flank composite testing procedure, tolerances are given in Appendix D.

z1 = 16; x1 = 0.0642

z2 10 20 30 40 50 60 70 80 90 100

01234

13.430713.883314.334414.784115.2524

18.063318.563419.063419.563420.0634

23.063523.563524.063524.563625.0636

28.063628.563629.063629.563630.0657

33.063733.563734.063734.563735.0637

38.063838.563839.063839.563840.0638

43.063843.563844.063844.563845.0638

48.063948.563949.063949.563950.0639

53.063953.563954.063954.563955.0639

58.063958.563959.063959.563960.0639

56789

15.679316.124816.568817.063317.5633

20.563421.063521.563522.063522.5635

25.563626.063626.563627.063627.5636

30.563731.063731.563732.063732.5637

35.563736.063836.563837.063837.5638

40.563841.063841.563842.063842.5638

45.563846.063846.563847.063847.5639

50.563951.063951.563952.063952.5639

55.563956.063956.563957.063957.5639

60.563961.063961.563962.063962.5639

z2 110 120 130 140 150 160 170 180 190 200

01234

63.063963.563964.363964.564065.0640

68.064068.564069.064069.564070.0640

73.064073.564074.064074.564075.0640

78.064078.563379.064079.564080.0640

83.064083.564084.064084.564085.0640

88.064088.564089.064089.564090.0640

93.064093.564094.064094.564095.0640

98.064098.564099.064099.5640

100.0640

103.0640103.5640104.0640104.5640105.0640

108.0641108.5641109.0641109.5641110.0641

56789

65.564066.064066.564067.064067.5640

70.564071.064071.564072.064072.5640

75.564076.064076.564077.064077.5640

80.564081.064081.564082.064082.5640

85.564086.064086.564087.064087.5640

90.564091.064091.564092.064092.5640

95.564096.064096.564097.064097.5640

100.5640101.0640101.5640102.0640102.5640

105.5640106.0641106.5641107.0641107.5641

110.5641111.0641111.5641112.0641112.5641

a. limits of tolerance on gear blanks (when applicable)

b. dual flank composite testing

c. assessment of elemental errors

d. combinations of b and c.

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Additionally, pin dimensions for taking measurements over pins in respect of spur gears, are given in Appendix E. It should be appreciated, however, that owing to radial run-out errors, the tooth thickness measured over pins will not necessarily equate with tooth thickness at the reference circle.The actual testing procedures to be adopted shall be the subject of agreement between purchaser and manufacturer and requirements shall be stated clearly on drawings (see Section 5 and Figure 6) and on purchase orders and contracts.IMPORTANT NOTE. Generally, a pair of mating gears are of identical accuracy grade but, by agreement between purchaser and manufacturer, finer or coarser grades may be adopted for the pinion or wheel, or for certain elements of a pinion or wheel.

3.2 Dual flank composite testing — test pressures and limits of toleranceThe product gear shall be rotated in close mesh with a calibrated master gear under just sufficient force to ensure adequate contact whilst permitting free rotation. Forces appropriate to the pitch suitable for brass and steel product gears are given in Table 4. The errors thus revealed shall not exceed the appropriate limits of tolerance as prescribed in Table 5.

Table 4 — Forces appropriate to the pitch suitable for brass and steel product gears

Table 5 — Limits of tolerance

24 to 80 Pn over 80 to 160 Pn over 160 Pn

Master worm 8 ozf 4 ozf 2 ozf

Master wheel 16 ozf 8 ozf 4 ozfNOTE These values may need to be reduced when checking product gears in soft materials such as plastics or aluminium.

Class A Class B Class C Class D

in in in in

Max. tooth totooth compositeerror tolerance

10 to 19 teeth20 to 29 teethover 30 teeth

0.00040.00030.0002

0.00070.00060.0005

0.00100.00090.0009

0.00250.00230.0023

Max. total composite error tolerance 0.0006 0.0010 0.0016 0.0040Max. departure from the centre distance appropriate to this combination of master gear and product gear when meshed with a theoretically correct master gear

– 0.0003

– 0.0011

– 0.0005

– 0.0019

– 0.0005

– 0.0027

– 0.0005

– 0.0060

Applicable to a pitch range ofa 24 to 200 Pn 24 to 160 Pn 24 to 80 Pn 24 to 40 Pn

NOTE Where for any reason it is desired to use a tooth thickness which is not that given for the Figure 1 basic rack, the centre distance tolerance zones given above apply.a Finer pitches are permissible provided that the contact ratio of the gear pair is not less than 1.1.

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3.3 Limits of tolerance on blanks and gear elements3.3.1 Gear blanks. Limits and tolerances on gear blanks shall be in accordance with Table 6. Where a topping hob or cutter is used the limits on blank diameter may not apply.

Table 6 — Limits of tolerance on gear blanks

Item Class A Class B Class C Class D

Blank diameter when used for location h7 of BS 1916a h7 of BS 1916a h8 of BS 1916a h9 of BS 1916a

Radial runout of periphery (or reference surface) relative to datum when used for setting or measurement of teeth (FIMb)

in in in in

0.000 2 0.000 2 0.000 3 0.000 1 da + 0.001

Axial runout at reference diameter (FIMb)

Flatness of end facesa BS 1916, “Limits and fits for engineering”.b Full indicated movement.

Figure 5 — Tolerance zone for profile error

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3.3.2 Profile. Limits of tolerance on tooth profile are given in Table 7. The limits given are in relation to the design profile that coincides with the actual profile at mid working depth (see Figure 5).

Table 7 — Limits of tolerance on tooth profile

3.3.3 Pitch. Limits of tolerance on pitch (adjacent and cumulative) are given in Table 8. Table 8 — Limits of tolerance on pitch

3.3.4 Tooth alignment. The tolerances are listed in Table 9. Table 9 — Limits of tolerance on tooth alignment

Class

Limits of toleranceGenerally

applicable to a pitch range ofMiddle third of

working depth

Outside middle third of

working depth

in in

A + 0.000 05– 0.000 10

0– 0.000 1

24 to 200 inc.

B + 0.000 05– 0.000 20

0– 0.000 2

24 to 160 inc.

C + 0.000 10– 0.000 30

0– 0.000 3

24 to 80 inc.

D + 0.000 10– 0.000 70

0– 0.000 7

24 to 40 inc.

Class Limits of tolerance Generally applicable to a pitch range of

in

A 0.000 2 + 0.000 1 24 to 200 inc.

B 0.000 32 + 0.000 16 24 to 160 inc.

C 0.000 5 + 0.000 25 24 to 80 inc.

D 0.000 8 + 0.000 4 24 to 40 inc.

where l = any selected length of arc, including an arc length of one pitch, but not greater than .

NOTE Limits of pitch tolerance are given with reference to the axis of rotation.

Face widthClass A Class B Class C Class D

Over up to and inc.

in in in in in in

0.5 0.000 16 0.000 25 0.000 4 0.000 60.5 1 0.000 2 0.000 32 0.000 5 0.000 81 2 0.000 25 0.000 4 0.000 6 0.001 02 4 0.000 32 0.000 5 0.000 8 0.001 3

l

l

l

l

;d2

-------

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3.3.5 Radial run-out of teeth. Tolerances are given in Table 10. Table 10 — Limits of tolerance on radial run-out of teeth

3.3.6 Tooth thickness. Limits of tolerance for tooth thickness are given in Table 11. Table 11 — Limits of tolerance on tooth thickness

4 Limits and tolerances of assembly

4.1 Centre distanceLimits of tolerance for centre distance of mounting shall be as given in Table 12.

Table 12 — Limits of tolerance on centre distance of mounting

Class A Class B Class C Class D

Pitch range generally applicable

24 to 100 Pn inc.

over 100 to 200 Pn

inc.

24 to 100 Pn inc.

over 100 to 160 Pn

inc.

24 to 80 Pn inc.

24 to 40Pn inc.

in in in in in in

Tolerance 0.000 3 0.000 2 0.000 4 0.000 3 0.000 6 0.001 6NOTE Where backlash is allowable the limit for radial run-out does not apply provided the pitch tolerances are within the limits specified in 3.3.3.

ClassLimits of tolerance Generally

applicable to a pitch range ofFigure 1 gears Figure 2 gears

A – 0.000 3– 0.000 6

± 0.000 25 24 to 200 inc.

B – 0.000 6– 0.001 0

± 0.000 4 24 to 160 inc.

C – 0.000 9– 0.001 6

± 0.000 8 24 to 80 inc.

D – 0.001 6– 0.003 0

± 0.001 6 24 to 40 inc.

NOTE 1 The above tolerances should be related to those of Table 5 when the dual flank method of composite testing is employed.NOTE 2 Measuring pin diameters for external and internal spur gears are given in Appendix E.

Class Limits of toleranceGenerally

applicable to a pitch range of

in in

A ± (0.000 08 + 0.000 08) 24 to 200 inc.

B ± (0.000 16 + 0.000 16) 24 to 160 inc.

C ± (0.000 32 + 0.000 32) 24 to 80 inc.

D ± (0.000 6 + 0.000 6) 24 to 40 inc.

where a is the centre distance in inches.

a

a

a

a

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4.2 Depth of engagementIt may be found necessary, in the finer pitches of gears, to resort to graded inspection and selective assembly in order to maintain a satisfactory minimum depth of engagement and a suitable contact ratio.Table 13 and Table 14 give recommended minimum values for working depth, based on contact ratios not less than 1.0 where the teeth have rounded tips or approximately 1.2 where the rounding is absent.The larger of the two values obtained from the tables should be taken.These data are applicable to spur gears. They will be applicable to helical or crossed helical gears if the number of teeth in each gear is multiplied by sec3 ".It should be noted that backlash is increased when the working depth is less than nominal, and in circumstances in which backlash has to be limited, tolerances affecting depth of engagement are governed by consideration of the backlash rather than by contact ratio.

Table 13 — Minimum depth of engagement for spur gear pairs with 28 to 33 teeth (z2 + z1)

Table 14 — Minimum depth of engagement for spur gear pairs with more than 33 teeth (z2 + z1)

5 Information to be given on drawingsIn accordance with the requirements of BS 3084) the following is recommended as a standard form showing essential information required on drawings for workshops and office reference (see Figure 6 which is for illustration purposes only).All manufacturing dimensions should be shown in the body of the drawing except those relating to gear cutting which should be shown in a table, either at the right hand side or bottom of the drawing.The following information should be given in the table:

Type of gearNumber of teethNormal diametral pitchBasic rack tooth formClass of gearReference circle diameterWhole depth of toothTooth thickness on reference circleHandLead

No. of teeth in pinion

(z1)

Minimum depth of engagement

Sum of number of teeth(z2 + z1)


10–12 1.85/Pn 28–29 1.80/Pn13–14 1.80/Pn 30–32 1.75/Pn15–16 1.70/Pn 33 1.7/Pn

No. of teeth in pinion

(z1)


Sum of number of teeth(z2 + z1)


8 1.8/Pn 34–59 1.70/Pn9 1.75/Pn 40–49 1.65/Pn10–11 1.70/Pn 50 and above 1.60/Pn12–16 1.65/Pn17 and above 1.60/Pn

4) BS 308, “Engineering drawing practice”.

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Helix angle at reference cylinderCentre distance with mating gear (optional)Drawing No. of mating gear (optional).

A table concerning inspection data and auxiliary information may also be included. When inserting information in this table care must be exercised to avoid conflict between requirements for accuracy of individual elements and dual flank testing requirements.

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Appendix A Centre distance and addendum modificationA.1 IntroductionThe centre distance of a pair of gears may have any value within certain limits since two gears generated by similar tools with equal base pitch will mesh correctly. The working pressure angle, the pitch diameters and the backlash will vary with change in centre distance.By taking advantage of these features in the design and manufacture of involute gears, the pitches listed in Table 1 will be adequate for most purposes. Gear diameters and centre distances may be varied by the choice of a suitable value for the addendum coefficients x1 and x2 within the upper and lower limits laid down by Figure 3.The case where there is no addendum modification is dealt with in 2.1. In other cases the rules given apply to gears generated from the Figure 1 basic rack tooth shape. They apply substantially to the Figure 2 basic rack tooth shape also except where reference is made to close mesh and minimum backlash.The chart given in Figure 3 has been prepared with the following points in mind:

1) Upper limits of addendum modification coefficient. Too large a value will lead to an undesirably narrow crest width which should be not lessthan 0.3/Pn.

If small wheels and pinions with excessively enlarged addenda are meshed together, the contact ratio becomes too low.

2) Lower limits of addendum modification coefficient. Where x has a smaller value than the following the gears become undercut by generation:

For Figure 1 type gears x =

Figure 2 type gears x =

The root fillets of gears extend a minimum distance from the root circle when x is slightly greater than + 1. As x varies from this value the root fillets extend progressively further up the teeth. A limiting negative value of x is reached when the root fillets are just clear of the path of contact during engagement.A.2 Addendum modification coefficient x1 and x2

A.2.1 Gears at predetermined centre distanceWhen the centre distance is predetermined the addendum modification coefficient x1 and x2 may have any value permitted by Figure 3 provided that x1 is within the limits imposed by equations (30) and (31).

Nominal tip diameters and tooth thicknesses are then obtained from:

(15)

(16)

Figure 1 type gears, (17)

(18)

Figure 2 type gears, (19)

1.14z sin2

!t2 cos"

----------------------–

1.066z sin2

!t2 cos"

----------------------–

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If the centre distance modification coefficient is equal to the sum of the addendum modification coefficients of pinion and wheel then:

and y has a positive or negative value other than zero;Figure 1 type external gears have backlash at nominal dimensionsFigure 1 type internal gears have interference at nominal dimensionsFigure 1 type crossed helical gears have zero backlash at nominal dimensions.The normal backlash (or interference) obtained is given by

where j* is obtained from Figure 7.For helical gears the normal backlash is obtained by using av in place of a in formula (22) and Figure 7, where

NOTE For internal gears the values of a, z2 and d2 are to be regarded as negative, and x2 as negative when its sense is to enlarge the wheel. All formulae are then applicable.

If it is desired to reduce (or increase) backlash it will be necessary to increase (or decrease) tooth thickness by a secondary addendum modification %x1 for the pinion and %x2 for the wheel.

%x1 and %x2 are then added to the initial values of x1 and x2 obtained by equations (21), (30), (31) and used in equations (15) – (20).In following this procedure it is necessary, if x1 + x2 have values toward the upper limits of Figure 3, to examine the root clearance and if insufficient, to modify the outside diameter of one or both gears by amounts;

and

A.2.2 Gears having zero backlash requirementCalculation of values of x1 + x2 (or a) for gears (other than crossed helical gears) which require zero backlash at nominal dimensions.

(20)

y = x1 + x2 = (21)

(22)

av = a/cos2" (23)

(24)

Given a, to find (x1 + x2).

(25)

(26)

(27)

ad1 d2+

2-------------------–

Pn

%x1 %x2+Pn

-------------------------- desired reduction in normal backlash0.6840

-------------------------------------------------------------------------------------------------------=

2 %x1Pn

---------------2 %x2

Pn---------------

where tan!ttan!cos"-------------=

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© BSI 10-1999 23

NOTE inv!t and inv!tw may be obtained from tables of involute functions. An involute function of an angle is the small difference between the tangent of the angle and the value of the angle in radians.

A.3 Limiting values of x1 and x2 Where x1 and x2 have been fixed by the foregoing formulae, x1 should lie between the following values:

In general, most favourable action is obtained when a high value of x1 is used with the pinion driving the wheel and a low value of x1 with the wheel driving the pinion.Where a negative value of the sum (x1 + x2) arises the value of x2 may be below the relevant line, XX or YY, of Figure 3 provided that the sum of minimum values of (x1 + x2) allowed by the graph is more negative than the sum required.

Appendix B Examples of calculationsExample 1. External spur gears at predetermined centre distance which differs from half the sum of the reference circles and a normal amount of backlash is permissible.

Given (x1 + x2), to find a.

(28)

(29)

Minimum x1 = (30)

Maximum x1 = (31)

Given Required

z2 = 63 x1 and x2z1 = 20 da2 and da1Pn = 24a = 1.8 inPinion drivingFigure 1 gears.

From formula (21), x1 + x2 =

= 1.7

From formula (30), x1 min. =

= 0.41

From formula (31), x1 max.=

= 0.81

z1z2 z1+------------------ x1 x2+( )

z1z2 z1+------------------ x1 x2+( ) 0.4+

1.8 24×( ) 63 20+( )2

------------------------–

2083------ 1.7×

2083------ 1.7 0.4+×

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From Figure 3, x1 must not exceed 0.75. Selecting this value of 0.75 for x1 then x2 = 1.7 – 0.75

Example 2. External spur gears at predetermined centre distance and minimum backlash.

Two different solutions, A and B, are given. A is derived by involute functions and B by the method of Figure 7.Solution A. By examination, tooth numbers which give a near approach to the required centre distance are 36 and 144. With these tooth numbers and unmodified gears the centre distance would be:

From (25) cos!w =

Whence !w = 22.89° and inv!w = 0.022 70 inv! = 0.014 904 and 0.022 700 — 0.014 904 = 0.007 796

From (26) x1 + x2 =

From (30) x1 (min.) =

From (31) (x1 max.) =

As the pinion is driving the maximum value of x1 may be taken and from Figure 3, x1 can be 0.78.Therefore x2 = 1.928 – 0.78 = 1.148From (17 and 18)

Note that s2 cannot be gauged at the reference diameter, but can be used for calculation of diameter over gauge pins.Ans. z1 = 36, z2 = 144, x1 = 0.78, x2 = 1.148, s1 = 0.0594 in, s2 = 0.0668 inch.Solution B. Taking alternative tooth numbers, z1 = 37 and z2 = 148, the centre distance of unmodified

gears would be:

= 0.95

From formula (16), da2 =

= 2.788 inches

From formula (15), da1 =

= 0.979 inch

Ans: da1 = 0.979 da2 = 2.788 x1 = 0.75 x2 = 0.95

Given Required

Pn = 36 z1, z2, x1, x2a = 2.55 s1 and s2Ratio = 4 : 1Pinion drivingFigure 1 gears.

6324------ 2 1 0.95+( )

24------------------------------+

2024------ 2 1 0.75+( )

24-----------------------------+

2.52.55----------- 0.939 69× 0.921 265=

0.007 796 180×2 0.363 97×

------------------------------------------- 1.928=

36180---------- 1.928× 0.3856=

36180---------- 1.928 0.4+× 0.7856, say 0.78=

s11.5708 0.7279 0.78( )+

36-------------------------------------------------------------- 0.0594 inch= =

s21.5708 0.7279 1.148( )+

36----------------------------------------------------------------- 0.0668 inch= =

z1 z2+2Pn

------------------ 18572---------- 2.569 45 inches= =

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From (21) x1 + x2 = (2.55 – 2.569 45) 36 = – 0.700

From A.3, this value may be used without restriction,

whence from (31), x max. = and x2 = – 0.700 – 0.260 = – 0.960.

To check the amount of backlash obtained, using Figure 7

From (22)

This is an acceptably small amount and no increase in x1 or x2 is justified.From (17) and (18)

Note that the reference circle is near the tip of the wheel and it will not be practicable to gauge s2, except by gauge pin measurement.Ans. z1 = 37, z2 = 148, x1 = 0.26, x2 = – 0.96, s1 = 0.048 86 inch, s2 = 0.024 22 inch.Example 3. External spur gears with no limitations other than avoidance of undercutting and backlash. (2.2.2.)

Two solutions are available, A) and B):A) From Table 2, x1 = 0.4151, x2 = 0,

B) x1 = 0.4150, x2 = – 0.4150

whence da1 and s1 are as obtained for solution A).

Given Required

z1 = 10 x1 and x2z2 = 60 s1 and s2Pn = 36 da1 and da2

a

37185---------- 0.7–( ) 0.4+ 0.26=

yPn------- 0.700–

36-------------------- 0.019 45–= =

yaPn--------- 0.019 45–

2.55-------------------------- 0.0076 whence j* 2.63=–= =

jn2.632.55----------- 0.019 452( ) 0.000 39 inch.= =

s11.5708 0.7279+ 0.26×

36------------------------------------------------------------- 0.048 86 inch= =

s21.5708 0.7279– 0.96×

36-------------------------------------------------------------- 0.024 22 inch= =

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Ans. (A and B): x1 = 0.4150, s1 = 0.0520 inch, da1 = 0.3564 inch.A; x2 = 0, s2 = 0.043 63 inch, da1 = 1.7222 inch, a = 0.9833 inch.B; x2 = – 0.4150, s2 = 0.035 24 inch, da2 = 1.699 17 inch, a = 0.9722 inch.Example 4. Helical gears at predetermined centre distance and minimum backlash.

From (25)

From (26) x1 + x2 = = – 0.517 54From (30)

x1 (min.) =

x2 (max.) = – 0.517 54 + 0.1279 = – 0.3896

From (31)x1 (max.) = – 0.1279 + 0.4 = 0.2721

x2 (min.) = – 0.517 54 – 0.2721 = – 0.789 64

To find the range of values of x1 and x2 which are permissible find zv1 and zv2, i.e. from (7)zv1 = 22 × 1.162 = 25.6

zv2 = 67 × 1.162 = 78

From Figure 3 we chose the value – 0.48 for x2 leaving x1 = – 0.517 54 + 0.48 = – 0.0375.From (15) and (16)

Given Required

z1 = 22 da1z2 = 67 da2Pn = 40 x1" = 18° x2a = 1.1562

Pinion drivingFigure 1 type gears.(Solution using involute functions)

Obtain, sec" = 1.051 46sec3" = 1.162tan! = 0.363 97cos! = 0.939 69

From (1) and (2)= 0.5783

= 1.7612

From (27) Tan!t = 0.363 97 × 1.051 46 = 0.3827whence !t = 20.942°cos!t = 0.933 94inv!t = 0.017 196

Cos!tw =

!tw= 19.119°inv!tw= 0.012 963

d122 1.051 46×

40------------------------------------=

d267 1.051 46×

40-----------------------------------=

1.7612 0.5783+( ) 0.933 942 1.1562×

------------------------------------------------------------------------- 0.944 84=

0.012 963 0.017 196–( ) 67 22+( )2 0.363 97×

-------------------------------------------------------------------------------------------

2222 67+-------------------- 0.517 54–( ) 0.1279–=

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BS 978-1:1968

© BSI 10-1999 27

da1 = 0.5783 + = 0.6264 inch

da2 = 1.7612 + = 1.7872 inch.

Ans. x1 = – 0.0375, x2 = – 0.48, da1 = 0.6264 inch, da2 = 1.7872 inches.

2 1 0.0375–( )40

--------------------------------------

2 1 0.48–( )40

-------------------------------

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BS 978-1:1968

© BSI 10-1999 29

Appendix C Comparable diametral pitches and metric modules

Appendix D Single flank composite testing: limits of toleranceWhen single flank testing is applied, the limits of tolerance are derived as follows:

1) Tooth-to-tooth composite error. For all grades, the tolerance is derived from: single pitch tolerance + tooth profile tolerance.2) Total composite error. For all grades, the tolerance is derived from: maximum cumulative pitch tolerance + tooth profile tolerance; where the maximum cumulative pitch tolerance is derived from the value of l = ;d/2.

The values derived represent errors in angular transmission when a product gear is rotated in mesh with a calibrated master gear under similar conditions to those prescribed in 3.1.

Appendix E Calculation of measuring pin dimensions for external and internal spur gearsIn order to overcome the difficulty of resetting on the gear-cutting machine gears which are found to be outside dual flank tolerances in respect of size, it is necessary either to carry out dual flank testing on the machine or to adopt other methods of test at that stage of manufacture. The former method is used only in exceptional cases, whilst the practice of measurement over pins is a practical method for this purpose although insufficient in itself to dispose of the final dual flank test.For external and internal spur gears the measuring pin diameter dR should be calculated from the following formulae. Further information on measurement of pins is given in B.R.6001 (1) “Precision gearing for control systems and armaments”*.For external gears of 7 to 17 teeth with positive addendum modification:

Diametral pitch Module

in mm

242832

1.0580.9070.794

364048

0.7060.6350.529

6480

100

0.3970.3180.254

120140160

0.2120.1810.159

180200

0.1410.127

For external gears:

For internal gears:

dR1.92Pn

-----------=

dR1.728Pn

-------------=

dR1.44Pn----------=

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BS 978-1:1968

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