Download - 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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2 © BSI 10-1999
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)
(Figure 2 type gears) (10)
(11)
x 1zv sin2 µ
2-------------------------n–=
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4 © BSI 10-1999
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.
(Figure 1 type gears) (12)
(Figure 2 type gears) (13)
(14)
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SI 10-1999
5
Figure 3 — Limiting values of addendum modification coefficient
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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
Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4
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
Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4
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
Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4
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
Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4
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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Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4
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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Table 3 — Centre distances for spur gear pairs of unit diametral pitch for the conditions given in clause 2.2.4
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)
Minimum depth of engagement
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)
Minimum depth of engagement
Sum of number of teeth(z2 + z1)
Minimum depth of engagement
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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Figure 6 — Example of information to be given on drawings
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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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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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26 © BSI 10-1999
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
28©
BS
I 10-1999
Figure 7 — Chart for normal backlash when x1 + x2 = y
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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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