1、BRITISH STANDARD CONFIRMED MARCH 1984 BS 721-1: 1963 Incorporating Amendment Nos. 1 and 2 Specification for Worm gearing Part 1: Imperial units UDC 621.833.38BS721-1:1963 This British Standard, having been approved by the MechanicalEngineering IndustryStandards Committeeand endorsed by theChairman o
2、f the EngineeringDivisional Council,was published undertheauthority of the GeneralCouncil on 25 April 1963 BSI 04-2000 First published February 1937 First revision April 1963 The following BSI references relate to the work on this standard: Committee reference MEE/17 Draft for comment A(MEE) 3326 IS
3、BN 0 580 34579 3 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 departmen
4、ts 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: Admiralty* Engineering Equipment Users Association Air Ministry Gas Council Associated Of
5、fices Technical Committee High Commission of India Association of Consulting Engineers Institute of Marine Engineers (Incorporated)* Institute of Petroleum Association of Mining Electrical and Institution of Civil Engineers Mechanical Engineers* Institution of Gas Engineers British Chemical Plant Ma
6、nufacturers Institution of Heating and Ventilating Engineers Association Institution of Mechanical Engineers* British Compressed Air Society Institution of Mechanical Engineers (Automobile British Electrical and Allied Manufacturers Division) Association* Institution of Production Engineers* British
7、 Engineers Association* Locomotive and Allied Manufacturers British Gear Manufacturers Association* Association of Great Britain British Internal Combustion Engine Machine Tool Trades Association* Manufacturers Association Ministry of Labour (H.M. Factory Inspectorate) British Iron and Steel Federat
8、ion Ministry of Power British Railways Board* Ministry of Public Building and Works Crown Agents for Oversea Governments and Ministry of Transport Administrations National Coal Board D.S.I.R. National Engineering Laboratory* National Physical Laboratory (D.S.I.R.) Electricity Council, The Generating
9、 Board and Radio Industry Council the Area Boards in England and Wales War Office* Admiralty-Vickers Gearing Research North East Coast Institution of Engineers and Association Shipbuilders Institution of Engineering Inspection Sheffield University Manufacturers of Worm Gears Society of British Aircr
10、aft Constructors Ltd. Milling, Cutter and Reamer Association Society of Motor Manufacturers and Ministry of Aviation TradersLtd. National Association of Lift Makers National Federation of Engineers Tool Manufacturers Amendments issued since publication Amd. No. Date Comments 5919 October 1966 4364 S
11、eptember 1983BS721-1:1963 BSI 04-2000 i Contents Page Co-operating organizations Inside front cover Foreword iii 1 Scope 1 2 General Information on worm gear elements 1 a) Module 1 b) Axial pitch and normal pitch designations 1 c) Diameter factor q 1 d) Worm gear designations 1 3 Notation 2 4 Form o
12、f threads and teeth 3 a) Standard worm thread surfaces 3 b) Basic rack 3 c) Undercutting of worm threads 4 d) Thread thickness 4 e) Wormwheel teeth and entry gaps 4 f) Wormwheel tooth fillet 4 g) Face width of wormwheel 4 5 Formulae for calculation of dimensions 5 a) Limiting values of centre distan
13、ce for given values of t, T, q and m 5 b) Limiting values of m for given values of C, t, T and q 5 c) Formulae for detail dimensions of worm and wheel 5 d) Rim section 6 6 The general system of worm gear design 8 a) Obtaining suitable values of t, T, q and m 8 b) Standard axial modules 8 c) Standard
14、 diameter factors (q) 8 d) Determinations of t and T 8 e) Guidance for determination of q 8 f) Procedure for selecting standard worms 8 7 Tables and dimensions of standard worms and wheels 9 a) Tables of worm gear designations 9 i) Standard centre distances for industrial worm gears 9 ii) Standard c
15、entre distances for axle transmission gears 9 b) Examples of worm gear designations 9 c) Detail dimensions of worms and wheels 9 8 Tolerances 16 a) Worms: 16 i) runout of tip diameter 16 ii) pitch tolerances 16 iii) profile tolerances 16 iv) thread thickness tolerances 16 b) Wormwheels: pitch tolera
16、nces 17 9 Normal backlash 17 10 Working temperature 17 11 Efficiency and lubrication 18 12 Irreversibility 18 13 Information to be given on drawings by the purchaser 18BS721-1:1963 ii BSI 04-2000 Page Appendix A Load capacity 21 A.1 Determination of load capacity 21 A.2 Determination of equivalent r
17、unning time for loading conditions other than a steady load 22 A.3 Momentary overload capacity 23 A.4 Axle transmission gears 23 Appendix B Examples of calculations 25 Appendix C Design procedure based on axial pitch of worm 32 Appendix D Procedure for the design of worms to suit standard diametral
18、pitch cutting tools corresponding to the normal pitch of the worm 33 Chart 1 Maximum positive value of addendum modification coefficient for 1 module (k w1 ) 34 Chart 2 Maximum negative value of addendum modification coefficient for 1 module (k w2 ) 34 Chart 3 Determination of q for worm speeds up t
19、o 300 rev/min 35 Chart 4 Determination of q for maximum efficiency for any worm speed 36 Chart 5 Coefficient of friction of worm gears 37 Chart 6 Speed factors for worm gears (for wear) (X c ) 38 Chart 7 Speed factors for worm gears (for strength) (X b ) 39 Chart 8 Expected life factors for strength
20、 and wear 40 Figure 1a Normal section of basic rack (dimensioned in terms of axial module) 3 Figure 1b Normal section of basic rack (dimensioned in terms of normal pitch) 4 Figure 2 Entry gap in wormwheel teeth 4 Figure 3 Wormwheel rim section 6 Figure 4 Wormwheel rim section 6 Figure 5 Wormwheel ri
21、m section 7 Figure 6a limiting values are given for variation in centre distance with the same object. 6) The formulae for allowable loads have been revised, the permissible load for strength having been greatly increased. These are now given in an appendix to the standard. NOTE 1The units given in
22、this standard are British units. BS350, “Conversion factors and tables” should be consulted when it is desired to make conversions to metric units. NOTE 2In place of the customary, but incorrect, use of the pound as a unit of force, the unit called a pound-force (abbreviation lbf) has been used in t
23、his standard. This is the force which, when acting on a body of mass one pound gives it an acceleration equal to that of standard gravity. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct applicati
24、on. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i to iv, pages1to 40 and a back cover. This standard has been updated (see copyright date) and may have had amendment
25、s incorporated. This will be indicated in the amendment table on the inside front cover.iv blankBS721-1:1963 BSI 04-2000 1 1 Scope This British Standard applies to worm gearing and comprises cylindrical involute helicoid worms and worm wheels conjugate thereto, the dimensions of which are expressed
26、in inches, Four classes of gears are provided which are related to function and precision. The range of modules is given in convenient steps from 0.052 to 1. This standard does not refer to pairs of cylindrical gears connecting non-parallel axes known as crossed helical gears. 2 General information
27、on worm gear elements a) Module. Axial modules in inch units are specified and a series of standard modules is listed inClause6 b). The lists of modules and diameter factors provide for a range of standard worms which is considered sufficiently wide for most requirements. Certain modules are “prefer
28、red” in order to encourage the smallest practicable range of tools. In order to help in the case of restricted conditions a list of “second choice” modules is also given. b) Axial pitch and normal pitch designations. It is recognized that existing hobs not made to this specification will continue to
29、 be used. In order that these may be employed in a manner consistent with this specification the method of application is given inAppendix C andAppendix D. c) Diameter factor q. Choice of worm diameter is limited by considerations of strength and efficiency. Since the efficiency of the gear increase
30、s as the worm diameter is reduced the worm diameter should be as small as possible consistent with adequate strength at the root section of the worm. Charts are provided for guidance for selecting suitable worm diameters (seeTable 4). The worm reference diameter is the product of the module and the
31、diameter factor q. For a given value ofq the reference diameter is therefore d f= qm. Standard values of q in this specification are given in Clause6 c). The larger worm diameter factors from 12 upwards are seldom required except when the worm is bored. In such cases it is recommended that the thick
32、ness of metal below the thread be approximately equal to the depth of the thread. The reference diameter of a worm is equal to qm and is thus similar to the reference diameter of a spur gear having q teeth and m module. In the same way, the centre distance of a pair of worm gears (unlessextended or
33、closed) is equal to that of a pair of spur gears having q and T teeth,i.e. C = 0.5 m(q + T) It is also to be noted that the calculation of the tip diameter of a worm is analogous to that of a spur gear with q teeth and m module. In the detail system of design, the worm addendum is always equal to th
34、e module and the tip diameter of a worm is found from d a= m(q + 2) The lead angle of the worm thread at the reference cylinder is found from: tan = t/q In the general design system defined, a restricted range of q values is recommended. This ensures geometric similarity between all worms having the
35、 same values of t and q. From any given combination of t and q, all angular dimensions of a worm can be calculated, and all linear dimensions will be proportional to the selected modules. Tables are included giving detail dimensions of worms of unit axial module for combinations of t with standard v
36、alues of q. d) Worm gear designations. A pair of worm gears is defined by the designation, written in the brief form t/T/q/m, and this information, together with the centre distance C is sufficient to enable all detail dimensions to be calculated from formulae or tables provided. For example a desig
37、nation3/38/8/0.30 at7-inch centres, signifies a38-tooth wheel working at7-inch centre distance with a3-start worm of0.30-inch axial module and of diameter factor8.BS721-1:1963 2 BSI 04-2000 3 Notation The terms and symbols given below are generally in accordance with those given in BS2519, “Glossary
38、 of terms and notation for toothed gearing”. The notations used are as follows: a Worm thread addendum b Worm thread dedendum c Clearance C Centre distance d a Worm tip diameter d f Worm reference circle diameter d o Base diameter of involute helicoid d r Worm root diameter D f Wormwheel reference c
39、ircle diameter D a Wormwheel tip diameter D r Wormwheel root diameter D t Wormwheel throat diameter f p Length of worm F e Wormwheel effective face width g Constant chord thickness G Gradient factor h Constant chord height k w Wheel addendum modification coefficient K Duty factor l r Length of root
40、of wormwheel teeth L Lead of worm threads L ap Axial distance between any two points at the same radial distance from the worm axis m Axial module m a Normal module M Maximum engine torque M w Torque on wormwheel n Rev/min of worm N Rev/min of wormwheel p n Normal pitch p a Axial pitch q Diameter fa
41、ctor r t Wormwheel throat radius r Rolling radius of tyre R 1 Gearbox ratio for lowest road speed R 2 Rear axle ratio R g Gear ratio S bp Bending stress factor: worm S bw Bending stress factor: wormwheel S cp Surface stress factor: worm S cw Surface stress factor: wormwheel t Number of threads in wo
42、rmBS721-1:1963 BSI 04-2000 3 4 Form of threads and teeth a) Standard worm thread surfaces. These are involute helicoids with a normal pressure angle of 20 degrees at the reference circle diameter d f= qm. b) Basic rack. A normal section of the basic rack is shown inFigure 1a and is dimensioned in te
43、rms of the axial module, and inFigure 1b in terms of the normal pitch. The working depth, tooth thickness and pressure angle are similar to those of the BS436 1)basic rack (Figure5of BS436:1940) but the clearance may vary from0.2 m cos to0.25 m cos according to the method of manufacture. T Number of
44、 teeth in wormwheel U Period of time for load cycle U b Equivalent running time per cycle for strength U c Equivalent running time per cycle for wear U bw Equivalent running time for strength U cw Equivalent running time for wear U eb Total equivalent running time for strength U ec Total equivalent
45、running time for wear V s Rubbing speed W l Load on driving axle W Gross laden weight of vehicle X bp Speed factor for strength: worm X bw Speed factor for strength: wormwheel X cp Speed factor for wear: worm X cw Speed factor for wear: wormwheel Z Zone factor Shaft angle Lead angle of worm thread o
46、 Base lead angle of worm thread Coefficient of friction n Normal pressure angle Angle of friction The number of degrees in the smaller angle between the plane containing the axis and one point, and the plane containing the axis and the other point. 1) BS 436, “Machine cut gears. A. Helical and straight spur.” Figure 1a Normal section of basic rack (dimensioned in terms of axial module)
