1、BSI BSX72L PART92 3 lb24669 0046964 B of this publication may be photocopied or otherwise reproduced without the prior permission in writing of BSI. British Standard Specification for Worm gearing Part 2. Metric units Roues vis sans fin - Spcifications Partie 2. Units mtriques Schneckenradverza h nu
2、 ng Teil 2. Metrische Einheiten British Standards Institution - - BSI BS*721 PART*2 83 W 162Ybb 00Llbb5 T W BS 721 : Part 2 : 1983 Contents Page Foreword Inside front cover Committees responsible Back cover Specification i. Scope 1 2. Definitions 1 3. Symbols 1 4. Form of worm threads and wormwheel
3、teeth 2 6. Information on worm gear elements 2 6. Formulae for calculation of dimensions 3 7. Accuracy of manufacture 4 8. Normal backlash 4 9. Load capacity 4 10. Efficiency and lubrication 7 Il, Irreversibility 7 12. Information to be given on drawings 7 Appendices A, Typical wormwheel rim section
4、s 18 B. Examples of calculations 19 C. Design procedure based on axial pitch of worm 22 Tables 1, Worm pitch tolerance 2. Worm profile tolerance 3. Worm thread thickness tolerance 4. Wormwheel pitch tolerance 5. Normal backlash Foreword This Part of this British Standard has been prepared under the
5、direction of the Mechanical Engineering Standards Committee and specifies worm gearing in metric units, 1 6. Worm gear zone factor Z I 8. Application factor KA 7. Basic stress factors for worm gears Figures I. Normal section of basic rack (dimensioned 2. Entry gap in wormwheel teeth 3. Determination
6、 of q for maximum efficiency for any worm speed 4. Determination of q for worm speeds up to 300 r/min 5. Maximum value of addendum modification coefficient (2, 1 6. Minimum value of addendum modification coefficient (2.1 1 7. Speed factor for worm gears (wear), X, 8. Speed factor for worm gears (str
7、ength), Xb 9. Total equivalent running time and related in terms of axial module) life factors for wear and strength 10. Coefficient of friction for worm gears 11. Typical drawing of a worm 12. Typical drawing of a wormwheel 13. Wormwheel rim section Page 8 9 9 2 2 10 10 11 11 12 13 14 15 16 17 18 1
8、4. Minimum thickness of wormwheel rim section 18 15. Wormwheel rim section: alternative design of centre 18 Part 1 of this standard specifies worm gearing in imperial units. Compliance with a British Standard does not of itself confer immunity from legal obligations. BS 721 : Part 2 : 1983 British S
9、tandard Specification for worm gearing Part 2. Metric units 1. Scope This Part of BS 721 specifies the requirements for worm gearing based on axial modules. Four classes of gear are specified, which are related to function and accuracy. This Part applies to worm gearing comprising cylindrical involu
10、te helicoid worms and wormwheels conjugate thereto. It does not apply to pairs of cylindrical gears connecting non-parallel axes known as crossed helical gears. Appendix A gives some typical wheel rim sections together with methods of attachment. Appendix B gives examples of calculations using the f
11、ormulae given in the standard. Provision is made in appendix C for a method of applica- tion of existing hobs designated in terms of axial pitch. NOTE 1. Worm gearing designed to this standard is not to be regarded as irreversible. NOTE 2. The titles of the publications referred to in this standard
12、ara listed on the inside back cover. 2. Definitions For the purposes of this British Standard, the definitions given in BS 2519 : Part 1 apply. 3. Symbols For the purposes of this British Standard, the following symbols apply. NOTE. Where applicable, the symbols are in accordance with BS 2519 : Part
13、 2. hC x2 0 KA Term Worm thread addendum Worm thread dedendum Clearance Centre distance Worm tip diameter Worm reference circle diameter Base diameter of involute helicoid Worm root diameter Wormwheel reference circle diameter Wormwheel tip diameter Wormwheel root diameter Wormwheel throat diameter
14、Length of worm Wormwheel effective face width Constant chord thickness Constant chord height Wormwheel addendum modification coefficient Application factor L lf.2 PZ Lx m mn Iw Mact N nl n2 Pn PX q T Y, ubm,l ubm,2 0crn.l 0cm,2 Z1 =2 H Hb HC W Hb,w 4.W H,C “S Heb xb, 1 Xb,2 XC, 1 XC.2 z Y Yb an Leng
15、th of arc (any selected) Length of root of wormwheel teeth Lead of worm threads Axial distance between any two points at the same radial distance from the worm axis Axial module Normal module Permissible torque on wormwheel Actual torque on wormwheel Speed of roadwheel (in r/min) Speed of worm (in r
16、/min) Speed of wormwheel (in r/min) Normal pitch Axial pitch Diameter factor Working temperature of oil (in OC) Wormwheel gorge radius Bending stress factor: worm Bending stress factor: wormwheel Surface stress factor: worm Surface stress factor: wormwheel Number of threads in worm Number of teeth i
17、n wormwheel Period (in h) in load cycle Equivalent running time (in h) per cycle for strength Equivalent running time (in h) per cycle for wear Period in load cycle during which torque changes uniformly Equivalent running time (in h) for period w for strength Equivalent running time (in h) for perio
18、d w for wear Total equivalent running time (in h) for strength Total equivalent running time (in h) for wear Rubbing speed Speed factor for strength: worm Speed factor for strength: wormwheel Speed factor for wear: worm Speed factor for wear: wormwheel Zone factor Lead angle of worm thread Base lead
19、 angle of worm thread Normal pressure angle 1 BSI BS*72L PART*E 83 i LbZllbb9 O046967 3 BS 721 : Part 2 : 1983 4 Angle of friction e The smaller of the two angles formed by radii through two points on a worm thread surface projected onto a transverse plane of the worm G Gradient factor“ Me Maximum e
20、ngine torque* Ut Rolling radius of tyre“ R1 Rz Rear axle ratio“ U, Gear ratio“ Wi Load on driving axle“ W IJ Coefficient of friction“ NOTE. In some mathematical progressions, symbols such as n, appear (e.g. see 9,3.1) where the first subscript refers to the worm and the second to the order in the pr
21、ogression. Gearbox ratio for lowest road speed“ Gross laden weight of vehicle“ 4. Form of worm threads and wormwheel teeth 4.1 Standard worm thread surfaces. The standard worm thread surfaces shall be involute helicoids with a normal pressure angle of 20 o at the reference circle diameter dl =qm. 4.
22、2 Basic rack. The basic rack tooth profile shall comply with BS 436 : Part 2 with the exception that variation of clearance shall be permitted within the limits 0.2m cos 7 to 0.26m cos 7 according to the method of manufacture (see figure I). iTm cos Y l-r7 2 m cos 0.3 mcosY 0.4 mcosr Figure 1. Norma
23、l section of basic rack (dimensioned in terms of axial module) Sharp edges shall be removed from the tips of the worm threads. NOTE. Certain worms with large lead angles would have undercut threads and/or too narrow thread crests unless modified. In such cases by withdrawal of the basic rack the roo
24、t diameter and thread thickness are increased and the dedendum decreased but the tip diameter and reference addendum remain unaltered. Formulae for calculating the necessary dimensions are given in 6.3. 4.3 Thread thickness. The thread thickness shall be gauged on the constant chord thickness Sc. 4.
25、4 Wormwheel teeth and entry gaps. The form of the wormwheel teeth shall be as defined in 4.1.2.2 of BS 2519 : Part 1 : 1976. NOTE. An entry gap giving a light load contact similar to that shown in figure 2 is permitted. 4.5 Wormwheel tooth fillet. This shall be such as would be generated by a hob ha
26、ving a radius at its tip not less than 0.25m cos 7 or 0.08pn, and not exceeding 0.3m cos 7 or 0.095. NOTE. Removal of sharp edges from the tips of the wormwheel teeth is optional. 4.6 Face width of wormwheel. The effective wormwheel face width, be, shall be equal to w(q + I), or the actual face widt
27、h, whichever is the lesser. Figure 2. Entry gap in wormwheel teeth 5. Information on worm gear elements 5.1 Worm gear designations. A pair of worm gears shall be defined by the designation of the number of threads in the worm, number of teeth in the wormwheel, diameter factor and axial module, writt
28、en in the brief form zl /zz/q/m. NOTE 1. This information, together with the centre distance a, is sufficient to enable all detail dimensions to be calculated from the formulae and tables given in this standard. For example, a designation 3/44/8/9.8 at 255 mm centres signifies a 44 tooth wormwheel w
29、orking at 255 mm centre distance with a 3 start worm of 9.8 mm axial module and a diameter factor 8. NOTE 2. In order that existing hobs designated in terms of axial pitch may be employed in a manner consistent with the require- ments of this standard, the method of application of such hobs should b
30、e as given in appendix C. 5.2 Determination of zl and 22. For industrial gears, z1 shall be taken as the nearest whole number to the value given by the following expression: 7 + 2.4da *These symbols apply only to vehicle axle transmission gears (e.g. see 9.5). 2 22 shall then be taken as the next wh
31、ole number below the value gzl, except in the case of single thread worms when zz = ,. The value of zz shall be not less than 17. For vehicle axle transmission gears, z1 shall be taken as the nearest whole number to the value given by: 7 -+ 1 .6da , 5.3 Diameter factor q 5.3.1 Choice of worm diamete
32、r, Choice of worm diameter is limited by considerations of strength and efficiency. Since the efficiency of the gear increases as the worm diameter is reduced, the worm diameter shall be as small as possible consistent with adequate strength at the root section of the worm, The worm reference circle
33、 diameter, di, is given by the product of the axial module, m, and the diameter factor q, For a given value of q (which shall be selected from the range given in 5.3.2) the reference circle diameter is therefore dl = qm. NOTE The worm reference circle diameter, d, , is equal to qm and is thus simila
34、r to the reference diameter of a spur gear having q teeth and m module, Similarly, the centre distance of a pair of worm gears (unless extended or closed) is equal to that of a pair of spur gears BSI BS*72L PART*2 83 162Li667 00467b8 5 having 9 and z, teeth, .e. a = O.5m (9 + 2% 1. The calculation o
35、f the worm tip diameter da is also analagous to that of a spur gear with 9 teeth and m module and is found from da,l = m9 + 2). 5.3.2 Choice of diameter factor q. For the purposes of this standard, values for q shall be selected from the following range of values: 6,6.5,7,7.5,8,8.5,9,9.5, 1 O, 11 ,
36、12, 13, 14, 17, 20 NOTE, This ensures geometric similarity between all worms having the same values of zI and 9, From any given combination of zl and q, all angular dimensions of a worm can be calculated end all linear dimensions will be proportional to the selected modules. 5.3.3 Determination of d
37、iameter factor q. A preliminary selection of the value of diameter factor q shall be made from figure 3, which may be used for any worm rotational speed. The value of q selected shall be as small as possible, except where low reversed efficiency is desired (see clause 11). For worm rotational speeds
38、 below 300 r/min, when some reduction of efficiency may be accepted in order to increase the worm bending strength, a preliminary selection of the value of q shall be made from figure 4. These methods of selecting values of q permit preparation of preliminary designs that shall be checked for accept
39、- ability of worm bending stress, and, if necessary, other values of q shall be chosen to maintain worm bending stress within specified limits, taking into account the bearing span. For vehicle axle transmission gears, the value of q shall be selected from figure 3. NOTE. The larger worm diameter fa
40、ctors from 12 upwards are seldom required except when the worm is bored. In such cases it is recommended that the thickness of metal below the thread be approximately aqua1 to the depth of the thread. 5.4 Lead angle of worm thread. The lead angle, 7, of the worm thread at the reference cylinder shal
41、l be determined from tan y = zl /q, 6. Formulae for calculation of dimensions 6.1 Limiting values of centre distance for given values of z1 , z2, q and m. The limiting values of centre distance a for given values of tl , z2, q and m shall be as follows: amax = 0.5m (22 + 4 + X2,max 1 where x, is as
42、given in figure 5. where x, is as given in figure 6. 6.2 Limiting values of axial module for given values of a, z1 ,z2 and q. The limiting values of axial module m for given values of a, zl, z2 and q shall be as follows: a amin = 0.5m (22 + q - X2,min) 2a 2a mmax = zz + - aZ,min mmin = zz + Q + a2,m
43、ax BS 721 : Part 2 : 1983 6.3 Formulae for detail dimensions of worm and wheel 6.3.1 Worm. Worm dimensions shall be calculated from the following formulae. tan Y = z1/q dl = qm ha, 1 =m *cmin = 0.2m COSY *Cmm = 0.25m cos? thf,l,min = m(2.2cosY- 1) thf,l,max = m(2.2507- 1) = dl + 2ha,l = m(q + 2) da,
44、 1 an = 2O0 df, 1 = dl - 2hf,1 Pz = nzlm cos Yb = cos Y cos an - PZ n tan Yb = 14m COSY = m (0.7444 cos Y + 0.6428) - db 4 tic = m- - SC tan 20“ 2 6.3.2 Wheel. Detail dimensions of wheels shall be calculated from the following formulae. d2 = 2a-dl dt df,Z da,t,max = dt+m = 2a - (df,l + 2c) = 2a - (d
45、a,l + 2c) da,Z,min = dt + 0.4171 7, = 0.5(df,i + 2C) *Cmin = 0.2m cos y *cmax = 0.25m cos y be = 2md(q+1) - Px m - n mn = mcosY Px = rm Pn = px COSY where the angle isfn radians. NOTE. Some typical wormwheel rim sections and methods of attachment of rim to hub are shown in appendix A. *C/eaiance. Th
46、e clearance is given maximum and minimum values (see 4.2). For new designs based on the module system, the clearance should be made to the minimum value given. If it is desired to use tools made to the depths given in BS 436 : Part 2 for cutting the worm threads, the maximum clearance may be adopted
47、 when the cutting is a finishing process, but if the cutting of the worm is used as a pre-grinding process, the clearance may be reduced to not less than the stated minimum, tepth reduction. Depth reduction is necessary on all worms on which the wormwheel throat would, from the above formulae. lie w
48、ithln the base circle of the worm. Those worms with a standard 9 value equal to or less than that given below for a given number of threads require a depth reduction. z,=3 4 5 6 7 9 =6.5 7 7.5 8 8 In such cases of depth reduction the formulae marked t become 3 BSI BSm721i PARTx2 83 Lb24bb7 0046767 7
49、 BS 721 : Part 2 : 1983 7. Accuracy of manufacture 7.1 Tolerances applicable to worms 7.1 .I Run out of worm tip diameter with reference to datum. This shall not exceed the appropriate value for grade 1 T7 of BS 4500 : Part 1. 7.1.2 Worm pitch tolerances. The tolerances for pitch accuracy shall not exceed the values shown in table 1, Table 1. Worm pitch tolerance Class A B C D Pitch tolerance mm 0.001 6 dfx t o.00008 L, is the axial distance between any two points at the same radial distance from the worm axis (in mm); 8 is the smaller of the two
