1、DC 621.833.16 DEUTSCHE NORM Auciust 1981 Geometrical design of cylindrical internal involute gear pairs Basic rules I 3993 Part 1 Geometrische Auslegung von zylindrischen Innenradpaaren mit Evolventenverzahnung; Grundregeln As it is current practice in standards published by the International Organi
2、zation for Standardization (ISO), the comma has been used throughout as a decimal marker. The concepts, terms and symbols used in this standard agree with DIN 3960, DIN 3998 Part 1 and Part 2 and DIN 3999. Figures 5.1 to 5.24, 11.1 to 11.25 and 16.1 to 16.10 referred to in the text will be found in
3、DIN 3993 Part 2 to Part 4 (see also Explanations). The bearing capacity and running properties of cylindrical internal gear pairs may be improved by modifying the tooth geometry, .e. by altering the number of teeth, module and addendum modification. In addition, operation and tooth generation may gi
4、ve rise to meshing interference which can be counteracted by addendum modification and, if necessary, by tip relief. Con tents Page 1 General 2 1 ,I Symbols and terms 2 1.2 Signs . 2 1.3 Scope . 3 2 Other relevant standards. 3 3 Determination of addendum modifica- tion .:. . 3 3.1 General 3 3.1 .I C
5、onditions for operation 4 3.1.2 Conditions for generation. . 4 3.2 Aggregate of addendum modification coefficients . 4 3.2.1 V-O gear pairs. . 4 3.2.2 V-gear pairs. 4 3.2.3 Epicyclic gear transmissions and similarly constructed fixed-axis gear transmissions 5 Distribution of the aggregate of adden-
6、dum modification coefficients for internal gear pairs . 5 3.3.1 V-O gear pairs. . 5 3.3.2 V-gear pairs. 6 4 Meshing interference in operation, assembly, double flank composite action method of gear inspection and generation. . 7 4.1 Meshing interference of the gear pair . . 7 4.1.1 Meshing interfere
7、nce due to insufficient involute lengths 7 4.1.2 Tooth face tip butting of internal gear against pinion outside the meshing area. 8 4.1.3 Tooth face tip butting in the case of radial assembly 8 4.1.4 Meshing interference in the double flank composite action method of gear inspection. . 8 3.3 Page 4.
8、2 Meshing interference when cutting the internal gear with the pinion type cutter. 8 4.2.1 Insufficient involute lengths through generation, . 8 4.2.2 Active and passive meshing interference when cutting the internal gear with the pinion type cutter. 9 4.2.3 Cut-awav of the tooth face tips of the 4.
9、3 4.4 5 5.1 5.2 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 internai gear. 9 Meshing interference when cutting the internal gear by skiving . 10 Meshing interference when cutting the 10 internai gear by broaching . Determining the tool data for the internal gear. 10 Limits on number of pinion type cutter teet
10、h for the internal gear . Special features of the machine setting for cutting the internal gear. . Examples 12 10 11 05-V-O tooth system according to section 3.3.1.1 . 12 G type V-O tooth system according to section 3.3.1.2 . 13 G type V-tooth system according to section 3.3.2 14 Epicyclic gear tran
11、smission according to section 3.2.3.1 . 15 Epicyclic gear transmission according to section 3.2.3.2 . 16 Internal gear pair according to section 3.2.3.3 17 Enlarging the utilizable root circle of the internal gear. . 18 Determining the pinion type cutter to be used 18 Continued on pages 2 to 36 Expl
12、anations on page 36 Solesele rights of Germen Standards (DIN-Normen) are with Beuth Verlag GmbH. Berlin 30 DIN 3993 Part 1 Engl. Price group 1. 07.82 SalesNo.0117 Page 2 DIN 3993 Part 1 1 General 1 .I Symbols and terms The following symbols and terms are used: a ad a0 b C d da dNal(0) dNal (2) dNa2(
13、0) dNa2(1) dNfl (O) dNfl (2) dNf2(0) Nf2(1 1 e gcl ha haP0 haPl ha0 i inv m Pet r s U 22 u0 =- 20 X XO z 2, znw 20 B centre distance reference centre distance generating centre distance for the internal gear facewidth bottom clearance diameter tip diameter utilizable tip diameter generated by tool o
14、n pinion utilizable, .e. largest possible, pinion tip diameter assigned to the mating gear utilizable tip diameter generated by the tool on the internal gear utilizable, .e. smallest permissible, internal gear tip diameter assigned to the pinion tooth root utilizable root diameter generated by the t
15、ool on the pinion utilizable, .e. largest possible, pinion root diameter assigned to the mating gear utilizable root diameter generated by the tool on the internal gear utilizable, .e. smallest permissible, internal gear root diameter assigned to the pinion tooth tip spacewidth length of path of con
16、tact addendum addendum of tool basic rack addendum of pinion basic rack tool addendum coefficient transmission ratio involute function module transverse pitch on path of contact radius tooth thickness gear ratio generating gear ratio for the internal gear addendum modification coefficient addendum m
17、odification coefficient of a pinion type cutter number of teeth for addendum modification calculations virtual number of teeth virtual number of teeth for base tangent length calculations number of teeth of a pinion type cutter amount of envisaged reduction of number of teeth of planet gears to prom
18、ote suitable over- all addendum modification design of an epicyclic gear transmission K WO WO an at awn aw no awt Zwto b 4 means that a long addendum gear pair is involved, such that aad (but la1 lad). in contrast with external gear pairs the working transverse pressure angle a, a. Helix angle p2 :
19、The helix angles of the two intermesh- ing gears of a cylindrical gear pair have opposite signs, SO that the sum of the helix angles yields an axis intersec- tion angle of zero. Hence 2 = - l Consistent application of the sign rules to the above- mentioned quantities automatically also establishes t
20、he signs for all the other quantities. This does not result in an alteration of the sign for the pressure angle. On the other hand, for this reason the speed equations for the internal gear yield negative values corresponding to the speed vector which is reversed in direction compared with an extern
21、al gear of like kind. Consequently all the geo- metrical equations relating to the cylindrical gear and the mating of cylindrical gears with an external tooth sys- tem also apply unchanged to the internal gear and to internal gear pairs. For data on drawings, however, it is the rule that, with the e
22、xception of the addendum modification coeffi- cients, the absolute values of the above data must be used, see DIN 3966 Part 1. Similarly, the data for the upper and lower deviation are referred to the absolute values in the accustomed manner. For further information concerning the geometrical rela-
23、tionships of internal gear pairs, see DIN 3960. 1.3 Scope This standard applies to straight and helical internal gear pairs having standard basic rack tooth profile according to DIN 867, number of pinion teeth z1 h (10) 14, (bracketed value is lowest extreme), number of teeth of internal gear z2 d (
24、- 23) - 40, hence 1.1 I(23) 40 1, total number of teeth d - 1 (absolutely: difference in number of teeth 1.1- z, L 11, aggregate addendum modification + 0,5 (for restrictions and extensions see figures 5.1 to 5.24), helix angle Dl 5 30, standard basic rack tooth profi!e of tool II according x = - 1,
25、5 to to DIN 3972 (h, = 1,25 .m). These addendum modification guidelines are not binding; deviations based on specialized experience may be desir- able. This standard also contains information on adden- dum modification in epicyclic gear transmissions and similarly constructed fixed-axis gear transmi
26、ssions. The limiting diameters (tip diameters or utilizable diam- eters) calculated for the purpose of avoiding meshing interference in operation and generation are calculation values which are subject to minor modifications in the light of the specified tooth system and transmission to ler a nces.
27、Wherever consideration is given to oblique gearing below, the virtual numbers of teeth z, in the normal section are to be taken as the basis, see also figure 12. The limits stated in this standard in this connection relate each tirne to the worst case between p=O” and p=30. The following apply z inv
28、 a, z, = “z- - znw (1 1 cos2b * cos inva, sinPb = sin - cosa, (2 1 2 Other relevant standards DIN 867 DIN 3960 DIN 3966 DIN 3972 DIN 3998 DIN 3998 DIN 3999 Basic rack of cylindrical gears with involute teeth for general and heavy engineering Concepts and parameters for cylindrical gears and cylindri
29、cal gear pairs with involute teeth Part 1 Information on gear teeth in drawings; information on involute teeth for cylindrical gears Reference profiles of gear-cutting tools for involute tooth systems according to DIN 867 Part 1 Designations on gears and gear pairs; general concepts Part 2 Designati
30、ons on gears and gear pairs; cylindrical gears and gear pairs Symbols for gear teeth 3 Determination of addendum modification 3.1 General The following considerations dictate the choice of the addendum modification: - avoidance of meshing interference in operation and assembly l) Seepage 19 Page 4 D
31、IN 3993 Part 1 - bearing capacity and running properties of the gear - avoidance of meshing interference when generating In the majority of cases the geometrical mating condi- tions are reconcilable with the generating conditions when using standard tools. A detailed investigation can be dispensed w
32、ith if the limits stated in sections 3.1 .I and 3.1.2 are not transgressed. Tooth systems of high bearing capacity are obtained by adopting, inter alia, the V-O tooth systems according to section 3.3.1 or the V-tooth system according to section 3.3.2 or with the aid of figures 10 or 11.1 to 11.25 (s
33、ee also Explanations). Here also a check must always be made to determine whether the limiting conditions according to sections 3.1.1 and 3.1.2 are fulfilled. If this is not the case, it is generally sufficient to select the addendum modification corresponding to the nearest geometrical limit. 3.1.1
34、 Conditions for operation 3.1.1.1 Pinion tooth system free of undercut, plus observance of the other limiting conditions according to figure 5 and figure 6. 3.1.1.2 Working transverse pressure angleawt = 20 to 26“, figure 1 3.1.1.3 Transverse contact ratio caz 1,1, see also sec- tions 3.3.1 to 3.3.2
35、. 3.1.1.4 Bottom clearance c 2 0.2 . m (is obtained when - as is usually the case - the range of the transverse pressure angle at generation stated in section 4.2.1.2 is observed, cf. also footnote 5). For internal gear tooth numbers, however, z2 2 - 80 or 1z21 5 80 must be observed. In consideratio
36、n of the generated internal gear root diameter df2(0) and a minimum bottom clearance of c = 0,2 . m, the pinion tip diameter is found as pair the internal gear. da, = 2 (a - 0,2 m) - (3 1 where dao) = 2 00 - dao (4) forawtO see equation 7 using the addendum modifica- tion coefficient of a pinion typ
37、e cutter xo, cf. equa- tion 21. If the result of this analysis reveals the necessity of shortening the pinion tooth tip, this step could, if necessary, be avoided by cutting the internal gear with a tool having a larger addendum. This, however, would mean that, the limits applying to generation woul
38、d be different from those stated in figures 16.0 to 16.10 (see Explanations), so that it would be recommendable to consult the tool manufacturer. 3.1.1.5 Pinion tooth tip thickness sml = 0,2 . m, figure 6. 3.1.1.6 The intersection point of the tip circles must lie above the transverse path of contac
39、t to avoid butting of the tip tooth faces of the internal gear against the pinion outside the meshing area, figure 20. Otherwise a more detailed investigation of freedom from interference will be needed, see section 4.1.2. 3.1.1.7 If radial assembly is to be feasible, the points of intersection of t
40、he tip circles must lie above the straight lines passing through the two intersection points of the base circles, figure 20. Otherwise a more detailed investi- gation of freedom from interference will be needed, see section 4.1.3. 3.1 -2 Conditions for generation 3.1.2.1 Rack type generating tool (h
41、ob, rack-shaped cutter, generating grinding or also a suitable pinion type cutter according to section 5.1 ) for cutting the pinion tooth system. 3.1.2.2 The pinion type cutter chosen for the internal tooth system must lie within the limits for zo and xo of figures 16.1 to 16.10 assigned to the inte
42、rnal gear tooth number z2 (see Explanations). 3.1.2.3 The number of pinion cutter teeth shall only be large enough to ensure that the maximum tool diameter as limited by the gearcutting machine is not exceeded (see also DIN 1825 to Din 1829). 3.1.2.4 da(1) 5 d*(,-,), see figure 14.1. This check can
43、be dispensed with if the condition indicated in sec- tion 3.1.2.2 is fulfilled. 3.1.2.5 dNfZ(0) 5 dNf21) see figure 15. This check can be dispensed with if a pinion type cutter having zo h z, is used for cutting the internal gear; otherwise see sec- tion 4.1 .I. 3.1.2.6 If radial assembly of the ext
44、ernal and internal gear is intended, the feasibility of this must be checked according to section 4.1.3 if the chosen design point in figure 5 is near the limiting line 3. 3.2 Aggregate of addendum modification coefficients Once the number of teeth and helix angles are deter- mined, the geometricall
45、y permissible range for the aggregate of the addendum modification coefficients E x = (xl + x2) can be found from figure 1. 3.2.1 V-O gear pairs V-O gear pairs are more advantageous in the case of internal gear pairs than with external gear pairs. For further details on this point, see sections 3.3.
46、1.1 and 3.3.1.2. 3.2.2 V-gear pairs V-gear pairs are preferably to be provided with a negative sum of the addendum modification. For further details on this point, see section 3.3.2. Apart from exceptional cases a positive sum of addendum modification is unfavourable although not so disadvantageous
47、as a corresponding negative sum in the case of external gear pairs. The centre distance, pressure angle and sum of the adden- dum modification of an addendum-modified internal gear pair are determined, depending on the basic quan- tities established, from the following equations, which are to be tra
48、nsformed as necessary, due attention being paid to the sign rules for internal gear pairs. 5, See page 19 DIN 3993 Part 1 Page 5 cosat z1 +z2 cosat cosawt 2cos cosawt a=ad -= m-.- EX 21 +z2 invawt = invat + 2 - - tan a, tan a, tan at = - cos ad cosawt = cosat - a (2, +z2 * (invawt - invat) zx = 2 ta
49、n a, - (IO) (z, + zm2) (inv awn - inv a,) 2 tan a, Figures 2,3 and 4 indicate the geometrical conditions for internal gear pairs with different values of addendum modification. Figures 5 and 6 give information about the numerical magnitude of geometrical limits of various kinds for gear pairings and for the individual gear. 3.2.3 Epicyclic gear transmission and similarly constructed fixed-axis gear transmissions 3.2.3.1 Simple epicyclic gear trans- For epicyclic gear transmissions according to figure 7 in which the planet gear meshes simultaneously with the
