1、UDC 621.833.1 DEUTSCHE NORM February 1986 DIN 867 Basic rack tooth profiles for involute teeth of cylindrical gears for general engineering and heavy engineering Addendum coefficient Dedendum of basic rack tooth profile Bezugsprofile fr Evolventenverzahnungen an Stirnrdern (Zylinderrdern) fr den all
2、gemeinen Maschinenbau und den Schwermaschinenbau In keeping with current practice in standards published by the International Organization for Standardization (ISO), a comma has been used throughout as the decimal marker. See Explanatory notes for connection with International Standard IS0 53- 1974
3、published by the International Organiza- tion for Standardization (ISO) Supersedes September 1974 edition. - mm 1 Scope and field of application This standard lays down rules for the basic rack tooth pro- file to be preferred for involute teeth of cylindrical gears for general and heavy engineering.
4、 It shall be used pre- dominantly for cylindrical gears as specified in DIN 3960 with module m, from 1 mm to 70mm. The basic rack tooth profile as specified in DIN 58400shall preferably be used for teeth in precision engineering (0,l mm to 1 mm module). 2 Symbols, quantities, units Consistent with t
5、he provisions of DIN 3960 (June 1984 draft), the following symbols and quantities are used in the present standard. Module Pitch Quantitv I Unit I rnm rnm Bottom clearance between basic rack tooth profile and counterpart tooth profile Bottom clearance coefficient Spacewidth of basic racktooth profil
6、e Angle given in formulae Tip rounding radius of tool basic rack tooth profile mm rad mm mm Fillet radius coefficient Addendum of basic rack tooth profile I mm I - Dedendum coefficient 1-1 Common tooth depth of basic rack and counterpart rack tooth profiles Common tooth depth coefficient Root form d
7、epth of basic rack tooth profile Tooth depth of basic rack tooth profile Tooth depth coefficient 1-1 I I Tooth thickness of basic rack tooth profile Pressure angle Io Fillet radius of basic rack tooth profile I mm I 3 Basic rack tooth profiles 3.1 Basic rack tooth profile of a cylindrical gear The b
8、asic rack tooth profile for the involute teeth of a cylin- drical gear has straight flanks, which extend up to the addendum line and down to the fillet radius and tooth root (see figure 1). 3.2 Datum line (PP), addendum line, dedendum line The datum line is that straight line on which the tooth thic
9、k- ness is equal to the space width or half the pitch: (1) The basic rack tooth profile is enclosed by the addendum line which runs parallel with the datum line and the deden- dum line which runs parallel with the latter. The basic rack tooth profiles of the cutting tool have been derived from the b
10、asic rack tooth profile of the teeth (see DIN 3972). sp = ep = p/2 3.3 Basic rack tooth profile of the mating gear (counterpart rack tooth profile) The basic rack tooth profile of the mating gear (counterpart rack tooth profile) is equal to the cylindrical gear basic rack tooth profile folded throug
11、h 180Oaround thedatum lineand displaced by half a pitch along this line. The counterpart rack tooth profile shall engage with its teeth in the tooth spaces in the basic rack tooth profile of the cylindrical gear. The teeth of the gear and mating gear as specified in this standard thus have the same
12、basic rack tooth profile. 4 Features of the basic rack tooth profile The dimensions of the basic rack tooth profile shall be nominal dimensions. 4.1 Module, pitch The module, m, is a length which determines the size of the basic rack tooth profile and thus of the associated cylin- drical gear teeth.
13、, All linear sizes of the basic rack tooth profile can also be specified as a multiple of the module; the corresponding factors are additionally identified by an asterisk (*). The basic rack tooth profile of module m has the pitch p=rc.m. (2) 4.2 Pressure angle The pressure angle, ap, is formed by t
14、he straight flanks and a line perpendicular to the datum line. The two flanks of a tooth are symmetrical about the midline of the tooth. ap is equal to 20Ofor a basic rack tooth profile as specified in this standard. Continued on pages 2 and 3 Beuth Verlag GrnbH. Berlin. has the exclusive right of s
15、ale for German Standards (DIN-Normen) 04.87 DIN 867 Eng/. Price group 5 Sales No. 0105 Page 2 DIN 867 4.3 Tooth depth, addendum, dedendum, bottom clearance, common tooth depth The tooth depth, hp, of the basic rack tooth profile is sub- divided by the datum line into the addendum, hap, and dedendum,
16、 hfp. The bottom clearance, cp, is the difference between the dedendum of the basic rack tooth profile and the adden- dum of the counterpart rack tooth profile. The common tooth depth, hwP, of the basic rack and counterpart rack tooth profiles is the total of the two tooth tip depths. For calculatin
17、g a basic rack tooth profile as specified in this standard, the following formulae shall be used: hp =h$ .m=2.m+cp (3) hap = h:p . m = 1 . m (4) hfP = hfp . m= i . m +cp (5) hWp=hzp, m=2. h,p=2. m (6) 4.4 Bottom clearance, Generally, the bottom clearance, cp, is equal to cb . m = 0,l . m to 0,4 . m.
18、 The bottom clearance to be used depends on the requirements to be met by the gear, and the gear manufacturing facilities. It limits the fillet radius of the basic rack tooth profile of the cylindrical gear and thus the tip rounding radius of the tool basic rack tooth profile. bottom clearance coeff
19、iclent 4.5 Fillet radius The fillet radius, efP, shall start on or below the common tooth depth. It is then defined by: CP 1 -sin ap QfP 5 (7) The fillet radius shall not exceed the value obtained when the left flank and right flank of a space on a basic rack tooth profile merge with the fillet with
20、out forming a tooth root surface. With hfP as specified in equation (5), aP is to be calculated using the following formula: efp 5 +sin . - . (f - tan ap) - cp . tan ap (8) cos ap The following shall apply to a basic rack tooth profile as speci- fied in this standard (with ap = 20 and hfp = 1 . m +
21、cp): formula (7) shall be used for cp not exceeding 0,295 m and formula (8) for cp exceeding 0,295 . m or hfp exceed- ing 1,295 . rn. The notation associated with formulae (7) and (8) is given in figure 2. Only one pair of values, cp = 0,25 . m and fp = 0,38 . m, has been specified in IS0 53. Note.
22、The fillet radius of the cylindrical gear basic rack tooth profile determines the tip rounding radius of the tool basic rack tooth profile. The radii of curva- ture of the fillet produced on the cylindrical gear shall be equal to or greater than the tip rounding radius of the tool according to the n
23、umbers of teeth and profile displacements of the generating gear. Figure 1. Figure 2. asic rack tooth profile edendum line Tooth root surface Basic rack tooth profile (with counterpart rack tooth profile) 0,s 0,4 O, 3 *- I0,2 b QI 0,l O O 0,l 02 0, 3 0,4 0,s 4 - Relationship between bottom clearance
24、 coefficient and fillet radius coefficient according to formulae (7) and (8) for ap = 20 and hfp = 1 . rn + cp. The part of the diagram shaded grey shows the area including possible pairs of values for the cases in which the tooth flanks merge with the fillet. The pairs of values outside the shaded
25、area are associated with basic racks the tooth flanks of which are undercut. Point A: pair of values specified in IS0 53. DIN867 Page3 ci Qbmmax 4.6 Usable flanks, root form depth Thestraight parts of the toothflanksform the usableflanks. Where theflanks mergewith the filletwithout forminga tooth ro
26、ot surface, the root form depth of the basic rack tooth profile is defined by: (9) hFfP = hfp - efp . (1 -sin ap) 0,17 025 03 04 0,25 0,38 0.45 0,39 4.7 Root undercut Basic rack tooth profiles for cylindrical gears with root undercut are not covered by this standard. See DIN 3960, Appendix A, for in
27、formation and explanatory notes. 5 Flank form corrections Flank form corrections are not dealt with in this standard. They are specified using the cylindrical gear teeth, not the cylin- drical gear basic rack tooth profile. See DIN 3960 and DIN 3972. Standards referred to DIN 3960 DIN 3972 DIN 58400
28、 IS0 53-1974 (at present at the stage of draft) drical gear pairs with involute teeth Reference profiles of gear-cutting tools for involute tooth systems as specified in DIN 867 Basic rack tooth profiles for involute teeth of cylindrical gears for precision mechanics Cylindrical gears for general an
29、d heavy engineering; basic rack Concepts and parameters associated with cylindrical gears and cylin- Previous editions DIN 867: 07.27, 09.63, 09.74. Amendments The following amendments have been made in comparison with the September 1974 edition a) Formulae for calculating the fillet radius have bee
30、n included. b) The root form height, hFp, has been introduced as a parameter for the first time. c) The standard has been restructured and editorially revised. d) Coefficients cp, h&, hfp. hGp, h$ and fp have been introduced for the first time. e) Notes on root undercut and flank form corrections ha
31、ve been added. Explanatory notes This standard corresponds to International Standard IS0 53 in its material content, but differs from the latter in the following points. 1. The symbols denoting the linear sizes (pitch, tooth depth, addendum, dedendum, bottom clearance and fillet radius) have been en
32、tered in the illustration of the basic rack tooth profile, whereas IS0 53specifies the factors by which the module is to be multiplied. In addition, the counterpart rack tooth profile is shown in the present standard. 2. IS0 53 specifies the tip relief and its maximum value. This specification has n
33、ot been adopted in DIN 867, because the requirements which make a rack relief necessary in specific cases vary so widely that they cannot be allowed for in a standard. 3. IS0 53-1974 specifies only a single basic rack tooth profile with a dedendum of 1,25 . rn and a fillet radius of 0,38 . rn. The f
34、ollowing table gives some values of the maximum possible fillet radius coefficient, &pm, as a function of the bottom clearance coefficient c$ (see also figure 2). 4. As a departure from IS0 53, the present standard makes it possible to use basic rack tooth profiles with a pressure angle 5. As a departure from IS0 53, the present standard makes it possible to use basic rack tooth profiles with larger addenda other than 209 and dedenda (extra-depth gearing) or smaller addenda and dedenda (stub gearing). International Patent Classification F 16 H 55/08
