1、UDC 621.833.1 : 620.1 .O5 DEUTSCHE NORM Feruarv 98 0,17 0,195 Measuring element diameters for the radial or diametral dimension for testing tooth thickness of cylindrical gears 0,895 3 63 16 1 3,25 7 18 - DIN 3977 C 5 o o Messstckdurchmesser fr das radiale oder diametrale Prfmass der Zahndicke an St
2、irnrdern (Zylinderrdern) As it is current practice in standards publishe by the International Organization for Standardization (ISOI, the comma has been used throughout as a decimal marker. To facilitate use of this Standard Appendix A includes a theoretical treatment of the relationships of the too
3、th thick- ness test dimensions. DIN 2269 DIN 3960 DIN 3975 1 Scope and purpose One of the tooth thickness test dimensions for cylindrical gears with involute gear teeth according to DIN 3960 is the radial or diametral dimension over measuring balls or measuring rollers (measuring wires, test pins).
4、The same principles may also be used for determining the tooth thickness on cylindrical worms according to DIN 3975 as well as on external and internal splines with involute teeth according to DIN 5480 Part 1. y to cylindrical gears with involute teeth N 3960. From them can be found what splines the
5、 measurina roller drical worm gears with shaft angle 90“ dM m, normal module p. axial pitch x addendum modification factor XE generating addendum modification coefficient z number of teeth zd virtual number of teeth for ball or roller dimensions As tooth thickness deviation DM diameter of measuring
6、ball or measuring roller (measuring element dia meter) Mr radial singleball dimension Ma radial single-roller dimension a, normal pressure angle at transverse pressure angle TKt transverse pressure angle on circle through centres of measuring balls a, pressure angle on measuring circle helix angle i
7、 - OS - 03 - 0,4 -95 - 0,6 - 02 - 0,s -1,o - 200 -100-90-80-70-60 -50 -40 -30 - 20 - 10 Virtual number of teeth zri Example: In the diagram point P corresponds to the values za = - 85 and x = - 0,45. By interpolating between the continuous-line curves DM k 1,756 is obtained. By interpolating between
8、 the dashed-line curves DM = 1,443 is obtained. Hence measuring balls with 1,443 * m, DM 1,756 m, are suitable. For an internal gear having a, = 20, za = - 85, = - 0,45 and rn, = 3,5 mm it is, therefore, possible, according to Table 1, to use measuring balls with diameters DM = 5.25 mm, 5,5 mm or 6
9、mm. If necessary, a check must be made to determine whether the measuring balls protrude beyond the tip cylinder and do not contact the root cylinder (especially in the case of cylindrical gears according to DIN 58 400). Figure 3. Limiting values for measuring ball diameters DM for internal gears ha
10、vinga, = 20 and rn, = 1 mm. The continuous-line curves give the largest usable diameters,thedashed-linecurvesthe smallest usablediameters. For other modules the DM values are to be multiplied by the numerical value of m,. For cylindrical gears with tooth thickness deviations xE supersedes x. Page 6
11、DIN 3977 Appendix A Theoretical treatment of relationships of the tooth thickness test dimensions For the inspection of cylindrical gears with involute teeth during production one of the tooth thickness test dimensions used - along with other test dimensions - is the single-ball or two-ball dimensio
12、n (or single-roller or two-roller dimen- sion) in which one or two measuring elements (measuring balls or measuring rollers or measuring wires, test pins) are introduced into the tooth spaces and the radial or diametral dimension over the measuring elements (or between the measuring elements) is det
13、ermined, see DIN 3960. From the measuring element diameter DM and the radial single-ball dimension MrK or single-roller dimension MtR is found the actual dimension of the tooth thickness or the actualdeviation A, of the tooth thickness by using the following equations. If the diametral two-ball dime
14、nsion MM or two-roller dimension hfdR is found, these dimensions have to be converted to the radial singlsball dimension accordingto DIN 3960 or the equations correspondingly restated. For the cylindrical gear parameters normal pressure anglea, normal module mb number of teeth z addendum modificatio
15、n coefficient Y helix anglep the measuring element diameter DM is found from Figs. 1 to 3 of this Standard or from the equations stated in DIN 3960. For measurement purposes it is usually convenient in the case of external gears - particularly when fairly large negative tooth thickness deviations ar
16、e involved - to adopt a somewhat larger diameter than determined acccording to Fig. 1. In the case of internalgears it is important to ensure that where relatively largediameters DM are concernedtheratioAA,/AMrK according to equation (6) is not too small or the deviation factor AGd or AM, respective
17、ly (see DIN 3960) is not too large. From the actual value of the measuring element diameter DM and the measured value of the radial single-ball dimension Ma the transverse pressure angle aKt on the circle through the centres of the measuring balls dK is first found as where the transverse pressure a
18、ngleat is calculated from tan a, tan at = - cos The actual tooth thickness deviation A, in the normal section is thus + inv aKt - invat - 1 cos DM a, n- 4 ex tana, (3) inv denotes the involute function inv a = tan a -a. The tooth thickness deviations are mostly negative. The measuring elements must
19、contact the teeth in the involute portion of the tooth flanks. If there is any doubt about this the measuring circle diameter dM (on which the contact points lie) must also be calculated. This is given by t m, cosat cos cos aM dM = where the pressure angleaM on the measuring circle diameter dM is ca
20、lculated from DM 1 - cosza, sinz tanaM = tanaKt - z-m, cos a, (4) (5) If necessary, measuring elements with the next larger (or next smaller) diameter are to be used. Differentiation of equations (1) and (3) and re-arrangement yields the following: If the measured value of the radial single-ball dim
21、ension Mr changes by a small amountAMrK (if, for example, a meas- uring error AMrK has occurred or if the measured value differs byAMrK from a specified value MrK), then the result for the tooth thickness deviation A, alters by 2 sin aKt cos cos at AAs *AMr backlash, tooth thickness deviations, tooth thickness tolerances, principles DIN 3976 Cylindrical worms; dimensions, allocation of centre distances and ratios of worm gear sets
