DIN_3967-1978_ENG

UDC 621.833.1 : 621.753.1 DEUTSCHE NORMEN August 1978 System of Gear Fits Back1 ash Tooth Thickness Allowances Tooth Thickness Tolerances Princbles - - DIN 3967 Getriebe-Passystem; Flankenspiel, Zahndickenabmasse, Zahndickentoleranzen, Grundlagen To facilitate use of this Standard, the calculation of tooth thickness allowances has been included as Appendix A. Information on converting the allowances for the various measuring methods is add& in Appendix B. The DIN backlash system of fits for gear pairs allows the limiting allowances of tooth thickness to be defined with attention given to all effects occurring in the operation of a gear transmission, and to all deviations throughout the gearing. The system of fits therefore consists on the one hand of the allowances and tolerances of the gear teeth, referred to their prevailing mounting arrangements, and on the other hand of the allowances and tolerances of all the other com ponents of the gear transmission in so far as they determine the position of the teeth relative to one another. These values defined for a reference temperature vary in operation through temperature changes in the upward or downward direction, through elastic deformation under load and possibly through swelling or contraction. The system of fits is defined as a tooth thickness system of fits in the normal section on the reference cylinder, i. e. all allowances, tolerances and operationally induced alterations in the gear transmission are treated as tooth thickness alterations and require to be converted to the nonnal section. The normal section was chosen because the production effort, i. e. the necessary tooth thickness tolerance in the normal section, is indëpendent of the helix angle. The normal section was also chosen for metrological reasons, since the normal chordal tooth thickness and the base tangent length are measured in the normal section. The calculation of the allowances however is made over the transverse section, since on the finished gear transmission the backlash is measured as circumferential backlash (see Appendix A). The system of f i ts provides for safeguarding the minimum backlash and limiting the maximum backlash. The reference basis of the system of fits is the zero-play condition at the nominal centre distance, with nominal adden- dum modification and with error-free components. The necessary negative allowances of tooth thickness can be produced by an additional addendum modification in the negative direction Ax. This however is not taken into account in the nominal addendum modification. Whether the weakening of the tooth thickness needs to be taken into Consideration in calculations of IoadCarryng capacity is something which has to be decided for the case concerned. In any event this should be done whenever *sni > 0.005. 1 Other relevant Standards DIN 3960 Definitions and parameters for cylindrical gears and cylindrical gear pairs with involute teeth DIN 3961 Tolerances for cylindrical gear teeth; principles DIN 3962 Part 1 Tolerances for cylindrical gear teeth; tolerances for deviations of individual para- meters DIN 3964 Centre distance allowances and shaft position tolerances of housings for cylindrical gear transm íssions DIN 3999 Symbols for gear teeth 2 Backlash The backlash value says nothing about the quality of the gear teeth although, on the other hand, the different gear tooth qualities demand given tooth thickness allowances in order to ensure the requisite or permissible backlash. The minimum backlash i s determined by the upper allow- ances. However it does not correspond.to the sum of the upper allowances because a whole series of factors alters the backlash (see Appendix A). The maximum backlash is determined by the lower tooth thickness allowances which result from the upper allow- ances and the tooth thickness tolerances. This also does not correspond to the sum of the allowances because here again a series of factors alters the backlash. 21 Theoretical backlash The theoretical backlash it results from the tooth thick- ness allowances converted to the transverse section and from the converted allowances of the centre distance. Continued on pages 2 to 23 Explanations on page 24 DIN3967 engL Preikgr. 7; !le sale rights of German Standards (DIN-Nonnen) are with Beuth Verlag GrnbH. Berlin 30 11.91 Verir.-Nr. O1 12 www.bzxzw.com Page 2 DIN 3967 - 10 2.2 Acceptance backlash The acceptance backlash is the backlash obtained with the unloaded gear transmission a t reference temperature when one of the gears is rotated against the other. It is uwally smaller than the theoretical backlash, since the backlash-reducing factors generally outweigh the factors tending to increase the backlash. Backlash-reducing factors are, for example, deviations in the gear teeth and also form and position deviations, see Appendix A. 2.3 Working backlash The working backlash is the backlash resulting when the gear transmission i s operating. It i s not constant. During the starting up of the gear transmikion in particular it is possible for the more rapid temperature rise of the gears compared with the housing to bring about larger changes in the working backlash. It is generally larger than accept- ance backlash when the linear coefficient of expansion of 10 - 100 - 85 - 70 - 58 - 48 - 40 - 33 - 22 - 10 - 5 O 50 - 1 3 5 - 1 1 0 - 9 5 - 7 5 - 6 5 - 5 4 - 4 4 - 3 0 - 1 4 - 7 O the housing is greater than that of the gears. Shaft deflec- tion and displacement also affect it. 50 125 3 Tooth thickness allowances Normally the tooth thickness allowances and tooth thick- ness tolerances can be found directly from Tables 1 and 2 on the basis of existing experience, such that, as a rule, the upper allowances for each gear should be at least as large (numerical value) as the lower allowance of the housing centre distance (without converting). If no empirical values are available for backlash and tooth thickness allowances, these must be calculated. A guide for this purpose will be found in Appendix A. The cal- culated values are usually rounded and then likewise taken from Tables 1 and 2. I f exceptionally small amounts of backlash are necessary for functional reasons, calcula- tion is indispensable. and tooth thickness tolerances 125 - 180 - 150 - 125 - 105 - 85 - 70 - 60 - 40 - 19 - 9 O 280 - 250 - 200 - 170 - 140 -115 - 95 - 80 - 56 - 26 - 12 O Table 1. Upper tooth thickness allowances A , in pn t I I 280 560 Reference diameter I imm) 560 - 330 - 280 - 230 - 190 -155 -130 -110 - 75 - 35 - 17 O 1000 - 450 - 370 - 310 - 260 -210 -175 -145 -100 - 48 - 22 O Allowance series 1000 1600 1600 - 600 - 500 - 420 - 340 -290 -240 -200 -135 - 64 - 30 O 2500 - 820 - 680 - 560 - 460 -390 -320 -270 -180 - 85 - 41 O 2500 4000 4000 -1100 - 920 - 760 - 620 -520 -430 -360 -250 -115 - 56 O 6300 -1500 -1250 -1020 - 840 -700 -5m -480 -330 -155 - 75 O over up to - 10 10 50 21 22 23 24 25 26 27 28 29 I 30 3 5 8 12 20 30 50 80 130 200 5 8 1 12 20 30 50 80 330 200 300 1 6300 I 10000 ~ - 2 0 0 0 ~ - 1 6 5 0 ~ - 1 3 5 0 ~ - 1 1 5 0 ~ -940 1-780 1-640 1-450 1-210 1-100 1 O 1 280 560 1000 Table 2. Tooth thickness tolerances TSn in pm I I i 560 10 16 25 40 60 100 160 250 400 600 1 000 12 20 30 50 80 130 200 300 500 800 1600 16 25 40 60 100 160 250 400 600 1000 Reference diameter I (mm) 1600 2500 4000 Tolerance series 2 500 20 30 50 80 130 200 300 500 800 1300 4 000 25 40 60 100 160 250 400 600 1000 1600 6 300 30 50 80 130 200 300 500 800 1300 2000 I 50 1 125 I 6 I 10 1 16 I 25 I 40 I 60 I 100 I 160 I 250 I 400 I I I loooo I 40 I 60 I I 160 I 250 I 400 I 600 I lm I 1600 r2400 I www.bzxzw.com DIN 3967 Page 3 3.1 Upper allowances The upper allowances are to be taken from Table 1 independently of the reference diameter and the allow- ance series. Their choice is largely independent of the gear tooth quality. As a rule for transmissions of the same kind it is possible to choose the upper allowance for pinion and gear in all cases from a single allowance series; it is also permissible however to select values from different allowance series. 3.2 Lower allowances The lower allowances are obtained by combining the upper allowances with the tooth thickness tolerances. Since the upper and lower allowances are always nega- tive the amount of the tolerance has to be deducted from the upper allowance. 3.3 Tooth thickness tolerances The tooth thickness tolerances are to be found from Table 2. Their choice is largely independent of the gear tooth quality and should be governed by the manufactur- ing facilities, although it should be borne in mind that the tooth thickness tolerance must be at least twice as large as the permissible tooth thickness fluctuation R, according to DIN 3962 Patt 1. I f a maximum backlash has to be watched for functional reasons, calculation according to Appendix A will be necessary. Quite generally it should be noted that small tooth thickness tolerances unfavourably affect the maintaining of gear tooth quality, since they unnecessarily limit the correc- tion possibilities during manufacture (see, for example, VDINDE 2608). In order to distinguish them clearly from the gear tooth qualities, the tolerance series have been given the num- bers 21 to 30. The preferred series are 24 to 27. 3.4 Information in drawings The limiting allowances can be indicated in the drawing either directly or by means of an code designation, see DIN 3966 Part 1. The symbol consists of the number of the tooth thickness tolerance series and the letter symbol of the series for the upper tooth thickness allowance. Example: 27cd; this designation yields, ford = 100 rnm for example, the limiting allowances A , = - 70 pm and A,, = - 170 pm. . 4 Converting the tooth thickness allowances for the different test methods The system of f i t s is referred to a theoretical value. This i s the tooth thickness in the normal section which, how- ever, i s not directly measurable. Therefore indirect meas- urements are made by various methods, see DIN 3960. For an error-free gear there are mathematical relation- ships connecting the different measured quantities. How- ever, since the individual measured quantities are affected differently by the individual deviations of the gear teeth a purely mathematical conversion of the tooth thickness allowances does not necessarily guarantee the required backlash. Where adequate experience i s available (e. g. in the case of tooth thickness tolerance zone 26e or coarser) the tooth thickness allowances can be converted directly into given test dimension allowances (e. g. base tangent length allowances) and these used for acceptance testing the gear. It may then happen, however, that acceptance testing by a different measuring method (e. g. pin dimen- sion measurement) will show that the tolerance is not fully complied with. With the closer tolerance zones it is therefore recommend- able when calculating different test dimensions and their allowances to apply appropriate corrections which take account of the influence of the individual deviations on these test dimensions empirically (statistically). Guidance on determining correction values is given in Appendix B. For calculating the allowance factors according to DIN 3960, October 1976 edition, Sections 4.1.3 and 5, the mean generating addendum modification coefficient xh, corresponding to the mean allowance should always be used. --``,`,,`,,```,,`,`,,,``,```,`-`-`,,`,,`,`,,`--- www.bzxzw.com Page 4 DIN 3967 Standard basic Gear teeth rack tooth profile Tool 5 Example Length dimensions in mrn ~ ~~ ~ DIN 867 DIN 3972 Helical gears Helix angle ß Flank direction External Pinion I Gear 9? 53? 49? DIN 3978 Left Right I Normal module rn, I 5 I Gear tooth quality Facewidth b I Number of teeth 2 1 20 I 97 I 6 7 70 Housing centre distance a Housing width ~~ 300 is 7 200 I Reference diameter d 1 101.517 1- 492.326 x 1 +0,4000 1 +O2389 I Addendum modification 1 coefficient to DIN 3992 Pinion 16 MnCr 5 Gear 42 CrMo 4V Material I Housing material I GG 22 I Pinion hardened and ground, gear heat-treated and milled. It is assumed that it is known from experience that the upper allowan,cesof tooth thickness of series cd are appropriate for this type of transmission. According to Table 1 the upper allowances are selected as A,, = - 70 pm for the pinion and A,, = - 130 pm for the gear. (These values are algebraically smaller than the lower allowance - 26 pn of the centre distance.) For the particular application concerned, the observance of a functionally imposed maximum backlash is not necessary. To cater for hardening distortion, and also to keep the grinding COR low, the tolerance for the pinion is made comparatively large. For series 27 Table 2 gives T, = 1 O0 pm and hence A , = - 70 pm = - 0,070 mm A , = - 170 pn = - 0,170 mm (lower allowance = upper allowance minus tolerance). Since the gear is milled, a tolerance of 1 O0 p n (Table 2 series 26) i s adequate. Consequently A , 2 = - 130 pm = - 0,130 mm Apii2 =-230pm=-0,230mm The adoption of these tolerance zones, which meet the manufacturing requirements, means that the tooth thick. nesses are not unacceptably weakened Since the tooth thickness fluctuation according to DIN 3962 Part 1 i s allowed to be 14 pm for the pinion and 25 pm for the gear, the tolerances are correctly selected in this respect also (see Section 3.3). --``,`,,`,,```,,`,`,,,``,```,`-`-`,,`,,`,`,,`--- www.bzxzw.com DIN3967 Page5 Number of teeth z Sn nenn 20 97 9.3099 8,7235 Tooth thidcness I 9,2399 sn mittel 9.1 899 8,5935 8,5435 Sn min I I I . I ~ I . . . . . 9,1399 8.1935 + 0,4000 I Xmin I +O9533 I +0,1757 + 0,2389 The above result in the following test dimensions with their allowances: + 0,3808 + 0,3670 maenaum moaiTicarion I + 0,2032 + 0.1 894 177,485 f 0,047 507,604 f 0,126 i-'. 507,670 f 0,126 Base taqent length W Measured number of teeth K Allowance factor A& Dimension over balls MdK Dimension over rollers MdR Ball and roller diameter D M Allowance factor AMa 39,619 f 0,047 3 0,940 1 17,472 f 0,099 9,297 = 9 1,988 Working distance with master gear Number of teeth of master gear (DIN 3970) 1) Allowance factor A;" a" ZL 129,314f0.061 323,962 f 0,066 30 30 1,218 1,325 --``,`,,`,,```,,`,`,,,``,```,`-`-`,,`,,`,`,,`--- www.bzxzw.com Page 6 DIN 3967 The calculated allowances of the measured values are shown in Fig. 1: these are values for ideal geometry. For use in practical measurements they may need to be corrected, see Section 4 and Appendix B (Fig. B.l and 8.3). The acceptance backlash may turn out to be smaller than the sum of t h e upper allowances, as dictated by the tolerance for the housing and other effects. It may, however, also turn out to be larger than the sum of the lower allowances, as dictated by the slope of the tooth and the housing tolerance, and further effects (see Appendix A). Figure 1. Tolerance zones of test dimensions after ideal-geometry conversion'of tooth thickness tolerance zone - - ` ` , ` , , ` , , ` ` ` , , ` , ` , , , ` ` , ` ` ` , ` - ` - ` , , ` , , ` , ` , , ` - - - DIN 3967 Page 7 Appendix A Calculation of tooth thickness allowances or backlash A.l General A.l.l Symbols and designations A.1.2 Connection between backlash and allowances A.2 Backlash-modifying effects A.2.1 Temperature rise A.2.2 Centre distance tolerance of the housing A 2 3 Non-parallelism of bore axes in the housing A.2.4 Gear tooth individual deviations A.2.5 Swelling or contraction A.2.6 Position, form a n d dimension deviations of components A.2.7 Elasticity A.3 Action of the backlash-modifying effects A.4 Calculation of the backlashmodifying effects A.4.1 Backlash modification through temperature rise Aje A4.2 Backlash modification through centre distance tolerance Aja A.4.3 Backlash modification through non-parallelism of bore axes Aics A.4.4 Backlash modification through gear tooth individual deviations AiF A.4.5 Backlash modification through swelling or con- traction AiQ A.4.6 Backlash modification through position, form and dimension deviations of components AiB A.4.7 Backlash modification through elasticity AiE Contents A.1 General Al .1 Symbols and designations U b d fD fZß it it, it, Centre distance Facewidth Reference diameter Individual pitch deviation Axial skew over length LG Theoretical backlash Acceptance backlash Working backlash Maximum circumferential backlash Minimum circumferential backlash Module Relative water absorption (relative volume expansion) Addendum modification coefficient with mean tooth thickness allowance A , Centre distance allowance A , Upper centre distance allowance A.5 Calculation of sum of upper allowances ZA* from minimum backlash jtmb and the badclash- modifying effects A.5.1 Determining the upper allowances of tooth thick- ness in the normal section A.6 Calculation of sum of lower allowances ZA& from maximum backlash it msx and the backlash- modifying effects A.6.1 Definitions A.6.2 Maximum backlash jt mu A.6.3 Calculation A.6.4 Determining the lower allowances of tooth thick- ness in the normal section A.7 Calculation of backlash from the tooth thickness allowances and the badclash-modifying effects A.8 Allowance diagram of tooth thickness in the normal section A.9 Example for determining tooth thickness allowances A9.1 Upper allowances A.9.2 Lower allowances A.9.3 Lower allowances without a specified maximum backlash A.9.4 Allowances under modified conditions A.9.5 Acceptance backlash A.10 Example for determining the backlash to be expected A.lO.l Determining the theoretical backlash A.102 Acceptance backlash A , Lower centre distance allowance A,, Asm Upper allowance of tooth thickness' in normal section Lower allowance of tooth thickness in normal section Upper allowance of tooth thickness in trans- verse section Lower allowance of tooth thickness in trans- verse section Total profile deviation 1) . Pitch span deviation over k pitches Concentricity deviation Tooth trace total deviation 1 ) Separation of bearing centres of a shaft Swelling of housing Swelling of gears 1) Measured according to DIN 3960 in the transverse section tangential to the base cylinder. DIN 3967 Tooth thickness fluctuation Tolerance Tolerance of two-flank working distance Tolerance of normal chordal tooth thickness fluctuation Tooth thickness tolerance in the normal section Tolerance of diametral two-ball or two-roller measurement Tolerance of radial single-ball or single-roller measurement Base tangent length tolerance Pressure angle Normal pressure angle Transverse pressure angle Linear coefficient of expansion of housing Linear coefficient of expansion of gears or gear rings Helix angle Backlash modification through centre distance tolerance Backlash modification through form and dimension deviations of the components Backlash modification through elasticity Backlash modification through gear tooth ind ividual deviations Backlash modification through swelling or contraction Backlash modification through temperature rise Backlash mcdif ication through non-parallelism of bore axes Temperature difference of housing relative to 20°C Temperature difference of gears relative to 20 "c Sum of upper allowances of tooth thickness of gear pair in the normal section Sum of lower allowances of tooth thickness of gear pair in the n