DIN 3961-1978圆柱齿轮啮合公差基础

DIN 3961-1978圆柱齿轮啮合公差;基础

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DIN 3961-1978圆柱齿轮啮合公差;基础

Page 2 DIN 3961

1.2 Gear tooth tolerances, system of gear fits To make sure a t all times that, apart from the interchangeability of the gears of gear transmission units which is governed by the mating dimensions, the respective functional requirements such as quiet running, trueangle transmission, lubrication facilities, loading capability, are upheld, it is essential for the deviations of certain parameters of the gear teeth as well as the mounting dimensions in the gear housing to be held within certain limits. The system of gear fits resembles the system for cylindrical fits. For each of the gears of a gear pair all form deviations, pitch deviations etc. lie within the dimensions of two notional, error-free, concentric gears, the tooth centres of which do not need t o coincide with those of the working gears, and the tooth thicknesses of which differ from the nominal dimension by the amount of the upper allowance in the case of one of the gears, and by the amount of the lower allowance in the case of the other gear. The backlash results not only from appropriately chosen allowances of tooth thickness, but also from the allowance of the centre distance and other individual deviations. The magnitude and scaling of the tooth thickness allowances are thus in a given ratio t o the magnitude and scaling of the centre distance allowances. Just as with I S 0 cylindrical fits there are two systems of fits, the hole basis and the shaft basis, so also are there two systems of gear fits, namely the centre distance basis and the tooth thickness basis. With the former, only one tolerance zone of the centre distance i s used and the magnitude of the clearance i s established by different tolerance zones of the tooth thickness. With the tooth thickness basis system the opposite applies. The sizes of the gear tooth tolerances are developed on the same principles as the tolerances for cylindrical fits. Thus, just as the latter are designed for accuracies which exceeded the requirements existing a t thc time of their origin, and are still in advance of their time, so also are the gear tooth tolerances arranged such that in all probability more exacting requirements and improved measuring methods available in the future are catered for.DIN 3962 Part 1 to Part 3 contain the tolerances for deviations of individual parameters of cylindrical gear teeth. DIN 3963 contains the tolerances for working deviations. DIN 3964 contains the centre distance allowances and shaft position tolerances for housings for cylindrical gear transm issio ns. DIN 3967 contains the system of gear f i t s with data on backlash, tooth thickness allowances and too

th thickness tolerances. The basis specified for the system of gear f i t s i s that of the centre distance. For this purpose it IS necessary so to arrange the centre distance allowances that when using gear transmissions with external and internal teeth the centre distance allowances are indicated in the same way, and in gear transmissions with many pairs of gears no unacceptably large deviations from the nominal dimension arise in the distance from the first t o the last transmission shaft. The limiting allowances are thus disposed symmetrically relative t o the zero line. The kind of gear tooth fit i s determined through the choice of

the upper allowance and the tolerance on tooth thickness in DIN 3967 and through the choice of zone for the centre distance allowances in DIN 3964.

1.3 Scope DIN 3962 Part 1 to Part 3 and DIN 3963 contain tolerances for gear teeth on cylindrical gears of module 1 t o 70 mm and with reference circle diameters d up t o 10 O00 mm, graded in 12 gear tooth qualities. The tolerances apply regardless of the pressure angle. For checking tooth thickness and determining backlash, the working pressure angles and helix angles have to be taken into account, see DIN 3967. For d exceeding 10 O 0 0 mm tolerances can be agreed which can be calculated by using the formulae given in Section 3.5.1 and in Section 3.5.2. I n the case of racks, the tolerances for their teeth shall not exceed those for the teeth of the mating gear. If the manufacturer has no knowledge of the mating gear, he may make the rack length equal to the mating gear circumference.

2 Other relevant StandardsDIN 3960 Definitions and parameters for cylindrical gears and cylindrical gear pairs with involute teeth DIN 3962 Part 1 Tolerances for cylindrical gear teeth; tolerances for deviations of individual parameters DIN 3962 Part 2 Tolerances for cylindrical gear teeth; tolerances for tooth trace deviations DIN 3962 Part 3 Tolerances for cylindrical gear teeth; tolerances for pitch-spandeviations DIN 3963 Tolerances for cylindrical gear teeth; tolerances for working deviations DIN 3964 Centre distance allowances and shaft position tolerances of housings for cylindrical gear transmissions DIN 3967 System of gear fits, backlash, tooth thickness allowances and tooth thickness tolerances; bases, calculation of tooth thickness allowances, conversion of allowances for the different measuring methods

3 Structure of the tolerance system3.1 Tolerance relationships The DIN gear tooth tolerance system has been derived from long experience in gear production. The aim has been as far as possible so to coordinate the various tolerances with one another that in a given gear tooth quality they correspond approximately to the average relationships in which the deviations occur in production. The bases of the tolerance system are thus productionoriented; the way in which this system can also be used for tolerancing to suit different functional requirements i s described in Sect

ion 4. The numerical equations for the tolerances and the values calculated from them in DIN 3962,Part 1, DIN 3963, DIN 3964 and DIN 3967 have also been extrapolated to ranges in which they can no longer be meaningful applied in all cases; for example, in gear tooth quality 12 it i s only very rarely that there will be any point in making

DIN 3961-1978圆柱齿轮啮合公差;基础

DIN 3961 Page 3a pitch test; the same also applies to the working test for gear tooth qualities 2 or 3. These extrapolated values in the Standards therefore do not imply that, for example, their direct verification can be expected, see Section 5. They only make sure that the tolerances are in a reasonable relationship to the"normal" range if they should happen to be needed a t some time; see also Section 6.3.

The tolerances calculated in this way are rounded t o preferred numbers. Hence t h e total number of values i s comparatively small. I n addition, knowledge of the preferred numbers can be used to calculate the next larger or smaller value from any known value. m,d, b, L in mm. Tolances in pm.

3.2 Individual parameters DIN 3962 Part 1 to Part 3 contain tolerances for:Profile form deviation Profile angle deviation Total profile deviation Individual pitch deviation Normal base pitch deviation Pitch error Total pitch deviation Pitch-spandeviation over k pitches Pitch-spandeviation over l/s of gear periphery

3.5.1 Individual deviations a) Profile form deviation f f=1,5+0,25(mn+9.Kn) Q= 1.4 up to gear tooth quality 9 p= 1.6 from gear tooth quality 9b) Profile angle deviation f H a= 2,5+ 0,25 (mn+ 3 9= 1.4 up to gear tooth quality 9= 1.6 from gear tooth quality 9 (P c) Total profile deviation

. Kn)

Ff=C'fia+fFp= 1.4 up to gear tooth quality 9 9= 1.6 from gear tooth quality 9d) Individual pitch deviation and normal base pitchdeviation

Concentricity deviation Tooth thickness fluctuation Tooth trace total deviation Tooth trace angle deviation Tooth trace form deviation For definitions see DIN 3960.

fp(PQ

=fpe= 4

+ 0,315 ( m,+ 0,25

vd)

= 1.4 up to gear tooth quality 9

3 3 Working deviations . I n DIN 3963 tolerances are presenpd for the followingworking deviations: Two-flank working deviation Two-flank working error Single-flank working deviation Single-flank working error For application of the working test see also Code VDIIVDE 2608. For definitions see DIN 3960.

= 1.6 from gear tooth quality 9 e) Pitch error f,= 5+ 0,4 ( m,+ 0,25@) Q= 1.4 up to gear tooth quality 9= 1.6 from gear tooth quality 9 Qf) Total pitch deviation

FI'

FpQ(P

= 7,25

*

frFI

d '13 z 117

fi

= 1.4 up t o gear tooth quality 9= 1.6 from gear tooth quality 9

Q) Pitch-spandeviation

3.4 Gear tooth qualities The DIN gear tooth tolerance system contains 12 gear tooth qualities. The finer qualitites are intended for master gears and special requirements. They are so grad. uated that the tolerances of each quality amount to p times the tolerances of the preceding quality. The increments p are s

tated in Section 3.5. The limiting values of the reference diameter and module ranges are taken from the preferred number series R 20.3.5 Calculation of tolerances The tolerances are calculated according to formulae exhibiting different kinds of dependence on the gear tooth data (reference circle diameter, module, number of teeth and facewidth). The numerical factors of the formulae reproduced below apply to the 5th gear tooth quality. For calculating the tolerances from the formulae, the geometrical mean values of the ranges stated i n the Tables are used for m, and d.

p= 1.4 up to gear tooth quality 9 p= 1.6 from gear tooth quality 9h) Concentricity deviation F,= 1,68+ 2,18 * Q= 1,4

6

f

(2,3+ 1,2 log m,)

*

d1/4

i) Tooth thickness fluctuation R,= 1+ 1,28+ (1.33+ 0,7 log mn) d1/4 p= 1,4

6

k) Tooth trace total deviation Fp= 0,8 * i/b+ 4 p= 1.25 up t o gear tooth quality 6 p= 1.4 gear tooth quality 6 to 8= 1.6 gear tooth quality 8 to 12 Q

I) Tooth trace angle deviation

fq=4,16 *= 1.32 up to gear tooth quality 6 Q bp= 1.4 gear tooth quality 6 to 8 p= 1.55 gear tooth quality 8 to 12

DIN 3961-1978圆柱齿轮啮合公差;基础

Page 4 DIN 3961 m) Tooth trace form deviation tional requirements made on a gear, the better must be the gear tooth quality produced, but on the other hand the more differentiated must be the tolerancing in order t o avoid unnecessary production cost. Hence it i s possible for fundamentally different gear tooth qualities t o be prescribed for the individual parameters. Such a linking is termed a tolerance family. However it i s not desirable to form tolerance families in which a different gear tooth quality is fixed for each critical parameter. The service properties required of a gear can be classified in the following function groups: - G: uniformity of transmission of motion - L: quiet running and dynamic load-carryingcapacity- T: static load-carryingcapacity - N: no information on function

fßf=3.5.2Working deviationsa) Two-flank working deviation Fi'= 2+ 2,57 *+ (3,12+ 0,432 log m,) cp= 1,4

G,

d'h

b) Two-flank working error

fi'rp

1,8= 1,4=

*En,+1 1,6 * d '/ a+ Ff)

c) Single-flank working deviation

FI= 0,8 * ( F,

cp cp= 1.6 from gear tooth quality 9 d) Single-flank working error

= 1.4 up to gear tooth quality 9

ficp cp

= 0,7= 1.6

*

(fp+ Ff)

= 1.4 up to gear tooth quality 9

from gear tooth quality 9

3 6 Tolerances for the diameter of the tip circle .(tip cylinder) Because of the module-dependentbottom clearance and the effect of the tip circle diameter on the transverse contact ratio of the gear teeth, the tolerance f 0.05 . m i s prescribed for the diameter of the tip cylinder in the case of non-overcut tooth tips, except where agreed to the contrary. I n the case of overcut tooth tips, which are mainly used on gears for light precision engineering, the diameter of the tip cylinder is employed for indirect checking of the tooth thickness. It is smaller than the nominal dimension by 2.747 times th

e tooth thickness allowance when a= 20' and by 3.732 times t h e tooth thickness allowance when 01= 15'. For further details see DIN 58 405 Part 2, May 1972 edition, Section 2.1.

These depend largely - if not exclusively - on specific geometrical requirements, see Table 1. When tolerance families with gear tooth qualities are formed it i s therefore desirable t o choose the same gear tooth qualities each time for the tolerances of a function group. In this way tolerance families with not more than three different gear tooth qualities can arise. I f a parameter occurs in several function groups, it is the group with the finer gear tooth quality which prevails for this parameter.

4 Tolerancing4.1 Tolerance families

The tolerances chosen must be correct from the functionalI and production viewpoint. The more exacting the funcTable 1. Function groups of deviations

4.2 Application of tolerance families It will often happen that for a particular gear it i s desirable or practicable to demand only a general service property without taking special functional requirements into account (function group NI. I n these cases only a single gear tooth quality i s prescribed, e. g. quality 8. (The points to be observed and checked in these and the following cases are described in Section 5). I n other cases fulfilment of the requirements of a specific function group will be stipulated. I n such cases the letter symbol of the function group must be quoted along with the required gear tooth quality. Examples are given i n Table 2. Basically, tolerances shall be agreed only for such function groups whose deviations really matter for the application concerned. As a rule, not more than two function groups should be agreed.~~~~~

_

_

_

_

_

_

~~~

~

~

~

Function group

Important deviations *)

GL T

Uniformity of transmission of motion Quiet running and dynamic load-carryingcapacity Static load-Carringcapacity

fififpefp

F p F' i(fJ

Fr

fi'Fp

fi' Ff fHp

(F,)

fHßfHp

TRAFt

N

No information on function

E'

DIN 3961-1978圆柱齿轮啮合公差;基础

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DIN 3961-1978圆柱齿轮啮合公差;基础

Page 6 DIN 3961

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DIN 3961-1978圆柱齿轮啮合公差;基础

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DIN 3961-1978圆柱齿轮啮合公差;基础

Page 8 DIN 3961I-

l i '

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Figure 1. Altered pattern of permissible range of profile deviations (examples)

Figure 2. AA, A'A' BB B'B', B"B" C'C', C"C" Corrected base lines bounding the test pattern within the evaluation range. Averaging actual tooth flank Actual tooth traces bounding the test pattern within the evaluation range. Non-correctednominal tooth traces through the points of intersection of the averaging actual tooth trace

BB with the boundary lines of the evaluation range.FßfHP

fßcb

f

cb actual

Tooth trace total deviation; results from the distance apart of the corrected base lines AA and A'A' as measured at right angles t o the chart feed. Tooth trace angle deviation; results from the distance apart of the nominal tooth traces C'C' and C"C". Tooth trace form deviation; results from the distance apart of the actual tooth traces B'B' and B"B" as measured at right angles t o the chart feed. Nominal crowning Actual crowning

DIN 3961-1978圆柱齿轮啮合公差;基础

DIN 3961 Page 9

6 3 Working test for fine gear tooth qualities .The permissibleworking deviations apply in principle t o the testing of a working gear with an error-free standard (master gear). I n practice it is necessary to limit the checking to determining that the deviations of the master gear compared with those of the test gear are sufficiently small (approximately in a 1: 5 ratio). Hence it would not be meaningful to state permissibleworking deviations for the gear tooth quality range from 1 to 4, since in practice there are no adequately error-free standard gears available for this purpose, or gears with known error pattern. Nevertheless, a working test of two gears of approximately the same gear tooth quality i s sometimes carried out. I n this case, however, the test must be repeated with the flanks interchanged (left and righ

t). I f there deviations are Fil and Fiz a measured value of

F~=

V F+~F;fi=

deviations over discretionary pitch-spans. Their values are found from the formula or the diagram in DIN 3962 Part 3 and they require separate agreement. A pitch-span measurement can be evaluated by plotting the positive and negative tolerance values on tracing paper versus the number of teeth z. The scales of Fp and z must agree with those of the test chart, and in this the z axis must be a t right angles t o the Fpkaxis. I f the zero point of the diagram i s moved along the pitch-spancurve of the test chart, keeping the z axes parallel, the pitchspan curve must lie a t all times within the two tolerance . curves, Fig. 3 Another method is t o determine the pitch-spandeviation Fpk and the associated span at the point of maximum increase in the test chart, Fig. 3 right. This measured value of Fp is then compared with the value permitted according to the diagram in DIN 3962 Part 3 for the same span.

will be expected according to the quadratic error propagation law. I n a working test of two gears (master gears) having approximately the same gear tooth quality, therefore, only 1.4 times the tolerance value of this quality can be accepted. Hence for these applications the standardized quoting of permissible working deviations is s t i l l meaningful for fine gear tooth qualities. A binding quality test according to this method i s however only possible if the uncertainty of measurement can be kept small enough, cf. VDINDE 2608.

6.5 Individual pitch deviations and pitch errorsIf mavericks occur in individual pitch measurements, it i s permissiblet o make measurements a t different points on the flanks and to derive averages for each pitch. The resulting series of measurements i s then used as the basis for assessing the individual pitch deviation and pitch error. No further mavericks are permissible in this. When making pitch measurementswith two spherical tracers it is important to ensure that the second tracer contacts the flanks each time a t exactly the same spot as the first tracer in the preceding pitch. Apart from the pitch deviation tolerances laid down in DIN 3962 Part 1 and Part 3 there are also other characteristics for assessing pitch, e. g. the arithmetic mean or root mean square values of the pitch deviations. They may form the subject of separate agreements;see also VDI/ VDE 2605.

6.4 Pitch-spandeviations over discretionary pitch-spans In general the tolerancing and testing of pitch-spansover 45" and 180' of the gear circumference according t o the values F p s/8 and Fp in DIN 3962 Part 1 i s perfectly adequate. ln some cases, however, and particularly where high-speed gears are involved, it may be necessary in certain circumstances to further restrict the pitch-span

Figure 3. Evaluation of pitch-spanmeasurement

DIN 3961-1978圆柱齿轮啮合公差;基础

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DIN 3961-1978圆柱齿轮啮合公差;基础

Page 12 DIN 3961Gear tooth quality 7 (AGMA gear tooth quality 1 1) Gear#oothquality 9 (AGMA gear tooth quality 9)

d=70mm20(

m=5mm b=50mm I d=300mm

Id=lSOmmm=12mm b=120mm d=300mm

IJm1BC

160

14í12c 1O0

8060

w:20

O

Reference circle diameter d= 300mm Module m= 5mm

DIN and IS0 gear too- quality ___F 1 2 3

4I

5I

15

1 4

1 3

6I I

7

ôI

9I

101

1 1I

12I I I

1 2

1 1 9 8 1 0 7 6 5 AGMA gear tooth quality

4

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