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है”ह”ह

IS 3756 (2002): Method for Gear Correction - AddendumModification for External Cylindrical Gears with ParallelAxes [PGD 31: Bolts, Nuts and Fasteners Accessories]

FRR tkilwl *‘HJ-1111’TI<

IS 3756:2002 i

I

(mm yR%PJl__ /

Indian Standard

METHOD FOR GEAR CORRECTION — ADDENDUMMODIFICATION FOR EXTERNAL CYLINDRICAL

GEARS WITH PARALLEL AXES

(First Revision)

0 BIS 2002

BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

October 2002 Price Group 4

Gears Sectional Committee, BP 13

FOREWORD

This Indian Standard (First Revision) was adopted by the Bureau of Indian Standards, after the draft finalizedby the Gears Sectional Committee had been approved by the Basic and Production Engineering Division Council.

This standard was originally published in 1966. The revision of the standard has been undertaken to provideguidelines regarding the limits of addendum modifications of teeth and distribution of addendum modificationsbetween mating gears through analytical equations and graphical representation, wherever necessary.

The gear is said to be corrected when the tooth form does not conform with the basic tooth form due toaddendum modification.

This standard deals with the addendum modification for external spur and helical gears with parallel axes usedin speed increasing and speed reducing gear pairs and of which the spur and helical gears are defined by thestandard basic rack tooth profile according to IS 2535 : 1978 ‘Basic rack and modules of cylindrical gears forgeneral engineering and heavy engineering (second revision)’.

In preparing this standard, considerable assistance has been derived tlom the following:

DIN 3992:1964 Addendum modification of external spur and helical gears.

Technical Report, lSO/TR 4467:1982 ‘Addendum modification of the teeth of cylindrical gears for speedreducing and speed increasing gear pairs’.

Maag Gear Book, Calculation and practice of gears, gear drives, toothed couplings and synchronousclutch couplings, 1990 edition.

For the purpose of deciding whether a particular requirement of this standard is complied with, the final value,observed or calculated, expressing the result of a test or analysis, shall be rounded off in accordance withIS 2:1960 ‘Rules for rounding off numerical values (revisec$’. The number of significant places retained in therounded off value should be the same as that of the specified value in this standard.

1S 3756:2002

Indian Standard

METHOD FOR GEAR CORRECTION — ADDENDUMMODIFICATION FOR EXTERNAL CYLINDRICAL

GEARS WITH PARALLEL AXES

(First Revision)1 SCOPE

This standard provides guidelines regarding the limitsof addendum modifications of teeth, distribution ofaddendum modification between the gears of externalcylindrical gear pairs with parallel axes, used for speedreducing and speed increasing applications.

2 SYMBOLS, NOMENCLATURE AND UNITS

Symbol Description Unit

acd

d,d.

haP

hfp

kmmn

San

u

x-7

zvaa

a:

;“

P,AXX

.2,

inv

Centre distance mmBottom clearance mmReference circle diameter mmTip diameter mmMean diameter mmAddendum of the basic rack profile mmDedendum of the basic rack profile mmAddendum shortening coefficient –Module mmNormal module mmConstant tip thickness mmGear ratio (ZJZ,) —

Addendum modification coefficient –Number of teeth —

Virtual number of teeth —

Pressure angle degNormal pressure angle degTransverse pressure angle degWorking transverse pressure angle degHelix angle degBase helix angle degFactor —

Sum of addendum modification —

coefficientsSum of virtual number teeth, –

pinion and gearInvolute function rad

NOTE— Suftix 1forpinionand Suffix2 forgear.

3 ADDENDUM MODIFICATION

When gears are produced by a generating process, thedatum line of the basic rack profile need not necessarilyfonm a tangent to the reference circle of the generatedgear. The tooth form may be altered by shifting the

1

datum line from the tangential position. The involuteshape of the tooth profile is retained and the effect ismerely to use parts farther from or nearer to the originof the involute.

The radial displacement from the tangential positionis termed as addendum modification or profile shift.The addendum modification is considered positivewhen the displacement is away from the centre of thegear and it is considered as negative when in thedirection towards the centre of the gear.

The effect of addendum modification on the tooth formis shown in Fig. 1. The load carrying capacity of theteeth without addendum modification as shown inFig. 1a may be improved by the positive addendummodification as shown in Fig. 1b. An extremely largeaddendum modification results in an undesirable toothform with pointed teeth as shown in Fig. 1c.

The teeth with different addendum modificationsfor 20° pressure angle are shown in Fig. 2.

The addendum modification coefficient x is theaddendum modification divided by the module, Thus,the amount of addendum modification equals to x.m.

4 IMPORTANCE OF ADDENDUM MODI-FICATION OF THE TEETH

4.1 The addendum modification gear teeth is carriedout in order to avoid undercut, improve strength andrunning properties or to adjust the centre distance.The addendum modification is generally recom-mended in the following cases:

a) of gears with critical number of teeth;

b) of non-standard centre distance;

c) to obtain balanced strength; and

d) to obtain reduction in sizes.

However, load capacity and running equalities do notattain optimum values, but the gear pairs of this systemhave essentially better equalities than X-2000 gearpairs.

4.2 Cost of Manufacture of Gear Pair .

The value of addendum modification of teeth dependssolely, during manufacture, on the relative position of

i?

.,. . w. ... ...

..

..

.<.

,, ,.

.;. .

1’-:

IS 3756:2002

DATUM LINEr

NO ADDENDUM MODIFICATION

REFERENCE CIRC~

FIG la

DATUM LINE~ FAVORABLE ADDENWM MOOFICATION~. . . . .. . . .. .. .. ..,.,O., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..”... . . .. .. .. ... ... ... .%,. . ., . . ,e..,.

. . . . . . . .. . . . . . . . ..-. .. . . . . . . . :9,*.:.:+ .*. :.; X.rn. . . . .. ... .. ...... . . . . . . . .. .. ..

V’f+.....,,+y,.-.+..+...4c .,...,. :... .,

. .. “w:::? :?.;+:.... :. . . . /.; . ...+ ●, .:..: .. . . .. .. . ........................... . . .), . . . . . . . . . . . . . +../ . . . . . . ,., . .

. . . J :.. ::.yf.:. . . .A. . . . . ..:.. ..,., . . .:.>y,fl,... .:. ..

.:.> . . . . . .. .%..-. ;*...,..:.../.:

. .. . . ...%.... - .%. .,&.. / . -

.:.. ,.:.. $ ~,o..:.,— . ..””-..+ .

..$ ;:..;. .%”.,. -..<:,,.,

REFERENCE CIRCL~

FIG.lb

DATUM LINE

EXCESSIVE ADDENDIJM MODIFICATION

—.

REFERENCE CIRCLE

FIG. lC

Fl~. 1 GEARS (MESHING WITH THE GENERATING RACK PROFILE) OF IDENTICAL MODULE, IDENTICAL REFERENCE

DIAMETER AND IDENTICAL NUMBER OF TEETH, BUT WITH DIFFERENTADDENDUM MODIFICATION x. m

the gear to be cut and the cutter, Hence, the influenceof addendum modification on the cost of toothed gearsis nil in the majority of cases.

4.3 Influence on the Normal Wear of a Gear

The addendum modification of teeth results in adecrease in specific slipping of tooth flanks andconsequent] y in a decrease in the normal wear of thetooth flanks.

4.4 Influence on the Load Capacity of the Gear

An increase in the sum of addendum modifications ofgear pair results in increase in the load capacity ofgear tooth under contact pressure (pitting) and alsothe bending strength at the root of the teeth.

4.5 Influence on the Shape of Teeth (see Fig. 1)

An increase in the addendum modification of the teethof a gear causes an increase in root thickness and adecrease in tip thickness. The decrease in theaddendum modification of the teeth has the reverseeffect on tip and root thickness and below a given valuewhich depends on the number of teeth in the gear inquestion, the addendum modification causes cutterinterference which grooves the tooth root. Theinterference cause weakening of the geir tooth andpoor functioning resulting in noise, rapid wear, etc.

Hence, for each gear, there is a maximum value forthe addendum modification which results in a pointedtooth and a minimum value causing cutter inter-ference.

2

I

IS 3756:2002

ADDENDUM MODIFICATION COEFFICIENT

2=12

Z=14

2=17

Z=20

2=25

2=35

2=50

2=100

-0.6 -0.3

Q

Q

A n

n n

n L

o

nnnnnnL

+0.3

n

nnn

+0.6

n

FtG. 2 EFFECT OF THE NUMBER OF TEETH AND THE ADDENDUM MODIFICATION COEFFICIENTx

ON THE TOOTH FORM FOR (x = 20°, h,P= 1.0 m, h~P= 1.25 m

4.6 Influence on Contact

An increase in the addendum modification of the teethof the mating gears causes a slight decrease in thecontact ratio of the gear pair. Hence, it is necessary totake into account while selecting the addendummodifications for high speed gear pairs to avoid speedirregularity and increase in the level of vibrations.

4.7 Influence on the Clearance at the Root of Teeth

Increase in the sum of the addendum modification inconjunction with small number of teeth in the gearpair may cause excessive increase in the bottomclearance resulting in detrimental phenomena, suchas interference, lubricant pressure, etc.

4.8 Speed Reducing and Speed Increasing GearPairs

By considering the kinematics of a gear pair, it isascertained that the slipping of the loading tooth

during approach time, is in the opposite direction tothe movement of the point of contact on the tooth flank.This results in a jamming effect which interferes withcorrect operation of the gear. A favorable solution isto reduce the approach time by giving the leading toothas large an addendum modification as possible. For agiven sum of addendum modifications, as small anaddendum modification as possible shall be chosenfor the driven gear.

For a speed reducing gear pair, the pinion is drivingand it is preferable to increase the addendum modi-fication of the pinion when the accompanyingreduction is the addendum modification of the gearhas no detrimental effect.

For a speed increasing gear pair, the gear is drivingand in this case, a reduction in the addendummodification of the driven pinion is detrimental to thegear pair, if it becomes too great. To obtain a suitablespeed increasing gear pair, an addendum modification

3

IS 3756:2002

smaller than in the case of speed reducing gear pairshall be chosen without however going to anunacceptable value.

5 SUM OF ADDENDUM MODIFICATIONCOEFFICIENTS

5.1 Virtual Number of Teeth (z,)

To include straight teeth and helical teeth in theidentical formulae, the virtual number of teeth definedby the following equation is used:

[

z~=COS2fib Cos p1

sinpA= sin~. cosa

5.2 General

The choice of sum of addendum modificationcoefficients, Z2 is arbitrary and depends on the centredistance variation of operating conditions desired. Toohigh or too low value of ,Zkmay be harmful to thesatisfactory functioning of the gear pair. Therefore,in this standard, conventional and recommended upperand lower limits are specified for Lk.

5.3 Conventional Limits

The following equations define the conventional limitsfor .ZXwhich shall not be exceeded under anycircumstances. Figure 3 is the graphical representation

FIG.

1.6

1.4

1.2

1.(J

0.8

0,6

0..4

042

0

-0.2

–0.4

-0.6

of these limits. The shaded parts of Fig. 3 indicate thezones for special cases and the verification of theoperating conditions is essential if Zk is chosen fromthese shaded areas.

5.3.1 Upper Conventional Limit for .?3

For 205 Z2V<80, a= (loo+ .2,)/120

For 80< .ZzV, h= 1.5

5.3.2 Lower Conventional Limit for .Xx

For 20<2, S 40, x = 0.0375 (40-2,)

For 40< .XzVS 160, a = 0.005 (40-Xzv)

For 160 <22,. ,Z!t= – 0.60

5.4 Recommended Limits

The following equations define the recommendedlimits for the sum of addendum modificationcoefficients, within which there is no risk of any faultyoperation and consequently no need for any type ofverification. Figure 3 also gives the graphical represen-tation of recommended limits for .Zx.

5.4.1 Upper Recommended Limit for .23

For 20s Zzv, a= 1.0

5.4.2 Lower Recommended Limit for .23

For 20< .22, s 60, ,2X= 0.025 (60 - .ZzV)

For 60<22,, a = 0.0

The sum of the number of teeth (normal or virtual) of

? L

7

1~~

II I I

L —-

20 40 60 80 100 120 140 160

Zy

3 COFIVENTIONALAND RECOMMENDED LIMITS FOR THE SUM OF THE ADDENDUM MODIFICATION COEFFICIENTS

AND ZONES FOR SPECIAL CASES

4

IS 3756:2002

the gear pair sha]] in no case be less than 20 for

addendum modification. Recommended sum ofnumber of teeth is 24,

5.5 Selection of the Sum of Addendum ModificationCoefficients

The choice of the sum of addendum modificationcoefficients shall be made taking into account thefollowing:

a) For any increase in the sum of addendummodification coefficients, there is a corres-ponding increase in the breaking load capa-city.

b) For any reduction in the sdm of addendummodification coefficients, there is a corres-ponding increase in the contact ratio.

5.5.1 Rekuion Be[ween Centre Dis(ance, Sum of theAddendum A40d(fication Coefficients and the

Operuling Pressure Angle .

These relations are expressed as follows:

--In

= (z, + z2)/2.0

d,” = (d, + cQ/2.O

The following values are recommended for k:

0.5 < k 50.75, for speed reducing gearso <A SO.5, for speed increasing gears

For the gears with gear ratio exceeding 5, thedistribution of sum of the addey~p+2Xndum modificationcoefficients is calculated with u = 5.

However, the final choice of addendum modificationcoefficients, xl and X2shall be done within the limitsspecified at 7.

7 LIMITING VALUES OF THE ADDENDUMMODIFICATION COEFFICIENT

Too small an addendum modification coefficient givesrise to cutter interference and too large an addendummodification coefficient produces a pointed tooth. Theexact values producing either cutter interference orpointed tooth for given virtual number of teeth are thelower and upper geometric limits respectively. Theconventional and recommended limits are givenbelow:

7.1 Conventional Limits

7.1,1 Upper Conventional Limil

tan cf = tan a Ices ~ For6 <z, < 10, X = 0.60

a cos a; = dl~. cos at ForlO<zv <50, x = ‘0.50+ 0.01 zv

xx == Z,n (inv a:– inv a,)/tan a For 50< z,, x= 1.0

inv at = tan a, – a,. 7r/180 7.1.2 Lower Conventional Limit

inv a’, = tan a;– a;. rd180 For6<zv <12, X = 0.05 (18.0 –Zv)

6 DISTRIBUTION OF SUM OF ADDENDUM For 12 <z, <20, x = 0.0375 (20.0 – z,)

MODIFICATION COEFFICIENTS ON THETWO MATING GEARS

For the distribution of the sum of addendummodification coefficients, Xxon the two mating gears,it is recommended to use the following formulae:

Addendum modification coefficient of the pinion:

For the straight teeth, P= Oand z, = z and where thenumber of teeth of the two mating gears appear bytheir ratio.

+=4-1+x{*I

For 20 <z, < 50, X = (20.0 – 2,)/60.0

For 50< Zv, x = – 0.50

The graphical representation of conventional limitsare given in Fig. 4.

7.2 Recommended Limits

7.2.1 Upper Recommended Limit

For 6 s Zv, X = 0.60

7.2.2 Lower Recommended Limit

For 6< z,s 50, X = 0.025 (30.0 – Z,)

For 50< z,, X=– O.50 -

The graphical representation of recommended limitsare given in Fig. 4. The virtual number of teeth of agear-shall alwa~s have 6 as its lower limit. The shaded

‘=’[s;+ ‘[+portions of Fig. 4 represent the zones in which thechoice of addendum modification coefficientnecessitates verification of the characteristics of the

X2=.X-X1 gear pair.

5

IS 3756:2002

1.0

0.8

0.6

O-L

0.2

0

– 0.2

–0.4

– 0.6

x

I.. . LIMIT

I I

If the selected addendum modification coefficient iswithin the recommended limits as given in Fig. 4, h

is not necessary to verify the operating characteristics

of the gear pair.

7.3 Tip Thickness

The Fig,’5 gives the curves for constant tip thicknessequal to O, 0.1 m,, 0.2 m., 0.3 m., and 0.4 m. for atooth depth in conformity with basic rack tooth profilewithout any reduction in the addendum.

Table 1 gives the values of addendum modificationcoefficient as a function of virtual number of teethrelating to these curves.

7.4 Reduction of the Addendum of Teeth

If it is desired to retain a tip thickness greater than0.2 m,,, in some cases, it is useful to reduce the

6

addendum of the teeth. Reduction in addendum, ‘k

can be calculated using the following formulae:

For x <0.6, k = 0.01 (50.0x – 3.0 Zv + 6.0)

For x >0.6, k = 0.01 (70.0X -3.0 Zv - 6.0)

[~+2.o(l.o+x–kwhere da = m. ~os~ 1

If k is calculated as negative, k = 0,

7.5 Values of Bottom Clearance

The sum of addendum modification coefficients of agear pair has an effect on the value of bottom clearance.Figure 6 gives the curves representing .22xas a functionof ZzV,the constant clearance for a given curve andtaking respectively the five values :0.05 mn, 0.1 mn,

0.15 m., 0.2 mn and 0.25 mn. Table 2 gives some valuesrelating to these curves.

—Zy

I I I 1 II

I, 1 i 1 1 1

I w I 1 I

I i I I— I I I

10 20 30 40 50 60 70

FIG. 4 CONVENTIONAL Afi~ RECOMMENDED LIMITS FOR THE ADDENDUM

MODIFICATION AND ZONES FOR SPECIAL CASES

I

IS 3756:2002

1.2

1.0

0.8

0.6

0.4

0.2

0

-0.22&6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

-o-2

-o.&

-0.6

(NOTE — Line k = Ois merged with S8n= 0.2 mn)

FIG. 5 CONSTANT TIP THICKNESSES

20 40 60 80 100 120 140 160

FIG. 6 CONSTANT BOTTOM CLEARANCES

7

\

IS 3756:2002

Tablel Values ofxasa Function ofz, Giving the Table 2 Values of Zx for Various Values of Bottomi

Tip Thicknesses, S,n Clearance Without Any Reduction in the Addendum f

(Cfuuse 7.3) (Clause 7.5)p

s“n

~. ().2 m. 0.3 m. 0.4 mn

x

8 0.385

9 0.443

10 0.499 0.388

II 0.552 0.436 0.309

12 ().602 0.481 0,350

13 0650 0.525 0.389

14 0,568 0.427

Is 0.609 0.464

16 0.648 0.499

[7 0.687 0.533

18 0.567

19 0.599

20 0.631

21 0.662

22 0.692

23 0.722

24 0.751

NO’l”E— [n the table, the intermediate values can be obtainedby linear interpolation.

c

12, 0.05 mn 0.1 mn 0.15 mn 0.2 mn

23

20 1.016 0.849 0.658 0.435

40 1.318 1.108 0.873 0.588

60 1,552 1.311 1.038 0.703

80 — 1.479 1.175 0.800

100 — 1.628 1.297 0.886

120 — 1.392 0.958

140 — — 1.508 1.033

160 — 1.600 1.094

NOTE — In thetable,the intermediatevaluescanbeobtainedbylinear interpolation.

I

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ThisIndian Standard has been developed from DOC : No. BP 13 (0036).

Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

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I