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IS : 9766 - 1966

I ndi an StandardMETHOD FOR GEAR CORRECTION

Fourth Reprint JUNE 1992( Incorporating Amendment No. 1 )

UDC 621.833-l : 53.088~6

63 Copyright 1975BUREAU OF INDIAN STANDARDS

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I6 t 3758 - 1966I ndian St andard

METHOD FOR GEAR CORRECTION

Gears Sectional Committee, EDC 59

ChairmanSHRI R. Yoatrzmiwnn

Members

RepresentingHindustan Machine Tools Ltd, Bangalorc

SRRI V. A. S. SETTY (Alternate toShri R. Yogeshwar )SHBI M. C. BAHETI New Allenberry Walks, CalcuttaSHRI J . Y. RA~HAVAN ( Alfcmafe )htOF B. M. BRL~AUMKAII In personal capacity ( Indian Znslitvle of Technelogl,Kharagpur )SHRI S. N. CHATTIXHJEE Directorate Cenerat, Ordnance Factories ( Ministryof Defence )Swr G. C. CHATTOPAD~YAY Jessop Rr Co Ltd, CalcuttaSEEI B. K. DAM Burn & Company Ltd, Howl-ahSHR~ P. N. GULATI The Associated Cement Companies Limited, BombaySEEI P. C. JAIN National Physical Laboratory ( CSIR ), New DelhiSH~I S. KUNDU Heavy Engineering Corporation Ltd, BurdwanSHRI D. MAS~ARI~NHAS David Brown Grravrs Ltd, PoonaSHRI M. NA~ARAJ ( Alternate )SHRIMATHEW ALAPATT Gears India, MadrasSARI P. M. NITYANANDAN ( Akmafc )SIIRI A. N. OAK Indian Diesel Engines Manufacturers Association,

SHRI R. WILBERT ( Allcrna;c )!kBI K. SURYANARlYANA RAO Ashok Levland Limitrd, MadrasSHEI V. M. RAo The R. C: P. Limited, MadrasS-1 K. SATYANA~AYANA( Al&tote )SHBI A. SARKAR Mining and Allied Machinery Corporation f,td.Burdwan

SARI S. K. KESH ( Allcrna~c)SHSI N. C. SUKHAXANwAL.4 The Mysorc Kirloskar Ltd, HariharSRRI R. K. RAMCIIANDRARaa ( Alternate )

SHBI V. VENKATA~AMAN Greaves Cotton & Co Ltd, MadrasSERI D. S. M. VISHNU Heavy Electricals ( India ) Ltd, BhopalSEBI W. WEI~XANN Kilburn and Company Limited, CalcuttaSHE1 M. V. PATANKAR, Director General, ISI ( Ex-ofiio Mcmba )Director ( Mech Engg ) ( Secrcfary )( Continued on page 2 )

RUREAU OF INDIAN STANDARDSMANAK BHAVAh, 9 BAHADUR SHAH ZAFAR MARC

NEW DELHI 110002

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lS:37!56-1966( Glatiaued~mJnpuge1 )

Panel for Corrections for Gears,.EDC 59/P-2Representing

Hindustan Machine Tools Ltd, Bangalore

S~lrrV. A.S. SISTTY (A&ma& toSbri R. Yngeshwar )3~11 MATEBW ALAPATT Gears India, MadrasSERI N. G. tk7KEURAXWALA The Myaorc Kirloskar Ltd, Harihar

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ISr3756- 196612 This standard covers the various types ofcorrections, the effect of correc-tions and the method ofdistribution ofcorrections on to the two mating gcan.2 TERMIN0LoGY20 For the purpose of this standard, the following symbols and terms shallapply in addition to IS s2458-1965* and IS : 2467-1963t.2.1 contrct Ratio ( e y) -The ratio of the length of path of contact tothe circular pitch and is &en by the relation:

e y = t fdk -dab;; zqyl iQd%2-2eas Sin a. .

whered,, =db =a=a=m=

tip circle diameter (see Note),base circle diameter (see Note),actual centre distance,pressure angle at pitch circle, andmodule.

NOTE - Suffix 1 is related to the pinion and suffix 2 to the wheel.

2.2 Equivalent Bending Stress (n) - The stress on the tooth caused bythe load, considering the tooth as a cantilever loaded at the free end andis given by the relation:uU = - .qv6.m

whereU = normal load on tooth,90 = tooth form factor,b = width of the gear, and

m = module.2.3 Noise - This is caused due to the inaccuracies of the gears, changesin tooth form, and frictional forces causing vibration. This may be reducedby increasing contact ratio.

*Glossary of terms for toothed gearing.TNotation for toothed gearing.

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IS : 3756 - 1966Specific Slidin&-- Th e ratio of the difference in tangentialmponents of velocities of the mating flanks to the tangential component

y.d : VT1 VTS =VT1

At the beginning of contactpl = a sin a - ~2, and p2 = HAP - Pbp

At the end of contactpr = 1/& - r bl , and pn = a sin a - pl

whereVT =P =i =a =r-a =lb =

tangential component of the peripheral velocity,instantaneous radius of curvature,gear ratio,pressure angle,tip circle radius, andbase circle radius.

Tooth Thickness at the Tip (s.) - The minimum thickness & shouldm. The value may be calculated using the following equation:so = da Cm(n/s+2Xtana)+fnv a_tnVaad I 1

whereCOY aa = r cos a ,

da =m =x =a =aa =d =

tip circle diameter,module,correction factor,pressure angle at pitch circle,pressure angle at the tip circle, andreference diameter.

Undercutting - The recess in the theoretical profile, resulting from

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IS t 3756 - 1966number of teethbeyond the base of the pinion is so small that the generating cutter extendscircle of the pinion and the dedendum profile does not getproperly generated.2.7 Wear Strength (PH ) - The capacity to resist wear, caused by thenormal load on the tooth and the sliding velocity.given by the relation: The wear strength is

pH -bd e-+

whereu =bd 1

4.1 =

normal load on tooth,width of the gear,pitch diameter, andwear strength factor of pinion.

3. TYPES OF CORRECTIONS3.1 ProHe Shifting - Shifting the basic rack either away or towards thereference cylinder by an amount xm is termed as profile shifting. Theformer is taken as positive and the latter as negative profile shifting.

3.1.1 &-Correction-The gears are said to be &-corrected when thesum of profile corrections on the two mating gears is equal to zero, that is,XI + XP = 0 or XI = --x2.3.1.2 S-Correction - The gears are said to be S-corrected when the sumof the profile corrections on the two mating gears is either positive ornegative.

3.2 Change of Pressure Angle - Change in the generating rack pressureangle results in the change of pressure angle of gears. The minimum numberof teeth to avoid undercutting, contact ratio and specific sliding factor maybe modified by suitably changing the pressure angle.3.3 Change of Addendum - The change in addendum when the toothheight factor qh is made either less than one or greater than one.3.4 Change of Module - This is attained by changing the pitch of thegenerating rack, that is, module of the gear, to suit to the given centredistance and number of teeth of the mating gears.4. EFFECTS OF CORRECTION4.1 Profile Shifting - Typical examples of change in the tooth form withthe positive and negative correction and tip formation are shown in Fig. 1.

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Root line of the rack cutter. 6 Pitch circle of the gear.Pitch line of the rack cutter. 7 Root circlebf the gear.Tangent to the root circle of the gear. 8 Base circle.C Pitch point.

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I8137$6- 196643.1 So-Correction Typical examples of the effect of &correction on

various factors for a particular gear pair are shown in Fig. 2.411.2 S-Correction Typical examples of the effect of S-correction onvarious factors for the above gear pair are shown in Fig. 3.

5. DISTRIBUTION OF CORRECTION5.1 Knowing the total number of teeth zi + tr, the value of total correctionfactor xl+xr should be taken to suit particular requirements of load-carryingcapacity, balanced conditions or sliding conditions ( PI, Pr, etc ) from Fig. 4.Figures 5 and 6 shall be used for distribution of total correction factor betweengear wheel and pinion, former for reduction gear drives and the latter forstep up gear drives. These are applicable for gears of teeth less than orequal to 150.

Xl+%;5.1.1 Through a point with co-ordinates 2 and a+t,- draw a line2parallel to the neighbouring line ( Fig. 5 or Fig. 6 ). Read out the valuesof xi and X* against 21 and LP respectively.5.2 For helical gears the total correction factors and the distribution ofcorrection factors may be obtained by the same method as for spur gears,after substituting the number of teeth of helical gears by the equivalentnumber of spur gear teeth obtained by the following formula:

Equivalent spur gear teeth - Number of teeth of helical geartoss g, cos gwhere

P = helix angle, and&I = base helix angle = sin-i ( sin b cos a ).

5.3 Adjustment of Correction for Centre Dintance+ - If two gearshaving number of teeth zi and ~2 and module m are operated at centredistance u then the total correction factor xt to be applied to the gears isobtained from the following formulae:For spu r gear s:

xt Inv a - Inv aI;, = tan a , &= cos ap-1cos a

*For cutter adjustment, etalsoAppendixA.8

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IS:3756-1966where

XI = Xl + XP,a - (IJJ=------- m

a=mzm,Zm = ( LI + zo )/2, and

Inv u = ( tan a - a ), a in radiansa = pressure angle at pitch circle = 20, anda = operating pressure angle at point of contact.

The first two equations can be solved with the help of Table 1.Once xt has been determined, it can be distributed between the two gtarsin the way described in 5.1.For helical gears:

Calculate -5,corresponding to & from Table 1where

.?m= ZICP + .22cs,2a - uy=-----, m

/3= helix angle, andzce = equivalent spur gear teeth according to the formulain 5.2.

Once xt has been determined it can be distributed between the twogears in the way described in 5.2.However, for accurate calculation ofxt, the following exact equationsmay be used:

xt Inv at - Inv at-=L, tan aY _ A___ -__ - 1os at-- cosp&l ( cos a( >

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IS : 3756 - 1966where

a - a m~~=a~+a~,y=-,a=-~,;co.3 (3

~ = L.T.1 + 22 ) ;: = tan-:(.s );at = transverse pressure angle; and

at = operating transverse pressure arqle.5.3.1 The tip diameters of the pinion and gear are given by:

&l=dl+Zm( I-xf+y)&=&+2m( l-xxl+y)

The root diameters are given by:dtl=dL--2m( 1 +c-xx,)&P=&--2M( 1 +CXx,)

whered = mz for spur gears and -?!% for helical gears, andcos pE = clearance coefficient in basic rack profile.

6. BASIC REQUIREMENTS6.1 The following conditions should be satisfied for any gear, &ercdrrectiofi.

6.1.1 The contact ratio should be greater than 1.1.6.1.2 The minimum addendum clearance of 0.1 m should be maintained.6.1.3 The tooth thickness at the tip should be greater than or equalto 0.4 m for hardened gears which may be reduced to 0.25 m in exceptitinalcases.6.1.4 Undercutting should be avoided.

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TABLE 1 TOTAL CORRECTION FACTOR, WORKI NG PRESMJ RE ANGLEAND CENTRE DISTANCE MODIFICATION FACTOR FORINVOLUTE GEARS ( PRESSURE ANGLE = 20 )( Clause 5.3 )

DIFF

666869::7475:;80ii85ii914,952101103105107109110113115116119121123125127130131134136:z

xtpm=E:i :-0~019 02-0.018 33--0*017 62=K% YZzcol: zi--0*013 84-z,:,t; ::zx:, :i-0tm 66-0.008 78=k%z t:-0*006 0 1--oft05 06--O+KM 08-Of)03 09--@002 08-0m105OmO 00ofJ O 07

0*002 160903 260~004 390*005 540+06 700.0 7 89B.00 100.010 330011 58MI12 850.014 15@f-l15 46O-n16 800.018 16::g it

a16 00IO

g:4017 fir10

32;:405018 0010w-v4050190 00;i:30405020 00;;:3040I

21::10g :40

22 ii:;o:2:

Y/tm-0.022 44-0.021 62-0.020 79-0*019 95-0~019 10-4l.018 24-0.017 37-0016 49-0015 60-0*014 71-0.013 80-0.012 88-0.0 195-0~01101-0~010 06-0%09 10-Oft08 13%zz fZ2.E ff-0m3 13-0.002 10-0m1050.000 000*00106

om2 14:::: ::0.005 i30906 55oflO 680.008 82om9 970.011 130.012 300.013 490.014 690~015890.017 10.018 350.019 59

DXFF

868788899:92ii9596

t:102103105105106108~~111112I!3il4115116117119120120122124124( Gmtimud )

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Sa Olst o-4

X

0 O-2 04 0.6 O-6 '------)X

Fm. 2 &CORRECTION (FOR Q = 14, zz = 60 AND a = 20 )

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,:3756-1966

-x

9~ 60

t 40

20

0 W2 04 b6 04 1.0-x

I-7 t 8 I I ICONTACT RATIO

0 04 04 06 0.6 19-x

FIG. 3 S-CORRECTION ( FOR ZI = 14, z2 = ROLAND a = 20 )14

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APPENDIX A( Clause5.3 )

A-l. UTTRR ADJ USTMENT FOR CORRECTED GEARSA-l.1 While cutting a gear of module m and having z number of teeth andcorrection factor x with a rack cutter or hob, the distance between the centreof the gear and the pitch line of the cutter is given by:m(--$-+xWhile cutting the above gear with a pinion cutter having zc number 01teeth, the centre distance of the cutter and gear is given by:

a = my +awhere

a=%(z+z.)( os ay=zm -cos a -_1 >,z,= z+a is obtained from the relation:

Inv a = y+ Invaor knowing x, z and zc, y can be found nut with the help of Table 1.

A-2. RXAMPLIRSA-2.1 Pair of speed reducing spur gears having ZI = 22, ~6 = 36, a = 20,m = 2, a = 59 mm, x1 and xs are to be found which is described below:

zqn= 22 + 362 = 29a=2 x 29=58mm

59 - 58y = =2 +0*5Y + 0.5-=-ZViI 29 = + 0.017 24

From Table 1 interpolating:%= + 0.01831 and a = 22j13xt = + 601831 x 29 = + 0.53099 e + 0.531

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IS:3736-1966From Fig. 5:

xl = + 030 and 1c= + 0.231d,l = 2 [ 22 + 2 ( 1 - @231 + 05 ) ] = 49076 mmd , = 2 [ 36 + 2 ( 1 - 0.30 + 0.5 ) ] = 76.8 mmdtl=2[22-2( 1 +0*25-030)]=40200mmd/r = 2 [ 36 - 2 ( 1 + 0.25 - O-231 ) ] = 67.924 mm

The distance of the pitch line of hob or rack type cutter from:the pinion centre line = 2 c F+ 0.30 1=2.60 mmthe gear centre line = 2 [?+0.231]=36.462mm

If these are cut by a pinion type cutter having 38 teeth, then thecentre distance betweeen pinion and cutter is fcund out as follows:22 -t 38zm= 2 = 30

for c= 0.3 = + 0010From Table 1, L =& +000966,y=+02898,a=30~2=60

So the required centre distance, a = 2 x O-289 8 + 60= 60579 6 mmSimilarly the centre distance between the gear and the cutter may beobtained.

A-2.2 Pair of speed increasing helical gears of module 4 and p = 15, zr= 2422 = 59, a - 173 mm, x1 and xs are to be found which is described below:

The equivalent spur gear teeth in gear and pinion are given by:Teq = tcos p* cos pwhere

cos &, is obtained from sin &, = sin !3 cos aHere @b = 14 4 34

24Lllq = o.908 8 = 26459

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ISr3736-1966m 4mt =- - - - - =cos p 0 965 93 - 4141

a=?(24 +59) = 171*85mm173 - 171.85 1.15Y= - -4 =4 + o-287 5

Y 0.287 5-_= --- =Zm 4565 + 0.006 30By interpolation from Table 1:

;:= + 000644xt = + 0006 44 x 4565 = + 0.294

with zm = 45.65 and?= + 0.147 from Fig. 6Corresponding to zrsr and zreRone obtains:

xl = + O-174 and 1c2= + 0120dr=4141 X 24=994mmds = 4141 x 59 = 24&5 mm

&I = 994 -I - 2 X 4 ( 1 - 0120 + 0287 5 ) = 10874 mmde = 2445 + 2 x 4 ( 1- O-174 + 0287 5 ) = 25341 mmd t l = 994-2 X 4 ( 1 + 025-00174) = 90792 mmd/s = 244.5 - 2 X 4 ( 1 + 0.25 -0 120 ) = 235460 mm

Cutter position for the pinion may be obtained in the same way asgiven in A-2.1.

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