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है”ह”ह

IS 7443 (2002): Methods for Load Rating of Worm Gears [PGD31: Bolts, Nuts and Fasteners Accessories]

Jij?_!l.

April 2002

I

Is 7443:2002

WRdm71m

WmwlhT?f?qh-qm(ml y@%wT)

Indian Standard

METHOD FOR LOAD RATING OF WORM GEARS

(First Revision )

ICS 21.200

..,

8+*

.

@ BIS 2002

BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

Price Group 6

‘7

Gears Sectional Committee, BP 13

FOREWORD

This Indian Standard (First Revision) was adopted by the Bureau of Indian Standards, on the recommendation

of the Gears Sectional Committee and approval of the Basic and Production Engineering Division Council,

This standard was originally published in 1974. This revision has been undertaken to align the standard withBS 721: Part 2:1983 ‘Specification for worm gearing : Part 2 Metric units’ issued by the British StandardsInstitution.

This standard has been prepared to rationalize the power rating of machine cut worm gears. The allowableloads on a pair of gears are calculated on the assumption that deflection of worm shaft does not exceed 0.3 percent

of worm diameter. It also assumed that gear housing has adequate housing and lubricating facility.

In this revision formulae of power, units of torque and Table 1 stress factors for worm gears S~ and SChave been

changed. The stress factors namely, bending stress factor and surface stress factor have also been reviewed andthe values which are more applicable to the types of materials in use have been included in the revision.

In the preparation of this revision, assistance has been derived from BS 721 : Part 2:1983 issued by British

Standards Institution (BSI), U.K.

For the purpose of dimensions for worm gearing, and the applicable tolerances reference may be made toIS 3734: 1983 ‘Dimensions for worm gearing (first revision) and IS 11863:1986’ Tolerances for worm gears’respectively.

In reporting the results of a test or analysis made in accordance with this standard, if the final value, observed

or calculated, is to be rounded off, it shall be done in accordance with IS 2:1960 ‘Rules for rounding offnumerical values (revised)’.

x

IS 7443:2002

Indian Standard

METHOD FOR LOAD RATING OF(First Revision )

1 SCOPE

This standard covers the method for load rating ofworm gears of involute helicoidal tooth form.

2 REFERENCES

The following standards contain provisions whichthrough reference in this text, constitute provision ofthis standard. At the time of publication, the editionsindicated were valid. All standards are subject torevision, and parties to agreements based on thisstandard are encouraged to investigate the possibilityof applying the most recent editions of the standardsindicat;d below:

1S No.2458:2001

2467: 19633734:1983

5267:19697403:1974

TitleVocabulary of gear terms —Defini-tions related to geometry (@t revi-sion)Notation for toothed gearingDimensions for worm gearing @strevision)Glossary of terms for worm gearsCode of practice for selection ofstandard worm and helical gearboxes

3 TERMINOLOGY

The definitions and notations used in this standardare the same as given in IS 2458, IS 2467 and IS 5267.

4 SYMBOLS, NOMENCLATURE AND UNITS

symbols Description Units

bcdda1,

mnn

9“’tthm

1cb

tec

1elm

Worm wheel effective face width mmClearance mmReference diameter mmTip diameter mmLength of root of the worm wheel teeth mm

Axial module mm

Speed of rotation rein-l

Mean speed rein-l

Diameter factor —

Running time hAverage running time for strength h

Total equivalent running time

for strength hTotal equivalent running time for wear h

Average running time for wear h

Symbols

v~

z

E

P

Sb

Sc

TT~

Tbm

q

TmXb

XeY,

T

4

WORM GEARS

Description Units

Rubbing speed mls

Number of starts or teeth —

Percentage efficiency —

Load N

Bending stress factor —

Surface stress factor —

Torque Nm

Permissible torque for strength Nm

Occasional momentary load for strength Nm

Permissible torque for wear Nm

Occasional momentary load for wear Nm

Speed factor for strength —

Speed factor for wear —

Zone factor —

Lead angle for the worm threads deg

Friction angle deg

NOTE — Suffix 1 for worm and suffix 2 for worm wheel are

used with the above notions wherever applicable.

5 REQUIREMENTS

5.1 Rubbing Speed

The rubbing speed V, (in m/s) is given by :

F( = 0.0000524 d, n, Sec ~and

~ = 0.0005204 m n, ~(zf + q’)

The rubbing speed shall be limited to 12.5 m/s (forsplash lubrication).

5.2 Speed Factor

The speed factor XC for wear corresponding tocombination of rotational speed and rubbing speedshall be in accordance with Fig. 1. The speed factorXb for strength corresponding to the rotational speed

only shall be in accordance with Fig. 2.

5.3 Surface Stress Factor SC

The surface stress factor SC corresponding to thecombination of materials used shall be in accordancewith Table 1.

5.4 Bending Stress Factor Sb

The bending stress factor Sb corresponding to thematerial used shall be in accordance with Table 1.

1

IS7443:2002

0l-lu-l

.2m

u-l

—z.

00

..’

.L

---

w

u 1 10 20 60

[ I 1 I I I I I I I 1 1 I I I 1

I I I I i I II

I I I I I I I I I100 200 400 600 8001000 2000 Ii 000 6000 8000 1000(

Jill I I I 1

REVOLUTIONS PER MINUTE

FIG. 2 SPEED FACTORS FOR WORM GEARS FOR STRENGTHX~

I.?

IS 7443:2002

Table 1 Stress Factors for Work Gears Sb and SC

(Clauses 5.3 and 5.4)

Material

—

Phosphor bronzecentrifugally cast

Phosphor bronze sand

A cast chilled

Phosphor bronze sandcast

B Grey cast iron

c 0.4 % carbon steelnormalised

D ().ss~. carbon steelnormalised

Carbon case hardeningsteel

Nickel molybdenumcase hardening steel

E

Nickel chromium casehardening steel

I) Maximum permissible speed= 2.54~S.2) permissible for hand motion only.

IS Reference

IS 28

BendingStressFactor,

Sb

69

Grade FG 200 I 40

+

=-b-1S5517 I

15C8 I 276

=--l-=-1S4432 I

Surface Stress Factor, S. When Running with

A B c D E

— 8.31’) 8.3 9 15.2

— 6.2’) 6.2 6.9 12.4

— 4.6!) 4.6 5.3 10.4

6.21) 4.1” 4.1” 4,,1) 5.2’)

10.8 6.9 — — —

15.2 8.32) _ _ _

48.3 30.42) — — 15.22)

53.1 30.42’ 15.22)

60.7 30.42’ — 15.22)

5.5 Normal Rating The values of these factors shall be obtained from

The normal rating is the loading to which the gearsFig. 3. In case of operation with shock loads, service

factors as indicated in IS 7403 are to be made use of.may safely be subjected for a period of 12 h per day,

for a total running time of 26000 h. If it is necessary 5.6 Permissible Torque for Wearto design worm gears on the basis on any other life,

the permissible power or worm wheel torque shall be For the normal rating the permissible torque on the

multiplied by the following expressions: worm wheel is limited by wear to the lower of thefollowing two values:

a) TCI= 0.00191 XC,SC1Y, d2’s m

a) ‘“rwear[(l::::cc)r

b) TC2= 0.00191 XC2SC2Y, d2ts m

5.6.1 The values of worm gear zone factor YZare givenin Table 2.

b) For strength5.7 Permissible Torque for Strength

[11/7

26200 For the normal rating the permissible torque on the

(200 + teb) worm wheel is limited by strength to the lower of thefollowing two values:

4

IS 7443:2002

100000\ I I I

I

70000 _ STRENGTH I

50000

30000

20000

10000

7000

5000

3000

2000

1000

700

5001 , , 1 t [ 1 I 1 1 1 \ 1 1 1

I i

-1 – . . . _ _ _ _300 1 1 I I I I I 1 I l\l I

\l i

t 1 I 1 I ! I I I N I I

I I I I I I I I I l\ I I I200

1000 0.5 1.0 1.5 2.0 2.5 3.0

LIFE FACTOR FOR WEAR ANO STRENGTH

,.

FIG. 3 LIFE FACTORS FOR WEAR AND STRENGTH

5

/

IS 7443:2002

Table 2 Worm Gear Zone Factor, Y,

(Clause 5.6.1)

<I ~ 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 16 17 18 20

z\ Yz

1 1.045 1,048 1,052 1.065 1,084 1.107 1.128 1.137 1.143 1.160 1.202 1.260 1.318 1.374 1.402 1.437 1.508

2 0.991 1.028 1.055 1.099 1.144 1.183 1.214 1.223 1.231 1.250 1.280 1.320 1.360 1.418 1.447 1.490 1.575

3 0.822 0.890 0.969 1.109 1.209 1.260 1.305 1.333 1.350 1.365 1.393 1.422 1.442 1.502 1.532 1.580 1.674

4 0.826 0.883 0.981 1.098 1.204 1.301 1.380 1.428 1.460 1.490 1.515 1.545 1.57(3 1.634 1.666 1.71t) 1.798

5 0.947 0.991 1.050 1.122 1.216 1.315 1.417 1.490 1.550 I.61O 1.632 1.652 1.675 1.735 1.765 1.805 1.886

6 1,132 1.145 1.172 1.220 1.287 1.350 1.438 1.521 1.588 1.675 1.694 1.714 1,733 1.789 1.8]8 1.854 1.928

7 1.316 1.340 ).370 1.405 1.452 1.540 1.614 1.704 1.725 1.740 1.760 1.817 1.846 1.880 1.950

8 1.437 1.462 1.500 1.557 1.623 1.715 1.738 1.753 1.778 1.838 1.868 1.898 1.960

9 1.573 1.604 1.648 1.720 1.743 1.767 1.790 1.850 1.880 1.910 1.970

10 1.680 1.728 1.748 1.773 1.798 1.858 1.888 1.920 1.980

11 1.732 1.753 1.777 1.802 1.862 1.892 1.924 1.987

1? 1.760 1.780 1.806 1.866 1.895 1.927 1.992

13 1.784 1.808 1.867 1.898 1.931 1.998

14 1.811 1.871 1.900 1.933 2.000

NOTES

1 The values are based on b = 2rrr~(g + 1), symmetrical about the centre plane of the wheel.

2 FOI-smaller face widths the value of Y,must be reduced proportionately.

3 When it is necessary to obtain greater load capacity the worm wheel face width may be increased up to a maximum of 2.3 m= andthe zone factor increased proportionately.

4 The table applied to worm wheels having 30 teeth; variation in the number of teeth produce negligible changes in the value of Y,.

a) T~,= 0.001 8 X~i S~, m 1,d2 Cos ~

b) Th2= 0.0018 X~zS~2m /, d2 Cos ~

where

/, = (d., + 2c) sin-’b

(da, + 2C)

the angle is in rdians

da, = m (q+ 2)c = 0.2 m Cos ~

b = 2m~(q+l)

6 RATING OF WORM WHEEL

6.1 Power

Subject to the provisions of working temperature(see 6.2), the normal power rating (in kW) of the wormwheel is given by:

Tnz

9550

\vllere T is thesmallestof the four Va]ues obtained in

accordance with 5.6 and 5.7 and n2 is the number ofrevolutions per minute of worm wheel.

6.2 Working Temperature

The continuous rating of worm gear operating in stillair may be limited by consideration of temperaturerise rather than by resistance to bending or surface

stresses.

6.2.1 Where the working oil temperature of 95°C isexceeded the maximum permissible torque on theworm wheel may be less than that indicated in 5.6and 5.7.

6.3 Efficiency and Lubrication

The efficiency (excluding bearing and oil-churninglosses) of gears is given by :

E (Worm driving)=tan T

Xlootart (T+ $)

E (Worm wheel driving)=tOIl(T-Lj)xloo

where

tan $

“,

tanT

is the co-efficient of friction between wormand worm wheel corresponding to therubbing speed which can be obtained fromFig. 4.

6

IS 7443:2002

0.150

0.120

0.100

0.090

0.080

0.070

0.060~G: 0.050u

8> 0.040yJgu.uIll: 0.030

0.020

0.015

0.012

1—.I

—..

-4--L-----

1+I I

0.005 0.05

—. ——.

=.25 0.5 1.0 2.5 5 10 15RUBBING SPEECI VS (m/s)

FIG. 4 COEFFICIENTOF FRICTION FOR WORM GEARS

The values of the co-efficient of friction given in Fig. 4

are based on the use of phosphor bronze wheels and

case hardened, ground and polished steel worms,lubricated by a mineral oil having a viscosity between60 mm2/s and 130 mm2/s (60 cSt and 130 cSt) at 60”C

(250 s and 500 s Redwood at 140°F).

6.4 Momentary Overload Capacity

The load whose duration is too short to be definedwith certainty shall be considered to act for a period

of not more than 15 s.

6.4.1 Worm gears designed in accordance with thisstandard shall be capable of transmitting occasionalmomentary loads not exceeding the values calculatedfrom either of the following:

a) T,n,= 0.00382 SCZYZd2’8m

b) ~~, = 0.004 S~z1,dz m Cos ~

7 DETERMINATION OF EQUIVALENT RUNNINGTIME FOR LOADING CONDITION OTHERTHAN A STEADY LOAD

7.1 The cycles of different uniform loads at differentspeeds are given in Fig. 5.

7.1.1 If the load cycle on the worm wheel comprises amaximum torque T1acting fort, hour at a mean speedof n, and smaller torques T2, T3 ..etc., acting for [2, t3,

..etc, hours at mean speeds n2,n3, ...etc.. the equivalentrunning time per cycle for wear at torque T, and speed

n, is given by:

tcm= t,+ t2[:1[:1+’3[:l[il+etc

in which each term represents the equivalent runningtime for the corresponding part of the cycle.

,

4

,.

7

IS 7443:2002

7.1.2 The total equivalent running time for wear attorque T] and worm wheel speed n, is then given by :

t = tC~x Number of complete cycles ex-e,petted during the life of the gears

7.1.3 The equivalent running time per cycle forstrength at torque 2“1and worm wheel speed n, is thengiven by:

in which each term represents the equivalent runningtime for the corresponding part of the cycle.

7.1.4 The total equivalent running time for strengthat torque T, and worm wheel speed n, is then given

by:

t = t~,nx Number of complete cycles ex-cb

petted during the life of the gears.

7.2 Irregular Variation of Load and Variable Speeds

The equivalent running time for a period of the load

cycle under 7.1 during which load and speed vary otherthan uniformly shall be determined by subdividing itinto periods during none of which the torque changesby more than T1/4. The equivalent running time forwear and strength corresponding to each such period

on the basis of the mean load and the mean speedduring the period shall be calculated in accordancewith 7.1.

7.3 Uniform Variation of Load and Variable Speeds

If during any period tof the load cycle under 7.1 thetorque changes uniformly from Ttl to Tt2at mean speedn~, the expression of the equivalent running time inhour per cycle for wear at torque T, and speed n, isgiven by:

The equivalent running time for strength at torque T,and speed n, is given by:

7.4 Load Varying in a Cycle Which is Repeated aWhole Number of Times in One Revolution of theWorm Wheel

If a whole number of load cycles are completed inexactly one revolution of the worm wheel, then thegear shall be designed to transmit the maximum torquecontinuously for an equivalent time equal to theexpected running life of the gears.

8 PARAMETERS OF WORM GEARS

These shall be based on IS 3734.

9 EXAMPLES OF CALCULATION

These are given in Annex A.

8

IS 7443:2002

ANNEX A

(Clause 9)

EXAMPLES OF CALCULATION

A-1 POWER CALCULATION

A-1.l To find the power ratings for wear and strength

of the gears having designation R2130110/1 0/200 andinput speed 1 000 rev/rein.

The permissible torque is limited by the lower of thefollowing two values for wear:

a) T,l = 0.00191 ~Cl SC1Y, dz’* m

b) TC2= 0.00191 ~CzS,2 YZd2’8 m

For centrifugally cast phosphor bronze worm wheeland a nickel-molybdenum case hardening steel worm

s,, = 53.1

SC, = 15.2S,, = 325S,, = 69

Y, = 1.231

~ “ 2(200-9=300mmRubbing speed

P’, = 0.0000524 xdxnx Sec~mls

V, = 0.0000524 x 100 x 1 000x Secmts

= 5.34 mls.

11.3166

From Fig. 1 ,YCl= 0.125, XC2= 0.24

T,l = 0.00191 x0.125 X53.1 X 1.231 X30018X10 Nnl=4489Nm

T,l = 0.00191 X 0.24 X 15.2 X 1.231 X 30018 X10 Nm=2467Nm

The permissible torque values for strength are givenby:

a) Th,0.001 8. X~, S~i m h dz Cos z

b) Thz0.0018. X~z S~zm k d2 Cos T

From Fig. 2

,Y~l= 0.27 xb2=0.45

I, =

and

d,, =f=

—.

b=

1, =

[1(da,+2c) sin-’ &al

m(q+2)= lo(lo+ 2)=1200.2m Cos7=0.2X 10 XCOS 11.31661.96

2m@y = 2 x 10 ~ = 66.33

[166.33123.92 sin-’ —

123.92

.

therefore

T~, =

.

T,, =

——

123.92 X 0.5648= 69.993

0.0018 X 0.27X 325X 10X 69.993X300x COS 11.3166Nm32521 Nm0.0018 X 0.45 X69X 10X 69.993 X300x COS 11.3166Nm11508 Nm.

The permissible torque is limited by the minimum ofTC,, TC2,T~l and T~2viz, 2467 Nm on worm wheel

therefore,

Normal power rating =2467x 1OOO =1722kW

15X9550 “

A-2 Determination of uniform loading equivalent tospecified varying loading duty comprising of 700cycles per day. Each cycle being made up of followingperiods:

Period 1

Torque falls uniformly from :2150 Nm to 1275 Nm

Time occupied :3s

Mean speed : 16 rpm

Period 2

Torque (constant) :880 Nm

Time occupied :10s

Mean speed :32 rpm

Period 3

Torque fall uniformly from :3330 Nm to 2150 Nm

Time occupied :2s

Mean speed : 16 rpm

Normal torque rating :3300 Nm

Speed : 16 rpm

A-2.1 Calculation of Equivalent TimesFactor for Wear

Period 1

and Life

3

[ 1[

16 2150 + 1275t ——emI = 3600x4 = 3330 3330 1

– 1.208 X 10q h—

.- --

.

9

Is 74/$3 :2f)02

Period 2

[ 1[–110 32 880 3X41=e,,}? 3600x4 ~ 3330

= 1.025 X 10qh

Period 3

2

[ 1[

16 3330+21501= ——

C1113 3600x4 ~- 3330 3330 1

= 3.23 X 10qh

Total equivalent running time per day

= 700X 5.463 X 10q = 0.383

Life = ?X 0.383 = 830 h

Life factor for wear = 2.45 (see Fig. 3)

h

Hence, the gear must be designed for a normal

3330Torque rating for wear = ~ = 1359 Nm of wheel

Shaft torque at 16 rpm = 2.28 kW

tl t3h

When the load variation is of the form shown in Fig. 5A with loads (Pl. rrl.fl: P2 . n2 .$: P3 . n3 .t3) and with the time of the working cyclet, = [1+ ~zL Ij, the equivalent time will be:

‘e=’+4w?3+’w?3wcyc’e

.d. . . .!

.!

{

where

P = load in N,

)1 = speed in rpm, and

/ = time in hours.

5A

10

IS 7443:2002

rrPI p/12

k==--If the load varies linearly during constant speed as shownin Fig. 5B, the equivalent time will be:

,e=,,+:[~][[~~+[;~]wcycle

whereP= load in N,n = speed inrpm, and[ = time in hours.

GPI

I P;

5B

1

‘ tc

- t-

During linear variation of load linear variation of speed as shown in Fig. SC, the equivalent mnning time will be:

where

P = loadin N,n = speed inrpm, andt = timein hours.

5C

FIG.5 CYCLES OF LOADS AT DIFFERENT SPEEDS

11

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Review of Indian Standards

Amendments are issued to standards as the need arises on the basis of comments. Standards are alsoreviewed periodically; a standard along with amendments is reaffirmed when such review indicates thatno changes are needed; if the review indicates that changes are needed, it is taken up for revision. Usersof Indian Standards should ascertain that they are in possession of the latest amendments or edition byreferring to the latest issue of ‘BIS Catalogue’ and ‘Standards: Monthly Additions’.

This Indian Standard has been developed from Doc: No. BP 13 [LM 13 (0329)].

Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

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