Disclosure to Promote the Right To Information Whereas the Parliament of India has set out to provide a practical regime of right to information for citizens to secure access to information under the control of public authorities, in order to promote transparency and accountability in the working of every public authority, and whereas the attached publication of the Bureau of Indian Standards is of particular interest to the public, particularly disadvantaged communities and those engaged in the pursuit of education and knowledge, the attached public safety standard is made available to promote the timely dissemination of this information in an accurate manner to the public. इंटरनेट मानक “!ान $ एक न’ भारत का +नम-ण” Satyanarayan Gangaram Pitroda “Invent a New India Using Knowledge” “प0रा1 को छोड न’ 5 तरफ” Jawaharlal Nehru “Step Out From the Old to the New” “जान1 का अ+धकार, जी1 का अ+धकार” Mazdoor Kisan Shakti Sangathan “The Right to Information, The Right to Live” “!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता ह ै” Bhartṛhari—Nītiśatakam “Knowledge is such a treasure which cannot be stolen” IS 2458 (2001): Vocabulary of Gear Terms - Definitions Related to Geometry [PGD 30: Transmission Devices]
Transcript
Disclosure to Promote the Right To Information
Whereas the Parliament of India has set out to provide a practical regime of right to information for citizens to secure access to information under the control of public authorities, in order to promote transparency and accountability in the working of every public authority, and whereas the attached publication of the Bureau of Indian Standards is of particular interest to the public, particularly disadvantaged communities and those engaged in the pursuit of education and knowledge, the attached public safety standard is made available to promote the timely dissemination of this information in an accurate manner to the public.
इंटरनेट मानक
“!ान $ एक न' भारत का +नम-ण”Satyanarayan Gangaram Pitroda
“Invent a New India Using Knowledge”
“प0रा1 को छोड न' 5 तरफ”Jawaharlal Nehru
“Step Out From the Old to the New”
“जान1 का अ+धकार, जी1 का अ+धकार”Mazdoor Kisan Shakti Sangathan
“The Right to Information, The Right to Live”
“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता है”Bhartṛhari—Nītiśatakam
“Knowledge is such a treasure which cannot be stolen”
“Invent a New India Using Knowledge”
है”ह”ह
IS 2458 (2001): Vocabulary of Gear Terms - DefinitionsRelated to Geometry [PGD 30: Transmission Devices]
~pD
IS 2458:2001ISO 1122-1:1998
( Wa7 ~y7awT)
Indian Standard
VOCABULARY OF GEAR TERMS — DEFINITIONSRELATED TO GEOMETRY
( First Revision)
ICS 21 .200; 01.040.2
December 2001
)
@ BIS 2001
BUREAU OF INDIAN STAN DARDSOMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG
NEW DELHI 110002
Price Group 11
Gears Sectional Committee, BP 13
NATIONAL FOREWORD
This Indian Standard ( First Revision ) which is identical with ISO 1122-1 :1998 ‘Vocabulary of gearterms — Part 1: Definitions related to geometry’ issued by the International Organization for Standardization( ISO ) was adopted by the Bureau of Indian Standards on the recommendation of the Gears SectionalCommittee and approval of the Basic and Production Engineering Division Council.
This standard was originally published in 1965. This revision of the standard has been made by adoptionof ISO 1122-1 : 1998 under dual numbering system. This standard covers the Vocabulary of Gearswhich devoted solely to geometrical definitions including Bevel and Hypoid Gears, The Bevel and HypoidGears were earlier covered in IS 2458 ( Part 2 ) :1984 ‘Glossary of terms for toothed gearing: Part 2Bevel and hypoid gears’. As such IS 2458 ( Part 2 ) :1984 now merged with this revision and standswithdrawn after publication of this standard.
The text of ISO Standard has been approved as suitable for publication as an Indian Standard withoutdeviations. In the adopted standard, certain conventions are not identical to those used in Indian Standard.Attention is especially drawn to the following:
a) Wherever the words ‘International Standard’ appear referring to this standard, they should beread as ‘Indian Standard’.
b) Comma (,) has been used as a decimal marker while in Indian Standards, the current practice isto use a full point (.) as the decimal marker.
Technical Corrigendum 1 to the above International Standard has been incorporated.
Only the English language text in the International Standard has been retained while adopting it in thisIndian Standard.
“.
IS 2458:2001
1
jISO 1122-1:1998 ‘;
,:}
Indian Standard 4
VOCABULARY OF GEAR TERMS — DEFINITIONSRELATED TO GEOMETRY
( First Revision)
Scope
This part of ISO 1122 concerns the part of theinternational vocabulary of gears which is devotedsolely to geometrical definitions.
It gives, for each of the geometrical terms relativeto gears, a standard definition which will be validinternationally, the corresponding term in eachlanguage being chosen as far as possible in sucha way as to directly reflect the meaning of thedefinition.
NOTE — Since the choice of corresponding terms canonly be partially fulfilled in any particular language, due tothe necessity of respecting certain established conventions,it is advisable, as far as translation into other languages isconcerned, to refer always to the meaning of the definitionitself, rather than to a simple transposition of the original term.
1 General definitions
1.1 Kinematic definitions
1.1.1 Relative position of axis
1.1.1.1toothed gear
toothed member designed to transmit motion to,or receive motion from, another toothed member,by means of successively engaging teeth
1.1.1.2gear pair
mechanism consisting of two gears rotatablearound axes relative positions of which are fixedand one gear turns the other by the action ofteeth successively in contact
1.1.1.3train of gears
any combination of gear pairs
1.1.1.4parallel gears
gear pair whose axes are parallel
@
!/”
—.— . .
1’
.
-/
1.1.1.5bevel gears
gear pair whose axes intersect
%
‘\\
\
,/
A :
1.1.1.6crossed gears
gear pair having skewed axes
1
IS 2458:2001ISO 1122-1:1998
1.1.1.7centre distance
shortest distancepair
between the axes of a gear
-c—.
1.1.1.8shaft angle
smallest angle through which one of the axesmust be rotated in order to bring the axes intocoincidence ( bevel gear pair), or must be swivelledso that the axes are parallel ( crossed gearpair ) and their directions of rotation are opposite
combination of coaxial elements, of which oneor more are annulus gears ( 1.1.2.8 ) and one ormore are planet carriers ( 1.1.2.10 ) which turnaround the common axes and support one ormore planet gears ( 1.1.2.9 ) which mesh withthe annulus gears and one or more sun gears(1.1.2.7)
A;
B:
D c:D:
Sun gear
Annulus gear
Planet gear(s)
Planet carriers
1.1.2 Mating gears
1.1.2.1mating gears
either one of the two gears of a pair, consideredin relation to the other
1.1.2.2
pinion
that gear of a pair which has the smaller numberof teeth
1.1.2.3wheelgear
that gear of a pair, which has the larger numberof teeth
NOTE — Wheel or gear is a simplification of “conjugategear wheel of pinion”, when the term is clearly used inopposition to “pinion”,
1.1.2.4driving gear
that gear of a pair which turns the other
,,.
2
1.1.2.5driven gear
that gear of a pair which is turned by the other
1.1.2.6idler gear with external teeth
gear that meshes with two other gears and whichis driven by one and drives the other
1.1.2.7sun gear with external teeth
( epicyclic train ) innermost gear with externalteeth
1.1.2.8annulus gear
( epicyclic train ) outermost gear with internalteeth
1.1.2.9planet gear
( epicyclic train) one of the idler gears mountedin a planet carrier
1.1.2.10planet carrier
( epicyclic train) coaxial member which supportsone or more planet gears
1.1.2.11gear segment
gear with teeth covering less then 360°
1.1.2.12number of teeth
number of the full complement of teeth of a gear
1.1.2.13sector of a gear
part of a gear with teeth
1.1.3 Relative speeds
1,1.3.1gear ratio
quotient of the number of teeth of the wheel divided
by the number of teeth of the pinion
1.1.3.2
transmission ratio
quotient of the angular speed of the first driving
IS 2458:2001ISO 1122-1:1998
gear divided by the angular speed of last drivengear of a gear train
NOTE — When necessary, a plus sign should be addedto the transmission ratio when the rotation directions arethe same and a minus sign added when they are opposite.
1.1.3.3speed reducing gears
pair or train of gears, of which the angular velocityof the last driven gear is less than that of thefirst driving gear
1.1.3.4speed increasing gears
pair or train of gears, of which the angular velocityof the last driven gear is greater than that of thefirst driving gear
1.1.3.5speed reducing ratio
transmission ratio of speed reducing gears
1.1.3.6
speed increasing ratio
inverse of the transmission ratio of speed reducinggears
1.1.4 Pitch and reference surfaces
1.1.4.1pitch surface
in a given gear pair, the geometrical surfacedescribed by the instantaneous axis of relativemovement of the mating gear, in relation to the
gear under consideration
NOTE — The pitch surfaces of parallel and bevel gearpairs roll together without slip. Pitch surfaces of crossed( cylindrical and hypoid ) gear pairs have a slidingcomponent along their tooth flanks.
1.1.4.2
reference surface
imaginary conventional surface relative to whichthe dimensions of the teeth of a gear are defined
qualification applicable to terms defined in relation quotient of n divided by the pitch at the referenceto the reference surface of a gear surface, expressed in inches
1.1.4.4 1.2.1.7operating 1)........... unity value of dimension
qualification applicable to terms defined in relation quotient of the dimension under consideration,to the pitch surface of a gear expressed in millimetres, divided by the module
1.1.4.5 NOTE — When the dimension under consideration is the
pitch plane profile shift, the value is called “coefficient”.
pitch surface of a rack or crown wheel, also any 1.2.1.8
plane tangent to the pitch surface of an individual effective facewidth
gear that part of the facewidth deemed to be bearing
NOTE —The pitch plane of a gear pair is a tangent plane load
through the line or, point of contact between their pitchsurfaces, 1.2.2 Tip and root surfaces
1.2 Tooth characteristics 1.2.2.1tip surface
1.2.1 Dimensions and coefficients
1.2.1.1coaxial surface of revolution bounding the outerextremities of external gear teeth or the inner
gear tooth extremities of internal gear teeth
each of those elements of a gear which enter — 1.221 —....,,
spaces between the corresponding elements of,,.
a mating gear and which, by virtue of their shape,ensure that one gear turns the other
1.2.1.2 m ‘m”
tooth space=
space between two adjacent teeth of a gear
1.2.1.3toothing
complete set of teeth of a toothed component
1.2.1.4pitch
dimension defining the uniform spacing, in anyspecified direction, of adjacent corresponding toothprofiles
1.2.1.5module
quotient of the pitch at the reference surface,expressed in millimetres, divided by n
1,2.2.2addendum
part of a gear tooth between the reference surfaceand the tip surface
1.2.2.3top land
portion of the tip surface between opposite flanksof a tooth
- -–1.2.2.3
* ~~
1,2.21— ---” — :
Y
— 1.2.2,2&-- —
:;l,/,, ‘? >P,””’
\>\_ ,, ‘,2
IJ By convention, the qualification “reference” maybe implied,unless a clear distinction between “reference” and “operating” 1.2.2.4
IS necessary, Use the qualification “tooth reference’’ when root surface
there may otherwise be a risk of confusion with speciallymachined datum surfaces which are also termed “reference coaxial surface of revolution bounding the inner
surfaces”. extremities of external gear tooth spaces or the
4
IS 2458:2001ISO 1122-1:1998
outer extremities of internal gear tooth spaces
&,.*.*.& ‘“’”’”2=:
1.2.2.5dedendum
part of a gear tooth between the reference surfaceand the root surface
1.2.2.6bottom land
part of the root surface between the fillets
1.2.2.7external gear
gear of which the tip surface is external to theroot surface
NOTES
1 In order to avoid any ambiguity, especially in the caseof bevel gears, consider the section of both surfaces bya plane perpendicular to the axis of the gears.
2 A rack ( 2.1.7.1 ) is considered to be an external gear.
1.2.2.8internal gear
gear of which the tip surface is internal to theroot surface
1.2.2.9external gear pair
gear pair in which both gears are external gears
I!31.2.2.10internal gear pair
gear pair in which one of the gears is an internalgear
---...,
5
IS 2458:2001ISO 1122-1:1998
1.2.3 Flanks and profiles
1.2.3.1tooth flank
part of the surface of a tooth which lies between
the tip surface and the root surface
1.2.3.2tooth trace
line of intersection of a tooth flank with thereference surface
NOTE — In order to avoid any ambiguity, especially in thecase of bevel gears, consider the section of both surfacesby a plane perpendicular to the axis of the gears.
,.
L-—_—._— —
1.2.3.3flank line
line of intersection of a tooth flank with a coaxialsurface of revolution
1.2.3.4tooth profile 2,
line of intersection of a tooth flank with any defined
surface which also cuts the reference surface
n
1.2.3.5transverse profile 2,
line of intersection of a tooth flank with a surfacewhich is perpendicular to the straight generatorsof the reference surface
1.2.3.6normal profile
line of intersection of a tooth flank with a surfaceorthogonal to the tooth traces
1.2.3.7axial profile
line of intersection of a tooth flank with a planecontaining the axis of the gear
1.2.3.8design profile
preferred profile defined by the designer
1.2.4 Flank qualifications
1.2.4.1mating flank
( gear pair) either one of the two flanks in contact,considered in relation to the other
wJ-1.2.4.2right flank
( observer looking at that end-face chosen asthe reference face of the gear ) that flank of atooth which is to the right of the uppermost toothwhen the gear is vertical
z) Term defined with respect to the reference surface ( qualification “reference” understood ). Add the qualification
“operating” for the corresponding term defined with respect to the pitch surface.
6
IS 2458:2001ISO 1122-1:1998
i
I
I
1.2.4.3left flank
flank of a tooth which is to the left of the uppermosttooth when the gear is vertical
1.2.4.2- t2.4.3~
1.2.4.4
corresponding flanks
( gear teeth) flanks which are all rightall left flanks
1.2.4.5opposite flanks
flanks or
( gear teeth ) one or more right flank in relationto one or more left flank
1.2.4.6operating flank
tooth flank by which motion is transmitted to, or
received from, a mating gear
*
1.2.4.7non-operating flank
opposite flank of an operating flank
-f@-
\‘ 1.2.L2A
1,2.4,3-1
1.2.5 Parts of flanks
1.2.5.1addendum flank
part of a flank lying between the tip surface andthe reference surface of a gear
1.2.5.2dedendum flank
part of a flank lying between the root surfaceand the reference surface of a gear
PF2’’-2’2’21.2.5.3active flank
part of a tooth flank which contacts the toothflanks of a mating gear
1.2.5.4usable flank
largest part of a tooth flank which maybe usedas active flank
,.
1.2.5.5fillet
curved surface between the usable flank and theroot surface
D /,/.,//A”
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IS 2458:2001ISO 1122-1:1998
1.2.5.6usable-contact limit radius
radius of an imaginary coaxial surface, containingthe junctions of the usable gear-flanks and fillets
1.2.5.7active-contact radius
radius of an imaginary coaxial surface, containingthe flank line at which effective contact ends
1.2.5.8tooth tip
intersection of the prolongation of the tooth flankwith the tip surface
1.2.6 Definitions in terms of tooth traces
1.2.6.1spur gear
cylindrical gear whose tooth traces are straightline generators of the reference cylinder ( 2.1.1.1 )
m1.2.6.2straight bevel gear
bevel gear whose tooth traces are straight linegenerators of the reference cone ( 3.1
/ ‘m1,2.6.3helical gear
1.1)
cylindrical gear whose tooth traces are helices( 1,4.1.1 )
mlm1.2.6.4right-hand teeth
teeth whose successive transverse profiles showclockwise displacement with increasing distancefrom an observer looking along the straight line
generators of the reference surface
1.2.6.5left-hand teeth
teeth whose successive transverse profiles showanti-clockwise displacement with increasingdistance from an observer looking along thestraight line generators of the reference surface
ENm1.2.6.6double helical gear
cylindrical gear having part of the facewidth withright-hand teeth and part with left-hand teeth,with or without a gap between them
RgEHi31.2.6.7spiral bevel gear
bevel gear whose tooth traces are curves otherthan helices
B--““”-——.- .
1.2.6.8helical bevel gearskew bevel gear
bevel gear whose tooth traces are non-cylindricalhelices
./3P++:-——
...--
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IS 2458:2001ISO 1122-1:1998
1.3 Generation of teeth
1.3.1 Generating gear, interference andmodification of flank shape
1.3.1.1gear action
action of rotatably mounted, meshing gears whenone is turned by another, and which have angularspeeds in a specified ratio
1.3.1.2generating gear (of a gear)
real or imaginary gear, used for defining thetoothing of the gear under consideration
NOTE — The usable flanks of this gear consist of theenvelope of those of its generating gear, under specifiedconditions of position and relative motion.
1.3.1.3tip interferencemeshing interference
( operating gear pair ) non-tangential contactbetween the tooth tips of one gear and the flanksof the other
1.3.1.4tip relief
intentional modification of the profiles of gear
teeth, involving removal of material near their
tips
1.3.1.5root relief
intentional modification of the profiles of gearteeth, involving removal of material near theirroots
1.3,1,5
a
1.3.1.6undercut
intentional modification of the root fillet byremoval of material using a protuberance type
of gear cutting tool, in order to facilitatesubsequent machining operations
1.3.1.7crowning
progressive reduction of tooth thickness overthe facewidth, towards each end face of a gear
1.3.1.8end relief
linear or progressive reduction of tooth thicknessover a small part of the facewidth, towards eachend face of a gear
I~ Length!
1.3.2 Definitions in terms of tooth generation
1.3.2.1cylindrical gear
gear whose reference surface is a cylinder
1.3.2.2bevel gear
gear whose reference surface is a cone
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IS 2458:2001ISO 1122-1:1998
1.3.2.3cylindrical gear pair
two mating cylindrical gears
NOTE — This gear pair is called a “spur gear pair” whenit is composed of two spur gears and a “helical gear pair”when it is composed of two helical gears.
1.3.2.7wormwheel
1.3.2.4double-helical gear pair
two mating double helical gears
1.3.2.5bevel gear pair
gear pair consisting of two mating bevel gears
NOTE — This gear pair is called a “straight bevel gearpair” when it is composed of two straight bevel gears, ora “helical (skew) bevel gear pair” when it is composed oftwo helical bevel gears, or a “spiral bevel gear pair” whenit is composed of two spiral bevel gears.
%
\‘1,
/’/“// “
,,, .,
+– -
1.3.2.6worm
gear of cylindrical or toroidal shape that mesheswith a worm wheel ( see 1.3.2.7 )
gear having flanks capable of linear contact withthe flanks of a worm
i
,/ ,
,;[
---
1.3.2.8worm gear pair
worm and wormwheel meshed with their axescrossed
#’
10
1.3.2.9hypoid gear pair
pair of gears of conical or approximately conical
shape which mesh with their axes crossed andoffset
1.3.2.10hypoid gear
either gear of a hypoid gear pair
1.4 Geometrical and kinematical notionsrelevant to gears
1.4.1 Geometrical lines
1.4.1.1helixright circular helix
( surface of a cylinder of revolution ) curve whosetangents are inclined at a constant angle to theaxis of the cylinder
1.4.1.2helix angle
acute angle between the tangent to a helix andthe straight generator of the cylinder on which itlies ---%
1.4.1.3spiral angle ( 3.1.2.12 )
1.4.1.4lead angle
acute angle between the tangent to a helix and
a plane perpendicular to the axis of the cylinder
on which the helix lies
,/+,
1.4.1.5lead
distance between two Consecutive intersections
of a helix with a straight generator of the cylinder
IS 2458:2001ISO 1122-1:1998
on which the helix lies
_$_._.– –
‘\
~‘\‘8,
I
1.4.1.6cycloid
plane curve described by a point on a circle( generating circle) which rolls without slip on afixed straight line ( base line )
1.4.1.7epicycloid
plane curve described by a point on a circle( generating circle ) which rolls without slip onthe outside of a fixed circle ( base circle )
1.4.1.8
hypocycloid
plane curve described by a point on a circle( generating circle ) which rolls without slip onthe inside of a fixed circle ( base circle )
1.4.1.9involute to a circle
plane curve described by a point on a straightline ( generating line) which rolls without slip onthe outside of a fixed circle ( base circle )
1.4.1.10spherical involute
( on the surface of a sphere ) curve describedby a point on a great circle ( generating circle )which moves over the sphere by rolling withoutslip on a fixed small circle in the spherical surface( base circle)
11
IS 2458:2001ISO 1122-1:1998
1.4.1.11 2 The intersection of an involute helicoid by a plane
octoid perpendicular to the axis of the base cylinder is an involuteto a circle.
adjective derived from the figure of eight shapesof the complete paths of contact described on 1.4.2.2
imaginary, spherical, boundary surfaces of bevel spherical involute helicoid
gears conjugate to crown wheels with plane tocthflanks
NOTE — This term is used to qualify terms referring tocommonly generated tooth forms ( approximatelyinvolute ) of bevel gear teeth.
1.4.1.12invoiute roil angle
1.4.1.11
angle whose arc on a circle of unit radius is equalto the tangent of the pressure angle at a givenpoint in an involute to that circle
1.4.1.13involute polar angle
angle between a radius vector to a point on aninvolute curve and a radial line through the originof the involute
1.63..1.13- — 1.4.1.12
1.4.2 Geometrical surfaces
1.4.2.1involute helicoid
surface generated by the movement of a straightline which lies in a plane tangent to a cone( base cone) and which is inclined at a constantangle to the line of contact between the planeand the cone
NOTE — The line moves only as a result of the movementof the plane which rolls without slipping on the base cone.
1.4.2.3
instantaneous axis of relative rotation
( parallel or bevel gear) axis about which, at agiven instant in time, a gear carries out a purerotation in relation to its mating gear
NOTE — Concerning crossed gears, text books on theapplications of vector analysis in mechanics should beconsulted.
1.4.2.4generator
moving point or line which traces out a line or asurface
2 Cylindrical gears and gear pairs
2.1 Cylindrical gears
NOTE —The following definitions are also valid for racks,which are considered to be cylindrical gears having infinitelylarge diameters.
2.1.1 Cylinders
2.1.1.1reference cylinder
reference surface of a cylindrical gear
44’
2.1.1.2
surface generated by the movement of a straight pitch cylinder
line which lies in a plane tangent to a cylicder each pitch surface of a cylindrical gear in a gear( base cylinder) and which is inclined at a constant pair with parallal axesangle to the line of contact between the planeand the cylinder
NOTES44?7
1 The line moves only as a result of the movement of theplane which rolls without slipping on the base cylinder.
v
12
IS 2458:2001ISO 1122-1:1998
2.1.1.3tip cylinder
the tip surface of a cylindrical gear
2.1.1.4root cylinder
root surface of a cylindrical gear
2.1.1.5transverse profile ( 1.2.3.5)
line of intersection of a tooth flank with a surfacewhich is perpendicular to the straight generatorsof the reference surface
2.1.1.6reference circles)
intersection of the reference cylinder and a planeperpendicular to its axis
2.1.1.7pitch circle3)
section of the pitch cylinder by aperpendicular to its axis
.2.1.1.8reference diameter
diameter of the reference circle
2.1.1.9pitch diameter
diameter of the pitch circle
2.1.1.10tip circle3)
intersection of the tip cylinder and aperpendicular to its axis
2.1.1.11root circle3)
plane
plane
intersection of the root cylinder and a planeperpendicular to its axis
2.1.1.12tip diameter
diameter of the tip circle
2.1.1.13root diameter
diameter of the root circle
2.1.1.14facewidth
width over the toothed part of a gear, measuredalong a generator of the reference cylinder
2.1.2 Helices of helical gears
2.1.2.1reference helix
tooth trace ( 1,2.3,2 ) of a helical gear
e ,//“
i
i
3, Precisely it is a circumference, but “circle” is the commonly used term. /’/
13
,,+
IS 2458:2001ISO 1122-1:1998
2.1.2.2pitch helix
flank line ( 1.2.3.3 ), at the pitch surface of ahelical gear
2.1.2.3base helix
[involute helical gear ( 2.1.7.4 )] curve ofintersection of the involute helicoid of a flankwith the base cylinder
2.1.2.4helix angle4J
helix angle of the reference helix of a helicalgear
diib2.1.2.5base helix angle
helix angle of the base helix of an involute helicalgear
2.1.2.6lead angle4)
lead angle of the reference helix of a helical gear
/’ ‘\
4 Term defined with respect to the reference surface
( qualification “reference” understood). Add the qualification“operating” for the corresponding term defined with respectto the pitch surface.
2.1.2.7base lead angle
lead angle of the base helix of an involute helicalgear
2.1.2.8lead
lead ( 1.4.1.5 ) of the helices of a helical gear
%,●✌
‘\ \\
—.— .—. — .—. —.— J?I
I!
2.1.2.9axial pitch
distance between the points of intersection ofany line parallel to the axis of a helical gear,with two consecutive corresponding flanks
2.1.3 Addendum and dedendum
2.1.3.1tooth depth
radial distance between the tip and root circles
I
14
IS 2458:2001ISO 1122-1:1998
2.1.3.2addendum (value)5)
radial distance between the tip and referencecircles
2.1.3.3dedendum (value)5)
radial distance between the root and referencecircles
2.1.4 Transverse dimensions51
2.1.4.1transverse plane
plane perpendicular to the axis
2.1.4.2transverse pressure angle at a point
acute angle between a radial line passing through
any point in a transverse profile and a tangent
to the profile at that point
~
A
/
/ ~
-.—
i;1
.’7
k
/
/ / i~ ,/4
2.1.4.3transverse pressure angle5)
transverse pressure angle at the point of intersectionof the profile with the reference circle
2.1.4.4transverse pitch5)
length of the arc of the reference circle betweenconsecutive corresponding profiles
F IA2.1.4.5engular pitch
quotient of the angular units in a circle dividedby the number of teeth of a gear
= 360” 2X rad‘c— =—
z z
2.1.4.6transverse module5)
quotient of the transverse pitch, expressed inmillimetres, divided by the number n ( or thequotient of the reference diameter, expressed inmillimetres, divided by the number of teeth )
2.1.4.7transverse tooth thickness)
length of the arc of the reference circle lyingbetween the two profiles of a tooth
= f ,“I
-
2.1.4.8transverse spacewidth5)
length of the arc of the reference circle lyingbetweerf’the two profiles at each side of a toothspace
w w’-i---+ +’--+
2.1.5 Normal dimensions of helical gears6)
2.1.5.1normal pressure angle at a point
acute angle between a radial line passing througha point in a tooth flank and a plane tangent tothe flank at that point
./--
,
5) Term defined with resPect to the reference surface ( qualification “reference” Understod ). Add the qUalifkatiOll
“operating” for the corresponding term defined with respect to the pitch surface.
6, For spur gears, normal and transverse elements are identical and the terms do not need qualification. Subscripts andsigns are therefore unnecessary for their symbols.
15
‘,
A,
IS 2458:2001ISO 1122-1:1998
~{’
,i. -
2.1.5.2
,.
2.1.6.3$
normal pressure angle’) constant chord
normal pressure angle at a point in a tooth trace ( involute gear) shortest distance between the
2.1.5.3lines of contact of the flanks of a tooth with thoseof its basic rack tooth space when the two are
normal pitch’) symmetrically superposed
length of the arc of a co-cylindrical normal helix,lying between the tooth traces of consecutive // /
corresponding flanks/ i
2.1.5.4 ,,normal module’) ,-’.
;.
quotient of the normal pitch, expressed inmillimetres, divided by the number z
2.1.5.5normal tooth thickness7J
length of a co-cylindrical normal helix, lying betweenthe two traces of a tooth 2.1.6.4
2.1.5.6constant chord height
normal spacewidth’) radial distance between the mid-point of the
length of a co-cylindrical normal helix, lyingconstant chord and the tooth crest
between the traces at each side of a tooth space
2.1.5.7crest width
in the tip surface, the shortest arc length between./’
the lines of intersection of the flanks of a toothwith the tip surface
2.1.6 Chords and sector span
2.1.6.1 1
normal chordal tooth thickness) 2.1.6.5
shortest distance between the two tooth traces span measurement
of a tooth distance between two parallel planes tangent to
*
the outer flanks of a number of consecutive teeth( external gears) or tooth spaces ( internal gears)
.’
,/
2.1.6.2chordal height7) ,.
shortest distance from the tooth crest to the mid-point of the normal chordal tooth thickness
75? 2.1.6.6
/ measurement over balls
. measurement over rollers
7, Term defined with respect to the reference surface( qualification “reference” understood). Add the qualification
distance measured over two balls or rollers placed
“operating” for the corresponding term defined with respectin tooth spaces lying as nearly as possible in
to the pitch surface. diametrical opposition
16
IS 2458:2001ISO 1122-1:1998
2.1.7 Types of cylindrical gears
2.1.7.1rack
flat plate or straight bar having a series of identicalequidistant teeth on one face
NOTE — A rackcan be regardedas pan ofa gear of infinitelylarge diameter.
Spur rack
2.1.7.2cycloidal gear
cylindrical gear of which the tooth profilescycloidal curves, exact or approximate
/’
/ ‘\/ ‘\
\,
are
2.1.7.3cylindrical lantern gear
cylindrical gear of which the teeth are cylindricalpins with axes parallel to the axis of the gear
P- e ‘Q ‘-.,,/
P. .
i
0
0\
1
Helical rack
17
IS 2458:2001ISO 1122-1:1998
2.1.7.4involute cylindrical gear
cylindrical gear of which every usable transverseprofile of the teeth is an arc or modified arc, ofan involute to a circle
/ ‘-,.
[!
2.1.7.5base circle
( involute cylindrical gear) “base circle” of theinvolutes of the tooth profiles ( 1.4.1.9 )
/
2.1.7.6base cylinder
cylinder, coaxial with the gear, having the basecircle as transverse section
E
.— —\
----s -,:..”: 1, , -.1
.—/’
/ “ /’=- ~+
2.1.7.7base diameter
diameter of the base circle
2.1.7.8transverse base pitch
length of the arc of the base circle lying betweenthe origins of the involutes of two consecutive
corresponding profiles
%
>b,
—. .
i 21.7.8’,/ p... -
2.1.7.9normal base pitch
i+-+
~ 2.1.7.10
length of the arc of a co-cylindrical normal helix,lying between the base helices from which theinvolute profile of consecutive corresponding flanksoriginate
2.1.7.10base pitch
distance between the involutes of two consecutivecorresponding profiles, measured along a commonnormal to these involutes
2.1.7.11transverse base thickness
length of the base circle lying between the originsof the involutes of the two profiles of a gear tooth
A.....-----——. . —....
2.1.7.12normal base thickness
the length of a co-cylindrical normal helix, lyingbetween the base helices of a tooth ( 2.1.2.3 )
2.1.8 Tooth generation
2.1.8.1standard basic rack tooth profile
rack tooth profile which is used as a basis fordefining the standard tooth dimensions of a systemof involute gears
/,—
... ----
18
_&
2.1.8.2basic rack
imaginary rack having the standard basic racktooth profile in the normal section
/
2.1.8.3counterpart rack
rack over which the basic rack can be superposed\ so that the teeth of each exactly fill the spaces
of the other
2.1.8.4datum plane
in the basic rack, the plane in which the ratio oftooth thickness to pitch has a specified standardvalue
2.1.8.5datum line
line of intersection of the datum plane with theplane of the basic rack tooth profile, or the linein relation to which the dimensions of the standardbasic rack tooth profiles are specified
2.1.8.6profile shift
distance measured along a common normalbetween the reference cylinder of the gear andthe datum plane of the basic rack, when the rackand the gear are superposed so that flanks of atooth of one are tangent to those of the other
NOTES
1 For external gears, the profile shift is positive if thedatum line of the basic rack is shifted away from the axisof the gear,
For internal gears, the profile shift is positive if the datumline of the basic rack is shifted towards the axis of thegear.
Consequently, the nominal tooth thickness increases inboth cases.
2 For internal gears, tooth profiles are considered asbeing those of the tooth spaces.
IS 2458:2001ISO 1122-1:1998
2.1.8.7truncation
reduction of the addendum, considering theaddendum defined by the standard basic racktooth profile
2.1.8.8profile shift coefficient
quotient of a profile shift, expressed in millimetres,divided by the normal module
2.1.8.9truncation coefficient
quotient of the truncation divided by the normalmodule
2.1.9Generating cutting tools and associatedfeatures
2.1.9.1rack-type cutter
generating cutting tool, in the form of a rack
2.1.9.2pinion-type cutter
generating cutting tool, in the form of a conicalinvolute gear
I ,
.>---“
,.
*
19
IS 2458:2001ISO 1122-1:1998
2.1.9.3hob
generating cutting tool, in the form of a worm
--l “t
2.1.9.4nominal pressure angle
normal pressure angle of the basic rack of thegears cut by the tool
—
+._L-2.1.9.5nominal pitch of the cutter
normal pitch of the basic rackby the tool
of the gears cut
,
2.1.9.6cutter module
quotient of the nominal pitchof the cutter, expressedin millimetres, divided by the number z
2.2 Cylindrical gear pairs
2.2.1 Types of cylindrical gear pairs
2.2.1.1cycio-idai gear pair
gear pair consisting of two mating cycloidal gears
2.2.1.2cylindrical iantern pinion and wheei
gear pair consisting of a cylindrical lantern pinionand its mating cylindrical gear
2.2.1.3invoiute spur gear pair
gear pair consisting of two mating involute spurgears
2.2.1.4paraiiel heiicai gears
gear pair consisting of matingparallel axes
2.2.1.5crossed heiicai gears
gear pair consisting of matingcrossed axes
lelical gears with
Ielical gears with
2.2.2 Depths and clearances
2.2.2.1iine of centres
common perpendicular to both axes of a gearpair, joining the centres of two coplanar pitchcircles
.--1--4+-1
/%‘./
(“ ‘ “\I.— —I
~\\ ‘ ~’”
i-2.2.2.2operating depth
distance, along the line of centres, between thetip surfaces of mating gears
&I
20
2.2.2,3clearance
distance, along the line of centres, between theroot surface of a gear and the tip surface of itsmating gear
IS 2458:2001ISO 1122-1:1998
2.2.2.8radial play
amount to be subtracted from the specifiedcentre distance so that both operating and non-operating flanks come into contact
2.2.3 Contact ratio ( parallel gears )8)\
2.2.3.1
r,’
I,/-
F’-’’_/-y----
2.2.2.4circumferential backlash
length of arc of the pitch circle through which agear can be turned when the mating gear is fixed
i,~
2.2.2.5normal backlash
shortest distance between non-operating flankswhen the operating flanks are in contact
fi
--> ~
\\ )/
~.----- - -
\
7-’-—’——--—.——————
2.2.2.6reference backlash
length of arc of the reference circle, equal to the
product of the reference diameter and the
circumferential backlash, divided by the pitch
diameter
2.2.2.7angular backlash
maximum value of the angle through which agear can be turned when the mating gear is fixedand the centre distance has the specified value
line of action
common normal to two transverse tooth profilesat their point of contact
NOTE — In involute parallel axes gear pairs, the lines ofaction are also common tangents to their base circles.
“\ \,—-----l/
2.2.3.2plane of action
plane containing theinvolute gear pair
lines of action of a parallel
2.2.3.3path of contact
locus of successive points of contact of transverse,mating, tooth profiles
NOTE — In involute parallel axes gear pairs, the transversepath of contact is that part of the line of action lying betweentheir tip circles.
o For spur gears, the overlap arc, angle and ratio are
zero. Also the total and transverse elements are identical.For spur gears, the terms do not need qualification andsubscripts and signs are unnecessary for their symbols.
.. - --
,“,-
m
21
----4IS 2458:2001ISO 1122-1:1998
2.2.3.4pitch point
point of contact of two pitch circles
—./ ‘\,
—— -
2.2.3.5total angle of transmission
angle through which a gear turns, from the
beginning to the ending of contact on a flank
2.2.3.6total arc of transmission
arc of the reference circle through which a gearturns, from the beginning to the ending of contacta flank
2.2.3.7transverse angle of transmission
angle through which a gear turns, from the beginning
to the ending of contact on a transverse profile
2.2.3.8transverse arc of transmission
arc of the reference circle through which a gear
turns, from the beginning to the ending of contact
on a transverse profile
I 1
2.2.3.9
overlap angle
angle between the axial planes containing the
ends of one tooth trace
NOthe
TE —The overlap angle is equal to the difference betweenangles defined in 2.2.3.5 and 2.2.3.7.
.—
2.2.3.10overlap arc
arc of the reference circle between the axial planescontaining the ends of one tooth trace
NOTE —The overlap arc is equal to the difference betweenthe arcs defined in 2.2.3.6 and 2.2.3.8.
2,2.3.11transverse contact ratio
quotient of transverse angle of transmission dividedby the angular pitch
2.2.3.12overlap ratio
quotient of overlap angle divided by the angularpitch, or the quotient of the facewidth dividedby the axial pitch
2.2.3.13total contact ratio
quotient of the total angle of transmission dividedby the angular pitch
NOTE — The total contact ratio is equal to the sum of thetransverse contact ratio and the overlap ratio.
2.2.4 Contact ( parallel involute gears )9)
2.2.4.1length of path of contact
length of the line of action between the tip circlesof mating gears
>,A,
-=.
$
/ ---
g) For spur gears, the overlap arc, an!jle and ratio are
zero, Also the total and transverse elements are identical.For spur gears, the terms do not need qualification andsubscripts and signs are unnecessary for their symbols.
j-,
22
IS 2458:2001ISO 1122-1:1998
2.2.4.2
approach contact
contact anywhere along the path of contact
between the tip circle of the driven gear and the
pitch point
2.2.4.3recess contact
contact anywhere along the path of contact
between the pitch point and the tip circle of thedriving gear
2.2.4.4length of approach path
length of that part of the path of contact alongwhich approach contact occurs
...
2.2.4.5length of recess path
length of that part of the path of contact alongwhich recess contact occurs
,/.. ,,,,,... -.”
‘\‘,
-...
2.2.4.6overlap length
length equal to the product of the facewidth andthe tangent of the base helix angle
W)( )i---l
3 Bevel and hypoid gears and gear pairs
3.1 Bevel gears
3.1.1 Cones ( right circular )
3.1.1.1reference cone
reference surface of a bevel gear
3.1.1.2reference cone apex
apex of the refrence cone of a bevel gear
3.1.1.3pitch cone
pitch surface of either gear of a bevel gear pair
3.1.1.4tip cone
tip surface of a bevel or hypoid gear
3.1.1.5root cone
root surface of a bevel or hypoid gear
3.1.1.6back conelOJ
cone at the outer end of the facewidthgenerators are perpendicular to thosereferent
“’\\‘\ \.
,,“L.—
whoseof the
10) BY convention, the qualification “reference” maY be
omitted as understood unless a clear distinction between“reference” and “operating” is necessary. Use the qualification“tooth reference” when there may otherwise be a risk ofconfusion with a specially machined datum surface alsotermed “reference surface”.
23
IS 2458:2001ISO 1122-1:1998
3.1.1.7 3.1.2.3inner conell) reference circle
cone at the inner end of the facewidth, whose circle of intersection of the reference cone withgenerators are perpendicular to those of the a plane perpendicular to the axis, on which thereference cone pitch has the specified value
3.1.1.8 NOTE — Commonly, this is the circle of intersection of
mean conel 1, the reference cone with the back cone.
cone at mid-f acewidth, whose generators areperpendicular to those of the reference cone
3.1.1.9inner ....’l J
qualification applicable to all terms defined fromthe inner cone
3.1.1.10mean ....11)
qualification applicable to all terms defined fromthe mean cone
3.1.1.11back cone tooth profileli)
section of a tooth flank of a bevel or hypoid gear,by the back cone
3.1.1.12virtual cylindrical gear of a bevel gearll)
imaginary cylindrical gear of which the transversesection is a development of the section by theback cone of a given bevel gear
3.1.2 Dimensions of cones
3.1.2.1reference cone angle
angle between the axis and the reference conegenerator which contains the root cone generator
3.1.2.2pitch angle
3.1.2.4reference diameter
diameter of the reference circle
3.1.2.5tip angle
angle between the axis and the tip cone generatorwhich contains the teeth of the gear
3.1.2.6root angle
angle between the axis and the Yootcone generatorwhich does not contain the teeth of the gear
A,- -+fi!!!l X3_!
angle between the axis and the pitch cone generatorwhich contains the root cone generator 3.1.2.7
back cone angle
acute angle between the axis and the generatorof the back cone which contains the bevel gear
3.1.2.8tip circle
(
circle of intersection of the tip cone with the back
/ cone
.,;,- 1 3.1.2.9root circle’2)
II) BY convention, the qualification “reference” maY be
omitted as understood unless a clear distinction between circle of intersection of the root cone with the“reference” and “operating” is necessary, Use the qualification back cone“tooth reference” when there may otherwise be a risk ofconfusion with a specially machined datum surface also IZ) preciselY itis a circumference, but “circle” k Metermed “reference surface”. commonly used term,
24
,.-
IS 2458:2001ISO 1122-1:1998
3.1.2.10tip diameter
diameter of the tip circle
3.1.2.11root diameter
diameter of the root circle
,/,
4“-3.1.2.12spiral angle
( at any point in the tooth flank of a spiral bevel
or hypoid gear ) angle in a tangent plane to thereference cone, between the cone generatrix andthe tangent to the tooth trace at that point
NOTE — Commonly, the spiral angle at mid-facewidth isspecified.
3.1.3 Longitudinal dimensions and associatedfeatures
3.1.3.1facewidth13J
width over the toothed part of a gear, measuredalong a generator of its reference cone
3.1.3.2cone distance
distance along a reference cone generator, fromthe cone apex to the specified cone
13) Term defined with respect to the reference Surface
( qualification “reference” understood). Add the qualification“operating” for the corresponding term defined with respectto the pitch surface.
NOTE — For example, mean distance, back cone distance.
,/+
3.1.3.3locating face
plane face perpendicular to the axis of the gearto be cut, by which its axial position is determined
3.1.3.4mounting distance
( bevel gear) axial distance from the referencecone apex to the location face
( hypoid gear ) distance along the gear axis fromits intercept with the perpendicular common tothe axes of the hypoid pair to the locating face
3.1,3.43.1.3.k
3.1.3.3—-3.1.3.3-
9Q”
\,‘:~..,/ .,,/’
\
—’> “- - —/+=
/ /
3.1.3.5tip distance
distance along the gear axis from the planecontaining the tipcircle to the locating face
3.1.3.6heel
end of a bevel or hypoid gear tooth near to theback cone
3.1.3.7toe
end of a bevel or hypoid gear tooth near the innercone
i
25
IS 2458:2001ISO 1122-1:1998
3.1.4 Addendum and dedendum
3.1.4.1tooth depth
distance along a back cone generator betweenthe tip circle and the root circle
11 . ..._ L__L_
3.1.4.2addendum ( value )14)
distance along a back cone generator betweenthe tip circle and the reference circle
3.1.4.3addendum angle’4J
deference betweenreference cone angle
the tip angle and the
7A
3.1.4.4dedendum ( value )14)
distance along a back cone generator betweenthe toot circle and the reference circle
3.1.4.5dedendum angle14)
difference betweenreference cone angle
the root angle and the
14)Term defined with respect to the reference surface( qualification “reference” understood). Add the qualification“operating” for the corresponding term defined with respectto the pitch surface.
3.1.5 Dimensions ( straight bevel gears)
3.1.5.1pressure angle at a point
acute angle between a tangent to a tooth profileand a line perpendicular to the reference coneand passing through the point of tangency
fi, -X
A
, ,;//HQ.—.
/iI /’y
/
/
,4 /4
3.1.5.2Pressure angle15)
pressure angle at the point where the tooth profilecuts the reference circle
3.1.5.3pitch15)
length of the arc of the reference circle betweentwo consecutive corresponding profiles
3.1.5.4module15)
quotient of the pitch, expressed in millimetres,divided by the number n, or thereference diameter, expresseddivided by the number of teeth
3.1.5.5diametral pitch 15)
quotient of the
in millimetres,
quotient of the number n divided by the pitch,expressed in inches, or the quotient of the numberof teeth divided by the reference diameter,expressed in inches
15)By conventicm,the qualification “reference” maybe omittedas understood unless a clear distinction between “reference”and “operating” is necessary, Use the qualification “toothreference” when there may otherwise be a risk of confusionwith a specially machined datum surface also termed“reference surface”.
“- ‘?y
26
3.1.5.6tooth thickness’GJ
length of the arc of the reference circle between
the two profiles of a tooth
3.1.5.7spacewidthl@
length of the arc of the reference circle between
the two profiles lying at each side of a tooth
space
m3.1.5.8tooth thickness half angle
half of the angle between the tooth traces of atoot h
A/;“22.2,.$, ,
.,__.— ,,-——+—— _
,/
;
,.:/,,.
/
,$ !/., / ,, , ,,;,,.,.‘, ..,., ,2 /.: ,,
3.1.5.9spacewidth half angle
half of the angle between
spacewidth
d.
the tooth traces of a
+.
IS 2458:2001ISO 1122-1:1998
3.1.6 Chords ( straight bevel gears)
3.1.6.1chordal tooth thickness’G)
(straight bevel gear) normal chordal tooth thicknessat the back cone
3.1.6.2chordal height’GJ
( straight bevel gear) chordal height at the backcone
3.1.7 Types of bevel and hypoid gears
3.1.7.1crown wheelcrown gear
bevel gear with a reference cone angle of 90°
3.1.7.2contrate gearface gear
bevel gear with tip and root cone angles of 90°
>
I
16) By convention, the qualification “reference” maybe omitted as understood unless a clear distinctionWmeen “reference”and “operating” is necessary. Use the qualification “tooth reference” when there may otherwise be a risk of confusionwith a specially machined datum surface also termed “reference surface”.
27
IS 2458:2001ISO 1122-1:1998
3.1.7.3helical bevel gearskew bevel gear
bevel gear conjugate to a crown gear whose toothtraces are straight lines tangent to a concentriccircle
3.1.7.4offset of tooth trace
shortest distance between the tooth trace produced
and the axis of the crown wheel to which the
helical bevel gear is conjugate
3.1.7.5
octoid gear
bevel gear conjugate to a crown wheel with straightsided tooth profiles in normal sections
NOTE —These profiles ‘@proximate both spherical involutesand the involute profiles of its virtual cylindrical gear.
3.1.8 Generating cutting tools
3.1.8.1cutter tip angle
( crown wheel) half the angle between the linesof intersection of the tip cone with the two flanksof the tooth space
3.1.8.2cutter module
coarsest standard module which can be cut tostandard tooth depth with the cutter
3.1.8.3cutter diametral pitch
coarsest standard diametral pitch which can becut to standard tooth depth with the cutter
3.2 Bevel and hypoid gear pairs
3.2.1 Types of gear pairs
3.2.1.1straight bevel gear pair
gear pair consisting of two mating, involute, straightbevel gears
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BIS has the copyright of all its publications. No part ofthese publications maybe reproduced in any form withoutthe prior permission in writing of BIS. This does not preclude the free use, in the course of implementing thestandard, of necessary details, such as symbols and sizes, type or grade designations. Enquiries relating tocopyright be addressed to the Director (Publications), BIS.
Review of Indian Standards
Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewedperiodically; a standard along with amendments is reaffirmed when such review indicates that no changes areneeded; if the review indicates that changes are needed, it is taken up for revision. Users of Indian Standardsshould ascertain that they are in possession of the latest amendments or edition by referring to the latest issueof ‘BIS Catalogue’ and ‘Standards : Monthly Additions’.
This Indian Standard has been developed from Doc : No. BP 13 [ LM 13 ( 0130 ) ].
Amendments Issued Since Publication
Amend No. Date of Issue Text Affected
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