Disclosure to Promote the Right To Information

Transcription

1 इ टरन ट म नक 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. ज न1 क अ+धक र, ज 1 क अ+धक र Mazdoor Kisan Shakti Sangathan The Right to Information, The Right to Live प0र 1 क छ ड न' 5 तरफ Jawaharlal Nehru Step Out From the Old to the New IS 2458 (2001): Vocabulary of Gear Terms - Definitions Related to Geometry [PGD 30: Transmission Devices]! न $ एक न' भ रत क +नम-ण Satyanarayan Gangaram Pitroda Invent a New India Using Knowledge! न एक ऐस खज न > ज कभ च0र य नहB ज सकत ह ह Bhartṛhari Nītiśatakam Knowledge is such a treasure which cannot be stolen

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4 ( Wa7 ~y7awt) Indian Standard VOCABULARY OF GEAR TERMS DEFINITIONS RELATED TO GEOMETRY ( First Revision) ICS ; BIS 2001 BUREAU OF INDIAN STAN DARDSO MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG NEW DELHI December 2001 Price Group 11

5 Gears Sectional Committee, BP 13 NATIONAL FOREWORD This Indian Standard ( First Revision ) which is identical with ISO :1998 Vocabulary of terms 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 Sectional Committee and approval of the Basic and Production Engineering Division Council. This standard was originally published in This revision of the standard has been made by adoption of ISO : 1998 under dual numbering system. This standard covers the Vocabulary of Gears which devoted solely to geometrical definitions including Bevel and Hypoid Gears, The Bevel and Hypoid Gears were earlier covered in IS 2458 ( Part 2 ) :1984 Glossary of terms for toothed ing: Part 2 Bevel and hypoid s. As such IS 2458 ( Part 2 ) :1984 now merged with this revision and stands withdrawn after publication of this standard. The text of ISO Standard has been approved as suitable for publication as an Indian Standard without deviations. 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 be read as Indian Standard. b) Comma (,) has been used as a decimal marker while in Indian Standards, the current practice is to 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 this Indian Standard.

6 Indian Standard VOCABULARY OF GEAR TERMS DEFINITIONS RELATED TO GEOMETRY ( First Revision) Scope This part of ISO 1122 concerns the part of the international vocabulary of s which is devoted solely to geometrical definitions. It gives, for each of the geometrical terms relative to s, a standard definition which will be valid internationally, the corresponding term in each language being chosen as far as possible in such a way as to directly reflect the meaning of the definition. NOTE Since the choice of corresponding terms can only be partially fulfilled in any particular language, due to the necessity of respecting certain established conventions, it is advisable, as far as translation into other languages is concerned, to refer always to the meaning of the definition itself, rather than to a simple transposition of the original term. 1 General definitions 1.1 Kinematic definitions Relative position of axis toothed toothed member designed to transmit motion to, or receive motion from, another toothed member, by means of successively engaging teeth train of s any combination of pairs parallel s pair whose axes are parallel bevel s pair whose axes intersect pair mechanism consisting of two s rotatable around axes relative positions of which are fixed and one turns the other by the action of teeth successively in contact crossed s % \,/ A : pair having skewed axes \ 1 1

7 centre shortest pair distance distance ȯ /=i- between the axes of a -c. + } \ ~ / \ + / shaft angle smallest angle through which one of the axes must be rotated in order to bring the axes into coincidence ( bevel pair), or must be swivelled so that the axes are parallel ( crossed pair ) and their directions of rotation are opposite epicyclic epicyclic planetary planetary train train combination of coaxial elements, of which one or more are annulus s ( ) and one or more are planet carriers ( ) which turn around the common axes and support one or more planet s ( ) which mesh with the annulus s and one or more sun s ( ) A; B: D c: D: Sun Annulus Planet Planet (s) carriers Mating s mating s either one of the two s of a pair, considered in relation to the other pinion that of a pair which has the smaller number of teeth wheel that of a pair, which has the larger number of teeth NOTE Wheel or is a simplification of conjugate wheel of pinion, when the term is clearly used in opposition to pinion, driving that of a pair which turns the other 2

8 driven divided by the angular speed of last driven of a train that of a pair which is turned by the other idler with external teeth that meshes with two other s and which is driven by one and drives the other sun with external teeth ( epicyclic train ) innermost with external teeth annulus ( epicyclic train ) outermost with internal teeth planet ( epicyclic train) one of the idler s mounted in a planet carrier planet carrier ( epicyclic train) coaxial member which supports one or more planet s segment with teeth covering less then number of teeth number of the full complement of teeth of a sector of a NOTE When necessary, a plus sign should be added to the transmission ratio when the rotation directions are the same and a minus sign added when they are opposite speed reducing s pair or train of s, of which the angular velocity of the last driven is less than that of the first driving speed increasing s pair or train of s, of which the angular velocity of the last driven is greater than that of the first driving speed reducing ratio transmission ratio of speed reducing s speed increasing ratio inverse of the transmission s Pitch and reference surfaces pitch surface ratio of speed reducing in a given pair, the geometrical surface described by the instantaneous axis of relative movement of the mating, in relation to the under consideration NOTE The pitch surfaces of parallel and bevel pairs roll together without slip. Pitch surfaces of crossed ( cylindrical and hypoid ) pairs have a sliding component along their tooth flanks. part of a with teeth Relative speeds reference surface 1,1.3.1 ratio quotient of the number of teeth of the wheel divided by the number of teeth of the pinion transmission ratio quotient of the angular speed of the first driving imaginary conventional surface relative to which the dimensions of the teeth of a are defined & 3

9 reference... ) diametral pitch qualification applicable to terms defined in relation quotient of n divided by the pitch at the reference to the reference surface of a surface, expressed in inches operating... 1) unity value of dimension qualification applicable to terms defined in relation quotient of the dimension under consideration, to the pitch surface of a expressed in millimetres, divided by the module 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 plane tangent to the pitch surface of an individual effective facewidth that part of the facewidth deemed to be bearing NOTE The pitch plane of a pair is a tangent plane load through the line or, point of contact between their pitch surfaces, Tip and root surfaces 1.2 Tooth characteristics tip surface Dimensions and coefficients coaxial surface of revolution bounding the outer extremities of external teeth or the inner tooth extremities of internal teeth each of those elements of a which enter,, ,, spaces between the corresponding elements of a mating and which, by virtue of their shape, ensure that one turns the other tooth space m = m space between two adjacent teeth of a toothing complete set of teeth of a toothed component pitch dimension defining the uniform spacing, in any specified direction, of adjacent corresponding tooth profiles module quotient of the pitch at the reference surface, expressed in millimetres, divided by n 1,2.2.2 addendum part of a tooth between the reference surface and the tip surface top land portion of the tip surface between opposite flanks of a tooth , : & ,2 Y :;l, /,,? > P, \>\_,,,2 * ~~ IJ By convention, the qualification reference maybe implied, unless a clear distinction between reference and operating IS necessary, Use the qualification tooth reference when root surface there may otherwise be a risk of confusion with specially machined datum surfaces which are also termed reference coaxial surface of revolution bounding the inner surfaces. extremities of external tooth spaces or the 4

10 outer extremities of internal tooth spaces &,.*.*.& 2=: dedendum part of a tooth between the reference and the root surface surface external pair pair in which both s are external s bottom land part of the root surface between the fillets external of which the tip surface is external to the root surface I!3 NOTES 1 In order to avoid any ambiguity, especially in the case of bevel s, consider the section of both surfaces by a plane perpendicular to the axis of the s. 2 A rack ( ) is considered to be an external internal pair pair in which one of the s is an internal internal of which the tip surface is internal to the root surface 5

11 1.2.3 Flanks and profiles tooth flank part of the surface of a tooth which lies between the tip surface and the root surface transverse profile 2, line of intersection of a tooth flank with a surface which is perpendicular to the straight generators of the reference surface normal profile tooth trace line of intersection of a tooth flank with the reference surface NOTE In order to avoid any ambiguity, especially in the case of bevel s, consider the section of both surfaces by a plane perpendicular to the axis of the s. line of intersection of a tooth flank with a surface orthogonal to the tooth traces axial profile line of intersection of a tooth flank with a plane containing the axis of the design profile flank line,. L- _._ preferred profile defined by the designer Flank qualifications mating flank ( pair) either one of the two flanks in contact, considered in relation to the other line of intersection of a tooth flank with a coaxial surface of revolution tooth profile 2, line of intersection of a tooth flank with any defined surface which also cuts the reference surface n right flank wj- ( observer looking at that end-face chosen as the reference face of the ) that flank of a tooth which is to the right of the uppermost tooth when the 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

12 left flank flank of a tooth which is to the left of the uppermost tooth when the is vertical t2.4.3~ 1.2.L2A \ 1,2.4, corresponding flanks ( teeth) flanks which are all right all left flanks flanks or Parts of flanks addendum flank part of a flank lying between the tip surface and the reference surface of a dedendum flank part of a flank lying between the root surface and the reference surface of a opposite flanks ( teeth ) one or more right flank in relation to one or more left flank PF active flank part of a tooth flank which contacts the tooth flanks of a mating operating flank tooth flank by which motion is transmitted to, or received from, a mating usable flank non-operating * flank opposite flank of an operating flank -f@- largest part of a tooth flank which maybe used as active flank fillet curved surface between the usable flank and the root surface D / /,.,//A 7

13 usable-contact limit radius generators of the reference surface radius of an imaginary coaxial surface, containing the junctions of the usable -flanks and fillets active-contact radius radius of an imaginary coaxial surface, containing the flank line at which effective contact ends tooth tip intersection of the prolongation of the tooth flank with the tip surface left-hand teeth teeth whose successive transverse profiles show anti-clockwise displacement with increasing distance from an observer looking along the straight line generators of the reference surface ENm double helical Definitions in terms of tooth traces spur cylindrical whose tooth traces are straight line generators of the reference cylinder ( ) m straight bevel bevel whose tooth traces are straight line generators of the reference cone ( ) m / 1,2.6.3 helical cylindrical whose tooth traces are helices ( 1,4.1.1 ) right-hand mlm teeth teeth whose successive transverse profiles show clockwise displacement with increasing distance from an observer looking along the straight line 8 cylindrical having part of the facewidth with right-hand teeth and part with left-hand teeth, with or without a gap between them RgEHi spiral bevel bevel whose tooth traces are curves other than helices helical bevel skew bevel B bevel whose tooth traces are non-cylindrical helices ++:- 3P./

14 1.3 Generation of teeth Generating, interference and modification of flank shape of cutting tool, in order to facilitate subsequent machining operations action action of rotatably mounted, meshing s when one is turned by another, and which have angular speeds in a specified ratio generating (of a ) real or imaginary, used for defining the toothing of the under consideration crowning progressive reduction of tooth thickness over the facewidth, towards each end face of a NOTE The usable flanks of this consist of the envelope of those of its generating, under specified conditions of position and relative motion tip interference meshing interference ( operating pair ) non-tangential contact between the tooth tips of one and the flanks of the other tip relief intentional modification of the profiles of teeth, involving removal of material near their tips root relief end relief linear or progressive reduction of tooth thickness over a small part of the facewidth, towards each end face of a intentional modification of the profiles of teeth, involving removal of material near their roots 1.3,1,5! I ~ Length a Definitions in terms of tooth generation cylindrical undercut intentional modification of the root fillet by removal of material using a protuberance type whose reference surface is a cylinder bevel whose reference surface is a cone 9

15 cylindrical pair two mating cylindrical s NOTE This pair is called a spur pair when it is composed of two spur s and a helical pair when it is composed of two helical s wormwheel double-helical pair having flanks capable of linear contact with the flanks of a worm two mating double helical s bevel pair pair consisting of two mating bevel s NOTE This pair is called a straight bevel pair when it is composed of two straight bevel s, or a helical (skew) bevel pair when it is composed of two helical bevel s, or a spiral bevel pair when it is composed of two spiral bevel s. \ 1, / / //,,,., worm pair i ---,; [,/, worm and wormwheel meshed with their axes crossed % worm of cylindrical or toroidal shape that meshes with a worm wheel ( see ) 10

16 hypoid pair pair of s of conical or approximately conical shape which mesh with their axes crossed and offset on which the helix lies _$_._. \ ~ \ 8, I hypoid either of a hypoid pair 1.4 Geometrical and kinematical notions relevant to s Geometrical lines helix right circular helix ( surface of a cylinder of revolution ) curve whose tangents are inclined at a constant angle to the axis of the cylinder helix angle acute angle between the tangent to a helix and the straight generator of the cylinder on which it lies ---% cycloid plane curve described by a point on a circle ( generating circle) which rolls without slip on a fixed straight line ( base line ) epicycloid plane curve described by a point on a circle ( generating circle ) which rolls without slip on the outside of a fixed circle ( base circle ) hypocycloid plane curve described by a point on a circle ( generating circle ) which rolls without slip on the inside of a fixed circle ( base circle ) involute to a circle plane curve described by a point on a straight line ( generating line) which rolls without slip on the outside of a fixed circle ( base circle ) spiral angle ( ) lead angle acute angle between the tangent to a helix and a plane perpendicular to the axis of the cylinder on which the helix lies,/+, spherical involute lead distance between two Consecutive intersections of a helix with a straight generator of the cylinder ( on the surface of a sphere ) curve described by a point on a great circle ( generating circle ) which moves over the sphere by rolling without slip on a fixed small circle in the spherical surface ( base circle) 11

17 The intersection of an involute helicoid by a plane octoid perpendicular to the axis of the base cylinder is an involute to a circle. adjective derived from the figure of eight shapes of the complete paths of contact described on spherical involute helicoid imaginary, spherical, boundary surfaces of bevel s conjugate to crown wheels with plane tocth flanks NOTE This term is used to qualify terms referring to commonly generated tooth forms ( approximately involute ) of bevel teeth surface generated by the movement of a straight line which lies in a plane tangent to a cone ( base cone) and which is inclined at a constant angle to the line of contact between the plane and the cone NOTE The line moves only as a result of the movement of the plane which rolls without slipping on the base cone instantaneous axis of relative rotation ( parallel or bevel ) axis about which, at a given instant in time, a carries out a pure rotation in relation to its mating NOTE Concerning crossed s, text books on the applications of vector analysis in mechanics should be consulted invoiute roil angle angle whose arc on a circle of unit radius is equal to the tangent of the pressure angle at a given point in an involute to that circle involute polar angle angle between a radius vector to a point on an involute curve and a radial line through the origin of the involute generator moving point or line which traces out a line or a surface 2 Cylindrical s and pairs 2.1 Cylindrical s NOTE The following definitions are also valid for racks, which are considered to be cylindrical s having infinitely large diameters Cylinders reference cylinder reference surface of a cylindrical Geometrical surfaces involute helicoid 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 in a ( base cylinder) and which is inclined at a constant pair with parallal axes angle to the line of contact between the plane and the cylinder NOTES 1 The line moves only as a result of the movement of the plane which rolls without slipping on the base cylinder ?7 v

18 tip cylinder the tip surface of a cylindrical pitch circle3) section of the pitch cylinder by a perpendicular to its axis plane root cylinder root surface of a cylindrical reference diameter diameter of the reference circle pitch diameter. diameter tip circle3) of the pitch circle intersection of the tip cylinder and a perpendicular to its axis plane root circle3) intersection of the root cylinder and a plane perpendicular to its axis transverse profile ( ) line of intersection of a tooth flank with a surface which is perpendicular to the straight generators of the reference surface tip diameter diameter root diameter of the tip circle diameter of the root circle reference circles) facewidth width over the toothed part of a, measured along a generator of the reference cylinder intersection of the reference cylinder and a plane perpendicular to its axis Helices of helical s reference helix tooth trace ( e,/ 1,2.3,2 ) of a helical / i / 3, Precisely it is a circumference, but circle is the commonly used term. / 13

19 pitch helix flank line ( ), at the pitch surface of a helical base helix [involute helical ( )] curve of intersection of the involute helicoid of a flank with the base cylinder base lead angle lead angle of the base helix of an involute helical helix angle4j helix angle of the reference helix of a helical diib lead lead ( ) of the helices of a helical %, \ \\ J? base helix angle helix angle of the base helix of an involute helical I I! axial pitch distance between the points of intersection of any line parallel to the axis of a helical, with two consecutive corresponding flanks lead angle4) lead angle of the reference helix of a helical / \ Addendum and dedendum tooth depth radial distance between the tip and root circles 4 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. 14

20 addendum (value)5) radial distance between the tip and reference circles transverse pitch5) length of the arc of the reference circle between consecutive corresponding profiles dedendum (value)5) radial distance between the root and reference circles Transverse dimensions transverse plane plane perpendicular to the axis transverse 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 -. ~ i ;1. 7 / / ~ A/ k / i~,/ transverse pressure angle5) transverse pressure angle at the point of intersection of the profile with the reference circle / engular pitch FA I quotient of the angular units in a circle divided by the number of teeth of a transverse = c 360 2X = rad z z module5) quotient of the transverse pitch, expressed in millimetres, divided by the number n ( or the quotient of the reference diameter, expressed in millimetres, divided by the number of teeth ) transverse tooth thickness) length of the arc of the reference circle lying between the two profiles of a tooth = f, I transverse spacewidth5) length of the arc of the reference circle lying betweerf the two profiles at each side of a tooth wspace w -i Normal dimensions of helical s6) normal pressure angle at a point acute angle between a radial line passing through a point in a tooth flank and a plane tangent to the 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 s, normal and transverse elements are identical and the terms do not need qualification. Subscripts and signs are therefore unnecessary for their symbols. 15

21 normal pressure angle ) constant chord normal pressure angle at a point in a tooth trace ( involute ) shortest distance between the lines of contact of the flanks of a tooth with those of 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 ,, ~{ normal module ),-. ;. quotient of the normal pitch, expressed in millimetres, divided by the number z normal tooth thickness7j length of a co-cylindrical normal helix, lying between the two traces of a tooth constant chord height normal spacewidth ) radial distance between the mid-point of the constant chord and the tooth crest length of a co-cylindrical normal helix, lying between the traces at each side of a tooth space crest width in the tip surface, the shortest arc length between the lines of intersection of the flanks of a tooth with the tip surface./ Chords and sector span normal chordal tooth thickness) 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 s) or tooth spaces ( internal s). *,/ chordal height7) shortest distance from the tooth crest to the midpoint of the normal chordal tooth thickness 75? measurement over balls /. measurement over rollers 7, Term defined with respect to the reference surface distance measured over two balls or rollers placed ( qualification reference understood). Add the qualification in tooth spaces lying as nearly as possible in operating for the corresponding term defined with respect to the pitch surface. diametrical opposition 16

22 2.1.7 Types of cylindrical s rack flat plate or straight bar having a series of identical equidistant teeth on one face NOTE A rackcan be regardedas pan ofa ofinfinitely large diameter. Spur rack Helical rack cycloidal cylindrical of which the tooth profiles cycloidal curves, exact or approximate are / / / \ \ \, cylindrical lantern cylindrical of which the teeth are cylindrical pins with axes parallel to the axis of the i 0.. P /, P- e Q -., 0 \ 1 17

23 involute cylindrical corresponding profiles cylindrical of which every usable transverse profile of the teeth is an arc or modified arc, of an involute to a circle / -,. [!,/% > b,.. i p i+ -+ ~ normal base pitch base circle ( involute cylindrical ) base circle of the involutes of the tooth profiles ( ) base cylinder cylinder, / coaxial with the, having the base circle as transverse section E / base diameter diameter. \ ----s -, :.. : 1,, -.1. / / =- ~+ of the base circle length of the arc of a co-cylindrical normal helix, lying between the base helices from which the involute profile of consecutive corresponding flanks originate base pitch distance between the involutes of two consecutive corresponding profiles, measured along a common normal to these involutes transverse base thickness Ȧ.---- length of the base circle lying between the origins of the involutes of the two profiles of a tooth normal base thickness the length of a co-cylindrical normal helix, lying between the base helices of a tooth ( ) Tooth generation standard basic rack tooth profile rack tooth profile which is used as a basis for defining the standard tooth dimensions of a system of involute s transverse base pitch length of the arc of the base circle lying between the origins of the involutes of two consecutive /, 18

24 basic rack imaginary rack having the standard basic rack tooth profile in the normal section / counterpart rack rack over which the basic rack can be superposed so that the teeth of each exactly fill the spaces of the other datum plane in the basic rack, the plane in which the ratio of tooth thickness to pitch has a specified standard value datum line line of intersection of the datum plane with the plane of the basic rack tooth profile, or the line in relation to which the dimensions of the standard basic rack tooth profiles are specified truncation reduction of the addendum, considering the addendum defined by the standard basic rack tooth profile profile shift coefficient quotient of a profile shift, expressed in millimetres, divided by the normal module truncation coefficient quotient of the truncation divided by the normal module Generating cutting tools and associated features rack-type cutter generating cutting tool, in the form of a rack profile shift distance measured along a common normal between the reference cylinder of the and the datum plane of the basic rack, when the rack and the are superposed so that flanks of a tooth of one are tangent to those of the other NOTES 1 For external s, the profile shift is positive if the datum line of the basic rack is shifted away from the axis of the, For internal s, the profile shift is positive if the datum line of the basic rack is shifted towards the axis of the pinion-type cutter generating cutting tool, in the form of a conical involute Consequently, the nominal tooth thickness increases in both cases. 2 For internal s, tooth profiles are considered as being those of the tooth spaces. I, 19

25 hob generating cutting tool, in the form of a worm invoiute spur pair pair consisting of two mating involute spur s --l t paraiiel heiicai s pair consisting parallel axes crossed heiicai s of mating lelical s with nominal pressure angle pair consisting crossed axes of mating Ielical s with normal pressure angle of the basic rack of the s cut by the tool +._L nominal pitch of the cutter normal pitch of the basic rack of the s by the tool cutter module quotient of the nominal pitchof the cutter, expressed in millimetres, divided by the number z 2.2 Cylindrical pairs Types of cylindrical pairs cycio-idai pair, cut Depths and clearances iine of centres common perpendicular to both axes of a pair, joining the centres of two coplanar pitch circles /%./ ( \. I ~ \ I \ ~ i operating depth distance, along the line of centres, between the tip surfaces of mating s pair consisting of two mating cycloidal s cylindrical iantern pinion and wheei pair consisting of a cylindrical lantern pinion and its mating cylindrical 20 &I

26 2.2.2,3 clearance radial play distance, along the line of centres, between the root surface of a and the tip surface of its mating \ amount to be subtracted from the specified centre distance so that both operating and nonoperating flanks come into contact Contact ratio ( parallel s )8) line of action common normal to two transverse tooth profiles at their point of contact I,/ circumferential r, F - _/-y---- backlash NOTE In involute parallel axes pairs, the lines of action are also common tangents to their base circles. \ \, -----l/ length of arc of the pitch circle through which a can be turned when the mating is fixed plane of action normal backlash ~ i, plane containing the involute pair lines of action of a parallel shortest distance between non-operating flanks when the operating flanks are in contact \\ --> ~ )/ ~. - - \ path of contact locus of successive points of contact of transverse, mating, tooth profiles reference fi backlash NOTE In involute parallel axes pairs, the transverse path of contact is that part of the line of action lying between their tip circles. length of arc of the reference circle, equal to the product of the reference diameter and the circumferential backlash, divided by the pitch diameter angular backlash maximum value of the angle through which a can be turned when the mating is fixed and the centre distance has the specified value o For spur s, the overlap arc, angle and ratio are zero. Also the total and transverse elements are identical. For spur s, the terms do not need qualification and subscripts and signs are unnecessary for their symbols. 21

27 pitch point NOTE The overlap angle isequal to the difference between the angles defined in and point of contact of two pitch circles. / \, overlap arc total angle of transmission angle through which a turns, from the beginning to the ending of contact on a flank total arc of transmission arc of the reference circle through which a turns, from the beginning to the ending of contact a flank transverse angle of transmission angle through which a turns, from the beginning to the ending of contact on a transverse profile transverse arc of transmission arc of the reference circle through which a turns, from the beginning to the ending of contact on a transverse profile arc of the reference circle between the axial planes containing the ends of one tooth trace NOTE The overlap arc is equal to the difference between the arcs defined in and , transverse contact ratio quotient of transverse angle of transmission divided by the angular pitch overlap ratio quotient of overlap angle divided by the angular pitch, or the quotient of the facewidth divided by the axial pitch total contact ratio quotient of the total angle of transmission divided by the angular pitch NOTE The total contact ratio is equal to the sum of the transverse contact ratio and the overlap ratio Contact ( parallel involute s )9) length of path of contact length of the line of action between the tip circles of mating s >,A, I 1 -=. / --- $ overlap angle angle between the axial planes containing the ends of one tooth trace g) For spur s, the overlap arc, an!jle and ratio are zero, Also the total and transverse elements are identical. For spur s, the terms do not need qualification and subscripts and signs are unnecessary for their symbols. 22

28 approach contact contact anywhere along the path of contact between the tip circle of the driven and the pitch recess point contact contact anywhere along the path of contact between the pitch point and the tip circle of the driving 3 Bevel and hypoid s and pairs 3.1 Bevel s Cones ( right circular ) reference cone reference surface of a bevel reference cone apex apex of the refrence cone of a bevel length of approach path length of that part of the path of contact along which approach contact occurs pitch cone... pitch surface of either of a bevel pair length of recess path length of that part of the path of contact along which recess contact occurs -...,... -.,,/..,,,, \ tip cone tip surface root cone of a bevel or hypoid root surface of a bevel or hypoid back coneloj cone at the outer end of the facewidth generators are perpendicular to those referent whose of the overlap length length equal to the product of the facewidth and the tangent of the base helix angle W ) ( ) i---l 23 \\ \ \.,,. L 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 of confusion with a specially machined datum surface also termed reference surface.

29 inner conell) reference circle cone at the inner end of the facewidth, whose circle of intersection of the reference cone with generators are perpendicular to those of the a plane perpendicular to the axis, on which the reference cone pitch has the specified value 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 are perpendicular to those of the reference cone inner... l J qualification applicable to all terms defined from the inner cone mean... 11) reference diameter diameter of the reference circle qualification applicable to all terms defined from the mean cone back cone tooth profileli) section of a tooth flank of a bevel or hypoid, by the back cone tip angle angle between the axis and the tip cone generator which contains the teeth of the virtual cylindrical of a bevel ll) imaginary cylindrical of which the transverse section is a development of the section by the back cone of a given bevel Dimensions of cones reference cone angle root angle angle between the axis and the Yootcone generator which does not contain the teeth of the angle between the axis and the reference cone generator which contains the root cone generator pitch angle --+fi!!!l A, X3_! angle between the axis and the pitch cone generator which contains the root cone generator back cone angle acute angle between the axis and the generator of the back cone which contains the bevel tip circle circle of intersection / ( cone.,;, root circle 2) II) BY convention, the qualification reference may be of the tip cone with the back omitted as understood unless a clear distinction between circle of intersection of the root cone with the reference and operating is necessary, Usethe qualification back cone tooth reference when there mayotherwise be a risk of confusion with a specially machined datum surface also IZ) precisely itis a circumference, but circle k Me termed reference surface. commonly used term, 24

30 tip diameter diameter of the tip circle NOTE For example, mean distance, back cone distance.,/ root diameter diameter of the root circle locating face spiral angle,/, ( at any point in the tooth flank of a spiral bevel or hypoid ) angle in a tangent plane to the reference cone, between the cone generatrix and the tangent to the tooth trace at that point NOTE Commonly, the spiral angle at mid-facewidth specified Longitudinal dimensions and associated features facewidth13j width over the toothed part of a, measured along a generator of its reference cone is plane face perpendicular to the axis of the to be cut, by which its axial position is determined mounting distance ( bevel ) axial distance from the reference cone apex to the location face ( hypoid ) distance along the axis from its intercept with the perpendicular common to the axes of the hypoid pair to the locating face Q tip distance 3.1, \, :~.., /.,, / \ k > - - /+= / / distance along the axis from the plane containing the tipcircle to the locating face cone distance distance along a reference cone generator, from the 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 respect to the pitch surface heel end of a bevel or hypoid tooth near to the back cone toe end of a bevel or hypoid tooth near the inner cone

31 3.1.4 Addendum and dedendum tooth depth distance along a back cone generator between the tip circle and the root circle _ L L_ addendum ( value )14) distance along a back cone generator between the tip circle and the reference circle addendum angle 4J Dimensions ( straight bevel s) pressure angle at a point acute angle between a tangent to a tooth profile and a line perpendicular to the reference cone and passing through the point of tangency Pressure A / fi, -X,,;// HQ.. / i I / y /,4 angle15) pressure angle at the point where the tooth profile cuts the reference circle /4 deference reference between cone angle the tip angle and the 7A pitch15) dedendum ( value )14) distance along a back cone generator between the toot circle and the reference circle dedendum difference reference angle14) between cone angle the root angle and the length of the arc of the reference circle between two consecutive corresponding profiles module15) quotient of the pitch, expressed in millimetres, divided by the number n, or the quotient of the reference diameter, expressed in millimetres, divided by the number of teeth diametral pitch 15) quotient of the number n divided by the pitch, expressed in inches, or the quotient of the number of teeth divided by the reference diameter, expressed in inches 14)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 )Byconventicm,the qualification reference maybe 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 of confusion with a specially machined datum surface also termed reference surface.

32 tooth thickness GJ length of the arc of the reference circle between the two profiles of a tooth Chords ( straight bevel s) chordal tooth thickness G) (straight bevel ) normal chordal tooth thickness at the back cone chordal height GJ ( straight bevel ) chordal height at the back cone Types of bevel and hypoid s spacewidthl@ crown crown wheel length of the arc of the reference circle between the two profiles lying at each side of a tooth space bevel with a reference cone angle of 90 m tooth thickness half angle half of the angle between the tooth traces of a toot h A / ; 22. 2,.$,,.,.,,- + _,/ ;,.:,$ /,,. /., /,,,!/,,;,,..,.,,2 /.:,.,.,, contrate face bevel with tip and root cone angles of spacewidth half angle half of the angle between spacewidth d. the tooth traces of a +. 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 confusion with a specially machined datum surface also termed reference surface. 27

33 helical bevel skew bevel bevel conjugate to a crown whose tooth traces are straight lines tangent to a concentric circle cutter diametral pitch coarsest standard diametral pitch which can be cut to standard tooth depth with the cutter 3.2 Bevel and hypoid pairs Types of pairs straight bevel pair pair consisting oftwo mating, involute, straight bevel s offset of tooth trace shortest distance between the tooth trace produced and the axis of the crown wheel to which the helical bevel is conjugate octoid bevel conjugate to a crown wheel with straight sided tooth profiles in normal sections helical bevel pair skew bevel pair I. - NOTE These both spherical involutes and the involute profiles of its virtual cylindrical. pair consisting of two mating, involute, helical bevel s Generating cutting tools cutter tip angle ( crown wheel) half the angle between the lines of intersection of the tip cone with the two flanks of the tooth space spiral bevel pair pair consisting of two mating spiral bevel s hypoid pair ( ) cutter module coarsest standard module which can be cut to standard tooth depth with the cutter contrate pair face pair contrate and its mating pinion, with either intersecting or crossed axes, with a shaft angle equal to

34 virtual cylindrical pair circumferential backlash imaginary pair composed of mating virtual cylindrical s of a bevel pair Depths and clearances ( bevel pairs ) greatest length of the arc of the reference circle through which a can be turned when the mating is fixed operating depth distance along a common generator of their back cones, between the tip circles of mating bevel s common apex r bevel clearance distance along a common generator of their back cones, between the tip circle of a bevel and the root circle of its mating common apex of the two pitch cones of a bevel pair shaft angle angle equal to the sum of the pitch angles of a bevel pair ( see ) NOTE This definition is not applicable to the reference angles of a hypoid pair.! -1 1! 29

35 Alphabetical index active flank active-contact radius addendum addendum (value) , addendum and dedendum 2.1.3,3.1.4 addendum angle addendum flank angular backlash angular pitch annulus approach contact axial pitch 2.1,2.9 axial profile back cone back cone angle back cone tooth profile base circle base cylinder base diameter base helix base helix angle base lead angle base pitch basic rack bevel clearance bevel bevel pair bevel s bottom land centre distance chordal height , 3.1.6,2 chordal tooth thickness chords ( straight bevel s ) chords and sector span circumferential backlash , clearance common apex cone distance 3.1.3,2 cones ( right circular) constant chord constant chord height contact ( parallel involute s ) contact ratio ( parallel s) contrate contrate pair corresponding flanks 1.2,4.4 counterpafi rack 2,1.8.3 crest width 2.1,5.7 crossed s crossed helical s crown 3,1.7.1 crown wheel 3,1.7.1 A B c crowning cutter diametral pitch cutter module , 3.1,8.2 cutter tip angle cycloid cycloidal cycloidal pair cylinders cylindrical cylindrical pair cylindrical lantern cylindrical lantern pinion and wheel datum line 2.1,8.5 datum plane dedendum dedendum ( value ) ,3.1,4.4 dedendum angle dedendum flank definitions in terms of tooth generation definitions in terms of tooth traces D depths and clearances depths and clearances ( bevel pairs) design profile diametral pitch ,3.1.5,5 dimensions ( straight bevel s) dimensions and coefficients dimensions of cones double helical double-helical pair driven driving 1.1.2,4 effective facewidth end relief epicyclic 1.1,1.9 epicyclic train epicycloid external external pair face 3.1.7,2 face pair facewidth , fillet flank qualification flank line flanks and profiles action pair 1.1,1.2 ratio segment E F G 30

36 tooth generating cutting tools generating cutting tools and associated features generating (of a ) generating, interference and modification of flank shape generator geometrical lines geometrical surfaces 1,4.2 heel helical bevel , H helical bevel pair helical helices of helical s 2.1,2 helix helix angle , hob hypocycloid hypoid hypoid pair ,3.2.1,4 idler with external teeth inner cone instantaneous axis of relative rotation internal internal pair involute cylindrical involute helicoid involute polar angle involute roll angle involute spur pair involute to a circle lead , lead angle , left flank left-hand teeth length of approach path 2,2.4.4 length of path of contact length of recess path line of action line of centres 2,2.2.1 locating face longitudinal dimensions and associated features mating flank mating mating s I L M mean cone measurement over balls 2,1.6.6 measurement over rollers meshing interference module , 3.1,5.4 mounting distance nominal pitch of the cutter nominal pressure angle non-operating flank normal backlash normal base pitch normal base thickness normal chordal tooth thickness normal dimensions of helical s normal moduls normal pitch normal pressure angle normal pressure angle at a point normal profile normal spacewidth 2,1,5.6 N normal tooth thickness number of teeth octoid octoid offset of tooth trace operating depth 2,2.2.2, operating flank opposite flanks overlap angle overlap arc overlap length overlap ratio parallel s parallel helical s parts of flanks path of contact pinion pinion-type cutter pitch , pitch and reference surfaces pitch angle 3.1,2.2 pitch circle pitch cone pitch cylinder pitch diameter pitch helix pitch plane pitch point pitch surface plane of action planet carrier 1.1.2,10 planet 1,1,2.9 planetary planetary train pressure angle pressure angle at a point profile shift profile shift coefficient 2.1.8,8 P 31