1012-g05 gear nomenclature, definition of terms

AN

SI/A

GM

A10

12-G

05ANSI/AGMA 1012-G05

[Revision ofANSI/AGMA 1012--F90]

AMERICAN NATIONAL STANDARD

Gear Nomenclature, Definition of Termswith Symbols

ii

Gear Nomenclature, Definitions of Terms with SymbolsANSI/AGMA 1012--G05[Revision of ANSI/AGMA 1012--F90]

Approval of an American National Standard requires verification by ANSI that the require-ments for due process, consensus, and other criteria for approval have been met by thestandards developer.

Consensus is established when, in the judgment of the ANSI Board of Standards Review,substantial agreement has been reached by directly and materially affected interests.Substantial agreement means much more than a simple majority, but not necessarily una-nimity. Consensus requires that all views and objections be considered, and that aconcerted effort be made toward their resolution.

The use of American National Standards is completely voluntary; their existence does notin any respect preclude anyone, whether he has approved the standards or not, frommanufacturing, marketing, purchasing, or using products, processes, or procedures notconforming to the standards.

The American National Standards Institute does not develop standards and will in nocircumstances give an interpretation of any American National Standard. Moreover, noperson shall have the right or authority to issue an interpretation of an American NationalStandard in the name of the American National Standards Institute. Requests for interpre-tation of this standard should be addressed to the American Gear ManufacturersAssociation.

CAUTION NOTICE: AGMA technical publications are subject to constant improvement,revision, or withdrawal as dictated by experience. Any person who refers to any AGMAtechnical publication should be sure that the publication is the latest available from theAssociation on the subject matter.

[Tables or other self--supporting sections may be referenced. Citations should read: SeeANSI/AGMA 1012--G05, Gear Nomenclature, Definitions of Terms with Symbols, pub-lished by the American Gear Manufacturers Association, 500 Montgomery Street, Suite350, Alexandria, Virginia 22314, http://www.agma.org.]

Approved September 29, 2005

ABSTRACT

This standard lists terms and their definitions with symbols for gear nomenclature.

Published by

American Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314

Copyright 2005 by American Gear Manufacturers AssociationAll rights reserved.

No part of this publication may be reproduced in any form, in an electronicretrieval system or otherwise, without prior written permission of the publisher.

Printed in the United States of America

ISBN: 1--55589--846--7

AmericanNationalStandard

ANSI/AGMA 1012--G05AMERICAN NATIONAL STANDARD

iii AGMA 2005 ---- All rights reserved

Contents

Foreword iv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Scope 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Normative references 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Terms and symbols 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Geometric definitions 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1 General designations 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Kinds of gears 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Principal planes 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4 Principal directions 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5 Surfaces and dimensions 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.6 Terms related to gear teeth 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.7 Terms related to gear pairs 26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.8 Terms related to tooth contact in a gear pair 27. . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Inspection definitions 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography 75. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Index of terms 53. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Annexes

A Abbreviations 41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B Glossary of trade terms 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C Terms and symbols 43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ANSI/AGMA 1012--G05 AMERICAN NATIONAL STANDARD

iv AGMA 2005 ---- All rights reserved

Foreword

[The foreword, footnotes and annexes, if any, in this document are provided forinformational purposes only and are not to be construed as a part of ANSI/AGMA1012--G05, Gear Nomenclature, Definitions of Terms with Symbols.]

In 1926 the AGMA adopted a recommended practice for gearing nomenclature, terms anddefinitions. It included some symbols and abbreviations.

A complete revision of terms and definitions by the AGMA Nomenclature Committee wasissued as AGMA 112.02 in October, 1948. This later became AGMA 112.03, and AmericanStandard B6.10--1954, with ASME as a co--sponsor.

A separate project dealing with Letter Symbols for Gear Engineering appeared in 1943 asAGMA 111.01, later becoming AGMA 111.03 and American Standard B6.5--1954.

Abbreviations for Gearing was another separate project released as AGMA 116.01 in 1955.Most of these abbreviations were already listed in American Standard Z32.13--1950Abbreviations for Use on Drawings, and it was, therefore, unnecessary to process gearingabbreviations as a separate American Standard. The number of abbreviations used ingearing has intentionally been kept very small to permit memorizing without the need torefer to the standard.

AGMA Standard 112.04, Gear Nomenclature (Geometry) Terms, Definitions, Symbols andAbbreviations, was a complete revision and integration of the three standards previouslymentioned. Because of the widespread acceptance of the previous standards, changeswere kept to a minimum. The standard in this form was approved by the AGMA Membershipon April 25, 1965.

AGMA 112.05 included several revisions to keep it abreast of the then current gearingtechniques. It was approved by Standards Committee B6, Gears, the Co--Secretariats andthe American National Standards Institute on February 3, 1976 and designated ANSIB6.14--1976.

ANSI/AGMA 1012--F90 was a revision of 112.05. This revision incorporated the terms fromAGMA Standard 116.01 (Oct., 1972), Glossary of Terms Used in Gearing, and terms fromANSI/AGMA 2000--A88, Gear Classification and Inspection Handbook, Tolerances andMeasuring Methods for Unassembled Spur and Helical Gears (Including MetricEquivalents). In addition, terms which started to be commonly used in gear load rating wereintroduced in the annex.

ANSI/AGMA 1012--G05 is a revision that updates the style of presentation, reordered thesequence of some terms, added definitions for right and left flank, and modified annexes Band C.

The first draft of ANSI/AGMA 1012--G05 was made in June 2002. It was approved by theAGMA membership in July, 2005. It was approved as an American National Standard onSeptember 29, 2005.

Suggestions for improvement of this standard will be welcome. They should be sent to theAmerican Gear Manufacturers Association, 500 Montgomery Street, Suite 350, Alexandria,Virginia 22314.


v AGMA 2005 ---- All rights reserved

PERSONNEL of the AGMA Nomenclature Committee

Chairman: Dwight Smith Cole Manufacturing Systems. . . . . . . . . . . . . . . . .

ACTIVE MEMBERS

M.R. Chaplin Contour Hardening, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . .R.L. Errichello GEARTECH. . . . . . . . . . . . . . . . . . . . . . . . . . .O.A. LaBath Gear Consulting Services of Cincinnati, LLC. . . . . . . . . . . . . . . . . . . . . . . . . . . .T. Miller CST Cincinnati. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J.M. Rinaldo Atlas Copco Comptec, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . .


vi AGMA 2005 ---- All rights reserved

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1 AGMA 2005 ---- All rights reserved


American National Standard --

Gear Nomenclature,Definitions of Terms withSymbols

1 Scope

This standard establishes the definitions of terms,symbols and abbreviations which may be used tocommunicate the technology and specifications ofexternal and internal gear teeth. It provides definitivemeanings by the use of words and illustrations, forcommonly used gearing terms.

2 Normative references

The following documents contain provisions which,through reference in this text, constitute provisions ofthe standard. At the time of publication, the editionswere valid. All publications are subject to revision,and the users of this standard are encouraged toinvestigate the possibility of applying the most recenteditions of the publications listed.

ISO 701:1998, International gear notation --Symbols for geometrical data.

3 Terms and symbols

3.1 Terms

The terminology used in this standard is intended foruse in all AGMA documents and is summarized inthe index.

Many terms are listed in the index more than once byrestating alphabetically with rearranged key words,to aid user look--up of related terms.

3.2 Symbols

The purpose of standard symbols for gear engineer-ing is to establish a uniform practice in mathematicalnotation for equations and formulas dealing withtoothed gearing. Such equations and correspondingcalculations may be used in connection with design,application, manufacture, inspection, new methods,and new problems.

NOTE: The symbols and definitions used in this stan-dard may differ from other AGMA standards. The usershould not assume that familiar symbols can be usedwithout a careful study of these definitions.

SI (metric) units of measure, where applicable, areshown in the text. Where equations require adifferent format or constant for use with SI units, theprimary equation has an (M) appended and thesecondary expression is shown after the first,indented.

Example:

d = z m (2M)D = N

Pd(2)

Symbols must be distinguished from abbreviationswhich are shortened forms of words often used ondrawings and in tables, but not suitable for mathe-matical work (see annex A). For example, thesymbol for circular pitch is p, whereas the abbrevi-ation is CP.

AGMA is changing to use symbols consistent withsymbols used by ISO. In the definition titles, wherethe old AGMA symbol is still commonly used butdiffers from the ISO symbol, both symbols are listedwith the ISO symbol at the end of the line. Annex Ccontains an alphabetical list of the old symbols withthe new symbols also listed.

3.2.1 Subscripts

A subscript following the general symbol may beused to indicate a value applying to a particular gearor tool, or a value taken at a particular position or in aparticular direction. For convenience and brevity, itis desirable to use a general symbol without asubscript when only one value of a given kind isinvolved. Thus, in a spur gear or a straight--toothbevel gear, there is occasion to consider only onecross section of the teeth, namely, the transverse



section, and it is convenient and natural to refer, forinstance, simply to the circular pitch, p, and thepressure angle, . In the case of gears with obliqueteeth, on the other hand, it is usually necessary to bespecific and to refer to the transverse pitch, pt, andthe transverse pressure angle, t, in order not toleave any doubt as to whether values are being givenfor the transverse plane or normal plane.

3.2.2 Typography

In accordance with the usual practice in publishedtext, symbols, whether upper or lower case, shouldbe printed in serif italic font. This is done to avoidconfusion in reading the symbols and to make adistinction between upper and lower case. Anexception is Greek capital letters and all subscripts,which are always vertical sans serif font.

Numbers appearing as coefficients, subscripts,superscripts, or exponents should be printed invertical Arabic numerals. Abbreviations shouldalways be printed vertical and are not recommendedfor use in formulas. Trigonometric functions shouldbe printed in lower case vertical type. Standardmathematical notation should be followed.

4 Geometric definitions

There is an old Chinese proverb that states: Thebeginning of wisdom is to call things by their rightnames. Unfortunately, gearing terms and meaningsvary in different offices, shops, textbooks, andamong gear authorities.

To obtain related continuity, the terms have beengrouped in what may be called a textbook arrange-ment in preference to alphabetical order. Many ofthe definitions have been written in a way that makesthem depend on one another, as a logical series.This arrangement leads to a more comprehensiveunderstanding of the concepts and geometricalrelations.

4.1 General designations

4.1.1 Gears

Gears are machine elements that transmit motion bymeans of successively engaging teeth, see figure 1.

4.1.2 Gear (wheel)

A gear (wheel) is a machine part with gear teeth. Oftwo gears that run together, the one with the larger

number of teeth is called the gear, see figure 1.(Wheel per ISO 1122--1:1998).

Pinion

Gear(wheel)

Rack

Figure 1 -- Gears

4.1.3 Pinion

A pinion is a machine part with gear teeth. Of twogears that run together, the one with the smallernumber of teeth is called the pinion, see figure 1.

4.1.4 Worm

A worm is a gear with one or more teeth in the form ofscrew threads, see figures 2 and 9.

Figure 2 -- Worm

4.1.5 Rack

A rack is a gear with teeth spaced along a straightline, and suitable for straight line motion. It can beregarded as part of a gear of infinitely large diameter,see figure 1.

4.1.6 Basic rack

For every pair of conjugate involute profiles, there isa basic rack (see 4.7.1). This basic rack is the profileof the conjugate gear of infinite pitch radius, seefigure 3.



Profile angle

Figure 3 -- Basic rack in normal plane

4.1.7 Generating rack

A generating rack is a rack outline used to indicatetooth details and dimensions for the design of agenerating tool, such as a hob or a gear shapercutter.

4.1.8 Number of teeth or threads, N, z

Number of teeth or threads is the number of teethcontained in the whole circumference of the pitchcircle.

4.1.9 Gear ratio, mG, u

Gear ratio is the ratio of the larger to the smallernumber of teeth in a pair of gears.

u = z2z1 (1M)

mG =NGNP

(1)

4.2 Kinds of gears

4.2.1 External gear

An external gear is one with the teeth formed on theouter surface of a cylinder or cone, see figure 4.

External gear Internal gear

Internal bevel gearExternal bevel gear

Figure 4 -- External and internal gears

4.2.2 Internal gear

An internal gear is one with the teeth formed on theinner surface of a cylinder or cone. For bevel gears,an internal gear is one with the pitch angle exceeding90, see figure 4.An internal gear can be meshed only with an externalpinion.

4.2.3 Parallel axis gears

Gears which operate on parallel axes. Externalhelical gears on parallel axes have helices ofopposite hands, see figure 5. If one of the membersis an internal gear, the helices are of the same hand.

Left hand

Right hand

Figure 5 -- Parallel helical gears

4.2.3.1 Spur gear

A spur gear has a cylindrical pitch surface and teeththat are parallel to the axis, see figure 6.

Pinion

Gear

Rack

Figure 6 -- Spur gears



4.2.3.2 Spur rack

A spur rack has a planar pitch surface and straightteeth that are at right angles to the direction ofmotion, see figure 6.

4.2.3.3 Helical gear

A helical gear has a cylindrical pitch surface andteeth that are helical, see figure 7.

4.2.3.4 Helical rack

A helical rack has a planar pitch surface and teeththat are oblique to the direction of motion, seefigure 7.

Helical rack

Helical gear

Figure 7 -- Helical gear and rack

4.2.3.5 Single helical gears

Single helical gears have teeth of only one hand oneach gear, see figure 8.

4.2.3.6 Double helical gears

Double helical gears have teeth of both right handand left hand on each gear. The teeth are separatedby a gap between the helices. Where there is nogap, they are known as herringbone, see figure 8.

4.2.3.7 Herringbone gears

Herringbone gears have teeth of both right hand andleft hand on each gear. The teeth are continuouswithout a gap between the helices, see figure 8.

Single helicalgears

Double helicalgears

Herringbonegears

Figure 8 -- Single and double helical

4.2.4 Wormgearing

Wormgearing includes worms and their matinggears. The axes are usually at right angles, seefigure 9.

Envelopingwormgear

Cylindrical(non--enveloping)

wormgear

Cylindricalworm

Figure 9 -- Wormgearing

4.2.4.1 Wormgear (wormwheel)

A wormgear (wormwheel) is the mate to a worm. Awormgear that is completely conjugate to its wormhas line contact and is said to be enveloping, seefigure 9. It is usually cut by a tool that is geometricallysimilar to the worm. An involute spur gear or helicalgear used with a cylindrical worm has only pointcontact.

4.2.4.2 Cylindrical worm

A cylindrical worm has one or more teeth in the formof screw threads on a cylinder, see figures 2 and 9.

4.2.4.3 Enveloping (hourglass) worm

An enveloping (hourglass) worm has one or moreteeth and increases in diameter from its middle



portion toward both ends, conforming to thecurvature of the gear, see figure 10.

Figure 10 -- Double--enveloping wormgearing

4.2.4.4 Double--enveloping wormgearing

Double--enveloping wormgearing comprises envel-oping (hourglass) worms mated with fully envelopingwormgears, see figure 10. Also known as globoidalwormgearing.

4.2.5 Crossed axis gears

Crossed axis gears are gears which operate onnon--parallel axes.

4.2.5.1 Crossed helical gears

Gears that operate on non--intersecting,non--parallel axes.

The term crossed helical gears has superseded theterm spiral gears. There is theoretically point contactbetween the teeth at any instant. They have teeth ofthe same or different helix angles, of the same oropposite hand. A combination of spur and helical orother types can operate on crossed axes, see figure11.

Figure 11 -- Crossed helical gears

4.2.5.2 Spiral gears

See 4.2.5.1.

4.2.5.3 Face gears

A face gear set consists of a face gear in combinationwith a spur, helical, or conical pinion. A face gear hasa planar pitch surface and a planar root surface, bothof which are perpendicular to the axis of rotation, seefigure 12.

Pinion on center Pinion off center

Offset

Figure 12 -- Face gears

4.2.5.4 Bevel gears

Bevel gears haveconical pitchsurfaces operatingonintersecting or non--intersecting axes, see figure 13.Bevel gears that operate on non--intersecting axesare known as hypoid gears, see 4.2.5.12. Whenbevel gears is used as a general term, it coversstraight, spiral, zerol, skew bevel and hypoid gears.

Practically all bevel gears have spiral teeth that arecurved and oblique. The axes may be at right anglesor otherwise. The tooth surfaces of a bevel gear and



pinion are both cut or generated by the same orsimilar tools.

4.2.5.5 Miter gears

Miter gears are mating bevel gears with equalnumbers of teeth and with axes at right angle, seefigure 13.

Gear

Pinion

Bevel gears

Miter gears

45_45_

90_

Figure 13 -- Bevel gears

4.2.5.6 Angular bevel gears

Angular bevel gears are bevel gears in which theaxes are not at right angles, see figure 14.

4.2.5.7 Crown gear

A crown gear is a bevel gear with a planar pitchsurface. The crown gear is analogous to the basicrack in spur gears, see figure 15.

Shaft angle greateror less than 90

Figure 14 -- Angular bevel gears

90

Figure 15 -- Crown gear

4.2.5.8 Straight bevel gears

Straight bevel gears have straight tooth elements,which if extended, would pass through the point ofintersection of their axes, see figure 16.

Straight bevelgears

Skew bevelgears

Figure 16 -- Straight and skewed bevel

4.2.5.9 Skew bevel gears

Skew bevel gears are those for which the corre-sponding crown gear has teeth that are straight andoblique, see figure 16.

4.2.5.10 Spiral bevel gears

Spiral bevel gears have teeth that are curved andoblique, see figure 17.



Spiral bevelgears

Zerol bevelgears

Figure 17 -- Spiral bevel and zerol

4.2.5.11 Zerol bevel gears

Zerol bevel gears have teeth that are curved but inthe same general direction as straight teeth. Theyare spiral bevel gears of zero spiral angle, see figure17.

4.2.5.12 Hypoid gears

Hypoid gears are similar in general form to bevelgears, but operate on non--intersecting axes, seefigure 18.

Offset

Figure 18 -- Hypoid gears

4.2.5.13 Other trade name gears

It is beyond the scope of this standard to define alltrade name kinds of gears, see annex B.

4.3 Principal planes

4.3.1 Axial plane

An axial plane may be any plane containing the gearaxis and a given point, see figure 19.

4.3.2 Plane of axes

The plane of axes is the plane that contains the twoaxes for parallel or intersecting axis gears, see figure19.

Pitchcylinder

Pitch plane

Transverseplane

Plane of axes

Figure 19 -- Principal reference planes

4.3.3 Pitch plane

The pitch plane of a pair of gears is the planeperpendicular to the axial plane and tangent to thepitch surfaces. A pitch plane in an individual gearmay be any plane tangent to its pitch surface, seefigure 19 and 4.5.1.

The pitch plane of a rack or in a crown gear is theimaginary planar surface that rolls without slippingwith a pitch cylinder or pitch cone of another gear.The pitch plane of a rack or crown gear is also thepitch surface, see figures 20 and 25.

Pitch plane of rack Pitch plane of crown gear

Pitch plane of cylindrical gears

Figure 20 -- Pitch plane of gears



4.3.4 Plane of rotation

A plane of rotation is any plane perpendicular to agear axis, see figure 21.

Plane ofrotation

Transverseplane

Spurgear

Bevelgear

Figure 21 -- Planes of rotation

4.3.5 Tangent plane

A tangent plane is tangent to the tooth surfaces at apoint or line contact.

4.3.6 Transverse plane

A transverse plane is perpendicular to the axial planeand to the pitch plane. In gears with parallel axes,the transverse plane and plane of rotation coincide,see figures 19 and 22.

4.3.7 Normal plane

A normal plane is normal to a tooth surface at a pitchpoint, and perpendicular to the pitch plane. In ahelical rack, a normal plane is normal to all the teeth itintersects. In a helical gear, however, a plane can benormal to only one tooth at a point lying in the planesurface. At such a point, the normal plane containsthe line normal to the tooth surface, see figure 22.

Important positions of a normal plane in toothmeasurement and tool design of helical teeth andworm threads are:

(1) the plane normal to the pitch helix at side of tooth;

(2) the plane normal to the pitch helix at center oftooth;

(3) the plane normal to the pitch helix at center ofspace between two teeth

In a spiral bevel gear, one of the positions of a normalplane is at a mean point and the plane is normal tothe tooth trace.

Pitch point

Normalplane

Transverseplanes

Pitchplane

Line normal totooth surface innormal plane

Figure 22 -- Planes at a pitch point on a helical tooth



4.3.8 Central plane

The central plane of a wormgear is perpendicular tothe gear axis and contains the common perpendicu-lar of the gear and worm axes. In the usual case withaxes at right angles, it contains the worm axis, seefigure 23.

Centralplane

Figure 23 -- Central plane

4.4 Principal directions

These are directions in the pitch plane, and corre-spond to the principal cross sections of a tooth.

4.4.1 Axial direction

The axial direction is a direction parallel to an axis,see figure 24.

Transverse direction

Normal direction

Axial direction

Direction of tooth

Figure 24 -- Principal directions

4.4.2 Transverse direction

The transverse direction is a direction within atransverse plane, see figure 24.

4.4.3 Normal direction

The normal direction is a direction within a normalplane, see figure 24.

4.5 Surfaces and dimensions

The pitch surface definitions are for gears havingtheir ratio of angular velocities constant, and axeseither parallel or intersecting, and, therefore, do notinclude crossed helical gears, wormgearing, hypoidgears, or offset face gears.

4.5.1 Pitch surfaces

Pitch surfaces are the imaginary planes, cylinders,or cones that roll together without slipping. For aconstant velocity ratio, the pitch cylinders and pitchcones are circular, see figures 25 and 26.

Cylindricalpitch surfaces

Rack pitch surface

Figure 25 -- Pitch surfaces

Figure 26 -- Pitch cones



4.5.1.1 Equivalent pitch radius

Equivalent pitch radius is the radius of the pitch circlein a cross section of gear teeth in any plane otherthan a plane of rotation. It is properly the radius ofcurvature of the pitch surface in the given crosssection. Examples of such sections are the trans-verse section of bevel gear teeth and the normalsection of helical teeth, see figure 27.

Bevel gear

Equivalent pitch radius(equals back cone distance)

Figure 27 -- Back cone equivalent

4.5.1.2 Equivalent number of teeth, Ne

Equivalent number of teeth is the number of teethcontained in the whole circumference of a pitch circlecorresponding to an equivalent pitch radius.

4.5.2 Gear center

A gear center is the center of the pitch circle, seefigure 28.

Line of centers

Pitch pointGear center

Pitch linePitch circle

Figure 28 -- Pitch circles and line

4.5.3 Cylindrical gear terms (surfaces anddimensions)

4.5.3.1 Pitch cylinder

A pitch cylinder is the imaginary cylinder in a spur orhelical gear that rolls without slipping on a pitch planeor pitch cylinder of another gear, see figure 25.

4.5.3.1.1 Pitch circle (operating)

A pitch circle (operating) is the curve of intersectionof a pitch surface of revolution and a plane ofrotation. It is the imaginary circle that rolls withoutslipping with a pitch circle of a mating gear, see figure28.

4.5.3.1.2 Pitch line

The pitch line corresponds, in the cross section of arack, to the pitch circle (operating) in the crosssection of a gear, see figure 28.

4.5.3.1.3 Pitch point

The pitch point is the point of tangency of two pitchcircles (or of a pitch circle and pitch line) and is on theline of centers, see figure 28.

4.5.3.2 Line of centers

The line of centers connects the centers of the pitchcircles of two engaging gears; it is also the commonperpendicular of the axes in crossed helical gearsand wormgears. When one of the gears is a rack, theline of centers is perpendicular to its pitch line, seefigure 28.

4.5.3.3 Outside (tip or addendum) cylinder

The outside (tip or addendum) cylinder is the surfacethat coincides with the tops of the teeth of an externalcylindrical gear, see figure 29.

Outside cylinder

Root cylinder

Figure 29 -- Cylindrical surfaces



4.5.3.3.1 Outside diameter, Do, da

Outside diameter is the diameter of the addendum(tip) circle, see figure 30. In a bevel gear it is thediameter of the crown circle, see figure 36. In athroated wormgear it is the maximum diameter of theblank, see figure 31. The term applies to externalgears (for internal gears, see 4.5.3.5).

Pitch diameter

Outside diameter

Root diameter

Figure 30 -- Diameters, external gears

Throatdiameter

Outsidediameter

Gear throatform radius

Figure 31 -- Wormgear diameters

4.5.3.3.2 Top land

Top land is the surface of the top of a tooth, see figure32.

Bottom land

Top land

Figure 32 -- Tooth lands

4.5.3.4 Inside cylinder

The inside cylinder is the surface that coincides withthe tops of the teeth of an internal cylindrical gear,see figure 33.

4.5.3.5 Inside diameter, Di

Inside diameter is the diameter of the addendumcircle of an internal gear, see figure 33.

Root diameter

Insidediameter

Rootcircle

Addendumcircle

Figure 33 -- Diameters, internal gear

4.5.3.6 Root cylinder

The root cylinder is the imaginary surface thatcoincides with the the bottoms of the tooth spaces ina cylindrical gear.

4.5.3.6.1 Root circle

The root circle coincides with the bottoms of the toothspaces, see figures 33 and 34.



Root circle

Addendum circle

Figure 34 -- Root circle

4.5.3.6.2 Root diameter, DR, df

Root diameter is the diameter of the root circle, seefigures 30 and 33.

4.5.3.6.3 Bottom land

Bottom land is the surface at the bottom of a toothspace adjoining the fillet, see figure 32.

4.5.3.7 Standard (reference) pitch circle

The circle which intersects the involute at the pointwhere the pressure angle is equal to the profile angleof the basic rack.

4.5.3.7.1 Standard reference pitch diameter, D, d

The standard reference pitch diameter is the diame-ter of the standard pitch circle. In spur and helicalgears, unless otherwise specified, the standard pitchdiameter is related to the number of teeth and thestandard transverse pitch. It is obtained as:

d = z m = z p = zmn

cos (2M)

D = NPd

= N p = NPnd cos(2)

4.5.3.8 Addendum circle

The addendum circle coincides with the tops of theteeth and is concentric with the standard (reference)pitch circle and radially distant from it by the amountof the addendum, see figures 33 and 34. Forexternal gears, the addendum circle lies on theoutside cylinder while on internal gears theaddendum circle lies on the internal cylinder.

4.5.3.9 Addendum, a, ha

Addendum is the height by which a tooth projectsbeyond (outside for external, or inside for internal)the standard pitch circle or pitch line; also, the radialdistance between the pitch circle and the addendumcircle, see figure 35.

Addendum

Dedendum

Working depth

Whole depthClearance

Figure 35 -- Principal dimensions

4.5.3.10 Dedendum, b, hf

Dedendum is the depth of a tooth space below thestandard (reference) pitch circle or pitch line; also,the radial distance between the pitch circle and theroot circle, see figure 35.

4.5.4 Crossed axis gear terms (surfaces anddimensions)

4.5.4.1 Pitch cone

A pitch cone is the imaginary cone in a bevel gearthat rolls without slipping on a pitch surface ofanother gear, see figure 26.

4.5.4.2 Face (tip) cone

The face (tip) cone is the imaginary surface thatcoincides with the tops of the teeth of a bevel orhypoid gear, see figure 36.

Crown circle

Back cone

Facecone

Rootcone

Frontcone

Figure 36 -- Conical surfaces



4.5.4.3 Root cone

The root cone is the imaginary surface that coincideswith the bottoms of the tooth spaces in a bevel orhypoid gear, see figure 36.

4.5.4.4 Back cone

The back cone of a bevel or hypoid gear is animaginary cone tangent to the outer ends of theteeth, with its elements perpendicular to those of thepitch cone. The surface of the gear blank at the outerends of the teeth is customarily formed to such aback cone, see figure 36.

4.5.4.4.1 Back cone distance

Back cone distance in a bevel gear is the distancealong an element of the back cone from its apex tothe pitch cone, see figure 37.

Apex of pitch cone

Apex to back

Back angle

Front angle

Back conedistance

Conedistance

Figure 37 -- Apex to back

4.5.4.4.2 Back angle

Back angle, in a bevel gear, is the angle between anelement of the back cone and a plane of rotation, andusually is equal to the pitch angle, see figure 37.

4.5.4.5 Front cone

The front cone of a bevel or hypoid gear is animaginary cone tangent to the inner ends of theteeth, with its elements perpendicular to those of thepitch cone. The surface of the gear blank at the innerends of the teeth is customarily formed to such afront cone, but sometimes may be a plane on apinion or a cylinder in a nearly flat gear, see figure 36.

4.5.4.6 Front angle

Front angle, in a bevel gear, is the angle between anelement of the front cone and a plane of rotation, andusually equals the pitch angle, see figure 37.

4.5.4.7 Crown circle

The crown circle in a bevel or hypoid gear is the circleof intersection of the back cone and face cone, seefigure 36.

4.5.4.8 Apex to back

Apex to back, in a bevel gear or hypoid gear, is thedistance in the direction of the axis from the apex ofthe pitch cone to a locating surface at the back of theblank, see figures 37 and 38.

Mountingdistance

Apex to back

Crossingpoint

Mountingdistance

Hypoid Gear and Pinion

Figure 38 -- Mounting distance

4.5.4.9 Mounting distance

Mounting distance, for assembling bevel gears orhypoid gears, is the distance from the crossing pointof the axes to a locating surface of a gear, which maybe at either back or front, see figure 38.

4.5.4.10 Crossing point

Crossing point is the point of intersection of bevelgear axes; also the apparent point of intersection ofthe axes in hypoid gears, crossed helical gears,wormgears, and offset face gears, when projected toa plane parallel to both axes, see figure 38.

4.5.4.11 Throat diameter, dt

Throat diameter is the diameter of the addendumcircle at the central plane of a wormgear or of adouble--enveloping wormgear, see figure 31.

4.5.4.12 Throat form radius, rt

Throat form radius is the radius of the throat of anenveloping wormgear or of a double--envelopingworm, in an axial plane, see figure 31.



4.6 Terms related to gear teeth

4.6.1 Involute teeth

Involute teeth of spur gears, helical gears, andworms are those in which the profile in a transverseplane (exclusive of the fillet curve) is the involute of acircle, see figure 39.

Involute

Base circle

Figure 39 -- Involute teeth

4.6.2 Base circle

The base circle is the circle from which involute toothprofiles are derived, see figure 39.

4.6.2.1 Base diameter, Db, db

Base diameter is the diameter of the base circle of aninvolute gear, see figure 40.

Base diameter

Basecircle

Involute

Involuteteeth

Figure 40 -- Base diameter

4.6.2.2 Base radius

Radius of a base circle.

4.6.2.3 Base cylinder

The base cylinder corresponds to the base circle,and is the cylinder from which involute tooth surfacesare developed, see figure 41.

Spur

Helical

Basecylinder

Involutesurface

Figure 41 -- Base cylinder

4.6.2.4 Cone gear base diameter

Cone gear base diameter, is the diameter of thebase circle in a Cone double--enveloping worm-gear. The base circle is tangent to straight lineextensions of the worm tooth profiles in the centralplane of the wormgear.

4.6.3 Crowned teeth

Crowned teeth have surfaces modified in the length-wise direction to produce localized contact or toprevent contact at their ends, see figure 42.Crowning can be applied to all types of teeth.

4.6.4 Pressure angle, , Pressure angle is in general the angle at a pitch pointbetween the line of pressure which is normal to thetooth surface, and the plane tangent to the pitchsurface. The pressure angle gives the direction ofthe normal to the tooth profile, see figure 43. Thepressure angle is equal to the profile angle at thestandard pitch circle and can be termed the stan-dard pressure angle at that point.



Crownmagnitude

Figure 42 -- Crowned gear

Pressureangle

Profileangle

ProfileangleCutting

tool

Figure 43 -- Pressure and profile angles

4.6.5 Profile angle

Profile angle is in general the angle at a specifiedpitch point between a line tangent to a tooth surfaceand the line normal to the pitch surface (which is aradial line of a pitch circle). This definition isapplicable to every type of gear for which a pitchsurface can be defined. The profile angle gives thedirection of the tangent to a tooth profile, see figure43.

In spur gears and straight bevel gears, tooth profilesare considered only in a transverse plane, and thegeneral terms profile angle and pressure angle arecustomarily used rather than transverse profileangle and transverse pressure angle. In helicalteeth, the profiles may be considered in differentplanes, and in specifications it is essential to use

terms that indicate the direction of the plane in whichthe profile angle or the pressure angle lies, such astransverse profile angle, normal pressure angle,axial profile angle.

4.6.6 Standard profile angles

In tools and gages for cutting, grinding, and gaginggear teeth, the profile angle is the angle between acutting edge or a cutting surface, and some principaldirection such as that of a shank, an axis, or a planeof rotation, see figure 43.

Standard profile angles are established in connec-tion with standard proportions of gear teeth andstandard gear cutting tools. Involute gears operatetogether correctly after a change of center distance,and gears designed for a different center distancecan be generated correctly by standard tools. Achange of center distance is accomplished bychanges in operating values for pitch diameter,circular pitch, diametral pitch, pressure angle, andtooth thicknesses or backlash. The same involutegear may be used under conditions that change itsoperating pitch diameter and pressure angle.Unless there is a good reason for doing otherwise, itis practical to consider that the pitch and the profileangle of a single gear correspond to the pitch and theprofile angle of the hob or cutter used to generate itsteeth, see figure 44.

Profileangle

Standardpitchcircle

Figure 44 -- Standard profile angle

4.6.7 Transverse pressure angle and transverseprofile angle, t, tTransverse pressure angle and transverse profileangle are the pressure angle and the profile angle ina transverse plane, see figure 45.



4.6.8 Normal pressure angle and normal profileangle, n, nNormal pressure angle and normal profile angle arethe pressure and profile angles in a normal plane of ahelical or a spiral tooth, see figure 45. In a spiralbevel gear, unless otherwise specified, profile anglemeans normal profile angle at the mean conedistance.

Axis

Transverseprofile angle

Axialprofile angle

Normalprofile angle

Figure 45 -- Profile angles

4.6.9 Axial pressure angle and axial profileangle, x, xAxial pressure angle and axial profile angle are thepressure angle and the profile angle in an axial planeof a helical gear or a worm, or of a spiral bevel gear,see figure 45.

4.6.10 Involute polar angle, Involute polar angle is the angle between a radiusvector to a point, P, on an involute curve and a radialline to the intersection, A, of the curve with the basecircle, see figure 46.

4.6.11 Involute roll angle, Involute roll angle is the angle whose arc on the basecircle of radius unity equals the tangent of thepressure angle at a selected point on the involute,see figure 47.

4.6.12 Pitch

Pitch is the distance between a point on one toothand the corresponding point on an adjacent tooth. Itis a dimension measured along a line or curve in thetransverse, normal, or axial directions. The use ofthe single word pitch without qualification may be

ambiguous, and for this reason it is preferable to usespecific designations such as transverse circularpitch, normal base pitch, axial pitch, see figure 48.

Involute

O

B

P

A

r

rb

Pressureangle

Point

Polarangle

Figure 46 -- Involute polar angle

Point

Basecircle

Cusp

Involute

Rollangle

Rollangle

Figure 47 -- Involute roll angle

Pitch

Circular pitch

Figure 48 -- Pitch



4.6.13 Circular pitch, p

Circular pitch is the arc distance along a specifiedpitch circle or pitch line between correspondingprofiles of adjacent teeth, see figure 48.

4.6.14 Transverse circular pitch, pt

Transverse circular pitch is the circular pitch in thetransverse plane, see figure 49.

Axis

Transversecircular pitch

Normalcircular pitch

Axial pitch

Figure 49 -- Tooth pitch

4.6.15 Normal circular pitch, pn, pe

Normal circular pitch is the circular pitch in thenormal plane, and also the length of the arc along thenormal pitch helix between helical teeth or threads,see figure 49.

4.6.16 Axial pitch, px

Axial pitch is linear pitch in an axial plane and in apitch surface. In helical gears and worms, axial pitchhas the same value at all diameters. In gearing ofother types, axial pitch may be confined to the pitchsurface and may be a circular measurement, seefigures 49 and 50.

The term axial pitch is preferred to the term linearpitch. The axial pitch of a helical worm and thecircular pitch of its wormgear are the same.

4.6.17 Base pitch, transverse, pb, pbt

Base pitch in an involute gear is the pitch on the basecircle or along the line of action. Correspondingsides of involute gear teeth are parallel curves, andthe base pitch is the constant and fundamentaldistance between them along a common normal in atransverse plane, see figures 50 and 51.

Axis

Axial pitch

Basepitch

Normalbasepitch

Helical rack

Figure 50 -- Base pitch relationships

Basepitch

Basecircle

Base tangent

Circularpitch

Base pitch

Figure 51 -- Principal pitches

4.6.18 Base pitch, normal, pN, pbnNormal base pitch in an involute helical gear is thebase pitch in the normal plane. It is the normaldistance between parallel helical involute surfaceson the plane of action in the normal plane, or is thelength of arc on the normal base helix. It is a constantdistance in any helical involute gear, see figure 50.

4.6.19 Diametral pitch (transverse), PdDiametral pitch (transverse) is the ratio of thenumber of teeth to the standard pitch diameter ininches.

Pd = ND =25.4

m = p (3)

4.6.20 Normal diametral pitch, PndNormal diametral pitch is the value of diametral pitchin a normal plane of a helical gear or worm.

Pnd =Pd

cos (4)4.6.21 Module (transverse), mtModule (transverse) is the ratio of the pitch diameterin millimeters to the number of teeth.

mt = Dz = 25.4Pd(5)



4.6.22 Normal module, mn

Normal module is the value of the module in a normalplane of a helical gear or worm.

mn = mt cos (6)4.6.23 Angular pitch, N, Angular pitch is the angle subtended by the circularpitch, usually expressed in radians.

= 360z degrees or 2 z radians (7)4.6.24 Tooth surface (flank)

The tooth surface (flank) forms the side of a geartooth, see figure 52.

4.6.25 Left or right flank

It is convenient to choose one face of the gear as thereference face and to mark it with the letter I. Theother non--reference face might be termed face II.

Transverseplane

Toothsurface

Profile Tip

Root

Filletcurve

Figure 52 -- Profile (spur gear)

For an observer looking at the reference face, so thatthe tooth is seen with its tip uppermost, the right flankis on the right and the left flank is on the left.

Right and left flanks are denoted by the letters Rand L respectively. See figures 53 and 54.

leftflank

30R 2L

tip

rightflank

29

30 12

I is reference face30 R = pitch No. 30, right flank

2 L = pitch No. 2, left flank

I

Figure 53 -- Notation and numbering for external gear

tip

left flank

2

1 30

29

rightflank

30R1L

I is reference face1 L = pitch No. 1, left flank

30 R = pitch No. 30, right flank

I

Figure 54 -- Notation and numbering for internal gear



4.6.26 Profile

A profile is one side of a tooth in a cross sectionbetween the outside circle and the root circle.Usually a profile is the curve of intersection of a toothsurface and a plane or surface normal to the pitchsurface, such as the transverse, normal, or axialplane, see figure 52.

4.6.26.1 Tip radius, rT, ra

Tip radius is the radius of the circular arc used to joina side--cutting edge and an end--cutting edge in gearcutting tools. Edge radius is an alternate term, seefigure 55.

Hob or tool

Tip radius

Figure 55 -- Tip radius

4.6.26.2 Profile radius of curvature, Profile radius of curvature is the radius of curvatureof a tooth profile, usually at the pitch point or a pointof contact, see figure 56. It varies continuously alongthe involute profile.

Profile radiusof curvatureFillet

radius

Figure 56 -- Fillet radius

4.6.26.3 Tip relief

Tip relief is a modification of a tooth profile whereby asmall amount of material is removed near the tip ofthe gear tooth, see figure 57.

4.6.27 Fillet curve (root fillet)

The fillet curve (root fillet) is the concave portion ofthe tooth profile where it joins the bottom of the toothspace, see figure 52.

4.6.27.1 Fillet radius, rf

Fillet radius is the radius of a circular arc approximat-ing the root fillet curve. In generated teeth, the fillet

curve has a varying radius of curvature,f, see figure56.

InvoluteTip relief

Figure 57 -- Tip relief

4.6.27.2 Undercut

Undercut is a condition in generated gear teeth whenany part of the fillet curve lies inside of a line drawntangent to the working profile at its point of juncturewith the fillet, see figure 58. Undercut may bedeliberately introduced to facilitate finishing opera-tions. With undercut the fillet curve intersects theworking profile. Without undercut the fillet curve andthe working profile have a common tangent.

Tangent atlowest pointof working

profileRadial line of base circle

Fillet curve

Lowest point of workingprofile on which contact

may occur

Base circle

Working profile(involute of circle)

UNDERCUT

Figure 58 -- Undercut

4.6.27.3 Form diameter

Form diameter is the diameter of a circle at which thetrochoid (fillet curve) produced by the tooling inter-sects, or joins, the involute or specified profile.Although these terms are not preferred, it is alsoknown as the true involute form diameter (TIF), startof involute diameter (SOI), or when undercut exists,



as the undercut diameter. This diameter cannot beless than the base circle diameter, see figure 59.

Start ofactive profile

(SAP)

yBase diameter

(Undercut tooth)

Limit diameterProfile control diameter

Form diameter

x 0y 0

x

Figure 59 -- Form diameter

4.6.28 Right hand helical gear or right handworm

A right hand helical gear or right hand worm is one inwhich the teeth twist clockwise as they recede froman observer looking along the axis, see figure 60.

The designations, right hand and left hand, are thesame as in the long established practice for screwthreads, both external and internal.

Two external helical gears operating on parallel axesmust be of opposite hand. An internal helical gearand its pinion must be of the same hand.

Right handhelical gear

Left handhelical gear

Right hand worm Left hand worm

Figure 60 -- Helical and worm hand

4.6.29 Left hand helical gear or left hand worm

A left hand helical gear or left hand worm is one inwhich the teeth twist counterclockwise as theyrecede from an observer looking along the axis, seefigure 60.

4.6.30 Cylindrical gear terms (related to teeth)

4.6.30.1 Helix angle, , Helix angle is the angle between any helix and anaxial line on its cylinder. In helical gears and worms,it is at the standard pitch circle unless otherwisespecified, see 4.5.3.7 and figure 61.

Axis

Helix

Helix angleTooth

Figure 61 -- Helix angle

4.6.30.2 Pitch helix

The pitch helix is the intersection of the tooth surfaceand the pitch cylinder of a helical gear or cylindricalworm, see figure 62.

Pitchcircle

Helical tooth

Base helix

Pitchhelix

Basehelixangle

Straight line elementof base cylinder

Base circle

Outside helix

Figure 62 -- Tooth helix

4.6.30.3 Base helix

The base helix of a helical, involute gear or involuteworm lies on its base cylinder, see figure 62.

4.6.30.3.1 Base helix angle, b, bBase helix angle is the helix angle on the basecylinder of involute helical teeth or threads, seefigure 62.

4.6.30.3.2 Base lead angle, bBase lead angle is the lead angle on the basecylinder. It is the complement of the base helix angle.



4.6.30.4 Normal helix

A normal helix is a helix on the pitch cylinder, normalto the pitch helix, see figure 63.

Pitch helix

Pitchcylinder

Normalhelix

90

Figure 63 -- Normal helix

4.6.30.5 Outside (tip or addendum) helix

The outside (tip or addendum) helix is the intersec-tion of the tooth surface and the outside cylinder of ahelical gear or cylindrical worm, see figure 62.

4.6.30.5.1 Outside helix angle, o, aOutside helix angle is the helix angle on the outsidecylinder.

4.6.30.5.2 Outside lead angle, oOutside lead angle is the lead angle on the outsidecylinder. It is the complement of the outside helixangle.

4.6.30.6 Lead, L, pz

Lead is the axial advance of a helix for one completeturn, as in the threads of cylindrical worms and theteeth of helical gears, see figure 64.

pz = px z = dtan = z mnsin (8)

4.6.30.7 Lead angle, Lead angle is the angle between any helix and aplane of rotation. It is the complement of the helixangle, and is used for convenience in worms andhobs. It is understood to be at the standard pitchdiameter unless otherwise specified, see figure 65.

Axis

Helix

Cylinder

Lead

Figure 64 -- Lead

Lead angle

Lead

Helix angle

Figure 65 -- Lead angle

4.6.30.8 Face width, F, b

Face width is the length of teeth in an axial plane, seefigure 66. For double helical, it does not include thegap.

Face width

Gap

Total face width

Effective face width

Figure 66 -- Face width



4.6.30.9 Total face width, Ft

Total face width is the actual dimension of a gearblank including the portion that exceeds the effectiveface width, see 4.7.11, or as in double helical gearswhere the total face width includes any distance orgap separating right hand and left hand helices, seefigure 66.

4.6.31 Crossed axis gear terms (related to teeth)

4.6.31.1 Right hand spiral bevel gear

A right hand spiral bevel gear is one in which theouter half of a tooth is inclined in the clockwisedirection from the axial plane through the midpoint ofthe tooth as viewed by an observer looking at theface of the gear, see figure 67.

Spiral bevel gears Spiral bevel pinions

Left hand

Right hand

Left hand

Right hand

Figure 67 -- Spiral bevel hand

4.6.31.2 Left hand spiral bevel gear

A left hand spiral bevel gear is one in which the outerhalf of a tooth is inclined in the counterclockwisedirection from the axial plane through the midpoint ofthe tooth as viewed by an observer looking at theface of the gear, see figure 67.

A spiral bevel gear and pinion are always of oppositehand, including the case when the gear is internal.

The designations right hand and left hand areapplied similarly to spiral bevel gears, zerol bevelgears, skew bevel gears, hypoid gears, and obliquetooth face gears, see figure 68.

In hypoid gear design, the pinion and gear arepractically always of opposite hand, and the spiralangle of the pinion is usually larger than that of the

gear. The hypoid pinion is then larger in diameterthan an equivalent bevel pinion.

Zerol bevel gears Zerol bevel pinions

Left hand

Right hand

Left hand

Right hand

Figure 68 -- Zerol hand

4.6.31.3 Spiral angle, , Spiral angle in a spiral bevel gear is the anglebetween the tooth trace and an element of the pitchcone, and corresponds to the helix angle in helicalteeth. Unless otherwise specified, the term spiralangle is understood to be the mean spiral angle, seefigures 69 and 70.

Spiral angle

Figure 69 -- Spiral angle

4.6.31.4 Mean spiral angle, m, mMean spiral angle is the specific designation for thespiral angle at the mean cone distance in a bevelgear, see figure 70.

4.6.31.5 Outer spiral angle, o, eOuter spiral angle is the spiral angle of a bevel gearat the outer cone distance, see figure 70.



Mean cone distance

Inner spiral angle

Toothspiral

Mean spiral angle

Outer spiral angle

Figure 70 -- Spiral angle relationships

4.6.31.6 Inner spiral angle, i, iInner spiral angle is the spiral angle of a bevel gear atthe inner cone distance, see figure 70.

4.6.31.7 Shaft angle, Shaft angle is the angle between the axes of twonon--parallel gear shafts. In a pair of crossed helicalgears, the shaft angle lies between the oppositelyrotating portions of two shafts. This applies also inthe case of wormgearing. In bevel gears, the shaftangle is the sum of the two pitch angles. In hypoidgears, the shaft angle is given when starting adesign, and it does not have a fixed relation to thepitch angles and spiral angles, see figure 71.

Helical gears

Crossing point of axes

Apex ofpitch cones

Shaft angle

Bevel gears

Figure 71 -- Shaft angle

4.6.31.8 Cone distance, A

Cone distance in a bevel gear is the general term forthe distance along an element of the pitch cone fromthe apex to any given position in the teeth, see figure72.

4.6.31.9 Outer cone distance, Ao

Outer cone distance in bevel gears is the distancefrom the apex of the pitch cone to the outer ends ofthe teeth. When not otherwise specified, the shortterm cone distance is understood to be outer conedistance, see figure 72.

Mean conedistance

Inner conedistance

Outer conedistance

Figure 72 -- Cone distance

4.6.31.10 Mean cone distance, Am

Mean cone distance in bevel gears is the distancefrom the apex of the pitch cone to the middle of theface width, see figure 72.

4.6.31.11 Inner cone distance, Ai

Inner cone distance in bevel gears is the distancefrom the apex of the pitch cone to the inner ends ofthe teeth, see figure 72.

4.6.31.12 Heel

The heel of a tooth on a bevel gear or pinion is theportion of the tooth surface near its outer end, seefigure 73.

Bevel gear

Toe

Heel

Figure 73 -- Heel and toe



4.6.31.13 Toe

The toe of a tooth on a bevel gear or pinion is theportion of the tooth surface near its inner end, seefigure 73.

4.6.31.14 Pitch angle, Pitch angle in bevel gears, is the angle between anelement of a pitch cone and its axis. In external andinternal bevel gears, the pitch angles are respective-ly less than and greater than 90 degrees, see figures74 and 75.

Face anglePitch angleRoot angle

Apex to backApex of pitch cone

Axis

Figure 74 -- Angle relationships

Addendum angle

Dedendum angle

Pitch angle

Apex of pitch cone

Face cone

Root cone

Axis

Figure 75 -- Angles

4.6.31.15 Face (tip) angle, oFace (tip) angle in a bevel or hypoid gear, is the anglebetween an element of the face cone and its axis,see figure 74.

4.6.31.16 Root angle, RRoot angle in a bevel or hypoid gear, is the anglebetween an element of the root cone and its axis, seefigure 74.

4.6.31.17 Addendum angle, Addendum angle in a bevel gear, is the anglebetween elements of the face cone and pitch cone,see figure 75.

4.6.31.18 Dedendum angle, Dedendum angle in a bevel gear, is the anglebetween elements of the root cone and pitch cone,see figure 75.

4.6.32 Terms related to tooth thickness

4.6.32.1 Circular thickness, t

Circular thickness is the length of arc between thetwo sides of a gear tooth, on the specified datumcircle, see figure 76.

Chordaladdendum

Circularthickness, t

Datumcircle

Chordalthickness

Figure 76 -- Tooth thickness

4.6.32.2 Transverse circular thickness, tt, s

Transverse circular thickness is the circular thick-ness in the transverse plane, see figure 77.

Normal circular thickness

Axial thickness

Helical rack tooth

Spiral crown gear toothSections in pitch surfaces

Transverse circularthickness

Axialplane

Transverse circularthickness

Figure 77 -- Thickness relationships



4.6.32.3 Normal circular thickness, tn

Normal circular thickness is the circular thickness inthe normal plane. In a helical gear it may beconsidered as the length of arc along a normal helix,see figure 77.

4.6.32.4 Axial thickness, tx

Axial thickness in helical gears and worms is thetooth thickness in an axial cross section at thestandard pitch diameter, see figure 77.

4.6.32.5 Base circular thickness, tb

Base circular thickness in involute teeth is the lengthof arc on the base circle between the two involutecurves forming the profile of a tooth.

4.6.32.6 Chordal thickness, normal, tnc, sc

Chordal thickness is the length of the chord thatsubtends a circular thickness arc in the plane normalto the pitch helix. Any convenient measuringdiameter may be selected, not necessarily thestandard pitch diameter, see figure 78.

Chordaladdendum

Normal chordalthickness

Circularthickness

Datumcircle

Normal plane

Figure 78 -- Chordal thickness

4.6.32.7 Chordal addendum (chordal height), ac,hca

Chordal addendum (chordal height) is the heightfrom the top of the tooth to the chord subtending thecircular thickness arc. Any convenient measuringdiameter may be selected, not necessarily thestandard pitch diameter, see figure 78.

4.6.32.8 Profile shift

The profile shift is the displacement of the basic rackdatum line from the reference cylinder, madenon--dimensional by dividing by the normal module.It is used to specify the tooth thickness, often for zero

backlash. See AGMA 913--A98 for profile shiftfactor, x.

4.6.32.9 Rack shift

The rack shift is the displacement of the tool datumline from the reference cylinder, made non--dimensional by dividing by the normal module. It isused to specify the tooth thickness. See AGMA913--A98.

4.6.32.10 Measurement over pins

Measurement over pins is the measurement of thedistance taken over a pin positioned in a tooth spaceand a reference surface. The reference surface maybe the reference axis of the gear, a datum surface oreither one or two pins positioned in the tooth space orspaces opposite the first. This measurement is usedto determine tooth thickness, see ANSI/AGMA2002--B88 and figure 79.

Figure 79 -- Tooth thickness measurement overpins

4.6.32.11 Span measurement

Span measurement is the measurement of thedistance across several teeth in a normal plane. Aslong as the measuring device has parallel measuringsurfaces that contact on an unmodified portion of theinvolute, the measurement will be along a linetangent to the base cylinder. It is used to determinetooth thickness, see ANSI/AGMA 2002--B88 andfigure 80.

4.6.32.12 Modified addendum teeth

Teeth of engaging gears, one or both of which havenon--standard addendum, see AGMA 913--A98.



M

Figure 80 -- Span measurement

4.6.32.13 Full--depth teeth

Full--depth teeth are those in which the workingdepth equals 2.000 divided by the normal diametralpitch.

4.6.32.14 Stub teeth

Stub teeth are those in which the working depth isless than 2.000 divided by the normal diametralpitch.

4.6.32.15 Equal addendum teeth

Equal addendum teeth are those in which twoengaging gears have equal addendums, see figure81.

a

aG

aP

Equal addendum teeth

Long and short addendum teeth

a

Figure 81 -- Long and short addendum

4.6.32.16 Long and short--addendum teeth

Long and short addendum teeth are those in whichthe addendums of two engaging gears are unequal,

see figure 81. For additional information, see AGMA913--A98 annex B, under addendum modification.

4.7 Terms related to gear pairs

4.7.1 Conjugate gears

Conjugate gears transmit uniform rotary motion fromone shaft to another by means of gear teeth. Thenormals to the profiles of these teeth, at all points ofcontact, must pass through a fixed point in thecommon centerline of the two shafts.

4.7.2 Center distance (operating), C, a

Center distance (operating) is the shortest distancebetween non--intersecting axes. It is measuredalong the mutual perpendicular to the axes, calledthe line of centers. It applies to spur gears, parallelaxis or crossed axis helical gears, and wormgearing,see figure 82.

Center distance

Internal

External

Figure 82 -- Center distance

4.7.3 Offset, E

Offset is the perpendicular distance between theaxes of hypoid gears or offset face gears, see figures12, 18, and 83.

In figure 83, for hypoid gears, (a) and (b) are referredto as having an offset below center, while those in (c)and (d) have an offset above center. In determiningthe direction of offset, it is customary to look at thegear with the pinion at the right. For below centeroffset the pinion has a left hand spiral, and for abovecenter offset the pinion has a right hand spiral.

4.7.4 Operating pressure angle

The operating pressure angle is determined by thebase circles of two gears and the center distance atwhich the gears operate. Various other pressureangles may also be considered in gear calculations.



Hypoid gears

Offset

Figure 83 -- Offset

4.7.5 Clearance, c

Clearance is the distance between the root circle of agear and the addendum circle of its mate, see figure35.

4.7.6 Working depth, hk, hw

Working depth is the depth of engagement of twogears, that is, the sum of their operating addendums,see figure 35.

4.7.7 Whole depth, ht, (tooth depth), he

Whole depth (tooth depth) is the total depth of a toothspace, equal to addendum plus dedendum, alsoequal to working depth plus clearance, see figure 35.

4.7.8 Pitch diameter

Pitch diameter is the diameter of a pitch circle, seefigure 30.

A bevel gear pitch diameter is understood to be at theouter ends of the teeth unless otherwise specified.

4.7.9 Operating pitch diameters, dP, dw1, and dG,dw2

Operating pitch diameters are the pitch diametersdetermined from the numbers of teeth and the centerdistance at which gears operate. Example for pinion:

dw = 2 au + 1 =2 az2z1 + 1

(9)

4.7.10 Backlash, B, j

Backlash is the amount by which the width of a toothspace exceeds the thickness of the engaging toothon the operating pitch circles, see figure 84.

As actually indicated by measuring devices, back-lash may be determined variously in the transverse,normal, or axial planes, and either in the direction ofthe pitch circles, or on the line of action. Suchmeasurements may be converted to correspondingvalues on transverse pitch circles for general com-parisons.

Operating pitch circles

Backlash(transverse operating)

Figure 84 -- Backlash

4.7.10.1 Backlash, minimum

Minimum backlash is the minimum transversebacklash at the operating pitch circle allowable whenthe gear tooth with the greatest allowable functionaltooth thickness is in mesh with the pinion toothhaving its greatest allowable functional tooth thick-ness, at the tightest allowable center distance, understatic conditions, see ANSI/AGMA 2002--B88.

4.7.10.2 Backlash variation

Difference between the maximum and minimumbacklash occurring in a whole revolution of the largerof a pair of mating gears.

4.7.11 Effective face width, Fe

For cylindrical gears, effective face width is theportion that contacts the mating teeth. One memberof a pair of gears may engage only a portion of itsmate, see functional face width, 5.1.6 and figure 66.

For bevel gears, different definitions for effectiveface width are applicable.

4.8 Terms related to tooth contact in a gearpair

4.8.1 Point of contact

A point of contact is any point at which two toothprofiles touch each other, see figure 85.



Path of action

Point of contact

Pitch point

Figure 85 -- Path of action

4.8.2 Line of contact

A line of contact is a line or curve along which twotooth surfaces are tangent to each other, see figures86 and 88.

4.8.3 Path of action

The path of action is the locus of successive contactpoints between a pair of gear teeth, during the phaseof engagement. For conjugate gear teeth, the pathof action passes through the pitch point. It is thetrace of the surface of action in the plane of rotation,see figures 85 and 88.

Helical line of contact

Spur line of contact

Tangent plane

Figure 86 -- Line of contact

4.8.4 Line of action

The line of action is the path of action for involutegears. It is the straight line passing through the pitchpoint and tangent to both base circles, see figure 87.

Base circle

Base circle

Line of action

Figure 87 -- Line of action

4.8.5 Surface of action

The surface of action is the imaginary surface inwhich contact occurs between two engaging toothsurfaces. It is the summation of the paths of action inall sections of the engaging teeth.

4.8.6 Plane of action

The plane of action is the surface of action forinvolute, parallel axis gears with either spur or helicalteeth. It is tangent to the base cylinders, see figure88.

Plane of action

Base cylinder

Line of contact

Figure 88 -- Plane of action

4.8.7 Zone of action (contact zone)

Zone of action (contact zone) for involute, parallel--axis gears with either spur or helical teeth, is the



rectangular area in the plane of action bounded bythe length of action and the effective face width, seefigure 89.

Facewidth

Length ofaction

Zone ofaction

Line of contact

Figure 89 -- Zone of action

4.8.8 Path of contact

The path of contact is the curve on either toothsurface along which theoretical single point contactoccurs during the engagement of gears withcrowned tooth surfaces or gears that normallyengage with only single point contact, see figure 90.

Points of contact(after surface is crowned)

Lines of contact(before surface is crowned)

Path of contact(after surface is crowned)

Figure 90 -- Lines of contact (helical gear)

4.8.9 Length of action, Z

Length of action is the distance on the line of actionthrough which the point of contact moves during theaction of the tooth profile, see figure 91.

Line ofaction

Length ofaction

Figure 91 -- Length of action

4.8.10 Arc of action, Qt

Arc of action is the arc of the pitch circle throughwhich a tooth profile moves from the beginning to theend of contact with a mating profile, see figure 92.

4.8.11 Arc of approach, Qa

Arc of approach is the arc of the pitch circle throughwhich a tooth profile moves from its beginning ofcontact until the point of contact arrives at the pitchpoint, see figure 92.

4.8.12 Arc of recess, Qr

Arc of recess is the arc of the pitch circle throughwhich a tooth profile moves from contact at the pitchpoint until contact ends, see figure 92.

Arc of recess Arc ofapproach

Directionof motion

Arc of action

Figure 92 -- Arc of action



4.8.13 Contact ratio, mc, Contact ratio in general is the number of angularpitches through which a tooth surface rotates fromthe beginning to the end of contact.

4.8.14 Transverse contact ratio, mp, Transverse contact ratio is the contact ratio in atransverse plane. It is the ratio of the angle of actionto the angular pitch. For involute gears it is mostdirectly obtained as the ratio of the length of action tothe base pitch.

4.8.15 Face contact ratio, mF, Face contact ratio is the contact ratio in an axialplane, or the ratio of the face width to the axial pitch.For bevel and hypoid gears it is the ratio of faceadvance to circular pitch.

4.8.16 Total contact ratio, mt, Total contact ratio is the sum of the transversecontact ratio and the face contact ratio.

= + (10M)mt = mp + mF (10)

4.8.17 Modified contact ratio, mo

Modified contact ratio for bevel gears is the squareroot of the sum of the squares of the transverse andface contact ratios.

mo = m2p + m2F0.5

(11)

4.8.18 Limit diameter

Limit diameter is the diameter on a gear at which theline of action intersects the maximum (or minimumfor internal pinion) addendum circle of the matinggear. This is also referred to as the start of activeprofile, the start of contact, the end of contact, or theend of active profile, see figures 93 and 59.

4.8.18 Start of active profile (SAP)

The start of active profile is the intersection of thelimit diameter and the involute profile, see figure 59.

4.8.19 Face advance, QF

Face advance is the distance on a pitch circlethrough which a helical or spiral tooth moves fromthe position at which contact begins at one end of thetooth trace on the pitch surface to the position wherecontact ceases at the other end, see figure 94.

Minimumoperating

centerdistance

Limitdiameter

Maximumaddendum

circleLine ofaction

Basecircle

Figure 93 -- Limit diameter

5 Inspection definitions

The following definitions are used in AGMA2000--A88, Gear Classification and InspectionHandbook, Tolerances and Measuring Methods forUnassembled Spur and Helical Gears (IncludingMetric Equivalents) and in ANSI/AGMA2015--1--A01, Accuracy Classification System --Tangential Measurements for Cylindrical Gears.

NOTE: ANSI/AGMA 2015--1--A01 replaces AGMA2000--A88. For bevel and wormgear inspection no-menclature, see ANSI/AGMA 2009--B01 and ANSI/AGMA 2011--A98 respectively.

Face advance

Figure 94 -- Face advance



5.1 Reference datum

5.1.1 Datum circle, Dc

A datum circle is a circle on which measurements aremade.

5.1.2 Datum axis

The datum axis of the gear is defined by the datumsurfaces. It is the axis to which the gear details, andin particular the pitch, profile, and helix tolerancesare defined. (ANSI/AGMA 2015--1--A01)

5.1.3 Datum tooth

A datum tooth is the designated tooth used as thestarting point for measuring other teeth.

5.1.4 Profile control diameter

A specified diameter of the circle beyond which thetooth profile must conform to the specified involutecurve. See functional profile. (ANSI/AGMA2015--1--A01)

5.1.5 Eccentricity

Eccentricity is the distance between the center of ameasurement circle and a datum axis of rotation.

5.1.6 Functional face width

The functional face width is that portion of the facewidth less the edge round or chamfer at each end.

5.1.7 Gear blank

A gear blank is the work piece used for themanufacture of a gear, prior to machining the gearteeth.

5.1.8 Inspection chart

An inspection chart is the generated recording ortrace from an inspection machine used to display ameasured variation of gear geometry.

5.1.9 Tolerance diameter, dT

For cylindrical gears, the diameter located onenormal module below the design outside diameter,thereby being approximately at mid--height. (ANSI/AGMA 2015--1--A01)

For bevel gears, the diameter is where the meancone distance and the midpoint of the working depthintersect. (ANSI/AGMA 2009--B01)

5.1.10 Gear form filter cutoff, gThe wavelength at which either involute profile orhelix measurement data are segregated by the lowpass filter, thereby including only longer wavelengthdeviations. (ANSI/AGMA 2015--1--A01)

This filter cutoff should be stated in terms of roll pathlength.

5.1.11 Roll path length

The linear distance along a base tangent line from itsintersection with the base circle to the given point onthe involute curve in the transverse plane, see 4.6.11and figure 47.

NOTE: Roll path length is an alternative to roll angle forspecification of selected diameter positions on an invo-lute profile.

5.1.12 Start of tip break

Minimum specified diameter at which the tip breakcan occur. (ANSI/AGMA 2015--1--A01)

5.1.13 Transmission error

The deviation of the position of the driven gear, for agiven angular position of the driving gear, from theposition that the driven gear would occupy if thegears were geometrically perfect. (ANSI/AGMA2015--1--A01)

5.1.14 Adjusted number of teeth, Ni

This number represents an editorial device fortabular convenience to allow use of spur gear tablesin a regular progression for an infinite combination ofhelical gears (see AGMA 2000--A88)

Ni = Ncos (12)5.1.15 Probe path

The path on a tooth by the measuring probe of agenerative profile or other similar inspection appara-tus.

5.2 Reference surfaces

5.2.1 Datum surface

Datum surface is a surface used as the basis formeasurements. The datum surface is establishedby the specific measuring device used. (ANSI/AGMA 2015--1--A01)

5.2.2 Indicated surface

Indicated surface is that surface from which thevariations from a datum surface are measured.(ANSI/AGMA 2015--1--A01)



5.2.3 Mounting surface

Mounting surface is a surface used to locate andsupport a gear in its final application. Usually, at leastone axial and one radial surface are involved.Preferably, these same surfaces should be used formanufacturing and inspection operations. (ANSI/AGMA 2015--1--A01)

5.2.4 Tip or edge break

Break (corner radius) refers to a rounding orchamfering of the edges formed by the intersectionof the tooth flank and the end or top surface of a geartooth.

5.3 Composite action terms

5.3.1 Master gear

Master gear is a gear of known quality and geometry,used to perform a composite action test.

5.3.2 Single flank measurements

For a description of the application of AGMA singleflank measurements, refer to ANSI/AGMA2015--1--A01.

5.3.2.1 Single flank composite test

A test of transmission error, performed where matinggears are rolled together, at their proper centerdistance, with backlash, and with only the driving anddriven flanks in contact. Deviations are measured interms of angular displacement and converted tolinear displacement at the pitch radius.

5.3.2.2 Single flank composite deviation,tooth--to--tooth (filtered), fis

The value of the greatest single flank compositedeviation over any one pitch (360/z), after removal ofthe long term component (sinusoidal effect ofeccentricity), during a single flank composite test,when the gear is moved through one revolution.

5.3.2.3 Single flank composite deviation, total,Fis

The maximum measured transmission error range,during a single flank composite test, when the gear ismoved through one revolution.

5.3.3 Composite (double flank) action

Composite (double flank) action is the variation incenter distance when two gears are rolled in tightmesh during a composite action test.

NOTE: ANSI/AGMA 2015--2--AXX will replace AGMA2000--A88.

5.3.3.1 Composite action test (double flank)

Composite action test (double flank) is a method ofinspection in which the work gear is rolled in tightdouble flank contact with a master gear or a specifiedgear, in order to determine (radial) compositevariations (deviations). The composite action testmust be made on a variable center distancecomposite action test device, see figure 95.

Work gear

Master gear

W

Dialindicator

Figure 95 -- Schematic of composite action test

5.3.3.2 Tooth--to--tooth radial compositedeviation (double flank), Vq, fid

Tooth--to--tooth radial composite deviation (doubleflank) is the greatest change in center distance whilethe gear being tested is rotated through any angle of360 degree/z during double flank composite actiontest, see figure 96.

5.3.3.3 Tooth--to--tooth radial compositetolerance (double flank), VqT, fidT

Tooth--to--tooth radial composite tolerance (doubleflank) is the permissible amount of tooth--to--toothradial composite deviation.

5.3.3.4 Total radial composite deviation (doubleflank), Vcq, Fid

Total radial composite deviation (double flank) is thetotal change in center distance while the gear beingtested is rotated one complete revolution during adouble flank composite action test, see figure 96.

5.3.3.5 Total radial composite tolerance (doubleflank), VcqT, FidT

Total radial composite tolerance (double flank) is thepermissible amount of total radial compositedeviation.



1 Revolution (360) of work gear

Total radialcompositedeviation

360/z

Maximumtooth--to--tooth

radialcompositedeviation

Figure 96 -- Total composite variation trace

5.3.3.6 Test radius, Rr

The test radius is a number used as an arithmeticconvention established to simplify the determinationof the proper test distance between a master and awork gear for a composite action test. It is used as ameasure of the effective size of a gear. The testradius of the master, plus the test radius of the workgear is the set up center distance on a compositeaction test device. Test radius is not the same as theoperating pitch radii of two tightly meshing gearsunless both are perfect and to basic or standardtooth thickness.

5.3.3.7 Test radius limits

The test radius limits define the allowable range oftest radii that takes into account tooth thickness andtotal composite variations.

5.4 Index of teeth

5.4.1 Index deviation

The displacement of any tooth flank from its theoreti-cal position, relative to a datum tooth flank, see figure97. (ANSI/AGMA 2015--1--A01)

Indexdeviation

theoreticalactual

pt

+fpt

k pt

Figure 97 -- Pitch deviations



Distinction is made as to the direction and algebraicsign of this reading. A condition wherein the actualtooth flank position was nearer to the datum toothflank, in the specified measuring path direction(clockwise or counterclockwise), than the theoreticalposition would be considered a minus (--) deviation.A condition wherein the actual tooth flank positionwas farther from the datum tooth flank, in thespecified measuring path direction, than the theoret-ical position would be considered a plus (+) devi-ation. (ANSI/AGMA 2015--1--A01)

ANSI/AGMA 2015--1--A01 specifies direction oftolerancing for index deviation to be along the arc ofthe tolerance diameter circle within the transverseplane.

5.4.2 Cumulative pitch deviation, total, Fp

The largest algebraic difference between the indexdeviation values for a specified flank. (ANSI/AGMA2015--1--A01)

Distinction is not made as to the direction oralgebraic sign of this reading.

ANSI/AGMA 2015--1--A01 specifies direction oftolerancing for total cumulative pitch deviation to bealong the arc of the tolerance diameter circle withinthe transverse plane.

5.4.3 Spacing

The term spacing is used as a general term toreference the accuracy with which teeth are posi-tioned around the gear. Spacing has no numericalvalue and refers only to a group of numericallyvalued tooth position measurements such as pitch orindex.

5.4.4 Spacing variation, Vs

Spacing variation is the difference between any two(2) adjacent measurements of pitch as obtained by atwo probe device, see figure 98, or is equal to thedifference between two (2) adjacent pitch variationvalues obtained from a single probe device.

5.5 Pitch of teeth

5.5.1 Pitch range

Pitch range is the difference between the longestand the shortest pitches on a gear.

5.5.2 True position pitch, pm

True position pitch is the circumference of the datumcircle divided by the number of teeth. This can bedetermined by the average of all pitch measure-ments of the entire gear taken on successive pairs of

teeth, or between corresponding points of adjacentteeth generated by an angular positioning device.

Datumcircle

Figure 98 -- Schematic of pitch measurement,two probe device

5.5.3 Pitch variation, Vp

Pitch variation is the algebraic plus or minus (+ or --)difference in the transverse plane, between the trueposition pitch and an actual pitch measurement. Ifpitch is measured in a plane other than the trans-verse plane, a correction using the appropriate helixangle must be applied to the measured value, seefigures 99 and 100.

Dashed lines representtheoretical location

--Vp

Trueposition

pitch

Circularpitch, p

+Vp

Figure 99 -- Pitch variation (plus and minus)

5.5.4 Allowable pitch variation, VpA

Allowable pitch variation is the maximum allowableamount of pitch variation. It is the permissible plus orminus variation from the true position pitch and it isthe amount shown in the tolerance tables or formulasof AGMA 2000--A88.

5.5.5 Normal pitch variation, Vpn

Normal pitch variation is the plus or minus pitchmeasured in the normal plane.



Sector of three pitches

+Vp

Vap--Vp

Tooth number

Inde

xva

riatio

n,V

x

+

0

--

1 2 3 4 5 6 7 8 9 10

Vap3

Figure 100 -- Accumulated pitch variation

5.5.6 Total accumulated pitch variation, Vap

Total accumulated pitch variation is equal to thealgebraic difference between the maximum andminimum values obtained from the summation ofsuccessive values of pitch variation and is the sameas total index variation, see figure 100.

5.5.7 Total accumulated pitch variationtolerance

Total accumulated pitch variation tolerance is thepermissible amount of total accumulated pitchvariation.

5.5.8 Total accumulated pitch variation, within asector of k pitches, Vapk

Total accumulated pitch variation, within a sector of kpitches is equal to the algebraic sum of individualplus or minus adjacent pitch variations within thatsector. The total accumulated pitch variation within aSector of three (k = 3) pitches is shown in figure 100.

5.5.9 Single pitch deviation, fpt

The displacement of any tooth flank from its theoreti-cal position relative to the corresponding flank of anadjacent tooth, see figure 97. (ANSI/AGMA2015--1--A01)

Distinction is made as to the algebraic sign of thisreading. Thus, a condition wherein the actual toothflank position was nearer to the adjacent tooth flankthan the theoretical position would be considered aminus (--) deviation. A condition wherein the actualtooth flank position was farther from the adjacenttooth flank than the theoretical position would beconsidered a plus (+) deviation.

ANSI/AGMA 2015--1--A01 specifies tolerancing di-rection of measurement for single pitch deviation to

be along the arc of the tolerance diameter circlewithin the transverse plane.

5.6 Runout of teeth

5.

1012-g05 gear nomenclature, definition of terms

Documents

definitions of terms

gear pairs

gear teeth

american nationalstandard

index of terms

geometric definitions

inspection definitions

ansi board of standards