1012-G05 Gear Nomenclature, Definition of Terms

ANSI/AGMA 1012- G05 [Revision of ANSI/AGMA 1012--F90]

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012- G05

Gear Nomenclature, Definition of Terms with Symbols

American National Standard

Gear Nomenclature, Definitions of Terms with Symbols ANSI/AGMA 1012--G05 [Revision of ANSI/AGMA 1012--F90] Approval of an American National Standard requires verification by ANSI that the requirements for due process, consensus, and other criteria for approval have been met by the standards 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 unanimity. Consensus requires that all views and objections be considered, and that a concerted effort be made toward their resolution. The use of American National Standards is completely voluntary; their existence does not in any respect preclude anyone, whether he has approved the standards or not, from manufacturing, marketing, purchasing, or using products, processes, or procedures not conforming to the standards. The American National Standards Institute does not develop standards and will in no circumstances give an interpretation of any American National Standard. Moreover, no person shall have the right or authority to issue an interpretation of an American National Standard in the name of the American National Standards Institute. Requests for interpretation of this standard should be addressed to the American Gear Manufacturers Association. CAUTION NOTICE: AGMA technical publications are subject to constant improvement, revision, or withdrawal as dictated by experience. Any person who refers to any AGMA technical publication should be sure that the publication is the latest available from the Association on the subject matter. [Tables or other self--supporting sections may be referenced. Citations should read: See ANSI/AGMA 1012--G05, Gear Nomenclature, Definitions of Terms with Symbols, published by the American Gear Manufacturers Association, 500 Montgomery Street, Suite 350, 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 Association 500 Montgomery Street, Suite 350, Alexandria, Virginia 22314 Copyright © 2005 by American Gear Manufacturers Association All rights reserved. No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without prior written permission of the publisher.

Printed in the United States of America ISBN: 1--55589--846--7

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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 B C

Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Glossary of trade terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Terms and symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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Foreword [The foreword, footnotes and annexes, if any, in this document are provided for informational purposes only and are not to be construed as a part of ANSI/AGMA 1012--G05, Gear Nomenclature, Definitions of Terms with Symbols.] In 1926 the AGMA adopted a recommended practice for gearing nomenclature, terms and definitions. It included some symbols and abbreviations. A complete revision of terms and definitions by the AGMA Nomenclature Committee was issued as AGMA 112.02 in October, 1948. This later became AGMA 112.03, and American Standard B6.10--1954, with ASME as a co--sponsor. A separate project dealing with Letter Symbols for Gear Engineering appeared in 1943 as AGMA 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--1950 Abbreviations for Use on Drawings, and it was, therefore, unnecessary to process gearing abbreviations as a separate American Standard. The number of abbreviations used in gearing has intentionally been kept very small to permit memorizing without the need to refer to the standard. AGMA Standard 112.04, Gear Nomenclature (Geometry) Terms, Definitions, Symbols and Abbreviations, was a complete revision and integration of the three standards previously mentioned. Because of the widespread acceptance of the previous standards, changes were kept to a minimum. The standard in this form was approved by the AGMA Membership on April 25, 1965. AGMA 112.05 included several revisions to keep it abreast of the then current gearing techniques. It was approved by Standards Committee B6, Gears, the Co--Secretariats and the American National Standards Institute on February 3, 1976 and designated ANSI B6.14--1976. ANSI/AGMA 1012--F90 was a revision of 112.05. This revision incorporated the terms from AGMA Standard 116.01 (Oct., 1972), Glossary of Terms Used in Gearing, and terms from ANSI/AGMA 2000--A88, Gear Classification and Inspection Handbook, Tolerances and Measuring Methods for Unassembled Spur and Helical Gears (Including Metric Equivalents). In addition, terms which started to be commonly used in gear load rating were introduced in the annex. ANSI/AGMA 1012--G05 is a revision that updates the style of presentation, reordered the sequence of some terms, added definitions for right and left flank, and modified annexes B and C. The first draft of ANSI/AGMA 1012--G05 was made in June 2002. It was approved by the AGMA membership in July, 2005. It was approved as an American National Standard on September 29, 2005. Suggestions for improvement of this standard will be welcome. They should be sent to the American Gear Manufacturers Association, 500 Montgomery Street, Suite 350, Alexandria, Virginia 22314.

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PERSONNEL of the AGMA Nomenclature Committee Chairman: Dwight Smith . . . . . . . . . . . . . . . . . Cole Manufacturing Systems

ACTIVE MEMBERS M.R. Chaplin . . . . . . . . . . . . . . . . . . . . . . . . . . . . R.L. Errichello . . . . . . . . . . . . . . . . . . . . . . . . . . . O.A. LaBath . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Miller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.M. Rinaldo . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contour Hardening, Inc. GEARTECH Gear Consulting Services of Cincinnati, LLC CST Cincinnati Atlas Copco Comptec, Inc.

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American National Standard --

Gear Nomenclature, Definitions of Terms with Symbols

ANSI/AGMA 1012--G05

3.2 Symbols The purpose of standard symbols for gear engineering is to establish a uniform practice in mathematical notation for equations and formulas dealing with toothed gearing. Such equations and corresponding calculations may be used in connection with design, application, manufacture, inspection, new methods, and new problems. NOTE: The symbols and definitions used in this standard may differ from other AGMA standards. The user should not assume that familiar symbols can be used without a careful study of these definitions.

1 Scope This standard establishes the definitions of terms, symbols and abbreviations which may be used to communicate the technology and specifications of external and internal gear teeth. It provides definitive meanings by the use of words and illustrations, for commonly used gearing terms.

SI (metric) units of measure, where applicable, are shown in the text. Where equations require a different format or constant for use with SI units, the primary equation has an (M) appended and the secondary expression is shown after the first, indented. Example: d=zm D= N Pd

2 Normative references The following documents contain provisions which, through reference in this text, constitute provisions of the standard. At the time of publication, the editions were valid. All publications are subject to revision, and the users of this standard are encouraged to investigate the possibility of applying the most recent editions 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 for use in all AGMA documents and is summarized in the index. Many terms are listed in the index more than once by restating alphabetically with rearranged key words, to aid user look--up of related terms.

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(2M) (2)

Symbols must be distinguished from abbreviations which are shortened forms of words often used on drawings and in tables, but not suitable for mathematical work (see annex A). For example, the symbol for circular pitch is p, whereas the abbreviation is CP. AGMA is changing to use symbols consistent with symbols used by ISO. In the definition titles, where the old AGMA symbol is still commonly used but differs from the ISO symbol, both symbols are listed with the ISO symbol at the end of the line. Annex C contains an alphabetical list of the old symbols with the new symbols also listed. 3.2.1 Subscripts A subscript following the general symbol may be used to indicate a value applying to a particular gear or tool, or a value taken at a particular position or in a particular direction. For convenience and brevity, it is desirable to use a general symbol without a subscript when only one value of a given kind is involved. Thus, in a spur gear or a straight--tooth bevel gear, there is occasion to consider only one cross section of the teeth, namely, the transverse

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section, and it is convenient and natural to refer, for instance, simply to the circular pitch, p, and the pressure angle, φ. In the case of gears with oblique teeth, on the other hand, it is usually necessary to be specific and to refer to the transverse pitch, pt, and the transverse pressure angle, φt, in order not to leave any doubt as to whether values are being given for the transverse plane or normal plane.

AMERICAN NATIONAL STANDARD

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

Pinion

3.2.2 Typography In accordance with the usual practice in published text, symbols, whether upper or lower case, should be printed in serif italic font. This is done to avoid confusion in reading the symbols and to make a distinction between upper and lower case. An exception 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 in vertical Arabic numerals. Abbreviations should always be printed vertical and are not recommended for use in formulas. Trigonometric functions should be printed in lower case vertical type. Standard mathematical notation should be followed.

4 Geometric definitions There is an old Chinese proverb that states: The beginning of wisdom is to call things by their right names. Unfortunately, gearing terms and meanings vary in different offices, shops, textbooks, and among gear authorities. To obtain related continuity, the terms have been grouped in what may be called a textbook arrangement in preference to alphabetical order. Many of the definitions have been written in a way that makes them depend on one another, as a logical series. This arrangement leads to a more comprehensive understanding of the concepts and geometrical relations. 4.1 General designations 4.1.1 Gears Gears are machine elements that transmit motion by means of successively engaging teeth, see figure 1. 4.1.2 Gear (wheel) A gear (wheel) is a machine part with gear teeth. Of two gears that run together, the one with the larger

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Gear (wheel)

Rack

Figure 1 -- Gears 4.1.3 Pinion A pinion is a machine part with gear teeth. Of two gears that run together, the one with the smaller number 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 of screw threads, see figures 2 and 9.

Figure 2 -- Worm 4.1.5 Rack A rack is a gear with teeth spaced along a straight line, and suitable for straight line motion. It can be regarded 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 is a basic rack (see 4.7.1). This basic rack is the profile of the conjugate gear of infinite pitch radius, see figure 3.

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ANSI/AGMA 1012--G05

4.2.2 Internal gear

Profile angle

An internal gear is one with the teeth formed on the inner surface of a cylinder or cone. For bevel gears, an internal gear is one with the pitch angle exceeding 90°, see figure 4. An internal gear can be meshed only with an external pinion. 4.2.3 Parallel axis gears Figure 3 -- Basic rack in normal plane

Gears which operate on parallel axes. External helical gears on parallel axes have helices of opposite hands, see figure 5. If one of the members is an internal gear, the helices are of the same hand.

4.1.7 Generating rack A generating rack is a rack outline used to indicate tooth details and dimensions for the design of a generating tool, such as a hob or a gear shaper cutter.

Left hand

4.1.8 Number of teeth or threads, N, z Number of teeth or threads is the number of teeth contained in the whole circumference of the pitch circle. 4.1.9 Gear ratio, mG, u Gear ratio is the ratio of the larger to the smaller number of teeth in a pair of gears. z u = z2

(1M)

Right hand Figure 5 -- Parallel helical gears

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4.2.3.1 Spur gear

N mG = G NP

(1)

4.2 Kinds of gears

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

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

Pinion

Gear External gear

Internal gear

Rack External bevel gear

Internal bevel gear

Figure 4 -- External and internal gears

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Figure 6 -- Spur gears

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4.2.3.2 Spur rack A spur rack has a planar pitch surface and straight teeth that are at right angles to the direction of motion, see figure 6. 4.2.3.3 Helical gear A helical gear has a cylindrical pitch surface and teeth that are helical, see figure 7. 4.2.3.4 Helical rack

Single helical gears

Double helical gears

Herringbone gears

Figure 8 -- Single and double helical

A helical rack has a planar pitch surface and teeth that are oblique to the direction of motion, see figure 7.

4.2.4 Wormgearing Wormgearing includes worms and their mating gears. The axes are usually at right angles, see figure 9. Cylindrical worm

Helical gear

Helical rack

Figure 7 -- Helical gear and rack 4.2.3.5 Single helical gears Single helical gears have teeth of only one hand on each gear, see figure 8. 4.2.3.6 Double helical gears Double helical gears have teeth of both right hand and left hand on each gear. The teeth are separated by a gap between the helices. Where there is no gap, they are known as herringbone, see figure 8. 4.2.3.7 Herringbone gears Herringbone gears have teeth of both right hand and left hand on each gear. The teeth are continuous without a gap between the helices, see figure 8.

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Enveloping wormgear

Cylindrical (non--enveloping) wormgear

Figure 9 -- Wormgearing 4.2.4.1 Wormgear (wormwheel) A wormgear (wormwheel) is the mate to a worm. A wormgear that is completely conjugate to its worm has line contact and is said to be enveloping, see figure 9. It is usually cut by a tool that is geometrically similar to the worm. An involute spur gear or helical gear used with a cylindrical worm has only point contact. 4.2.4.2 Cylindrical worm A cylindrical worm has one or more teeth in the form of screw threads on a cylinder, see figures 2 and 9. 4.2.4.3 Enveloping (hourglass) worm An enveloping (hourglass) worm has one or more teeth and increases in diameter from its middle

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ANSI/AGMA 1012--G05

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

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 combination with a spur, helical, or conical pinion. A face gear has a planar pitch surface and a planar root surface, both of which are perpendicular to the axis of rotation, see figure 12. Figure 10 -- Double--enveloping wormgearing Offset

4.2.4.4 Double--enveloping wormgearing Double--enveloping wormgearing comprises enveloping (hourglass) worms mated with fully enveloping wormgears, see figure 10. Also known as globoidal wormgearing. Pinion on center

Pinion off center

4.2.5 Crossed axis gears Crossed axis gears are gears which operate on non--parallel axes. Figure 12 -- Face gears 4.2.5.1 Crossed helical gears 4.2.5.4 Bevel gears Gears that operate non--parallel axes.

on

non--intersecting,

The term crossed helical gears has superseded the term spiral gears. There is theoretically point contact between the teeth at any instant. They have teeth of the same or different helix angles, of the same or opposite hand. A combination of spur and helical or other types can operate on crossed axes, see figure 11.

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Bevel gears have conical pitch surfaces operating on intersecting or non--intersecting axes, see figure 13. Bevel gears that operate on non--intersecting axes are known as hypoid gears, see 4.2.5.12. When “bevel gears” is used as a general term, it covers straight, spiral, zerol, skew bevel and hypoid gears. Practically all bevel gears have spiral teeth that are curved and oblique. The axes may be at right angles or otherwise. The tooth surfaces of a bevel gear and

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

Shaft angle greater or less than 90°

4.2.5.5 Miter gears Miter gears are mating bevel gears with equal numbers of teeth and with axes at right angle, see figure 13.

Pinion

Figure 14 -- Angular bevel gears

90°

Gear Bevel gears

Figure 15 -- Crown gear 4.2.5.8 Straight bevel gears

45_ 45_ 90_

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

Miter gears

Figure 13 -- Bevel gears

4.2.5.6 Angular bevel gears Angular bevel gears are bevel gears in which the axes are not at right angles, see figure 14. 4.2.5.7 Crown gear A crown gear is a bevel gear with a planar pitch surface. The crown gear is analogous to the basic rack in spur gears, see figure 15.

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Straight bevel gears

Skew bevel gears

Figure 16 -- Straight and skewed bevel 4.2.5.9 Skew bevel gears Skew bevel gears are those for which the corresponding crown gear has teeth that are straight and oblique, see figure 16. 4.2.5.10 Spiral bevel gears Spiral bevel gears have teeth that are curved and oblique, see figure 17.

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AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05 Pitch plane

Spiral bevel gears

Zerol bevel gears

Transverse plane Pitch cylinder

Figure 17 -- Spiral bevel and zerol 4.2.5.11 Zerol bevel gears Zerol bevel gears have teeth that are curved but in the same general direction as straight teeth. They are spiral bevel gears of zero spiral angle, see figure 17.

Plane of axes

Figure 19 -- Principal reference planes

4.2.5.12 Hypoid gears

4.3.3 Pitch plane

Hypoid gears are similar in general form to bevel gears, but operate on non--intersecting axes, see figure 18.

The pitch plane of a pair of gears is the plane perpendicular to the axial plane and tangent to the pitch surfaces. A pitch plane in an individual gear may be any plane tangent to its pitch surface, see figure 19 and 4.5.1.

Offset

The pitch plane of a rack or in a crown gear is the imaginary planar surface that rolls without slipping with a pitch cylinder or pitch cone of another gear. The pitch plane of a rack or crown gear is also the pitch surface, see figures 20 and 25.

Figure 18 -- Hypoid gears 4.2.5.13 Other trade name gears It is beyond the scope of this standard to define all trade name kinds of gears, see annex B. 4.3 Principal planes

Pitch plane of cylindrical gears

4.3.1 Axial plane An axial plane may be any plane containing the gear axis and a given point, see figure 19. 4.3.2 Plane of axes The plane of axes is the plane that contains the two axes for parallel or intersecting axis gears, see figure 19.

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Pitch plane of rack

Pitch plane of crown gear

Figure 20 -- Pitch plane of gears

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4.3.4 Plane of rotation

4.3.6 Transverse plane

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

A transverse plane is perpendicular to the axial plane and 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 pitch point, and perpendicular to the pitch plane. In a helical rack, a normal plane is normal to all the teeth it intersects. In a helical gear, however, a plane can be normal to only one tooth at a point lying in the plane surface. At such a point, the normal plane contains the line normal to the tooth surface, see figure 22.

Spur gear

Bevel gear

Plane of rotation

Important positions of a normal plane in tooth measurement and tool design of helical teeth and worm threads are: Transverse plane

Figure 21 -- Planes of rotation

(1) the plane normal to the pitch helix at side of tooth; (2) the plane normal to the pitch helix at center of tooth; (3) the plane normal to the pitch helix at center of space between two teeth

4.3.5 Tangent plane A tangent plane is tangent to the tooth surfaces at a point or line contact.

Normal plane

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

Transverse planes

Pitch plane

Line normal to tooth surface in normal plane

Pitch point

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

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AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

4.3.8 Central plane

4.4.2 Transverse direction

The central plane of a wormgear is perpendicular to the gear axis and contains the common perpendicular of the gear and worm axes. In the usual case with axes at right angles, it contains the worm axis, see figure 23.

The transverse direction is a direction within a transverse plane, see figure 24. 4.4.3 Normal direction The normal direction is a direction within a normal plane, see figure 24. 4.5 Surfaces and dimensions

Central plane

The pitch surface definitions are for gears having their ratio of angular velocities constant, and axes either parallel or intersecting, and, therefore, do not include crossed helical gears, wormgearing, hypoid gears, or offset face gears. 4.5.1 Pitch surfaces Pitch surfaces are the imaginary planes, cylinders, or cones that roll together without slipping. For a constant velocity ratio, the pitch cylinders and pitch cones are circular, see figures 25 and 26.

Cylindrical pitch surfaces

Figure 23 -- Central plane 4.4 Principal directions These are directions in the pitch plane, and correspond 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.

Rack pitch surface

Figure 25 -- Pitch surfaces

Transverse direction Normal direction

Axial direction

Direction of tooth

Figure 24 -- Principal directions

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Figure 26 -- Pitch cones

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4.5.3 Cylindrical gear terms (surfaces and dimensions)

4.5.1.1 Equivalent pitch radius Equivalent pitch radius is the radius of the pitch circle in a cross section of gear teeth in any plane other than a plane of rotation. It is properly the radius of curvature of the pitch surface in the given cross section. Examples of such sections are the transverse section of bevel gear teeth and the normal section of helical teeth, see figure 27.

4.5.3.1 Pitch cylinder A pitch cylinder is the imaginary cylinder in a spur or helical gear that rolls without slipping on a pitch plane or pitch cylinder of another gear, see figure 25. 4.5.3.1.1 Pitch circle (operating) A pitch circle (operating) is the curve of intersection of a pitch surface of revolution and a plane of rotation. It is the imaginary circle that rolls without slipping with a pitch circle of a mating gear, see figure 28.

Equivalent pitch radius (equals back cone distance)

Bevel gear

4.5.3.1.2 Pitch line The pitch line corresponds, in the cross section of a rack, to the pitch circle (operating) in the cross section of a gear, see figure 28. 4.5.3.1.3 Pitch point

Figure 27 -- Back cone equivalent

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

4.5.1.2 Equivalent number of teeth, Ne

4.5.3.2 Line of centers

Equivalent number of teeth is the number of teeth contained in the whole circumference of a pitch circle corresponding to an equivalent pitch radius.

The line of centers connects the centers of the pitch circles of two engaging gears; it is also the common perpendicular of the axes in crossed helical gears and wormgears. When one of the gears is a rack, the line of centers is perpendicular to its pitch line, see figure 28.

4.5.2 Gear center A gear center is the center of the pitch circle, see figure 28.

Line of centers

4.5.3.3 Outside (tip or addendum) cylinder The outside (tip or addendum) cylinder is the surface that coincides with the tops of the teeth of an external cylindrical gear, see figure 29. Outside cylinder

Pitch point

Pitch circle

Gear center

Pitch line Root cylinder

Figure 28 -- Pitch circles and line

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Figure 29 -- Cylindrical surfaces

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AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

4.5.3.3.2 Top land

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 the diameter of the crown circle, see figure 36. In a throated wormgear it is the maximum diameter of the blank, see figure 31. The term applies to external gears (for internal gears, see 4.5.3.5).

Top land is the surface of the top of a tooth, see figure 32.

Top land

Bottom land Outside diameter

Figure 32 -- Tooth lands Pitch diameter

4.5.3.4 Inside cylinder The inside cylinder is the surface that coincides with the tops of the teeth of an internal cylindrical gear, see figure 33. Root diameter

4.5.3.5 Inside diameter, Di Inside diameter is the diameter of the addendum circle of an internal gear, see figure 33.

Figure 30 -- Diameters, external gears

Root circle

Root diameter

Gear throat form radius Inside diameter Throat diameter Addendum circle

Figure 33 -- Diameters, internal gear 4.5.3.6 Root cylinder Outside diameter

The root cylinder is the imaginary surface that coincides with the the bottoms of the tooth spaces in a cylindrical gear. 4.5.3.6.1 Root circle

Figure 31 -- Wormgear diameters

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

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AMERICAN NATIONAL STANDARD Working depth

Addendum circle

Root circle

Addendum

Dedendum Clearance

Figure 34 -- Root circle

Whole depth

Figure 35 -- Principal dimensions

4.5.3.6.2 Root diameter, DR, df Root diameter is the diameter of the root circle, see figures 30 and 33. 4.5.3.6.3 Bottom land Bottom land is the surface at the bottom of a tooth space adjoining the fillet, see figure 32. 4.5.3.7 Standard (reference) pitch circle The circle which intersects the involute at the point where the pressure angle is equal to the profile angle of the basic rack. 4.5.3.7.1 Standard reference pitch diameter, D, d The standard reference pitch diameter is the diameter of the standard pitch circle. In spur and helical gears, unless otherwise specified, the standard pitch diameter is related to the number of teeth and the standard transverse pitch. It is obtained as: zp mn d=zm= π =z cos β Np N D= N = π = Pd P nd cos ψ

(2M)

4.5.3.10 Dedendum, b, hf Dedendum is the depth of a tooth space below the standard (reference) pitch circle or pitch line; also, the radial distance between the pitch circle and the root circle, see figure 35. 4.5.4 Crossed axis gear terms (surfaces and dimensions) 4.5.4.1 Pitch cone A pitch cone is the imaginary cone in a bevel gear that rolls without slipping on a pitch surface of another gear, see figure 26. 4.5.4.2 Face (tip) cone The face (tip) cone is the imaginary surface that coincides with the tops of the teeth of a bevel or hypoid gear, see figure 36.

(2)

4.5.3.8 Addendum circle

Face cone

Back cone

The addendum circle coincides with the tops of the teeth and is concentric with the standard (reference) pitch circle and radially distant from it by the amount of the addendum, see figures 33 and 34. For external gears, the addendum circle lies on the outside cylinder while on internal gears the addendum circle lies on the internal cylinder.

Front cone

4.5.3.9 Addendum, a, ha Addendum is the height by which a tooth projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line; also, the radial distance between the pitch circle and the addendum circle, see figure 35.

12

Root cone

Crown circle

Figure 36 -- Conical surfaces

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ANSI/AGMA 1012--G05

4.5.4.3 Root cone

4.5.4.6 Front angle

The root cone is the imaginary surface that coincides with the bottoms of the tooth spaces in a bevel or hypoid gear, see figure 36.

Front angle, in a bevel gear, is the angle between an element of the front cone and a plane of rotation, and usually equals the pitch angle, see figure 37. 4.5.4.7 Crown circle

4.5.4.4 Back cone The back cone of a bevel or hypoid gear is an imaginary cone tangent to the outer ends of the teeth, with its elements perpendicular to those of the pitch cone. The surface of the gear blank at the outer ends of the teeth is customarily formed to such a back cone, see figure 36. 4.5.4.4.1 Back cone distance

The crown circle in a bevel or hypoid gear is the circle of intersection of the back cone and face cone, see figure 36. 4.5.4.8 Apex to back Apex to back, in a bevel gear or hypoid gear, is the distance in the direction of the axis from the apex of the pitch cone to a locating surface at the back of the blank, see figures 37 and 38.

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

Mounting distance

Mounting distance

Back angle Front angle Crossing point Cone distance

Back cone distance

Apex to back Hypoid Gear and Pinion

Figure 38 -- Mounting distance 4.5.4.9 Mounting distance Apex of pitch cone Apex to back

Figure 37 -- Apex to back

Mounting distance, for assembling bevel gears or hypoid gears, is the distance from the crossing point of the axes to a locating surface of a gear, which may be at either back or front, see figure 38. 4.5.4.10 Crossing point

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

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

4.5.4.5 Front cone

4.5.4.11 Throat diameter, dt

4.5.4.4.2 Back angle

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

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Throat diameter is the diameter of the addendum circle at the central plane of a wormgear or of a double--enveloping wormgear, see figure 31. 4.5.4.12 Throat form radius, rt Throat form radius is the radius of the throat of an enveloping wormgear or of a double--enveloping worm, in an axial plane, see figure 31.

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4.6 Terms related to gear teeth

4.6.2.2 Base radius

4.6.1 Involute teeth

Radius of a base circle.

Involute teeth of spur gears, helical gears, and worms are those in which the profile in a transverse plane (exclusive of the fillet curve) is the involute of a circle, see figure 39.

4.6.2.3 Base cylinder The base cylinder corresponds to the base circle, and is the cylinder from which involute tooth surfaces are developed, see figure 41.

Involute

Involute surface

Base cylinder Spur

Base circle

Figure 39 -- Involute teeth

Helical

Figure 41 -- Base cylinder

4.6.2 Base circle The base circle is the circle from which involute tooth profiles are derived, see figure 39. 4.6.2.1 Base diameter, Db, db Base diameter is the diameter of the base circle of an involute gear, see figure 40.

Involute

Base circle

Involute teeth

4.6.2.4 Cone® gear base diameter Cone® gear base diameter, is the diameter of the base circle in a Cone® double--enveloping wormgear. The base circle is tangent to straight line extensions of the worm tooth profiles in the central plane of the wormgear. 4.6.3 Crowned teeth Crowned teeth have surfaces modified in the lengthwise direction to produce localized contact or to prevent contact at their ends, see figure 42. Crowning can be applied to all types of teeth. 4.6.4 Pressure angle, φ, α

Base diameter

Figure 40 -- Base diameter

14

Pressure angle is in general the angle at a pitch point between the line of pressure which is normal to the tooth surface, and the plane tangent to the pitch surface. The pressure angle gives the direction of the normal to the tooth profile, see figure 43. The pressure angle is equal to the profile angle at the standard pitch circle and can be termed the “standard” pressure angle at that point.

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ANSI/AGMA 1012--G05 Crown magnitude

terms that indicate the direction of the plane in which the profile angle or the pressure angle lies, such as transverse profile angle, normal pressure angle, axial profile angle. 4.6.6 Standard profile angles In tools and gages for cutting, grinding, and gaging gear teeth, the profile angle is the angle between a cutting edge or a cutting surface, and some principal direction such as that of a shank, an axis, or a plane of rotation, see figure 43.

Figure 42 -- Crowned gear Profile angle Pressure angle

Cutting tool

Profile angle

Standard profile angles are established in connection with standard proportions of gear teeth and standard gear cutting tools. Involute gears operate together correctly after a change of center distance, and gears designed for a different center distance can be generated correctly by standard tools. A change of center distance is accomplished by changes in operating values for pitch diameter, circular pitch, diametral pitch, pressure angle, and tooth thicknesses or backlash. The same involute gear may be used under conditions that change its operating pitch diameter and pressure angle. Unless there is a good reason for doing otherwise, it is practical to consider that the pitch and the profile angle of a single gear correspond to the pitch and the profile angle of the hob or cutter used to generate its teeth, see figure 44. Profile angle

Figure 43 -- Pressure and profile angles 4.6.5 Profile angle

Standard pitch circle

Profile angle is in general the angle at a specified pitch point between a line tangent to a tooth surface and the line normal to the pitch surface (which is a radial line of a pitch circle). This definition is applicable to every type of gear for which a pitch surface can be defined. The profile angle gives the direction of the tangent to a tooth profile, see figure 43. In spur gears and straight bevel gears, tooth profiles are considered only in a transverse plane, and the general terms profile angle and pressure angle are customarily used rather than transverse profile angle and transverse pressure angle. In helical teeth, the profiles may be considered in different planes, and in specifications it is essential to use

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Figure 44 -- Standard profile angle 4.6.7 Transverse pressure angle and transverse profile angle, φt, αt Transverse pressure angle and transverse profile angle are the pressure angle and the profile angle in a transverse plane, see figure 45.

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4.6.8 Normal pressure angle and normal profile angle, φn, αn Normal pressure angle and normal profile angle are the pressure and profile angles in a normal plane of a helical or a spiral tooth, see figure 45. In a spiral bevel gear, unless otherwise specified, profile angle means normal profile angle at the mean cone distance.

ambiguous, and for this reason it is preferable to use specific designations such as transverse circular pitch, normal base pitch, axial pitch, see figure 48. Point P

Pressure angle

r A

Transverse profile angle Polar angle

Axis

Involute

θ φ B rb O

Normal profile angle

Figure 46 -- Involute polar angle Axial profile angle

Point Involute

Figure 45 -- Profile angles 4.6.9 Axial pressure angle and axial profile angle, φx, αx Axial pressure angle and axial profile angle are the pressure angle and the profile angle in an axial plane of a helical gear or a worm, or of a spiral bevel gear, see figure 45.

Roll angle

ε

Cusp

Base circle φ ε Roll angle

4.6.10 Involute polar angle, θ Involute polar angle is the angle between a radius vector to a point, P, on an involute curve and a radial line to the intersection, A, of the curve with the base circle, see figure 46. 4.6.11 Involute roll angle, ε Involute roll angle is the angle whose arc on the base circle of radius unity equals the tangent of the pressure angle at a selected point on the involute, see figure 47.

Figure 47 -- Involute roll angle Pitch

Circular pitch

4.6.12 Pitch Pitch is the distance between a point on one tooth and the corresponding point on an adjacent tooth. It is a dimension measured along a line or curve in the transverse, normal, or axial directions. The use of the single word “pitch” without qualification may be

16

Figure 48 -- Pitch

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ANSI/AGMA 1012--G05

4.6.13 Circular pitch, p Helical rack

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

Base pitch

Axis

4.6.14 Transverse circular pitch, pt Transverse circular pitch is the circular pitch in the transverse plane, see figure 49. Normal base pitch

Transverse circular pitch

Axial pitch

Figure 50 -- Base pitch relationships Base pitch

Axis Normal circular pitch

Circular pitch

Axial pitch Base pitch Base circle Base tangent

Figure 49 -- Tooth pitch

Figure 51 -- Principal pitches 4.6.15 Normal circular pitch, pn, pe

4.6.18 Base pitch, normal, pN, pbn

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

Normal base pitch in an involute helical gear is the base pitch in the normal plane. It is the normal distance between parallel helical involute surfaces on the plane of action in the normal plane, or is the length of arc on the normal base helix. It is a constant distance in any helical involute gear, see figure 50.

4.6.16 Axial pitch, px Axial pitch is linear pitch in an axial plane and in a pitch surface. In helical gears and worms, axial pitch has the same value at all diameters. In gearing of other types, axial pitch may be confined to the pitch surface and may be a circular measurement, see figures 49 and 50.

4.6.19 Diametral pitch (transverse), Pd

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

4.6.20 Normal diametral pitch, Pnd

4.6.17 Base pitch, transverse, pb, pbt

Pd cos ψ 4.6.21 Module (transverse), mt

Base pitch in an involute gear is the pitch on the base circle or along the line of action. Corresponding sides of involute gear teeth are parallel curves, and the base pitch is the constant and fundamental distance between them along a common normal in a transverse plane, see figures 50 and 51.

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Diametral pitch (transverse) is the ratio of the number of teeth to the standard pitch diameter in inches. π P d = N = 25.4 m =p D

(3)

Normal diametral pitch is the value of diametral pitch in a normal plane of a helical gear or worm. P nd =

(4)

Module (transverse) is the ratio of the pitch diameter in millimeters to the number of teeth. 25.4 mt = D z = P d

(5)

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4.6.22 Normal module, mn

Profile

Normal module is the value of the module in a normal plane of a helical gear or worm. m n = m t cos β

Tip

Transverse plane

(6)

4.6.23 Angular pitch, θN, τ

Root

Angular pitch is the angle subtended by the circular pitch, usually expressed in radians. 2π τ = 360 z degrees or z radians 4.6.24 Tooth surface (flank)

(7)

Fillet curve Tooth surface

The tooth surface (flank) forms the side of a gear tooth, see figure 52. 4.6.25 Left or right flank It is convenient to choose one face of the gear as the reference face and to mark it with the letter “I”. The other non--reference face might be termed face “II”.

Figure 52 -- Profile (spur gear) For an observer looking at the reference face, so that the tooth is seen with its tip uppermost, the right flank is on the right and the left flank is on the left. Right and left flanks are denoted by the letters “R” and “L” respectively. See figures 53 and 54.

30R

2L tip

left flank

right flank 30

1

29

2

I I is reference face 30 R = pitch No. 30, right flank 2 L = pitch No. 2, left flank Figure 53 -- Notation and numbering for external gear 30R 1L tip

left flank

right flank 2

I

29 1

30

I is reference face 1 L = pitch No. 1, left flank 30 R = pitch No. 30, right flank Figure 54 -- Notation and numbering for internal gear

18

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4.6.26 Profile A profile is one side of a tooth in a cross section between the outside circle and the root circle. Usually a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane, see figure 52.

ANSI/AGMA 1012--G05

curve has a varying radius of curvature, ρf, see figure 56. Involute

Tip relief

4.6.26.1 Tip radius, rT, ra Tip radius is the radius of the circular arc used to join a side--cutting edge and an end--cutting edge in gear cutting tools. Edge radius is an alternate term, see figure 55. Hob or tool

Figure 57 -- Tip relief 4.6.27.2 Undercut

Tip radius

Figure 55 -- Tip radius 4.6.26.2 Profile radius of curvature, ρ Profile radius of curvature is the radius of curvature of a tooth profile, usually at the pitch point or a point of contact, see figure 56. It varies continuously along the involute profile.

Undercut is a condition in generated gear teeth when any part of the fillet curve lies inside of a line drawn tangent to the working profile at its point of juncture with the fillet, see figure 58. Undercut may be deliberately introduced to facilitate finishing operations. With undercut the fillet curve intersects the working profile. Without undercut the fillet curve and the working profile have a common tangent. Working profile (involute of circle)

Profile radius of curvature

Fillet radius

Lowest point of working profile on which contact may occur UNDERCUT

Figure 56 -- Fillet radius Base circle

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

Fillet curve Tangent at lowest point of working profile

Radial line of base circle

Figure 58 -- Undercut 4.6.27 Fillet curve (root fillet) The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the bottom of the tooth space, see figure 52. 4.6.27.1 Fillet radius, rf Fillet radius is the radius of a circular arc approximating the root fillet curve. In generated teeth, the fillet

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4.6.27.3 Form diameter Form diameter is the diameter of a circle at which the trochoid (fillet curve) produced by the tooling intersects, or joins, the involute or specified profile. Although these terms are not preferred, it is also known as the true involute form diameter (TIF), start of involute diameter (SOI), or when undercut exists,

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

4.6.29 Left hand helical gear or left hand worm A left hand helical gear or left hand worm is one in which the teeth twist counterclockwise as they recede from an observer looking along the axis, see figure 60. 4.6.30 Cylindrical gear terms (related to teeth) 4.6.30.1 Helix angle, ψ, β

Start of active profile (SAP)

x≥0 y≥0

x

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

Limit diameter Profile control diameter Form diameter

Helix

y Base diameter

Tooth

Helix angle Axis

(Undercut tooth)

Figure 59 -- Form diameter Figure 61 -- Helix angle 4.6.28 Right hand helical gear or right hand worm A right hand helical gear or right hand worm is one in which the teeth twist clockwise as they recede from an observer looking along the axis, see figure 60. The designations, right hand and left hand, are the same as in the long established practice for screw threads, both external and internal.

4.6.30.2 Pitch helix The pitch helix is the intersection of the tooth surface and the pitch cylinder of a helical gear or cylindrical worm, see figure 62. Outside helix Helical tooth Pitch circle

Pitch helix Base helix angle

Two external helical gears operating on parallel axes must be of opposite hand. An internal helical gear and its pinion must be of the same hand.

Straight line element of base cylinder Base helix

Base circle

Figure 62 -- Tooth helix 4.6.30.3 Base helix Right hand helical gear

Left hand helical gear

The base helix of a helical, involute gear or involute worm lies on its base cylinder, see figure 62. 4.6.30.3.1 Base helix angle, ψb, βb Base helix angle is the helix angle on the base cylinder of involute helical teeth or threads, see figure 62.

Right hand worm

Left hand worm

Figure 60 -- Helical and worm hand

20

4.6.30.3.2 Base lead angle, λb Base lead angle is the lead angle on the base cylinder. It is the complement of the base helix angle.

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ANSI/AGMA 1012--G05 Cylinder

4.6.30.4 Normal helix A normal helix is a helix on the pitch cylinder, normal to the pitch helix, see figure 63. Axis

Pitch helix

Helix

90° Lead

Pitch cylinder

Figure 64 -- Lead

Normal helix

Lead

Figure 63 -- Normal helix Helix angle

4.6.30.5 Outside (tip or addendum) helix The outside (tip or addendum) helix is the intersection of the tooth surface and the outside cylinder of a helical gear or cylindrical worm, see figure 62. 4.6.30.5.1 Outside helix angle, ψo, βa

Lead angle

Figure 65 -- Lead angle 4.6.30.8 Face width, F, b

Outside helix angle is the helix angle on the outside cylinder. 4.6.30.5.2 Outside lead angle, λo Outside lead angle is the lead angle on the outside cylinder. It is the complement of the outside helix angle.

Face width is the length of teeth in an axial plane, see figure 66. For double helical, it does not include the gap. Face width Gap

4.6.30.6 Lead, L, pz Lead is the axial advance of a helix for one complete turn, as in the threads of cylindrical worms and the teeth of helical gears, see figure 64. z mn pz = px z = π d = π tan β sin β

(8)

Total face width

4.6.30.7 Lead angle, λ Lead angle is the angle between any helix and a plane of rotation. It is the complement of the helix angle, and is used for convenience in worms and hobs. It is understood to be at the standard pitch diameter unless otherwise specified, see figure 65.

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Effective face width

Figure 66 -- Face width

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4.6.30.9 Total face width, Ft Total face width is the actual dimension of a gear blank including the portion that exceeds the effective face width, see 4.7.11, or as in double helical gears where the total face width includes any distance or gap separating right hand and left hand helices, see figure 66.

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

Left hand Right hand

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 the outer half of a tooth is inclined in the clockwise direction from the axial plane through the midpoint of the tooth as viewed by an observer looking at the face of the gear, see figure 67.

Zerol bevel gears

Zerol bevel pinions

Left hand

Right hand

Figure 68 -- Zerol hand Left hand

4.6.31.3 Spiral angle, ψ, β

Right hand

Spiral bevel gears

Spiral bevel pinions

Spiral angle in a spiral bevel gear is the angle between the tooth trace and an element of the pitch cone, and corresponds to the helix angle in helical teeth. Unless otherwise specified, the term spiral angle is understood to be the mean spiral angle, see figures 69 and 70.

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 outer half of a tooth is inclined in the counterclockwise direction from the axial plane through the midpoint of the tooth as viewed by an observer looking at the face of the gear, see figure 67. A spiral bevel gear and pinion are always of opposite hand, including the case when the gear is internal. The designations right hand and left hand are applied similarly to spiral bevel gears, zerol bevel gears, skew bevel gears, hypoid gears, and oblique tooth face gears, see figure 68. In hypoid gear design, the pinion and gear are practically always of opposite hand, and the spiral angle of the pinion is usually larger than that of the

22

Spiral angle

Figure 69 -- Spiral angle 4.6.31.4 Mean spiral angle, ψm, βm Mean spiral angle is the specific designation for the spiral angle at the mean cone distance in a bevel gear, see figure 70. 4.6.31.5 Outer spiral angle, ψo, βe Outer spiral angle is the spiral angle of a bevel gear at the outer cone distance, see figure 70.

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ANSI/AGMA 1012--G05

4.6.31.9 Outer cone distance, Ao Tooth spiral

Mean cone distance Inner spiral angle Mean spiral angle

Outer cone distance in bevel gears is the distance from the apex of the pitch cone to the outer ends of the teeth. When not otherwise specified, the short term cone distance is understood to be outer cone distance, see figure 72.

Outer spiral angle Outer cone distance Inner cone distance

Figure 70 -- Spiral angle relationships 4.6.31.6 Inner spiral angle, ψi, βi Inner spiral angle is the spiral angle of a bevel gear at the inner cone distance, see figure 70.

Mean cone distance

4.6.31.7 Shaft angle, Σ Shaft angle is the angle between the axes of two non--parallel gear shafts. In a pair of crossed helical gears, the shaft angle lies between the oppositely rotating portions of two shafts. This applies also in the case of wormgearing. In bevel gears, the shaft angle is the sum of the two pitch angles. In hypoid gears, the shaft angle is given when starting a design, and it does not have a fixed relation to the pitch angles and spiral angles, see figure 71. Crossing point of axes

Shaft angle

Figure 72 -- Cone distance 4.6.31.10 Mean cone distance, Am Mean cone distance in bevel gears is the distance from the apex of the pitch cone to the middle of the face width, see figure 72. 4.6.31.11 Inner cone distance, Ai Inner cone distance in bevel gears is the distance from the apex of the pitch cone to the inner ends of the teeth, see figure 72. 4.6.31.12 Heel The heel of a tooth on a bevel gear or pinion is the portion of the tooth surface near its outer end, see figure 73.

Helical gears

Heel Apex of pitch cones

Toe Bevel gears

Figure 71 -- Shaft angle 4.6.31.8 Cone distance, A Cone distance in a bevel gear is the general term for the distance along an element of the pitch cone from the apex to any given position in the teeth, see figure 72.

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Bevel gear

Figure 73 -- Heel and toe

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4.6.31.13 Toe

4.6.31.17 Addendum angle, α

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

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

4.6.31.14 Pitch angle, Γ

4.6.31.18 Dedendum angle, δ

Pitch angle in bevel gears, is the angle between an element of a pitch cone and its axis. In external and internal bevel gears, the pitch angles are respectively less than and greater than 90 degrees, see figures 74 and 75.

Dedendum angle in a bevel gear, is the angle between 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 the two sides of a gear tooth, on the specified datum circle, see figure 76.

Face angle Pitch angle Root angle

Circular thickness, t

Chordal addendum

Datum circle

Axis Apex of pitch cone

Apex to back

Chordal thickness

Figure 74 -- Angle relationships Figure 76 -- Tooth thickness Face cone

4.6.32.2 Transverse circular thickness, tt, s

Root cone Pitch angle Addendum angle

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

Dedendum angle Normal circular thickness Axial thickness Axis

Transverse circular thickness

Apex of pitch cone

Figure 75 -- Angles

Helical rack tooth

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

Transverse circular thickness Axial plane

4.6.31.16 Root angle, ΓR Root angle in a bevel or hypoid gear, is the angle between an element of the root cone and its axis, see figure 74.

24

Spiral crown gear tooth Sections in pitch surfaces

Figure 77 -- Thickness relationships

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AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

4.6.32.3 Normal circular thickness, tn Normal circular thickness is the circular thickness in the normal plane. In a helical gear it may be considered 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 the tooth thickness in an axial cross section at the standard pitch diameter, see figure 77. 4.6.32.5 Base circular thickness, tb Base circular thickness in involute teeth is the length of arc on the base circle between the two involute curves forming the profile of a tooth. 4.6.32.6 Chordal thickness, normal, tnc, sc Chordal thickness is the length of the chord that subtends a circular thickness arc in the plane normal to the pitch helix. Any convenient measuring diameter may be selected, not necessarily the standard pitch diameter, see figure 78.

Circular thickness

backlash. factor, x.

See AGMA 913--A98 for profile shift

4.6.32.9 Rack shift The rack shift is the displacement of the tool datum line from the reference cylinder, made non-dimensional by dividing by the normal module. It is used to specify the tooth thickness. See AGMA 913--A98. 4.6.32.10 Measurement over pins Measurement over pins is the measurement of the distance taken over a pin positioned in a tooth space and a reference surface. The reference surface may be the reference axis of the gear, a datum surface or either one or two pins positioned in the tooth space or spaces opposite the first. This measurement is used to determine tooth thickness, see ANSI/AGMA 2002--B88 and figure 79.

Chordal addendum

Normal chordal thickness

Datum circle

Normal plane

Figure 78 -- Chordal thickness 4.6.32.7 Chordal addendum (chordal height), ac, hca Chordal addendum (chordal height) is the height from the top of the tooth to the chord subtending the circular thickness arc. Any convenient measuring diameter may be selected, not necessarily the standard pitch diameter, see figure 78. 4.6.32.8 Profile shift The profile shift is the displacement of the basic rack datum line from the reference cylinder, made non--dimensional by dividing by the normal module. It is used to specify the tooth thickness, often for zero

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Figure 79 -- Tooth thickness measurement over pins 4.6.32.11 Span measurement Span measurement is the measurement of the distance across several teeth in a normal plane. As long as the measuring device has parallel measuring surfaces that contact on an unmodified portion of the involute, the measurement will be along a line tangent to the base cylinder. It is used to determine tooth thickness, see ANSI/AGMA 2002--B88 and figure 80. 4.6.32.12 Modified addendum teeth Teeth of engaging gears, one or both of which have non--standard addendum, see AGMA 913--A98.

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see figure 81. For additional information, see AGMA 913--A98 annex B, under addendum modification.

M

4.7 Terms related to gear pairs 4.7.1 Conjugate gears Conjugate gears transmit uniform rotary motion from one shaft to another by means of gear teeth. The normals to the profiles of these teeth, at all points of contact, must pass through a fixed point in the common centerline of the two shafts. 4.7.2 Center distance (operating), C, a Figure 80 -- Span measurement 4.6.32.13 Full--depth teeth Full--depth teeth are those in which the working depth equals 2.000 divided by the normal diametral pitch.

Center distance (operating) is the shortest distance between non--intersecting axes. It is measured along the mutual perpendicular to the axes, called the line of centers. It applies to spur gears, parallel axis or crossed axis helical gears, and wormgearing, see figure 82. Center distance

4.6.32.14 Stub teeth Stub teeth are those in which the working depth is less than 2.000 divided by the normal diametral pitch. 4.6.32.15 Equal addendum teeth Equal addendum teeth are those in which two engaging gears have equal addendums, see figure 81. a

Internal External Figure 82 -- Center distance 4.7.3 Offset, E

Equal addendum teeth

Offset is the perpendicular distance between the axes of hypoid gears or offset face gears, see figures 12, 18, and 83.

Long and short addendum teeth

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

a

aP

aG

Figure 81 -- Long and short addendum 4.6.32.16 Long and short--addendum teeth Long and short addendum teeth are those in which the addendums of two engaging gears are unequal,

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4.7.4 Operating pressure angle The operating pressure angle is determined by the base circles of two gears and the center distance at which the gears operate. Various other pressure angles may also be considered in gear calculations.

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4.7.10 Backlash, B, j Backlash is the amount by which the width of a tooth space exceeds the thickness of the engaging tooth on the operating pitch circles, see figure 84. As actually indicated by measuring devices, backlash may be determined variously in the transverse, normal, or axial planes, and either in the direction of the pitch circles, or on the line of action. Such measurements may be converted to corresponding values on transverse pitch circles for general comparisons.

Offset

Operating pitch circles Hypoid gears

Figure 83 -- Offset Backlash (transverse operating)

4.7.5 Clearance, c Clearance is the distance between the root circle of a gear and the addendum circle of its mate, see figure 35. 4.7.6 Working depth, hk, hw Working depth is the depth of engagement of two gears, 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 tooth space, equal to addendum plus dedendum, also equal to working depth plus clearance, see figure 35. 4.7.8 Pitch diameter Pitch diameter is the diameter of a pitch circle, see figure 30. A bevel gear pitch diameter is understood to be at the outer ends of the teeth unless otherwise specified. 4.7.9 Operating pitch diameters, dP, dw1, and dG, dw2 Operating pitch diameters are the pitch diameters determined from the numbers of teeth and the center distance at which gears operate. Example for pinion: 2a dw = 2 a = z2 u+1 z1 + 1

 

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Figure 84 -- Backlash 4.7.10.1 Backlash, minimum Minimum backlash is the minimum transverse backlash at the operating pitch circle allowable when the gear tooth with the greatest allowable functional tooth thickness is in mesh with the pinion tooth having its greatest allowable functional tooth thickness, at the tightest allowable center distance, under static conditions, see ANSI/AGMA 2002--B88. 4.7.10.2 Backlash variation Difference between the maximum and minimum backlash occurring in a whole revolution of the larger of a pair of mating gears. 4.7.11 Effective face width, Fe For cylindrical gears, effective face width is the portion that contacts the mating teeth. One member of a pair of gears may engage only a portion of its mate, see functional face width, 5.1.6 and figure 66. For bevel gears, different definitions for effective face width are applicable. 4.8 Terms related to tooth contact in a gear pair 4.8.1 Point of contact

(9)

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

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Point of contact

4.8.4 Line of action Pitch point

The line of action is the path of action for involute gears. It is the straight line passing through the pitch point and tangent to both base circles, see figure 87. Base circle

Line of action

Path of action

Figure 85 -- Path of action Base circle

4.8.2 Line of contact A line of contact is a line or curve along which two tooth surfaces are tangent to each other, see figures 86 and 88.

Figure 87 -- Line of action 4.8.5 Surface of action

4.8.3 Path of action The path of action is the locus of successive contact points between a pair of gear teeth, during the phase of engagement. For conjugate gear teeth, the path of action passes through the pitch point. It is the trace of the surface of action in the plane of rotation, see figures 85 and 88.

The surface of action is the imaginary surface in which contact occurs between two engaging tooth surfaces. It is the summation of the paths of action in all sections of the engaging teeth. 4.8.6 Plane of action The plane of action is the surface of action for involute, parallel axis gears with either spur or helical teeth. It is tangent to the base cylinders, see figure 88.

Line of contact

Plane of action

Tangent plane Helical line of contact

Base cylinder

Figure 88 -- Plane of action Spur line of contact

Figure 86 -- Line of contact

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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

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rectangular area in the plane of action bounded by the length of action and the effective face width, see figure 89.

Zone of action

Length of action

Line of action

Face width

Line of contact Length of action

Figure 91 -- Length of action 4.8.10 Arc of action, Qt

Figure 89 -- Zone of action

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

4.8.8 Path of contact

4.8.11 Arc of approach, Qa

The path of contact is the curve on either tooth surface along which theoretical single point contact occurs during the engagement of gears with crowned tooth surfaces or gears that normally engage with only single point contact, see figure 90.

Arc of approach is the arc of the pitch circle through which a tooth profile moves from its beginning of contact until the point of contact arrives at the pitch point, see figure 92. 4.8.12 Arc of recess, Qr Arc of recess is the arc of the pitch circle through which a tooth profile moves from contact at the pitch point until contact ends, see figure 92.

Lines of contact (before surface is crowned)

Path of contact (after surface is crowned) Arc of action Points of contact (after surface is crowned)

Arc of recess

Arc of approach

Figure 90 -- Lines of contact (helical gear) 4.8.9 Length of action, Z Length of action is the distance on the line of action through which the point of contact moves during the action of the tooth profile, see figure 91.

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Direction of motion

Figure 92 -- Arc of action

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4.8.13 Contact ratio, mc, ε Contact ratio in general is the number of angular pitches through which a tooth surface rotates from the beginning to the end of contact.

Maximum addendum circle

Line of action

4.8.14 Transverse contact ratio, mp, εα Transverse contact ratio is the contact ratio in a transverse plane. It is the ratio of the angle of action to the angular pitch. For involute gears it is most directly obtained as the ratio of the length of action to the base pitch. 4.8.15 Face contact ratio, mF, εβ Face contact ratio is the contact ratio in an axial plane, or the ratio of the face width to the axial pitch. For bevel and hypoid gears it is the ratio of face advance to circular pitch.

Minimum operating center distance Base circle Limit diameter

4.8.16 Total contact ratio, mt, εγ Total contact ratio is the sum of the transverse contact ratio and the face contact ratio. εγ = εα + εβ

(10M) (10)

mt = mp + mF

4.8.17 Modified contact ratio, mo Modified contact ratio for bevel gears is the square root of the sum of the squares of the transverse and face contact ratios. m o = m 2p + m 2F

Figure 93 -- Limit diameter

0.5

(11)

4.8.18 Limit diameter Limit diameter is the diameter on a gear at which the line of action intersects the maximum (or minimum for internal pinion) addendum circle of the mating gear. This is also referred to as the start of active profile, the start of contact, the end of contact, or the end of active profile, see figures 93 and 59.

5 Inspection definitions The following definitions are used in AGMA 2000--A88, Gear Classification and Inspection Handbook, Tolerances and Measuring Methods for Unassembled Spur and Helical Gears (Including Metric Equivalents) and in ANSI/AGMA 2015--1--A01, Accuracy Classification System -Tangential Measurements for Cylindrical Gears. NOTE: ANSI/AGMA 2015--1--A01 replaces AGMA 2000--A88. For bevel and wormgear inspection nomenclature, see ANSI/AGMA 2009--B01 and ANSI/ AGMA 2011--A98 respectively.

Face advance

4.8.18 Start of active profile (SAP) The start of active profile is the intersection of the limit diameter and the involute profile, see figure 59. 4.8.19 Face advance, QF Face advance is the distance on a pitch circle through which a helical or spiral tooth moves from the position at which contact begins at one end of the tooth trace on the pitch surface to the position where contact ceases at the other end, see figure 94.

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Figure 94 -- Face advance

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5.1 Reference datum

5.1.10 Gear form filter cutoff, λg

5.1.1 Datum circle, Dc

The wavelength at which either involute profile or helix measurement data are segregated by the low pass filter, thereby including only longer wavelength deviations. (ANSI/AGMA 2015--1--A01)

A datum circle is a circle on which measurements are made. 5.1.2 Datum axis The datum axis of the gear is defined by the datum surfaces. It is the axis to which the gear details, and in particular the pitch, profile, and helix tolerances are defined. (ANSI/AGMA 2015--1--A01) 5.1.3 Datum tooth A datum tooth is the designated tooth used as the starting point for measuring other teeth.

This filter cutoff should be stated in terms of roll path length. 5.1.11 Roll path length The linear distance along a base tangent line from its intersection with the base circle to the given point on the involute curve in the transverse plane, see 4.6.11 and figure 47. NOTE: Roll path length is an alternative to roll angle for specification of selected diameter positions on an involute profile.

5.1.4 Profile control diameter

5.1.12 Start of tip break

A specified diameter of the circle beyond which the tooth profile must conform to the specified involute curve. See functional profile. (ANSI/AGMA 2015--1--A01)

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

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

5.1.13 Transmission error The deviation of the position of the driven gear, for a given angular position of the driving gear, from the position that the driven gear would occupy if the gears were geometrically perfect. (ANSI/AGMA 2015--1--A01)

5.1.6 Functional face width

5.1.14 Adjusted number of teeth, Ni

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

This number represents an editorial device for tabular convenience to allow use of spur gear tables in a regular progression for an infinite combination of helical gears (see AGMA 2000--A88)

5.1.7 Gear blank A gear blank is the work piece used for the manufacture of a gear, prior to machining the gear teeth. 5.1.8 Inspection chart An inspection chart is the generated recording or trace from an inspection machine used to display a measured variation of gear geometry.

Ni =

N cos ψ

(12)

5.1.15 Probe path The path on a tooth by the measuring probe of a generative profile or other similar inspection apparatus. 5.2 Reference surfaces 5.2.1 Datum surface

5.1.9 Tolerance diameter, dT For cylindrical gears, the diameter located one normal 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 mean cone distance and the midpoint of the working depth intersect. (ANSI/AGMA 2009--B01)

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Datum surface is a surface used as the basis for measurements. The datum surface is established by the specific measuring device used. (ANSI/ AGMA 2015--1--A01) 5.2.2 Indicated surface Indicated surface is that surface from which the variations from a datum surface are measured. (ANSI/AGMA 2015--1--A01)

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5.2.3 Mounting surface Mounting surface is a surface used to locate and support a gear in its final application. Usually, at least one axial and one radial surface are involved. Preferably, these same surfaces should be used for manufacturing and inspection operations. (ANSI/ AGMA 2015--1--A01) 5.2.4 Tip or edge break Break (corner radius) refers to a rounding or chamfering of the edges formed by the intersection of the tooth flank and the end or top surface of a gear tooth.

AMERICAN NATIONAL STANDARD NOTE: ANSI/AGMA 2015--2--AXX will replace AGMA 2000--A88.

5.3.3.1 Composite action test (double flank) Composite action test (double flank) is a method of inspection in which the work gear is rolled in tight double flank contact with a master gear or a specified gear, in order to determine (radial) composite variations (deviations). The composite action test must be made on a variable center distance composite action test device, see figure 95.

Work gear Master gear

5.3 Composite action terms 5.3.1 Master gear

Dial indicator

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 single flank measurements, refer to ANSI/AGMA 2015--1--A01. 5.3.2.1 Single flank composite test A test of transmission error, performed where mating gears are rolled together, at their proper center distance, with backlash, and with only the driving and driven flanks in contact. Deviations are measured in terms of angular displacement and converted to linear 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 composite deviation over any one pitch (360/z), after removal of the long term component (sinusoidal effect of eccentricity), 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 is moved through one revolution.

W

Figure 95 -- Schematic of composite action test 5.3.3.2 Tooth--to--tooth radial deviation (double flank), Vq, fid

composite

Tooth--to--tooth radial composite deviation (double flank) is the greatest change in center distance while the gear being tested is rotated through any angle of 360 degree/z during double flank composite action test, see figure 96. 5.3.3.3 Tooth--to--tooth radial tolerance (double flank), VqT, fidT

composite

Tooth--to--tooth radial composite tolerance (double flank) is the permissible amount of tooth--to--tooth radial composite deviation. 5.3.3.4 Total radial composite deviation (double flank), Vcq, Fid Total radial composite deviation (double flank) is the total change in center distance while the gear being tested is rotated one complete revolution during a double flank composite action test, see figure 96.

5.3.3 Composite (double flank) action

5.3.3.5 Total radial composite tolerance (double flank), VcqT, FidT

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

Total radial composite tolerance (double flank) is the permissible amount of total radial composite deviation.

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1 Revolution (360°) of work gear

Total radial composite deviation

Maximum tooth--to--tooth radial composite deviation

360°/z

Figure 96 -- Total composite variation trace

5.3.3.6 Test radius, Rr

5.3.3.7 Test radius limits

The test radius is a number used as an arithmetic convention established to simplify the determination of the proper test distance between a master and a work gear for a composite action test. It is used as a measure of the effective size of a gear. The test radius of the master, plus the test radius of the work gear is the set up center distance on a composite action test device. Test radius is not the same as the operating pitch radii of two tightly meshing gears unless both are perfect and to basic or standard tooth thickness.

The test radius limits define the allowable range of test radii that takes into account tooth thickness and total composite variations. 5.4 Index of teeth 5.4.1 Index deviation The displacement of any tooth flank from its theoretical position, relative to a datum tooth flank, see figure 97. (ANSI/AGMA 2015--1--A01)

+fpt

pt

k ⋅ pt

Index deviation

theoretical actual Figure 97 -- Pitch deviations

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Distinction is made as to the direction and algebraic sign of this reading. A condition wherein the actual tooth flank position was nearer to the datum tooth flank, in the specified measuring path direction (clockwise or counterclockwise), than the theoretical position would be considered a minus (--) deviation. A condition wherein the actual tooth flank position was farther from the datum tooth flank, in the specified measuring path direction, than the theoretical position would be considered a plus (+) deviation. (ANSI/AGMA 2015--1--A01)

AMERICAN NATIONAL STANDARD

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

Datum circle

ANSI/AGMA 2015--1--A01 specifies direction of tolerancing for index deviation to be along the arc of the tolerance diameter circle within the transverse plane. 5.4.2 Cumulative pitch deviation, total, Fp The largest algebraic difference between the index deviation values for a specified flank. (ANSI/AGMA 2015--1--A01) Distinction is not made as to the direction or algebraic sign of this reading. ANSI/AGMA 2015--1--A01 specifies direction of tolerancing for total cumulative pitch deviation to be along the arc of the tolerance diameter circle within the transverse plane. 5.4.3 Spacing The term spacing is used as a general term to reference the accuracy with which teeth are positioned around the gear. Spacing has no numerical value and refers only to a group of numerically valued tooth position measurements such as pitch or index.

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 true position pitch and an actual pitch measurement. If pitch is measured in a plane other than the transverse plane, a correction using the appropriate helix angle must be applied to the measured value, see figures 99 and 100. +Vp --Vp

Circular pitch, p

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

True position pitch

Dashed lines represent theoretical location

Figure 99 -- Pitch variation (plus and minus)

5.5 Pitch of teeth

5.5.4 Allowable pitch variation, VpA

5.5.1 Pitch range

Allowable pitch variation is the maximum allowable amount of pitch variation. It is the permissible plus or minus variation from the true position pitch and it is the amount shown in the tolerance tables or formulas of AGMA 2000--A88.

Pitch range is the difference between the longest and the shortest pitches on a gear. 5.5.2 True position pitch, pm True position pitch is the circumference of the datum circle divided by the number of teeth. This can be determined by the average of all pitch measurements of the entire gear taken on successive pairs of

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5.5.5 Normal pitch variation, Vpn Normal pitch variation is the plus or minus pitch measured in the normal plane.

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Sector of three pitches

be along the arc of the tolerance diameter circle within the transverse plane. 5.6 Runout of teeth

Index variation, Vx

+

Vap3

--Vp Vap

0 +Vp

5.6.1 Runout Runout is the maximum variation of the distance between a surface of revolution and a datum surface, measured perpendicular to that datum surface. 5.6.2 Axial runout (wobble)

--

Axial runout (wobble) is the runout of the teeth measured in a direction parallel to the datum axis of rotation.

1 2 3 4 5 6 7 8 9 10 Tooth number

Figure 100 -- Accumulated pitch variation 5.5.6 Total accumulated pitch variation, Vap

5.6.3 Radial runout, Vr Radial runout is the runout measured in a direction perpendicular to the datum axis of rotation.

Total accumulated pitch variation is equal to the algebraic difference between the maximum and minimum values obtained from the summation of successive values of pitch variation and is the same as total index variation, see figure 100.

5.6.4 Radial runout tolerance, VrT

5.5.7 Total tolerance

Indicating over pins is the measurement of the change in radial distance over pins or wires placed in each tooth space to determine runout with reference to the rotating axis.

accumulated

pitch

variation

Total accumulated pitch variation tolerance is the permissible amount of total accumulated pitch variation. 5.5.8 Total accumulated pitch variation, within a sector of k pitches, Vapk Total accumulated pitch variation, within a sector of k pitches is equal to the algebraic sum of individual plus or minus adjacent pitch variations within that sector. The total accumulated pitch variation within a Sector of three (k = 3) pitches is shown in figure 100. 5.5.9 Single pitch deviation, fpt

Radial runout tolerance is the permissible amount of radial runout. 5.6.5 Indicating over pins

5.7 Profile of teeth 5.7.1 Functional profile That portion of the tooth flank between the profile control diameter and the start of tip break, see figure 101.

Functional profile

The displacement of any tooth flank from its theoretical position relative to the corresponding flank of an adjacent tooth, see figure 97. (ANSI/AGMA 2015--1--A01) Distinction is made as to the algebraic sign of this reading. Thus, a condition wherein the actual tooth flank position was nearer to the adjacent tooth flank than the theoretical position would be considered a minus (--) deviation. A condition wherein the actual tooth flank position was farther from the adjacent tooth flank than the theoretical position would be considered a plus (+) deviation. ANSI/AGMA 2015--1--A01 specifies tolerancing direction of measurement for single pitch deviation to

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External tooth

Addendum (outside) diameter Start of tip break Pitch diameter Profile control diameter Base circle Root diameter

Root diameter Profile control diameter Pitch diameter

Functional profile

Start of tip break

Internal tooth

Addendum (inside) diameter Base circle

Figure 101 -- Functional profile

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5.7.2 Profile variation, Vφ

5.7.4 Design profile

Profile variation is the difference between the measured and the specified functional profile. If measured in a normal plane a correction using the appropriate helix angle must be applied to the measured value, see figure 102.

The profile specified by the designer as shown on the design specification. When not specified, it is an unmodified involute. (ANSI/AGMA 2015--1--A01) 5.7.5 Functional profile length, Lαc The difference between the roll path lengths at the points that define the limits of the functional profile. (ANSI/AGMA 2015--1--A01)

True involute

5.7.6 Profile deviation Plus profile

Minus profile

Profile control diameter

Figure 102 -- Profile (plus and minus) 5.7.3 Profile tolerance, VφT In AGMA 2000--A88, the profile tolerance is the permissible amount of profile variation in the functional profile; designated by a specified “K” chart envelope as shown in figure 103. Plus material at the tip which increases the amount of variation outside the functional profile is not acceptable. Minus material beyond the start of tip break can be disregarded, see figure 103. Profile tolerance VφT

Addendum diameter

Distance between two design profile lines which enclose the actual profile trace over the functional profile length. (ANSI/AGMA 2015--1--A01) 5.7.8 Profile evaluation range The profile is evaluated over the specified functional profile length. (ANSI/AGMA 2015--1--A01)

Distance between two facsimiles of the mean profile line, which are each placed with constant separation from the mean profile line, so as to enclose the actual profile trace over the functional profile length. (ANSI/AGMA 2015--1--A01) 5.7.10 Profile slope deviation, fHα Functional profile

Space (+)

Tooth (--)

Profile control diameter 0 Reference line

Figure 103 -- Profile “K” chart

36

5.7.7 Profile deviation, total, Fα

5.7.9 Profile form deviation, ffα

Start of tip break

High point of tooth chart must be tangent to reference line

Amount by which a measured profile deviates from the design profile. Deviations caused by plus material beyond the tip break must be included in the calculation of the profile form deviation and total profile deviation. Minus material beyond the tip break may be ignored. ANSI/AGMA 2015--1--A01 specifies the direction of tolerancing for profile deviation to be in a transverse plane, on a line tangent to the base circle. (ANSI/AGMA 2015--1--A01)

Distance between two design profile lines which intersect the mean profile line at the endpoints of the functional profile length. (ANSI/AGMA 2015--1--A01) The profile slope deviation is deemed to be positive and the corresponding pressure angle deviation is deemed to be negative when the mean profile line shows an increase in material toward the tooth tip, relative to the design profile. 5.7.11 Profile chart Chart upon which profile variations are recorded.

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5.8 Alignment of teeth and helix

5.8.3 Tooth alignment tolerance, VψT, (formerly, lead tolerance)

5.8.1 Tooth alignment Tooth alignment is the alignment, normal to the helix, between the line of intersection of actual and theoretical tooth surfaces on the pitch cylinder. 5.8.2 Tooth alignment variation, Vψ, (formerly lead variation) Tooth alignment variation (formerly, lead variation) is the difference between the measured tooth alignment and the specified tooth alignment measured normal to the specified tooth alignment and the tooth surface on the functional face width, see figure 104.

Tooth alignment tolerance (formerly, lead tolerance) is the permissible amount of tooth alignment variation, designated by the specified “K” chart envelope as shown in figure 105. Tolerance values in AGMA 2000--A88 are normal to the tooth surface. 5.8.4 Tooth alignment trace (formerly measured lead trace) Tooth alignment trace (formerly, measured lead trace) is the trace recorded on an inspection chart that indicates variations from the reference tooth alignment generated by an appropriate inspection machine. 5.8.5 Design helix

Variation, Vψ

Specified

The helix specified by the designer as shown on the design specification. When not specified, it is an unmodified helix. (ANSI/AGMA 2015--1--A01)

Measured

5.8.6 Helix deviation Amount by which a measured helix deviates from the design helix. Deviations caused by plus material outside the helix evaluation range must be included in the calculation of helix form deviation and total helix deviation. Minus material outside the helix evaluation range may be ignored. ANSI/AGMA 2015--1--A01 specifies the direction of tolerancing for helix deviation to be in a transverse plane, on a line tangent to the base circle. (ANSI/AGMA 2015--1--A01)

Contact path of measuring point + Gear axis

5.8.7 Helix deviation, total, Fβ

Figure 104 -- Tooth alignment variation

Distance between two design helix lines which enclose the actual helix trace over the evaluation range. (ANSI/AGMA 2015--1--A01)

Functional face width Reference line

0

VψT

Facewidth

Figure 105 -- Tooth alignment “K” chart

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5.8.8 Helix evaluation range, Lβ Unless otherwise specified, the helix length of trace shortened at each end by the smaller of the following two values: 5% of the helix length of trace, or the length equal to one module. (ANSI/AGMA 2015--1--A01) NOTE: It is the responsibility of the gear designer to assure that the helix evaluation range is adequate for the application.

5.8.9 Helix form deviation, ffβ Distance between two facsimiles of the mean helix line, which are each placed with constant separation from the mean helix line, so as to enclose the actual helix trace over the evaluation range. (ANSI/AGMA 2015--1--A01) 5.8.10 Helix length of trace Unless otherwise specified, full facewidth is limited toward the ends of the teeth by the end faces or, if present, the start of end chamfers, rounds, or other modification intended to exclude that portion of the tooth from engagement. The helix length of trace should be stated as the axial component of the helix. (ANSI/AGMA 2015--1--A01) 5.8.11 Helix slope deviation, fHβ Distance between two design helix lines which intersect the mean helix line at the end points of the evaluation range. (ANSI/AGMA 2015--1--A01) Deviations are deemed to be positive when helix angles are larger and negative when helix angles are smaller, than the designed helix angle. The helix deviations of spur gears if other than zero are indicated by the subscripts “R” and “L”, instead of an algebraic sign, implying deviations in the sense of right or left helices respectively. 5.8.12 Mean helix line A line (or curve) that has the same shape as the design helix, but aligned with the measured trace. It is developed by subtracting the ordinates of a straight--line gradient from the ordinates of the design helix. Within the evaluation range the straight--line gradient is found by applying the least squares method to the deviation of the measured helix trace from the specified design helix. (ANSI/ AGMA 2015--1--A01) 5.8.13 Mean profile line A line (or curve) that has the same shape as the design profile, but aligned with the measured trace.

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AMERICAN NATIONAL STANDARD

It is developed by subtracting the ordinates of a straight--line gradient from the ordinates of the design profile. Within the functional profile length the straight--line gradient is found by applying the least squares method to the deviation of the measured profile trace from the specified design profile. (ANSI/AGMA 2015--1--A01) 5.9 Size of teeth 5.9.1 Tooth thickness variation Tooth thickness variation is the variation from a specified value of transverse circular tooth thickness. 5.9.2 Tooth thickness tolerance, tT Tooth thickness tolerance is the permissible amount of tooth thickness variation. 5.9.3 Functional tooth thickness Functional tooth thickness is the tooth thickness as determined by meshing with a master gear or specified gear on a calibrated composite action test fixture, see figure 95. 5.10 Accuracy grade, A or B For cylindrical gears, the accuracy grade is an integer that identifies the accuracy level of the tolerances according to ANSI/AGMA 2015--1--A01. The ANSI/AGMA 2015--1--A01 classification system consists of a prefix letter “A” identifying the tolerance source, and an accuracy grade identifying the specific tolerances. For bevel gears, the classification system according to ANSI/AGMA 2009--B01 uses the prefix letter “B” for identifying the tolerance source. 5.11 Gear quality For a description of the application of AGMA gear tooth quality, refer to AGMA 2000--A88. NOTE: ANSI/AGMA 2015--1--A01 replaces AGMA 2000--A88.

5.11.1 Quality Quality is the characteristic properties of a gear distinguishing the nature of its manufacturing tolerances. 5.11.2 Quality number, Q Quality number is a number representative of the level of quality possessed by a gear, as determined by AGMA 2000--A88 for cylindrical gears, or AGMA 390.03a for bevel gears.

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AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

5.11.3 Variation

5.11.5 Tolerance, T (subscript)

Variation is the measured plus or minus change from the specified value, see figure 106.

Tolerance is the amount by which a specific dimension is permitted to vary. The tolerance is the difference between the maximum and minimum limits and is an absolute value without sign, see figure 108.

Specified distance Measured distance

Minimum limit

Variation

Specified dimension

Figure 106 -- Variation

Tolerance

Maximum limit Tolerance

5.11.4 Allowable variation, A (subscript) Allowable variation is the permissible plus or minus deviation from the specified value, see figure 107.

Specified dimension

Minus variation

Minimum limit

Maximum limit

Figure 108 -- Tolerance

Plus variation Allowable measurement (minimum)

Allowable measurement (maximum)

Figure 107 -- Allowable variation

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39

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

(This page is intentionally blank)

40

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AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

Annex A (informative) Abbreviations [This annex is provided for informational purposes only and should not be construed as a part of ANSI/AGMA 1012--G05, Gear Nomenclature, Definitions of Terms with Symbols.]

A. Purpose This annex is for common abbreviations. In 2.2, it is indicated that abbreviations must be distinguished from symbols. The symbol for circular pitch is the single lower--case italic letter p, whereas the abbreviation is CP. Abbreviations are shortened forms of words often used on drawings, in correspondence, in tables, in texts, and for stamping tools, but are not suitable for use in equations. Accepted abbreviations are given in tables A.1 and A.2. Table A.1 -- Abbreviations Abbreviation ADD AP APA BD BHA BP CD CP DED DP DIA FIN FL FW HA ID L LA LH NCP NDP NPA OD OHA PA PD PRE--S RGH RH T THD TOP TR WD

Term addendum axial pitch axial pressure angle base diameter base helix angle base pitch center distance circular pitch dedendum diametral pitch diameter finishing flute lead face width helix angle inside diameter; internal diameter lead lead angle left hand normal circular pitch normal diametral pitch normal pressure angle outside diameter outside helix angle pressure angle; profile angle pitch diameter preshaving roughing right hand teeth thread topping test radius whole depth

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In published material abbreviations are always printed in Roman (vertical type), whereas symbols are always in italics. The use of abbreviations is approved only when there can be no possible misunderstanding as to their meaning.

Table A.2 -- Other selected abbreviations Abbreviation BHN C comp Hz cw ccw deg db EP F fpm ft--lb gal hp in in--lb kg lb max min min No. psi rpm SSU tir tiv

Term Brinell hardness number degrees Centigrade compounded cycles per second clockwise counterclockwise degree decibel extreme pressure degrees Fahrenheit feet per minute foot--pounds gallons horsepower inches inch--pounds kilograms pounds maximum minimum microinches number pounds per square inch revolutions per minute Saybolt Seconds Universal total indicator runout total indicator variation

41

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

Annex B (informative) Glossary of trade terms [This annex is provided for informational purposes only and should not be construed as a part of AGMA 1012--G05, Gear Nomenclature, Definitions of Terms with Symbols.]

B.1 Purpose This annex is intended to be a reference for trade terms in AGMA literature. B.2 Tradenames The following is a non--inclusive list of tradenames which are sometimes used to describe gear geometry. Beveloid®. Gears are general involute helicoids conjugate to a basic rack. They are characterized by a tapered depth and a tapered tooth thickness. They allow backlash adjustment and feature insensitivity to mismatch and misalignment. They allow meshing in any geometric configuration and with any conjugate mate, spur, helical, worm, rack, face, internal, etc. Cone® wormgearing is double enveloping produced by a particular process, see 4.2.4.4. Coniflex® bevel gears. A straight bevel gear that is generated by a special process which crowns the teeth and gives localized tooth contact.

42

Formate® bevel gears are bevel gears in which the gear member of the pair has nongenerated teeth, usually with straight tooth profiles, and in which the pinion member of the pair has generated teeth that are conjugate to the mating gear. Helicon® gearing. A helicon gear set is essentially a Spiroid gear set with no taper in the pinion or gear face. The pinion is cylindrical and the face of the gear lies in a plane. Revacycle® gears. A straight bevel gear generated by a special process with a special tooth form. Spiroid® gearing. A spiroid gear set consists of tapered worm pinion of unequal pressure angles and constant lead meshing with a spiral tooth face gear. Zerol. See 4.2.5.11. B.3 Other tradenames Other trade names include Planoid® and Spheroid®.

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ANSI/AGMA 1012--G05

Annex C (informative) Terms and symbols [This annex is provided for informational purposes only and should not be construed as a part of AGMA 1012--G05, Gear Nomenclature, Definitions of Terms with Symbols.]

C. Purpose This annex is intended to be a reference for additional terms and symbols used within AGMA

standards, where meaning is established by their usage and verbiage within the respective standards.

Table C.1 -- Symbols used in gear rating equations New Old AGMA AGMA/ISO Symbol Symbol A A A A Ai AiG Ri2 Am Rm AmG Rm2 AmP Rm1 Ao Re AoG Re2 acG ham2 acP ham1 aG ham2 anc aoG hae2 aoP hae1 aP ham1 B B jen Bn jn Bt jt b bG hfm2 boG hfe2 boP hfe1 bP hfm1 biP hfi1 bilP hfi lim1 C a Ca Cc Ce Cf CG

Description

Cone distance Accuracy grade Accuracy grade identifier prefix Inner cone distance Gear inner cone distance Mean cone distance Gear mean cone distance Pinion mean cone distance Outer cone distance Gear outer cone distance Gear mean chordal addendum Pinion mean chordal addendum Gear mean addendum Normal chordal addendum Gear outer addendum Pinion outer addendum Pinion mean addendum Backlash Outer normal backlash allowance Normal backlash Transverse backlash Dedendum Gear mean dedendum Gear outer dedendum Pinion outer dedendum Pinion mean dedendum Pinion inner dedendum Pinion limit inner dedendum Center distance Application factor for pitting resistance Curvature factor at pitch line Mesh alignment correction factor Surface condition factor for pitting resistance Gear ratio factor

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43

ANSI/AGMA 1012--G05

Old AGMA New Symbol AGMA/ISO Symbol CH CL CM KM Cm Cma Cmc Cmf Cmt Cp Cpf Cpm CR CSF Cs CT Cv Cx Cψ c c cp c1 cham D d D de2 Db Dc Di Dm dm2 Do dae2 Do DR d d de1 di dHe ref1 dm dm1 do dae1 dp dT dt E a E EG EP et F b F b

44

AMERICAN NATIONAL STANDARD

Description

Hardness ratio factor for pitting resistance Life factor for pitting resistance Material factor Load distribution factor for pitting resistance Mesh alignment factor Lead correction factor Face load distribution factor Transverse load distribution factor Elastic coefficient Pinion proportion factor Pinion proportion modifier Reliability factor for pitting resistance Service factor for pitting resistance Size factor for pitting resistance Temperature factor for pitting resistance Dynamic factor for pitting resistance Contact height factor Helical overlap factor Clearance Contact pattern measurement Mean addendum factor Reference standard pitch diameter Outer gear pitch diameter Base diameter (of an involute gear) Datum circle Internal diameter Gear mean pitch diameter Gear outside diameter Outside diameter Root diameter Diameter, pitch Outer pinion pitch diameter Reference hypoid pinion pitch diameter Pinion mean pitch diameter Pinion outside diameter Operating pitch diameter Tolerance diameter Throat diameter Hypoid offset Offset of axes Young’s modulus for gear Young’s modulus for pinion Total lead mismatch Net face width Face width

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Old AGMA New Symbol AGMA/ISO Symbol Fe Fis FisT Fp FpT Ft Fα FαT Fβ FβT ffα ffαT ffβ ffβT fHα fHαT fis fisT fp fpt fptT FiP bRi1 FP b1 FoP bRe1 G Go tGo GR tRG HBG HBP h hmw ha hap hc he he max hk hk hew hm hm ht ht he htG h2 htP h1 I J K

ANSI/AGMA 1012--G05

Description

Effective or active face width Single flank composite deviation, total Single flank composite tolerance, total Cumulative pitch deviation, total Cumulative pitch deviation tolerance, total Total face width Profile deviation, total Profile tolerance, total Helix deviation, total Helix tolerance, total Profile form deviation Profile form tolerance Helix form deviation Helix form tolerance Profile slope deviation Profile slope tolerance Single flank composite deviation, tooth--to--tooth (filtered) Single flank composite tolerance, tooth--to--tooth Pinion surface finish Single pitch deviation Single pitch deviation tolerance Pinion face width from calculating point to inside Pinion face width Pinion face width from calculating point to outside Tooth stiffness constant Pinion face apex beyond crossing point Pinion root apex beyond crossing point Brinell hardness of gear Brinell hardness of pinion Mean working depth Addendum Chordal addendum Total case depth for nitrided gears Effective case depth Maximum effective case depth Working depth Outer working depth Mean whole depth Gear tooth whole depth Outer whole depth Gear whole depth Pinion whole depth Geometry factor for pitting resistance Geometry factor for bending strength Contact load factor for pitting resistance

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45

ANSI/AGMA 1012--G05

Old AGMA New Symbol AGMA/ISO Symbol Ka Kac KB Kf KL Km Ko KR KS KF Ks KT Kv Ky K1 K1 k k1 k1 k2 k2 k3 k3 L pz LBG tB2 LBP tB1 LFG tF2 LFP tF1 LG LP LW LXG tE2 LXP tE1 Lαc Lβ M m mB mc met mF εβ mG mG u mN mn mn mo mt mp εα mt εγ

46

AMERICAN NATIONAL STANDARD

Description

Application factor for bending strength Allowable contact load factor Rim thickness factor Stress correction factor Life factor for bending strength Load distribution factor for bending strength Overload factor Factor of safety Size factor for bending strength Service factor for bending strength Size factor Temperature factor Dynamic factor Yield strength factor Approximate hypoid dimension factor Number of pitches in a sector Depth factor Clearance factor Circular thickness factor Lead Gear back angle distance Pinion back angle distance Gear face angle distance Pinion face angle distance Lead of gear Lead of pinion Lead of worm Gear crown to back Pinion crown to back Functional profile length Helix evaluation range Bending moment Module Back--up ratio Contact ratio Outer transverse module Face contact ratio Gear ratio (always > 1.0) Gear ratio Load sharing ratio Normal module Modified contact ratio Transverse module Transverse contact ratio Total contact ratio

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AMERICAN NATIONAL STANDARD

Old AGMA New Symbol AGMA/ISO Symbol m90 u90 N N z2 NC Nc Nc zP Ne NG z2 NP z1 NS z0 n n n z1 nG nP nP n P P P Pac Pat Pd Pd met Pdm Pnd Psc p pb pm pm pm pN pn pt pX px Q Q Q Qa QF Qr Qt Qv R R rmpt2 Rb Rc RiG ript2

ANSI/AGMA 1012--G05

Description

Equivalent 90° ratio Number of teeth or threads Number of gear teeth Number of teeth in crown gear Number of teeth in cutter Number of crown gear teeth Equivalent number of teeth Number of teeth in gear Number of teeth in pinion Number of blade groups Revolutions per unit of time Number of pinion teeth Revolutions per unit of time of gear Revolutions per unit of time of pinion Pinion speed Transmitted power Power Allowable transmitted power for pitting resistance Allowable transmitted power for bending strength Diametral pitch Outer transverse diametral pitch Mean diametral pitch Normal diametral pitch Service horsepower Circular pitch Base pitch True position pitch Mean circular pitch Normal base pitch Normal circular pitch Transverse circular pitch Axial base pitch Axial pitch Quality number Intermediate variable Arc of approach Face advance Arc of recess Arc of action Transmission accuracy level number Pitch radius of gear Gear mean pitch radius Base radius of gear Pitch radius of cutter Gear inside pitch radius

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47

ANSI/AGMA 1012--G05

Old AGMA New Symbol AGMA/ISO Symbol RP rmpt1 RiP ri1 Ro RR Rr R2P rmn1 rc rc0 rc1 ρlim r rb rf ro rR rt rT S S1 S1 Md s sa sac sat say sc ss sw T TG TG T2 Tn smn2 Tnc smn2 TP T1 s sb tG sn tn smn1 tnc sc to tP tR tT tt tx Uat

48

AMERICAN NATIONAL STANDARD

Description

Mean pinion radius Inner pinion radius Outside radius of gear Root radius of gear Test radius Approximate pinion mean radius Cutter radius Limit curvature radius Pitch radius of pinion Base radius of pinion Fillet radius, when constant Outside radius of pinion Root radius of pinion Throat--form radius Tip or edge radius of tool Bearing span Pinion offset Crown gear to cutter center distance Stress Allowable contact stress number Allowable contact stress number Allowable bending stress number Allowable yield stress number Contact stress number Shear stress Working contact stress number Torque Torque of gear Torque transmitted by the gear Gear mean normal circular tooth thickness Gear mean normal chordal tooth thickness Pinion torque Circular tooth thickness Base circular thickness Circular thickness of gear Normal circular thickness Pinion mean normal circular tooth thickness Normal chordal thickness Tooth thickness on outside diameter Circular thickness of pinion Gear rim thickness Tooth thickness tolerance Transverse circular thickness Axial thickness Allowable unit load for bending strength

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AMERICAN NATIONAL STANDARD

Old AGMA New Symbol AGMA/ISO Symbol Uc UH UL Vap Vap FpK Vapk Vcq VcqT VK νK Vp Vp max fpt max VpA Vpn Vq VqT Vr VrT Vs Vx Vφ VφT Vψ VψT Vφ VφT Vψ VψT v vN vn vt vt max vx W Wa Wd Wmax WN Wn Wr Wr Wr Wt Wt Wt WtG Wt2 WtP Wt1

ANSI/AGMA 1012--G05

Description

Core hardness coefficient Hardening process factor Unit load for bending strength Total accumulated pitch variation Accumulated pitch variation Total accumulated pitch variation, within a sector of k pitches Total composite variation (double flank) Total composite tolerance (double flank) Kinematic viscosity Pitch variation Maximum pitch variation Allowable pitch variation Normal pitch variation Tooth--to--tooth composite variation (double flank) Tooth--to--tooth composite tolerance (double flank) Radial runout Radial runout tolerance Spacing variation Index variation Profile variation Profile tolerance Tooth alignment variation Tooth alignment tolerance Profile variation Profile tolerance Tooth alignment variation Tooth alignment tolerance Linear velocity Velocity normal to surface Velocity in normal direction in pitch plane Pitch line velocity Pitch line velocity maximum Velocity in axial direction Load Allowable tangential load Incremental dynamic tooth load Maximum peak tangential load Load normal to surface Load component normal to helix in pitch plane Radial component of load Radial force Transverse or tangential component of load Tangential force Tangential force at mean diameter of gear Tangential force at mean diameter of pinion

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49

ANSI/AGMA 1012--G05

Old AGMA New Symbol AGMA/ISO Symbol Wx Wx Wx w Xo txo2 xi xi xo txo1 Y y Z Z tz2 Za ZiP tzi1 Zo tzo2 ZP tzm1 ZR tzR2 ZR Z2 Z1 z α αG θa2 αP θa1 β Γ Γ δ2 Γi δint 2 Γo Γo δa2 ΓR ΓR δf2 γ γ δ1 γi δi γo δa1 γR δf1 γ2 δint1 Δ Δ ΔB Δj ΔBG Δj2 ΔBi Δgxi ΔBo Δgxe ΔBP Δj1 bRi2 ΔFi bRe2 ΔFo ΔFoP Δbx1

50

AMERICAN NATIONAL STANDARD

Description

Axial component of load Axial force Load per unit length Gear pitch cone apex to crown (crown to crossing point, hypoid) Pinion front crown to crossing point Pinion pitch cone apex to crown Tooth--form factor for diametral pitch Tooth--form factor for circular pitch Length of action in transverse plane Gear pitch apex beyond crossing point Approach portion of line of action Crossing point to inside point along pinion axis Gear face apex beyond crossing point Crossing point to mean point along gear axis Gear root apex beyond crossing point Recess portion of line of action Number of teeth in gear Number of teeth in pinion Number of teeth Addendum angle Gear addendum angle Pinion addendum angle Helix angle Pitch angle Gear pitch angle Approximate gear pitch angle Face tip angle Gear face angle Root angle Gear root angle Pitch angle of pinion Pinion pitch angle Pinion inside pitch angle Pinion face angle Pinion root angle Intermediate pinion pitch angle Iteration factor Total change in backlash Change of backlash for gear Increment along pinion axis from calculating point to inside Increment along pinion axis from calculating point to outside Change of backlash for pinion Gear face width from point to inside Gear face width from point to outside Pinion face width increment

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AMERICAN NATIONAL STANDARD

Old AGMA New Symbol AGMA/ISO Symbol ΔG ΔXG ΔK ΔK ΔP Δa1 ΔRP Δrmpt1 ΔRP/R Δrmpt1--2 ΔΣ ΔΣ Δt Δs δG θf2 δP θf1 ε εi εi ε′i ε′i εo εo εR εR ε1 ε1 ε′1 ε′1 ε2 ε2 ε′2 ε′2 θ θN τ λ λ λ λ′ λ′ λb λg λo λp mG mP Ã Ã Ãf ÃG Ãn Ão ÃP Σ Σδ ΣδD ΣδS ΣδT ΣδU σ φ

ρmβ

Σ Σθf ΣθfD ΣθfS ΣθfT ΣθfU

ANSI/AGMA 1012--G05

Description

Axial movement of gear Increment in hypoid dimension factor Axial movement of pinion Pinion mean radius increment Ratio of pinion mean radius increment to gear mean pitch radius Shaft angle departure from 90° Thickness change Gear dedendum angle Pinion dedendum angle Involute roll angle Pinion offset angle in axial plane at inside Pinion offset angle in pitch plane at inside Pinion offset angle in face plane Pinion offset angle in root plane Pinion offset angle in axial plane Pinion offset angle in pitch plane Intermediate pinion offset angle in axial plane Intermediate pinion offset angle in pitch plane Involute polar angle Angular pitch Lead angle First auxiliary angle Angle between the projection of pinion axis into pitch plane and the pitch element Base lead angle Gear form filter cutoff Outside lead angle Pitch lead angle Poisson’s ratio for gear Poisson’s ratio for pinion Lengthwise tooth mean radius of curvature Profile radius of curvature Radius of curvature Profile radius of curvature in gear Profile radius of curvature in normal plane Relative radius of curvature Profile radius of curvature in pinion Shaft angle Sum of dedendum angles Sum of dedendum angles for duplex taper Sum of dedendum angles for standard taper Sum of dedendum angles for tilted root line taper Sum of dedendum angles for uniform depth taper Dedendum angle Pressure angle

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51

ANSI/AGMA 1012--G05

Old AGMA New Symbol AGMA/ISO Symbol αn φ φc φn αlim φo αit φTi φt φx φxW αcv1 φ1 αcx1 φ2 ψ ψ βm ψb ψG βm2 ψi ψm ψiG βi2 ψiP βi1 ψo ψo βe ψoG βe2 ψoP βΔ1 ψP ψP βm1 ψs ψ2P βm int1 ω ωG ωP ζo ζo ζR ζR η η ηo ηo ηi ηi η1 η1 ν ν0 vet νt

52

AMERICAN NATIONAL STANDARD

Description

Normal pressure angle at pitch surface Pressure angle of cutter Normal pressure angle Limit pressure angle Inner transverse pressure angle Transverse pressure angle Axial pressure angle Axial pressure angle of worm Pressure angle on concave side of pinion Pressure angle on convex side of pinion Spiral angle Mean spiral angle at pitch surface Base helix angle Gear spiral angle Spiral angle at inner cone distance Spiral angle at mean cone distance Inner gear spiral angle Inner pinion spiral angle Spiral angle at outer cone distance Outer spiral angle Outer gear spiral angle Desired pinion spiral angle Spiral angle of pinion Pinion mean spiral angle Helix angle at standard pitch diameter Intermediate pinion mean spiral angle Angular velocity Angular velocity of gear Angular velocity of pinion Auxiliary angle for calculating pinion offset angle in face plane Auxiliary angle for calculating pinion offset angle in root plane Gear offset angle at axial plane Intermediate angle Gear offset angle at inside Second auxiliary angle Lead angle of cutter Pitch line velocity

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AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

Index of terms [The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be construed as a part of AGMA 1012--G05, Gear Nomenclature, Definitions of Terms with Symbols.]

abbreviations

Paragraph Figure number number A.1 -- --

Reference page 41

accumulated pitch variation, total accumulated pitch variation tolerance, total accumulated pitch variation, total, within a sector of k pitches

5.5.6 5.5.7 5.5.8

100 -- -100

35 35 35

accuracy grade

5.10

-- --

38

action test (double flank), composite action, arc of action, composite (double flank) action, length of action, line of action, path of action, plane of action, surface of action, zone of

5.3.3.1 4.8.10 5.3.3 4.8.9 4.8.4 4.8.3 4.8.6 4.8.5 4.8.7

95 92 -- -91 87, 91, 93 85, 88 88 -- -89

32 29 32 29 28 28 28 28 28

active profile, start of

4.8.18

59

30

addendum addendum angle addendum circle addendum teeth, modified addendum, chordal

4.5.3.9 4.6.31.17 4.5.3.8 4.6.32.12 4.6.32.7

35 75 33, 34 -- -78

12 24 12 25 25

adjusted number of teeth

5.1.14

-- --

31

advance, face

4.8.19

94

30

alignment tolerance, tooth alignment trace, tooth alignment variation, tooth alignment, tooth

5.8.3 5.8.4 5.8.2 5.8.1

104, 105 -- --- --- --

37 37 37 37

allowable pitch variation allowable variation

5.5.4 5.11.4

-- -107

34 39

angle, addendum angle, axial pressure angle, axial profile angle, back angle, base helix angle, base lead

4.6.31.17 4.6.9 4.6.9 4.5.4.4.2 4.6.30.3.1 4.6.30.3.2

75 45 45 37 62 -- --

24 16 16 13 20 20

Term

© AGMA 2005 ---- All rights reserved

53

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

angle, dedendum angle, face (tip) angle, front angle, helix angle, inner spiral angle, involute polar angle, involute roll angle, lead angle, mean spiral angle, normal pressure angle, normal profile angle, operating pressure angle, outer spiral angle, outside helix angle, outside lead angle, pitch angle, pressure angle, profile angle, root angle, shaft angle, spiral angle, standard profile angle, transverse pressure angle, transverse profile

Paragraph number 4.6.31.18 4.6.31.15 4.5.4.6 4.6.30.1 4.6.31.6 4.6.10 4.6.11 4.6.30.7 4.6.31.4 4.6.8 4.6.8 4.7.4 4.6.31.5 4.6.30.5.1 4.6.30.5.2 4.6.31.14 4.6.4 4.6.5 4.6.31.16 4.6.31.7 4.6.31.3 4.6.6 4.6.7 4.6.7

75 74 37 61, 65 70 46 47 65 70 45 45 -- -70 -- --- -74, 75 43, 46 43, 44 74 71 69, 70 44 45 45

Reference page 24 24 13 20 23 16 16 21 22 16 16 26 22 21 21 24 14 15 24 23 22 15 15 15

angular bevel gear angular pitch

4.2.5.6 4.6.23

14 -- --

6 18

apex to back

4.5.4.8

37, 38

13

approach, arc of

4.8.11

92

29

arc of action arc of approach arc of recess

4.8.10 4.8.11 4.8.12

92 92 92

29 29 29

axes, plane of

4.3.2

17

7

axial pitch axial plane axial pressure angle axial profile angle axial runout axial thickness

4.6.16 4.3.1 4.6.9 4.6.9 5.6.2 4.6.32.4

49, 50 19 45 45 -- -77

17 7 16 16 35 25

axis, datum

5.1.2

-- --

31

back angle back cone

4.5.4.4.2 4.5.4.4

37 36

13 13

Term

54

Figure number

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

back cone distance back, apex to

Paragraph Figure number number 4.5.4.4.1 37 4.5.4.8 37, 38

Reference page 13 13

backlash backlash variation backlash, minimum

4.7.10 4.7.10.2 4.7.10.1

84 -- --- --

27 27 27

base circle base circular thickness base cylinder base diameter base diameter, Cone® gear base helix base helix angle base lead angle base pitch, normal base pitch, transverse base radius

4.6.2 4.6.32.5 4.6.2.3 4.6.2.1 4.6.2.4 4.6.30.3 4.6.30.3.1 4.6.30.3.2 4.6.18 4.6.17 4.6.2.2

39, 40, 47 78 41, 88 40, 59 -- -62 62 -- -50 50, 51 -- --

14 25 14 14 14 20 20 20 17 17 14

basic rack

4.1.6

3

2

bevel gear bevel gear, angular bevel gears, Formate® bevel gear, left hand spiral bevel gear, right hand spiral bevel gear, skew bevel gear, spiral bevel gear, straight bevel gear, zerol bevel gears, Coniflex®

4.2.5.4 4.2.5.6 B.2 4.6.31.2 4.6.31.1 4.2.5.9 4.2.5.10 4.2.5.8 4.2.5.11 B.2

13 14 -- -67, 68 67, 68 16 17 16 17 -- --

5 6 42 22 22 6 6 6 7 42

Beveloid®

B.2

-- --

42

blank, gear

5.1.7

-- --

31

bottom land

4.5.3.6.3

32

12

break, start of tip break, tip or edge

5.1.12 5.2.4

-- --- --

31 32

center distance (operating) center, gear center, line of central plane

4.7.2 4.5.2 4.5.3.2 4.3.8

82, 93 28 28 23

26 10 10 9

chart, inspection chart, profile

5.1.8 5.7.11

-- --- --

31 36

Term

© AGMA 2005 ---- All rights reserved

55

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

chordal addendum chordal height chordal thickness, normal

Paragraph Figure number number 4.6.32.7 78 4.6.32.7 78 4.6.32.6 78

Reference page 25 25 25

circle, addendum circle, base circle, crown circle, datum circle, pitch (operating) circle, root circle, standard (reference) pitch

4.5.3.8 4.6.2 4.5.4.7 5.1.1 4.5.3.1.1 4.5.3.6.1 4.5.3.7

33, 34 39, 40, 47 36 76, 78 28, 84 33 44

12 14 13 31 10 11 12

circular pitch circular pitch, normal circular pitch, transverse circular thickness circular thickness, base circular thickness, normal circular thickness, transverse

4.6.13 4.6.15 4.6.14 4.6.32.1 4.6.32.5 4.6.32.3 4.6.32.2

48 49 49 76 78 77 77, 78

17 17 17 24 25 25 24

clearance

4.7.5

35

27

composite (double flank) action composite action test (double flank) composite deviation, single flank, tooth--to--tooth composite deviation, single flank, total composite test, single flank composite tolerance, tooth--to--tooth radial (double flank) composite tolerance, total radial (double flank) composite deviation, tooth--to--tooth radial (double flank) composite deviation, total radial (double flank)

5.3.3 5.3.3.1 5.3.2.2 5.3.2.3 5.3.2.1 5.3.3.3 5.3.3.5 5.3.3.2 5.3.3.4

-- -95 -- --- --- --- --- -96 -- --

32 32 32 32 32 32 32 32 32

cone distance cone distance, inner cone distance, mean cone distance, outer Cone® gear base diameter Cone® wormgearing cone, back cone, back, distance cone, face (tip) cone, front cone, pitch cone, root

4.6.31.8 4.6.31.11 4.6.3.10 4.6.31.9 4.6.2.4 B.2 4.5.4.4 4.5.4.4.1 4.5.4.2 4.5.4.5 4.5.4.1 4.5.4.3

70 70 70 70 -- --- -36 37 36 36 25, 26 36, 75

23 23 23 23 14 42 13 13 12 13 12 13

Coniflex® bevel gears

B.2

-- --

42

conjugate gear

4.7.1

-- --

26

Term

56

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

contact ratio contact ratio, face contact ratio, modified contact ratio, total contact ratio, transverse contact zone contact, line of contact, path contact, point

Paragraph number 4.8.13 4.8.15 4.8.17 4.8.16 4.8.14 4.8.7 4.8.2 4.8.8 4.8.1

-- --- --- --- --- -89 86, 88, 89 90 85, 90

Reference page 30 30 30 30 30 28 28 29 27

control diameter, profile

5.1.4

59

31

crossed axis gears crossed helical gears

4.2.5 4.2.5.1

-- -11

5 5

crossing point

4.5.4.10

38

13

crown circle crown gear

4.5.4.7 4.2.5.7

36 15

13 6

crowned teeth

4.6.3

42

14

cumulative pitch deviation, total

5.4.2

-- --

34

curvature, profile radius

4.6.26.2

56

19

curve, fillet

4.6.27

52, 58

19

cutoff, gear form filter

5.1.10

-- --

31

cylinder, base cylinder, inside cylinder, outside (tip or addendum) cylinder, pitch cylinder, root cylindrical gear terms cylindrical worm

4.6.2.3 4.5.3.4 4.5.3.3 4.5.3.1 4.5.3.6 4.6.30 4.2.4.2

41, 88 33 29 24, 63 -- --- -2, 9

14 11 10 10 11 20 4

datum axis datum circle datum surface datum tooth

5.1.2 5.1.1 5.2.1 5.1.3

-- -76, 78 -- --- --

31 31 31 31

dedendum dedendum angle

4.5.3.10 4.6.31.18

35 75

12 24

depth, whole depth, working

4.7.7 4.7.6

35 35

27 27

Term

© AGMA 2005 ---- All rights reserved

Figure number

57

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

design helix design profile

Paragraph Figure number number 5.8.5 -- -5.7.4 -- --

Reference page 37 36

deviation, cumulative pitch, total deviation, helix deviation, helix form deviation, helix slope deviation, index deviation, profile deviation, profile form deviation, profile slope deviation, total profile deviation, single pitch deviation, tooth--to--tooth radial (double flank) composite deviation, tooth--to--tooth single flank, composite deviation, total helix deviation, total radial (double flank) composite deviation, total single flank composite

5.4.2 5.8.6 5.8.9 5.8.11 5.4.1 5.7.6 5.7.9 5.7.10 5.7.7 5.5.9 5.3.3.2 5.3.2.2 5.8.7 5.3.3.4 5.3.2.3

-- --- --- --- -97 -- --- --- --- --- -96 -- --- -96 -- --

34 37 38 38 33 36 36 36 36 35 32 32 37 32 32

diameter, base diameter, Cone® gear base diameter, form diameter, inside diameter, limit diameter, operating pitch diameter, outside diameter, pitch diameter, profile control diameter, root diameter, standard (reference) pitch diameter, throat diameter, tolerance diameter, undercut

4.6.2.1 4.6.2.4 4.6.27.3 4.5.3.5 4.8.18 4.7.9 4.5.3.3.1 4.7.8 5.1.4 4.5.3.6.2 4.5.3.7.1 4.5.4.11 5.1.9 4.6.27.3

40, 59 -- -59 33 59, 93 -- -30, 31 30 59 30, 33 -- -31 -- --- --

14 14 19 11 30 27 11 27 31 12 12 13 31 20

diametral pitch (transverse) diametral pitch, normal

4.6.19 4.6.20

-- --- --

17 17

direction, axial direction, normal direction, transverse

4.4.1 4.4.3 4.4.2

24 24 24

9 9 9

distance, back cone distance, center, (operating) distance, cone distance, inner cone distance, mean cone distance, mounting distance, outer cone

4.5.4.4.1 4.7.2 4.6.31.8 4.6.31.11 4.6.31.10 4.5.4.9 4.6.31.9

37 82, 93 70 70 70 38 70

13 26 23 23 23 13 23

Term

58

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

double flank composite action double flank composite action test double flank tooth--to--tooth radial composite tolerance double flank tooth--to--tooth radial composite deviation double flank total radial composite tolerance double flank total radial composite deviation

Paragraph number 5.3.3 5.3.3.1 5.3.3.3 5.3.3.2 5.3.3.5 5.3.3.4

-- -95 -- -96 -- --- --

Reference page 32 32 32 32 32 32

double--enveloping wormgearing

4.2.4.4

10

5

double helical gear

4.2.3.6

8

4

eccentricity

5.1.5

-- --

31

effective face width

4.7.11

66

27

enveloping (hourglass) worm

4.2.4.3

10

4

equal addendum teeth

4.6.32.15

81

26

equivalent number of teeth equivalent pitch radius

4.5.1.2 4.5.1.1

-- -27

10 10

error, transmission

5.1.13

-- --

31

evaluation range, helix evaluation range, profile

5.8.8 5.7.8

-- --- --

38 36

external gear

4.2.1

4

3

face (tip) angle face (tip) cone face advance face cone face contact ratio face gear face width face width, effective face width, functional face width, total

4.6.31.15 4.5.4.2 4.8.19 -- -4.8.15 4.2.5.3 4.6.30.8 4.7.11 5.1.6 4.6.30.9

74 36 94 75 -- -12 66, 89 66 -- -66

24 12 30 24 30 5 21 27 31 22

fillet curve (root fillet) fillet radius fillet, root

4.6.27 4.6.27.1 4.6.27

52, 58 56 -- --

19 19 19

filter cutoff, gear form

5.1.10

-- --

31

flank measurement, single flank, left flank, right

5.3.2 4.6.25 4.6.25

-- -53, 54 53, 54

32 18 18

Term

© AGMA 2005 ---- All rights reserved

Figure number

59

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

form deviation, helix form deviation, profile form diameter (true involute form, TIF) form filter cutoff, gear

Paragraph number 5.8.9 5.7.9 4.6.27.3 5.1.10

-- --- -59 -- --

Reference page 38 36 19 31

Formate® bevel gear

B.2

-- --

42

front angle front cone

4.5.4.6 4.5.4.5

37 36

13 13

full--depth teeth

4.6.32.13

-- --

26

functional face width functional profile functional profile length functional tooth thickness

5.1.6 5.7.1 5.7.5 5.9.3

-- -101 -- --- --

31 35 36 38

gap

-- --

66

21

gear (wheel) gear blank gear center gear form filter cutoff gear quality gear ratio gear, angular bevel gear, bevel gear, bevel, Formate® gear, bevel, skew gear, bevel, spiral gear, bevel, straight gear, bevel, zerol gear, conjugate gear, crossed axis gear, crossed helical gear, crown gear, double helical gear, external gear, face gear, Formate® bevel gear, helical gear, herringbone gear, hypoid gear, internal gear, left hand helical gear, left hand spiral bevel gear, master gear, miter gear, parallel axis

4.1.2 5.1.7 4.5.2 5.1.10 5.11 4.1.9 4.2.5.6 4.2.5.4 B.2 4.2.5.9 4.2.5.10 4.2.5.8 4.2.5.11 4.7.1 4.2.5 4.2.5.1 4.2.5.7 4.2.3.6 4.2.1 4.2.5.3 B.2 4.2.3.3 4.2.3.7 4.2.5.12 4.2.2 4.6.29 4.6.31.2 5.3.1 4.2.5.5 4.2.3

1 -- -28 -- --- --- -14 13 -- -16 17 16 17 -- --- -11 15 8 4 12 -- -7 8 18 4 60 67, 68 -- -13 5

2 31 10 31 38 3 6 5 42 6 6 6 7 26 5 5 6 4 3 5 42 4 4 7 3 20 22 32 6 3

Term

60

Figure number

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

gear, right hand helical gear, right hand spiral bevel gear, single helical gear, skew bevel gear, spiral gear, spiral bevel gear, spur gear, straight bevel gear, zerol bevel gears

Paragraph number 4.6.28 4.6.31.1 4.2.3.5 4.2.5.9 4.2.5.1 4.2.5.10 4.2.3.1 4.2.5.8 4.2.5.11 4.1.1

60 67, 68 8 16 -- -17 6 16 17 1

Reference page 20 22 4 6 5 6 3 6 7 2

generating rack

4.1.7

-- --

3

grade, accuracy

5.10

-- --

38

heel

4.6.31.12

73

23

height, chordal

4.6.32.7

78

25

helical gear helical gear, left--hand helical gear, right--hand helical rack

4.2.3.3 4.6.29 4.6.28 4.2.3.4

7 58 60 7

4 20 20 4

Helicon® gearing

B.2

-- --

42

helix helix angle helix angle, base helix angle, outside helix deviation helix deviation, total helix evaluation range helix form deviation helix length of trace helix line, mean helix slope deviation helix, base helix, design helix, normal helix, outside (tip or addendum) helix, pitch

-- -4.6.30.1 4.6.30.3.1 4.6.30.5.1 5.8.6 5.8.7 5.8.8 5.8.9 5.8.10 5.8.12 5.8.11 4.6.30.3 5.8.5 4.6.30.4 4.6.30.5 4.6.30.2

64 61, 65 62 -- --- --- --- --- --- --- --- -62 -- -63 62 62, 63

21 20 20 21 37 37 38 38 38 38 38 20 37 21 21 20

herringbone gear

4.2.3.7

8

4

hourglass (enveloping) worm

4.2.4.3

10

4

hypoid gear

4.2.5.12

18

7

Term

© AGMA 2005 ---- All rights reserved

Figure number

61

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

index deviation

Paragraph Figure number number 5.4.1 97

Reference page 33

indicated surface

5.2.2

-- --

31

indicating over pins

5.6.5

-- --

35

inner cone distance inner spiral angle

4.6.31.11 4.6.31.6

70 70

23 23

inside cylinder inside diameter

4.5.3.4 4.5.3.5

33 33

11 11

inspection chart

5.1.8

-- --

31

internal gear

4.2.2

4

3

involute involute form diameter, true (TIF) involute polar angle involute roll angle involute teeth

-- -4.6.27.3 4.6.10 4.6.31.20 4.6.1

39 59 46 47 39, 40

14 19 16 16 14

K chart, profile

-- --

103

36

land, bottom land, top

4.5.3.6.3 4.5.3.3.2

32 32

12 11

lead lead angle lead angle, base lead angle, outside lead tolerance lead trace, measured lead variation

4.6.30.6 4.6.30.7 4.6.30.3.2 4.6.30.5.2 5.8.3 5.8.4 5.8.2

64, 65 65 -- --- -104, 105 -- --- --

21 21 20 21 37 37 37

left flank left hand helical gear left hand spiral bevel gear left hand worm

4.6.25 4.6.29 4.6.31.2 4.6.29

53, 54 60 67, 68 60

18 20 22 20

length of action length of trace, helix length, functional profile length, roll path

4.8.9 5.8.10 5.7.5 5.1.11

91 -- --- --- --

29 38 36 31

limit diameter limits, test radius

4.8.18 5.3.3.7

59, 93 -- --

30 33

Term

62

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

line of action line of center line of contact line, mean helix line, pitch

Paragraph number 4.8.4 4.5.3.2 4.8.2 5.8.12 4.5.3.1.2

Figure number 87, 91 93 28 86, 88, 89, 90 -- -28

Reference page 28 10 28 38 10

long addendum teeth

4.6.32.16

-- --

26

master gear

5.3.1

-- --

32

mean cone distance mean helix line mean profile line mean spiral angle

4.6.31.10 5.8.12 5.8.13 4.6.31.4

70 -- --- -70

23 38 38 22

measured lead trace

5.8.4

-- --

37

measurement over pins measurement, single flank measurement, span

4.6.32.10 5.3.2 4.6.32.11

79 -- -80

25 32 25

minimum backlash

4.7.10.1

-- --

27

miter gear

4.2.5.5

13

6

modified addendum teeth modified contact ratio

4.6.32.12 4.8.17

-- --- --

25 30

module (transverse) module, normal

4.6.21 4.6.22

-- --- --

17 18

mounting distance mounting surface

4.5.4.9 5.2.3

38 -- --

13 32

normal base pitch normal chordal thickness normal circular pitch normal circular thickness normal diametral pitch normal direction normal helix normal module normal pitch variation normal plane normal pressure angle normal profile angle

4.6.18 4.6.32.6 4.6.15 4.6.32.3 4.6.20 4.4.3 4.6.30.4 4.6.22 5.5.5 4.3.7 4.6.8 4.6.8

50 78 49 77 -- -24 63 -- --- -78 45 45

17 25 17 25 17 9 21 18 34 8 16 16

Term

© AGMA 2005 ---- All rights reserved

63

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

number of teeth number of teeth, equivalent number of threads number, quality

Paragraph number 4.1.8 4.5.1.2 4.1.8 5.11.2

-----

offset

4.7.3

12, 18, 83

26

operating center distance operating pitch diameter operating pressure angle

4.7.2 4.7.9 4.7.4

82, 93 -- --- --

26 27 26

outer cone distance outer spiral angle

4.6.31.9 4.6.31.5

70 70

23 22

outside (tip or addendum) cylinder outside (tip or addendum) helix outside diameter outside helix angle outside lead angle

4.5.3.3 4.6.30.5 4.5.3.3.1 4.6.30.5.1 4.6.30.5.2

29 62 30, 31 61 65

10 21 11 21 21

parallel axis gear

4.2.3

5

3

path length, roll path of action path of contact path, probe

5.1.11 4.8.3 4.8.8 5.1.15

47 85, 88 90 -- --

31 28 29 31

pinion

4.1.3

1

2

pins, indicating over pins, measurement over

5.6.5 4.6.32.10

-- -79

35 25

pitch pitch angle pitch circle (operating) pitch circle, standard (reference) pitch cone pitch cylinder pitch deviation, cumulative, total pitch deviation, single pitch diameter pitch diameter, operating pitch diameter, standard (reference) pitch helix pitch line pitch plane pitch point pitch radius, equivalent pitch range

4.6.12 4.6.31.14 4.5.3.1.1 4.5.3.7 4.5.4.1 4.5.3.1 5.4.2 5.5.9 4.7.8 4.7.9 4.5.3.7.1 4.6.30.2 4.5.3.1.2 4.3.3 4.5.3.1.3 4.5.1.1 5.5.1

48 73, 74 28 44 25, 26 24, 63 -- --- -30 -- --- -62, 63 28 19 28 27 -- --

16 24 10 12 12 10 34 35 27 27 12 20 10 7 10 10 34

Term

64

Figure number -----

Reference page 3 10 3 38

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

pitch surfaces pitch variation pitch variation tolerance, total accumulated pitch variation, allowable pitch variation, normal pitch variation, total accumulated pitch variation, total accumulated, within a sector of k pitches pitch, angular pitch, axial pitch, base, normal pitch, base, transverse pitch, circular pitch, diametral (transverse) pitch, normal circular pitch, normal diametral pitch, transverse circular pitch, true position

Paragraph number 4.5.1 5.5.3 5.5.7 5.5.4 5.5.5 5.5.6 5.5.8 4.6.23 4.6.16 4.6.18 4.6.17 4.6.13 4.6.19 4.6.15 4.6.20 4.6.14 5.5.2

Figure number 25, 26 99 -- --- --- -100 100 -- -49, 50 50 50, 51 48 -- -49 -- -49 -- --

Reference page 9 34 35 34 34 35 35 18 17 17 17 17 17 17 17 17 34

plane of action plane of axes plane of rotation plane, axial plane, central plane, normal plane, pitch plane, tangent plane, transverse

4.8.6 4.3.2 4.3.4 4.3.1 4.3.8 4.3.7 4.3.3 4.3.5 4.3.6

88 19 21 19 23 3, 78 19 21, 66 19, 21, 22, 52

28 7 8 7 9 8 7 8 8

point of contact point, crossing point, pitch

4.8.1 4.5.4.10 4.5.3.1.3

85, 90 38 28

27 13 10

polar angle, involute

4.6.10

46

16

position pitch, true

5.5.2

-- --

34

pressure angle pressure angle, axial pressure angle, normal pressure angle, operating pressure angle, transverse

4.6.4 4.6.9 4.6.8 4.7.4 4.6.7

43, 46 45 45 -- -45

14 16 16 26 15

principal directions

4.4

24

9

probe path

5.1.15

-- --

31

profile profile angle profile angle, axial

4.6.26 4.6.5 4.6.9

52 43 45

19 15 16

Term

© AGMA 2005 ---- All rights reserved

65

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

profile angle, normal profile angle, standard profile angle, transverse profile chart profile control diameter profile deviation profile deviation, total profile evaluation range profile form deviation profile length, functional profile line, mean profile radius of curvature profile shift profile slope deviation profile tolerance profile variation profile, design profile, functional profile, start of active

Paragraph number 4.6.8 4.6.6 4.6.7 5.7.11 5.1.4 5.7.6 5.7.7 5.7.8 5.7.9 5.7.5 5.8.13 4.6.26.2 4.6.32.8 5.7.10 5.7.3 5.7.2 5.7.4 5.7.1 4.8.18

45 44 45 -- -59 -- --- --- -103 -- --- -54 -- --- -103 102 -- -101 59

Reference page 16 15 15 36 31 36 36 36 36 36 38 19 25 36 36 36 36 35 30

quality quality number quality, gear

5.11.1 5.11.2 5.11

-- --- --- --

38 38 38

rack rack shift rack, basic rack, generating rack, helical rack, spur

4.1.5 4.6.32.9 4.1.6 4.1.7 4.2.3.4 4.2.3.2

1 -- -3 -- -7 6

2 25 2 3 4 4

radial runout radial runout tolerance

5.6.3 5.6.4

-- --- --

35 35

radius limits, test radius, base radius, equivalent pitch radius, fillet radius, profile, curvature radius, test radius, throat form radius, tip

5.3.3.7 4.6.2.2 4.5.1.1 4.6.27.1 4.6.26.2 5.3.3.6 4.5.4.12 4.6.26.1

-- --- -27 56 56 -- -31 55

33 14 10 19 19 33 13 19

range, helix evaluation range, pitch range, profile evaluation

5.8.8 5.5.1 5.7.8

-- --- --- --

38 34 36

Term

66

Figure number

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

ratio, contact ratio, face contact ratio, gear ratio, modified contact ratio, total contact ratio, transverse contact

Paragraph number 4.8.13 4.8.15 4.1.9 4.8.17 4.8.16 4.8.14

-------

recess, arc of

4.8.12

92

29

relief, tip

4.6.26.3

57

19

Revacycle® gears

B.2

-- --

42

right flank right hand helical gear right hand spiral bevel gear right hand worm

4.6.25 4.6.28 4.6.31.1 4.6.28

53, 54 60 67, 68 60

18 20 22 20

roll angle, involute roll path length

4.6.11 5.1.11

47 47

16 31

root root angle root circle root cone root cylinder root diameter root fillet

-- -4.6.31.16 4.5.3.6.1 4.5.4.3 4.5.3.6 4.5.3.6.2 4.6.27

52 74 33 36, 75 -- -30, 33 -- --

18 24 11 13 11 12 19

rotation, plane

4.3.4

21

8

runout runout tolerance, radial runout, axial runout, radial

5.6.1 5.6.4 5.6.2 5.6.3

-----

-----

35 35 35 35

SAP

4.8.18

59

30

shaft angle

4.6.31.7

71

23

shift, profile shift, rack

4.6.32.8 4.6.32.9

-- --- --

25 25

short addendum teeth

4.6.32.16

-- --

26

single flank composite deviation, tooth--to--tooth single flank composite deviation, total single flank composite test single flank measurement

5.3.2.2 5.3.2.3 5.3.2.1 5.3.2

-----

32 32 32 32

Term

© AGMA 2005 ---- All rights reserved

Figure number -------

-----

Reference page 30 30 3 30 30 30

67

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

single pitch deviation single helical gear

Paragraph Figure number number 5.5.9 -- -4.2.3.5 6

Reference page 35 4

skew bevel gear

4.2.5.9

16

6

slope deviation slope deviation, profile

5.8.11 5.7.10

-- --- --

38 36

spacing spacing variation

5.4.3 5.4.4

-- --- --

34 34

span measurement

4.6.32.11

80

25

spiral angle spiral angle, inner spiral angle, mean spiral angle, outer spiral bevel gear spiral bevel gear, left hand spiral bevel gear, right hand spiral gear

4.6.31.3 4.6.31.6 4.6.31.4 4.6.31.5 4.2.5.10 4.6.31.2 4.6.31.1 4.2.5.1

69, 70 70 70 70 17 67 67 -- --

22 23 22 22 6 22 22 5

Spiroid® gearing

B.2

-- --

42

spur gear spur rack

4.2.3.1 4.2.3.2

6 6

3 4

standard (reference) pitch circle standard (refernence) pitch diameter standard profile angle

4.5.3.7 4.5.3.7.1 4.6.8

44 -- -44

12 12 15

start of active profile start of tip break

4.8.18 5.1.12

59 -- --

30 31

straight bevel gear straight line element of base cylinder

4.2.5.8 -- --

16 62

6 20

stub teeth

4.6.32.14

-- --

26

surface of action surface, datum surface, indicated surface, mounting surface, pitch surface, tooth (flank)

4.8.5 5.2.1 5.2.2 5.2.3 4.5.1 4.6.24

-- --- --- --- -25, 26 52

28 31 31 32 9 18

symbols

C.1

-- --

43

tangent plane

4.3.5

21, 86

8

Term

68

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

teeth, adjusted number teeth, crowned teeth, equal addendum teeth, equivalent number teeth, full--depth teeth, involute teeth, long addendum teeth, modified addendum teeth, number teeth, short addendum teeth, stub

Paragraph number 5.1.14 4.6.3 4.6.32.15 4.5.1.2 4.6.32.13 4.6.1 4.6.32.16 4.6.32.12 4.1.8 4.6.32.16 4.6.32.14

-- -42 81 -- --- -39, 40 81 -- --- -81 -- --

Reference page 31 14 26 10 26 14 26 25 3 26 26

test radius test radius limits test, composite action (double flank) test, single flank composite

5.3.3.6 5.3.3.7 5.3.3.1 5.3.2.1

-- --- -95 -- --

33 33 32 32

thickness tolerance, tooth thickness variation, tooth thickness, axial thickness, base circular thickness, chordal, normal thickness, circular thickness, functional tooth thickness, normal circular thickness, transverse circular

5.9.2 5.9.1 4.6.32.4 4.6.32.5 4.6.32.6 4.6.32.1 5.9.3 4.6.32.3 4.6.32.2

-- --- -77 78 78 76 -- -77 77, 78

38 38 25 25 25 24 38 25 24

threads, number

4.1.8

-- --

3

throat diameter throat form radius

4.5.4.11 4.5.4.12

31 31

13 13

TIF

4.6.27.3

59

19

tip tip (face) angle tip (face) cone tip break, start of tip or edge break tip radius tip relief

-- -4.6.31.15 4.5.4.2 5.1.12 5.2.4 4.6.26.1 4.6.26.3

52 74 36 -- --- -55 57

18 24 12 31 32 19 19

toe

4.6.31.13

73

24

tolerance tolerance diameter tolerance, lead tolerance, profile tolerance, radial runout

5.11.5 5.1.9 5.8.3 5.7.3 5.6.4

108 -- -104, 105 103 -- --

39 31 37 36 35

Term

© AGMA 2005 ---- All rights reserved

Figure number

69

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

tolerance, tooth alignment tolerance, tooth thickness tolerance, total accumulated pitch variation tolerance, total radial composite (double flank)

Paragraph number 5.8.3 5.9.2 5.5.7 5.3.3.5

Figure number 104, 105 -- --- --- --

Reference page 37 38 35 32

tooth alignment tooth alignment tolerance tooth alignment trace tooth alignment variation tooth depth tooth surface (flank) tooth thickness tolerance tooth thickness variation tooth thickness, functional tooth, datum tooth--to--tooth radial composite tolerance (double flank) tooth--to--tooth radial composite variation (double flank)

5.8.1 5.8.3 5.8.4 5.8.2 4.7.7 4.6.24 5.9.2 5.9.1 5.9.3 5.1.3 5.3.3.3 5.3.3.2

-- -104, 105 -- --- -35 52 -- --- --- --- --- -96

37 37 37 37 27 18 38 38 38 31 32 32

top land

4.5.3.3.2

32

11

total accumulated pitch variation total accumulated pitch variation tolerance total accumulated pitch variation, within a sector of k pitches total radial composite tolerance (double flank) total radial composite deviation (double flank) total contact ratio total cumulative pitch deviation total face width total helix deviation total profile deviation

5.5.6 5.5.7 5.5.8 5.3.3.5 5.3.3.4 4.8.16 5.4.2 4.6.30.9 5.8.7 5.7.7

100 -- -100 -- --- --- --- -66 -- --- --

35 35 35 32 32 30 34 22 37 36

trace, helix length trace, measured lead trace, tooth alignment

5.8.10 5.8.4 5.8.4

-- --- --- --

38 37 37

tradenames

B.2

-- --

42

transmission error

5.1.13

-- --

31

transverse base pitch transverse circular pitch transverse circular thickness transverse contact ratio transverse diametral pitch transverse direction transverse module transverse plane transverse pressure angle transverse profile angle

4.6.17 4.6.14 4.6.32.2 4.8.14 4.6.19 4.4.2 4.6.21 4.3.6 4.6.7 4.6.7

50, 51 49 77, 78 -- --- -24 -- -19, 22, 52 45 45

17 17 24 30 17 9 17 7 15 15

Term

70

© AGMA 2005 ---- All rights reserved

AMERICAN NATIONAL STANDARD

ANSI/AGMA 1012--G05

true involute form true position pitch

Paragraph Figure number number 4.6.27.3 -- -5.5.2 -- --

Reference page 19 34

undercut

4.6.27.2

58, 59

19

variation variation tolerance, total accumulated pitch variation, allowable variation, allowable pitch variation, backlash variation, lead variation, normal pitch variation, pitch variation, profile variation, spacing variation, tooth alignment variation, tooth thickness variation, total accumulated pitch

5.11.3 5.5.7 5.11.4 5.5.4 4.7.10.2 5.8.2 5.5.5 5.5.3 5.7.2 5.4.4 5.8.2 5.9.1 5.5.6

106 -- -107 -- --- --- --- -99 102 -- --- --- -100

39 35 39 34 27 37 34 34 36 34 37 38 35

wheel, gear

4.1.2

1

2

whole depth

4.7.7

35

27

width, effective face width, face width, functional face width, total face

4.7.11 4.6.30.8 5.1.6 4.6.30.9

66 66, 68 -- -66

27 21 31 22

wobble

5.6.2

-- --

35

working depth

4.7.6

35

27

worm worm, cylindrical worm, enveloping (hourglass) worm, left hand worm, right hand wormgear wormgearing wormgearing, Cone® wormgearing, double--enveloping wormwheel

4.1.4 4.2.4.2 4.2.4.3 4.6.29 4.6.28 4.2.4.1 4.2.4 B.2 4.2.4.4 4.2.4.1

2, 9 2, 9 10 60 60 9 9 -- -10 9

2 4 4 20 20 4 4 42 5 4

zerol bevel gear

4.2.5.10

17

7

zone of action (contact zone) zone, contact

4.8.7 4.8.7

89 89

28 28

Term

© AGMA 2005 ---- All rights reserved

71

ANSI/AGMA 1012--G05

AMERICAN NATIONAL STANDARD

Bibliography The following documents are either referenced in the text of ANSI/AGMA 1012--G05, Gear Nomenclature, Definition of Terms with Symbols, or indicated for additional information. AGMA 913--A98, Method for Specifying the Geometry of Spur and Helical Gears

Straight Bevel, Zerol Bevel and Spiral Bevel Gear Teeth

AGMA 915--3--A99, Inspection Practices -- Gear Blanks, Shaft Center Distance and Parallelism

ANSI/AGMA 2005--D03, Design Manual for Bevel Gears

AGMA 2000--A88, Gear Classification and Inspection Handbook, Tolerances and Measuring Methods For Unassembled Spur and Helical Gears (Including Metric Equivalents) ANSI/AGMA 2001--D04, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth ANSI/AGMA 2002--B88, Tooth Specification and Measurement

ANSI/AGMA 2009--B01, Bevel Gear Classification, Tolerances, and Measuring Methods ANSI/AGMA 2015--1--A02, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears ANSI/AGMA 2101--D04, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth (Metric Edition)

Thickness

ISO 1122--1:1998, Glossary of gear terms -- Part 1: Definitions related to geometry

ANSI/AGMA 2003--F97, Rating the Pitting Resistance and Bending Strength of Generated

ISO 1122--2:1999, Vocabulary of gear terms -- Part 2: Definitions related to worm gear geometry

72

© AGMA 2004 ---- All rights reserved

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