ANSI_AGMA_2015-1-A01

ANSI/AGMA 2015- 1- A01 (Replaces ANSI/AGMA 2000--A88)

AMERICAN NATIONAL STANDARD

ANSI/AGMA 2015- 1- A01

Accuracy Classification System Tangential Measurements for Cylindrical Gears

American National Standard

Accuracy Classification System - Tangential Measurements for Cylindrical Gears ANSI/AGMA 2015--1--A01 [Revision of ANSI/AGMA 2000--A88] 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 quoted or extracted. Credit lines should read: Extracted from ANSI/AGMA 2015--1--A01, Accuracy Classification System -Tangential Measurements for Cylindrical Gears, with the permission of the publisher, the American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314.]

Approved August 1, 2002

ABSTRACT This standard, for spur and helical gearing, correlates gear accuracy grades with gear tooth tolerances. It provides information on minimum requirements for accuracy groups as well as gear measuring practices. Annex material provides guidance on filtering and information on comparison of gear inspection methods. Published by

American Gear Manufacturers Association 1500 King Street, Suite 201, Alexandria, Virginia 22314 Copyright  2002 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--797--5

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ANSI/AGMA 2015--1--A01

Contents Page

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv 1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Symbols, terminology and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Manufacturing and purchasing considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 Application of the AGMA classification system . . . . . . . . . . . . . . . . . . . . . . . . . 14 6 Measuring methods and practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 7 Tolerance values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 8 Master gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Annexes A B C D E

Tolerance tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tolerance system development and comparison . . . . . . . . . . . . . . . . . . . . . . . . Example of statistical process control (SPC) application . . . . . . . . . . . . . . . . . Involute and helix data filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sector pitch deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 21 31 33 35

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Figures 1 2 3 4 5

Helix deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Profile deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Functional profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Pitch deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Illustration of AGMA classification number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Tables 1 2 3 4 5

Alphabetical table of terms with symbols, by terms . . . . . . . . . . . . . . . . . . . . . . . 2 Alphabetical table of symbols with terms, by symbols . . . . . . . . . . . . . . . . . . . . 3 Reference for methods and tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Gear types and measurement methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Minimum number of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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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 Standard 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears.] This standard provides tolerances for different gear accuracy grades from A2 to A11 for unassembled spur and helical gears. Applicable definitions are provided. The purpose is to provide a common basis for specifying accuracy, and for the procurement of unassembled gears. It is not a design manual for determining the specific quality levels for a given application. AGMA 390.03 of 1973 was a consolidation of several AGMA publications, including: AGMA 235.02 (Feb. 1966), Information Sheet for Master Gears AGMA 239.01 (Oct. 1965), Measuring Methods and Practices Manual for Control of Spur, Helical and Herringbone Gears AGMA 239.01A (Sept. 1966), Measuring Methods and Practices Manual for Control of Bevel and Hypoid Gears, and parts of AGMA 236.05 (ASA B6.11, June 1956), Inspection of Fine--Pitch Gears AGMA 390.02 (Sept. 1964), Gear Classification Manual originally published as AGMA 390.01 (1961) Data was added for Gear Rack and Fine--Pitch Worms and Wormgears. The former AGMA 390.02 for Coarse--Pitch and Fine--Pitch Spur, Helical and Herringbone Gearing was enhanced to offer a single, compatible classification system. The tolerance identifier “Q” was added to indicate that the tolerances in 390.03 apply. If Q is not used as a prefix in the quality number, tolerances in AGMA 390.01 and 390.02 applied. ANSI/AGMA 2000--A88 was an update of those sections from AGMA 390.03 for parallel axis gears only. Additionally, the formulas stated the tolerances in metric terms. The content was revised, but basic tolerance levels were unchanged from AGMA 390.03. The other material in AGMA 390.03 on Bevels and Worms was replaced by ANSI/AGMA 2009--A99 and ANSI/AGMA 2011--A98, respectively. ANSI/AGMA 2000 was approved by AGMA membership in January 1988, and as a American National Standard Institute (ANSI) standard on March 31, 1988. The user of this American National Standard is alerted that differences exist between it and ANSI/AGMA 2000--A88. Differences include, but are not limited to: -- Accuracy grade numbering system is reversed, such that the smallest number represents the smallest tolerance; -- Relative magnitudes of elemental tolerances for a single grade are in a different proportion; -- The “helix evaluation range”, where the tolerances are applied, are defined for less flank area than in ANSI/AGMA 2000--A88; --

The “K Chart” is not used for the permissible tolerance values;

--

Runout is not included as one of the elements with a tolerance;

-- Concepts of “mean measurement trace”, “design profile”, “slope deviation” and “form deviation” are added, similar to ISO 1328--1. Therefore, the user of ANSI/AGMA 2015--1--A01 must be very careful when comparing tolerance values formerly specified using ANSI/AGMA 2000--A88. iv



ANSI/AGMA 2015--1--A01 is a replacement for ANSI/AGMA 2000--A88 and ANSI/AGMA ISO 1328--1. It is a complete revision, including accuracy grades, in order to be more compatible with ISO. It combines the grading system of ISO 1328--1 with the methods of ANSI/AGMA 2000--A88, and adds concepts of accuracy grade grouping for minimum measurement requirements, filtering, data density, and roughness limits to form deviations. This revision was started by the AGMA Inspection and Handbook Committee in 1997. It was approved by the AGMA membership in June, 2001. It was approved as an American National Standard on August 1, 2002. Suggestions for improvement of this standard will be welcome. They should be sent to the American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314.

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PERSONNEL of the AGMA Inspection and Handbook Committee Chairman: Edward Lawson . . . . . . . . . . . . . . . . . . . . . . . . . . . M&M Precision Systems Corp.

ACTIVE MEMBERS W.A. Bradley . . . . D.R. Choiniere . . J. Clatworthy . . . . B.L. Cox . . . . . . . T.C. Glasener . . . G.G. Grana . . . . . B. Hofrichter . . . . I. Laskin . . . . . . . .

Consultant Profile Engineering, Inc. Gear Metrology, Inc. BWXT Y--12, LLC Xtek, Incorporated The Gleason Works Arrow Gear Company Consultant

S. Lindley . . . . . . M. May . . . . . . . . . D.A. McCarroll . . D.R. McVittie . . . . S. Moore . . . . . . . L.J. Smith . . . . . . R.E. Smith . . . . . .

The Falk Corporation The Gleason Works ZF Industries Gear Engineers, Inc. Martin Sprocket & Gear, Inc. Consultant R.E. Smith & Company, Inc.

W.E. Lake . . . . . . A.J. Lemanski . . . G.A. Luetkemeier D. Matzo . . . . . . . P.A. McNamara . W.J. Michaels . . . M. Milam . . . . . . . T. Miller . . . . . . . . M. Nanlawala . . . M. Octrue . . . . . . T. Okamoto . . . . . J.A. Pennell . . . . . K.R. Price . . . . . . R.S. Ramberg . . . V.Z. Rychlinski . . D.H. Senkfor . . . . S. Shariff . . . . . . . E. Storm . . . . . . . T. Waldie . . . . . . . R.F. Wasilewski . F.M. Young . . . . . P. Zwart . . . . . . .

Mitsubishi Gear Tech. Center (AG) Penn State University Rockwell Automation/Dodge Northwest Gears, Inc. Caterpillar, Inc. Sundstrand Corporation Amarillo Gear Company The Cincinnati Gear Company IIT Research Institute/INFAC Centre Technique Des Ind. Mec. Nippon Gear Company, Ltd. Univ. of Newcastle--Upon--Tyne Eastman Kodak Company The Gear Works -- Seattle, Inc. Brad Foote Gear Works, Inc. Precision Gear Company PMI Food Equipment Group Consultant Philadelphia Gear Corporation Arrow Gear Company Forest City Gear Company Caterpillar, Inc.

ASSOCIATE MEMBERS M. Antosiewicz . . M.J. Barron . . . . . D. Behling . . . . . . M.K. Considine . . R. Considine . . . . J.S. Cowan . . . . . M.E. Cowan . . . . B. Cowley . . . . . . C. Dick . . . . . . . . . H.D. Dodd . . . . . . R. Green . . . . . . . D. Gregory . . . . . B. Gudates . . . . . J.S. Hamilton . . . H. Harary . . . . . . . D. Heinrich . . . . . G. Henriot . . . . . . J. Horwell . . . . . . S. Johnson . . . . . T. Klemm . . . . . . . D.E. Kosal . . . . . . J. Koshiol . . . . . .

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The Falk Corporation Gear Motions, Inc. Hamilton Sundstrand Aero. Considine Associates Considine Associates Eaton Corporation Process Equipment Co. Mahr Corporation The Horsburgh & Scott Co. Caterpillar, Inc. R--7 Group, Gear Consultants Gear Products, Inc. Fairfield Manufacturing Co., Inc. Regal--Beloit Corporation NIST Xtek, Incorporated Consultant Brown & Sharpe The Gear Works -- Seattle, Inc. Liebherr National Broach & Machine Co. Columbia Gear Corporation


American National Standard --

Accuracy Classification System -- Tangential Measurements for Cylindrical Gears 1 Scope This part of ANSI/AGMA 2015 establishes an accuracy grade system relevant to tangential measurements on flanks of individual cylindrical involute gears. It specifies definitions for gear tooth accuracy terms, the structure of the gear accuracy grade system, and allowable values. It is strongly recommended that any user of this part of ANSI/AGMA 2015 be very familiar with the methods and procedures outlined in AGMA 915--1--A02. Use of techniques other than those of AGMA 915--1--A02 combined with the limits described in this part of ANSI/AGMA 2015 may not be suitable. This standard provides the gear manufacturer and the gear buyer with a mutually advantageous reference for uniform tolerances. Ten accuracy grades are defined in this standard, numbered A2 through A11, in order of decreasing precision. 1.1 Equations for tolerances Equations for tolerances and their ranges of validity are provided in 7.2 for the defined accuracy of gearing. In general, these tolerances cover the following ranges: 5 ≤ z ≤ 1000 or 10 000/mn whichever is less 5 mm ≤ D ≤ 10 000 mm 0.5 ≤ mn ≤ 50 4 mm ≤ b ≤ 1000 mm β ≤ 45°


where D

is pitch diameter;

mn

is normal module;

b

is facewidth (axial);

z

is number of teeth;

β

is helix angle.

See clause 4 for required and optional measuring methods. 1.2 Exceptions This standard does not apply to enclosed gear unit assemblies, including speed reducers or increasers, gear motors, shaft mounted reducers, high speed units, or other enclosed gear units which are manufactured for a given power, speed, ratio or application. Gear design is beyond the scope of this standard. The use of the accuracy grades for the determination of gear performance requires extensive experience with specific applications. Therefore, the users of this standard are cautioned against the direct application of tolerance values to a projected performance of unassembled (loose) gears when they are assembled. Refer to the latest AGMA Publications Index for applicable standards. NOTE: Tolerance values for gears outside the limits stated in this standard should be established by determining the specific application requirements. This may require setting a tolerance smaller than calculated by the formulas in this standard.

2 Normative references The following standards contain provisions which, through reference in this text, constitute provisions of this American National Standard. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this American National Standard are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below. AGMA 915--1--A02, Inspection Practices -- Part 1: Cylindrical Gears -- Tangential Measurements AGMA 915--3--A99, Inspection Practices -- Gear Blanks, Shaft Center Distance and Parallelism

1



ANSI/AGMA 1012--F90, Gear Nomenclature, Definitions of Terms with Symbols ANSI/AGMA 2110--A94, Measuring Instrument Calibration -- Part I, Involute Measurement (Metric) ANSI/AGMA 2113--A97, Measuring Instrument Calibration, Gear Tooth Alignment Measurement ANSI/AGMA 2114--A98, Measuring Instrument Calibration, Gear Pitch and Runout Measurements ISO 701:1998, International gear notation -Symbols for geometrical data

3 Symbols, terminology and definitions The symbols, terminology and definitions pertaining to the tolerances and inspection of spur and helical gear teeth are listed here for use in this standard. For other definitions of geometric terms related to gearing, see ANSI/AGMA 1012--F90.

NOTE: Some of the symbols and terminology contained in this document may differ from those used in other documents and AGMA standards. Users of this standard should assure themselves that they are using the symbols, terminology and definitions in the manner indicated herein.

3.1 Fundamental terms and symbols The terminology and symbols used in this standard are listed alphabetically by term in table 1, and alphabetically by symbol in table 2. 3.2 Definitions cumulative pitch deviation, total, Fp The largest algebraic difference between the index deviation values for a specified flank. Distinction is not made as to the direction or algebraic sign of this reading. Such a distinction would require a purely arbitrary specification of a direction (clockwise or counterclockwise) traveled between the two teeth comprising the total cumulative pitch deviation.

Table 1 -- Alphabetical table of terms with symbols, by terms Terms Accuracy grade Accuracy grade identifier prefix Contact pattern measurement Cumulative pitch deviation, total Cumulative pitch deviation tolerance, total Design outside diameter Diameter, pitch Facewidth (axial) Functional profile length Gear form filter cutoff Helix angle Helix deviation, total Helix evaluation range Helix form deviation Helix form tolerance Helix slope deviation Helix slope tolerance Helix tolerance, total Normal module Number of teeth Number of pitches in a sector Pitch, transverse circular Profile deviation, total Profile form deviation Profile form tolerance Profile slope deviation Profile slope tolerance

2

Symbol A A cp Fp FpT Do D b Lαc λg β Fβ Lβ ffβ ffβT fHβ fHβT FβT mn z k pt Fα ffα ffαT fHα fHαT

Units -- --- --- -mm mm mm mm mm mm mm deg mm mm mm mm mm mm mm mm -- --- -mm mm mm mm mm mm

Where used 7.1.2 1 Table 3 3.2 7.2.2 Eq 2 1.1 1.1 3.2 Eq 1 1.1 3.2 3.2 3.2 7.2.6.3 3.2 7.2.6.2 7.2.6.1 1.1 1.1 Figure 4 Figure 4 3.2 3.2 7.2.5.3 3.2 7.2.5.2 (continued)



Table 1 (concluded) Terms Profile tolerance, total Single flank composite deviation, tooth--to--tooth (filtered) Single flank composite deviation, total Single flank composite tolerance, tooth--to--tooth Single flank composite tolerance, total Single pitch deviation Single pitch deviation tolerance Tolerance diameter Tooth thickness measurement

Symbol FαT fis Fis fisT FisT fpt fptT dT s

Units mm mm mm mm mm mm mm mm -- --

Where used 7.2.5.1 3.2 3.2 7.2.3 7.2.4 3.2 7.2.1 3.2 Table 3

Table 2 -- Alphabetical table of symbols with terms, by symbols Symbol A A b cp D Do dT Fis FisT Fp FpT Fα FαT Fβ FβT ffα ffαT ffβ ffβT fHα fHαT fHβ fHβT fis fisT fpt fptT k Lαc Lβ mn pt s z β λg

Terms Accuracy grade identifier prefix Accuracy grade Facewidth (axial) Contact pattern measurement Diameter, pitch Design outside diameter Tolerance diameter Single flank composite deviation, total Single flank composite tolerance, total Cumulative pitch deviation, total Cumulative pitch deviation tolerance, total 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 Helix slope deviation Helix slope tolerance Single flank composite deviation, tooth--to--tooth (filtered) Single flank composite tolerance, tooth--to--tooth Single pitch deviation Single pitch deviation tolerance Number of pitches in a sector Functional profile length Helix evaluation range Normal module Pitch, transverse circular Tooth thickness measurement Number of teeth Helix angle Gear form filter cutoff

Units -- --- -mm -- -mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm -- -mm mm mm mm -- --- -deg mm

Where used 1 7.1.2 1.1 Table 3 1.1 Eq 2 3.2 3.2 7.2.4 3.2 7.2.2 3.2 7.2.5.1 3.2 7.2.6.1 3.2 7.2.5.3 3.2 7.2.6.3 3.2 7.2.5.2 3.2 7.2.6.2 3.2 7.2.3 3.2 7.2.1 Figure 4 3.2 3.2 1.1 Figure 4 Table 3 1.1 1.1 Eq 1

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This standard specifies direction of tolerancing for total cumulative pitch deviation to be along the arc of the tolerance diameter, dT, circle within the transverse plane. Tolerances for total cumulative pitch deviation are provided by the formula in 7.2.2 of this standard.

the datum surfaces. It is the axis to which the gear details, and in particular the pitch, profile, and helix tolerances are defined. See AGMA 915--3--A99. design helix The helix specified by the designer as shown on the design specification. When not specified, it is an unmodified helix. See figure 1.

datum axis The datum axis of the gear is defined by Key

: Mean helix line

: Measured helix

: Design helix

i)

Design helix: unmodified helix Measured helix: with minus material outside the evaluation range

ii)

Design helix: modified helix (example) Measured helix: with minus material outside the evaluation range

iii)

Design helix: modified helix (example) Measured helix: with excess of material outside the evaluation range

-Lβ

-Lβ

-Lβ

b

b

b

Fβ

+ -Lβ

b

b

+

+

ffβ

Lβ

-Lβ

iii)

+

b a) Total helix deviation

-Lβ b b) Helix form deviation

Figure 1 -- Helix deviations 4

fHβ

--

ffβ

Fβ

+

-Lβ b

+ fHβ

i)

ii)

+

+ fHβ

ffβ

Fβ

+

-Lβ b c) Helix slope deviation



design profile The profile specified by the designer as shown on the design specification. When not specified, it is an unmodified involute. See figure 2.

functional profile That portion of the tooth flank between the profile control diameter and the start of tip break, see figure 3.

Key

Start of tip break Profile control diameter

i)

Design profile: unmodified involute Measured profile: with minus material outside the evaluation range

ii)

Design profile: modified involute (example with tip relief only) Measured profile: with minus material outside the evaluation range

iii)

Design profile: modified involute (example with full contour) Measured profile: with excess of material near the tip ffα

Fα

fHα

fHα

ffα TB

Lαc

Lαc

--

CD

CD

Fα

ffα

fHα

TB

Lαc

Lαc

--

CD b) Profile form deviation

+

--

a) Total profile deviation

+

+ CD

TB

TB

--

--

CD

TB

+

ii)

TB

+

+

Lαc

CD

--

-Fα

Lαc

Lαc

Lαc

CD

CD

iii)

TB

+

--

+

i)

TB

+

Lαc

TB

--

TB CD

: Mean profile line

: Measured profile

: Design profile

CD c) Profile slope deviation

Figure 2 -- Profile deviations

5



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.

Outside diameter Start of tip break

Functional profile

Pitch diameter

External tooth

Profile control diameter Base circle Root diameter

NOTE: It is the responsibility of the gear designer to assure that the helix evaluation range is adequate for the application.

Root diameter Profile control diameter Pitch diameter

Functional profile

Start of tip break

Internal tooth

Inside diameter Base circle

Figure 3 -- Functional profile functional profile length, Lαc The difference between the roll path lengths at the points that define the limits of the functional profile. gear form filter cutoff, λg The wavelength at which either involute profile or helix measurement data are segregated by the low--pass filter, thereby including only longer wavelength deviations. This filter cutoff should be stated in terms of roll path length. It shall be calculated as follows: L λ g = αc but not less than 0.25 mm 30

(1)

where λg

is the gear form filter cutoff, mm.

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, ffβ, and total helix deviation, Fβ. Minus material outside the helix evaluation range may be ignored. This standard specifies the direction of tolerancing for helix deviation to be in a transverse plane, on a line tangent to the base circle. helix deviation, total, Fβ Distance between two design helix lines which enclose the actual helix trace over the evaluation range, Lβ, see figure 1a. 6

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, Lβ, see figure 1b. 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. helix slope deviation, fHβ Distance between two design helix lines which intersect the mean helix line at the end points of the evaluation range, Lβ, see figure 1c. 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. index deviation The displacement of any tooth flank from its theoretical position, relative to a datum tooth flank, see figure 4. 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.



+fpt pt

k ⋅ pt

Index deviation

theoretical actual Figure 4 -- Pitch deviations This standard specifies direction of tolerancing for index deviation to be along the arc of the tolerance diameter, dT, circle within the transverse plane. 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, Lβ, 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. NOTE: This helix is an aid in the determination of the deviations ffβ (figure 1b) and fHβ (figure 1c).

mean profile line A line (or curve) that has the same shape as the design profile, but aligned with the measured trace. It is developed by subtracting the ordinates of a straight--line gradient from the ordinates of the design profile. Within the functional profile length, Lαc, 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. NOTE: This profile is an aid in the determination of ffα (figure 2b) and fHα (figure 2c).

profile control diameter A specified diameter of the circle beyond which the tooth profile must conform to the specified involute curve. See functional profile. profile deviation 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, ffα, and total profile deviation, Fα. Minus material beyond the tip break may be ignored. This standard specifies the direction of tolerancing for profile deviation to be in a transverse plane, on a line tangent to the base circle. profile deviation, total, Fα Distance between two design profile lines which enclose the actual profile trace over the functional profile length, Lαc, see figure 2a. profile evaluation range The profile is evaluated over the specified functional profile length. profile form deviation, ffα α 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, Lαc, see figure 2b. profile slope deviation, fHα α Distance between two design profile lines which intersect the mean profile line at the endpoints of the functional profile length, Lαc, see figure 2c. 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. 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. NOTE: Roll path length is an alternative to roll angle for specification of selected diameter positions on an involute profile.

7



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. 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. 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. single pitch deviation, fpt The displacement of any tooth flank from its theoretical position relative to the corresponding flank of an adjacent tooth, see figure 4. 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. This standard specifies tolerancing direction of measurement for single pitch deviation to be along the arc of the tolerance diameter, dT, circle within the transverse plane. Tolerances for single pitch deviation are provided by the formula in 7.2.1 of this standard. start of tip break Minimum specified diameter at which the tip break can occur. See ANSI/AGMA 1012--F90. tolerance diameter, dT The diameter located one normal module below the design outside diameter, thereby being approximately at mid--height. d T = D o − 2m n where:

8

dT

is tolerance diameter, mm;

Do

is design outside diameter, mm;

mn

is normal module, mm.

(2)

The location of pitch and helix measurements shall be at the tolerance diameter. See 4.3.3. 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.

4 Manufacturing and purchasing considerations This standard provides classification tolerances and measuring methods for unassembled gears. This clause presents considerations for control of the various phases of manufacturing, including the recommended methods of measurement control. These methods provide the manufacturer and purchaser with recommendations for verifying the accuracy of a manufactured product, as well as information relative to the interpretation of measurement data. Some design and application considerations may warrant measuring or documentation not normally available in standard manufacturing processes. Specific requirements are to be stated in the contractual documents. In the previous (AGMA 2000--A88) classification system, higher AGMA accuracy numbers designated higher precision. In this standard, lower AGMA accuracy grades designate higher precision in order to be consistent with international standards. To avoid confusion, the designator “A” shall be used when specifying accuracy grades from this standard. 4.1 Manufacturing certification Certification of variations in accordance with the gear’s specific AGMA accuracy grade and inspection charts or data can be requested as part of the purchase contract. The manufacturing of gearing to a specified accuracy may or may not include specific measurements. When applications warrant, detailed specific measurements, data analysis, and additional considerations may be necessary to establish acceptance criteria for a gear. The specific methods of measurement, documentation of accuracy grade, and other geometric tolerances of a gear are



normally considered items which are to be mutually agreed upon between manufacturer and purchaser.

ance of the necessary accuracy having been built--in through careful manufacturing control at each step.

For information on the use of statistical process control (SPC), see annex C.

NOTE: Documentation may be deemed unnecessary for products manufactured under process control when inspection records are not specified in the purchase contract.

NOTE: Specifying an AGMA accuracy grade or measurement criteria that requires closer tolerances than required by the application may increase the cost unnecessarily.

4.2 Process control Process control is defined as the method by which gear accuracy is maintained through control of each individual step of the manufacturing process. Upon completion of all manufacturing operations, a specific gear has been given an inherent level of accuracy; this level of accuracy was established during the manufacturing process, and it is totally independent of any final inspection. Process control includes elements such as manufacturing planning, maintenance of machine tools, cutting tool selection and maintenance, heat treatment control, and accuracy assurance programs, as needed, to achieve and maintain the necessary gear accuracy. When properly applied, gears manufactured by specific control techniques will be found to be of uniform accuracy. Therefore, little or no final inspection may be necessary for a gear, particularly in some classification levels; assur-

With proper application of process control, relatively few measurements may be made on any one gear. For example, tooth size may be evaluated by a measurement on only two or three sections of a given gear. It is assumed that these measurements are representative of all the teeth on the gear. Gears made in quantity may be inspected at various steps in their manufacturing process on a sampling basis. It is possible that a specific gear can pass through the entire production process without ever having been measured. Based on appropriate confidence in the applied process control, the manufacturer of that gear must be able to certify that its accuracy is equal to those gears that were measured. 4.3 Measurement methods Gear geometry may be measured by a number of alternate methods as shown in table 3. The selection of the particul ar method depends on the magnitude of the tolerance, the size of the gear, the production quantities, equipment available, accuracy of gear blanks, and measurement costs.

Table 3 -- Reference for methods and tolerances Parameter symbol Elemental: Fp fpt Fα ffα fHα Fβ ffβ fHβ Composite: Fis fis cp Size: s

Measurement description

Location of tolerance (clause)

Cumulative pitch, total Single pitch Profile, total Profile form Profile slope Helix, total Helix form Helix slope

7.2.2 7.2.1 7.2.5.1 7.2.5.3 7.2.5.2 7.2.6.1 7.2.6.3 7.2.6.2

Single flank composite, total Single flank composite, tooth--to--tooth Contact pattern

7.2.4 7.2.3 -- --

Tooth thickness

-- --

9



The manufacturer or the purchaser may wish to measure one or more of the geometric features of a gear to verify its accuracy grade. A gear which is specified to an AGMA accuracy grade must meet all the individual tolerance requirements applicable to the particular accuracy grade and size as noted in tables 4 and 5. Unless otherwise specified, all measurements are taken and evaluated at the

tolerance diameter, dT, as specified in 3.2. Normally the tolerances apply to both sides of the teeth unless only one side is specified as the loaded side. In some cases, the loaded side may specify higher accuracy than the nonloaded or minimum-loaded side; if applicable, this information is to be specified on the gear engineering drawing (see 4.4.6).

Table 4 -- Gear types and measurement methods Accuracy group

Grade designator

Low (L) ( )

A10--A11

Medium (M)

A6--A9

High (H)

A2--A5

Minimum acceptable parameters Fp, fpt, s Fp, fpt, s, Fα, Fβ Fp, fpt, s Fα, ffα, fHα Fβ, ffβ, fHβ

Alternative method Group M Group H s, radial method1) Group H cp, Fis, fis, s

NOTE: 1) See ANSI/AGMA ISO 1328--2.

Table 5 -- Minimum number of measurements Method designator Elemental: Fp: Cumulative pitch, total fpt: Single pitch Fα: Profile, total ffα: Profile form fHα: Profile slope Fβ: Helix, total ffβ: Helix form fHβ: Helix slope Composite: Fis: Single flank composite, total fis: Single flank composite, tooth--to--tooth cp: Contact pattern Sizes: s: Tooth thickness

NOTE: 1) See 4.3 for location of measurements.

10

Typical yp measuring g method

Minimum number of requirements for1) Group L Group M Group H

Two probe Single probe Two probe Single probe

All teeth All teeth All teeth All teeth



Profile test

-- --

3 teeth

4 teeth

Helix test

-- --

3 teeth

4 teeth

All teeth

All teeth

All teeth

All teeth

All teeth

All teeth

3 places

3 places

3 places

2 teeth 1 place

3 teeth 1 place

4 teeth 2 places

1 place All teeth

2 places All teeth

3 places All teeth

Tooth caliper Measurement over or between pins Span measurement Composite action test



If prior agreement between the manufacturer and purchaser specifies measurement of gears, unless otherwise specified, the manufacturer may select: -- the measurement method to be used from among the applicable methods described in AGMA 915--1--A02 and summarized in table 4; -- the piece of measurement equipment to be used by the selected measurement method, provided it is in proper calibration; -- the individual teeth to be measured, as long as they are approximately equally spaced and meet the minimum number required by the method as summarized in table 5. NOTE: This standard provides tolerances for unassembled gears. The measurement of gearing mated in an assembly for a specific application is beyond the scope of this document.

4.3.1 Equipment verification Equipment used for the elemental measurement of product gears should be verified periodically according to standard calibration procedures such as those in ANSI/AGMA 2110--A94, ANSI/AGMA 2113--A97 and ANSI/AGMA 2114--A98. This should also include a determination of the uncertainty of the measuring process. 4.3.2 Recommended measurement control methods The recommended methods of measurement control for each AGMA accuracy grade and type of measurement are listed in tables 4 and 5. NOTE: No particular method of measurement or documentation is considered mandatory unless specifically agreed upon between manufacturer and purchaser. When applications require measurements beyond those recommended in this standard, special measurement methods must be negotiated prior to manufacturing the gear.

4.3.3 Considerations measurements

for

elemental

Before elemental measurement values can be compared with tolerance values, certain operational parameters of the measurement instrument must be known. This includes: --

datum axis;

--

direction of measurement;

--

direction of tolerancing;

--

tolerancing diameter;

--

data filtering;

--

data density.

In some cases, measurement instruments follow the minimum requirements by default. When other conditions exist, it is required that causes of the resulting measurement differences are known and compensated. It is important to distinguish between measurement location (the tolerance diameter), measurement direction, and tolerancing direction. In this standard, the tolerancing direction for pitch measurements is along the arc of the tolerance diameter, dT, circle within the transverse plane, while the tolerancing direction for helix is tangent to the base circle within the transverse plane. 4.3.3.1 Datum axis Specification of the design profile, design helix, and design pitch requires definition of an appropriate reference axis of rotation, called the datum axis. It is defined by specification of datum surfaces. See AGMA 915--3--A99. The datum axis determines tooth geometry, thereby being the reference for measurements and associated tolerances. The location and orientation of the tolerance diameter circle are determined by the datum axis. 4.3.3.2 Direction of measurement Measurements of the shape or the position of any surface can be made in a direction normal to that surface, inclined at some angle, or along the arc of a specified circle. Common metrology practice is to measure in a direction normal to the surface being tested. At any point on a gear tooth surface, the normal vector is oriented 1) tangent to the base cylinder of the gear, and 2) inclined relative to the transverse plane at the base helix angle. Measurements taken in this direction have the following characteristics: -- Measurements will always be the smallest when the direction of measurement is normal to the surface. Measurements at any other inclination will be larger. -- Measurements made in the normal direction are not affected by the tolerancing diameter selected by the test operator. -- Measurements taken in other directions may be affected by force vectors acting upon the probe mechanism. -- As gear teeth move through mesh, the lines (or points) of contact between mating tooth

11


surfaces proceed along lines of action within the plane of action. Measurements made in the normal direction coincide with this direction of tooth meshing motion. When converted to angular units of measure, they correlate well with transmission errors. It is important to understand that various gear measuring instruments use different testing procedures, some measuring in the normal direction, some measuring in other directions. 4.3.3.3 Direction of tolerancing Tolerances on the shape or the position of gear tooth surfaces must specify the direction in which given measurements are to be considered. This specified direction, called the tolerancing direction, may be normal to that surface, inclined at some angle, or along the arc of a specified circle. When the tolerancing direction is inclined at some angle to the normal direction, it is specified by two parameters: -- the diameter to which the measurements shall be tangent; -- the angle of inclination, relative to the transverse plane. In this standard the tolerancing direction varies with the given toleranced elemental parameter. Tolerancing direction requirements are listed in 3.2. Original measurement values must be compensated if the actual measurement direction and the tolerancing direction specified for the given parameter are different. When the measurement instrument’s direction of measurement is normal and the tolerancing direction is other than normal, measurement values must be increased before analysis and comparison to tolerances. Typically, the factor for this adjustment is the cosine of the angle between the normal direction and the specified tolerancing direction. For example, when testing helix with a normal direction of measurement (within the base tangent plane) the measurement values must be divided by the cosine of the base helix angle to compensate those values to the transverse plane as required by clauses 3 and 7. Measurement values from elemental test instruments that measure in a direction other than normal and not in the specified tolerancing direction, require more complex adjustments before comparison to tolerances. 12


4.3.3.4 Tolerance diameter This standard specifies the tolerance diameter, dT, as defined in 3.2 as the location for measurement of helix and pitch parameters. Also see 4.3.3.2 and 4.3.3.3. 4.3.3.5 Measurement data filtering Any tooth surface will exhibit a wide spectrum of deviations from the specified tooth flank form. This includes, at one extreme, those of long duration, such as a general concavity. At the other end of the spectrum are short duration irregularities, such as surface roughness. Measurement and control of short duration roughness is beyond the scope of this standard. See ISO/TR 10064--4. This standard requires modification of original measurement values for involute profile and helix parameters so as to include only long duration irregularities before analysis and comparison to tolerances. This modification is called low--pass filtering. It will minimize or exclude all irregularities with wavelengths shorter than the specified filter cutoff wavelength. The filter cutoff specified by this standard is the gear form filter cutoff, λg, as defined in 3.2. The actual filter type and attenuation should be indicated on the data sheet. A Gaussian type filter with 50% attenuation of cut--off is recommended. See Annex D for additional information. 4.3.3.6 Measurement data density Measurement data density is closely related to measurement data filtering in that the data sampling rate limits the wavelength of surface irregularities that can be observed. The number of data points included in the evaluation length should be shown on the inspection record. This standard therefore requires that involute profile measurement data sets include a minimum of 200 samples. Helix measurement data sets include a minimum of 200 samples or 5 Lβ / λg, whichever is greater, in order to ensure that the filter is effective. 4.3.4 Tooth contact pattern inspections Checking tooth contact patterns with a mate or master gear is a method of inspection of either assembled gears, or gears mounted on a gear testing machine. It provides an indication of compatible tooth shape, both up and down the tooth profile, and lengthwise on the tooth. It evaluates that portion of the gear tooth surface which actually makes contact with its mate. With this technique, the areas that contact can be observed by coating the teeth with a very thin layer of marking compound and



meshing the gears, see AGMA 915--1--A02. A judgement of compatibility may be made by the position and size of the contact area. It does not necessarily indicate compatible tooth shape for loaded conditions. Axial runout may also be indicated by a shifting of the tooth contact from side to side, progressively around the gear. This test can include the effect of tooth element variations, such as a variation in helix. This standard does not provide tolerances relating these tests to gear accuracy.

The methods of determining the backlash required for individual applications are beyond the scope of this standard (for additional information see ANSI/ AGMA 2002--B88).

4.3.5 Inspection by sound test

4.4.3 Matching gears as sets

The accuracy of a pair of gears may also be evaluated by running them in a suitable sound testing machine. The acceptability is characterized by periodic variation in sound during each revolution, or high levels of noise. This standard does not provide specific limits for this test, which is normally based on experience.

Matched sets can be provided, usually at extra cost, and are required in many applications. In such a case, the purchaser must agree on the details of the additional specifications concerning how the matching is to be performed and verified. Applications requiring high accuracy gearing may necessitate the matching, or modifying, of pinion and gear profiles and helix such that the matched set is satisfactory for the application.

4.4 Additional considerations When specifying the accuracy of a gear, there are additional or special considerations that must be reviewed. These considerations may include items such as: --

backlash allowances in tooth thickness;

--

materials furnished by the purchaser;

--

matching gears as sets;

--

master gears for composite measurement;

--

replacement gearing;

--

modified AGMA accuracy grade;

patterns

When heat treating operations are required, the gear manufacturer shall assume the responsibility for the final accuracy only when the material furnished is in accordance with the agreed upon material specifications.

NOTE: This standard provides tolerances for unassembled gears only. The inspection of gearing mated in an assembly for a specific application is beyond the scope of this standard. The matching process for such gears sold as pairs assumes greater importance than the individual absolute measurements.

4.4.4 Master gears for composite action tests

-- center distance and backlash markings on gear and pinion; -- record of tooth contact photographs, transfer tapes, etc.

4.4.2 Material furnished by the purchaser

by

The listed items and other special considerations are to be reviewed and agreed upon by the manufacturer and purchaser. 4.4.1 Backlash An individual gear does not have backlash. Backlash is only present when one gear mates with another. The backlash of a gear set is based on the tooth thickness of each member in mesh, as well as the center distance at which the gears are assembled. The functional backlash is dependent upon the tolerances of tooth thickness, runout, tooth geometry, and center distance.

A master gear may be used for single flank composite tests. A master gear is a gear of known accuracy, designed specifically to mesh with the gear to be inspected for composite variation. The design, accuracy, and cost of a master gear must be negotiated between the manufacturer and purchaser. Usually, a specific master is required for each different production gear design. Providing or manufacturing a special master gear must be scheduled to be available when the manufactured gear is to be inspected by composite measurements. 4.4.5 Replacement gearing For replacement gearing, the performance obtained from the previous gearing should be evaluated. If satisfactory, replace with similar material and accuracy. If improved performance is desired, modifications of material, heat treatment, and accuracy level should be considered. Consult with the manufacturer for appropriate recommendations. 4.4.6 Modified AGMA accuracy grade Conditions may require that one or more of the individual elements or composite tolerances be of a lower or higher accuracy grade than the other

13



tolerances. In such cases, it is possible to modify the accuracy grade to include an accuracy grade for each gear element or composite tolerance.

Ten accuracy grades are provided in this standard, numbered A2 through A11 in order of decreasing precision.

4.4.7 Additional criteria

5.2 Additional characteristics

Gear blank dimensions supplied by the purchaser must be mutually agreed upon to permit the gear manufacturer to hold the tolerances for the specified accuracy grade. See AGMA 915--3--A99.

The tolerances, methods, and definitions contained in this standard prevail unless contractual agreements between the manufacturer and purchaser contain specific exceptions.

In certain applications there may be additional characteristics that may require tolerances in order to assure satisfactory performance. For example, if dimensions for tooth thickness or surface finish tolerances are desirable in order to assure satisfactory performance in special applications, such dimensions and tolerances should appear on drawings or purchase specifications. Methods of measuring some of these characteristics are discussed in AGMA 915--1--A02, and in the annexes.

4.5.1 Evaluation of accuracy grade

5.3 Accuracy tolerances

4.5 Acceptance criteria

The overall accuracy grade of a gear is determined by the largest accuracy grade number measured for any toleranced parameter specified for the gear by this standard.

The tolerances for each item that govern the accuracy of gears are calculated by the equations given in clause 7.

6 Measuring methods and practices 5 Application of the AGMA classification system 5.1 Basis of classification system The AGMA classification system is an alpha numeric code which contains two items, accuracy grade and prefix. The AGMA classification number shall consist of a prefix letter “A” identifying the tolerance source, and an accuracy grade identifying the specific tolerances. An example of how to establish an AGMA classification number for a given set of conditions is presented in figure 5.

The measuring methods and practices for spur and helical gears can be found in AGMA 915--1--A02.

7 Tolerance values The tolerance values for each item that govern the accuracy are calculated by the equations given in 7.2. For convenience, some tolerance tables are provided in annex A, and additional tables covering all tolerances, grades, and sizes in both metric and U.S. customary units are available in the Supplemental Tables for AGMA 2015/915--1--A02. Accuracy grade

Typical AGMA grade number

A 5

Tolerance source identifier Indicates the tolerances in ANSI/AGMA 2015--1--A01. The letter Q was used to designate tolerances from AGMA 2000--A88 and 390.03. If no letter is shown, tolerances in AGMA 390.01 or 390.02 apply. (See clauses 1 and 4.)

Accuracy grade This integer (ranging from 2 through 11) identifies the accuracy level of the tolerances. (See clauses 6 and 7.) Figure 5 -- Illustration of AGMA classification number 14



7.1 Use of equations

The equations for the single flank composite tolerances are different from the corresponding tangential composite equations in ISO 1328--1. Calculated values for tooth--to--tooth single flank composite tolerance have been reduced to account for the filtered analysis used within this standard.

7.1.1 Range of application

7.2.1 Single pitch deviation tolerance, fptT

Values outside the limits of the equations are beyond the scope of this standard and are not to be extrapolated. The specific tolerances for such gears are to be agreed upon by the buyer and the seller.

Unless otherwise stated, the range of the application is as per 1.1. 7.1.2 Step factor

Single pitch deviation, fptT, is to be calculated according to equation 3 or 4. For gears with 5 ≤ dT ≤ 400 mm

 

f ptT = 0.3m n + 0.003d T + 5.2 × 2

The step factor between two consecutive grades is 2. Values of the next higher (or lower) grade are determined by multiplying (or dividing) by 2. The

For gears with 400 < dT ≤ 10 000 mm

required value for any accuracy grade may be determined by multiplying the unrounded calculated

f ptT = 0.3m n + 0.12 d T + 4 × 2

 A−5 

value for grade 5 by 2 where A is the number of the required accuracy grade. 7.1.3 Rounding rules Values calculated from the equations in 7.2 are to be rounded as follows: -- If greater than 10 micrometers, round to the nearest integer micrometer; -- If 5.0 micrometers or greater but less than or equal to 10 micrometers, round to the nearest 0.5 micrometer;



  

 A−5 

(4)

Accuracy grades A2 through A11 0.5 ≤ mn ≤ 50 5 ≤ z ≤ 1000 or 10 000/mn whichever is less 5 ≤ dT ≤ 10 000 mm 7.2.2 Cumulative pitch deviation tolerance, total, FpT Total cumulative pitch deviation tolerance, FpT, is to be calculated according to equation 5 or 6. For gears with 5 ≤ dT ≤ 400 mm

 

F pT = 0.3m n + 0.03d T + 20 × 2

NOTE: If the measuring instrument reads in inches, values calculated from the equations in 7.2 are to be converted to ten thousandths of an inch and then rounded according to the rules for micrometers (i.e., substitute the word tenths for micrometers in the rules above).

For gears with 400 < dT ≤ 10 000 mm

The single pitch deviation tolerance and total cumulative pitch deviation tolerance equations for diameters greater than 400 mm are identical to the corresponding equations in ISO 1328--1, except in all cases, the actual values for module, diameter and face width shall be used (in all equations) rather than the geometrical mean values which are used to generate the tolerance tables in ISO 1328--1. For smaller gears the change in tolerance as diameter decreases is less than ISO 1328--1, with the resulting value slightly higher for a given diameter.

(3)

where the range of application is restricted as follows:

-- If less than 5.0 micrometers, round to the nearest 0.1 micrometer.

7.2 Tolerance equations

 A−5 



 A−5 

  

F pT = 0.3m n + 1.25 d T + 7 × 2

(5)  A−5 

(6)

where the range of application is restricted as follows: Accuracy grades A2 through A11 0.5 ≤ mn ≤ 50 5 ≤ z ≤ 1000 or 10 000/mn whichever is less 5 ≤ dT ≤ 10 000 mm 7.2.3 Single flank composite tolerance, tooth--to--tooth, fisT Single flank composite tolerance, tooth--to--tooth, fisT, is to be calculated according to equation 7.

 

f isT = 0.03m n + 0.003d T + 2 × 2

 A−5 

(7)

15



where the range of application is restricted as follows if fisT is specified: Accuracy grades A2 through A11 0.5 ≤ mn ≤ 50 5 ≤ z ≤ 1000 or 10 000/mn whichever is less 5 ≤ dT ≤ 2500 mm 7.2.4 Single flank composite tolerance, total, FisT Single flank composite tolerance, total, FisT, is to be calculated according to equation 8.

 

F isT = 0.33m n + 0.033d T + 22 × 2

 A−5 

(8)

where the range of application is restricted as follows if FisT is specified: Accuracy grades A2 through A11 0.5 ≤ mn ≤ 50 5 ≤ z ≤ 1000 or 10 000/mn whichever is less 5 ≤ dT ≤ 2500 mm 7.2.5 Profile tolerances The range of profile tolerance application is restricted as follows: Accuracy grades A2 through A11 0.5 ≤ mn ≤ 50 5 ≤ z ≤ 1000 or 10 000/mn whichever is less 5 ≤ dT ≤ 10 000 mm 7.2.5.1 Profile tolerance, total, FαT





 A−5 

(9)

7.2.5.2 Profile slope tolerance, fHα αT Profile slope tolerance, fHαT, is to be calculated according to equation 10.



  

f HαT = 2 m n + 0.14 d T + 0.5 × 2

 A−5 

(10)

7.2.5.3 Profile form tolerance, ffα αT Profile form tolerance, ffαT, is to be calculated according to equation 11.



  

f fαT = 2.5 m n + 0.17 d T + 0.5 × 2

16

The range of helix tolerance application is restricted as follows: Accuracy grades A2 through A11 0.5 ≤ mn ≤ 50 5 ≤ z ≤ 1000 or 10 000/mn whichever is less 5 ≤ dT ≤ 4000 mm 4 ≤ b ≤ 1000 mm 7.2.6.1 Helix tolerance, total, FβT Total helix tolerance, FβT, is to be calculated according to equation 12.



  

F βT = 0.1 d T + 0.63 b + 4.2 × 2

 A−5 

(12)

7.2.6.2 Helix slope tolerance, fHβT Helix slope tolerance, fHβT, is to be calculated according to equation 13.



  

f HβT = 0.07 d T + 0.45 b + 3 × 2

 A−5 

(13)

7.2.6.3 Helix form tolerance, ffβT Helix form tolerance, ffβT, is to be calculated according to equation 14.



  

f fβT = 0.07 d T + 0.45 b + 3 × 2

 A−5 

(14)

8 Master gears

Total profile tolerance, FαT, is to be calculated according to equation 9. F αT = 3.2 m n + 0.22 d T + 0.7 × 2

7.2.6 Helix tolerances

 A−5 

(11)

Master gears are used mainly for composite error testing. The determining of individual deviations in cylindrical gears calls for special equipment. In addition, the master gears can also be used for verifying gear testers. The calibration certificates of master gears shall contain detailed results of all the required measured values, uncertainty for each measured value, and the measurement conditions. Master gears shall conform to clause 7 tolerances, for accuracy grade 2, 3 or 4. Master gears of accuracy grade 2 are recommended for verifying gear testers and checking production gears primarily of grades 4 and 5. Master gears of grade 3 are recommended for checking gears primarily of grade 6 and 7. Master gears of grade 4 are recommended for checking gears of grade 8 and higher.



Annex A (informative) Tolerance tables [The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be construed as a part of ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears.]

should not be interpolated or extrapolated. For more detailed tables of diameter, number of teeth and module, see Supplemental Tables for AGMA 2015/915--1--A02.

A.1 Purpose This annex provides a graphical presentation of the values for tolerances of accuracy grade 5. These tables are calculated from the equations in 7.2, but

Table A.1 -- Spur and helical gear classification, single pitch deviation tolerance, fptT, grade 5 Table values in micrometers Tooth size Diametral Module pitch 50.8 0.5 25.4 1 12.7 2 8.5 3 6.4 4 5.1 5 4.2 6 3.6 7 3.2 8 2.8 9 2.5 10 1.7 15 1.3 20 1.0 25 0.5 50

100

200

Tolerance diameter, mm 300 400 600

800

1000

5.5 6.0 6.0 6.5 6.5 7.0 7.5 7.5 8.0 8.0 8.5 10 12 ---

6.0 6.0 6.5 6.5 7.0 7.5 7.5 8.0 8.0 8.5 9.0 11 12 14 --

-6.5 6.5 7.0 7.5 7.5 8.0 8.0 8.5 9.0 9.0 11 12 14 21

--8.0 8.5 8.5 9.0 9.0 9.5 10 10 10 12 13 15 22

---8.5 9.0 9.5 9.5 10 10 10 11 12 14 15 23

-6.5 7.0 7.5 7.5 8.0 8.0 8.5 9.0 9.0 9.5 11 12 14 21

--7.5 8.0 8.0 8.5 8.5 9.0 9.5 9.5 10 11 13 14 22

35 30

fptT, micrometers

25 20 15 10 1 module 20 module 50 module

5 0

0

100

200

300

400 500 600 700 800 900 1000 Tolerance diameter, mm Figure A.1 -- Spur and helical gear classification, single pitch deviation tolerance, grade 5

17



Table A.2 -- Spur and helical gear classification, cumulative pitch deviation tolerance, total, FpT, grade 5 Table values in micrometers Tooth size Diametral Module pitch 50.8 0.5 25.4 1 12.7 2 8.5 3 6.4 4 5.1 5 4.2 6 3.6 7 3.2 8 2.8 9 2.5 10 1.7 15 1.3 20 1.0 25 0.5 50

100

200

Tolerance diameter, mm 300 400 600

800

1000

23 23 24 24 24 25 25 25 25 26 26 28 29 ---

26 26 27 27 27 28 28 28 28 29 29 31 32 34 --

-29 30 30 30 31 31 31 31 32 32 34 35 37 44

--43 43 44 44 44 44 45 45 45 47 48 50 57

---47 48 48 48 49 49 49 50 51 53 54 62

-32 33 33 33 34 34 34 34 35 35 37 38 40 47

--38 39 39 39 39 40 40 40 41 42 44 45 53

80 70 60

FpT, micrometers

50 40 30 20 1 module 10 0

20 module 50 module 0

100

200

300

400

500

600

700

800

900

1000

Tolerance diameter, mm Figure A.2 -- Spur and helical gear classification, cumulative pitch deviation tolerance, total, grade 5 18



Table A.3 -- Spur and helical gear classification, single flank composite tolerance, tooth to tooth, fisT, grade 5 Table values in micrometers Tooth size Diametral Module pitch 50.8 0.5 25.4 1 12.7 2 8.5 3 6.4 4 5.1 5 4.2 6 3.6 7 3.2 8 2.8 9 2.5 10 1.7 15 1.3 20 1.0 25 0.5 50

80

200

400

Tolerance diameter, mm 600 800 1000 1200 1400

-2.3 2.3 2.3 2.4 2.4 2.4 2.5 2.5 2.5 2.5 2.7 2.8 ---

-2.6 2.7 2.7 2.7 2.8 2.8 2.8 2.8 2.9 2.9 3.1 3.2 3.4 --

-3.2 3.3 3.3 3.3 3.4 3.4 3.4 3.4 3.5 3.7 3.8 3.8 4.0 4.7

--3.9 3.9 3.9 4.0 4.0 4.0 4.0 4.1 4.1 4.3 4.4 4.6 5.5

--4.5 4.5 4.5 4.6 4.6 4.6 4.6 4.7 4.7 4.9 5.0 5.0 6.0

---5.0 5.0 5.0 5.0 5.0 5.0 5.5 5.5 5.5 5.5 6.0 6.5

---5.5 5.5 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.5 7.0

----6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 7.0 7.0 7.5

1600

1800

2000

----7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.5 7.5 7.5 8.5

-----7.5 7.5 7.5 7.5 7.5 7.5 8.0 8.0 8.0 9.0

-----8.0 8.0 8.0 8.0 8.5 8.5 8.5 8.5 9.0 9.5

10

fisT, micrometers

8

6

4

1 module

2

0

20 module 50 module

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Tolerance diameter, mm Figure A.3 -- Spur and helical gear classification, single flank composite tolerance, tooth to tooth, grade 5

19



Table A.4 -- Spur and helical gear classification, single flank composite tolerance, total, FisT, grade 5 Table values in micrometers Tooth size Diametral Module pitch 50.8 0.5 25.4 1 12.7 2 8.5 3 6.4 4 5.1 5 4.2 6 3.6 7 3.2 8 2.8 9 2.5 10 1.7 15 1.3 20 1.0 25 0.5 50

80

200

400

Tolerance diameter, mm 600 800 1000 1200 1400

-25 25 26 26 26 27 27 27 28 28 30 31 ---

-29 29 30 30 30 31 31 31 32 32 34 35 37 --

-36 36 36 37 37 37 38 38 38 39 40 42 43 52

--42 43 43 43 44 44 44 45 45 47 48 50 58

--49 49 50 50 50 51 51 51 52 53 55 57 65

---56 56 57 57 57 58 58 58 60 62 63 72

---63 63 63 64 64 64 65 65 67 68 70 78

1600

1800

2000

----76 76 77 77 77 78 78 80 81 83 91

-----83 83 84 84 84 85 86 88 90 98

-----90 90 90 91 91 91 93 95 96 105

----70 70 70 71 71 71 72 73 75 76 85

120 100

FisT, micrometers

80 60 40 1 module

20 0

20 module 50 module 0

200

400

600

800

1000

1200

1400

1600

1800

2000

Tolerance diameter, mm Figure A.4 -- Spur and helical gear classification, single flank composite tolerance, total, grade 5

20



Annex B (informative) Tolerance system development and comparison [The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be construed as a part of ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears.]

B.1 Purpose This annex gives the reasoning leading to the spur and helical gear classification system of this standard, and comparisons of pitch tolerances and cumulative pitch tolerances with other systems. B.2 Development The gear classification system was changed from the previous AGMA 2000--A88 for several reasons: -- The nonlinear formulas and tables made interpolation of values within the applied ranges difficult; -- The tolerance trends did not relate well to typical manufacturing capabilities for very small gears; -- The old system was outdated for gear manufacturer’s and customer’s applications. The committee agreed that a new gear classification system was needed: one that used more linear formulas, was easier to understand by users, and allowed for an expanded range of application (but only with agreement between manufacturer and user). In addition to AGMA 2000--A88, the committee studied the other cylindrical gear classification system, ISO 1328--1:1995. It was noted that for many typical gears (100 mm to 800 mm diameter and 2 to 20 module), relatively small differences occurred between the classification systems. In both systems, the classes or grades are separated by a square root of 2 stepping factor. Initial investigations by the committee for ANSI/ AGMA 2009--A99 (bevel gears) indicated that a tolerance system in which the tolerance curves were linear with changes in diameter may have been appropriate. The following formulas were then developed:

 

f ptT = 0.003 d T + 0.3 m n + 5 × 2

 A−5 

(B.1)

 

F pT = 0.03 d T + 0.3 m n + 19 × 2

 A−5 

(B.2)

The committee then elected to adopt the tolerance formulas from ISO 1328--1 and ISO 1328--2, with modifications for the smaller diameters. This assured some harmony with existing international standards and eliminated the difficulties associated with interpolating some non--linear values from AGMA 2000--A88. The limits were established to set the tolerances at points the committee thought were valid. The single flank tolerances are different than those given in annex A of ISO 1328--1:1995. Based on committee experience, the single flank tolerances shown in this standard are more appropriate for functional considerations. After much study and discussion, the classification system in this standard was agreed upon. The system of classifying very accurate gears with a low number, instead of retaining the method of AGMA 390.03, was done for two reasons: -- The system is established internationally by ISO and other standards; -- A new labeling system was necessary to distinguish the difference of the new tolerance grades and those of AGMA 2000--A88. A general comparison between the new system and AGMA 2000--A88 systems may be made by subtracting the class or grade number of one system from 17 to find an approximate class or grade number for the other system. B.3 Comparison See figures B.1 through B.18 for a comparison of the new system with AGMA 2000--A88 and ISO 1328--1. Tolerance values from ISO 1328--1 are plotted as step functions as per the standard’s tables.

21



140 120

FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A6

400 500 600 Tolerance diameter, mm

700

ISO 1328--1, 6

800

900

1000

AGMA 2000--A88, runout, Q12

Figure B.1 -- Tolerance comparison, cumulative pitch deviation, total, class Q12 and grade A6 for module 12.7 140 120

FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A5

400 500 600 Tolerance diameter, mm ISO 1328--1, 5

700

800

900


Figure B.2 -- Tolerance comparison, cumulative pitch deviation, total class Q12 and grade A5 for module 12.7

22

1000



140 120

FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A5


700

ISO 1328--1, 5

800

900

1000



FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A5


700

800

900

1000


Figure B.4 -- Tolerance comparison, cumulative pitch deviation, total, class Q12 and grade A5 for module 1.6

23



140 120

FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A7

400

500

600

700

Tolerance diameter, mm ISO 1328--1, 7

800

900

1000



FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A7


700

800

900



24

1000



140 120

FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A7


700

ISO 1328--1, 7

800

900

1000


Figure B.7 -- Tolerance comparison, cumulative pitch deviation, total, class Q10 and grade A7 for module 1.6 160 140 120

FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A8


700

800

900

1000



25



140 120

FpT, micrometers

100 80 60 40 20 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A8


700

ISO 1328--1, 8

800

900

1000



fptT, micrometers

25 20 15 10 5 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A5


700

800

900

AGMA 2000--A88, pitch, Q12

Figure B.10 -- Tolerance comparison, allowable single pitch deviation, class Q12 and grade A5 for module 12.7

26

1000



35 30

fptT, micrometers

25 20 15 10 5 0

0

100

200

300


ANSI/AGMA 2015--1--A01, A5

700

800

900

1000


ISO 1328--1, 5

Figure B.11 -- Tolerance comparison, allowable single pitch deviation, class Q12 and grade A5 for module 6.4 35 30

fptT, micrometers

25 20 15 10 5 0

0

100

200

300

400

500

600

700

800

900

1000

Tolerance diameter, mm ANSI/AGMA 2015--1--A01, A5

ISO 1328--1, 5



27



35 30

fptT, micrometers

25 20 15 10 5 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A7


700

800

900

1000

AGMA 2000--A88 pitch, Q10

ISO 1328--1, 7


fptT, micrometers

25 20 15 10 5 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A7


700

800

900



28

1000



35 30

fptT, micrometers

25 20 15 10 5 0

0

100

200

300

400

500

600

700

800

900

1000

Tolerance diameter, mm ANSI/AGMA 2015--1--A01, A7

ISO 1328--1, 7



35 30

fptT, micrometers

25 20 15 10 5 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A8


700

800

900

1000



29



35 30 25

fptT, micrometers

20 15 10 5 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A8


700

ISO 1328--1, 8

800

900

1000



fptT, micrometers

25 20 15 10 5 0

0

100

200

300

ANSI/AGMA 2015--1--A01, A8


700

800

900


Figure B.18 -- Tolerance comparison, allowable single pitch deviation, class Q9and grade A8 for module 1.6

30

1000



Annex C (informative) Example of statistical process control (SPC) application [The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be construed as a part of ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears.]

Determination steps:

C.1 Purpose When gears are to be manufactured to a statistical requirement, the gears will have to be made more accurately than the tolerance listed. This annex provides a rule of thumb to determine the accuracy levels needed to meet the statistical requirements. C.2 Statistical process control (SPC) Statistical process control may not be achievable for very accurate gears due to the uncertainty in the measurement values. The variability of the measuring process contributes to the variability of the manufacturing process. For more information, see ANSI/AGMA 2114--A98, annex E. To achieve statistical compliance, the manufacturing tolerance must be smaller than the specified tolerance. To determine the manufacturing requirement, the following starting recommended:

tolerance point is

1.

F pT = 0.050 mm

2.

1 + C pk = 1 + 1.33 = 2.33

3.

F pT 1 + C pk

= 0.050 = 0.021 mm 2.33

4. Therefore the new tolerance required is accuracy grade A4. All manufacturing parameters must consider the need to produce the equivalent of accuracy grade A4 gears to meet the SPC requirements. This includes the gear blank tolerances (see AGMA 915--3--A99) and other gear tooth tolerances listed in this standard. NOTE 1: For unilateral (one sided) tolerances: C pk = USL − X 3 σ n−1 where

1. Add 1 to the required Cpk value. See note.

USL

= upper specification limit;

2. Divide the total cumulative pitch deviation tolerance, FpT, by this value.

X

= average;

σn--1

= σ of a sample.

3. The results indicate the tolerance that the parts will have to meet to pass the SPC requirements. Example: Given:

NOTE 2: For bidirectional tolerances:

C pk = Lesser of USL − X or X − LSL 3 σ n−1 3 σ n−1 0.5

dT = 150 mm

 n X − X2 m m = σ n−1 =  i=1 n − 1  

Accuracy grade = A7

where

mn = 12 mm

Cpk = 1.33

LSL

= lower specification limit.

31



(This page is intentionally left blank.)

32



Annex D (informative) Involute and helix data filtering [The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be construed as a part of ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears.]

D.1 Purpose

D.4 Electrical filtering

Involute and helix test data are usually conditioned by low--pass filtering prior to analysis procedures. The choice of filtering method and cutoff wavelength will influence analysis results. This annex provides descriptions of filtering practices.

Electrical filtering limits the test data gathered to longer wavelength (lower frequency) values and is thus a low--pass type filter. During electrical filtering, the test data signal passes from the probe head through an electrical filtering (RC) circuit and finally on to the data analysis and output devices.

D.2 Filtering Measurements include variations of many different wavelengths or frequencies. The exclusion of certain portions of the test data frequency spectrum is called filtering. A filter that excludes short wavelength (high frequency) data is called a low-pass filter. A filter that excludes long wavelength (low frequency) data is called a high--pass filter. A filter that excludes the shortest and longest wavelengths (highest and lowest frequencies) of variations, thereby leaving only medium wavelength (medium frequency) data, is called a bandpass filter. For gear metrology purposes, a low--pass filter is usually applied to remove the influences of high frequency surface finish conditions from the observations of total, form, and slope deviations of involute and helix. Several types of filtering may be implemented in the gear measuring system. D.3 Mechanical filtering

Electrical filtering circuits are designed to accomplish the elimination of high frequency test data at a specified wavelength called the cutoff. All data at frequencies significantly higher than the cutoff are eliminated. High frequency test data that is near but not exactly at the cutoff is filtered proportionally according to its proximity to the cutoff wavelength. An unfortunate effect of RC electrical filtering is a phase shifting of data that can influence analysis of test results. Electrical filtering is most commonly encountered on older instruments; newer instruments employ mathematical filtering. All RC electrical filters produce phase shifting of test data. Electrical filtering is an acceptable practice, provided that its limitations are understood. D.5 Mathematical filtering

Mechanical filtering limits the involute and helix test data gathered to longer wavelength (lower frequency) values and is thus a low--pass type filter. Mechanical filtering occurs as the geometry of the probe (i.e., tip radius) bridges and thereby suppresses the shorter wavelength (higher frequency) variations.

Mathematical filtering requires that test data first be converted from analog to digital to permit processing by a digital computer. Two general types of mathematical filter are commonly available. One type emulates the characteristics of electrical filters (with or without the phase shifting characteristic of RC circuits). The other type employs Gaussian mathematics.

In applications that require inclusion of this very high frequency data, smaller probe tip radii can be specified. Since gear involute and helix data is normally subjected to intentional low--pass filtering, this is rarely required. Evaluation of gear surface finish is best accomplished with specialized surface finish instruments, rather than involute or helix test instruments.

The transmission characteristics of a phase correct Gaussian filter are such that 50% of the amplitude of a sinusoidal waveform with a wavelength equal to the long--wavelength cutoff will be transmitted. Other frequencies are passed proportionally, according to their proximity to the cutoff. When a phase correct Gaussian filter is used, vertical distortions are reduced and phase shift is eliminated. Based

33


upon sine wave amplitude transmission characteris-


tics and compliance with ISO standards, use of the

data with different (or no) mathematical filtering applied.

digital Gaussian filter is recommended.

D.6 Cutoff selection

It is also advantageous to be able to view the test

Standard involute and helix data cutoff values for use in this document are specified in clause 3.

34



Annex E (informative) Sector pitch deviation [The foreword, footnotes and annexes, if any, are provided for informational purposes only and should not be construed as a part of ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears.]

E.1 Purpose This annex provides the definition, measurement practices, recommended tolerances, and guidance for application of sector pitch deviation, Fps/8. E.2 Definition sector pitch deviation, Fps/8 Sector pitch deviation is equal to the largest algebraic difference between the index deviation values for a specified flank within any sector of k pitches such that: k≈z 8

(E.1)

where: k

is the number of pitches in the sector;

z

is the number of teeth in the gear.

NOTE: When equation E.1 produces a non--integer result for k, round to the nearest whole number of pitches.

The smallest useful value of k is 2. Therefore this parameter is only applicable to gears with 12 or more teeth. Distinction is made as to the algebraic sign of this reading. Thus, a condition wherein the distance between the two teeth comprising the sector pitch deviation was shorter than the theoretical distance would be considered a minus (--) deviation. A condition wherein the distance between the two teeth comprising the sector pitch deviation was longer than the theoretical distance would be considered a plus (+) deviation. The tolerancing direction for sector pitch deviation is along the arc of the tolerance diameter circle, dT, within the transverse plane. E.3 Measurement practice Gear tooth position data gathered by either a pitch comparator (two--probe) device or an indexing (single--probe) device can be used to determine sector pitch deviation. In either case, index values must first be found. Determination of the sector pitch deviation, Fps/8, requires the algebraic summation of the maximum positive index value and the maximum

negative index value within every group of k pitches (k + 1 adjacent teeth), as defined in clause E.2. The sector pitch deviation, Fps/8, is the largest of these summation values. E.4 Comparison to similar parameters It is important to understand that this parameter is not equivalent to certain other similar parameters such as cumulative pitch deviation, Fpk, as included in ISO 1328--1. That parameter observes only the deviation in position of the first and last teeth of each sector of k pitches. Observation of sector pitch deviation, Fps/8, described in this clause, includes the positions of all teeth within each sector of k pitches. An example of the differences between these analysis methods is provided by figure E.1. That figure shows the index data for a gear with 35 teeth, thus having a value of k equal to 4. In this example the value of cumulative pitch deviation, Fps/8, is 3.8, occurring between teeth 18 and 22 which are 4 pitches apart. The value of sector pitch deviation, Fps/8, is 4.7, occurring between teeth 18 and 20 which are contained within a sector of 4 pitches. E.5 Tolerance, sector pitch deviation, FpsT A recommended tolerance for sector pitch deviation, FsT, could be calculated according to equation E.2. F psT = 0.5 × F pT

(E.2)

where: FpsT

is the tolerance, sector pitch deviation;

FpT

is the tolerance, total cumulative pitch.

A recommended range of application for sector pitch deviation follows the same restrictions as those specified for total cumulative pitch tolerance, FpT. E.6 Guidance to application Unless otherwise specified in procurement documents, the measurement of sector pitch deviation is not mandatory. Information pertaining to this parameter is therefore not included in the main body of the standard.

35



However, when agreed between supplier and purchaser, the method may be valuable. If index deviations over relatively small numbers of pitches are too large, substantial acceleration forces can be

generated. This is especially true for high speed gears, where dynamic loads can be considerable. Hence the value of measuring and tolerancing sector pitch deviation.

10

Sector with largest deviation

8 6

Cumulative pitch deviation, Fpk (Fpz/8) per ISO 1328--1

Deviation

4 2 0

1 2

3 4 5 6

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

--2 --4 --6

Sector pitch deviation, Fps/8

--8

Tooth number Figure E.1 -- Index data

36



Bibliography

The following documents are either referenced in the text of ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears or indicated for additional information. AGMA 2000--A88, Gear Classification and Inspection Handbook -- Tolerances And Measuring Methods For Unassembled Spur And Helical Gears (Including Metric Equivalents) AGMA ISO 10064--1, Cylindrical Gears -- Code of Inspection Practice -- Part 1: Inspection of Corresponding Flanks of Gear Teeth, 2001 ANSI/AGMA ISO 1328--1, Cylindrical Gears -- ISO System of Accuracy -- Part 1: Definitions and Allowable Values of Deviations Relevant to Corresponding Flanks of Gear Teeth, 2000 ANSI/AGMA ISO 1328--2, Cylindrical Gears -- ISO System of Accuracy -- Part 2: Definitions and Allowable Values of Deviations Relevant to Radial Composite Deviations and Runout Information, 2000 ANSI/AGMA 2002--B88, Tooth Thickness Specification and Measurement ANSI/AGMA 2009--B01, Bevel Gear Classification, Tolerances, and Measuring Methods ISO/TR 10064--4:1998, Cylindrical gears -- Code of inspection practice -- Part 4: Recommendations relative to surface texture and tooth contact pattern checking

37

PUBLISHED BY AMERICAN GEAR MANUFACTURERS ASSOCIATION 1500 KING STREET, ALEXANDRIA, VIRGINIA 22314

ANSI_AGMA_2015-1-A01

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