AGMA 915-1-A02 Gears Inspect

AGMA 915- 1- A02

AMERICAN GEAR MANUFACTURERS MANUFACTURERS ASSOCIATION ASSOCIATION

Inspection Practices - Part 1: Cylindrical Gears Tangential Measurements 2 0 A 1 5 1 9 A M G A

AGMA INFORMATION INFORMATION SHEET (This Information Sheet is NOT an AGMA Standard)

Inspection Practices -- Part 1: Cylindrical Gears -- Tangential American Measurements Gear AGMA 915--1 915--1---A02 Manufacturers CAUTION NOTICE: NOTICE : AGMA technical publications publications are subject to constant improvement, Association

revision revision or withdrawal withdrawal as dictated dictated by experience. experience. Any person who refers to any AGMA techni technical cal pub public licati ation on should should be sure sure tha thatt the pub public licati ation on is the latest latest availa available ble from from the Association on the subject matter. [Tables or other self--supporting sections may be quoted or extracted. Credit lines should read: Extracted from AGMA 915--1915--1--A02, -A02, Inspection Inspection Practices Practices -- Part 1: Cylindric Cylindrical al Gears -- Tangential Measurements, with the permission of the publisher, the American Gear Manufacturers Association, Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314.]

Approved April 16, 2002

ABSTRACT This information sheet provides a code of practice dealing with inspection relevant to tangential element and composite deviations of cylindrical involute gears (measurements referred to single flank contact) and serves as a supplemen supplementt to ANSI/AGMA ANSI/AGMA 2015--1--A01, -1--A01, Accuracy Accuracy Classification System --- Tangential Measurements for Cylindrical Gears. Published Published by

American Gear Manufacturers Association 1500 King Street, Street, Suite 201, Alexandria, Alexandria, Virginia 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--555891--55589--798 -798---3

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AMERICAN GEAR MANUFACTURERS ASSOCIATION

AGMA 91591 5--1 -1 --A02 -A 02

Contents Page

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Symbols and corresponding terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 Extent of gear inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 Identification of deviation position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 Measurement of pitch deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 7 Measurement of profile deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 8 Measurement of helix deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 9 Measurement of single flank composite deviations . . . . . . . . . . . . . . . . . . . . . . 26 10 Contact pattern checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Figures 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

Notation and numbering for external gear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 No N otation and numbering for internal gear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Schematic of single probe measuring device . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Single pitch deviation, single probe device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Pitch measurement with a pitch comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Circular pitch measurement, two probe device . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Si S ingle pitch deviation, two probe device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Sample Sample table table with hypothetic hypothetical al deviation deviation values values obtained obtained by pitch comparator (two probe) device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Sample Sample table table with hypothetic hypothetical al deviation deviation values values obtai obtained ned by indexing indexing (single probe) device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Sample Sample graphic graphic represent representation ation of single single pitch pitch deviat deviations, ions, f pt . . . . . . . . . . . . . . 10 Sample graphic representation of index deviations . . . . . . . . . . . . . . . . . . . . . . 10 Base pitch measurement, two probe device . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Schematic of involute inspection device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Profile measuring method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Profile inspection by coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Typical tooth profile measurement charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Tooth profile and profile diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Mean profile profile slope deviation deviation,, f H!m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Profile inspection by optical projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Pr Profile inspection by gear tooth caliper method . . . . . . . . . . . . . . . . . . . . . . . . . 18 Profile inspection by measurement over pins . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Helix deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Graphic charting of helix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Helix diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Traces generated from four tooth flanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Helix of right hand helical gear with short lead (+ helix angle) le) . . . . . . . . . . . . . 23 Helix of right hand helical gear with ith long lead (-- helix lix angle) . . . . . . . . . . . . . 23 Helix of left hand helical gear with long lead (-- helix angle) . . . . . . . . . . . . . . . 24 Helix of left hand helical gear with short lead (+ helix angle) . . . . . . . . . . . . . . 24 Principle of undulation inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Co C omposite gear testing, double and single flank . . . . . . . . . . . . . . . . . . . . . . . . 26 Sc Schematic of a single flank measuring device . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Individual tooth devia viations revealed by single flank testing . . . . . . . . . . . . . . . 27 Filtered signal from figure 33 (eccentricity removed) . . . . . . . . . . . . . . . . . . . . 28 Angular motion curves from tooth modification . . . . . . . . . . . . . . . . . . . . . . . . . 29

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AGMA 915 -- 1 -- A02


36

Effect Effect of contact contact transfer transfer on the the profile profile compone component nt in a tangent tangential ial composite deviation diagram (spur gears) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Influence of overlap ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Single flank composite strip chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Single flank composite test, low number of teeth . . . . . . . . . . . . . . . . . . . . . . . . 40 Single flank composite test, high number of teeth . . . . . . . . . . . . . . . . . . . . . . . 41a Total composite deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41b Long term component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41c Short term component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Manual interpretation of composite test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Part Part of tan tangen gentia tiall compos composite ite deviat deviation ion diagra diagram m -- Interp Interpret retati ation on examp example le . . . 44 Tangential angential composi composite te deviatio deviation n diagrams diagrams showing showing influe influence nce of mesh mesh relocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Match tching ing pro profile iles, wit with toot tooth h alig alignm nmen entt mism ismatch tch and end end reli relief ef . . . . . . . . . . . 46 Matching helix, with profile mismatch and end relief . . . . . . . . . . . . . . . . . . . . . 47 Waviness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Typical Typical specific specificatio ation: n: approxima approximately tely 75% contact contact,, excluding excluding extremes extremes of tooth, which are intentionally relieved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30 31 32 33 33 34 34 35 36 36 37 38 38 39 39

Tables 1

iv

Symbols and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1


AGMA 915--1 --A02

Foreword This Information Sheet, AGMA 915--1--A02, Inspection Practices -- Part 1: Cylindrical Gears -- Tangential Measurements is provided for informational purposes and is intended for use with the Standard ANSI/AGMA 2015--1--A01, Accuracy Classification System -Tangential Measurements for Cylindrical Gears. AGMA 915--1--A02 replaces AGMA ISO 10064--1, Cylindrical Gears -- Code of Inspection Practice -- Part 1: Inspection of Corresponding Flanks of Gear Teeth. and the information on similar subjects as covered in ANSI/AGMA 2000--A88, Gear Classification and Inspection Handbook -- Tolerances and Measuring Methods for Unassembled Spur and Helical Gears. The user of this Information Sheet is alerted that differences exist between it and ANSI/AGMA 2000--A88 and AGMA ISO 10064--1. These include, but are not limited to: -- Measuring methods refer to an accuracy grade numbering system that is reversed, such that the smallest number represents the smallest tolerance; -- Probe direction and measurement requirements for elemental and composite tolerances may differ from ANSI/AGMA 2000--A88 or AGMA ISO 10064--1; -- The measurement “profile evaluation range” and “helix evaluation range”, where the tolerances are applied, are defined for differentarea than in ANSI/AGMA 2000--A88 or AGMA ISO 10064--1; --

The measurement of undulations is included;

-- Concepts of “mean measurement trace”, “design trace”, “slope deviation”, “form deviation”, “gear form filter cutoff”, “tolerance diameter” and “data density” are defined. Therefore, the user of this information sheet must be very careful when comparing measurement methods formerly specified using ANSI/AGMA 2000--A88 or AGMA ISO 10064--1. The first draft of AGMA 915--1--A02 was made in May, 1998. This document was approved by the Inspection Handbook Committee on January 31, 2002. It was approved by the Technical Division Executive Committee as an AGMA Information Sheet on April 16, 2002. Suggestions for improvement of this document 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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AGMA 915--1--A02


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

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

Consultant Profile Engineering, Inc. Gear Metrology, Inc. BWXT Y12 LLC Xtek, Incorporated The Gleason Works Arrow Gear Company Milwaukee Gear Consultant

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

The Falk Corporation The Gleason Works ZF Industries Gear Engineers, Inc. Martin Sprocket & Gear, Inc. Caterpillar, Inc. Atlas Copco Comptec, 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 . . . . . . . R.F. Wasilewski . F.M. Young . . . . . P. Zwart . . . . . . . .

Mitsubishi Gear Technology Ctr. 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 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 . . . . . .

vi

The Falk Corporation Gear Motions, Inc. Hamilton Sundstrand Aero. Considine Associates Considine Associates Eaton Corporation Process Equipment Company Mahr Corporation The Horsburgh & Scott Co. Caterpillar, Inc. R7 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 Gear Manufacturers Association --

Inspection Practices -Part 1: Cylindrical Gears -- Tangential Measurements

AGMA 915 --1 --A02

At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this document are encouraged to investigate the possibility of applying the most recent editions of the standards indicated. AGMA 915--3--A99, Inspection Practices -- Gear Blanks, Shaft Center Distance and Parallelism ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears ISO 53:1998, Cylindrical gears for general and heavy engineering -- Standard basic rack tooth profile ISO 54:1996, Cylindrical gears for general engineering and for heavy engineering -- Modules

1 Scope This information sheet constitutes a code of practice dealing with tangential measurements on flanks of individual cylindrical involute gears., i.e., with the measurement of pitch, profile, helix and tangential composite characteristics. In providing advice on gear measuring methods and the analysis of measurement results, it supplements the standard ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears.

2 References The following standards contain provisions which are referenced in the text of this information sheet.

ISO 701:1998, International gear notation -Symbols for geometrical data ISO 1122--1:1998, Vocabulary of gear terms -- Part 1: Definitions related to geometry

3 Symbols and corresponding terms The symbols and terms used throughout this manual are in basic agreement with the symbols and terms given in ISO 701:1998, International gear notation -Symbols for geometrical data. In all cases, the first time that each symbol is introduced, it is defined and discussed in detail. See table 1. NOTE: The symbols and definitions used in this information sheet may differ from other AGMA standards. The user should not assume that familiar symbols can be used without a careful study of their definitions.

Table 1 -- Symbols and definitions Definition1)

Symbols b D Db d d b eff d T F "

Facewidth Design pitch diameter Design base diameter Reference diameter Effective base diameter Tolerance diameter Total helix deviation

Units mm mm mm mm mm mm mm

Where first used Figure 24 Eq 4 Eq 3 Eq 24 6.5.3 6.2 Figure 22 (continued)

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AGMA 915--1--A02


Table 1 (continued) Symbols F is F p F ps/8 F r F ! f dbm f e f f ! f f " f H! f H!m f H" f H"m f H"mt f id f is f Lm f pbm f pbn f pt f w" f 1, f 2 f ! f !mn f !mt f " f "m g! k

L L Leff L! L!c L" L#

l mn N n pb pbn pm

Definition1) Total single flank composite deviation Total cumulative pitch deviation Sector pitch deviation2) Radial runout Total profile deviation Mean base diameter difference2) Eccentricity between gear axis and axis of gear teeth Profile form deviation Helix form deviation Profile slope deviation2) Mean profile slope deviation2) Helix slope deviation2) Mean helix slope deviation2) Mean helix slope deviation, in the transverse plane and tangent to the tolerance diameter2) Tooth--to--tooth double flank composite deviation Tooth--to--tooth single flank composite deviation Mean lead difference2) Mean normal base pitch deviation2) Normal base pitch deviation2) Single pitch deviation2) Undulation height (along helix) Reading head frequency Pressure angle deviation2) Mean normal pressure angle deviation2) Mean transverse pressure angle deviation2) Helix angle deviation2) Mean helix angle deviation2) Length of path of contact Number of pitches in a sector Left flank Lead of the design helix Effective lead Profile evaluation range Functional profile length Helix evaluation range Base tangent length to start of active profile Left hand helix Normal module Pitch number Number of deviation values included in the mean Base pitch Theoretical normal base pitch True position pitch2)

Units mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm

mm

mm mm mm mm mm pulses/sec degrees degrees degrees degrees degrees mm -- --- -mm mm mm mm mm mm -- -mm -- --- -mm mm mm

Where first used 9.1 6.1 6.2 9.3.6 Figure 17 6.5.3 Figure 18 Figure 17 Figure 24 Figure 17 7.6 Figure 24 8.6 Eq 18 9.3.6 9.1 8.7 6.5.3 6.5 6.1 Figure 24 Figure 32 7.5 6.5.3 6.5.3 8.5 8.7 Figure 36 5.6 5.2 Eq 17 8.7 Figure 17 Eq 9 Figure 24 Figure 17 5.3 Eq 1 5.5 Eq 8 Figure 36 6.5 6.3.2 (continued)

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AGMA 915--1 --A02

Table 1 (concluded) Definition1)

Symbols R Right flank r Right hand helix s Undulation measurement bar length z Number of teeth z M z 1 z 2

!Tt !n !n eff !t !t eff " "b "eff "T eff #$ %" %"x & I II

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

Where first used 5.2 5.3 Figure 30 Eq 2

Number of teeth in master indexing worm wheel Driving gear Driven gear Transverse pressure angle at the tolerance diameter Normal pressure angle Effective normal pressure angle Design transverse pressure angle

-- --- --- -degrees degrees degrees degrees

Eq 24 Figure 32 Figure 32 6.5.2 Eq 1 6.5.3 Eq 6

Effective transverse pressure angle Helix angle Design base helix angle Effective helix angle at the standard pitch diameter Effective helix angle at the tolerance diameter Total contact ratio Undulation wave length Axial wavelength of undulation Involute roll angle

degrees degrees degrees degrees degrees -- -mm mm degrees

6.5.3 Eq 5 Eq 2 8.7 8.7 9.3.5 Eq 24 Figure 24 Figure 17

Reference face Non--reference face

-- --- --

5.2 5.2

NOTE: 1) Symbols used for deviations of individual element measurements from specified values are composed of lower case letters “ f ” with subscripts (exceptions include f e, f 1 and f 2) whereas symbols used for “cumulative” or “total” deviations, which represent combinations of several individual element deviations,are composed of capital letters “ F ” also with subscripts. It is necessary to qualify some deviations with an algebraic sign. A deviation is positive when e.g., a dimension is larger than optimum and negative when smaller than optimum. 2) These deviations can be + (plus) or -- (minus).

4 Extent of gear inspection It is rarely necessary or economical to measure all possible deviations on all gears manufactured. Certain elements may not significantly influence the function of the gear under consideration. Some measurements can be substituted for others. Stable manufacturing processes allow a relatively small number of samples to be measured and still ensure that the required quality level is maintained. It is recommended that specific measuring plans be negotiated between purchaser and supplier. 4.1 Required inspection information Certain necessary information should be provided to the operator(s) of the measuring equipment. The information required will vary depending on the type of measurement(s) required. Most measurement

processes require basic gear and blank data, number of teeth, pitch, pressure angle, helix angle, tooth size, outside diameter, root diameter, face width, design profile, design helix, etc. Certain measuring tasks require additional information. For example, to measure profile, the profile control diameter and start of tip break must be provided. With mechanical measuring equipment, additional information may be required: base circle diameter (radius), base helix angle, sine bar setting, etc. The design engineer or engineering department should be responsible for supplying this minimum required inspection information to those performing the measurements. 4.2 Measurement selection Inspection may be carried out using a number of alternate methods. Some measurements may be

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AGMA 915--1--A02

substituted for others. For example single flank composite measurement may be substituted for pitch measurement, or radial composite measurement may replace runout measurement. A number of factors should be considered when selecting the measurements, including the quality level required, size of the gear, manufacturing cost and most important the application of the product gear. 4.2.1 Sampling Gears, like other parts,are manufactured to a certain level of accuracy dependant on the production process used. When the process used is proven capable of producing the required accuracy level using statistical methods, sampling inspection may be utilized. Many factors may influence the sample size and frequency, foremost among these should be the assurance that the required accuracy level of the parts is met. 4.2.2 First piece inspection It may be possible to inspect only the first piece of a batch to verify that the setup is correct, allowing the inherent accuracy of the process to assure the quality of subsequent parts.


Ideally the surfaces used to construct the datum axis, the surfaces used to locate the gear for manufacturing, and the functional surfaces that define the gear axis of rotation in its final assembly would all be the same. In practice this is often not the case. For example, shaft type parts are often manufactured and inspected using female centers to define the datum axis. In cases where the inspection, manufacturing, and/or functional datum surfaces are different, these surfaces must be coincident with each other to a level of accuracy sufficient to assure the final quality of the gear is adequately represented during measurement. The gear being measured should be oriented so that its datum axis is coincident with the axis of rotation of the measuring instrument. In the case of mounting the gear between centers, care must be taken to assure that the mounting arbor, if used, is in good condition, and the female centers are clean and concentric with thedatumsurfaces of thegear. In the case of computer controlled measuring instruments, it may be possible to mount the gear with significant deviation to the instrument’s axis of rotation. In that case, the measuring program must be capable of mathematically correcting the errors resulting from this off axis mounting condition. 5.2 Right or left flank

5 Identification of deviation position It is convenient to identify deviations associated with measurements of gear teeth by specific reference to individual right flanks, left flanks, pitches or groups of these. In the following, conventions are described which enable positive determination of the location of deviations. 5.1 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

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”. 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. 5.3 Right hand or left hand helical gears The helix of an external or internal helical gear is referred to as being right hand or left hand. The hand of helix is denoted by the letters “r” and “l” respectively. The helix is right hand (left hand) if, when looking from one face, the transverse profiles show successive clockwise (counter--clockwise) displacement with increasing distance from an observer. 5.4 Numbering of teeth and flanks Looking at the reference face of a gear, the teeth are numbered sequentially in the clockwise direction. The tooth number is followed by the letter R or L,


indicating whether it is a right or a left flank. Example: “Flank 29 L”.

AGMA 915--1 --A02

6 Measurement of pitch deviations 6.1 Pitch deviation

5.5 Numbering of pitches The numbering of individual pitches is related to tooth numbering as follows: pitch number “ N ” lies between the corresponding flanks of teeth numbers “ N --1” and “ N ” ; with a letter R or L it is indicated whether the pitch lies between right or left flanks. For example “Pitch 2 L”, (see figures 1 and 2).

Index, single pitch ( f pt), and total cumulative pitch ( F p) are elemental parameters relating to theaccuracy of tooth locations arounda gear. The following is a description of the measuring methods and a guide to the interpretation of data generated by the measuring devices. 6.2 Pitch deviation measurement

5.6 Number of pitches “k ” The subscript “k ” of a deviation symbol denotes the number of consecutive pitches to which thedeviation applies. In practice, a number is substituted for “k ” , for example F p3 indicates that a given cumulative pitch deviation refers to three pitches.

Measurements for determining index, single pitch ( f pt), and total cumulative pitch ( F p) are made: --

relative to the datum axis of the gear;

--

at the tolerance diameter, d T ;

-- In the specified tolerancing direction (within thetransverse plane along the arc of thetolerance diameter).

30R

2L tip

left flank

right flank 30

1

29

2 30 R = pitch No. 30, right flank 2 L = pitch No. 2, left flank Figure 1 -- Notation and numbering for external gear 30R

1L tip

left flank

right flank 2

29 1

30

1 L = pitch No. 1, left flank 30 R = pitch No. 30, right flank Figure 2 -- Notation and numbering for internal gear

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AGMA 915--1--A02


Measurements made at different diameters or in other directions must be adjusted so that they are equivalent to measurements at the tolerance diameter and in the tolerance direction. This adjustment must be made before comparison of test results to tolerances. Sector pitch deviation ( F ps/8) is an optional parameter described in Annex E of ANSI/AGMA 2015--1--A01. Measurements of sector pitch deviation are also expected to conform to the above specified requirements. Pitch should be measured on both left and right flanks. However, if the specific operating direction of the gear is known, only the loaded flanks need to be measured. 6.3 Pitch deviation measurement methods Pitch parameters can be measured by either of two types of device. The indexing (single probe) device determines the location of each tooth around a gear, relative to a datum tooth (the index). The pitch comparator (two probe) device compares the distances between adjacent tooth flanks to the distance

between an initial reference pair of adjacent tooth flanks. The various pitch parameters can all be determined by either measuring device with the application of suitable calculations. The indexing method is usually preferred because of its accuracy and simplicity. However, for large diameter gears, use of the pitch comparator method may be preferable. Coordinate measuring machines without a rotating table can also be used for measurements of pitch parameters by probe movements that correspond to the principle of the indexing method. 6.3.1 Indexing pitch measurement method The indexing (single probe) device uses an angular indexing apparatus such as an index plate, circle divider, optical or electronic encoder, or polygon and auto collimator to precisely rotate the gear by an angular increment equal to its pitch, or 360" / z (see figure 3). The degree of its precision must be consistent with the quality grade and diameter of the gear.

Index mechanism 5

Tolerance diameter, d T

4

3 -- Index deviation

2 1

Dash lines represent theoretical location

+ Index deviation

Index readings

Figure 3 -- Schematic of single probe measuring device

6


The single probe should be oriented to contact the tooth flanks at the tolerance diameter, d T, and to gather measurements in the specified measurement direction. The single probe is adjusted to indicate zero while the device is contacting the randomly selected initial test tooth flank. As the gear is incrementally rotated around its datum axis, the single probe moves in and out on a precision slide and stop, measuring each successive tooth flank position, relative to the indexing mechanism. This process is repeated until every tooth has been measured. It is common practice to complete this series of measurements by taking a final measurement on the initial reference tooth, thereby closing the circle. Ideally, this would produce a second measurement value of zero for the first tooth, as was set at the beginning of the process. Excessive deviation of this second measurement value from zero indicates a problem with the measurement. 6.3.1.1 Calculation of index If the indicator always reads plus material as a plus reading and the gear is indexed counterclockwise (teeth are numbered clockwise), then the right flank measurement values provided by the indexing (single probe) pitch measurement device can be used directly as the plus and minus values of index for each tooth of the gear (see figure 3). Left flank single probe measurement values must be multiplied by –1 to produce plus and minus index values. Other pitch parameters may then be calculated from that data. If a graphical recorder is used, data gathered by the single probe measurement device will appear in the form shown in figure 4. This figure shows the measurement value of the initial measured tooth set to zero, thereby establishing it as the reference. The measured values shown for all other teeth then represent the positional deviations of those teeth from the initial reference tooth. 6.3.1.2 Calculation of single pitch, f pt Subtraction of each successive pair of index values produces the plus and minus values of single pitch deviation for each adjacent pair of tooth flanks of the gear. See Clause 5 for specified tooth numbering, pitch numbering, and flank naming conventions. The number 1 single pitch deviation value is equal to the index value of the last tooth subtracted from the index value of the first tooth. The number 2 single

AGMA 915--1 --A02

pitch deviation value is equal to the index value of the first tooth subtracted from the index value of the second tooth. Since the index value of the first tooth is set to zero, the number 2 single pitch deviation value is equal to the index value of the second tooth. The number 3 single pitch deviation value is equal to the index value of the second tooth subtracted from the index value of the third tooth, and so on.

+

n o i t a i v e d0 x e d n I

--f pt

+ f pt

-1 2 3 4 5 6 7 8 9 10 Tooth number Figure 4 - Single pitch deviation, single probe device If a graphical recorder is used, data gathered by the single probe measurement device will appear in the form shown in figure 4. Single pitch deviation values, f pt, are shown as the differences between adjacent index values. 6.3.1.3 Calculation of total cumulative pitch deviation, F p The total cumulative pitch deviation, F p, is equal to the difference between the most positive and the most negative index value for the complete gear. 6.3.1.4 Calculation of sector pitch deviation, F ps/8

Calculation of the sector pitch deviation, F ps/8, is presented in Annex E of ANSI/AGMA 2015--1--A01. 6.3.2 Comparator pitch measurement method The pitch comparator (two probe) device may be mechanized or hand--held. Measurements made by the mechanized version are preferred. In either case, both probes should be oriented to contact adjacent tooth flanks at the tolerance diameter. One probe serves to establish a reference position upon a tooth flank. The second probe is fitted with either a mechanical or an electronic indicator to measure variations of its position from the first probe. The device is adjusted to indicate zero while the probes are contacting the randomly selected initial pair of teeth (see figure 5).

7

AGMA 915--1--A02


spring loaded Tolerance diameter, d T

Figure 6 -- Circular pitch measurement, two probe device

Figure 5 -- Pitch measurement with a pitch comparator

The mechanized pitch comparator is a device with a rotational axis that positions the gear for measurement. The gear must be mounted with its datum axis coincident with the pitch comparator’s rotational axis. The two probes should be oriented to contact the adjacent tooth flanks within the same transverse plane, at the tolerance diameter, d T. As the gear is rotated around its datum axis, the pitch comparator moves in and out on a precision slide and stop, measuring each successive adjacent tooth pair. This process is repeated until every adjacent pair of teeth has been measured. The hand--held pitch comparator is a portable device that lacks a means of referencing the datum axis of the gear. It is therefore fitted with a positioning stop that contacts the outside diameter of the gear, which thereby becomes the reference for pitch measurements. This method requires that special consideration be given to the concentricity of the outside diameter of the gear with its datum axis. The two probes must be oriented to contact the adjacent tooth flanks within a normal plane. The hand--held pitch comparator is applied successively to each pair of teeth with each indicator measurement observed and recorded. This process is repeated until every adjacent pair of teeth has been measured (see figure 6).

8

Since the hand--held pitch comparator measures in the normal plane, the measurements must be converted to transverse pitch deviations before being summed to determine index as described in 6.3.2.3. It is important to understand that the readings collected from two probe pitch comparators are relative to a randomly selected tooth pair of unknown position. They must not be compared to the single pitch tolerances, until they are adjusted by true position pitch, p m. 6.3.2.1 Calculation of true position pitch, p m The true position pitch, pm, is the measurement value for any perfectly spaced tooth pair, with the given setup of the pitch comparator. It is equal to the average value found by summing all the adjacent tooth pair measurements then dividing the result by the number of tooth pairs (i.e., the number of teeth). If a graphical recorder is used, data gathered by the pitch comparator method will appear in the form shown in figure 7. This figure shows the measurement value of the initial pair of teeth (1-- 2) set to zero. Also shown is the true position pitch, pm, as the calculated mean of pitch comparator measurement values. 6.3.2.2 Calculation of single pitch deviation, f pt Subtraction of the true position pitch, p m, from each adjacent tooth pair measurement produces the plus and minus values of single pitch deviation, f pt, for each tooth pair of the gear. See Clause 5 for specified tooth numbering, pitch numbering, and flank naming conventions. If a graphical recorder is used, data gathered by the pitch comparator method will appear in the form shown in figure 7. Single pitch deviation values, f pt,


are shown as the deviations of individual pitch comparator measurement values to the true position pitch, p m.

AGMA 915--1 --A02

6.3.2.4 Calculation of total cumulative pitch deviation, F p The total cumulative pitch deviation, F p, is equal to the difference between the most positive index value and the most negative index value for the complete gear. 6.3.2.5 Calculation of sector pitch deviation,

s g + n i d a e r r o 0 t a r a pm p m o c - h c t i P

F ps/8

+ f pt pm

-- f pt 1--2 2--3 3--4 4--5 5--6 6--7 7--8 8--9 9--10 10--11

Pairs of adjacent teeth Figure 7 -- Single pitch deviation, two probe device

6.3.2.3 Calculation of index The plus and minus index values for each tooth ofthe gear can be produced by successive summation of the single pitch deviation values. See clause 5 for specified tooth numbering, pitch numbering, and flank naming conventions. In all cases, the number one (first) tooth shall be the datum tooth and its index value set to zero accordingly. The index value of the second tooth is equal to the index value of the first tooth plus the number 2 single pitch deviation value. Since the index value of the first tooth is set to zero, the index value of the second tooth is equal to number 2 single pitch deviation value. The index value of the third tooth is equal to the index value of the second tooth plus the number 3 single pitch deviation value, and so on. At the end of this process, the index value of the first tooth will be found by adding the number 1 single pitch deviation value to the index value of the last tooth. Ideally, this would produce a second index value of zero for the first tooth. Excessive deviation from zero, of this calculated index value, for the first tooth indicates a problem with the measurement.

Calculation of the sector pitch deviation, F ps/8, is presented in Annex E of ANSI/AGMA 2015--1--A01. 6.4 Relationships of pitch parameters and measuring methods The relationships of pitch parameters using different measuring methods is illustrated within figures 8 through 11. 6.5 Base pitch measurement The normal base pitch measurement device is a two probe instrument of similar construction to the hand--held pitch comparator. However, its measuring principles are substantially different from those described under 6.3.2: -- Rather than measuring the relative normal pitch at a given measurement (tolerance) diameter, it measures the normal base pitch, p bn, which is the shortest distance between adjacent tooth flanks (see figure 12). -- This method cannot directly or indirectly reference the datum axis of the gear. The tooth flank features themselves become the reference. Therefore, observations of index and total cumulative pitch, F p, can not be properly made with this device. -- If the instrument is adjusted to the specified normal base pitch of a gear prior to commencing measurements, it can provide an observation of normal base pitch deviation, f pbn. The normal base pitch parameter provides a localized composite observation of gear tooth flank accuracy. It is localized, in that the observation is made only at a single point on the tooth flank. It is composite in that it combines the effects of involute profile, helix, and pitch into a single observation that directly relates to the gear’s ability to achieve smooth, conjugate meshing action with its mate.

9

AGMA 915--1--A02


Tooth numbers of pitches 18:1 Pitch number 1 2--probe pitch 0 comparator readings True position pitch pm (mean of readings) Singlepitch deviations f pt 2 (readings -- p m) Tooth numbers for Index 1 values Index deviations (calcu0 lated)

1:2

2:3

3: 4

4: 5

5:6

6:7

7:8

8:9

9:10

10:11

11:12

12: 13

13:14

14:15

15:16

16:17

17:18

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

1

--1

1

--1

--3

-5

--4

--4

-5

--6

--4

--3

--3

--1

1

1

0

--2 3

1

3

1

--1

--3

--2

--2

--3

--4

--2

--1

--1

1

3

3

2

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

3

4

7

8

7

4

2

0

--3

--7

--9

--10

--11

--10

--7

--4

--2

Figure 8 -- Sample table with hypothetical deviation values obtained by pitch comparator (two probe) device (In practice, integer values are seldom encountered. Maximum value of f pt and minimum and maximum values for index deviations are shaded.)

1--probe readings, 0 right flanks Index deviations 0 Singlepitchdeviations 2 f pt (calculated)

3

4

7

8

7

4

2

0

--3

--7

--9

--10

--11

--10

--7

--4

--2

3 3

4 1

7 3

8 1

7 4 2 0 --3 --1 --3 --2 --2 --3

--7 --4

--9 --2

--10 --1

--11 --1

--10 1

--7 3

--4 3

--2 2

Figure 9 - Sample table with hypothetical deviation values obtained by indexing (single probe) device (In practice, integer values are seldom encountered. Maximum value of f pt and minimum and maximum values for index deviations are shaded.)

Single pitch deviations, f pt

12 10 8 6 4 m 2 m 0 1 ---2 0 -4 0 . --6 0 --8 --10 --12

1

2

3

4

5

6

7

8 9 10 Pitch number

11

12

13

14

15

16

17

18

17

18

Figure 10 -- Sample graphic representation of single pitch deviations, f pt Index deviations

12 10 8 6 4 m 2 m 0 --2 1 --4 0 0 . --6 0 --8 --10 --12

1

10

2

3

4

5

6

7

8 9 10 11 12 13 14 15 Flank number Figure 11 -- Sample graphic representation of index deviations

16


AGMA 915--1 --A02

6.5.2 Calculation of single pitch deviation, f pt, from normal base pitch measurements Normal base pitch measurements are inherently composite observations, combining the influences of pitch, profile, and helix deviations. It is not possible to decompose normal base pitch deviations into observations of those individual constituent deviations such as single pitch. However, since normal base pitch is a better indicator of gear quality than single pitch, this document permits comparison of normal base pitch deviations to single pitch tolerances.

pbn

Base circle Figure 12 -- Base pitch measurement, two probe device The theoretical normal base pitch can be calculated as follows: bn

! m n '

cos ! n

(1)

where pbn

is the theoretical normal base pitch, mm;

mn

is the normal module, mm;

!n

is the normal pressure angle, degrees.

6.5.1 Normal base pitch measurement device The normal base pitch measurement device is usually a hand--held device, which can either be set to measure directly the deviations from the theoretical normal base pitch, with the aid of a suitable gage, or set to reference a randomly selected initial pair of adjacent teeth. The two measurement probes of the device are oriented to contact adjacent tooth flanks within a base tangent plane. In practice, this involves rocking the device through the possible range of contact of the measuring probe with the tooth flank while observing the measurement indicator. The observed minimum deviation of the indicator will occur at the point of contact corresponding with a base tangent plane. It is important to ensure that the points of contact of the probes do not lie in zones with profile or helix modifications, especially when measuring deviations from the theoretical normal base pitch. The normal base pitch measurement device is applied successively to each pair of teeth with each indicator measurement recorded. This process is repeated until every adjacent pair of teeth has been measured.

Before commencing to calculate single pitch deviations, the direction in which normal base pitch deviation values are reported must be converted from normal to the tooth surface to along the arc of the tolerance diameter, d T, circle within the transverse plane, as required by ANSI/AGMA 2015--1--A01. The first step is to convert the normal base pitch values to the transverse plane, which requires dividing each by the cosine ofthe base helix angle,cos "b. Then, dividing the results by the cosine of the transverse pressure angle at the tolerance diameter, cos ! Tt, converts the values to a direction along the arc of the tolerance diameter circle. As is the case with any pitch comparator (two probe) measurements, these values must be compared with the true position pitch, p m, to derive single pitch values. This method can be applied to measurements made by devices set relative to a randomly selected tooth pair or relative to the theoretical normal base pitch. The true position pitch, p m, is equal to the average value found by summing all the adjacent tooth pair measurements, then dividing the result by the number of tooth pairs (i.e., the number of teeth). Subtraction of the true position pitch, p m, from each adjacent tooth pair measurement produces the plus and minus values of single pitch deviation, f pt, for each tooth pair of the gear. 6.5.3 Additional calculations for normal base pitch measurements When the normal base pitch measurement device is initially set to the theoretical normal base pitch, resulting measurements can be used to calculate a variety of parameters that are useful for controlling the quality of gear involute profiles. It is important to understand that these calculations are based upon the assumption that the helical lead of the gear, which also affects normal base pitch

11

AGMA 915--1--A02


measurements, is correct. Included in these calculated parameters are: --

normal base pitch deviation, f pbn;

--

mean normal base pitch deviation, f pbm;

--

mean base diameter difference, f dbm;

--

effective base diameter, d b eff ;

--

effective transverse pressure angle, ! t eff ;

--

effective normal pressure angle, ! n eff ;

mean normal pressure angle deviation, f !mn.

6.5.3.1 Calculation of normal base pitch deviation, f pbn Determination of normal base pitch deviation, f pbn, requires setting of the normal base pitch measurement device to the theoretical normal base pitch, with theaid of a suitable gage, before measurements are taken. Resulting measurement values can then be used directly as the plus and minus values of normal base pitch deviation, f pbn, for each adjacent tooth pair of the gear. 6.5.3.2 Calculation of mean normal base pitch deviation, f pbm The mean normal base pitch deviation, f pbm, is equal to the average value found by summing all the adjacent tooth pair deviations of normal base pitch, f pbn, then dividing the result by the number of tooth pairs (i.e., the number of teeth).

Effective transverse pressure angle, !t eff , can be calculated as follows:

# &

Mean base diameter difference, f dbm, can be calculated as follows:

(4)

D

where !t eff is the effective transverse pressure angle, degrees; D

is the design pitch diameter, mm.

6.5.3.6 Calculation of effective normal pressure angle, ! n eff Effective normal pressure angle, !n eff , can be calculated as follows:

#

&

! n eff ! atan tan !t eff cos "

(5)

where !n eff is the effective normal pressure angle, degrees;

"

is the helix angle, degrees.

6.5.3.7 Calculation of mean transverse pressure angle deviation, f !mt

!mt

! ! t eff % ! t

(6)

where f !mt is the mean transverse pressure angle

pbm z

(2)

cos " b

deviation, degrees;

!t

where f dbm is the mean base diameter difference, mm; f pbm is the mean normal base pitch deviation, mm;

z

is the number of teeth;

"b

is the design base helix angle, degrees.

6.5.3.4 Calculation of effective base diameter,

is the design transverse pressure angle, degrees.

6.5.3.8 Calculation of mean normal pressure angle deviation, f !mn Mean normal pressure angle deviation, f !mn, can be calculated as follows: f !mn ! ! n eff % ! n

(7)

where

d b eff

Effective base diameter, d b eff , can be calculated as follows:

#

&

d b eff ! D b " f dbm $ 10 %3

12

d b eff

! t eff ! acos

Mean transverse pressure angle deviation, f !mt, can be calculated as follows:

6.5.3.3 Calculation of mean base diameter difference, f dbm

! '

is the design base diameter, mm.

6.5.3.5 Calculation of effective transverse pressure angle, ! t eff

mean transverse pressure angle deviation, f !mt;

dbm

d b eff is the effective base diameter, mm; Db

---

where

(3)

f !mn is

the mean normal pressure deviation, degrees;

!n

angle

is the design normal pressure angle, degrees.


7 Measurement of profile deviations 7.1 Profile Profile is the shape of the tooth flank from its root to its tip. The functional profile is the operating portion, which is in actual contact during tooth mesh, and cannot extend below the base cylinder. Profile deviation is the difference between the specified and the measured profile of the gear. Unless modifications are specified, the shape of the profile in the transverse plane is an involute curve. ANSI/AGMA 2015--1--A01 specifies the direction of tolerancing for profile deviation to be within the transverse plane, tangent to the base circle. 7.2 Profile inspection methods The standard methods of profile measurement are with generative, coordinate, or portable involute measurement instruments. 7.2.1 Generative involute measurement instruments Generative involute measuring instruments measure the deviation of the actual profile from a nominal involute profile, which is generated by the instrument. Generating the nominal involute requires a tangential movement of a measurement probe, within the plane tangent to the base cylinder of the given gear, together with a rotational movement of the gear mounted on the instrument spindle. These movements must be synchronized such that the linear movement of the probe is equal to the distance along the circumference of the base circle diameter associated with the rotational movement (see figure 13).

Spindle

AGMA 915--1 --A02

master base circle. Generative involute measuring instruments may use a computer numerical control electronic drive system to generate the nominal involute curve. Profile measurements must be made relative to the datum axis of rotation of the gear. Refer to 5.1 for more information concerning the datum axis of rotation. The probe tip must be accurately positioned within the plane tangent to the base cylinder, with its zero roll position precalibrated (see figure 14). Probe tips may be chisel point, disk, or spherical, provided that accurate positioning of the point of contact between the probe tip and the gear tooth surface is maintained within the base tangent plane. Measurement of extreme profile modifications may be adversely affected by shifting of the probe contact vector. Root circle Base circle

Outside circle Pitch circle

Base tangent plane Probe

Axis

Figure 14 -- Profile measuring method It is often desirable to orient the measurement probe path of motion normal to the tooth surface. ANSI/AGMA 2015--1--A01 specifies profile tolerances in the transverse plane. If measurements are made normal to the tooth surface, all values must be corrected by dividing by the cosine of the base helix angle, cos "b, before comparison against the tolerances. 7.2.2 Coordinate measurement inspection instruments

Base circle

Figure 13 -- Schematic of involute inspection device

Involute profile can be inspected by non--generative, coordinate measurement instruments. Such instruments indicate the tooth profile by a series of points, storing the coordinates of each point. The deviation of the actual profile from the nominal is then determined by comparison of the stored test point coordinates against calculated coordinates of the theoretical nominal profile (see figure 15).

Generative involute measurement instruments may employ a master base circle or master involute cam to generate the nominal involute curve. Such instruments may include a ratio mechanism, which relates the actual workpiece base circle to the

Coordinate measurement inspection instruments may operate in two dimensions (X and Y coordinates) or three dimensions (X, Y, and Z coordinates). Measurement of an involute profile with two-dimensional systems requires accurate mounting of

Probe

13

AGMA 915--1--A02


the gear with its datum axis perpendicular to the X--Y plane. Three--dimensional systems require alignment of the gear datum axis parallel to one of the three instrument axes. This may be accomplished by accurate mounting of the part, or mathematically adjusting the instrument axes to coincide with the gear axis. Coordinate measurement inspection instruments may use spherical measurement probe tips, which require correction for shifting of the probe contact vector.

X1 X2 X3 Y2 Y3

Y1

Figure 15 -- Profile inspection by coordinates 7.2.3 Portable involute measurement instruments Profile measuring instruments are generally fixed type machines. Gears to be tested must be brought to the instrument and accurately mounted, typically on--axis, between centers or on a table. For very large gears it may be necessary to employ a portable involute measuring instrument that can be taken to the gear. Such instruments may operate on a variety of generative or non--generative principles. The portable instrument must be accurately mounted at a

known distance from, and in alignment with, the gear axis. This requires care in design and manufacture of the gear blank. 7.3 The profile diagram Amplified traces of the profile inspection test results should be presented on charts that are graduated for rolling path length or degrees of roll. They should also be labeled for magnification and evaluation points in conformance with the specification. An unmodified involute profile with no deviations will be charted as a straight line. Deviations of the curve from a straight line represent, in magnified form, deviations of the actual profile from an unmodified involute. Profile modifications introduced by the designer also appear as departures from the straight line, but they are not considered to be deviations from the “design profile”. Excess material on the profile is considered a plus deviation, while insufficient material is considered a minus deviation. In addition to identifying the location and magnitude of the highest point on the profile or the maximum profile deviation, these charts are valuable for determining profile characteristics such as tip break, undercut, and tip or root relief (see figure 16). Any point along the profile diagram can be related to a diameter (radius), a base tangent length and an involute roll angle. Figure 17 shows a sample tooth profile and the relation to the corresponding profile trace, together with the appropriate terms. Details of terms, definitions and concepts concerning the profile trace, are provided in ANSI/AGMA 2015--1--A01. Tip break

Undercut True involute profile True involute

Profile control diameter

Plus profile (minus pressure angle)

Minus profile (plus pressure angle)

Undercut & tip chamfer

Tip break

Undercut

Figure 16 -- Typical tooth profile measurement charts

14


AGMA 915--1 --A02

f H! f f !

A B 1

C

L!c

2 3

D E +

F ! L!c L#

A

A

B

2

tip circle of mating gear

1

Q

C

tip circle reference circle

E F

D E

&C F

root circle base circle 1 2 3

Design profile Measured profile Mean profile line

C--Q &c

A B D E F B--D B--E

Tip circle point Start of tip break (chamfer) Start of active profile Profile control diameter Origin of involute Active profile Usable profile

L!c L# F ! f f ! f H!

Q

Base tangent length to point C Involute roll angle to point C Start of roll (point of tangency of transverse base tangent) Profile evaluation range Base tangent length to start of active profile Total profile deviation Profile form deviation Profile slope deviation

Figure 17 -- Tooth profile and profile diagram

15

AGMA 915--1--A02


7.4 Evaluation of profile diagrams

7.6 Mean profile slope deviation, f H!m

Depending on accuracy class specified, it may only be necessary to measure total profile deviation, F !. See ANSI/AGMA 2015--1--A01, clause 4. It may also be necessary to determine the profile slope deviation, f H!, and the profile form deviation, f f !. For this it is necessary to superpose the mean profile line onto the diagram as shown in figure 17, also in figure 2 of ANSI/AGMA 2015--1--A01. Allowable values of f H! and f f ! can be calculated in accordance with ANSI/AGMA 2015--1--A01, clause 7. 7.5 Algebraic signs of f H! and f ! The profile slope deviation, f H!, is termed positive and the corresponding pressure angle deviation, f !, is termed negative when the mean profile line rises towards thetooth--tip endA of thediagram,as shown in figure 17. In figure 18, both positive and negative slopes, caused by eccentricity of mounting on the gear generating machine, are shown. If the slopes seen in the profile diagrams of mating gears are equal and have the same sign, the deviations are mutually compensating. This applies to both external and internal gears. A B

The effect of eccentricity on profile slope, and the determination of mean profile slope deviation, are illustrated in figure 18. Calculating the mean profile slope deviation is a step towards the correction of manufacturing processes or other suitable action. For all practical purposes, it is usually sufficient to calculate the arithmetic mean of the profile slope deviations by calculating the average of the deviations measured on three or more corresponding flanks of equally spaced teeth around the gear circumference according to the following equation: H!m

! 1n # f H!1 " f H!2 "''' " f H!n&

(8)

where: f H!m is the mean profile slope deviation, m m; f H!n is the individual profile slope deviations, mm; n

is the number of profile slope deviation values included in the mean.

E

+

1 . 1 1 -

Slope deviations of individual profiles can be caused by eccentricity due to inaccuracies of manufacturing or inspection set--up. Such deviations will vary around the gear. The use of mean profile slope deviations cancels out the influence of eccentricity on individual profile traces.

3

1 --

+

6 . 6 -

e f

2

--

2

C I

(

1

+

7 . 5

M

3 - !

H f

L!c f H#m ! 1 (% 11.1 % 6.6 " 5.7) ! % 4mm

3

M = axis of rotation of the gear on the machine tool. I = axis of rotation of the gear on the inspection apparatus.

C = position of tool or profile measuring probe 1, 2, 3 = Positions of the profiles from which the traces were obtained (at 45 ", 165", 285") and relevant profile traces Figure 18 -- Mean profile slope deviation, f H!m 16


AGMA 915--1 --A02

7.7 Additional calculations for profile measurements

7.7.3 Calculation of effective transverse pressure angle, ! t eff

The mean profile slope deviation, f H!m, can be used to calculatea variety of parameters that areuseful for controlling the quality of gear involute profiles. Included in these calculated parameters are:

Effective transverse pressure angle, !t eff , can be calculated as follows:

# & d b eff

! t eff ! acos

D

(11)

--

mean base diameter difference, f dbm;

--

effective base diameter, d b eff ;

--

effective transverse pressure angle, ! t eff ;

!t eff is the effective transverse pressure angle, degrees;

--

effective normal pressure angle, ! n eff ;

D

where:

is the design pitch diameter, mm.

mean transverse pressure angle deviation, f !mt;

7.7.4 Calculation of effective normal pressure angle, ! n eff

--

Effective normal pressure angle, !n eff , can be calculated as follows:

--

mean normal pressure angle deviation, f !mn.

All of the following equations are based upon the mean profile slope deviation, f H!m. Alternatively, the same formulas could be applied to the case of individual tooth data. The calculation sequence would then commence with the entry of the individual profile slope deviation, f H!.

Mean base diameter difference, f dbm, can be calculated as follows:

! L b

!c

(9)

f H!m

&

(12)

where:

!n eff is the effective normal pressure angle, degrees; is the helix angle, degrees.

"

7.7.1 Calculation of mean base diameter difference, f dbm

dbm

#

! n eff ! atan tan ! t eff cos "

7.7.5 Calculation of mean transverse pressure angle deviation, f !mt Mean transverse pressure angle deviation, f !mt, can be calculated as follows: !mt

! ! t eff % ! t

(13)

where:

where: f dbm is the mean base diameter difference, mm; Db

is the base diameter, mm;

L!c

is the functional profile length, mm;

f !mt is the mean transverse pressure angle

deviation, degrees; is the design transverse pressure angle, degrees.

!t

f H!m is the mean profile slope deviation, m m.

A positive mean profile slope deviation (profile trace rising towards its tooth tip end) implies that the effective base diameter is too large, and visa versa. when f H!m > 0, then f dbm > 0 7.7.2 Calculation of effective base diameter,

Alternatively, f !mt can be calculated (in degrees) by: !mt

! % 1

#

#

&# &

f H!m

L !c tan ! t

&$

10 3

180 '

(14)

A positive mean profile slope deviation (profile trace rising towards its tooth tip end) implies that the effective pressure angle is too small, and visa versa. when f H!m > 0, then f !mt < 0

d b eff

Effective base diameter, d b eff , can be calculated as follows:

#

&

d b eff ! D b " f dbm $ 10 %3

where: d b eff is the effective base diameter, mm.

(10)

7.7.6 Calculation of mean normal pressure angle deviation, f !mn Mean normal pressure angle deviation, f !mn, can be calculated as follows: !mn

! ! n eff % ! n

(15)

where:

17

AGMA 915--1--A02


f !mn is

the mean normal pressure deviation, degrees;

angle

!n eff is the effective normal pressure angle, degrees; !n

is the design normal pressure angle, degrees.

an indication of profile accuracy (see figure 20). However, readings give no indication as to which profile may have an error, since two flanks of a measured tooth are contacted at the same time. This method will not reveal deviations that cancel each other, such as those caused by a form cutter, which has been offset from a true radial position.

A positive mean profile slope deviation (profile trace rising towards its tooth tip end) implies that the effective pressure angle is too small, and visa versa. when f H!m > 0, then f !mn < 0 7.8 Other profile measuring methods While not commonly used or recommended, the following profile measuring methods may prove valuable when more conventional methods are not practical or available. 7.8.1 Projection A shadow of the gear tooth under inspection may be optically magnified and directly or reflex projected to permit comparison of the profile to a large scale layout of a specified profile (see figure 19). This method is normally applied only to fine pitch gears. When gears are too large to be mounted in the projector, a thin wafer (manufactured simultaneously with the gear), or a mold of a gear tooth form may be used for projection. This method requires two known reference surfaces to locate the image both radially and angularly.

Scale layout

Figure 20 -- Profile inspection by gear --tooth caliper method -- Auxiliary gaging elements. The theoretical position of wires, rolls, pins, or balls of several different diameters placed in a tooth space may be computed and compared to actual measurements (see figure 21). This method has limitations similar to those of gear tooth caliper measurements.

Projection Figure 19 -- Profile inspection by optical projection 7.8.2 Indirect profile inspection methods The following techniques may be employed for inspection of gear profiles. These methods do not yield actual measurements of deviation of an inspected profile from a nominal. -- Multiple thickness measurement. The chordal tooth thickness and associated addendum depth for several positions on a tooth may be computed for a gear tooth caliper. Comparison of measurements with the computed values will give

18

Figure 21 -- Profile inspection by measurement over pins


AGMA 915--1 --A02

7.8.3 Profile measuring with master gear

8.2 Helix inspection methods

Contact pattern checking with a master gear may be used to check the profile deviation of gears in place or when gears are too large to be accommodated by a profile measuring instrument. The axis of the gear and master must be parallel. Refer to clause 10 for more information concerning this method.

The standard methods of helix measurement are with generative, coordinate, or portable helix measuring instruments.

8 Measurement of helix deviations 8.1 Helix Helix is the lengthwise shape of the tooth flank across the face from one end to the other. The theoretical helix of a helical gear is contained on the surface of a cylinder, which is concentric with the datum axis of rotation of the gear, at the intersection of that cylinder with the tooth flank. The theoretical helix of a spur gear is a straight line parallel to its rotating axis. Helix is restricted to the operating portion, which is intended to be in contact during loaded operation, and does not include edge rounds or chamfers.

8.2.1 Generative helix measuring instruments The most common instruments used for measurement of helix are generative helix measurement instruments. Such instruments measure the deviation of the actual helix from a nominal helix, which is generated by the instrument. Generation of the nominal helix requires the axial movement of a measurement probe together with a rotational movement of the gear mounted on the instrument spindle. These movements must be synchronized according to the specified lead of the gear (see figure 23). When measuring spur gears, the rotational movement is eliminated. Total helix deviation, F "

Reference zero

0

Lead, as a term used for helical gears, is the axial advance of a helix for one complete turn of the gear. The lead of a spur gear, therefore, is infinite. The lead of a helical gear is commonly defined by the angle between the helix at the standard pitch diameter and the axis of rotation. Helix deviation is the difference between the specified and the measured helix of the gear (see figure 22). ANSI/AGMA 2015-- 1--A01 specifies the direction of tolerancing for helix deviation to be within the transverse plane, tangent to the base circle.

Probe travel

Helix angle

Measured helix

Total helix deviation, F "

Figure 23 -- Graphic charting of helix Design helix

Helical tooth Figure 22 -- Helix deviation

Generative helix measuring instruments may employ a variety of mechanical configurations to generate the nominal helix. For example, the gear can be rotated by a master disk driven by a straight edge, which in turn is driven by the axial movement of the probe slide. The tangential movement of the

19

AGMA 915--1--A02

straight edge is translated into axial movement of the probe by a ratio mechanism. Combination instruments also capable of measuring involute profile often utilize their master base circle mechanisms in this manner. Other configurations include master lead bar and follower mechanisms, and master lead screw and change gearing mechanisms. Newer generative helix measuring instruments typically use a computer numeric control drive system to generate the nominal helix. Helix measurements must be made relative to the datum axis of rotation of the gear. Refer to 5.1 for more information concerning the datum axis of rotation. Probe tips most commonly used are spherical or disk--shaped. The probe tip must be positioned to contact the tooth surface at the specified tolerance diameter, d T. It is often desirable to orient the measurement probe path of motion normal to the tooth surface. ANSI/AGMA 2015--1--A01 specifies helix tolerances in the transverse plane. If measurements are made normal to the tooth surface, all values must be corrected by dividing by the cosine of the base helix angle, cos "b, before comparison against the tolerances. 8.2.2 Coordinate measurement inspection instruments Helix can be inspected by non--generative, coordinate measurement instruments. Such instruments probe the tooth lengthwise at a series of points, storing the coordinates of each point. The deviation of the actual helix from the nominal is then determined by comparison of the stored test point coordinates against calculated coordinates of the theoretical nominal helix. Coordinate measurement inspection instruments operate in three dimensions (X, Y, and Z coordinates) to measure helix. The gear axis must be aligned parallel with one of the three instrument axes. This may be accomplished by accurate mounting of the part, or mathematically adjusting instrument axes to coincide with the gear axis. Coordinate measurement inspection instruments commonly use spherical measurement probe tips, which require correction for shifting of the probe contact vector.

20


8.2.3 Portable helix measuring instruments Helix measuring instruments are generally fixed type machines, which require that gears to be tested must be brought to the instrument and accurately mounted, typically on--axis between centers or on a table. However, for very large gears it may be preferable to employ a portable helix measuring instrument, which can be taken to the gear. The portable instrument must be accurately mounted at a known distance from, and in alignment with, the gear axis. This often requires extra care in design and manufacture of the gear blank. 8.3 The helix diagram Amplified traces of helix inspection test results should be presented on charts that are calibrated for axial probe travel as well as magnification of measured deviation. Sometimes trace lengths are magnified representations of small facewidths, or reduced representation of large facewidths. An unmodified helix with no deviations will be charted as a straight line. Deviations of the curve from a straight line represent, in magnified form, deviations of the actual helix from an unmodified helix. Helix modifications introduced by the designer also appear as departures from the straight line, but they are not considered to be deviations from the design helix. Excess material on the helix is considered a plus deviation while insufficient material is considered a minus deviation. In addition to identifying the location and magnitude of the helix deviation, these charts are valuable for determining helix characteristics such as edge rounds, crowning, and end relief. Relevance to right hand and left hand helices can be indicated by means of the letters “r” and “l”, respectively, used either as symbols or as subscripts. In figure 24, a typical example of a helix diagram shows the helix deviations of a tooth flank of which the design helix is an unmodified helix. Had the design helix been crowned, end relieved or otherwise modified, traces representing it would be appropriately formed curves. Details of terms, definitions and concepts concerning the helix trace are provided in ANSI/AGMA 2015--1--A01.


able values of f H" and f f " can be calculated in accordance with ANSI/AGMA 2015--1--A01, clause 7.

%$x %$x "

w f

2

8.5 Algebraic signs of f H" and F "

3

$

H f

$

F

$

f f

1 L$

I

II

b

1

Design helix

F "

2

Actual helix trace

f f "

3

Mean helix line

f H"

b

Facewidth or %"x distance between chamfers Helix evaluation f w" Undulation height range Reference face II Non--reference face

L" I

AGMA 915--1 --A02

Total helix deviation Helix form deviation Helix slope deviation Axial wavelength of undulation

Helix slope deviation, f H", and the total helix deviation, F ", are to be reported with an algebraic sign. Deviations are deemed to be positive ( f H" > 0 and F " > 0) when helix angles are larger, and negative when helix angles are smaller, than the design 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 hand helices, respectively. In figure 25, both positive and negative slopes, caused by eccentricity or wobble of mounting on the gear generating machine, are shown. H$ 1

$ b L

--

+

H$2

H$3

-- +

-- +

H

%$--

+

Figure 24 -- Helix diagram 0" (360") The helix evaluation range, L ", is equal to the length of trace, reduced at each end by the smaller of two values: 5% of the helix length of trace, or the length equal to one module. This reduction is made in order to ensure that unintentional, slight end reliefs caused by some machining conditions, are not normally included in the assessment of the deviation magnitudes intended for comparison with stringent tolerances. For assessment of the total helix deviation, F ", and the helix form deviation, f f ", excess material within the end zones of 5%, which increases the amount of deviation shall be taken into account. 8.4 Evaluation of helix diagrams For purpose of gear quality classification, it may be necessary to measure only “total helix deviation”, F ". See ANSI/AGMA 2015--1--A01, clause 4. It may also be necessary to determine the “helix slope deviation”, f H", and the “helix form deviation”, f f ". For this it is necessary to superpose the “mean helix line” onto the diagram as shown in figure 24 (also in ANSI/AGMA 2015--1--A01, figure 1). Allow-

90"

180"

270"

Figure 25 - Traces generated from four tooth flanks If the helix slope deviation, f H", (assuming equal evaluation ranges) of the corresponding flanks of two mating gears are equal in magnitude and algebraic sign, the deviations are mutually compensating. 8.6 Mean helix slope deviation, f H"m For correction of machine tool settings or adaptation to a mating gear, determination of the mean helix slope deviation, f H"m, of the gear is useful. If the helix slope deviations are either random or are fairly consistent, then the mean helix slope deviation may be used to correct the helix setting of the machine used to manufacture the gear. In the case of a matched set of mating gears where one has been manufactured and inspected, then the mean helix slope deviation may be used to adjust the manufacture of the other gear in the set. This will result in improved contact between the gears without

21

AGMA 915--1--A02


the need to make corrections to the previously finished gear. If the helix slope deviation, f H", varies in a regular pattern around the circumference of a helical gear, then the datum axis of the gear was probably tilted, offset, or mis--orientated relative to the machine axis during either manufacture or inspection. See figure 25. Tilting affects spur gears in the same manner, but offset (eccentricity) does not. -- Eccentricity: The variation of helix slope deviation caused by eccentricity (if within specified limits) is not normally detrimental to the operation of the gear. -- Tilting: Variation of helix slope deviation caused by mis--orientation of the gear teeth relative to the datum axis may affect the proper functioning of the gear. The helix slope deviations will cause the center of contact pressure to shift axially back and forth with each revolution. This may in turn cause premature gear tooth failure and/or bearing problems. Therefore, attention should be drawn to this condition even if the deviations are within tolerance. The mean helix slope deviation, f H"m, is calculated by averaging the helix slope deviation, f H", observed on the corresponding flanks of three or more teeth equally spaced around the circumference of the gear. 1 H"m ! n

# f

&

H"1 " f H"2 "''' " f H"n

(16)

where: f H"m is the mean helix slope deviation, m m;

controlling the quality of gear helices. Included in these calculated parameters are: --

effective helix angle at the diameter, " T eff ;

--

effective lead, L eff ;

--

effective helix angle at the standard pitch diameter, " eff ;

--

mean lead difference, f Lm;

--

mean helix angle deviation, f "m.

All of the following equations are based upon the mean helix slope deviation, f H"m. Alternatively, the same formulas could be applied to the case of individual tooth data. The calculation sequence would then commence with the entry of the individual helix slope deviation, f H". 8.7.1 Required preliminary data The following data is required for the additional calculations for helix measurements. Lead, L , can be calculated as follows:

!

is the number of helix slope deviation values included in the mean.

A suitable mean value can be obtained from the helix diagrams of corresponding flanks of two diametrically opposite teeth. However, if the helix slope deviations vary around the gear, this will not always be disclosed unless traces of at least three equispaced flanks are obtained.

22

(17)

L

is the lead of the design helix, mm;

D

is the standard pitch diameter, mm;

"

is the helix angle at the standard pitch diameter, degrees.

Mean helix slope deviation, in the transverse plane and tangent to the tolerance diameter, f H"mt, can be calculated as follows:

!

H"mt

H"m

#& D b d T

(18)

where: f H"mt is the mean helix slope deviation, in the

transverse plane and tangent to the tolerance diameter, m m; f H"m is the mean helix slope deviation, in the

transverse plane and tangent to the base diameter (the tolerance direction specified in ANSI/AGMA 2015--1--A01), mm;

8.7 Additional calculations for helix measurements The mean helix slope deviation, f H"m, can beused to calculate a variety of parameters that are useful for

' tan "

where:

f H"n are the individual helix slope deviations, mm; n

tolerance

Db

is the base diameter, mm;

d T

is the tolerance diameter, mm.


AGMA 915--1 --A02

8.7.2 Calculation of effective helix angle at the tolerance diameter, " T eff

Desired lead of helix

Actual lead of helix

Effective helix angle at the tolerance diameter, "T eff , can be calculated as follows:

) ( (( *

+,

f H"mt $ 10 %3 L L " "T eff ! atan

" # d T'

L

Facewidth

&( (( . (19)

Path of contact of measuring pointer

where:

"T eff is the effective helix angle at the tolerance diameter, degrees; is the helix evaluation range, mm.

L"

Facewidth

8.7.3 Calculation of effective lead, L eff Effective lead, L eff , can be calculated as follows: Leff !

d T '

(20)

tan "T eff

Figure 26 -- Helix of right hand helical gear with short lead (+ helix angle)

where: Leff

is the effective lead.

8.7.4 Calculation of effective helix angle at the standard pitch diameter, " eff Actual lead of helix

Effective helix angle at the standard pitch diameter, "eff , can be calculated as follows:

# &

"eff ! atan D '

L eff

(21)


Facewidth

8.7.5 Calculation of mean lead difference, f Lm Mean lead difference, f Lm, can be calculated as follows: Lm

! L eff % L


(22)

where: f Lm

is the mean lead difference, mm Facewidth

A positive mean lead difference implies that the effective lead is too long, and visa versa. See figures 26, 27, 28 and 29. A positive mean helix slope deviation implies that the effective lead is too short, and visa versa. when f H"m > 0, then f Lm < 0

Figure 27 -- Helix of right hand helical gear with long lead (-- helix angle)

23

AGMA 915--1--A02



8.7.6 Calculation of mean helix angle deviation, f "m


Facewidth

Mean helix angle deviation, f "m, can be calculated as follows: "m

! " eff % "

(23)

where: Path of contact of measuring pointer

f "m

is the mean helix angle deviation, degrees.

A positive mean helix slope deviation implies that the effective helix angle is too large, and visa versa. when f H"m > 0, then f "m > 0 8.8 Undulations Undulations are helix form deviations having constant wavelength and almost constant height. Perturbations of gear production machine transmission elements are their most common cause, especially those of:

Facewidth

a) the cutter saddle feed--screw drive, and b) the worm of the indexing wormgear drive. Figure 28 -- Helix of left hand helical gear with long lead (-- helix angle)

The wavelength of undulations caused by a), measured in direction of helix, is equal to the pitch of the feed--screw divided by cos " . Of undulations due to cause b) the wavelength is:


% " !


d ' z M sin "

(24)

where:

Facewidth


Facewidth

%"

is the undulation wavelength, m m;

d

is the reference diameter, mm;

z M

is the number of teeth in the master indexing worm wheel.

The number of undulations generated as a result of b), projected into a transverse plane, are equal to the number of teeth, z M, of the master indexing worm wheel. These can be sources of objectionable pure--tone components of noise spectra, also known as ghost harmonics,at frequencies corresponding to the rotational speed (revolutions) of the affected gear multiplied by z M. The method of application of the undulation measuring attachment of a helix measuring apparatus is shown in the diagram in figure 30. This is discussed in the following.

Figure 29 -- Helix of left hand helical gear with short lead (+ helix angle)

24

When undulations due to the cause a) or b) mentioned above are to be measured, the appropriate wavelength is calculated and the spherical


AGMA 915--1 --A02

location feet of the attachment are set at an odd number of wavelengths distant from each other.

outlined in 8.2 are impractical, these indirect methods may prove valuable.

The amount of the undulations is indicated by a probe situated midway between the feet as the latter are slid along the helix.

8.9.1 Helix indication using axial pitch

It can be seen in the figure that the displacement of the probe,whena peak and next a trough are sensed by the probe, is equal to twice the height of the undulation as shown in figure 30. This feature enhances the sensitivity of the apparatus, which also plots the results in the form of a diagram. It should be noted that the undulations would not be indicated if the feet were spaced at a distance equal to an even numberof wavelengths as shown in figure 30 with s = 4&". 8.9. Indirect helix inspection methods The following indirect methods may be employed for inspection of gear helix. These methods do not provide the actual levels of helix deviation. However, in instances where the measurement methods

+ f w$

An indication of helix accuracy may be derived from inspection of axial pitch on gears with sufficient helix angle and face width to have multiple axial overlaps. The measurement must be made parallel to the gear axis at increments equal to the axial pitch. The deviation in resulting measurement values is indicative of deviation of helix. Pitch deviations of the measured teeth can affect axial pitch measurements, and must be considered. The axial pitch method of helix inspection is especially attractive for large diameter, wide facewidth gears with large helix angles. 8.9.2 Helix measuring with a master gear Contact pattern checking with a master gear may be used to check the helix deviation of gears in place, or when gears are too large to be accommodated by a helix inspection instrument. The axes of the gear and master must be parallel. Refer to clause 10 for more information concerning this method.

-- f w$

f w$

s

f w$

s = % $

s

s = 4 % $

Figure 30 - Principle of undulation inspection

25

AGMA 915--1--A02


9 Measurement of single flank composite deviations 9.1 Single flank composite Tangential (single flank) composite measurement can provide valuable information about the transmission error of a gear, a pair of gears, or an entire gear train. Transmission error is the deviation of the position of a driven gear from the position that the driven gear would occupy if all the gears involved in the measurement were geometrically perfect. ANSI/AGMA 2015--1--A01 provides tolerances for two characteristics of transmission error for individual product gears measured with a master gear, total single flank composite deviation, F is, and tooth--to-tooth single flank composite deviation, f is. The following is a description of the measuring methods and a guide to interpretation of the data generated during single flank measurement of individual gears measured with a master gear. Single flank measurement of a pair of product gears is also described. Single flank measurement of more than a single mated pair of gears is the assessment of the kinematics of a gear transmission. This is not considered to be within thescope of this documentor ANSI/AGMA 2015--1--A01. 9.2 Single flank composite measurement For measurement of single flank composite deviations, two gears are mounted rotatably in mesh at an appropriate center distance. The gears are mounted with backlash so that contact occurs only on one set of corresponding flanks. Rotating synchronously with each gear is a device capable of

Double flank gear test

Measures variation in center distance

measuring angular motion. These are typically rotary optical encoders (gratings and reader head assemblies). Rotary accelerometers and velocity transducers have also been used as sensing devices. See figures 31 and 32. During measurement one gear acts as the driver, rotating the other gear. During rotation, the angular positions of the driven gear relative to the driver is calculated through ratioing of the signals from the two sensing devices using analog or digital electronics. These relative positions are recorded either on a strip chart or into digital storage on a computer until a complete diagram has been generated. To compare these angular readings to the tolerances provided in ANSI/AGMA 2015--1--A01 they must first be converted to linear values at the tolerance diameter specified. Single flank composite measurements are performed with tooth flank contact maintained, under very light load, and with low angular velocities. The results generated reflect the combined elemental deviations (profile, helix, pitch) of both gears. Single flank composite deviations of heavily loaded gears can also be similarly measured. Under these conditions, recorded deviations are influenced by load induced tooth deformations, by mesh stiffness variation, and depending on the speed of rotation by impact effects, as well as by imperfections of tooth geometry. ANSI/AGMA 2015--1--A01 does not apply to this kind of measurement. 9.2.1 Single flank composite deviations Total single flank composite deviation, F is, is the maximum measured transmission error range when the gear is moved through one complete revolution. See figure 33.

Single flank gear testing

Measures rotational movements

Figure 31 -- Composite gear testing, double and single flank

26


AGMA 915--1 --A02

z 1 = Driving gear

z 2 = Driven gear

z 1

z 2

Optical gratings

Reading heads f 1 pulses/sec f 2 pulses/sec

Multiplier z 1

Phase comparator

Divider z 2

z 1 z 2 f 1

# & ! f pulses/sec 2

Figure 32 -- Schematic of a single flank measuring device

One gear revolution

40 30 20

f pt

m m 1 10 0 0 . 0 , e 0 d u t i l p --10 m A

F p F is

--20 --30 --40 0

1

2

3

4

5 6 7 Tooth number

8

9

10

11

12

Figure 33 -- Individual tooth deviations revealed by single flank testing

27

AGMA 915--1--A02


40 30 20 m 10 m 1 0 0 . 0 0 , e d u t i --10 l p m A--20

f is

--30 --40 0

1

2

3

4

5 6 Tooth number

7

8

9

10

11

12

Figure 34 -- Filtered signal from figure 33 (eccentricity removed)

Tooth--to--tooth single flank composite deviation, f is is the value of the greatest measured transmission error over any one pitch (360/ z ) after removal of the long term component (sinusoidal effect of eccentricity) when the gear is moved through one complete revolution. See figure 34. 9.3 Single flank measurement with master gear Recorded diagrams of single flank composite measurements generally include short period components corresponding to successive cycles of tooth engagement, superposed on long period components associated with complete revolutions of each of the meshing gears. The diagram in figure 33 represents the record of single flank composite deviations generated during one revolution of a pinion having 12 teeth when meshed with a master gear. 9.3.1 Master gear requirements For single flank measurement of individual product gears, a master gear of known accuracy (calibrated) and specifically designed to mesh with the product gear to be inspected should be used. Attention must be paid to the fact that the quality of the master gear

28

will influence the measurement of product gears. If the quality of the master is at least 4 accuracy grades better than the required grade of the product gear, inaccuracies of the master are usually ignored. If the quality of the master is less than 4 accuracy grades better than the required grade of the product gear, inaccuracies of the master should be taken into account. 9.3.2 Influence of profile deviations When using a master gear in the measuring of single flank composite deviations, the assumption that the master gear is perfectly accurate implies that the generated single flank composite deviation diagram represents only the combined deviations of the tooth elements of the product gear. Figure 35 shows schematically, single flank composite recordings of three consecutive cycles of tooth engagement of a master gear and product gear. Each corresponds to a different tooth profile. The first is unmodified and faultless, the second being progressively modified from mid--depth towards each limit of the active profile, and the third with negative profile slope deviation.


progressively decreasing trend as contact approaches the end of the tooth engagement cycle.

A

tip master test gear

perfect conjugate tooth shape

root t + n e m r e a c l a 0 u l g p s n i a d

1 pitch

1 pitch

1 pitch

angular motion curve

--

B

tip master

modified tooth shape [profile barrelling C!]

test gear root t + n e m r e a c l a 0 u l g p s n i a d

1 pitch

--

1 pitch

master

C

test gear

modified tooth shape [modified pressure angle]

root t + n e m 0 r e c a l l a u p g s n i - a d

1 pitch


tip

1 pitch

1 pitch

AGMA 915--1 --A02

1 pitch


Figure 35 -- Angular motion curves from tooth modification Figure 35(A) shows the straight line diagram generated by a product gear and master gear that both have fault--free unmodified teeth. In figure 35(B), the record indicates the influence of tip and root relief in the form of a modification over the whole profile. From the start of the tooth engagement cycle with first contact at the tooth tip of the driven product gear, the deviation value increases progressively to zero as contact nears mid--depth, then changes to a

In figure 35(C), the saw tooth components of the diagram show progressive single flank composite deviation from zero to a negative value as contact moves from the product gear tooth tip towards the start of active tooth profile. At this point, contact abruptly transfers to the following tooth with the introduction of an equally abrupt positive deviation. It must be noted that diagrams of single flank composite measurements do not merely reflect influences of profile deviations revealed by measurements made on a few teeth, but may be influenced by contact involved in any prominences on the working surfaces of the teeth of the product gear. 9.3.3 Influence of pitch deviations Each single pitch deviation introduces a local tangential component, which will show on the single flank composite diagram as a displacement of the corresponding profile generated component of the diagram. The schematic diagram in figure 33 illustrates the influence of single pitch deviations, f pt, on the single flank composite diagram. Single pitch deviations have a cumulative effect on the single flank composite displacement arc as they pass through the mesh. Their influence is clearly visible on the single flank composite diagram. This enables values of cumulative pitch deviations (e.g., when k =2, k = 3, etc.) to be determined as the ordinates of tangents to the apices at appropriate numbers of pitches apart. The principle is illustrated in figure 33, in which influences of single pitch deviation and the approximate total cumulative pitch deviation, F p , are indicated. 9.3.4 Influence of helix deviations A helix slope deviation that is constant in magnitude and sign, (i.e., is common to every tooth of a gear) results in consistent localized bearing in the mesh. This does not substantially influence the single flank composite deviations of spur gears. The single flank composite deviations of helical gears, however, may be adversely effected by a constant helix slope deviation. This is due to the different nature of the path of contact of helical gears. When helix slope deviations vary in magnitude and/or sign around a product gear, the bearing

29

AGMA 915--1--A02


contact location will vary around the gear. This condition may adversely effect single flank composite deviations of both spur and helical gears.

recognized that the maximum length of the single-pair tooth contact path is realized when the contact ratio, #$, is equal to one. As the contact ratio increases, this length reduces and when the contact ratio is equal to or greater than two, there is no single--pair tooth contact at all.

Helix form deviations do not substantially influence the single flank results of spur gears. Single flank composite deviations of helical gears, however, may be adversely effected by helix form deviations.

When the total contact ratio, #$ exceeds two, which is normally the case for helical gears, the short period components which represent profile irregularities are smoothed to some extent because in general, simultaneous contact takes place on two or more tooth pairs.

9.3.5 Influence of contact ratio A single flank composite deviation diagram generated from a master-- gear and product--gear combination is composed of successive curves representing for the most part the profile deviations, as shown in figure 36. Single--pair and two--pair tooth engagements and the single flank composite deviation diagram during a complete cycle of tooth engagement is clearly illustrated. It can easily be

Diagrams in figure 37 with the two cases “A” (generated from helical gears) and “B” (from spur gears) illustrate the difference between the ways in which the influence of the overlapping teeth of the two types combine.

root

tip

master gear profile deviation diagrams product gear root

tip direction of paper feed tangential composite 1 deviation

2

3 stylus profile component

3 product gear 2

1

master gear

pb pb = base pitch g! = length of path of contact

pb g!

Figure 36 -- Effect of contact transfer on the profile component in a tangential composite deviation diagram (spur gears)

30


AGMA 915--1 --A02

number of tooth pairs in mesh 3

2

3

2

3

A

number of tooth pairs in mesh 2

1

2

B

Figure 37 -- Influence of overlap ratio Single flank composite results can be very different from what is expected, especially if these expectations are derived from consideration of theoretical contact ratio and an assumption that contact is perfect over the tooth profiles and facewidth of helical gears. Single flank composite deviations can be influenced by modification of tooth profile and helix (tip relief, crowning, etc.) introduced to accommodate possible deformations of shafts, housings and teeth under load. If under full load the tooth bearing is uniformly distributed over the working surfaces of the teeth, such is not likely to be the case under the light load conditions used during single flank composite measurement where the tooth bearing may be localized. Given these circumstances, the contact ratio during measurement is likely much less than elementary theory would suggest. 9.3.6 Interpretation of results This section contains information and techniques for interpreting single flank composite results beginning with a comparison to methods used for traditional double flank (radial composite) testing. Double flank composite data charts are made up primarily of information related to radial runout, F r (long term component), and deviations of tooth--to--

tooth composite of both flanks, f id (short term component). Single flank composite data charts are made up primarily of information related to cumulative pitch, F p (long term component) deviations, and deviations in tooth form of the single flank in contact, f is (short term component). 9.3.6.1 Traditional interpretation In ANSI/AGMA 2000--A88 and ISO 1328--2, double flank composite measurements were toleranced for total composite variation, and tooth--to--tooth composite variation. They were interpreted from a recorded chart for one revolution of the product gear as shown in figure 38. The total composite variation was defined as the difference between the highest to lowest point on the chart. The tooth--to--tooth variation was defined as the greatest change in any 360 degree/ z part of the chart. This may be acceptable for evaluation of the final gear quality relative to the application for some purposes. However, traditional double flank testing has some limitations. For example, it cannot detect cumulative pitch deviation that occurs without radial runout deviation. Double flank testing is not considered a reliable method for determining noise potential. Double flank testing also provides little information for diagnoses of tooth--to--tooth deviations.

31

AGMA 915--1--A02


5.0 4.0 3.0 2.0 1.0 e d u 0.0 t i l p m A --1.0

Unfiltered tooth--to-tooth

Total composite

--2.0 --3.0 --4.0 --5.0 0

1

2

3

4

5 6 7 8 Tooth number Figure 38 -- Single flank composite strip chart

The traditional analysis method used for calculation of tooth--to--tooth composite deviation may give a distorted indication of the tooth form that the machine and tool is producing. This is due to the influence of the long term component on the tooth--to--tooth composite deviation. This distortion is best explained by the case of a gear that had identical tooth form on all teeth being measured with a perfect master. In this case the greatest tooth--to--tooth variation will be along the part of the long term component curve that has the greatest slope. This has the effect of distorting the amplitude of the data relating to that particular tooth. For the same quality of tooth form and runout, the tooth--to--tooth composite deviation would be greater for a gear with a lower number of teeth than it will for higher numbers of teeth. See figures 39 and 40 for a comparison. 9.3.6.2 Relationship between tolerances Because of the relationship between the long term component and the tooth--to--tooth deviation, tolerances have had unrealistic values in some cases. In previously existing standards, the tooth--to--tooth composite tolerance has been approximately 1/3 to

32

9

10

11

12

1/2 of the total composite tolerance. This is partly in order to accommodate the distortion of tooth--to-tooth data, by the long term component, especially for low numbers of teeth. Inthe case of a gear with very little or no runout, there should be a greater difference between total and tooth--to--tooth composite deviation tolerances. In this case the tooth--to--tooth composite tolerance should be 0.1 to 0.2 times the total composite tolerance. This more appropriate tolerance ratio is feasible regardless of the amplitude of the long term component if the tooth--to--tooth composite deviations are separated from the long term component prior to analysis. 9.3.6.3 Separation of tooth -- to -- tooth composite observations The separation of eccentricity effects from observations of tooth--to--tooth composite deviations can be done by different techniques. The preferred method is by use of a digital computer program that is capable of fitting and extracting a sine wave according to the given test data. This would result in charts as shown in figures 41a, 41b, and 41c.


AGMA 915--1 --A02

5.0 4.0 3.0 2.0 e 1.0 d u t i l p 0.0 m A

Unfiltered tooth--to--tooth (12 tooth gear)

--1.0 --2.0 --3.0 --4.0 --5.0 0

1

2

3

4

5 6 Tooth number

7

8

9

10

11

12

Figure 39 -- Single flank composite test, low number of teeth

5.0 4.0 3.0 2.0

Unfiltered tooth--to-tooth (30 tooth gear)

e d 1.0 u t i l p m 0.0 A

--1.0 --2.0 --3.0 --4.0 --5.0 0

5

10

15 Tooth number

20

25

30

Figure 40 -- Single flank composite test, high number of teeth

33

AGMA 915--1--A02


5.0 4.0 n o i t ) a k i v n e a f d l e e l t i g s n o i p S m o s c i l F a ( t o T

3.0 2.0 e 1.0 d u t i l p 0.0 m A

--1.0 --2.0 30 tooth gear

--3.0 --4.0 --5.0 0

5

10

15 Tooth number

20

25

30

25

30

Figure 41a -- Total composite deviation

5.0 4.0 3.0 t n e n o p m o c m r e t g n o L

2.0 e d 1.0 u t i l p m 0.0 A

--1.0 --2.0 --3.0

30 tooth gear

--4.0 --5.0 0

5

10

15 Tooth number

20

Figure 41b -- Long term component

34


AGMA 915--1 --A02

5.0

t n e ) n k o n a p l f m e o l c g n i m r S e t t s r f i o ( h S

4.0 3.0 2.0 e d 1.0 u t i l p m 0.0 A

--1.0 --2.0 --3.0

Composite tooth--to --tooth 30 tooth gear

--4.0 --5.0 0

5

10

15 Tooth number

20

25

30

Figure 41c -- Short term component

If this method is not available in the measuring system, an approximation can be done manually. This involves drawing an upper and lower envelope of essentially sinusoidal shape enclosing the measured data. The vertical distance between these upper and lower envelope lines is the tooth--to--tooth composite error, f is. This is shown in figure 42. 9.3.6.4 Additional diagnostics These techniques are focused on evaluation of the final gear quality relative to the given application. However, it may be desirable to carryout additional analysis for diagnostic purposes, such as noise potential or manufacturing process monitoring. In such cases more comprehensive data filtering is appropriate. Most situations with long term component deviations will be in the sinusoidal form, which is caused by eccentricity, as shown in figures 41a, 41b, 41c and 42. There are cases, however, where long term deviations will show up in higher orders, such as shown in figures 33 and 34. This can be caused by oval shapes, triangular shapes, etc. This is common

in ring gears where heat treat distortions occur at the location of each bolt hole in the blank. Even the short term componentcan have distortions fromvariations in the tooth shape. Analysis of composite test data can be enhanced by the use of analog or digital filters that segregate long and short term component deviations at a selected “cutoff” wavelength. Still more comprehensive analysis of higher order deviations is possible by use of Fourier analysis techniques, such as a Fast Fourier Transform (FFT) analyzer. 9.4 Single flank measurement of product gear pair The single flank tooth--to--tooth and total composite deviations involving a mated pair of product gears are termed “transmission deviations of a gear pair”. To fully explore the complete spectrum of the deviations, it is necessary to continue rotation until the complete meshing period of both gears has been explored. The number of revolutions required corresponds to the number of teeth in the larger member divided by the largest factor common to both members.

35

AGMA 915--1--A02


5.0 4.0 n o i t ) a k i r n a l a v f e e t i l s g n o i p S m o s c i l F a ( t o T

3.0 2.0 Short term component ( f is -- Single flank)

1.0 e d u 0.0 t i l p m A--1.0

t n ) e k n n o a p l f m e o l c g n i m r S e t g p n F o ( L

--2.0 --3.0

12 tooth gear

--4.0 --5.0 0

1

2

3

4

5 6 Tooth number

7

8

9

10

11

12

Figure 42 -- Manual interpretation of composite test Analysis is similar to that described in 9.3.6 for a product gear with a master gear, except that the deviations should be calculated based on the complete meshing period of both gears rather than on a single revolution of the product gear. 9.4.1 Identification and location of defects The measurement of tangential composite deviations facilitates the identification and location of defects (nicks or burrs) which may degrade the quality of transmission. For example, as indicated in the diagram in figure 43, the presence of a defective tooth can readily be seen. Furthermore, it is sometimes possible to carry out corrective measures while still connected to the measuring appara-

tus, in which case the effectiveness of the adjustments can be verified without delay. 9.4.2 Selective meshing of gears In some exceptional cases, involving mated pairs of gears with equal numbers of teeth or other integer ratios, special steps can be taken to ensure that optimum performance is realized. Such gears can be meshed to best advantage by remeshing the gears with a phase shift of ninety degrees to find the quadrant in which single flank composite deviations are smallest. Following this, the process is repeated by remeshing the gears with phase shifts less than ninety degrees in order to find the optimum meshing phase.

representing one pitch

damaged tooth

Figure 43 -- Part of tangential composite deviation diagram -- Interpretation example

36


In figure 44 diagrams are shown which were generatedfrom a pair of gears at the differentphases of mesh indicated. It is quite evident that the single flank composite deviation diagrams for the left flanks and right flanks are not the same. It may be necessary to choose an intermediate meshing position that provides the best compromise solution if a high degree of transmission accuracy is needed for both directions of rotation.

10 Contact pattern checking

AGMA 915--1 --A02

10.1 Control of test conditions The reproducibility of contact pattern checks is dependent upon careful control of the test conditions. A small variation, 0.01 mm, in location of the gears from test to test may have a significant effect on the results. Caution should be used when static contact checks are performed on gears and shafts mounted in dynamic bearings. The shafts should be located in a fixture in such a way that they represent the final operating conditions. 10.1.1 Gear axes parallel

Contact checking is used for the inspection of mating gear sets to determine their operational compatibility and for the inspection of gears which will not fit into available measuring machines because of size and weight limits. This clause explains a quasi--static method of obtaining and analyzing contact patterns, and a method for evaluating the observed deviations from designed contact. Contact checking is commonly used on bevel, mill, marine, and high speed gears.

When the gears are tested outside the housing in which they may be used, or if the assembled centers are adjustable, the gears are normally mounted with their axes parallel. This is usually accomplished in an adjustable testing frame with the line of centers horizontal, so that a precision level and micrometers can be used to establish parallel axes at the given center distance in a common plane. The absolute value of center distance is not as important as maintaining the gear axes parallel.

representing one gear revolution

0"L

0"R

90"L

90"R

180"L

180"R

270"L

270"R

90" + 1 tooth (L)

90" + 1 tooth (R)

Figure 44 -- Tangential composite deviation diagrams showing influence of mesh relocation

37

AGMA 915--1--A02


10.1.2 Test gears

10.4 Interpretation of results

If test gears are being compared to a master gear, the master gear must be of known quality, and of sufficient accuracy to assure that errorsin themaster gear will not appreciably affect the results.

Typical values for carefully applied marking compound thickness are from 0.008 mm to 0.012 mm.

Gears may also be tested as matched pairs. 10.1.3 Marking compound Various marking compounds can be used including Prussian blue, dye check developer, and proprietary compounds. It is important that the compound be controlled carefully, since its viscosity and the method of application will affect the film thickness, which is critical to the interpretation of results.

Figure 45 shows a contact pattern obtained with good profile contact, and some tooth alignment mismatch. If the marking compound thickness is 0.01 mm, the tooth misalignment shown over the length of the contact pattern is also 0.01 mm. An angular correction in helix angle or mounting of 0.01 mm divided by the length of contact should produce full contact. Length of contact

10.1.4 Test load Usually, the test load is very light. In some gear testing machines, the test load can be varied and controlled. 10.1.5 Operator training Since operator skill is an important factor in application of the marking compound and control of the test load, it is important that uniform procedures be established and that operators be trained in these procedures, so that reproducible results may be obtained. 10.2 Calibration Calibration of the thickness of the marking compound is essential to interpretation of contact pattern test results. Once an operator has developed a consistent technique, it is possible to establish the thickness of the marking compound by shifting the axes of the gears out of parallel in a vertical direction in the tangential plane by a known angle; i.e., shimming one bearing support and observing the change in the pattern. This calibration should be performed regularly to be sure that the marking compound, test load, and operator technique have not varied.

Figure 45 -- Matching profiles, with tooth alignment mismatch and end relief The contact pattern shown in figure46 shows perfect tooth helix alignment with profile mismatch. Using the same marking compound calibration as the example above, the profile mismatch is 0.02 mm, since contact extends over only one--half of the profile.

10.3 Recording results Contact patterns are usually recorded by photography, sketches, or tapes. Instant developing colorfilm and digital photography are particularly useful for recording contact patterns. Tapes are made by carefully applying transparent mending tape (such as Scotch' tape) over the contact pattern, removing the tape, and applying the tape with the adhering pattern to white paper.

38

Figure 46 -- Matching helix, with profile mismatch and end relief Figure 47 shows an undulating contact pattern which might be caused by periodic error in the generating machine.


AGMA 915--1 --A02

tions of approximately 75 percent of contact, excluding extremes of tooth which are intentionally relieved.

Figure 47 -- Waviness 10.5 Specifications Contact pattern acceptability is specified by defining the area in whichcontact may not occur, the areas in which contact should occur, and the percentage of contact required in the desired area. Figure 48 illustrates a contact pattern which meets a specifica-

Figure 48 -- Typical specification: approximately 75% contact, excluding extremes of tooth, which are intentionally relieved

39

AGMA 915-1-A02 Gears Inspect

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