AGMA 915-2-A05
May 4, 2017 | Author: Simo_83 | Category: N/A
Short Description
AGMA 915-2-A05...
Description
AGMA 915- 2- A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
AGMA 915- 2- A05
Inspection Practices - Part 2: Cylindrical Gears - Radial Measurements
AGMA INFORMATION SHEET (This Information Sheet is NOT an AGMA Standard)
Inspection Practices - Part 2: Cylindrical Gears - Radial Measurements American AGMA 915--2--A05 Gear Manufacturers CAUTION NOTICE: AGMA technical publications are subject to constant improvement, revision or withdrawal as dictated by experience. Any person who refers to any AGMA Association technical publication should be sure that the publication is the latest available from the Association on the subject matter.
[Tables or other self--supporting sections may be quoted or extracted. Credit lines should read: Extracted from AGMA 915--2--A05, Inspection Practices -- Part 2: Cylindrical Gears -- Radial Measurements, with the permission of the publisher, the American Gear Manufacturers Association, 500 Montgomery Street, Suite 350, Alexandria, Virginia 22314.] Approved May 3, 2005
ABSTRACT This information sheet discusses inspection of cylindrical involute gears using the radial (double flank) composite method, with recommended practices detailed. Also included is a clause on runout and eccentricity measurement methods. This information sheet is a supplement to the standard ANSI/AGMA 2015--2--AXX. Published by
American Gear Manufacturers Association 500 Montgomery Street, Suite 350, Alexandria, Virginia 22314 Copyright © 2005 by American Gear Manufacturers Association All rights reserved. No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without prior written permission of the publisher.
Printed in the United States of America ISBN: 1--55589--843--2
ii
AMERICAN GEAR MANUFACTURERS ASSOCIATION
AGMA 915--2--A05
Contents Page
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv 1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Symbols, corresponding terms and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 Measurement of radial composite deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 Tooth thickness measurement with radial composite measurement . . . . . . . 12 6 Verification of master gears and fixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 7 Runout and eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Figures 1 2 3 4 5a 5b 6a 6b 6c 7 8 9 10 11 12 13 14 15 16 17 18
Principle of measuring radial composite deviations . . . . . . . . . . . . . . . . . . . . . . 3 Radial composite deviation diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Interpretation of radial composite deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Strip chart of double flank composite test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Double flank composite test, low number of teeth (12 tooth gear) . . . . . . . . . . 8 Double flank composite test, high number of teeth (30 tooth gear) . . . . . . . . . 9 Total composite deviation of 30 tooth gear (unfiltered) . . . . . . . . . . . . . . . . . . . 10 Long term component (30 tooth gear) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Short term component (30 tooth gear) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Manual interpretation of composite test (12 tooth gear) . . . . . . . . . . . . . . . . . . 11 Complex deviations with first order removed (one revolution) . . . . . . . . . . . . 12 Radial composite action test measurement of tooth thickness . . . . . . . . . . . . 14 Principle of measuring radial runout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Anvil size for measuring radial runout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Runout from coordinate measuring machine . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Runout diagram of a gear with 16 teeth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Runout and pitch deviations of an eccentric gear . . . . . . . . . . . . . . . . . . . . . . . 21 Gear with zero runout, but with considerable pitch and cumulative pitch deviations (all space widths are equal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Gear with pitch and cumulative pitch deviations and zero runout . . . . . . . . . . 22 Actual gear with little runout and substantial cumulative pitch deviation . . . . 23 Runout measurement with a rider when all space widths are equal and pitch deviations are present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Tables 1 2
Symbols and terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Recommended checking load for metallic gears with 2.5 mm face width . . . . 7
© 2005 AGMA ---- All rights reserved
iii
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
Foreword This Information Sheet, AGMA 915--2--A05, Inspection Practices -- Part 2: Cylindrical Gears -- Radial Measurements, is provided for informational purposes and is intended for use with Standard ANSI/AGMA 2015--2--AXX, Accuracy Classification System -- Radial Measurements for Cylindrical Gears. AGMA 915--2--A05 replaces AGMA ISO 10064--2, Cylindrical Gears -- Code of Inspection Practice -- Part 2: Inspection Related to Radial Composite Deviations, Runout, Tooth Thickness and Backlash, and the information on similar subjects as covered in 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 AGMA 2000--A88, AGMA ISO 10064--2 and this document. This includes that measuring methods refer to an accuracy grade numbering system that is reversed, such that the smallest number represents the smallest tolerance. Therefore, the user of this information sheet must be very careful when comparing measurement methods formerly specified using AGMA 2000--A88 or AGMA ISO 10064--2. The first draft of AGMA 915--2--A05 was made in March, 1999. It was approved by the Technical Division Executive Committee (TDEC) in May, 2005. Suggestions for improvement of this document will be welcome. They should be sent to the American Gear Manufacturers Association, 500 Montgomery Street, Suite 350, Alexandria, Virginia 22314.
iv
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
AGMA 915--2--A05
PERSONNEL of the AGMA Gear Accuracy Committee Chairman: Edward Lawson . . . . . . . . . . . . . . . . . . . . . . Gleason -- M&M Precision Systems Vice Chairman: Steve Lindley . . . . . . . . . . . . . . . . . . . Falk Corporation
ACTIVE MEMBERS J. Clatworthy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.E. Cowan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.L. Cox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Frazer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Griffieth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Klaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Layland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. May . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R.W. Ott . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.M. Rinaldo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert E. Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
© 2005 AGMA ---- All rights reserved
Gear Metrology, Inc. Gleason -- M&M Precision Systems BWXT Y--12, LLC University of Newcastle--Upon--Tyne M&M Precision Systems Corporation Milwaukee Gear Company Precision Gage Company, Inc. Gleason Works Caterpillar, Inc. Atlas Copco Compressors, Inc. R. E. Smith & Company, Inc.
v
AMERICAN GEAR MANUFACTURERS ASSOCIATION
AGMA 915--2--A05
American Gear Manufacturers Association --
ANSI/AGMA 2002--B88, Tooth Specification and Measurement
Inspection Practices -Part 2: Cylindrical Gears -- Radial Measurements
ANSI/AGMA 2015--2--AXX, Accuracy Classification System -- Radial Measurements for Cylindrical Gears
1 Scope This information sheet constitutes a code of practice dealing with inspection relevant to radial composite deviations and runout of cylindrical involute gears; i.e., with measurements referred to double flank contact. In providing advice on gear checking methods and the analysis of measurement results, it supplements standard ANSI/AGMA 2015--2--AXX, where most of the terms used are defined.
2 References The following standards contain provisions which, through reference in this text, constitute provisions of this information sheet. 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 below. AGMA 915--1--A02, Inspection Practices -- Part 1: Cylindrical Gears -- Tangential Measurements AGMA 915--3--A99, Inspection Practices -- Gear Blanks, Shaft Center Distance and Parallelism AGMA 935--AXX, Recommendations Relative to the Evaluation of Radial Composite Gear Double Flank Testers ANSI/AGMA 1012--G05, Gear Nomenclature, Definition of Terms with Symbols
© 2005 AGMA ---- All rights reserved
Thickness
ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for Cylindrical Gears
ANSI/AGMA 2116--AXX, Evaluation of Double Flank Testers for Radial Composite Measurement of Gears ISO/TR 10064--2:1996, Cylindrical gears -- Code of inspection practice -- Part 2: Inspection related to radial composite deviations, runout, tooth thickness and backlash
3 Symbols, corresponding terms and definitions 3.1 Symbols and terms The symbols and terms used throughout this information sheet are in basic agreement with the symbols and terms given in AGMA 900--G00, Style Manual for the Preparation of Standards, and ANSI/AGMA 1012--G05, Gear Nomenclature, Definition of Terms with Symbols. In all cases, the first time that each symbol is introduced, it is defined and discussed in detail. 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.
The symbols and terms are listed in alphabetical order by symbol in table 1. 3.2 Definitions The terms used, wherever applicable, conform to ANSI/AGMA 1012--G05 and ANSI/AGMA 2015--2--AXX. The reference axis of a component is defined by means of datum surfaces. In most cases the axis of the bore can be adequately represented by the axis of the mating product arbor (see AGMA 915--3--A99).
1
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
Table 1 -- Symbols and terms Symbols a Center distance
Terms
Units mm
ad d
Test center distance Diameter, reference pitch
mm mm
db
Diameter, base circle
mm
Fid
Radial composite deviation, total
mm
Fp Fr
Total cumulative pitch deviation Runout
mm mm
fe
Eccentricity
mm
fid fpt Lg mn
Radial composite deviation, tooth--to--tooth Single pitch deviation Gage block stack height Module, normal
mm mm mm -- --
pb Rr s x
Pitch, base Test radius Tooth thickness Profile shift coefficient
mm mm mm -- --
z
Number of teeth
-- --
α
Pressure angle
degrees
β
Helix angle
degrees
δ
Prism (anvil) half angle
degrees
εβ
Helical overlap ratio
-- --
η Tooth thickness half angle Subscripts 3 Master gear a
Arbor
b n T t w y
Base Normal plane Tolerance Transverse plane Product gear, operating Any (specified) diameter
The geometric axis of the teeth for radial composite deviation is that axis which, if used for the measurement, would give the minimum root mean square (rms) total radial composite deviation over a complete revolution.
degrees
(radial direction) as a gear rotates in tight mesh with a master gear. The single flank composite action test measures transmission error in the tangential direction with gears that are not in tight mesh, and is described in ANSI/AGMA 2015--1--A01 and AGMA 915--1--A02. 4.1 Checking principle
4 Measurement of radial composite deviations There are two composite measurement methods for gear inspection. This information sheet contains a description of the double flank composite action test, which measures variations in the center distance
2
Radial composite deviations are checked on a device on which pairs of gears are assembled with one gear on a fixed spindle, the other on a spindle carried on a slide provided with a spring arrangement enabling the gears to be held radially in close mesh (see figure 1). The variations in center
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
distance, which occur as the gears are rotated together in tight mesh, are recorded. This recording may be done manually while observing a dial indicator, with a stylus on a chart, or electronically. Gear deviations evaluated by the composite action test are tooth--to--tooth composite deviation and total radial composite deviation. In certain cases, functional tooth thickness and radial runout can also be evaluated. For most inspection purposes, product gears are tested against a master gear. Measured composite errors always include deviations associated with the master gear. Minimizing master gear deviations allows more of the tolerance for errors in the product gears. The total radial composite deviation, Fid, of the gear under inspection is equal to the maximum variation
AGMA 915--2--A05
of center distance during one revolution. It can be determined from a recorded diagram. The tooth--to-tooth radial composite deviation, fid, is equal to the variation of center distance during rotation through one pitch angle (see figure 2). The tolerance values given in ANSI/AGMA 2015--2--AXX are valid for measurements made using a master gear. It is important to note that the accuracy and design of the master gear, especially its engagement with the product gear, can influence the test results. The master gear should have sufficient depth of engagement to be capable of contact with the entire functional profile of the product gear, but should not contact its non--functional or root parts. Such contact can be avoided when the master gear teeth are thick enough to compensate for the product gear backlash allowance.
mesh without backlash view Z (enlarged)
Z master gear
measuring direction product gear
During rotation, variation of center distance is measured Figure 1 -- Principle of measuring radial composite deviations
fe Fid 360° z
Maximum value of fid
0°
360° Figure 2 -- Radial composite deviation diagram
© 2005 AGMA ---- All rights reserved
3
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
When they are to be used for the quality grading of accurate gears, the accuracy of the master gear and the measuring procedure used should be agreed between the manufacturer and purchaser.
deviation between the geometrical axis of the teeth and the reference axis (i.e., the bore or shaft).
The design of the master gear shall be agreed upon between manufacturer and purchaser. The overlap ratio, εβ test, may influence the results of radial composite measurements of helical gears. The effects of profile deviations which would be evident with spur gears may be concealed because of the multiple tooth and diagonal contact lines with helical gears. A helical gear face width such that εβ test is less than or equal to 0.5 with the product gear should be used. However, the full face width of the product gear should be explored.
Radial composite deviations include components from the combined deviations of right and left flanks. Therefore, determination of the individual deviations of corresponding flanks is not feasible. The measurement of radial composite deviations quickly provides information on deficiencies of quality related to the production machine, the tool, or the product gear setup. The method is chiefly used for carrying out checking of large quantities of product gears, as well as fine pitch gears.
A chart recording of approximate sinusoidal form (with amplitude 2fe) over a single revolution indicates eccentricity, fe, of the gear teeth. Reference to figure 2 shows how such a sinusoidal curve can be drawn on the diagram. Eccentricity of a gear is the
4.2 The utility of radial composite deviation data
Tooth--to--tooth composite deviations occurring at each pitch increment tend to indicate profile deviations (often profile slope deviations). A large isolated tooth--to--tooth composite deviation may indicate a large single pitch deviation or damaged tooth (see figure 3).
1 revolution Runout These are fluctuations in center distance during one revolution of the product gear. They appear in the diagram as slowly increasing and decreasing curves corresponding to the ratio of the gears.
damaged tooth Pitch deviations They are revealed in the diagram as sudden and irregular deflections of the recording pen of varying magnitude between two adjacent teeth.
Profile deviations The slight undulations in the curve indicate deviations of the tooth form from the theoretical involute profile. Each wave corresponds to the period of contact of one tooth.
Pressure angle deviations (profile slope deviation) The chart reveals them as regularly spaced and sharp--pointed vertical deflections, whereby each deflection corresponds to the period of contact of one tooth.
Figure 3 -- Interpretation of radial composite deviation
4
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
With appropriate calibration of the product gear setup and checking methods, the measuring process can also be used to determine the center distance at which the product gear may be meshed with minimum backlash. See AGMA 915--3--A99 for recommendations on shaft center distance and parallelism of axes. Furthermore, the procedure is useful for checking gears required to operate with minimum backlash, since the range of functional tooth thickness can readily be derived from the radial composite deviations. For the determination of an accuracy grade, the product gear should be checked against a master gear exploring 100% of the functional flanks. See clause 8 of ANSI/AGMA 2015--2--AXX. The tolerance values of total and tooth--to--tooth radial composite deviations to determine an accuracy grade for product gears are given in ANSI/AGMA 2015--2--AXX. It is emphasized that because of the simultaneous contributions from both sets of tooth flanks, such an accuracy grade cannot be directly related to an accuracy grade determined by inspection of individual element deviations. 4.3 Double flank composite action test data Gear rolling fixtures indicate changes in tight mesh center distance by either a dial indicator, or recording devices that may produce charts. Composite action charts are amplified traces of the measured radial displacement of composite deviation versus product gear rotation. Figure 2 is a typical chart showing the content of the data for tooth--to--tooth composite deviation and total radial composite deviation. The deviations shown in figure 2 include the effects of the deviations which exist in both the product gear and the master gear. When required, the results of composite action tests should be reported in accordance with 4.3.1 and 4.3.2. 4.3.1 Tooth--to--tooth composite deviation data Tooth--to--tooth composite deviation data, during a composite action test, is obtained as the product gear is rotated through any angle of 360/z. This test indicates values which include the effects of profile, pitch, tooth thickness, and tooth alignment deviations in both the product gear and in the master gear. There is no practical way of subtracting the deviations in the specified (master) gear from the recorded values. The permissible values of tooth-to--tooth composite deviation toleranced in ANSI/ AGMA 2015--2--AXX are the maximum values as read on a dial or from a chart for any 360_/z segment.
© 2005 AGMA ---- All rights reserved
AGMA 915--2--A05
4.3.2 Total radial composite deviation data Total radial composite deviation data, during a composite action test, is obtained when the product gear is rotated through one complete revolution. The effects of total radial composite deviation in the specified (master) gear may be compensated for by the following: -- determine the total radial composite deviation, Fid, as measured on the chart or dial indicator; -- obtain the total radial composite deviation, Fid3, of the master gear (obtained from calibration); -- determine the total radial composite tolerance, FidT, allowed on drawing. Then the following cases apply: If Fid ≤ FidT -- Fid3, product gear is acceptable. If Fid > FidT + Fid3, product gear is rejected. If neither of these conditions exist, the product gear is in question. Compensation for deviations may be made by phasing, which can be done by indexing the master gear with respect to the product gear, repeating the test and analyzing the results. The product gear is acceptable, if the highest of the phased readings is: Fid ≤ FidT + Fid3 4.4 Equipment requirements for composite action testing Figure 1 shows a schematic diagram of a gear rolling fixture. This figure and the following discussion is intended to show the basic kinematic and mechanical requirements of the equipment necessary to comply with this information sheet. It is not intended to imply that this is the only acceptable construction. Some items to be considered, which influence the composite action test measurements, are: -- Minimum Runout or Wobble. Provisions should be made for the master gear to rotate with a minimum of runout and lateral wobble. Fixed hardened and ground studs are generally used for mounting of master gears with hardened bores. Precision interference ball bushings or centers, for use with shank type master gears, should be considered. Any clearance between the master gear bore or hub and its mounting stud or bushing may be reflected in the inspection results. -- Parallelism of Axes. The fixture should be designed for holding the product gear on a datum axis which is parallel to the master gear axis.
5
AGMA 915--2--A05
Some fixtures provide a means of tilting the master gear and product gear axes in relation to each other. Such fixtures should incorporate provisions for accurately setting the tilt angle and re--aligning the axis to the zero position with precision. This requirement also implies that provision should be made for keeping a fixed angular relationship between the axis of the product gear and that of the master gear during their movement toward and away from each other. -- Mounting. Provision should be made for holding the product gear in the gear rolling fixture by the same mounting surfaces as those which will be used in the final assembly, when those surfaces are specified on the gear drawing. Although not essential to the conduct of the inspection, the use of these mounting surfaces will eliminate differences which may be due to radial and lateral runout deviations in the mounting. -- Maintaining Prescribed Mesh. Provision should be made for adjusting the force keeping the product gear and master gear in tight mesh. This force should be uniform over the entire reading scale. Two traditional methods of doing this are: (a) by means of a weight, or (b) by means of a spring. -- Changes in Center Distances. Provision should be made for accurately indicating the changes in the center distance that occur during the testing. This may be done by means of a dial indicator or a recording device. If recording is employed, it is desirable to have a definite relationship between the position on the chart and a circumferential position on either the product gear or master gear. An accurate method of calibrating the dial indicator or recording equipment over its working range is essential.
AMERICAN GEAR MANUFACTURERS ASSOCIATION
-- Solid bases and a dust free, temperature controlled environment are requirements for the measurement of gears of extreme accuracy. 4.5 Inspection equipment In order to achieve the most accurate economical inspection, the procedure used and the quality of the rolling fixtures and master gears should be selected based on the quality of the gears to be inspected. 4.5.1 Gear rolling fixture Any inaccuracies in the fixture will reduce the tolerance allowed for the inspected gear. The fixture quality and the reliability of calibration must be compatible with the product gear tolerance,see AGMA 935--AXX. 4.5.2 Master gears Master gears used for composite action inspection may be one of three types of known quality: -- A master gear designed specifically to inspect the composite deviation of a product gear. It normally will assure proper and complete inspection. -- A standard master gear of known size and outside diameter which may be used to inspect several different product gears of the same circular pitch or module. Caution must be taken to assure that acceptable gears are not being rejected because of excessive depth of contact by an oversize outside diameter on the master gear. Similarly, caution must be taken to avoid the possibility of accepting gears with a short depth of functional profile when the master gear has an undersize outside diameter. -- A selected mating gear of known quality, which should be adjudged as to the degree of complete inspection by calculation and calibration.
-- Other Considerations. Additional features which contribute to the ease of operation and the accuracy of the results are:
4.6 Method of conducting composite inspection
-- Means of quickly and accurately setting different center distances on the fixture.
-- A gear rolling fixture should be calibrated as outlined in AGMA 935--AXX.
-- Means of driving the gears mechanically at low speed in preference to turning them by hand. This reduces the chance that small variations will be undetected if the gear is driven too fast and also reduces handling of the master gear.
-- The master gear should be verified in accordance with AGMA 2015--2--AXX.
-- Means of protecting the equipment from contaminants and accidental damage.
6
The following procedure should be applied when using the radial composite deviation test:
-- The gear to be inspected and the master gear are mounted on the gear rolling fixture. If mounting surfaces are specified, these are to be used. Set the checking load in accordance with 4.7 and table 2.
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
-- The product gear is then rotated through at least one complete revolution, in double flank contact with the master gear. -- The product gear is accepted or rejected on the basis of the specified tolerances and the method given in 4.3. The interpretation of the recorded chart is given in figure 2 or alternatively in figures 6, 7 and 8. 4.7 Checking spring load and mass weight The amount of applied spring load or dead weight (mass) is important when checking gears on a gear rolling fixture. Excessive load on fine tooth gears of narrow face width, or gears made of soft materials, or on journal type gears having slender shafts, will result in incorrect readings caused by the deflection of the gear teeth or shaft. Conversely, too light a load on coarse gears of relatively wide face width will result in incorrect readings, because of deviations in the contact between the product gear and the master gear. 4.7.1 Recommended loads The recommended loads between product gear and master gear are based on tooth size, and are given in table 2. 4.7.2 Alternate loads The loads in table 2 were determined empirically for metallic gears, and are based on a face width of 2.5 mm. For other face widths, the load should be changed proportionally, and should be agreed upon by the manufacturer and purchaser of the product gear. The loads are based on anti--friction mountings for the movable head and include the force on the indicating device.
AGMA 915--2--A05
4.8 Interpretation of composite data Double flank composite data charts are made up primarily of information related to radial runout and variations in tooth form. 4.8.1 Traditional interpretation Radial composite measurements are toleranced for total composite deviation, Fid, and tooth--to--tooth composite deviation, fid. They have been interpreted from the charts as shown in figure 4. The total composite variation was read as the difference between the highest to lowest point on the chart. The tooth--to--tooth variation was read 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, it does not tell the true picture for diagnostic purposes. For example, it doesn’t help in the case of determining noise potential. Also, if one is trying to evaluate the manufacturing process, it gives a distorted picture of the tooth form that the machine and tool is producing. Ideally, one should be able to sort out the effects of involute variations from runout variations. These problems should be dealt with separately in the manufacturing process. The problem is that the tooth--to--tooth variation is exaggerated along the part of the runout 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 variation will be greater for a gear with a lower number of teeth than it will for higher numbers of teeth. See figures 5a and 5b for a comparison.
Table 2 -- Recommended checking load for metallic gears with 2.5 mm face width Module 2.5 to less than 25.0 1.25 to less than 2.5 0.80 to less than 1.25 0.60 to less than 0.80 0.50 to less than 0.60 0.40 to less than 0.50 0.30 to less than 0.40 0.25 to less than 0.30 0.20 to less than 0.25
Load1), kg 1.0 to 1.2 0.9 to 1.1 0.8 to 1.0 0.7 to 0.8 0.6 to 0.7 0.5 to 0.6 0.3 to 0.4 0.1 to 0.2 0.1 to 0.2
Equivalent diametral pitch 1 to 9 10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 60 to 79 80 to 99 100 to 120
Load1), ounces 33 to 39 29 to 35 25 to 31 21 to 27 17 to 23 13 to 19 6 to 10 3 to 5 3 to 5
NOTES: 1) For non--metallic gears use 1/2 of the listed value.
© 2005 AGMA ---- All rights reserved
7
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
5.0 4.0 3.0 2.0
Unfiltered tooth--to--tooth
Amplitude
1.0 Total composite
0.0 --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 4 -- Strip chart of double flank composite test
5.0 4.0 3.0 Unfiltered tooth--to--tooth
Amplitude
2.0 1.0 0.0 --1.0 --2.0 --3.0 --4.0 --5.0 0
1
2
3
4
5 6 7 Tooth number
8
9
10
11
12
Figure 5a -- Double flank composite test, low number of teeth (12 tooth gear)
8
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
AGMA 915--2--A05
5.0 4.0 3.0
Amplitude
2.0
Unfiltered tooth--to--tooth
1.0 0.0 --1.0 --2.0 --3.0 --4.0 --5.0 0
5
10
15 Tooth number
20
25
30
Figure 5b -- Double flank composite test, high number of teeth (30 tooth gear)
4.8.2 Relationship between tolerances Because of this relationship between runout and the tooth--to--tooth variation, the previous tolerances had unrealistic values in some cases. In previously existing standards, the tooth--to--tooth tolerance is about 1/2 to 1/3 of the total composite tolerance. This has come about in order to accommodate the distortion of tooth--to--tooth data, by runout, and especially for low numbers of teeth. There should be a greater difference between total and tooth--to-tooth (fidT= 0.1 to 0.2 x FidT). This is feasible when the tooth--to--tooth variations are separated from the runout variations. 4.8.3 New method The separation of tooth--to--tooth from total variation can be done by different techniques. Electronic filters can be either analog circuits or digital in a computer. This results in charts as shown in figure 6a, b and c. If these methods are not available in the measuring system, a very good approximation can be done manually. Manual interpretation can be done by drawing in the upper and lower envelope of the measured data. The upper envelope is the long term component and the vertical distance between the upper and lower
© 2005 AGMA ---- All rights reserved
envelope is the short term component. This is shown in figure 7. These methods sort out the long term component of the data from the short term component. For double flank composite tests, the long term component represents radial runout, Fr, and the short term component represents the tooth form variations, fid. 4.8.4 Additional diagnostics Most situations with long term component variations will be in the sinusoidal form as shown in figures 6 and 7. This is caused by eccentricity. There are cases, however, where long term variations will show up at higher orders, such as shown in figure 8. 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 component can have distortions from variations in the tooth shape. These higher order variations can be analyzed by the use of Fourier analysis techniques, such as a Fast Fourier Transform (FFT) analyzer or by digital filtering techniques. They also can be analyzed, to some extent, by manual techniques using the upper and lower envelope curves as drawn in figure 8.
9
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
5.0 4.0 Total composite variation Fid -- Double flank
3.0
Amplitude
2.0 1.0 0.0 --1.0 --2.0 --3.0 --4.0 --5.0 0
5
10 15 Tooth number
20
25
30
Figure 6a -- Total composite deviation of 30 tooth gear (unfiltered)
5.0 4.0
Long term component Fr -- Double flank
3.0
Amplitude
2.0 1.0 0.0 --1.0 --2.0 --3.0 --4.0 --5.0 0
5
10
15 Tooth number
20
25
30
Figure 6b -- Long term component (30 tooth gear)
10
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
AGMA 915--2--A05
Short term component fid -- Double flank
5.0 4.0 3.0
Amplitude
2.0 1.0 0.0 --1.0 --2.0 --3.0 --4.0 --5.0 0
5
10
15 Tooth number
20
25
30
Figure 6c -- Short term component (30 tooth gear)
5.0 4.0
2.0 Short term component (fid -- Double flank)
Amplitude
1.0 0.0 --1.0
Long term component Fr -- Double flank
Total composite variation Fid -- Double flank
3.0
--2.0 --3.0 --4.0 --5.0 0
1
2
3
4
5 6 Tooth number
7
8
9
10
11
12
Figure 7 -- Manual interpretation of composite test (12 tooth gear)
© 2005 AGMA ---- All rights reserved
11
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
40 30 20
Amplitude
10 0 --10 --20 --30 --40 0
1
2
3
4
5 6 Tooth number
7
8
9
10
11
12
Figure 8 -- Complex deviations with first order removed (one revolution)
5 Tooth thickness measurement with radial composite measurement Radial composite measurement may be used to measure functional tooth thickness. The functional tooth thickness includes the effects of all tooth variations, and the radial composite action test measures every tooth of the product gear in one operation. It is much faster than making multiple measurements with another method. This is the best method for measuring tooth thickness when the tooling can be justified. However, this method is limited to medium and smaller gears, since testing machines capable of more than 500 mm center distance are rarely available. In special circumstances testing can be accomplished in place on the cutting machine. Special attention must be paid to the mounting surfaces to assure that the test performed is representative of the gear as it will be installed. Special machines or attachments are required for internal gears. Test machines must be carefully calibrated, particularly for fine pitch and high accuracy gears.
12
5.1 Test fixture calibration The composite action tooth thickness measurement method utilizes a calibrated master gear and a gear rolling device for composite action (double flank) that has been calibrated for center distance. The calibration of the gear rolling device is done with the product gear and master gear holding arbors. In the case of a journal type gear, the calibration should be done with a precision setup arbor that is within 10% of the product gear length over journals. These arbors should not exceed 0.001 mm in taper, runout, concentricity and measurement diameter. This center type rolling fixture is set up as follows: -- Select a master gear and obtain the actual test radius, Rr3. -- Establish the test radius of each of the arbors: Product gear arbor, Rraw, and master gear arbor, Rra3. -- Obtain the maximum and minimum allowable test radii from the product gear drawing (Rrw max and Rrw min). -- Calculate the maximum and minimum test center distance, ad. ad
max
= R r3 + R rw
max
ad
min
= R r3 + R rw
min
(1) (2)
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
where Rrw min is the test radius, product gear, minimum allowable; Rrw max is the test radius, product gear, maximum allowable; is the test radius, master gear.
Rr3
-- Calculate the maximum and the minimum gage stack height, Lg. Lg
max
= ad
max −
Lg
min
= ad
min −
Rraw + R ra3
R raw + Rra3
(3) (4)
where Lg max is the gage block stack height, maximum; Lg min
is the gage block stack height, minimum;
Rra3
is the test radius, master gear arbor;
Rraw
is the test radius, product gear arbor.
-- With the test arbors in place, set the maximum stack of gage blocks, Lg max, in place between the arbors, and with a testing pressure equal to that used to perform the composite action test, record the maximum test center distance shown. Repeat the procedure using the minimum stack of blocks, Lg min, and record the minimum test center distance shown by the dial or on the recording device. NOTE: Other methods of setting the minimum and maximum test center distances are acceptable if they can be shown to be of similar accuracy.
-- The diameter of arbors for bored type product gears and master gears shall be such as to ensure that the gears will be wrung onto their test arbors. Arbor sets having a diameter difference of 0.002 mm for accuracy grade 7 or better are convenient. Ball--bushing arbors with interference fits can also be used. It is important when composite checking gears in this accuracy range, to remove all possible looseness between the arbors and bores of both master gear and inspected gear, by one of these methods, so that additional runout is not reflected in the composite chart due to inaccurate mounting. -- In the case of gears of appreciable size, the member having the least weight should be placed on the movable centers. -- The product gear should be rotated through a minimum of one complete revolution.
© 2005 AGMA ---- All rights reserved
AGMA 915--2--A05
-- The gear is to be accepted or rejected for functional tooth thickness on the basis of all measurements being within the limits set by the recorded maximum and minimum test center distance. 5.2 Calculations for radial composite action test measurement The following method applies to external gears. The proportions of the master gear must be checked for proper meshing with the product gear to be sure that contact takes place near to the tip and true involute form diameters. There must be clearance between the tips and roots. Master gears may be marked with a test radius which is the radial distance from the center line of the master gear to the reference pitch line of a mating standard rack that has its tooth thickness equal to its space width. This is also the radius at which they would mesh with a standard mating gear having a tooth thickness, stw, at the reference diameter, dw, of: s tw =
π dw 2 zw
(5)
Special master gears are often required for spur gears with nonstandard proportions. Helical gears usually require special master gears. Master gears must be made very accurately since any deviation in the master gear is added, in the test results, to the deviations in the product gear. 5.2.1 Maximum test radius The maximum test radius is based on the maximum tooth thickness. The calculation method assumes that the errors in the master gear are too small to affect the test results. This requires a very accurate master gear, if precision gears are to be measured. If two gears are in tight mesh, the sum of their tooth thicknesses on their operating pitch circles is equal to the circular pitch on that circle. Also, the operating pitch diameters of the two gears must be in proportion to the numbers of teeth. These relationships, with the fundamental tooth thickness equations, yield simultaneous equations, from which the operating transverse pressure angle can be found. inv α wt3 =
s btw + s bt3 − p bt d bw + d b3
(6)
where sbtw is maximum transverse base tooth thickness of product gear, mm;
13
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
sbt3 is transverse base tooth thickness of master gear, mm; dbw is base circle diameter of product gear, mm; db3
The value of the maximum center distance, ad max,is given by:
is base circle diameter of master gear, mm;
αwt3 is transverse operating pressure angle in tight mesh, degrees;
is number of teeth in master gear.
z3
ad
max
R rw
αwt3 can also be calculated from:
where
⎡snwm+sn3 − π⎤ inv α wt3 =⎪ z n+ z ⎪+ inv αt w 3 ⎣ ⎦
max
Rr3
(8)
= ad
max − R r3
(9)
is the master gear test radius, mm.
5.2.2 Minimum test radius
(7)
where snw is normal tooth thickness of the product gear at the reference diameter, mm; sn3
is normal tooth thickness of the master gear at the reference diameter, mm;
zw
is number of teeth in product gear; Effect of tooth thickness deviation s wtT 2 tan α wt3
m n cos α n z + z 3 2 cos β b cos α wt3 w
The maximum test radius, Rrw max, is:
is transverse base pitch.
pbt
=
Figure 9 illustrates a typical radial composite action test chart. The “trace for maximum gear” represents a gear which has a tooth at the maximum effective thickness, swt max. The tolerance band for radial composite action test or test center distance must allow the full deviation of the total radial composite tolerance plus the tooth thickness tolerance. Both components vary with the product gear size and accuracy. INCREASING “a” INCREASING “s”
TEST RADIUS FOR swt max
TEST RADIUS FOR swt min
TRACE FOR MINIMUM GEAR
TRACE FOR MAXIMUM GEAR
ONE REVOLUTION OF PRODUCT GEAR
RUNOUT TOTAL COMPOSITE DEVIATION, Fid
Figure 9 -- Radial composite action test measurement of tooth thickness
14
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
In the following formula for ad min , the use of αwt3 for the minimum pressure angle is an approximation. If greater accuracy is required, recalculate using equations 7 or 8 and ad min , iterating for a final value. ad
min
= ad
max − F id − 2
s wtT tan α wt3
(10)
is minimum center distance;
swtT is transverse tooth thickness tolerance at operating diameter with the master. R rw
min
s wtT =
= ad
min − R r3
s wnT d w cos β d
Master gears may be calibrated for either of two different measurements. The method of verification to be given is dictated by the end use of the master, based on comprehensive inspection. 6.1.1 Suitability of master gear The suitability of a specific master gear for inspecting a given design of product gear should be established by each of the following:
where ad min
AGMA 915--2--A05
(11) (12)
5.3 Tight mesh center distance
-- establish that the master gear will inspect the functional profile of the product gear; -- establish that the tips of the product gear teeth will not interfere with the roots of the master gear teeth, and that the product gear teeth will not contact below the form diameter of the master gear;
Equations 8 and 10 can be used to calculate maximum and minimum tight mesh center distance to control the functional tooth thickness.
-- establish that the tolerance grade of the master gear is equal to, or better than, the master gear tolerances specified in ANSI/AGMA 2015--2--AXX.
This method is recommended when the master gear is used to inspect product gears of non--standard tooth proportions.
6.1.2 Verification procedure
5.4 Measurement of backlash at operating center distance (test) This is another measure of product gear functional tooth thickness with a master gear. The test center distance is fixed and it must be accurately determined that the axes are parallel and in the same plane. The backlash of the test set should be measured in at least two places, preferably four, at equal intervals around the gear. The product gear is accepted for tooth thickness on the basis that the backlash at a fixed test distance is within the designed tolerance.
6 Verification of master gears and fixtures This clause describes a procedure for verifying master gears or specified gears and gear rolling fixtures for use in performing composite action tests (double flank). 6.1 Verification of master gears or specified gears Prior to verification, the master or specified gear should be inspected to assure that it meets all of the individual tooth and gear blank tolerances for its quality class.
© 2005 AGMA ---- All rights reserved
Verification can be performed in two ways as follows: 6.1.2.1 When high quality master gear available If a master gear of two or more tolerance grades better than that of the master being calibrated is available, proceed as follows: Step 1. Mark one tooth of the high quality master. Step 2. Mark three teeth approximately 120_ apart on the master to be calibrated. Step 3. Mesh the marked tooth of the high quality master with one of the marked teeth of the master being calibrated and rotate the master gear being calibrated through one revolution. Note the total composite variation reading, and repeat this procedure for each of the two remaining marked teeth. Step 4. From the largest reading obtained in Step 3, subtract the known value of total composite variation of the high quality master gear. This difference is the value of the composite variation to be assigned to the master being calibrated. 6.1.2.2 Verification procedure for two master gears of similar quality If two master gears of similar quality are to be evaluated, proceed as follows: Step 1. Mark three teeth on each master gear at approximately 120 degree increments and identify each by 1, 2, 3.
15
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
Step 2. Mesh each pair of master gears together on a gear rolling fixture. Starting with tooth 1 of Master A, rotate it starting with tooth 1 of Master B, through one full revolution of each. Next, rotate tooth 2 of Master B with tooth 1 of Master A, and so on for nine combinations. Note the tooth combination that produces the maximum total composite variation.
7.2 Forms of radial runout
Step 3. If only two gears are to be evaluated, assign to each gear one--half of the maximum value of total composite variation, as noted in Step 2.
Eccentricity is often the principal contributor to radial runout. It is often caused by the difference in centers used during cutting and running (or testing), by distortions in mounting, or by a combination of both.
Step 4. If three or more gears are to be evaluated, mesh each gear with each of the other gears. Select the pair and meshing combination that exhibits the lowest maximum value of total composite variation.
7.2.2 Out--of--roundness
Step 5. For the pair found to have the lowest maximum total composite variation in Step 4, assign one--half of the maximum value found to each member. Call these the best masters.
Out--of--roundness may be caused by errors in machine tools, cutting tools, lack of rigidity in setup, hardness variation in the gear blank, or heat treat distortion.
Step 6. For each of the remaining combinations in which either of the best master gears noted in Step 5 were used, assign to the unmarked member the value of maximum total composite variation minus the amount assigned to the best master in Step 5.
7.2.3 Indicating over a pin
6.2 Gear--rolling fixture verification The verification of a gear--rolling fixture consists of establishing the accuracy with which the fixture can hold the product gear and the master gear in relation to each other, and the sensitivity of its indicating or recording mechanism. The rolling fixture should be calibrated in accordance with ANSI/AGMA 2116--AXX.
Radial runout is formed by variations in the distance perpendicular to the axis of rotation between the indicated surface and a datum surface. Eccentricity and out--of--roundness are components of radial runout. 7.2.1 Eccentricity
Out--of--roundness is the irregular radial variation from a datum surface in a given plane of rotation, exclusive of eccentricity.
Runout of the gear teeth is measured by indicating a difference in the indicated value of the position of a pin or ball device, placed in each tooth space, relative to an axis of rotation. 7.2.4 Ball probe test Radial runout can be measured by indicating the position of a ball probe (see figure 10). Other types of probes can be used if applicable. anvil or prism
7 Runout and eccentricity Runout is the total variation of the distance between a datum surface and an indicated surface, measured perpendicular to the datum surface. In order to be meaningful, the datum surface and the indicated surface must be specified or identified. Typical specified runouts are axial and radial runout.
ball or cylinder
1
Fr
2
7.1 Axial runout
16
N
Axial runout (wobble) exists when the axis of rotation and datum indicating surface are not perpendicular. This is normally measured in a direction parallel to the axis of rotation.
Figure 10 -- Principle of measuring radial runout
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
7.2.5 Composite action test Radial runout may be measured by observing the change in center distance during one revolution of the product gear and a master gear on a gear rolling fixture (see figure 1). The gears are rolled together in tight mesh, with one member on a movable center which is spring or weight loaded. The readings include variations of the reference (master) gear and the tooth--to--tooth composite variations in the product gear being tested. These variations should be considered when judging the acceptability of the product gear.
AGMA 915--2--A05
The diameter of the ball shall be selected such that it contacts the tooth at mid--tooth depth and it should be placed at mid--facewidth. For the calculation of ball diameter see ANSI/AGMA 2002--A88. 7.4 Anvil size for measuring runout The anvil size is chosen so that it contacts the flanks on each side of the space approximately at the reference circle. The prism half angle, δyt , can be determined by the following approximations, where δyt , αyt , and ηyt are meshing angles to the point of contact on the measuring circle (see figure 11).
7.2.6 Root circle or outside diameter runout test Runout may be measured by indicating the root circle or the outside diameter, when the finishing tool has machined these surfaces simultaneously with the tooth profiles. Machining variations may affect these measurements, but readings obtained do not include the effects of various other items described in 7.3.
ηyt
r ry
αyt
rb
7.3 Measuring principle
δyt
Relative to the gear reference axis, the runout, Fr, of gear teeth is the difference between the maximum and the minimum radial positions of a suitable probe tip: ball, anvil, cylinder or prism, which is placed successively in each tooth space as the gear is rotated (see figure 10). Radial runout, Fr, measurements may include the effects of the following: -- eccentricity of the datum circle relative to the datum axis;
δyn
-- out--of--roundness of the datum circle; -- axial runout (wobble) of gear blank relative to the datum axis of rotation; -- tooth alignment variation; -- profile variation; -- pitch variation; -- tooth thickness variation. If a ball, cylinder, or anvil that contacts both sides of a tooth space is used, tolerances of ANSI/AGMA 2015--2--AXX may be applied. In some instances, it is desirable to use a rider that contacts both sides of a tooth. If this is done, the tolerances are not intended to apply.
© 2005 AGMA ---- All rights reserved
Figure 11 -- Anvil size for measuring radial runout
The anvil should touch the tooth flanks at mid--face width on the measuring circle with diameter dy.
17
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
δ yt = α yt + η yt
(13)
measurement. CNC results are affected by helix angle at the point of probe contact.
d cos α t cos α yt = dy
(14)
7.5.2 Measurement with continuously rotating product gear
tan α n cos β
(15)
dy = d + 2 mn x
(16)
tan α t =
π s yt η yt = 180 π z − dy
(17)
For external gears st =
(18a)
(18b)
mn π + 2 tan α n x cos β 2
For internal gears st =
mn π − 2 tan α n x cos β 2
For external gears s yt = d y
(19a)
sd − inv α + inv α
(19b)
st + inv α t − inv α yt d
For internal gears s yt = d y
t
t
dy tan β d tan δ yn = tan δ yt cos β y tan β y =
yt
(20) (21)
7.5 Measuring runout The simple nature of the measurement permits a wide range of choices of measuring equipment and degree of automation. Some methods are briefly described in the following paragraphs. 7.5.1 Measurement with intermittent indexing of the product gear A simple method in which the gear is intermittently rotated by hand is often used for small gears. The probe, placed in successive tooth spaces, is brought into line for measurement and recording of any deviation of radial position relative to a datum radial setting. When indexing and alignment are affected by an indexing device, the gauging instrument must have sufficient lateral movement to take into account the effects on alignment of pitch and helix deviations. This freedom of movement is necessary to ensure contact between the gauging equipment and both tooth flanks. Multi--coordinate numerical control (CNC) measuring machines may also be used for this method of
18
The anvil, in contact with both flanks of a tooth space, moves with rotation of the gear through a preset arc length. Radial deviations are measured either at the highest point of the arc, or at some other fixed point during the passage through the arc. This is a practical method for measuring the runout of large gears. Measurements can be made on measuring machines or generating machines, but care must be taken to ensure that the reference axis of the gear is concentric with the axis of rotation of the machine, and that the arc length is sufficient to indicate maximum deviation. 7.5.3 Approximation of runout from radial composite deviation Runout may be approximated from a radial composite test as 2fe (see 4.2), by observing the change in center distance during one revolution of the product gear and a master gear on a gear rolling fixture (see figures 1 and 2). The gears are rolled together in tight mesh, with one member on a movable center which is spring or weight loaded. The readings include variations of the reference (master) gear and the deviations in the product gear being tested. These should be considered when judging the acceptability of the product gear. 7.5.4 Measuring with coordinate measuring machine When using coordinate measuring machines, runout and pitch can be measured simultaneously. Two methods are described. a) Measurement with 2 flank contact. The probing sphere with an appropriate diameter is moved inside the tooth space until 2 flank contact is realized. Depending on the device and the gear parameters, the measurement can be produced with a rotating table or without one, by means of an axis parallel probe or a star probe. See figure 12. If a probe with a standard diameter is used, the runout deviation in every tooth space has to be recalculated for the diameter given in the drawing. Considering the same pitch deviation in the tooth space, the recorded runout deviation depends on the diameter used in centering the sphere. Because of the changing profile angle at the touching points, a smaller probe is more sensitive than a bigger one and gives greater deviation.
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
a) Runout test with rotating table (four axes) and axis parallel probe
AGMA 915--2--A05
b) Runout test without rotating table (three axes) with star probe
Figure 12 -- Runout from coordinate measuring machine b) Measurement with 1 flank contact. A probe with a small diameter is moved inside the tooth space. The left and right flanks are probed at the measurement circle. With these measurements the position of a sphere with a diameter as defined in ISO/TR 10064--2, clause 6.3 is calculated. Depending on the device and the gear parameters, the measurement can be processed with a rotating table or without one, with an axis parallel probe or by a star probe.
7.6 Evaluation of measurement 7.6.1 Runout, Fr The runout, Fr, is, with reference to the gear axis, equal to the algebraic difference between the maximum and minimum values of the radial deviation measured in accordance with 7.5. It is composed of roughly twice the eccentricity, fe, together with superimposed effects of pitch and profile deviations of the gear (see figure 13).
20 18 16
micrometers
14 12
Fr fe
10 8 fe
6 4 2 0
1
2
3
4
7 8 9 10 11 12 13 14 15 16 Tooth space number Figure 13 -- Runout diagram of a gear with 16 teeth
© 2005 AGMA ---- All rights reserved
5
6
1
19
AGMA 915--2--A05
7.6.2 Eccentricity, fe A diagram showing runout measured is shown in figure 13. The sinusoidal component of the curve roughly drawn by hand, or calculated by the least squares method, indicates (in the plane of measurement) the eccentricity of the teeth to the reference axis by an amount fe. 7.7 Value of runout measurement Control of runout of gears which are required to operate with minimal backlash, and of master gears to be used in the measurement of radial composite deviations, is of particular importance. Measurement of runout as described is not necessary when the radial composite deviations of gears are to be measured. It is clear that details of single flank deviations such as pitch or profile deviations, cannot be derived from measured values of runout. For example, two gears of very different accuracy grades, with respect to ANSI/AGMA 2015--1--A01, can have the same value of runout. This is because a gear contacts its mate on either right or left flanks, whereas runout values may be influenced by simultaneous measurement contact with both right and left flanks. The deviations of both flanks can have mutually compensated influences on runout. The extent of information which can be derived from the measurement of runout is largely dependent on knowledge of the machining process and the characteristics of the machines. However, when the first batch of gears produced by a given method is inspected in detail in order to monitor compliance with a specified accuracy grade, variation in further production can be detected by measuring radial composite deviations, instead of repeating the detailed inspection. 7.8 The relation between runout and pitch deviations When an otherwise perfect gear has an eccentric bore, eccentricity, fe, as in figure 14, and it rotates
20
AMERICAN GEAR MANUFACTURERS ASSOCIATION
about the axis of the bore, the runout Fr will approximately equal 2 fe. Eccentricity causes single pitch deviations around the circumference of the gear with a maximum value of fpt max of 2fe[sin(180°/z)]/cos αyt. The resulting cumulative pitch deviation also has a sinusoidal form, with a maximum value of Fp max of 2fe/cos αyt. As shown in figure 14, the angle between the maximum cumulative pitch deviation and the “runout” is about 90°. The approximate value of this angle is 90° + αt on the left flanks and 90° -- αt on the right flanks. Runout, caused by eccentricity, results in a variation in backlash, accelerations and decelerations due to pitch deviations. However, when little or no runout is measured it does not mean that no pitch deviations are present. Machining using single indexing can create a gear as shown in figure 15, in which all tooth spaces are equal, resulting in no runout, while substantial pitch and cumulative pitch deviations are present. Figure 16 shows this condition graphically. Figure 17 shows an example of an actual gear with little runout and relatively large cumulative pitch deviations. This condition occurs with double flank processes, such as with form grinding or generating grinding (both of which index between grinding successive tooth spaces), when the bore of the gear is concentric with the axis of the machine table and the indexing mechanism generates a sinusoidal cumulative pitch deviation. The source of this cumulative pitch deviation may be eccentricity of the machine index wheel. To reveal this condition on the gear, a modified runout check can be applied using a “rider” as a probe, see figure 18. The reason why this check detects the effect of the pitch deviations is that here the pitch deviation results in tooth thickness deviations, which a rider indicates as a radial change when contacting both flanks.
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
AGMA 915--2--A05
High point of Runout, Fr High point of eccentricity
Theoretical pitch Measured pitch
Low point of eccentricity
reference axis
High point of pitch deviation, Fp Eccentricity, fe
Runout, Fr
2fe
(approximately 90° from high point of Fr)
Total cumulative pitch deviation, Fp
Reference circle Measuring circle
Figure 14 -- Runout and pitch deviations of an eccentric gear
© 2005 AGMA ---- All rights reserved
21
AGMA 915--2--A05
Theoretical centerline of tooth space
All space widths are equal
AMERICAN GEAR MANUFACTURERS ASSOCIATION
Actual centerline
FpR FpL
Fr = 0
Figure 15 -- Gear with zero runout, but with considerable pitch and cumulative pitch deviations (all space widths are equal)
Theoretical gear Actual gear
Pitch deviation
Cumulative pitch deviation Runout
Figure 16 -- Gear with pitch and cumulative pitch deviations and zero runout
22
© 2005 AGMA ---- All rights reserved
AMERICAN GEAR MANUFACTURERS ASSOCIATION
F pL = 58 mm
AGMA 915--2--A05
Pitch number F pR = 55 mm
F r = 15 mm
Figure 17 -- Actual gear with little runout and substantial cumulative pitch deviation
Fr(s)
rider type A
Fr(s)
rider type B 1
2
N Figure 18 -- Runout measurement with a rider when all space widths are equal and pitch deviations are present
© 2005 AGMA ---- All rights reserved
23
AGMA 915--2--A05
AMERICAN GEAR MANUFACTURERS ASSOCIATION
Bibliography
The following documents are either referenced in the text of AGMA 915--2--A05, Inspection Practices-- Part 2: Cylindrical Gear -- Radial Measurements, or indicated for additional information. AGMA 2000--A88, Gear Classification and Inspection Handbook -- Tolerances and Measuring Methods for Unassembled Spur and Helical Gears (Including Metric Equivalents) 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 ISO 701: 1998, International gear notation -- Symbols for geometrical data ISO 1122--1:1998, Glossary of gear terms -- Part 1: Definitions related to geometry ISO/TR 10064--4:1998, Cylindrical gears -- Code of inspection practice -- Part 4: Recommendations relative to surface texture and tooth contact pattern checking
24
PUBLISHED BY AMERICAN GEAR MANUFACTURERS ASSOCIATION 500 MONTGOMERY STREET, SUITE 350 ALEXANDRIA, VIRGINIA 22314
View more...
Comments
