1、06FTM16Certificate for Involute Gear Evaluation Softwareby: F. Hrtig, Physikalisch-Technische BundesanstaltTECHNICAL PAPERAmerican Gear Manufacturers AssociationCertificate for Involute Gear Evaluation SoftwareFrank Hrtig, Physikalisch-Technische BundesanstaltThe statements and opinions contained he
2、rein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractA test for the verification of involute gear software has been developed at the Physikalisch-TechnischeBundesanstalt (PTB). The paper show the critical infl
3、uence on the measurement uncertainty of uncertifiedinvolute evaluation software. Beside the test parameter information of the most dominant effects of softwareerrorswillbeexplained.Thealgorithmsdevelopedduringthisprojectshouldinfluenceandcompleteexistingstandards and guidelines.Copyright 2006America
4、n Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2006ISBN: 1-55589-898-X1Certificate for Involute Gear Evaluation SoftwareFrank Hrtig, Physikalisch-Technische Bundesanstalt, GermanyIntroduction and backgroundIn the past, the reliability of an involu
5、te gear mea-surement is verified only by measurements on cali-brated artifacts. Commonly, these artifacts arerepresentingall importantgear parametersof anin-volute gear with unmodified flank surfaces. Be-cause of their physical shape, these artifacts (e.g.profile-, lead- and pitch-artifacts) are in
6、the follow-ing referred to as “geometrical artifacts”.The results of the measurementson geometricarti-facts mainly allow conclusions regarding errors re-sulting from the operation of the measuringinstrument, influences from environmental condi-tionsanderrorsofthemeasuringprocess.Geomet-ric artifacts
7、 are therefore used as masters to adjustthe measuring instrument, to perform the accep-tance test on measuring instruments or to validateand monitor measuring processes.With the evaluation of modified flank surfaces andthe spatial determination of the measurementpoints,theinfluenceofdataprocessingon
8、theaccu-racy of a measuring process has considerably in-creased. In 1982, this development caused theexpert committee “Measurements on Gears andGearings“ofthe VereinDeutscher Ingenieure(VDI,AssociationofGermanEngineers)toperformafirstinvestigation. Amongthe members,who aremainlycomposed of manufactu
9、rers of measuring instru-mentsandgears,testdataweredistributedwiththeaid of which the different software products were.The test data were based on measurement valuesrecordedonmodifiedprofileandflanksurfaces.Theresults were alarming. In many cases, the valuesdiffered by several micrometers. Due to th
10、e lack ofreference algorithms or reference data sets, nostatements could at that time be made on the accu-racy of the individual software products.In view of this alarming situation, the Physikalisch-Technische Bundesanstalt(PTB) hasin 2001takenup activities for the validation of evaluation algo-rit
11、hms.Togetherwith7partnersfromindustry,afirstresearch project “Evaluation of gearing algorithms”was initiated 1. Its aim was the certification ofevaluationalgorithmsonthebasisofexistingguide-linesand standards.Taking intoaccount theexperi-ence already gained, the decision was taken togenerate the mea
12、surement values synthetically.This strategy allowed suitable test cases to be es-tablished and contradictions to be eliminated in asimpleway.Asinthecaseofthefirsttestperformed19 years ago, test data were distributed among theprojectpartners.Asexpected,thedifferencesagainlay far above the specified t
13、olerance of the respect-iveinvolutegear(Figure1a).Towardstheendoftheproject (Figure 1b), the measurement results lay,however,withinthepermissibledeviationof0.1mm.Figure 1: Measurement results at thebeginning a) and at the end b) of the firstsoftware testSince September 2005, the second research proj
14、-ect“Evaluationofgearingalgorithms- phaseII“hasbeen performed also in cooperation between in-2dustry and PTB. In contrast to the first project, it isfocussed on the computation of spatial measure-ment points. This step takes the development from2D metrology to 3D metrology into account whichhas been
15、 implemented by almost all manufacturesof CNC based measuring instruments. In this proj-ect it must be considered that the mathematicalbases have so far not been described in guidelinesor standards. The aim of the project therefore is thecommon definition of bases for the computation of3D measuremen
16、t points and the establishment of3D test data sets.Software testThesoftwaretestisrealizedonthebasisoftestdatawhich must be considered as numerical artifacts.Incontrast to the known geometrical artifacts for pro-file, lead or pitch, the test data are a reference forformandlengthparameterswithamodifie
17、dinvoluteshape. In the ideal case, the test data are based onexisting standards and guidelines and cover a widespectrum of possible involute gears.Fundamentals of the software testNormative referencesThe algorithms of the software test relate to stan-dardS DIN 3960 2and to the GuidelinesS VDI/VDE 26
18、07 3S VDI/VDE 2612 4S VDI/VDE 2613 5inwhichthemostimportantparametersandevalua-tion instructions for modified profile and leadevaluations and of the pitch evaluation are de-scribed.The principle of the software testThe principle of the software test is shown in Fig-ure 2.Itisbasedontestdata.Theyares
19、yntheticallygenerated by a data generator and made availablein a formatted ASCII file. After that, the test datapass a reference software of PTB which is used togenerate the reference results. The products to betested also access to the test data and pass theirown evaluation. Subsequently, the resul
20、ts arecompared with the reference results of PTB. Thetestisconsideredtohavebeenpassedsuccessfullyifthedeviationofallresultsdoesnotexceed0.1mm.Figure 2: Development of the software testSpecimen coordinates of an involute gearAn involute gear can spatially described in Carte-siancoordinates.Correspond
21、ingdefinitionsinstan-dards and guidelines are so far lacking. They are,however, of fundamental importance for phase II ofthe software test, as the test data are described inthe form of 3D stylus centre coordinates. The ar-rangement of the coordinate system is shown inFigure 3.Figure 3: Definition of
22、 a Cartesian coordinatesystem for involute gears3Test data setsThe test data sets shall cover a broad spectrum ofpossible evaluations. They therefore representmeasurements on internal and external gearingswith left-hand flanks, right-hand flanks and spurgears.Allcurrentmeasurementparametersforpro-fi
23、le, lead, pitch, run-out and dimension over ballsare tested. For the test data for profile and leadmeasurements, crowned flanks and flank correc-tions have been taken into account.The test data are generated synthetically. Thismakes it possible to respond to the experience andwishes of the participa
24、nts in the project. Problemswithdue regardto practicecan besimulated aswellas problems which are not practice-oriented.Table 1 shows examples of testdata. Ifno otherde-finitions have been given, the test data describe anexternal gear with a normal pressure angle of 20and an addendum modification of
25、0. For profile andlead, the helix angle on the left amounts to 30.Forpitch, run-out and dimension over balls, spurgauges are used as a basis.Table 1: Test dataEvaluationNumber ofteeth/module/typeCommentprofile 18/12/external linear evaluation pro-file, foot and tip reliefprofile 18/12/external parab
26、olic evaluation,big lead error, outlierat tiplead 18/12/external spur gear, tip relieflead 18/12/external crowninglead 18/12/external crowning, reliefpitch/run-out 18/10/external even number of teethpitch/run-out 11/10/external odd number of teeth,small run-out errorspitch/run-out 18/2/external even
27、 number of teeth,small run-out errorspitch/run-out 18/2/external even number of teeth,almost no pitch errorspitch/run-out 181/2.5 exter-nalbig number of teeth,big run-out errorpitch/run-out 18/10/internal internal gear, almostnor pitch errors, smallrun-out errorsAs an example, Figure 3 shows a test
28、data set forthe profile test. The profile has both, tip and root re-lief. The central part of the profile range is error-free. In the area of root relief, a prominent point hasbeenprovidedinaddition.Itliesinthetransientareabetweenrootrelief andcentral profile.The testdataare used to check the evalua
29、tions of the profile re-liefs. Height and length of the reference side areevaluated. In addition, the evaluations for the meanevaluation range are checked. For determination ofthe form error, the profile in transient areas must betaken into account in addition. As a result, the ap-parently flat prof
30、ile has a form error of 7.5 mm. Themeasurement results are shown in Table 2.Figure 3: Test data set for profileTable 2: Profile results in mmroot_relief_length LCf5.6948root_relief_depth Cf0.1017root_relief_form ffF0.0000total_actual F0.0075slope_actual fk0.0000form_actual ff0.0075crowning_actual C-
31、tip_relief_length LCa8.2164tip_relief_depth Ca0.0988tip_relief_form ffK0.0000Data interfaceA data interface must comply with special require-ments. The most importantprerequisites areavoid-ance of redundant data, realization of all data inmetric units (length in mm, angle in rad) and a sim-ple file
32、structure. As a suitable data format whichmeets all these rudimentary requirements is notavailable in gearing metrology, an appropriate for-mat was defined.The test data are exchanged in formatted ASCIIfiles, based on the representation of the measure-4mentdataintheform ofCartesian coordinates.Theco
33、ordinates relate to the specimen coordinate sys-temofthe gearand arerealized withan accuracyof0.0001 mm.A new procedures for the profileevaluationAutomatic measuring processes on gears can con-siderably falsify the profile evaluations. This is dueto the correlation between profile deviations andpitc
34、herrors.ThecorrelationisillustratedinFigure4.Itshowsthemeasurementonanerror-freegear.Asexpected, the measurement points lie on the flankof the gear. If the measurement is, however, per-formed on a gear affected by a pitch error (Figure4b), the roll lengths become larger or shorter by thecurrent accu
35、mulated pitch error. If this influence re-mains unconsidered, the measurement points areshifted with respect to the evaluation axes and leadto an incorrect result.The influence of pitch errors on the profile evalua-tion has exerted an effect only since the measuringprobes have been automatically pos
36、itioned in themeasurement process. Each measurement posi-tion is calculated on the basis of its nominal geardata and as a function of a reference positionwhichisdeterminedduringthemounting processon aref-erence gear or a reference space width. At theflanks of the reference gear or reference spacewid
37、th,theeffectivepitcherrorsarezero.Theyhave,therefore, no influence on the profile evaluation.During the profile measurement of all other teeth orspacewidths,criticaloverlappingofpitcherrorsandroll lengths, however, occur.Figure 4: Influence of pitch errors on theprofile testThe relationship between
38、profile deviations andpitch errors has so far not been described in stan-dardsorguidelines.Anotheraggravatingfactisthatanidealcorrectionforseparationofprofileandpitcherrors is not available. To achieve an agreement ofthe measurement results in spite of this, an evalua-tioninstructionhasbeendeveloped
39、forthesoftwaretest which allows the fraction of the accumulatedpitch error from theprofile measurementto bemini-mized. The evaluation instruction makes a distinc-tion between gears with flat or crowned profile.1. Within the profile evaluation range, a linear or aparabolic regression is performed. Ar
40、eas of rootor tip relief are not taken into account.2. Ontheleastsquareline,acorrectionpoint isde-termined (cf. Figure 3). It is located in the centreof the profile evaluation range. After that, allmeasurement valuesare shiftedtowards theer-ror axis and the roll path by the value of thecorrection po
41、int with the sign.S In the case of excessive material, the mea-surement points are shifted towards the ma-terial and towards the positive roll lengthaxis.S If material is lacking, the measurementpoints are shifted opposite to the material di-rection andto thedirection ofthe positiverollaxis.3. The c
42、orrected measurement values (cf. Figure5; points 1, 2, 3, 4) are used to perform a newevaluation.Notes:S Correction is performed only once.S After a displacement, the correction valuehas the error value zero.S After a displacement, the correction pointlies outside the centre of the evaluationrange.F
43、igure 5: Schematic representation of theprofile pre-fit5Pitch errors can only falsify profile deviations, theyhave no influence on helix deviations.Experience gained in the software testThe extensive experience gained in the softwaretest allowed conclusions with respect to the errorsourcesofthegeari
44、ngevaluationtobedrawn.Theycan be subdivided into two groups:S Different evaluations as a result of incompletestandards and guidelinesS Incorrect data processingThe existing standards and guidelines describegearing evaluations as 2D elements. These are inaccordance with the traditional, manual gear m
45、ea-surement which considers every profile, lead, pitchandrun-outmeasurementasanindependentmea-surement.Today,CNCbased gearmeasuring instrumentsareuniversal measuring instruments and, on the otherhand, universal coordinate measuring instrumentsare used to measure gears. This is why a gearingsoftware
46、must describe and evaluate gears in spa-tial coordinates. This development has so far notbeen considered in the standards.Although the measuring processes of manually op-erated and CNC-controlled gear measurementslook alike at first sight, they may lead to differentmeasurementresults.Thisisduetothed
47、efinitionofthe reference systems. In the case of manually op-erated measuring instruments, each measurementhad its own reference system. For the CNC-con-trolled measurement, however, only one referencesystem is determined to which all other measure-ments relate. This leads to correlations which mayf
48、alsify the measurement result if they are not takeninto account.Sign errors andwrong assignationof theevaluationranges were the most frequent errors observed inthe course of the software tests, although they areunequivocally described in standards and guide-lines. The subject is, however, very diffi
49、cult andabove all the sign conventions for description of thedeviationscantimeandagainevenconfusegearingexperts. A wrong sing is, however, fatal as it indi-cates a measurement value which is incorrect bytwice the amount.The application of erroneous algorithms was de-tected only in the case of the calculation of the di-mension over balls. The calculation is based on the3D coordinates from the pitch measurement. Here,some of the participants in the project had appliedsimplifications which resulted in inadmissibly largedeviations of t
