1、12FTM18AGMA Technical PaperAnalysis of Ripple onNoisy GearsBy G. Gravel, Hamburg Universityof Applied Sciences (HAW)Analysis of Ripple on Noisy GearsProf. Dr.-Ing. Gnther Gravel, Hamburg University of Applied Sciences (HAW)The statements and opinions contained herein are those of the author and shou
2、ld not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractA low noise level is an important quality feature in modern gearboxes for passenger cars. But a troublesomenoisecanhavemanycauses.Thenoiseoriginationandtransmissionisamongstothersaffectedbythed
3、esignlayout, by the actual deviations of the components, by the assembly of the components and also by themounting situation of the complete gearbox.Damages,formerrorsanddisplacementerrorsorripplesareoftenpresentontheflanksofagear,ifitisfoundto be the cause of problems in a noise check. Especially r
4、ipples or ghost frequencies of a gear areproblematic,becauseuptonowtheyrarelycanbedetectedonagearmeasuringdevicebutonlyinarelativecomplex single-flank roll checking procedure.A new evaluation method now allows to identify and to describe ripples on the flanks of gears based on theresultsofanormalgea
5、rmeasurement.Thedeviationcurveswereapproximatedbysinefunctions,theresultsare displayed graphical and by characteristic values. A combination of the deviation of each measured pointwithitsrotationangleallowsanevaluationequaltoarollingwiththematinggear.Theresultsshowaverygoodcorrelation to a noise che
6、ck and to a single-flank roll check.The application of the software is demonstrated by practical examples of the manufacturing methodsgenerating grinding, honing, broaching and shaving. Vibrations of machine tool and ripple generatinginfluences in the manufacturing process can be verified down to a
7、level of a few tenth micrometers. At thesametimethismethodiswellsuitedtodescribelong-waveformdeviationslikeanovalityora3-or4-foldripplecaused by the clamping or by a square blank.With thisnewevaluationmethod gearscan be testedin an earlystate of production for known, criticalripplesand conclusions c
8、an be drawn on the state of machine tool, cutting tool and clamping device.Copyright 2012American Gear Manufacturers Association1001 N. Fairfax Street, Suite 500Alexandria, Virginia 22314October 2012ISBN: 978-1-61481-049-03 12FTM18Analysis of Ripple on Noisy GearsProf. Dr.-Ing. Gnther Gravel, Hambur
9、g University of Applied Sciences (HAW)IntroductionIn modern passenger car transmissions, a low noise level is an extremely important quality feature. Noisegeneration is influenced by many variables, ranging from the structural design, to deviations in thecomponents, to the mounting position of the f
10、inished transmission. If, during a noise test, a gear is identifiedas the cause, the problem can often be attributed to damage, irregularities in position or geometricalvariations, or to geometrical ripples on the tooth flanks 1 2. This paper presents a closer examination ofripple. The development o
11、f ripple is influenced by such factors as deviations in the tool, the stiffness of theworkfixture,theparametersofthemanufacturingprocess,andofcourse,excitationsandnaturalfrequenciesof the tool machine 1. See Figure 1.Gear measurementInspectionsofgeargeometry aregenerally carriedout duringproduction
12、ongear measuringdevices thatuseaprobetotracethetoothflanksatindividualpointsoroncurves(Figure 2,left). Byconductingsuchindividualerror tests, it is possible to arrive at definite conclusions with respect to the quality of the gearing and correc-tions for the production process 3 4 5. This holds true
13、 to the extent that the errors occur over large areasand systematically on a number of teeth, as is the case for a great deal of production errors.If damage occurs on individual teeth, however, or if the behavior of the gear is to be inspected as installed inthe transmission, a working inspection is
14、 used. Here, a complete inspection of the tooth flanks is carried outbyrollingwithahigh-qualitymastergear(figure2,right). Allerrorsofthegearact asa composite,in theformin which they have an effect when the gear is generated. A spectral analysis of the single flank generatingsignalrevealsvibrationsov
15、ertheangleofrotation,whicharecausedbyripplesonthetoothflanksandarealsoknown as ghost frequencies 6. Extended outfitting of the measuring device allows noise testing usingstructure-borne sound sensors and generation at higher rotational speeds and under load.Figure 1. Sources of noise caused by a tra
16、nsmission4 12FTM18Figure 2. Inspection procedures when facing noise problemsWhen facing common noise problems, it is desirable to be able to easily identify ripples on the tooth flanks inthe early stages, in order to intervene in the production process 7. To this end, a software tool for rippleanaly
17、sis has been developed, making it possible to describe ripples in a deviation curve based on the resultsof an individual error test.Calculation of rippleThe most important step in the ripple calculation is the calculation of the amplitudes of compensating sinewave functions in a selected frequency r
18、ange. The compensating sine wave with the largest amplitude isconsidered the first dominant frequency, and is plotted on the profile and displayed as a parameter. Thisdominant sine wave function is then eliminated from the deviation curve, and the remaining deviations arere-analyzed 8. After 10 cycl
19、es, this ultimately produces a frequency spectrum of the 10 maximum amp-litudes. InFigure 3,thefirstdominantfrequencyineachcaseisplottedonthe deviationcurve. With thistypeofanalysis,eachflankisevaluatedindependentlyoftheothers;often,thecalculatedfrequenciesofindividualteeth are not precisely identic
20、al due to form variations.When analyzing a gears running behavior, it is interesting to link the deviation curves so as to resemble theway in which they mesh during the rolling process 9. For a specific angle of rotation, Figure 3 shows theintersection of the gear with the plane of action. During th
21、e rolling with the mating gear, all points at the inter-sectioncurvesoftheflanksinthispositionwouldideallycomeintocontactwiththeplanebetweentheworkingtip and root circle. The measured curves of the profile and line measurement are also plotted. Owing to theoverlap, it is possible to assign 2 profile
22、 measuring points and 2 tooth trace measuring points each to thecurrentangleofrotation. Itbecomesevidentherethattheratioofmeasuringpointsto actualcontact pointsisalwaysextremelyunfavorable. Aconclusionbasedonthesefewmeasuringpointsisthereforeonlypossibleifthey are representative of the entire flank.
23、 If the gear does not even contact in the measured areas, forexample, the calculated ripples will not be functionally effective, of course.5 12FTM18Figure 3. Methods of ripple evaluationEvery measuring point on the tooth flank has a rotation angle that characterizes its position during thegenerating
24、process. AsillustratedinFigure 4therotationangleofasinglepointiscalculatedasthesumofitsrolling angel, the rotation resulting from its axial position and its pitch angel. When all measuring points arelinedupaccordingtotheirangleofrotation,thisproducesacontinuous,closedmeasuredcurvemadeupofallmeasured
25、 teeth over the circumference. For such a measured curve, a common ripple can be calculated.However,theevaluationalgorithmmustbecapableofproperlytakingintoaccounttheoverlapsandgapsthatoccur in the curve. This is the reason, why a compensating sine wave function is used here - a Fast FourierTransform
26、ation(FFT)needsequidistantpointsandwillnotworkproperlywithgapsandoverlaps8. Becausethe curve is closed, only whole-number ripples can occur over the circumference.Figure 4. Calculation of the rotation angle6 12FTM18In order to evaluate low frequenciesper rotationin addition,pitch variationsmust beta
27、ken intoaccount inthemeasured curves. If only 4 teeth are evaluated over the circumference, this means that the gaps in thecontinuous curve are very large, and the calculated ripples are therefore very uncertain. Measurement of allteeth, or a good number of them, is therefore highly recommended. For
28、 the profile evaluation, this type ofevaluation corresponds for all intents and purposes to a single-flank working test 10 with an extremelynarrow master gear that has no deviations, and for thetooth trace,it correspondsto atest witha mastergearthat only makes contact within the reference circle. Wh
29、ile a single flank tester is covering the envelopedeviation of the surface that is rolling with the master gear, here a selective test for selected areas isconstituted.Analysis of a honed gearTheevaluationresultsofcommonripplesofanoisy,honedgearareshowninFigure 5. Theprofiledeviationsoftheleftflanks
30、areplottedtogetherasdeviationcurvesforallmeasuredteethovertheangleofrotation. Theripplewithfrequency 1represents therunout deviationcaused bythe eccentricposition ofthe gearaxis. Thenext maximum occurs at 4 ripples per rotation. This ripple here is caused by a machine vibration. Generallyspeaking,ho
31、wever,itisalsopossiblethatthediagramcoulddepictasquareblankasthestartingmaterialora4-jaw chuck. This makes itclear thatthis evaluationmethod isalso well-suitedfor describingsuch thingsasovality or deformation caused by a chuck. Finally, a frequency 28 is shown. In a noise measurement, thisfrequencyw
32、asclearlyattributabletothisgear,andresultedinarejectionofthetransmission. Thecomparisonmeasurement of a quiet gear does not show a frequency 28, but does likewise show a frequency 4.Figure 6 shows the spectra of the ripple evaluation for profile and tooth trace separately for the right and leftsides
33、. Frequency 28, that means 28 ripples per circumference, is clearly evident in all spectra.Figure 5. Deviation curves of common ripples of a honed gear7 12FTM18Figure 6. Spectra of common ripples of a honed gearCrowning and systematic slope deviationsTheevaluationbecomesproblematicifthegearhascrowne
34、dflanksorsystematicslopedeviations. Becausethese deviations are lined up one behind the other, a dominant ripple with the frequency of tooth count fzshowsupintheevaluation. Theevaluationofameasurement takenon agear witha crownedtooth flankandslopedeviationsisshowninFigure 7. Sincecrowningandslopedev
35、iationscannotbeexactlyreproducedbyacompensationsinewave,thisresultsinmultiplesoffzduetotheresidualerrors. Ifthecrowningisevenlarger,it can completely dominate the evaluation.For this reason, an evaluation for high frequencies was introduced. When this evaluation setting is used,theindividual crownin
36、g and the slope deviation are eliminated before the curves are merged. This evaluationdoesnottakepitchvariationintoaccount,either. AscanbeseeninFigure 7,thereisnow asignal thatclearlycontainsonlyfrequency36. Allmeshfrequencieshavedisappeared,butso,too,havealllowfrequenciesthatare actually present in
37、 the signal.The ripple analysis of a gear made by generation grinding is shown in Figure 8. In the non-correctedevaluation, called a “middle frequency” evaluation, low-frequency ripples of frequency 1 to 8 appear, as wellasthefirstandsecondmeshfrequency. Thisevaluationshouldalwaysbethefirststepinana
38、nalysisofripple.Inthenextstep,the“highfrequency”evaluation,thelow-frequencycomponentsdisappear,as expected,buta significant portion of the mesh frequency remains, even though the crowning has been eliminated. Uponcloser examination, it becomes evident that the gear in fact does exhibit a ripple with
39、 mesh frequency in theprofile. Because there is more than one ripple in the evaluation range due to the high overlap, it is noteliminated by correcting the crowning.It is evident here that ripples with mesh frequency can also occur, which are due to form deviations or rippleson the flanks that overl
40、ap appropriately. The cause of these ripples may be attributed to an axial vibration ofthe grinding wheel or a vibration of the work fixture. These vibrations can be excited by tool deviations or bythe machining process.8 12FTM18Figure 7. Analysis of gears with crowningFigure 8. Analysis of a gear m
41、ade by generation grindingGhost frequency and meshing frequencyFigure 9 illustrates a comparison of the deviation curves of 4 teeth measured in succession with ghostfrequencyandwithmeshfrequency. Ifaghostfrequencyispresent,thetoothflanksshowaripplewithvaryingphase position, and the form changes from
42、 tooth to tooth. When evaluating a standard measurement on 4distributed teeth, a varying form deviation is a good indication of a possible ghost frequency. For a reliableanalysis, however, all teeth must be measured and evaluated. In contrast, a ripple with mesh frequency andmultiples exhibits a con
43、stant phase position and very similar form deviations. Here, a ripple analysis of thestandard measurement on 4 teeth is able to provide reliable results.9 12FTM18Figure 9. Types of ripplesExamples of applicationThe following section presents the results of a ripple analysis on gears that have been m
44、anufactured usingvarious production processes, some of which have resulted in noise problems. Figure 10 shows the meas-urement of a broached internal gear for an evaluation with “high frequency”. The broaching tool produces aripple of frequency 95 ripples per rotation, which results in noise excitat
45、ion in the transmission. The bottompart of the figure shows the ripple analysis of a gear made by generationgrinding. In anevaluation with“highfrequency”, the previously described ripple with mesh frequency is seen, which is represented here as an Sformonasingleflank. Astheseconddominantfrequency,ah
46、igh-frequencyripplewith345ripples occursonthe circumference. It is clearly recognizable on the flanks, but is not relevant for noise during operation.Figure 10. Analysis of gears made by broaching and by generation grinding10 12FTM18Thequestionoftheprecisionofameasuringdeviceisalsoraisedhere. Itisce
47、rtainlytruethatvibrationsofthemeasuring device can skew the results of the ripple analysis, particularly in the high-frequency range, andmust therefore be avoided. Moreover, amplitudes of 0.15 micrometer, which may very well be relevant tonoise at high frequencies, or an S form with a 0.38-micromete
48、r amplitude can only be reliably detected withextremely precise measuring devices. The measuring system needs to have a resolutionof 0.1micrometerand a very exact rotary table, like the gear measuring device mentioned in Figure 2 left. In the case at hand,the high-frequency vibration is definitely n
49、ot attributable to the measuring device because, as a ghost fre-quency, it demonstrates a phase position that varies from tooth to tooth. A vibration during measurementwould not follow this context, but rather would show the same phase position on each tooth.Figure 11 shows the results of the ripple analysis on two gears made by shaving. The gear above exhibits arelativelybroad,low-frequencyspectrum,inwhichtheovalityisnoticeable. Eventhisripple,whichshouldbeconsideredmoreasaformdeviationoverthecircumference,canbedescribedwellwitharippleanal
