1、11FTM03AGMA Technical PaperTowards an ImprovedAGMA AccuracyClassification Systemon Double FlankCompositeMeasurementsBy E. Reiter, Web GearServices Ltd.Towards an Improved AGMA Accuracy Classification Systemon Double Flank Composite MeasurementsErnie Reiter, Web Gear Services Ltd.The statements and o
2、pinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractAGMAintroducedANSI/AGMA2015-2-A06,AccuracyClassificationSystemRadialSystemforCylindricalGears in 2006 as the first major rewrite of the
3、double flank accuracy standard in over eighteen years.This document explains the concerns related to the use of ANSI/AGMA 2015-2-A06 as an AccuracyClassification System and recommends a revised system which can be of more service to the gearingindustry.Copyright 2011American Gear Manufacturers Assoc
4、iation1001 N. Fairfax Street, 5thFloorAlexandria, Virginia 22314October 2011ISBN: 978-1-61481-002-53 11FTM03Towards an Improved AGMA Accuracy Classification System on Double FlankComposite MeasurementsErnie Reiter, Web Gear Services Ltd.IntroductionIn 2001, AGMA introduced the first of two documents
5、 ANSI/AGMA 2015-1-A01, Accuracy ClassificationSystem - Tangential Measurements for Cylindrical Gears followed in 2006 by the release of ANSI/AGMA2015-2-A06, Accuracy Classification System - Radial System for Cylindrical Gears. Both of these docu-ments,whencombined,officiallyreplacethestillwidelyused
6、standard,AGMA2000-A88, GearClassificationand Inspection Handbook.Although ANSI/AGMA 2015-2-A06 was adopted by the general membership, it is likely that most memberseven to this day do not fully understand how this document differs from AGMA 2000-A88 in its application tothe double flank measurement
7、of a gear. In the authors viewpoint, some of the improvements thatANSI/AGMA2015-2-A06washopingtoachievemostlikelyerodesitsactualbenefitresultinginmoreuncer-tainty in terms of product quality than what existed previously. It is recommended that the ANSI/AGMA2015-2-A06 be revised to reflect the concer
8、ns expressed in this document.Concerns with ANSI/AGMA 2015-2-A06 and how to resolve themRemoval of the long term component in the calculation of tooth-to-tooth deviationsANSI/AGMA 2015-2-A06 in its definition of the tooth-to-tooth radial composite deviation, fid, recommendsthat“Thelongtermcomponents
9、inusoidaleffectofeccentricityshouldberemovedfromthewaveformbeforedetermining the tooth-to-tooth deviation value” whereas the AGMA 2000-A88 document just uses the rawdata.This long term component, its definition and its implications are the crux of the concerns relating toANSI/AGMA 2015-2-A06. AGMA u
10、sed techniques from single flank testing in relation to data filtering andlong term component removal and applied it to double flank testing on the assumption that its use would beabetter predictor of noise quality. This co-relation between tooth-to-tooth radial composite deviation meas-ured in this
11、 manner and noise has never been proven, but as will be demonstrated, will cause problems thatput any unproven usefulness to predict noise better than AGMA 2000-A88 in doubt.TheexplanationofthemeasurementandapplicationofthelongtermcomponentisdetailedintheInformationsheetAGMA915-2-A05,InspectionPract
12、ices - Part2: CylindricalGears- RadialMeasurements. Inusingadouble flank tester, AGMA 915-2-A05 recommends filtering of the data either by analogue or digitalelectronic means.Essentially, the technique is to take all of the collected data and then by applying a Fast Fourier Analysis, thedataissepara
13、tedintodifferentorders. Alloftheorderscombinedresultsinthetotaldatacollected. Ofparticu-larinterestinthisdocumentisthefirstorderdatawhichisdefinedasthelongtermcomponent. Thefirstorderdataconsistsofasinglesinusoidalwaveformthatiscalculatedbasedon allof theoriginal dataand isrepres-entative of the rad
14、ial runout Frof the gear. AGMA 915-2-A05 recommends that the first order data beremoved from the original measurements for the purposes of reporting the tooth-to-tooth radial compositedeviation. An example of the resulting charts are shown in Figure 1, which is extracted from AGMA915-2-A05. Ifonemat
15、hematicallysubtractsthesinusoidalwaveformofthemiddleFigure 1fromtheoriginaldata in the upper Figure 1, we obtain the filtered result of the lower Figure 1.4 11FTM030 5 15 2510 20 305.04.03.02.0- 1.0- 2.0- 3.00.01.0- 4.0- 5.0AmplitudeTooth numberTotalcompositevariationFid-DoubleflankUnfiltered result
16、Amplitude0 5 15 2510 20 305.04.03.02.0- 1.0- 2.0- 3.00.01.0- 4.0- 5.0Tooth numberLongtermcomponentFr-DoubleflankFirst order long term component0 5 15 2510 20 305.04.03.02.0- 1.0- 2.0- 3.00.01.0- 4.0- 5.0AmplitudeTooth numberShorttermcomponentfid-DoubleflankFiltered resultFigure 1. Double flank tight
17、 mesh center distance data taken for a 30 tooth gear(Extracted from AGMA 915-2-A05)5 11FTM03AGMA915-2-A05recommendsthisdatafilteringtechniqueinordertoseparateoutthesuperimposingoftheinvolutevariationswiththerunoutvariations,sinceinthegearmanufacturingprocess,thecorrection oftheseissues is done indiv
18、idually as well. An example of such an effect is shown in Figure 2 where in the unfilteredrawdata,thetooth-to-toothvariationisexaggeratedalongtheslopeoftherunoutcurvethathasthegreatestslope while in the filtered result, a smaller tooth-to-tooth variation is shown.Unfiltered result with first order l
19、ong term componentFiltered resultFigure 2. Tight mesh center distance showing the highest unfiltered tooth-to-tooth variationalong the greatest slope of the runout curve(Adapted from ANSI/AGMA 2015-2-A06)6 11FTM03Someflawsexistinthe approachused inANSI/AGMA 2015-2-A06which wereunintended inthe creat
20、ionofthestandard. Themostsignificantissue isthat inpractical use,the maximumtooth-to-tooth deviationrarelyoccurs exactly at the position ofthe greatestslope ofthe runoutcurve asshown inthe upperFigure 2. ANSI/AGMA 2015-2-A06 incorrectly assumes that if the worst tooth-to-tooth occurs in this positio
21、n, the filteredtooth-to-tooth deviation magnitude will be dramatically reduced compared to the unfiltered deviation. As aresult, the magnitude of the tooth-to-tooth deviation tolerances in relation to the total composite tolerancesare greatly reduced in this standard as compared to AGMA 2000-A88.Inf
22、act,thepositionoftheworsttooth-to-toothdeviationonanygivenpartisindependentofthepositioningofthe sine wave of the runout curve, and as a result, the tooth-to-tooth deviations with filteringare typicallynotdramatically better (or worse) than the unfiltered results. It is even possible that the magnit
23、ude of the filteredtooth-to-tooth variation is larger than the unfiltered variation if the worst unfiltered tooth-to-tooth variationoccurs in proximity to the peak or valley of the sine wave of the runout curve as shown in Figure 3a andFigure 3b where theunfiltered resultwas 9microns andthe filtered
24、result was11 microns. Ofinterest tonotein looking at Figure 3a and Figure 3b is that the position of the worst tooth-to-tooth deviation as indicatedbythe vertical hashed boundary is shifted showing two different positions by the two approaches. This is notuncommon. Depending on the nature of the gea
25、r, the worst tooth-to-tooth deviations can be in completelydifferent parts of the gear when analyzed by the two different methods.The difference in the result between the filtered and unfiltered tooth-to-tooth deviations are typically only afewmicrons. Infact,outofhundredsofdifferentgearsmeasuredove
26、rarangeinmodule of0.5 - 3.0 andwithtoothcountsbetween10and120,allexhibitedsimilardifferencesinreadingsoflessthanabout+/- 0.003mm.Thisleadsonetoquestionthevalueof anelaborate filteringtechnique thatrequires computerizedequipmentif the results are not dramatically different than the AGMA 2000-A88 appr
27、oach. If the results are so similar,how can this actually be a better predictor of noise as was a stated goal in ANSI/AGMA 2015-2-A06? Therehas been no published information to date about how such a technique is a better predictor of noise.It is recommended that any subsequent change to ANSI/AGMA 20
28、15-2-A06 return to the AGMA2000-A88approach to measuring tooth-to-tooth deviation and that the revised standard clearly specify that filtering ofdata by electronic or mathematical means is not allowed in determining whether a part meets the AGMAaccuracy class requirements.Gears with significant high
29、er order effects superimposed on the long term componentAnothershortcomingoftheANSI/AGMA2015-2-A06approachisthatnotallgearsexhibitwellbehavedtightmeshcenterdistanceplotswhereeccentricityisthemajoreffect. Althoughonecan mathematicallycalculatethe first order sine wave that exists in the data, it is n
30、ot always the only predominant effect in all gearing.Considerforexampleaplasticgearthatisinjectionmoldedwiththreegates. Itiscommontoseetheeffectofathird order wave from the gates superimposed on the first order effect of the eccentricity. Yet when this hap-pens, since only the first order effect is
31、removed in the calculation of the tooth-to-tooth deviation, the effectmay be an increase in the tooth-to-tooth deviation value reported using ANSI/AGMA 2015-2-A06 asopposed to AGMA 2000-A88 even if the maximum tooth-to-tooth deviation occurs at the greatest slope ofthe runout curve.This situation is
32、 shown inFigure 4a andFigure 4b fora 45tooth 30%glass fillednylon gear. Inthe figure,thepeaksinthetightmeshcenterdistanceareactuallytheweldlinesbetweenthegates. Thethreevalleysinthetightmeshcenterdistanceplotarethepositionsofthegates. Superimposedontheplotistheonceperrevolu-tionrunoutcurvewhichcanbe
33、seengenerallyfollowsshapeofthetightmeshcenterdistancecurve,howeveronecanalsoclearlyseethatahigherorderwaveisalsoanoverridingeffectonthedata. Thewriters ofANSI/AGMA2015-2-A06recognizedthat higherorder wavescan beproblematic inthis filteringtechnique, butdidnot have a clear standardized way to deal wi
34、th these higher orders so this issue was ignored in the ANSI/AGMA 2015-2-A06 standard. In Figure 4a and Figure 4b it can be seen that the unfiltered tooth-to-toothdeviation on this part was 0.024 mm while the filtered result was 0.026 mm. The complexity of filtering doesnot really provide any signif
35、icant benefit to the measurement result on this part which as previously stated isquite typical amongst all gears measured.7 11FTM03Figure 3a. Unfiltered test showing worst tooth-to-tooth deviation near the peak of the runoutcurveFigure 3b. Filtered test result of Figure 3a with shifted worst tooth-
36、to-tooth position andincreased magnitude (displayed with increased vertical axis scale)8 11FTM03Figure 4a. Unfiltered double flank test of a triple gated plastic gearFigure 4b. Filtered double flank test of a triple gated plastic gear9 11FTM03This type of higher order effect is not just evident in p
37、lastic gears with multiple gates. Similar higher orderissues may exist in hobbed and shaved gears steel gears, heat treated gears where distortions may beaffectedbygraindirection,ringgearswiththinrims,fineblankedgearswithirregularshapesonthesamepart,powder metal gears with lightening holes, or steel
38、 gears with lightening holes, etc.Reduced tooth-to-tooth tolerances compared to total composite tolerance in each accuracyclassThe filtered tooth-to-tooth variation was expected by the writers of the standard to be significantly smallerthan the unfiltered tooth-to-tooth variation. Hence, the tooth-t
39、o-tooth tolerances of ANSI/AGMA2015-2-A06 in any accuracy class are considerably smaller as a percentage to total composite tolerance ascomparedtoAGMA2000-A88. Table 1showsexamplesofhowthesetolerancesaresmallerinANSI/AGMA2015-2-A06 at a fixed level of 18.52% of the total composite tolerance compared
40、 to AGMA 2000 at 35-60%of the total composite tolerance.As previously explained, the difference in the result between the filtered and unfiltered tooth-to-toothdeviationsareonlyafewmicrons;notnearlythedifferenceasthetolerancesthatTable1wouldsuggest. Mostusers of ANSI/AGMA 2015-2-A06 are coming to th
41、e realization that this shift in tolerances has much largerimplications than what was originally anticipated. Under the AGMA 2000-A88 approach, most geardesignersusuallyselectaqualityclasslevelbasedonthemagnitudeofthetotalcompositedeviationsinceitismore difficult to control relative to a tooth-to-to
42、oth deviation in any quality class. Now with tooth-to-toothtolerances being so small relative to the total composite tolerances, a supplier usually cannot achieve thetooth-to-tooth requirements and the total composite requirements in the same accuracy class. It is evenlikely that they may be two acc
43、uracy classes apart.The bigger concern is if the accuracy class is only specified based on the more difficult tooth-to-toothspecification resulting in an overly generous total composite specification. For example, under ANSI/AGMA2015-2-A06 a 1.0 module, 20 tooth spur gear using a C11 accuracy class
44、results in a typical tooth-to-toothtolerance of 0.032 mm which may be a reasonable tolerance for such a gear. If C11 is also specified for thetotalcompositedeviationtolerance,thetolerancewouldbeawhopping0.171mm. MostlikelyaC9specifica-tion would need to be made for the total composite tolerance at 0
45、.086 mm which would be more reasonablerelated to the 0.032 mm tooth-to-tooth tolerance.Table 1. Comparison examples for quality class Q8 to accuracy class C9 and the magnitude ofthe tooth-to-tooth tolerance (B) compared to the total composite tolerance (A)Tolerances per AGMA 2000-A88, Q8Tolerances p
46、er ANSI/AGMA2015-2-A06, C9Totalcompositetolerance,mm, ATooth-to-toothtolerance,mm, BB/A, %Totalcompositetolerance,mm, ATooth-to-toothtolerance,mm, BB/A, %0.5 module,10 tooth spur 0.045 0.031 68.9% 0.083 0.01518.52%0.5 module,40 tooth spur 0.047 0.025 53.2% 0.085 0.0160.5 module,60 tooth spur 0.050 0
47、.025 50.0% 0.086 0.0161.5 module,10 tooth spur 0.074 0.041 55.4% 0.086 0.0161.5 module,40 tooth spur 0.077 0.031 40.3% 0.089 0.0161.5 module,60 tooth spur 0.085 0.032 37.6% 0.094 0.0172.0 module,10 tooth spur 0.086 0.043 50.0% 0.087 0.0162.0 module,40 tooth spur 0.089 0.033 37.1% 0.091 0.0172.0 modu
48、le,60 tooth spur 0.099 0.035 35.4% 0.098 0.01810 11FTM03However, the majority of users of AGMA accuracy grades do not even realize that a different accuracygradecanbespecifiedfortooth-to-toothasopposedtototalcompositetolerances. Practicallyhowever,specifyingdifferent classes is self defeatingsince o
49、necan ask the questionof why an accuracy classification system isneeded at all under those circumstances as opposed to explicitly stating the tolerances.It is recommended that a new accuracy class methodology be adopted based on the suggestions outlinedbelow to correct for the condition that exists today in ANSI/AGMA 2015-2-A06.Step factor in tolerances between accuracy classesANSI/AGMA2015-2-A06issimilartomostot
