1、09FTM06AGMA Technical PaperDependency of thePeak-to-Peak-Transmission-Error on theType of ProfileCorrection and theTransverse ContactRatio of the Gear PairBy U. Kissling, KISSsoft AGDependency of the Peak-to-Peak-Transmission-Error on theType of Profile Correction and the Transverse Contact Ratioof
2、the Gear PairDr.-Eng. Ulrich Kissling, KISSsoft AGThe statements and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractProfile corrections on gears are a commonly used method to reduce
3、transmission error, contact shock, andscoringrisk.Therearedifferenttypesofprofilecorrections. Itisaknownfact,thatthetypeofprofilecorrectionused will have a strong influence on the resulting transmission error. The degree of this influence may bedetermined by calculating tooth loading during mesh. Th
4、e current method for this calculation is verycomplicated and time consuming; however, a new approach has been developed which could reduce thecalculation time.This approach uses an algorithm which includes the conventional method for calculating tooth stiffness inregardstobendingandshearingdeformati
5、on,flatteningduetoHertzianpressure,andtiltingofthetoothinthegear body. The new method was tested by comparing its results with FEM and LVR.This paper illustrates and discusses the results of this study. Furthermore the maximum local power lossesarecomparedwiththescoringsafetycalculatedfollowingthefl
6、ashtemperaturecriteriaofAGMA925andDIN3990.Copyright 2009American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314September 2009ISBN: 978-1-55589-959-23Dependency of the Peak-to-Peak-Transmission-Error on the Type of ProfileCorrection and the Transverse Contac
7、t Ratio of the Gear PairDr.-Eng. Ulrich Kissling, KISSsoft AGIntroductionProfile corrections (PC) on gears are a commonlyused method to reduce the transmission error (TE)of a gear pair, the contact shock (corner contact)and the scoring risk. There are different types ofprofile corrections as short o
8、r long linear correc-tions, short or long corrections in arc form, fullycrowned profile and others.The calculation of the meshing of a gear pair underload is very complicated and therefore time con-suming. Over the gear meshing cycle, from thestart of contact in the pinion root area to the end ofcon
9、tact on thetip, asufficient numberof stepsmustbe calculated. Using a FEM program, this requiresmany hours. More specialized programsas LDPorLVR perform this process in much shorter time, buteven then the evaluation of different variants needsmuch time.Based on a new approach for the calculation of t
10、hemeshing under load, the calculation time could fur-thermorebereduced. Analgorithmusingaconven-tional method for the calculation of the tooth stiff-ness considering bending and shearingdeformation, flattening due to Hertzian pressureandtiltingofthetoothinthegearbody,isused. Withthis approach the ca
11、lculation of a gear mesh is car-ried out within seconds. In combinationwith aneffi-cient user interface, this allowed to perform an ex-tended study of the effect of different profilecorrections.The aim of the study is to analyze the effectproduced by short linear, long linear, short arc-like,long ar
12、c-like and fully crowned profile correctionson gears with different transversecontact ratio(),as standard reference profile gears and high toothprofile gears may show very differentcharacteristics when using profile corrections.Effect of profile corrections ontransmission error and noise in literatu
13、reTipreliefisappliedfortworeasons,thefirst beingtominimizecornercontact(toothinterference)andthesecond being to reduce dynamic excitation(transmission error).In literature few comments about the effect ofdifferent profile corrections (or profile modificationsas called by ISO) types can be found. In
14、theAmerican literaturesome informationcan befound,mainly from or in connection with research done atthe Ohio state university 1. In the Germanliterature, where many publications about gear andgearbox design exist, only very limited informationcan be found. For example in the classic Niemannbook abou
15、t cylindrical gear design 3, only fewwordsarereservedontheeffectproducedbyprofilecorrections. Little bit more is explained in the bookofLinke2fromthe DresdenUniversity. Also inUKliterature some few specific literature is available4.A simple variant of a profile correction is a tip relief.When defini
16、ng a tip relief, two mayor parametersare important, the tip relief Ca (figure 1) and the re-lieflengthLCa. Inliterature,everybodyagrees,thatthe tip relief Ca has to be dimensioned in such away, that the tooth bending and may be a part ofmanufacturing errors (pitch deviation) is compen-sated. There i
17、s also agreement, that the profilemodification affects strongly the Peak-to-Peak-Transmission-Error (PPTE). Furthermore, it isevident that the PPTE is quite directly related to thenoise level produced by a gear pair.TherearebasicallytwooptionsforthelengthLCaoftheprofilecorrection,thesocalled“short”a
18、nd“long”relief design (figure 2).About the optimum length LCa of the profile correc-tion for best result in reduction of the TransmissionError (TE), the opinions are diverging (table 1).The indications in literature are partiallycontradictive. The reason is possibly that theeffectof long or short pr
19、ofile correction depends also onthe transverse contact ratio of the gear pair.4Key1 Space2 ToothArrow Indicates the start point ofthe tip modification)Figure 1. Linear tip and root relief as defined by ISO 21771:2007Transverse profile contact ratio ofthe not modified part of the flanks: =1.0Transver
20、se profile contact ratio ofthe not modified part of the flanks: =2.0-2.0)nopm0” for gears having 2.0; Curve “Average_nopm0” for all gears; Curve“Average_nopm3” for all gears with pitch error 3 m.12Figure 11. Ratio of PPTEwithPC to PPTEnoPC for different gear pairs, with = 1.4 to 2.4, withshort profi
21、le correction, depending on torque.The result is completely different when using a longprofile correction (figure 12). All gear sets above80% of nominal torque have a significantly reducedPPTE(from30%upto70%reduction). Onlyforlowload(60%andlessofnominaltorque)thePPTEwillincrease compared to the gear
22、 set with no correc-tion. But the increase is smaller than it is for shortcorrections.To get such a significant difference between theshort and the long correction mainly for any trans-verse contact ratio was a certain surprise. Theresultisinagreementwithsomewellknownauthors(Houser 1 and Niemann 3),
23、 but the fact that,when using the long corrections, the transversecontact ratio of the not modified part of the flanks isfar lower than 1 (figure 2), somehow was reducingour expectancy of such a good result for the longcorrection.Influence of curvature of the profile correctionIt may be interesting
24、to analyze the influence ofdifferent curvatures of the profile correction on thePPTE. For the short profile correction a linear(figure1)andanarc-like(figure4)curvewereused.Thesamewasused alsofor thelong correctionandadditionally also profile crowning (figure 3).When using the short profile correctio
25、n (figure 13),fornormalgears(2.0) theform ofthe curvehasno significant influence, but for high tooth gears thearc-like curve is much better.With a long profile or crowned correction there isnoreallysignificantdifferencebetweentheeffectofdif-ferent curve types, when comparing the effect overthe full
26、-scale. It looks like that the linearcorrectionisabitbetterthanthearc-like(figure14).Interesting is the effect when displayed torque-dependent (figure 15). The linear correction is verygood for design torque and higher up, but worsethan the other corrections for lower torque.13Figure 12. PPTE(above)
27、 and Ratio(below) of PPTEwithPC to PPTEnoPC for different gear pairs,with = 1.4 to 2.4,with long profile correction, depending on torque14Figure 13. Mean PPTE (average over torque from 50 to 150%) depending on with short profilecorrection, for linear and for arc-like correction curveFigure 14. Mean
28、PPTE (average over torque from 50 to 150%) depending on with long profilecorrection, for linear, arc-like and for crowned correction curve15Figure 15. Mean PPTE (average over from 1.4 to 2.4 depending on torque with long profilecorrection, for linear, arc-like and for crowned correction curveInfluen
29、ce of manufacturing errors on thePPTEThe calculations were repeated with a manufactur-ing error, to evaluate the capability of the differentcorrectionstocompensatetoothformerrors. Inthiscase a pitch error of 3 mm was applied. 3 mm is halfofthemaximaladmittederrorforquality6(ISO1328or AGMA 2015) for
30、this size of gears. The PPTE ofgears with the manufacturing error is clearly in-creased, but the mean increase of the PPTE ismuch smaller than the pitch error (table 2). Figure10 shows that the 3 m pitch error increases thePPTE on gears with no modification only by 1 m orless.If specific profile cor
31、rections havebetter capacitytoabsorb pitch errors, is not evident, as the evalua-tion of the increase of PPTE due to a 3 mmpitcherrorintable2shows. Arc-like(shortandlong)andshort linear corrections gives best results, but weassume that further checks should be executed, tomake sure, that this result
32、 is significant. Further-more also profile errors and other types ofmanufacturing errors should be checked to get amore complete picture.Table 2. Mean increase of PPTE due to a pitch error of 3 mm for the nominal torque (100%)ProfilecorrectionMean PPTE (mm)with no pitch errorMean PPTE (mm)with pitch
33、 error of3 mmMean increase ofPPTE (mm)Increase ofPPTE in % ofthe pitch errorNo correction 4.8 5.8 0.99 33.0Short, linear 6.2 6.9 0.69 23.2Short, arc-like 5.4 6.1 0.71 23.8Long, linear 1.9 2.9 1.05 35.0Long, arc-like 3.1 3.9 0.78 26.1Crowning 2.5 3.7 1.18 39.216Supplementary study of the length of th
34、eprofile correctionUp to now, the effect of short or long profilecorrection was considered. The results showedclearly that the long correction reduces the PPTE.Houser 1 recommends to use a “medium” profilecorrectionas“longandshortreliefsrepresentusefuldesign limits for spur gears, and generally some
35、 in-termediatetypeofreliefgivesthebestcompromise,depending upon the range of operating loads thatthe gear meet”. It is clearly possible, that an inter-mediate length of the correction could give evenbetter results, so it should be checked.The PPTE calculated on a specific gear with differ-ent length
36、 of profile correction is shown in figure16.In this typical example, the PPTE increases slightlyfrom zero to the short profile correction. Withincreasing correction length, then the PPTE de-creases significantly, quicker with linear correctionthan with arc-like correction. The PPTE reaches aminimum
37、around the long profile correction. Withlinearcorrectiontheminimumisreachedshortlybe-fore the long profile correction , with arc-likecorrection shortly after. Clearly the curves maychange with torque and gear geometry, but thetendency is repeatable.Different profile corrections and the flashtemperat
38、ureNormally the local flash temperature is the highestat begin and end of the contact between two gears.Asthetooth thicknessreduction producedby apro-file correction is reducing the Hertzian pressureexactly in these points, the consequence of thereduced load is, that the local temperature at beginan
39、d end of the contact will decrease. Therefore itislogical, that any profile correction will be helpful forreducing the risk of scoring.Figure 16. PPTE at design torque depending on the length of profile correction (for a gear setwith = 1.6), when using linear or arc-like tip correction17Figure 17 sh
40、ows the relative reduction of the flashtemperature when using a short PC, figure 18shows the same with a long PC. Basically the re-sultsareverysimilar,sothereisnosignificantdiffer-ence between short and long correction. With fewexceptions the reduction of the flash temperature,when using any PC, is
41、very relevant.It is interesting, that the reduction of flash tempera-ture (always compared to the gear without PC) issmallest with = 1.4; then the temperaturedecreasessignificantlywithhigher,havinganop-timumat= 2.0(a temperaturedecrease of60%),then with even higher , the reduction is againlesssignif
42、icant.Figure 17. Ratio of HEATwithPC to HEATnoPC for different gear pairs, with = 1.4 to 2.4, withshort profile correction, depending on torqueFigure 18. Ratio of HEATwithPC to HEATnoPC for different gear pairs, with = 1.4 to 2.4, withlong profile correction, depending on torque.18There is no signif
43、icant influence of differentcurvatures of the profile correction on the flashtemperature.Dimensioning the tip relief CaMay be it is important to discuss the lay-out of theoptimum tip relief Ca (figure 1). For this study, thetip relief was designed in order to eliminatecompletely the corner contact i
44、n the beginning andthe end of the contact at design torque, without re-ducing the length of the contact between the gears.Figure19explains,howtheeffectofthetipreliefhasto be checked.In this study the tip relief was not varied. WithoutanyprofilecorrectionthePPTEisquiteproportionalto the torque (figur
45、e 9), but when applying a profilecorrection, than (see chapter 4.2 and figure 12) thePPTE is lowest at 75% of design torque, but getshigher with smaller torque. Therefore changing theamount of Ca by -5% doesnot givethe sameresultasachangeofthetorqueof+5%;thiswouldbetrue,as somebody could suggest, if
46、 torque and PPTE isproportional.So the amount of Ca is an additional parameter,which could be investigated.SummaryTheeffectonthetransmissionerrorand thescoringrisk produced by short linear, long linear, short arc-like, long arc-like and fully crowned profilecorrections on gears with different transv
47、ersecontact ratio () was analyzed.In literature only few, and partly contra-dictionary,statements can be found. For this analysis impor-tant parameters were systematically varied andhundreds of PPTE calculations performed.High tooth gear sets (with transverse contact ratio2.0) have in most cases onl
48、y about half of thePPTE, compared to normal gear sets, when no PCis applied. With PC, high tooth gears have alsolower PPTE, but the difference to normal gear issmaller.A profile correction, short or long, is reducing verywell the scoring risk and the contact shock (cornercontact). For thePPTE, thedi
49、fference betweentheshort and the long correction mainly for any trans-verse contact ratio is very significant. Whereshort PC shows even at design torque a small in-crease of the PPTE compared with gears withoutPC, long PC shows a reduction of 30 up to 70%.The result is in agreement with some authors, butthe fact that, when using the long correction, to getoverallsuchagoodresult,issurprising. Howeveritisalsoimportanttoknow,thatanyPC increasesthePPTE with small torque (50% or
