1、08FTM19AGMA Technical PaperHow Are You Dealingwith the Bias Error inYour Helical Gears?By J. Lange, The Gleason WorksHowAreYouDealingwiththeBiasErrorinYourHelicalGears?John Lange, The Gleason WorksThe statements and opinions contained herein are those of the author and should not be construed as ano
2、fficial action or opinion of the American Gear Manufacturers Association.AbstractThe paper initially defines bias error (“the twisted tooth phoneme”). Using illustrations we explain that biaserrorisabyproductofapplyingconventionalradialcrowningmethodstoproducedcrownedleadsonhelicalgears. The methods
3、 considered are gears that are finished, shaped, shaved, form and generated ground.The paper explains why bias error occurs in these methods. It then addresses what techniques are used tolimit/eliminatebiaserror. Sometimestheremaybeapossibilitytoapplytwomethodstoeliminatebiaserror.Inthosecasesthepro
4、s/consofthesemethodswillbereviewed. Profileandleadinspectionchartswillbeusedto detail bias error and the ability to eliminate it.The paper details the simultaneous interpolation of multiple axes in the gear manufacturing machine toachieve the elimination of bias error. It also explains that the CNC
5、machine software can be used to predictbias error. Equally important that it could be used to create an “engineered bias correction” to increase theload carrying capacity of an existing gear set.Copyright 2008American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia
6、, 22314October, 2008ISBN: 978-1-55589-949-33How Are You Dealing with the Bias Error in Your Helical Gears?John Lange, The Gleason WorksIntroductionBiaserrororcorrection(alsoknownas“TheTwistedTooth Error” and topological correction) was under-stood and addressed in the mid 1970s. It was notusedbydesi
7、gnerstoincreaseatransmissionsgearload capacity and noise reduction, but rather in amanufacturing process to finish automatic trans-mission gears to a quality level similar to a shavedfinished quality. The finish rolling process requiredthe use of dies that required bias error correction.Without bias
8、 correction the rolling dies and theworking pressure of the process would produce er-rors similar to bias. The bias correction processwas applied to a finishing tool. However, there waslittlechancetoapplybiascorrectioneconomicallytoconventional gearing.Thepushinalmosteverygearingfieldistoincreasethe
9、 durability, load carrying capacity and a reducednoises level for given gear set. It is stated as theneedforhigherpowerdensity,weneedmoretorquecapability,weneedaquietergearbox,and weneedlongerlifeandsoon. Fromtheaerospaceindustryitmight be twisted around a bit (pun intended). Theywant a smaller ligh
10、ter gear set but having the sameloadcarryingcapacity. Dealingwiththelossofinvo-lute contact ratio and tooth face width bearing pat-tern contact because ofbias error,reduces theloadcarrying capacity of a given gear set. So “dealingwith it” just might make it possible to meet thedemands of higher powe
11、r density without an entireredesign of the gear set.DiscussionBiaserrorisanonuniformprofileandleadgeometryacross the facewidth of a helical gear. “The twistedtooth” appears as if one end of a gear tooth was ro-tated one clockwise and the other counter clock-wise. It is the direct result of making a
12、lead crowncorrection using the conventional method of theradial displacement of the “tool” (cutting or other-wise) as it moves along the facewidth of the gear.Pinions, the lower number of teeth component in agear set, are more prone to “inherit” this uniquemanufacturing error. The pinion, being the
13、smallergearcomponent,is moreapt todeflect underheavyloads. That deflection occurs in the lead and invo-lute planes. It is ironic that gear designers, in aneffort to maintain a reasonable face contact patternatpeakloads;specifyleadcrownsthatinrealitycanhave an adverse affect. There is a need to under
14、-stand a lead crown correction with bias errorcompensation will achieve the goals of thedesigners.The contributing factors creating bias error andthose increasing the amount of bias error are:S The helical aspect relates the line of actioncontactpatternoftwohelicalgearsin mesh,seeFigure 1.Figure 1.
15、Line of action contactS The pinion is the gear normally modified and ithas the highest degree of tooth curvature. Thehigher the tooth curvature, lower number ofteeth,thegreaterthepotentialforbiaserror,seeFigure 2;Involute gear tooth shapesFigure 2. Curvature of the involute4S The coarser the module/
16、DP, the greater thebias;S The higher the helix angle, the greater the bias;S The larger the facewidth, the greater the bias;S A higher amount of lead crown correction, thegreater the bias.Figures 3, 4 and 5 illustrate bias error and acorrected bias error. The red section of the plottedtooth represen
17、ts unwanted plus error; yellow signi-fiesthetransitionzonetobeginningoftoothcontact;andgreen,theidealtoothgeometryalongthelineofcontact.Figure 3. Amount of bias, sFigure 4. Flank topography5Figure 5. Impact of bias on tooth contactWhat does a gear designer consider andhow does bias error affect thos
18、edecisions?Threesignificantfactorsfigureintotheloadcarryingcapacity rating and noise of a gear set:- Involute contact ratio: A theoretical calcula-tion of an average number of teeth in contact asmating gears roll in mesh, 2 or greater isdesirable;- Loaddistribution: Distributedacrosstheface-width of
19、 the gear which can also simultaneouslyaffect the involute contact ratio negatively if thetwo gearsin meshare notcontacting eachotheralong the designated facewidth, normally 80%or more when under load, see Figure 6;- In the finished gear plus error needs to beavoided. If not high contact stress coul
20、d lead totooth pitting in those areas of plus error.Because of varying load, tooth and gear blank/shaft bending under severe load-ing, there is a need to create gear tooth modifications.Figure 6. Load distribution6Sotodealwithit,thedesignerwillneedtodefinetheamount of bias error being dealt with, se
21、e Figure 7.Once the designer is informed as to the amount ofbias a decision can be made to either reduce thecrown to reduce the bias or discuss with manufac-turing engineering the ability to eliminate it. It maybe that prototypes need to be made and inspectedfor bias error. See Figures 8 through 11
22、forexamples of bias error evaluation methods.Nowtheamountofbiaserrorhasbeendefined. Thenextstepistoapproachthegeardesigners,andde-scribe the errors that were caused when creatingthespecifiedcrowncorrection. Itmaybenecessaryto show the following schematics illustrating howtheleadcrownwascreated. Poin
23、toutthepluserrorissue. In addition, inquire if: the crown is requiredon both flanks; and if the root diameter changed inrelation to the crown is desirable or required. Thesignificanceoftheseanswerswillbecomeapparenta bit later in this discussion.Figure 7. Inspecting for bias lead andinvolute measure
24、ments of a single toothFigure 8. Single tooth with bias error7Figure 9. Single tooth without bias errorFigure 10. Typical four teeth inspection technique with bias error8Figure 11. Typical four teeth inspection technique with bias correctionMethods to make a lead crown correctionForm grinding will b
25、e used as a means to demon-strate how the kinematics of creating a lead crowncreates a bias error. See Figures 12 through 18.Traditional path of hob, threaded wheel grindingand form grinding tools. This method of crowningwill create bias error.Figure 12. Traditional method for lead crowncorrection w
26、ith a circular toolHow is bias error created?Figure 13. Form grinding exampleInvolute profilegrinding wheelFigure 14. Form grinding method9Form grinding wheel path required to create asymmetrical lead crown using the conventionalcrowning technique of radial displacement of thegrinding wheel relative
27、 to Z axis position along thegear facewidth. See figure 15.Figure 15. Form grinding wheel path for aconvex crownPath of form grindingwheel to create alead crownFigure 16. Tool path for a 0.030” crown perflankTheoretical profile compared to actual profileFigure 17. Involute profile “radial shift”resu
28、lting in involute errors when creating a0.030” crown (Note: A 0.030” crown isinordinately large but that was done for a visualeffect)Figure 18. Lead slope error as the result of0.030” crownThe gear shaping process creating a lead crownwitharadialpositionchangeofthepathoftheshap-er cutter as it passe
29、s along the facewidth of thegear. Thismethodofcrowningwillcreatebiaserror.See figure 19.Intheshavingprocess,thecrownedleadcreatedbychanging the center distance between the shavecutter and gear as the contact point moves right toleft as the work slide “rocks up and down”. Thismethodofcreatingacrowned
30、leadwillproducebiaserror. See figure 20.10Figure 19. Shaping method for lead correctionFigure 20. Shaving a lead crown correction by “rocking” the gearNOTE: Plunge shaving and honing having the leadcrownedcorrectiondressedintotheshavecutterandhone stone and consequently will not produce biaserror. T
31、he Gleason Hurth Honing machine has theability to make bias error correction usingfour axisofmotion. It“knows”wherethecenterpointofcontactisatalltimesandcontrolsitsposition/motiontoproducebias error correction.How to deal with unwanted bias error -How not to make bias error.- Do not make a lead crow
32、n correction using thetraditional radial displacement of the tool orworkpiece. Thismaynotbepracticalasthegearmanufacturing equipment in use in a plant mostlikely has no other method of making a leadcrown.- An important point about a machines CNC ca-pability with special software and various CNCcontr
33、olled axes needs to be known. If the ma-chine can cut a part cutting only one flank at atime it may be possible to use the work tablerotation or another rotary axis to make a leadcrown and not cause bias error. This one flankfinishing process applies to form grinding andshaping. Thegeardesignershoul
34、dbeaskedifitis really necessary for both flanks lead to havealead crown correction. If yes, then a two finish-ingpassesarerequired tomake thisgear. Morecycletimeisrequired. Thissingleflankcrowningmethoddoesnotchangetherootdiameter. Onecouldactuallyconsiderifmakingacrownedleadwithout a root diameter
35、change, might you havea stronger tooth?11- If finished hobbed, there is nothing that can bedone. Bias error will occur.- If finished shaped, bias error will occur unlessthe machine has a CNC guide capability andspecialsoftware. Thenthefinishcuttingmethodistocutaflankatatimemakingarighthandheli-cal u
36、ntil mid face and then a left hand helical. Itwould be the opposite for the other flank. Onewouldthinkthatthiscrowncuttingmethodwouldmake a lead correction that would look like achevron. This is not the case, see the examplelead chart made on a Gleason Pfauter GearShaping Machine with an electronic
37、guide andspecial software, Figure 21. Note, theintentional asymmetrical and symmetrical leadcorrections.- If a shaved part use only the plunge shavingprocess. Plunge shaving will not create bias er-ror. This is not practical if the part has a face-width larger than 2” (50 mm) andor ifthe pitchiscoar
38、ser than 6 DP (4.23 module). With the par-allelanddiagonal shavingmethod abias erroriscreated when making a lead crown correction.- If grinding you need to do the following:S Form grinding: Use the single flank grindingprocess with work spindle rotation, not “X”radial axis displacement, as the grind
39、ingwheels moves along the facewidth of thepart. If both flanks require a crown then anadditional finishing pass is needed. OR, ifthe machine has a veryspecial softwareandmulti axes interpolation motion capabilitythen a dual flank grinding process can bedone saving an enormous amount of time.See Figu
40、res22 through24 foran exampleofa Gleason Pfauter CNC Grinder using pat-ented software producing bias error correc-tion and in the second example totallydifferent lead correction. Knowing the con-tact point of the grinding wheel at all times isparamount to this successful and uniquelead correct techn
41、ique.Figure 21. Lead crown correction made with a CNC guide12S Threaded wheel grinding: Special patentedsoftware and machine dressing capability isappliedtocreateonthegrindingwheeldiffer-ent geometric proportions over its length.This is an example of a Gleason softwaresolutiontoeliminatebiaserrororm
42、akeabiascorrection, see Figures 25 through 27.Axes being interpolated when making bias errorcorrection (X, Y, A and C depending on Z-position)Figure 22. Multi axes gear grinding machineinterpolating 5 axes of motion to eliminatebias error when creating a lead crowngrinding two flanksProfile chartsFi
43、gure 23. Dual flank grinding withoutproducing bias errorFigure 24. Dual flank grinding without producing bias error13Principle of bias compensationFigure 25. Special dressing technology applied to the grinding wheel to eliminate bias errorwhen making a lead crownFigure 26. Special dressing technolog
44、y and shifting strategy to eliminate bias error when makinga lead crown14Figure 27. Threaded wheel grinding with lead crown correction and no bias errorConclusionGear designers and manufacturing engineers needto know that it is now possible to make lead crowncorrections and not create bias error. Th
45、ey need touse this knowledge and processes to create a faceload distribution over the typical 80% which manygear designers consider for their designs. Why noteven90%whenthedesignerisforcedtocontinuetouse an existing gear box at higher rated loadcapacity? Designers may even rethink bias errorand consider to use this ability to manipulate biasvalues into a bias correction.References1. MAAG Gearbook, Maag Gear Wheel, Switzer-land, 1990, pp. 181-188.2. ES 422 Topological Modifications, Maag GearWheel, Switzerland, June 1982.3. Topological Modification, Maag Gear Wheel,Switzerland, June 1975.
