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1、93FTM12 The Generationof PrecisionSpurGears ThroughWire ElectricalDischargeMachining by: Roderick and Jack Kleiss, Kleiss Engineering and Scott Hoffmann, Accu-prompt EDM AmericanGearManufacturersAssociation TECHNICALPAPER Copyright American Gear Manufacturers Association Provided by IHS under licens
2、e with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- The Generationof Precision Spur Gears Through Wire ElectricalDischargeMachining Roderickand Jack Kleiss, Kleiss Engineeringan
3、d Scott Hoffmann, Accu-promptEDM Thestatementsandopinionscontained he,_inarethose oft,heauthorand shouldnotbeconstruedas anofficial actionor opinion of the American Gear ManufacturersAssociation. ABSTRACT: The new generationofwire ElectricalDischargeMachines (EDM) arecapableof quite good generating
4、accuracy. We have maximizedtheaccuracyandrepeatabilityofthistoolthroughfixturing,controlledcutting methods,and optimized mathematicalalgorithms forthecuttingpath. Theresultis theverifiedgenerationofprecise spurgearsinpitchesranging from 5 to 41 DP. The advantageofthe methodis short lead timeswith ac
5、curacyapproachingform groundwhilebeing cost competitive. The method is alsosuitable forproducing small to medium lots of very accurate spur gears in any electricallyconductivematerial. Copyright 1993 AmericanGear ManufacturersAssociation 1500 King Street, Suite201 Alexandria,Virginia, 22314 October,
6、 1993 ISBN: 1-55589-624-3 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- TheGenerationof Preci
7、sionSpurGearsThrough WireElectricalDischargeMachining Roderickand JackKleiss KleissEngineering 3006 EdgertonStreet,LittleCanada,MN 55117 and Scott Hoffmann,President Accu-PromptEDM, Inc. 100 83rd AvenueNorthNE, Fridley,MN55432 Introductionotherforms of gear generation. In plasticgear mold-making,the
8、 wire EDMThe EDM Process is often usedto createthe involuteshapein the mold cavity.This has been a point of contentionElectricalDischargeMachiningis based on withintheplasticcommunityforyears,withthe principaloferosionofanelectricallyconductive traditionalistsarguingthata cavity burnedwith amaterial
9、bycontinuoussparkdischargetoits hob cut electrode is inherentlymore accuratethansurface(1).With wireEDM, a metallicwireis a wire-burnedcavity.Withour own historyofcontinuouslyfedthrougharmssuspendedabove successusingtheEDMmethod,wedecidedtheandbelowtheworkpiece(Fig.1).Thischarged ultimatetest would
10、be to cut externalspur gears inwire is thenguided throughthe specifiedtool path thisfashionandusetraditionalgearinspectionwhile cuttingits way throughthe material.The techniques to quantify theiraccuracy,processisrelativelyslowdependingonwire diameter,workpiecethickness,andmachine Ourexperimentwasmo
11、reoverbasedonsettings.The servo-controlledtool pathis quite need.The plasticgears we had designedfor a gearaccurate,typical for CNC type machinery.And the drivenlawnsprinklerrequireduniquemasterbenignenvironmentof the EDM machinery,with gears.Leadtimesfor formgroundgearswereslow feed rates,extremely
12、low forces, verylittle unacceptable.Withourcustomerssupportwefrictionor vibration,andcontrolledtemperature developeda methodof cuttingthesegearsthatmakeeven finer accuracy possible.The tool path achievedthedesiredshapeson timeandwithincaneitherbe point-to-pointor viasimplearcs. cost constraintsfor f
13、ine pitchmastergears.WeAdvancedmathematicalcurvesarenotdirectly thenemployedthesame techniquesto cut a 19programmablebysoftware;thesemustbe tooth5 DPmastergearinordertodetermineapproximatedwitharcsand/orlinemovements. possibleerrorsof scale.Profile inspectionrevealedBoth the involuteand trochoidalse
14、ctionsof a gear similar accuracy of tolerancewas possible for largefallintothisgeneralcategory.Specified coarse pitchgears as for fine pitch.In the followingdimensionalaccuracyand repeatabilityof the more sections,we will presentthe methodswe employedadvancedwireEDMsareon theorderof .0001 to achieve
15、this level of accuracy,the inspectiondatainches.Surfacefinishesof 16 micro-inchcanbe from our work,comparisonswithprecisionhob cutattainedthroughcarefulselectionofmachining gears,and possibleapplicationsof this methodtoparametersalong with multiplefinishingskim cuts on low powersettings. Copyright A
16、merican Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- Figure1 - Wire EDM gear cuttingsetup GearCuttingWithWireDi
17、fficultieswiththismethodofgenerationare immediatelyapparent.By focusingonlyon the ThewireEDMisprimarilyatwo-involute profile, the trochoidal(or root) area is left dimensionalprocess,althoughthe two wire guidesarbitraryand undefined.No provisionis made for can follow independentpathsallowing slight 3
18、-Dundercutevenifitisrequired.Oneof the modifications.EDM softwareexists that claims toadvantagesof a hob cut gear is thatany similar createa wirepathfor thespurinvolute.Thephysical gear will fit within the envelope created by softwarerequiresstandardgeargeometryto be,the generatinghob.The reason for
19、 this is that the inputalong with tooth thickness,root, and outsidehob removesany possibleinterferingmaterialin diameters.Approximatearc segmentsarethenthe root areathatmay physicallyinterferewith fitted to the involutecurve down to the root or toanothergear.A majorityof non-undercutstandard the bas
20、e circle diameter,whichevercomes first.Ifgearsare not sensitiveto thispossibletrochoidal the base circle is located above the root circle, ainterferencesincethestandardwholedepth straightradiallineis connectedfromthebaseprovidessufficientclearanceandmatingteeth circle to theroot diameter,and the use
21、r has theneverreach below the basecircle.However,as optionofspecifyingafilletradiusforthedesignersmodifygeargeometrytomaximize intersection of those two features (Fig. 2).function or if undercutexists, this areabecomes -_,critical through possibleinterference,or weakened ?_i_by excessiverelief.Thema
22、thematicalgeneration of gearteethmustprovidenotonlyconjugate action but also designedclearancewith any mating gear. _-_._:_-Another not-so-apparent difficultywith the L-_- _-“-_-_,-_-_=_ _“generationofapproximatearcstotheinvolute concernsthe natureof the involuteitself.Withits , _llleTL_everincreasi
23、ngradiusof curvaturefromthe base -RadiusJ“_b (userI_circle,the involuteis anything but a trivial curve specified)J_fittingexercise.Thedesirabilityofmaking BaseRoot 01 a_eter01 ameterintersectingarcstangentattheirendpoints compoundsthe problemof fittingthesearcs to the Typical E0M_ear Involuteinvolut
24、e.Withoutcarefulfittingit is possibleto Figure Z 2 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,
25、-,- have considerable errorintheapproximation, especiallyin thecriticalregionof thebasecircle. The trochoidalsurfacecanalsobe intricateand requiresan equivalentattentionto detailin any generatingcurve-fittingscheme. MathematicalGeneration Manytextsdescribethemathematical generationoftheinvolute.Buck
26、ingham(2) describedboth polar and CartesianequationsforFigure4- Optimal curve fit the involuteprofile.Pointby pointdevelopmentof thegeneratedtrochoidalregionislesswell documented.However,Khiralla(3) and Colbourne( and multi-valued)and becausethe functionthat (4) have both publishedmethodsto find poi
27、ntsonrepresentsa splinedseries of arc segmentsincludes the trochoidalcurve for any involuterack.Theynon-linearparameters,thisis not thecase.The also describe the necessaryiterativeschemes tocurvefittingtaskisdifficultbutnot determinetheexactinvoluteformdiameterforinsurmountable.Numerousgeneralpurpos
28、e undercutgears.Solutionof these equationsyieldoptimizationalgorithmscan beadaptedto solve an arrayof discretecoordinatepointsthatexactlythis kind of problem(5). The use of these methods describe the entiresurface of the gear tooth (Fig. 3).to solvecurvefittingproblemsis notanexact scienceandhassome
29、timesbeencalledanart. Withcarefulselectionandtuningof methods,we havebeenabletogenerate splined arc approximationsof theinvoluteandtrochoidwith arbitrarilyspecifiedmaximumerrorcriteria (Fig. 5). 15_i0-_ l:evIatI on between Sp IIned ar_s and Invn Iute Figure5 Figure3 - Gear surfacecoordinates Initial
30、Setup CurveFitting Fourexternalgearsweremade.The The wire EDM tool pathis constrainedtoDiametralPitcheswere32,36,40,and41. follow eitherstraightlinesor simplesinglearcInspectionequipmentincludeda Mahrmodel 896 segments.The involuteand trochoidhowever aregearrolltesterandaZeissZMC550gear curveswithco
31、ntinuouslychangingradiiofcoordinatemeasurementmachinefor profile,lead, curvature.The designermightcreatea tool pathand spacing checks.The 36, 40, and 41 DP gears withinfinitesimallysmalllinearmovestowere EDMd andthe 32 DP gear was cut with a 1“ maximizethe EDMs resolution,but the resultingdia. Grade
32、 AA precisionhob in order to get a sense NCprogramwouldbeexcessivelylongandof the relativeaccuracy possiblewitheach method. cumbersome.A more efficientapproachwould beTwo of each gear weremade so theycould be roll- to allow the machinesown softwareto optimizethetestedagainstthemselvesto examineclose
33、 meshed cuttingpath.A mathematicallysatisfyingcurveconjugacy.Theyweretheninspected fittingroutinewouldlinkapproximatedarcs withindependentlyon theCMM for absoluteaccuracy. commontangentsto theprofiles(Fig.4).TheIt was felt that roll testing was imperativefor wire- machinetool wouldthenfollow thenear
34、estx-ycutgearssincethecuttingprocesswaspurely pathto this profileAt first glance, it would appearmathematicalin function.Any local aberrationin a simpletaskto approximatetheinvoluteandthe cutting or fixturingof the gear thatmight not trochoidalcurves,in theminimumleastsquaresbe detectedby thesinglep
35、ointof a profilometer sense,withsplinedarcs; however,since anyarcwould be more easilyseen on a double flankroll segmentismathematicallynon-lineartester. 3 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie No
36、t for Resale, 04/18/2007 11:53:51 MDTNo reproduction or networking permitted without license from IHS -,-,- Discussionof Resultspurpose ofplastic gear inspection. Both profile and formdeviationforthesegearsweregenerally Figures6, 7, 8, and 9 show profilometryofimprovedovertheirhobbedcounterpart.Tota
37、l the fine pitch gears as measuredon the Zeiss CMM.runeutof thesegears was slightlygreaterthanfor Total profile deviation(Ff) for the EDM gearsinthe cut gear, but furthermodificationsin fixturing Figures 7, 8, and 9 varied between.0001 and .0003and machinesetupshould improve this feature.At inches,
38、while the profile form deviation consistentlypresent,thismethodhasnotreachedthesame stayedwithin.0001 inch.The hob cutgearinaccuracy as form groundmasters,but they cost Figure6maintainedprofiledeviationbetweenlessandcanbecutina week.Forcertain .0002and.0003inches,howevertotalformapplications,thatcan
39、 be the deciding factor.The deviationalso variedby thatamount.TheEDMcoarse pitch gear in this experimentbenefitedfrom profile tracesappearmore as straightlines whilethelessonslearnedonthesmallergears.It thehobbedprofileexhibitswaviness.Theleadsuffered no degradationin tolerancesdespitean 8x error on
40、 all gears was .0001 inches maximum,andincreasein size.This5 DPgearsatisfiesthe the adjacent pitch deviation(fp) remainedless thancriteriafor a Class 2 mastergear, with similarcost .0002 inchesfor all gears.In totalrunout,theand productionadvantagesover form ground gears. hobbedgearheld.0002inches,w
41、hiletheEDM gears variedbetween.0003and.0005inches.Theinvoluteshapeisnotparticularly difficultfor the wire EDM.Any mathematicalpath Roll testsof the gearsagainstthemselvesarethatcan be describedin arcsand/orlinescan be presentedin Figure10.A comparisontraceof 32generatedwithsimilaraccuracy.Tip relief
42、,root DP form-groundmastergears rolled againsteachrelief,andnon-involutetoothformscanbe other is includedas reference.Scale is identicalforgeneratedwith very littleadded complexityor cost. all traces at .0003 inches per large division.TheseThe abilityof cuttingtwo separateshapesat the tracesweretake
43、nwhenthegearswerenewsame time with the upper and lower cuttingarms withoutrunningthemin lightly first.Later tracesopen otherpossibilitiesas well.We havealready were more uniform.Unfortunatelythey were notproducedbevelgearsusingTregolds retained.Webelievethatlightrunning-inofapproximationof theequiva
44、lentspurgearform EDMd gears is desired to polish the mattesurface(Fig. 12).Low helix angle gears can be accurately and de-burredges,cut with onlyslight ove_cutofthe root area at one ACoarse Pitch Exampleendofthegear.Evencrowning canbe approximated.Inmanyways,theuseof this A questionremainedwhetherED
45、M errorsprocessisonly limitedby theuserscleverness. wouldbemagnifiedbyscalingthegeneration process for coarse pitchgearing.We decided to_ wire-cuta 5 DP 19 toothgear andconcentrateon improvingrunoutandoptimizingthecurvefit. Thisgearwouldbe roughly8x thesize of the previouslycut fine pitchgears.We ge
46、nerated15 arcsforthisinvolutewithamaximum mathematicalerrorof +/-15micro-inches.The materialwas through-hardened420 stainlesssteel. A completeprofileinspectionwasdonefor each flankof thisgear.A representativesampleof resultsis given in Figure11. Total profile and form deviationstayedwithin.0001and.0
47、002inches, and totalrunoutwas held between.0002 and .0003 inches.Spacingand lead were bothheld to .0001 inches.In effect we were able to improve theFigure12- EDMd bevel gear dimensionalcharacteristicsof thelargergearby improved cuttingmethodsand closer mathematicalFurtherinvestigationneedsto be done
48、 on approximations.Thiswire-EDMdgearwastheproductionandeffect of theEDMprocess. ultimatelyusedto monitora productionrunofSincethegeneratingmethodis new,current thread ground spur gears,standardinspection criteriamay not adequately coverallpossibleproductionerrors.Simply Conclusionsspecifying maximum
49、tooth-to-tooth andtotal compositeerrorwouldnot be sufficient.It would ThewireEDMprocessissuitableforalso be interestingto investigatethe effect of EDM producingaccuratespurgearshapes.These earlymetallurgyon life, wear, pittingetc.For instance, fine pitchgearswere adequatefor theirintendedhardeningwithEDMisachievedwiththrough 4 C