Bevel Gears in ProE

Table of Contents:

TableofC TableofConten ontents:.............. ts:.......................... ...................... ..................... ....................... ....................... ...................... ..................... ...................... ....................... ...................... ........... i Disclaime Disclaimerr ....................... .................................. ..................... ...................... ....................... ...................... ....................... ...................... ..................... ...................... ....................... .............. .. 1 Preamble Preamble ...................... ................................. ..................... ...................... ....................... ...................... ....................... ...................... ..................... ...................... ....................... ................ .... 1 DevelopmentFlowChart..................................................................................................................2 BevelGear BevelGearFoun Foundatio dation n ....................... ................................. ...................... ....................... ....................... ....................... ..................... ..................... ...................... ................ ..... 2 Setup............................. Setup........................................ ..................... ...................... ....................... ...................... ....................... ..................... ..................... ....................... ...................... ............. 2 TemplateP TemplateParame arameters ters ...................... ................................ ..................... ....................... ....................... ....................... ..................... ..................... ....................... ............. 2 Relations.......... Relations..................... ....................... ...................... ..................... ....................... ....................... ...................... ..................... ...................... ....................... .....................3 ..........3 Straight/Sp Straight/Spiral iralTooth ToothBase Base ...................... ................................ ...................... ....................... ...................... ..................... ..................... ....................... ......................3 ..........3 ToothDatum ToothDatums s ....................... .................................. ...................... ...................... ...................... ....................... ....................... ....................... ....................... ...................... .............. ... 3 ToothCoord ToothCoordinat inateSys eSystem[T tem[TCSYS] CSYS] ...................... .................................. ....................... ...................... ....................... ..................... ..................... .............. 3 ToothDatum ToothDatumPla Planes nes ...................... ................................. ...................... ...................... ...................... ....................... ..................... ..................... ....................... .............. ... 3 SectionDa SectionDatumPo tumPointL intLayou ayout[SDP t[SDP]] ..................... ................................. ....................... ...................... ....................... ...................... ..................... .............. ... 3 SpiralGea SpiralGearSpe rSpecific cificFeat Features ures ...................... ................................. ...................... ....................... ....................... ..................... ..................... ....................... .................. ......5 5 PitchCone PitchConeSurfa Surface[P ce[PCS] CS] ...................... ................................. ...................... ....................... ....................... ...................... ..................... ...................... ....................5 ........5 SpiralPla SpiralPlaneAx neAxis[S is[SPA] PA] ....................... ................................. ...................... ....................... ...................... ....................... ....................... ....................... ......................6 ..........6 SpiralAnglePlane[SAP]..............................................................................................................6 PostFeatureCreation...............................................................................................................7 SpiralCu SpiralCurvePa rvePath th ....................... .................................. ..................... ...................... ....................... ...................... ..................... ...................... ....................... .....................7 ..........7 Geometry Geometry ...................... .................................. ...................... ..................... ....................... ....................... ...................... ..................... ..................... ....................... ....................8 ........8 ProjectontoPitchCone................................................................................................................8 Reference References s ....................... .................................. ...................... ...................... ...................... ....................... ....................... ..................... ..................... ....................... ................ ....9 9 SpiralCu SpiralCurveDa rveDatumPo tumPoints ints[S#CD [S#CDP] P] ...................... .................................. ....................... ....................... ....................... ..................... ..................... .............. ... 9 Reference References s ....................... .................................. ...................... ...................... ...................... ....................... ....................... ..................... ..................... ....................... ................ ....9 9 SectionC SectionCoordi oordinate nateDatum Datums s ..................... ................................ ....................... ....................... ...................... ...................... ..................... ...................... ......................9 ..........9 Primary[SX Primary[SXPCSYS PCSYS]] ...................... .................................. ...................... ..................... ....................... ....................... ..................... ..................... ....................... .................. ......9 9 Reference References s ....................... .................................. ...................... ...................... ...................... ....................... ....................... ..................... ..................... ....................... ................ ....9 9 Secondary[S#SCSYS]...............................................................................................................10 Relation...................................................................................................................................10 Tertiary[S Tertiary[S#TCS #TCSYS] YS].......... ..................... ....................... ...................... ..................... ....................... ....................... ..................... ..................... ....................... .................. ...... 10 Relation...................................................................................................................................10 ProtoTooth ProtoTooth ....................... .................................. ..................... ...................... ....................... ...................... ....................... ..................... ..................... ....................... .....................10 ..........10 SectionCu SectionCurves rves ....................... .................................. ..................... ...................... ....................... ....................... ..................... ..................... ....................... .......................10 ............10 ParametricEquations..............................................................................................................10 InvoluteC InvoluteCurve[ urve[S#C{ S#C{1;3}] 1;3}] ....................... .................................. ...................... ...................... ....................... ...................... ..................... ...................... .............. ... 10 Side(AxistoInvolute)Curve[S#C{2;4}] Side(AxistoInvolute)Curve [S#C{2;4}] .......................... .............. ......................... .......................... ........................... ........................... ............... .. 11 GroupSec GroupSection tionFeatu Features res ...................... ................................ ...................... ....................... ...................... ....................... ...................... ..................... .....................11 ..........11

SideSurface[T{L/R}S] ............................................................................................................... 11 RevolvedTubeSurface[RTS]....................................................................................................12 StraightToothGears:..............................................................................................................12 SpiralToothGears:.................................................................................................................12 SketchReferences:.................................................................................................................12 Geometry ................................................................................................................................12 SurfaceMerge........................................................................................................................... 12 FirstFeature ........................................................................................................................... 13 SecondFeature ......................................................................................................................13 SolidTooth .................................................................................................................................13 GearTemplate ............................................................................................................................... 13 UsingtheTemplates ......................................................................................................................14 InitialModification.......................................................................................................................14 Pinion/Miter .............................................................................................................................. 14 ToothGroup............................................................................................................................14 Pattern ....................................................................................................................................14 Core........................................................................................................................................ 15 Gear ...........................................................................................................................................17 GearTooth..............................................................................................................................17 GearPartAssembly................................................................................................................17 GearCore ............................................................................................................................... 17 Merge...................................................................................................................................... 18 MatingPairs ...................................................................................................................................18  AssemblySetup .........................................................................................................................18 ExistingShafts........................................................................................................................18 FirstParts ...............................................................................................................................18  AngleModification ......................................................................................................................19 ModifyingGears.............................................................................................................................19 ZerolBevelGears ......................................................................................................................19 Crowning ....................................................................................................................................19

ii

Disclaimer

Thetemplates,suppliedwithorcreatedusingthisdocument,areintendedfortechnicalillustrative purposesonly.Theauthorlaysnoclaimthattheresultingmodelsaretruerepresentationsof bevelgearsproducedbygearmanufacturers. Preamble

Duringthedevelopmentofthismethod,theauthordiscoveredaproblemwithinthe Pro/ENGINEERWildfiresoftware.Whenmodifyingtheparameterstocreategears,thesurface mergefeaturesfail.Fixingthisandthentryingtopatternthetooth,themergesfailagain.Pitch coneanglesgreaterthan45°leadtofailures.Aworkaroundwasdevisedtocircumventthe problem. TheauthorinitiallyusedEmptyfilestocreatealltemplates.Allpartdatumfeatures,coordinate systemanddatumplanesweregeneratedandrenamedinaccordancetothenamingconvention displayedinthisdocument.Anydefaultsketchreferencesweredeleted.

1

Development Flow Chart

Bevel Gear Foundation

Bevel Gear Core

Bevel Gear Part  Assembly

Straight Tooth Base

Cup Face Tooth Pinion

Spiral Tooth Base

Left-Hand

Flat Faced Tooth Pinion

Cup Face Tooth Gear

Cup Face Tooth Pinion

Right-Hand

Flat Faced Tooth Pinion

Cup Face Tooth Gear Cup Face Tooth Pinion

Flat Faced Tooth Pinion

Cup Face Tooth Gear Bevel Gear Foundation

SETUP

Template Parameters Parameter Name Tooth Parameters DIAMETRAL_PITCH NUMBER_OF_TEETH

Real Number Integer

10 20

Pinion ● ●

NUMBER_OF_TEETH_MG

Integer

20

●

●

FACE_WIDTH

Real Number

0.5

●

●

PRESSURE_ANGLE

Real Number

20

●

SHAFT_ANGLE

Real Number

90

●

SPIRAL_ANGLE

Real Number

30

●

CLEARANCE

Real Number

0.01

●

●

MOUNTING_DISTANCE

Real Number

0

●

●

BORE_DIAMETER

Real Number

0

●

●

BORE_LENGTH

Real Number

0

●

●

HUB_DIAMETER

Real Number

0

●

●

HUB_LENGTH Real Number 0   APEX_TO_BACK Real Number BOLT_CIRCLE Real Number 0 THROUGH_HOLE Real Number 0 NUMBER_OF_HOLES Integer 0 CBORE_DIAMETER Real Number 0 CBORE_DEPTH Real Number 0 WEB_THICKNESS Real Number 0

●

●

Type

Initial  Value

Designate Where Used Gear(Assy) ●

Gear(Core) ● ●

●

Gear Blank Parameters

0

● ●

● ● ●

● ● ● ● ● ● ●

2

Relations CUTTER_DIAMETER=(NUMBER_OF_TEETH+NUMBER_OF_TEETH_MG)/(2*DIAMETRAL_PITCH) IF NUMBER_OF_TEETH_MG>NUMBER_OF_TEETH PITCH_CONE_ANGLE=ATAN(SIN(SHAFT_ANGLE)/((NUMBER_OF_TEETH_MG/NUMBER_OF_TEETH)+COS(SHAFT_ANGLE))) ELSE PITCH_CONE_ANGLE=SHAFT_ANGLE ATAN(SIN(SHAFT_ANGLE)/((NUMBER_OF_TEETH/NUMBER_OF_TEETH_MG)+COS(SHAFT_ANGLE))) ENDIF PITCH_DIAMETER=NUMBER_OF_TEETH/DIAMETRAL_PITCH  ADDENDUM=DIAMETRAL_PITCH^-1 DEDENDUM=CLEARANCE+ADDENDUM PITCH_CONE_RADIUS=PITCH_DIAMETER/(2*SIN(PITCH_CONE_ANGLE))  ADDENDUM_ANGLE=ATAN(ADDENDUM/PITCH_CONE_RADIUS) DEDENDUM_ANGLE=ATAN(DEDENDUM/PITCH_CONE_RADIUS)  ANGULAR_ADDENDUM=ADDENDUM*COS(PITCH_CONE_ANGLE) OUTER_DIAMETER=PITCH_DIAMETER+(2*ANGULAR_ADDENDUM) FACE_ANGLE=PITCH_CONE_ANGLE+ADDENDUM_ANGLE ROOT_ANGLE=PITCH_CONE_ANGLE-DEDENDUM_ANGLE  VERTEX_DISTANCE=OUTER_DIAMETER/(2*TAN(FACE_ANGLE)) PHI=((180/PI)*(TAN(PRESSURE_ANGLE)-(PRESSURE_ANGLE*PI/180)))/COS(PITCH_CONE_ANGLE) TCRA=(90/NUMBER_OF_TEETH)+PHI

Straight / Spiral Tooth Base

TOOTH DATUMS

Thesearetheinitialdatumfeaturesusedintheprimarytooth’sdevelopment. Tooth Coordinate System [TCSYS]

Thiscoordinatesystemistheonlyconnection fortheprimarytoothtotherestofthemodel.  Allfurtherdatumsandgeometrywillbebased offofthisfeature.Thesinglenon-zero dimensionisusedforcreatingthetoothpattern. UsethePartCSYS[PCSYS]asthereference. RotatethefeatureabouttheZ-axisanarbitrary angle. Note:Unlessotherwisenoted,theauthoruses Note: 30°forallarbitraryangles. SeeFigure1 Tooth Datum Planes

Figure1 Figure1:ToothCoordinateSystemDefinition :ToothCoordinateSystemDefinition

Therearethreedatumplanesneededfor referencinglaterfeaturesandgeometry.Theyhaveazero(0)offsetalongeachaxisofthe TCSYScoordinatesystem. •

X [TYZPLN]

•

 Y [TXZPLN]

•

Z [TXYPLN] Section Datum Point Layout [SDP]

ThisisaSketchedDatumPointfeature.Thisfeaturecontainsthepointsandreference dimensionsnecessarytocreatethepropertoothcross-sections. ThesketchingplaneistheTYZPLNplaneandthetopreferenceistheTXZPLNplane. 3

Note:Forall“sideview”sketches,theauthordoesnotusethedefaultreferences.Theusercan Note: usethedefaults,ifsodesired,andmodifythesubsequentinstructionsaccordingly. ThereferenceforthesketchitselfistheTCSYScoordinatesystem. SKETCH

CreateaHorizontalConstructionLine(CL)throughtheTCSYS;thisisthegear’s‘RotationAxis’. Next,createonemore,angledthroughtheTCSYSfromthelowerlefttotheupperright;thisisthe gear’s‘PitchLine’(PL).ThedimensionshouldbeangularandbasedfromtheHorizontalCL. ModifythevaluetoberelatedtothePITCH_CONE_ANGLE(PCA). POINTS ALONG PITCH LINE  HeelPitchPoint HeelPitchPoint  

PlaceasketchpointontheupperportionofthePL.ModifytheWeakDimensiontoberelatedto PITCH_DIAMETER/2. ToePitchPoint ToePitchPoint  

PlaceanotherpointonthePLbetweenthe heelpointandtheTCSYS.Thisistobe dimensionedfromheelpointalignedwiththe PL.Thedimensionvalueisequaltothe FACE_WIDTH(FW)[sd3 ].  Atthispointintheconstruction,thefour variancesbegintodiverge. SeeFigure2. InternalPoints InternalPoints 

Note:ThesearenotrequiredfortheStraight Note: Toothedgears. Theinternalpointsareusedforthecreationof additionalsectionssothatSpiralGearsare generatedwithasmootherprofile.

Figure2 Figure2:BasicToothDimensions :BasicToothDimensions

FortheSpiralGears,placethree(3)pointsbetween theHeelandToepoints.SeeFigure3.Dimension betweenthemalignedtothePLwiththedimensions equaltoFW/4.Theinitialrelationcanbeequalto sd3/4 andthetwo(2)successivedimensionsequalto theinitial. ExternalPoints ExternalPoints 

Figure3 Figure3:SpiralPitchPints :SpiralPitchPints

Theexternalpointsallowthesidesurfacestoextend pasttherevolvedsurfacefeaturetobecreatedlater. Thiscanbethenextmajordifferentiationpointinthe development,butthesingledimensionalmodification canbeperformedatalatertime.Thisallowsfora morestraightforwarddevelopment.

OnepointistobeplacedalongthePLontheoutside oftheHeelpoint.Thealigneddimensionisequaltosd3/4 ,thesameastheInternalPointsabove.  AnotherpointislocatedalongthePLbetweentheToepointandTCSYS.Thisisthedimension thatneedstodifferentiate.ForParallelteeth,thedimensionisthetypicalFW/4 . SeeFigures3&4.

4

FLAT FACE TOOTH EXCEPTION 

Toallowforthetoothsidestopassthroughthe rotatedtoeendsurface,thisdimensionmustbe doubledtoFW/2  .Asstatedbefore,thiscanbe modifiedpost,deviation,aftertheclosed rotatedsurfaceisgenerated. POINTS ALONG REVOLUTION AXIS  ConstructionLines ConstructionLines 

Theconstructionlinesdeterminethelocationof thedatumpointsthatfollow.Thepoints,in turn,willbethelocationmarkersfortheprimary coordinatesystemusedtogeneratethe involutecurves.  AllconstructionlinesareNormaltothePL.

Figure4 Figure4:StraightPitchPoints :StraightPitchPoints

ForStraightToothGears,onlytheouterpoints alongthePLareused. ForSpiralToothGears,thelinespassthrougheachpointalongthePLisused. Points Points 

 AsketchpointisplacedateveryintersectionoftheConstructionLinesandHorizontalCL. REFERENCE DIMENSIONS 

Theequationusedindeterminingthebaseradiusoftheinvoluterequiresthepitchdiameter.The teetharenotorientedonacylinder,butratheracone.Thesedimensionssimplifythe development,bygivingtheproper,required“pitchradius”forthesections. Goto:Sketch>Dimension>Reference.Dimensionbetweencorrespondingpointsandalignedto theCL. SeeFigures5&6.

Figure5 Figure5:CompletedStraightSketch :CompletedStraightSketch

Figure6 Figure6:CompletedSpiralSketch :CompletedSpiralSketch

Spiral Gear Specific Features

PITCH CONE SURFACE [PCS]

ThisisaR Revolved evolvedSurfaceFeature SurfaceFeature.Itisrevolvedthrough90°includedangleonBothSides BothSides. SurfaceFeature BothSides Forthesketchplacement:UsePrevious . ThesketchreferencesaretheTCSYSandtheouter-mostdatumpointsalongthepitchline.

5

ThissketchconsistsofahorizontalconstructionlinethroughtheTYSCSandageometryline betweentheexternalendpoints.SeeFigures7&8.

Figure7 :CompletedPCSSketch Figure 7:CompletedPCSSketch

Figure8 Figure8:PitchConeSurface :PitchConeSurface

SPIRAL PLANE AXIS [SPA]

ThisfeatureisusedtoproperlylocatetheSpiralPlane. CreateaDatumAxisthroughthemiddledatumpointalongPitchLineandnormaltothePCS. SeeFigure9. SPIRAL ANGLE PLANE [SAP]

Thisfeatureisusedtoproperlyorientthesketchgeometrythatwillbecomethecurvepath. PlacetheplanethroughtheSPAandangledfromtheTYZPLNplane,thedefaultvalueOK. NexteditthedimensionsothatitisequaltotheSPIRAL_ANGLEparameter. SeeFigure10.

Figure9 Figure9:SpiralPlaneAxis :SpiralPlaneAxis

Figure10 Figure 10:SpiralAnglePlane 10:SpiralAnglePlane :SpiralAnglePlane

6

Post Feature Creation

DuetothegeometryoftheSpiralcurveisbestatthisjuncturetodivergethemodelintotheLeft Hand/RightHandspirals. •

Save the file.

•

Save a copy to indicate the proper hand, as indicated by the current SAP orientation.

•

Comment out the SPIRAL_ANGLE relation, place “/*” at the start of line containing the relation.

•

Edit Feature and add a negative “-” sign in front of the value.

•

Regenerate.

•

Remove the comment, delete the “/*”.

•

Save a copy to indicate the new SAP orientation.

•

Erase the template from memory.

•

Open one of the diverged models. SPIRAL CURVE PATH

Theactualcurveisanarcsegment,whichisprojectedontothePCS.UsetheSketchToolto createthesketch[SPCRVSKTCH].Thesketchplaneismade‘onthefly’. Usethefollowing,intheorderindicated,tocreateit. 1. Middle SDP Point along the Pitch Cone - Thorough (default) 2. TYZPLN - Normal 3. Pitch Cone - Tangent

TheorientationreferenceshoulddefaulttotheTYZPLN.ThisisOK. SeeFigures11&12.

Figure11 Figure11:SpiralCurveSketchPlane 11:SpiralCurveSketchPlane :SpiralCurveSketchPlane

Figure12 Figure12:SpiralCurveSketchPlane 12:SpiralCurveSketchPlane :SpiralCurveSketchPlane

7

SketchReferences Thefollowingisalistforthesketchreferences. •

SPA or middle SDP point

•

SAP

•

Inner Arc Edge of PCS

SeeFigure13. Geometry

PlaceaConstructionLinethroughtheSPA/middle SDPreferenceandnormaltotheSAPreference. PlaceacirclecenteredontheCLsothatthecenteris locatedonthearccenterreferencesideoftheSAP. ThecirclecanbeeitherTangenttotheSAPor coincidentwiththeSPAreferencepoint.

Figure13 Figure13:SpiralCurveReferences 13:SpiralCurveReferences :SpiralCurveReferences

Thediameterdimensionisequalto:CUTTER_DIAMETER.Convertthecircleintoconstruction geometry,RMB>Construction. CreateanOffsetsegmentusingtheouterPCSedge. Theoffsetdistanceisequalto:2*CLEARANCE.This willallowthearcsegmenttointersecttheouteredge whenprojectedontoit. Note:Thiscannotbeconvertedintoconstruction Note: geometry. Next,drawanarcconcentrictotheConstruction CirclebetweentheintersectionsoftheConstruction Circleandtheinnerarcreferenceandtheoffset segment. Figure14 Figure14:CompletedSpiralCurveSketch 14:CompletedSpiralCurveSketch :CompletedSpiralCurveSketch (Right(Right-Hand) Hand)

Thesketchiscomplete.SeeFigure14.

PROJECT ONTO PITCH CONE

ThesketchnowneedstobeprojectedontothePCS.Select Edit> Edit>ProjectfromthePull-DownMenu(PDM). roject ThetypeofitemtobeprojectedisCURVE.Selecttheconcentricarc fromsketchfeature. Forthedirection,selectNormaltosurfaceandselectthePCS. SpecialNote:Fromthispointon,itisbesttocreateeachsection SpecialNote: (markedwithS#...)independentlyfromtheothersections. SeeFigure15.

Figure15 Figure15Section 15Section Section Grouping Grouping

8

SectionPlanes[S#PDP] Thisfeaturesetsupthedatumpointusedto orienttheprimarycoordinatesystem. References

SelecttheSectionPitchLinePoint(SDP)then theTXZPLN.Itshoulddefaulttothroughand parallelrespectively. EXCEPTION

FortheCenter,FW/2,point,thisfeatureisnot created;thepointisthereference. Figure16 Figure 16:SectionPlane(TYP) 16:SectionPlane(TYP) :SectionPlane(TYP)

SeeFigure16.

SPIRAL CURVE DATUM POINTS [S#CDP]

Thisisusedtoorientthesection’sprimary coordinatesystem’s‘X’axis. References

SelecttheS#PDPandtheSpiralCurvePath. Note:TheS#PDPshouldautomaticallybe Note: selectedifcreatedimmediatelyafteritscreation. EXCEPTION

FortheCenter,FW/2,point,thisfeatureisnot created;thepointisthereference. SeeFigure17. Figure17 Figure17:SpiralCurveDatumPoint(TYP) 17:SpiralCurveDatumPoint(TYP) :SpiralCurveDatumPoint(TYP)

ThisconcludestheSpiralGearSpecificFeaturecreation. Section Coordinate Datums

Therearethree(3)coordinatesystemsneededtocreatethetooth.Thesecondaryandtertiaryare copiesoftheprimary. PRIMARY [SXPCSYS]

References

TheOriginforallPCSYS’sisthecorrespondingAxial DatumPointfromtheSDPfeature. Thepositive‘X’directionissetusingthe: STRAIGHT TOOTH GEARS

CorrespondingSDPpointalongPitchLine SPIRAL TOOTH GEARS

CorrespondingPrimaryDatumPlane/CurvePoint, S#CDP Thepositive‘Z’directionissetusingtheZ-axisofthe TCSYS.

Figure18 Figure18:PrimaryCSYSReferences 18:PrimaryCSYSReferences :PrimaryCSYSReferences

SeeFigure18&19. 9

SECONDARY [S#SCSYS]

ThisisaRotatedCopyofthePCSYS.Select Edit>F Copy, dit>Feature >FeatureO eatureOperations OperationsfromthePDM.SelectC perations opy, thenM Move/ Dependent//Done. ove/Dependent one PicktheS#PCSYSthenD Done.SelectR Rotate/ one otate/CSYS SYS andpicktheTCSYS.SelectZ Zaxis Zaxis/ axis/Okay. kay Enteranarbitraryangle.SelectD DoneM oneMove Movethen ove Done/ one/OK. OK Relation Figure19 Figure 19:SectionPrimaryCoordinateSystem 19:SectionPrimaryCoordinateSystem :SectionPrimaryCoordinateSystem

Editthefeatureandsetthedimensionvalueequalto TCRA(relationequation).

TERTIARY [S#TCSYS]

ThisisaRotatedCopyofthePCSYS.SelectE Edit>F dit>Feature >FeatureO eatureOperations OperationsfromthePDM.Select perations Copy,thenM Move opy, ove/Dependent Dependent ependent/Done. one PicktheS#TCSYSthenD Done.SelectR Rotate/ Zaxis Flip one otate/CSYSandpicktheTCSYS.SelectZ SYS Zaxis/ axis/F /Okay /Okay. kay Enteranarbitraryangle.SelectD DoneM oneMove Done/ one/OK. OK MovethenD ove Relation

EditthefeatureandsetthedimensionvalueequaltoTCRA(relationequation). Proto Tooth

Foreachsection,regardlessoftoothtype,therearefour(4)curvestobegenerated. SECTION CURVES

Theauthoremployedthefollowingstrategy.TheinvolutecorrespondingtotheS#SCSYSwas created,followedbythesidecurve.Thiswasrepeatedfortheoppositeside.Thecurvesare numbered1through4. Parametric Equations R=D##*COS(PRESSURE_ANGLE) THETA=T*45 THETA_RAD=PI/180*THETA  X=R*(COS(THETA)+(THETA_RAD*SIN(THETA)))  Y=R*(SIN(THETA)-(THETA_RAD*COS(THETA)))

Hint:Entertheequationsintoatextdocumentforeasyaccess. Hint: Involute Curve [S#C{1;3}]

CreatethisfeaturewiththeD DatumC atumCurve Curve>FromEquat urve>FromEquation >FromEquationoption. ion SelectthecoordinatesystemfromthemodeltreeandusetheCartesian Cartesianequationstyle. Cartesian FortheS#SCSYS: Enterequations,substitutingthesection’scorrespondingSDPreferencedimensionfortheD##in the‘R=D##…’part.Adanegativesign(-)infrontofthe‘R’forthe‘Y’equationsothatitresembles ‘Y=-R…’ FortheS#TCSYS:

10

The‘D##’isthesameasaboveforthesectionbeingcreated.Thenegativesign(-)isnotapplied inthisinstance. Side (Axis to Involute) Curve [S#C{2;4}]

ThisiscreatedwiththeDatumCurve>ThruPoints DatumCurve>ThruPointsoption.Thereferencesarefromthe DatumCurve>ThruPoints correspondingAxialDatumPointfromtheSDPfeaturetotheinnerendpointoftheInvoluteCurve. SeeFigure20. Tangencycanbeapplied,selectingEnd Endfromthemenuandpicktheinvolutecurve.Thetangency End arrowshouldpointawayfromtherotationaxis. SeeFigure21.

Figure20 Figure 20:SideCurveCreation 20:SideCurveCreation :SideCurveCreation

Figure21 Figure21:SideCurveTangency 21:SideCurveTangency :SideCurveTangency

GROUP SECTION FEATURES

Fororganizationalpurposes,itisagoodpracticetogroupspecificsectionfeaturestogether. ForStraightToothedgears,grouptheCoordinateSystemsplustheCurves. ForSpiralToothedgears,groupallfeaturesfromtheS#PDPtoS#C4. Collapsethecopiedcoordinatesystemsifnecessary. Hint:Hidingthegroupaftercreationallowseasier Hint: visibilitywhenconstructingproceedingsections. SIDE SURFACE [T{L/R}S]

Forthesesurfaces,usetheInsert>Blend>Surface Insert>Blend>Surface Insert>Blend>Surface optionfromthePDM.UsetheGeneral General; SelectSec; General SelectSec andSmoothselectionstodefinethefeature. Smooth Foreachsection,selectadjoiningcurves.Repeatas necessary.Thenrepeatfortheoppositeside. Hint:SelectingtheSideCurvefirsteliminatestheneed Hint: tomodifythestartpoints. SeeFigure22. Figure22 Figure22:SideSurfaceSelection(TYP) 22:SideSurfaceSelection(TYP) :SideSurfaceSelection(TYP)

11

REVOLVED TUBE SURFACE [RTS]

Thisfeaturesetsupthesurfaceinwhichthesidesurfacesenclosetobecomethesolidtooth.Itis aRevolved Revolved BothSides. RevolvedSurface SurfaceFeature rfaceFeaturerevolvedthrough90°onBothSides Feature BothSides ForthePlacement: Straight Tooth Gears:

PicktheUsePrevious option. Spiral Tooth Gears:

ThesketchplaneisdefinedastheTYZPLN,withthetopreferenceastheTXZPLN. Sketch References: •

TCSYS

•

Heel Pitch Point (PITCH_DIAMETER/2)

•

Toe Pitch Point (FACE_WIDTH) Geometry

DrawaConstructionLine(CL)horizontallythroughtheTYSCSreferencepoint.PlaceanotherCL throughbothPitchPoint(PP)references;thisdefinesthePitchLine.  AddadditionalCLsthrougheachPPthatarenormaltothePitchLine. OnthenormallinethroughtheheelPP,placeoneSketchPointabovethePitchLineandone below.DimensionthepointsfromthePitchLine.Theupperdimensionisequaltothe  ADDENDUM.ThelowerisequaltotheDEDENDUM. Througheachpoint,makeaCLatananglewithnootherconstraints.Theweakdimensions shouldbeangularfromthehorizontalCL.Modifytheupperpoint’sdimensiontobeequaltothe FACE_ANGLEandthelowerequaltotheROOT_ANGLE. TraceageometrylinebetweenthesketchpointsandalongthefaceangleCLtotheintersection withthetoePPnormalCL.  Atthispoint,thegeometrydiffersforeachtoothtype. CUP FACE TOOTH

DrawalinealongtheCLtowardstherootangleCL. SeeFigure23. Tip:Azoominmayberequiredforproperlyconstrainingthegeometry. Tip: FLAT FACE TOOTH

DrawalineverticallydowntowardsrootangleCL. SeeFigure24. ClosethegeometrybydrawingalinealongtherootangleCLtothededendumpoint.

Figure23 Figure23:CompletedFlatFacedToothSketch 23:CompletedFlatFacedToothSketch :CompletedFlatFacedToothSketch

Figure24 Figure24:CompletedCupFacedToothSketch 24:CompletedCupFacedToothSketch :CompletedCupFacedToothSketch

12

SURFACE MERGE

ReferringtotheFlatFaceToothExceptionintheSectionDatumPointLayoutsection,the modificationtotheinnermostpoint’sdimension,changetoFW/2  ,mustbeperformedbefore proceedingforthattypeofgear. First Feature

SelecttheRTSandone(1)sidesurface(theorderisunimportant).FromthePDM,select Edit>Merge.Flippingthesidesmaybenecessaryforproperclosure. Edit>Merge SeeFigure25. Second Feature

Selectthefirstmergefeatureandtheremainingsurfaceandrepeattheprocedureasstated above. SeeFigure26.

Figure25 Figure 25:FirstSurfaceMerge(Representative) 25:FirstSurfaceMerge(Representative) :FirstSurfaceMerge(Representative)

Figure26 Figure26:SecondSurf. 26:SecondSurf.Merge(Rep.) :SecondSurf.Merge(Rep.) Merge(Rep.)

Figure27showsthefinalresultsforthelatFacedStraightToothandCupFaced(right-hand) SpiralTooth.

Figure27 Figure27FinalToothForms 27FinalToothForms FinalToothForms SOLID TOOTH

SelectthesecondmergefeatureandfromthePDMselectEdit>Solidify Edit>Solidify Edit>Solidify ThePinion/Mitertemplateisnowcomplete,sosave. Gear Template

TomaketheGeartemplateitisbesttousethePiniontemplateasatemplate,doublingthe NUMBER_OF_TEETHparameter.Geometryconstructionfailurewilloccurforthesecondsurface feature,andthusthesolidifyfeatureaswell. 13

ChoosetoClipSuppress ClipSuppressthefaults. ClipSuppress Redefinethefirstmergeflippingthedirectionsasnecessaryforproperclosure. Un-suppressthesecondmergefeatureandperformthesameredefinitionroutine. Finally,un-suppressthesolidifyfeature. TheGeartemplateisnowcomplete,sosave. Tip:Todisplayabettermeshrepresentationinuse,modifyeitherthePinionortheGearTCSYS Tip: dimensionfromthearbitraryangleuseduponcreationtoeither0°or90/NUMBER_OF_TEETH. Thematinggear’stemplatedimensionisthenadjustedtotheremainingvalue.Anexception pertainswhenMiterGearsarecreatedsincebotharederivedfromPiniontemplates.

Using the Templates

Thefollowingnowdescribesthemethodtobuildagearset. INITIAL MODIFICATION

 Afteropeninganewpartwithatemplate,PinionorGear,itisbesttomodifyanyknowntooth geometrytothemanufacturer’svalues. Therearefourmainvaluesthatcanbemodifiedtoadjustthetoothform. •

 ADDENDUM

•

DEDENDUM

•

FACE_ANGLE

•

ROOT_ANGLE

ThesearethedrivingdimensionsfortheRTS,tomodifythem,openTools>Relations Tools>Relationsfromthe Tools>Relations PDM.Atthebeginningofeachdefinition,place‘/*’(slashstar).Thisactioncommentsoutthatline. NextopenTools>Parameters Tools>Parametersandphysicallymodifythevaluestothe Tools>Parameters knownvaluesandregeneratethemodel.  AnyflatsorroundscanbeaddedbymodifyingtheRTSsketchwiththe appropriategeometry. Tip:Asketchpointwillneedtobeplacedattheintersectionofthetoe Tip: normalCLandthefaceangleCLasadimensionreference. PINION / MITER

Tooth Group

Toefficientlypatterntheprototooth,allfeaturesfromtheTCSYStothe Solidifyaregrouped.Ensureallbrancheswithinthesefeaturesare collapsed.SelecttheTCSYSand,withthe‘Shift’keydepressed,select theSolidifyfeature.PresstheRightMouseButton(RMB)andselect Group. Group SeeFigure28. Pattern

SelectthegroupcreatedaboveandRMBandselectPattern Pattern.Select Pattern theTCSYSzrotationalangleasthedrivingdimension.Enteran arbitraryangleandleavethenumberofcopiesatthedefaultvalueof two(2). SeeFigure29.

Figure28 Figure28:GroupFeatures 28:GroupFeatures :GroupFeatures

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RELATIONS

SelectthepatternandRMB.PickEdit Editfromthe Edit menu.Selecttheangledimensionandenter NUMBER_OF_TEETH,agreeingwiththerelation uponexiting. FromthePDMpickInfo>Switch Info>SwitchDims Info>SwitchDims.Notethe Dims dimensionforthenumberofcopiesinthepattern, P##  . OpentheTools>Relations Tools>RelationsfromthePDM.Scroll Tools>Relations tothebottomandentertherelation: P##=NUMBER_OF_TEETH.Thisdimensional typecannotbedirectlymodifiedintoarelation. Figure29 Figure 29:ToothPatternDimension 29:ToothPatternDimension :ToothPatternDimension

SeeFigure30.

Note:Awarningwilldisplayinformingofdisconnection Note: inallcopiesofthetooth.Afterthecoreisbuilt connectionwilloccur. Core

Forclarityofworkspace,itwouldbebeneficialtomodify thedisplayto“WireFrame”mode. ThecoreisaRevolvedSolidFeature RevolvedSolidFeaturerotatedthrough RevolvedSolidFeature 360°. Note:Therearemanyvarietiesofgearblanks.Forthe Note: sakeofsimplicity,onlythebasicmiterstyleinstructions aregiven.Othergeneraltypesareintheexamplefiles forreference.

Figure30 Figure30:CompletedPattern(Rep.) 30:CompletedPattern(Rep.) :CompletedPattern(Rep.)

SKETCH PLANE

ThesketchplaneistheRight(PYZPLN)withtheTop(PXZPLN)asthetopreference. REFERENCE GEOMETRY

SelectthePartCoordinateSystem(PCSYS)asthereference. SKETCH, CONSTRUCTION GEOMETRY

ThecoresketchbeginsasacombinationoftheSPDandRTSsketches.AhorizontalCLisplaced throughthePCSYSreference.Asecond,angledCLisplacedthroughtheTCSYSfromthelower lefttotheupperright,thePL.ModifytheweakdimensiontobeequaltothePCA. PlaceasketchpointontheupperportionofthePL,theHeelPitchPoint(HPP).ModifytheWeak DimensiontoberelatedtoPITCH_DIAMETER/2. PlaceanotherpointonthePLbetweentheHPPandthePCSYS,theToePitchPoint(TPP).This istobedimensionedfromheelpointalignedwiththePL.Thedimensionvalueisequaltothe FACE_WIDTH(FW).  AddadditionalCLsthrougheachPPthatarenormaltothePL. OnthenormallinethroughtheHPP,placeoneSketchPointbelowthePL.Dimensionthepoint fromthePLequaltotheDEDENDUM. Throughthepoint,makeaCLatananglewithnootherconstraints.Theweakdimensionsshould beangularfromthehorizontalCL.Modifythepoint’sdimensiontobeequaltotheROOT_ANGLE.

15

FLAT FACE GEARS 

 AddanadditionalpointabovetheHPP.TheupperdimensionisequaltotheADDENDUM. Throughthepoint,makeaCLatananglewithnootherconstraints.Theweakdimensionsshould beangularfromthehorizontalCL.Modifythepoint’sdimensiontobeequaltotheFACE_ANGLE. PlaceaVerticalCLthroughtheintersectionthefaceangleandToenormalCL. SKETCH, FEATURE GEOMETRY

DrawahorizontallinebetweentheTPPpasttheHPP,thenaverticallineuptoaboutmidwayto theHPP.Next,drawanotherhorizontallinetowards,butnotto,theHPPNormalCL. Note:ForFlatFaceGears,ignorethenextinstruction. Note: Modifythefirstline’sweakdimensiontobeequaltotheBORE_LENGTH. Modifythelastline’sweakdimension(itshouldbethelengthfromthesecondline)tobeequalto theHUB_LENGTH.  AddahorizontaldimensionfromthePCSYS referencetothevertical(second)line.Thisis equaltotheMOUNTING_DISTANCE.Besure thatthecoordinatereferencepointisselected. SeeFigure31.  AddadiametricaldimensionbetweentheBore LengthlineandtheHorizontalCL.Thisisequal totheBORE_DIAMETER.  AddadiametricaldimensionbetweentheHub LengthlineandtheHorizontalCL.Thisisequal totheHUB_DIAMETER. DrawalinefromtheappropriateToeDedendum Figure31 Figure 31: 31:PCSYSReference :PCSYSReference PCSYSReference Point,forthetypebeingconstructed,totheHeel DedendumPoint.Then,drawalinealongtheHPPnormalCLsothattheendpointisconstrained collinearlytotheHubLengthline.Fillanygap,ifoneexists,betweentheendpointsofthetwo lines. SeeFigure32. CUP FACE GEARS 

DrawalinealongtheTPPnormalCLtowardsthe horizontalCL,butnottoit.Drawaverticallinefrom thefreeendpointoftheBoreLengthlineuptowards thepreviousline.Trimtointersect. SeeFigure33. FLAT FACE GEARS 

Figure32 Figure 32:GapFiller 32:GapFiller :GapFiller

DrawalinefromtheDedendumCLandVerticalCL intersection,atthetoeend,verticallydownwards towardstheBoreLengthline.Trimtointersect.

Thesketchisnowcomplete.Saveandclosethesketchandfeature.SeeFigure34.

16

Figure33 Figure33:CoreSketch&Relations 33:CoreSketch&Relations :CoreSketch&Relations GEAR

Gear Tooth

Usetheappropriatetoothtemplateandmodifytheparameters forthetooth. Note:Theauthorusesthenamingstructure:PARTNote: NAME_T.PRTforthetooth.Thegearassemblyisnamed: PART-NAME_PRT.PRT.ThegearcoreisnamedPARTNAME.PRT,sincethiswillbethepartusedwithitsmate. Figure34 Figure 34:Pinion 34:Pinion :Pinion

Gear Part Assembly

Theonlyaddition,besidestheNUMBER_OF_TEETH parameter,toabasicassemblyfileistheadditionofadatumaxisusedtoalignthetoothpart. UsetheassemblytemplateandmodifytheNUMBER_OF_TEETHparameter.Assemblethetooth (PART-NAME_T.PRT)usingthePCSorRTSaxisasanAlignoptiontotheGEAR_AXISaxis. UsethePXZPLNorPYZPLNtomateusingtheanglealigntypeofconstrainttotherespective assemblyplane.AssemblethePXYPLNtothe PAXYPLNwithazero(0)offset. Patternthetooth,RMB>Pattern RMB>Pattern,andusethezero(0) RMB>Pattern dimensiontodrivethepattern.Theincrementis 360/NUMBER_OF_TEETH,agreeingtotherelation. Leavethenumberofcopiesasthedefaultvalue(2). UnderTools>Relations Tools>Relations,enter Tools>Relations Dy=NUMBER_OF_TEETH,whereDyisthedimension forthenumberofcopies(Info>SwitchDims Info>SwitchDimstoverifythe Info>SwitchDims dimensionnumberbeforehand). SeeFigure35.

Figure35 Figure35:PatternedGearToothPart 35:PatternedGearToothPart :PatternedGearToothPart

Gear Core

DrawthecoreinasimilarmannerasthatoutlinedinthePinion/MiterCoresectionabove, modifyingtheproceduretosuitthetype. SeeFigure36. Insertintothegearpartassemblyusingacoordinatesystemmate.SeeFigure37.

17

Figure36 Figure 36:GearCoreSketch&Relations 36:GearCoreSketch&Relations :GearCoreSketch&Relations

Merge

Figure37 Figure37:GearPartAssembly 37:GearPartAssembly :GearPartAssembly

Nowthepatternedteethareaddedtothecore. UnderEdit>ComponentOperations>Merge Edit>ComponentOperations>Merge,SelectthecorepartandclickOK OK. Edit>ComponentOperations>Merge OK IntheModelTree,expandthetoothpatternsothatallinstancesaredisplayed. Selectfirstinstance,andwiththeShift  keyhelddown,selectthelastinstanceandclickOK OK. OK Fortheoptions,selectReference Reference,OK NoDatums. Reference OK,andNoDatums OK NoDatums SelectDone Doneonetimeforeveryinstance! Done ThenselectDone/Return Done/Returnafterthelasttoothhasbeenadded. Done/Return Mating Pairs

 ASSEMBLY SETUP

Therearetwomethodsinwhichthegearpairisusedinanoverallassembly. Existing Shafts

Thisisthemostlikelymethodtobeemployed. Usetheboreandtheappropriateshaftsegmentasmatingreferences.Matethemountingsurface totheshaft.Mateoneofthepartplanesperpendiculartothegearaxistoasimilarshaftplane. Tip:Useanangulartypeonthelastconstraintsothatanangleisathandtoallowrotational Tip: adjustment,ifrequired(seebelow). First Parts

Twoaxesarerequiredwiththemutualincludedshaftanglebetweenthem.Alsorequiredaretwo planes(orsurfaces),eachnormaltotherespectiveaxisforthegear.Theplanescanbeateither thecommonvertexortheactualmatingdistanceforthegear.Itwouldbebeneficial,forrotational alignment,tohaveacommonassemblylevelplanethroughbothaxes. Theauthor,intestcases,usedplanesatthecommonvertex. MATING CONSTRAINTS

Eachgearisassembledwitha“PinConnection”constraint.Thisallowsfortheapplicationof BehavioralModeling. Thepredefinedassemblyaxisisconstrainedtothe‘core’featureaxisofthegearfortheAxis alignment. ThePXYPLNortheactualmountingsurfaceisthepartreferencewhiletheprescribedmating surfacesaretheassemblyreferencefortheTranslation. TheRotationAxisreferencewouldbethecommonplanethroughbothaxesasmentionedabove. Setthezeropositionforbothgearsinthesetsothatthepairappearsinmesh. Remembertocheckthe“Enableregenerationvalue”toregainmeshappearance. 18

 ANGLE MODIFICATION

Onoccasion,todisplaythegearpairinproper mesh,itwillbecomenecessarytomodifythevalue fortheRotationAxistosomevalueotherthanzero (0).Intestcases,thevaluewas5°.Rememberto resettheregenvalue(makezero).SeeFigure38.

Figure38 Figure 38:AssemblyAngleModification 38:AssemblyAngleModification :AssemblyAngleModification

Modifying Gears

ZEROL BEVEL GEARS

BysettingtheSpiralAngletozero(0),thegearwillgeneratewith “Zerol”styleteeth.

CROWNING

Bymodifyingtherotationalangleamount,viapercentages,Tooth Crowningcanbesimulated.SeeFigure39.

Figure39 Figure39:Crowning 39:Crowning :Crowning Modification Modification

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