1、11FTM25AGMA Technical PaperControlling GearDistortion and ResidualStresses DuringInduction HardeningBy Z. Li, and B.L. Ferguson,Deformation Control Technology,Inc.Controlling Gear Distortion and Residual Stresses DuringInduction HardeningZhichao (Charlie) Li, and B. Lynn Ferguson, Deformation Contro
2、l Technology, Inc.The 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.AbstractInduction hardening is widely used in both the automotive and aerospace gear industries to minimiz
3、e heattreat distortion and obtain favorable compressive residual stresses for improved fatigue performance. Theheating process during induction hardening has a significant effect on the quality of the heat-treated parts.However,thequenchingprocessoftenreceiveslessattentioneventhoughitisequallyimport
4、ant. DCTspastexperiences have shown that the cooling rate, the fixture design and the cooling duration can significantlyaffectthequalityofthehardenedpartsintermsofdistortion,residualstresses,andthepossibilityofcracking.DANTE,acommercialFEAbasedsoftwaredevelopedformodelingheattreatmentprocessesofstee
5、lparts,was used to study an induction hardening process for a helical ring gear made of AISI 5130 steel. Prior toinduction hardening, the helical gear was gas carburized and cooled at a controlled cooling rate. Thedistortion generated in this step was found to be insignificant and consistent. Theref
6、ore, the modelinginvestigation in this paper focused on the spray quench of induction hardening process. Two inductionfrequenciesinasequentialorderwereusedtoheatthegearteeth. Afterinductionheating,thegearwassprayquenched using a polymer/water solution. By designing the spray nozzle configuration to
7、quench the gearsurfaceswithdifferentcoolingrates,thedistortionandresidualstressesofthegearcanbecontrolled. Toothcrown and unwind were predicted and compared for different quenching process conditions. The studydemonstrates the importance of the spray duration on the distortion and residual stresses
8、of the quenchedgear.Copyright 2011American Gear Manufacturers Association1001 N. Fairfax Street, 5thFloorAlexandria, Virginia 22314October 2011ISBN: 978-1-61481-025-43 11FTM26Controlling Gear Distortion and Residual Stresses During Induction HardeningZhichao (Charlie) Li, and B. Lynn Ferguson, Defor
9、mation Control Technology, Inc.IntroductionHigh frequency induction hardening is more environmentally friendly than traditional quench hardeningprocesses such as gas furnace heating followed by immersion quenching in oil. It also provides flexibility incontrol on the case depth, residual stress stat
10、e, and part distortion. Due to these advantages, the inductionhardening process is widely used in the gear industry for case hardening. During induction heating, theenergy to heat the part is generated internally by eddy currents in response to the imposed alternatingmagnetic field. The energy densi
11、ty distribution in the near-surface layer is directly related to the distancebetween the inductor and the part, as well as the frequency of the inductor. Lower frequency heats the partdeeper over longer time period because the eddy current gradient in the part surface is lower, meaning theJouleheati
12、ngextends deeper intothepart interior. Incontrast, higher induction frequency heats ashallowerlayer over shorter time. The temperature distribution in the part is a combined result of induction heating,thermal conduction and phase transformations.In many induction hardening processes, both medium an
13、d high frequencies are used to reach the desiredtemperature field and hardened case depth. The heating may be a two step process, i.e., a differentfrequencyforeachstep,orasinglestepwithdualfrequencyapplication. Simultaneousdualfrequency(SDF)induction heating applies both medium and high frequencies
14、in the part simultaneously to generate a moreuniform temperaturedistributionincurved surfaces such as gear toothprofile. 1 Theenergy percentageofmediumandhighfrequenciesduringSDFinductionheatingcanbeadjusted,whichprovidesgreater flexibilityin controlling temperature distribution in complicated part
15、shapes. The other common induction hardeningprocess for gear components is to apply two sequential induction frequencies. Lower frequency is normallyused first to heat the gear root, followed by higher frequency to heat the gear tip. A time delay can also beapplied between the two frequencies to mor
16、e flexibly control the temperature distribution in the component.Inductionhardeningisatransientthermalprocess. Duringinductionhardeningofsteelcomponents,boththethermalgradientandtheextent ofphasetransformationsimultaneously contributetotheevolutionofinternalstresses and distortion. Recent developmen
17、ts in heat treatment modeling technologies make it possible tounderstand the materials response during heat treatment processes, such as how theinternal stresses anddistortion are generated. DANTE is a commercial FEA based software developed for heat treatmentmodelingof steelcomponents,includingfurn
18、aceheatingwithliquidorgas quenching,or inductionhardeningprocesses with spray quenching. 2 DANTE was not developed to model the electromagnetic physics ofinductionheating. Atemperaturedistributionpredictedfromaninductionheatingmodelorfromexperimentalmeasurements can be imported to drive the model. D
19、ANTE can also be effectively used to simulate thetemperature field produced during induction heating by using Joule heating, i.e., i2r heating, based on thedepthof thehardenedcaseinthepart.3 Inthispaper, acarburizedhelicalgear wasinductionheatedusingtwo sequential induction frequencies, followed by
20、spray quenching. The effect of spray quenching on thedistortion was studied using the modeling results.Material characterization for heat treatment modelingThe ring gear studied in this paper was made of AISI 5130 with a chemical composition of 0.83% Mn,0.22% Si, 0.15%Ni, 0.80%Cr, 0.04%Mo, and0.30%C
21、inweight percentage. The gear was gas carburizedprior to induction hardening to improve the strength of the surface layer. To model the induction hardeningprocess, the phase transformation data of base carbon and high carbon steels of this grade are needed.Dilatometryexperimentsweredonepreviouslyfor
22、thissteelgradewithseriesofcarbonlevels.4 Figure 1(a)shows the dilatometry experimental data for continuous cooling of AISI 5140. The phase transformationkinetics for bothmartensitic anddiffusivephasetransformations werefittedfromthis typeof dilatometrydata4 11FTM26with different carbon levels and te
23、sting conditions. Isothermal transformation diagrams, i.e., TTT diagrams,canbegeneratedfromDANTEdatabaseasshowninFigure 1(b) forAISI 5130. Theisothermalandcontinu-ous coolingdiagrams canbegeneratedtoevaluatethehardenability of agivensteelgradeand carbonlevel.Themechanicalpropertiesarealsorequiredtom
24、odelthedistortionandresidualstresses fromtheheattreat-ment of steelparts. Themechanicalproperties,i.e., yield,hardeningandrecovery changewiththecomposi-tionof different phases, carboncontent andtemperature. InDANTE, themechanicalproperties of individualphasesaredefinedbasedonexperiments. Amixturelaw
25、isusedtodescribetheglobalresponseofthemater-ial linking with the phase transformation kinetics.Finite element modelingA CADmodelof theringgear is showninFigure 2(a). Thegear has 92inner teethwithhelicalangle. Thetipdiameteris155mm,theouterdiameteris182mm,andtheheightis32mm. Asingletoothfiniteelement
26、modelwascreatedandis showninFigure 2(b). Thefiniteelementmodelhas23,372nodesand20,784hexahedralelements. Fineelementsareusedintheshallowsurfaceofthegeartomoreaccurately catchthecarbonandthermal gradients during heat treatment. Cyclic symmetric boundary conditions are applied, so the singletooth mode
27、l represents the whole gear with assumption that all the teeth behave the same during the heattreatment process.a) Dilatometry test of AISI 5140 b) Isothermal transformation diagram of AISI4130 generated from DANTE databaseFigure 1. Phase transformation kineticsFigure 2. (a) CAD model of transmissio
28、n gear, and (b) single tooth finite element model5 11FTM26Pre-Induction hardening processPriortoinductionhardening,thegearwasgascarburized,followedbyacontrolledslowcooling. Thecarburiz-ationprocesswasusedtoincreasethehardnessandstrengthofthesurfacelayer. Thecarburizationtemper-ature was 875 C, and t
29、he carbon potential of the furnace was 0.80%. The total carburization time was 2.0hours. Figure 3(a) shows acut viewof carbondistributionat theendof thecarburizationprocess. Thesharpcorner of the gear tip has a slightly higher carbon than the other surfaces due to the geometry effect. Thecarbondistr
30、ibutioninterms of depthfrom theoutersurfaceisshowninFigure 3(b). Theapproximatecarboncasedepth,definedby0.45%carbon,is0.35mm. Aftercarburization,thegearwascooledtoroomtemperat-ureinacontrolledatmosphere. Theobtainedmicrostructureinthecoreofthegearis mainlypearlite, andthecarburized case has a combin
31、ation of martensite andbainite. The distortionfrom thecontrolled coolingpro-cessisconsistent,whichcanbecompensatedfromthegeardesignbyadjustingthegreenshapedimensions.Therefore, this study focused on the induction effect of the induction hardening process.Induction hardening processTwo sequential ind
32、uction frequencies were used to heat the inner gear teeth, and there was a short delaybetween the two heating stages. A brief schedule of the induction hardening is listed below:S Medium frequency heating for 4.0 seconds,S Dwell for 0.75 seconds,S High frequency heating for 0.45 seconds,S Spray quen
33、ch.Instead of modeling the physics of the electromagnetic filed generated by the inductor, the DANTE modeldirectlyappliestheheatpowerbytheeddycurrentinthepartfollowingtheJoulerule,asshownschematicallyin Figure 4. Uniform heat energy distribution in the gear axial direction was assumed. Medium freque
34、ncyheating generates more heat in the gear root, while high frequency heating generates moreheat inthe tipofthetooth. Thedwelltimebetweenthetwoheatingstagesisimportantasthisallowstimeforthermaldiffusion.The heat energy applied in the model can be adjusted to improve model accuracy using data from ex
35、peri-ments with thermocouples and metallography of the hardened case profile. The latter method is used inthispaper. Alternatively, thepower distributionpredictedby inductionsoftwaresuch as ELTA couldalso beusedtodrivetheDANTE model.5 Inthis paper, results for oneinduction heatingand twospray quench
36、ingscen-arios are presented. Spray quenching is assumed to start immediately after the heating step without delay.ResidualstressstatesanddistortionwerepredictedusingDANTE,andtheeffectsoftheprocessvariablesondistortion are discussed.a) Contour plot b) Curve plotFigure 3. Carbon distribution6 11FTM26F
37、igure 4. Schematic plot of eddy currents in the part during induction heatingThe temperature and austenite distributions after each heating stage are shown in Figure 5. After 4.0seconds of heating using a medium frequency, the surface temperature of the gear root is about 815C, thetooth tip is about
38、 700C, and the ODsurface temperatureis about 280C. The gear root areais predictedtohave formed austenite, but the tooth tip has not. During the 0.75 seconds dwell, the heat diffuses from theinnertotheoutersurfacebythermalconduction. Asmallamountofheatislosttotheenvironmentbyradiationand air convecti
39、on, which is also included in model. At the end of the 0.75 second dwell period, the gear tiptemperaturehas hadasmalldrop, but thetemperatureat thegear root has droppedsignificantly from 815Cto595C.Thetemperatureattheouterdiametersurfacehasincreasedfrom280Cto350C. Nophasetrans-formation occurs durin
40、g the dwell time. The third stage is a high frequency heating for 0.45 seconds. At theendof thethirdstageheating, thetemperatureat thetoothtiphas increasedto1050C,theroottemperaturehas increasedto850C, andtheODsurfacetemperaturehasincreasedto380C. Theaustenitedistributionprofile is shown in Figure 5
41、(c).After induction heating, the gear is spray quenched to room temperature without any delay. As shown inFigure 6,thegearsurfaceisdefinedas4regionstomodelthequenchingprocess:toothsurface,ODsurface,top end surface and bottom end surface. Quench fixture and spray nozzle configuration were designed to
42、flexibly quencheachindividualsurfacewithcontrolledrate. Inthis paper, awater/polymer solutionwas usedas the quenching media. The average heat transfer coefficient was assumed tobe 5.0(kW/m2K) duringthesprayquench. Twosprayscenariosweremodeledtoinvestigatethequenchingeffectondistortion. Scenario1 spr
43、ayed all the exposed surfaces, and scenario 2 sprayed the tooth surface only.Distortion analysis using finite element modelsThe gear modeled in this paper has a thin wall thickness, and the cooling rate of the water/polymer spray issufficiently fast tomiss thenoseof thediffusivephasetransformations
44、inFigure 1(b). Themartensiticphasedistribution in the actual hardened ring gear closely matches the predicted austenite distribution shown inFigure 5(c). The crown distortion and unwind of the teeth are the two main distortion modes for this gear.DANTE models predicted the nodal displacements after
45、the heat treatment process, and these nodal dis-placementswereusedtocalculatethecrowndistortionandunwindangle. Thecrowndistortioninthispaperisdefinedasthebowingamountofthetoothfaceatthepitchdiameterline,asshownbytheline3inFigure 7forboth sides of the tooth. A simplified equation is used to convert t
46、he predicted nodal displacements to thevalues of bowing.(1)d = U1sin2+ U2cos2whered is bowing value, representing how far the surface point moving away from its original position;7 11FTM26U1 is radial displacements from the model results;U2 is circumferential displacements from the model results; is
47、 tooth angle as shown in Figure 7.The crown distortion is defined as the maximum bowing value from the original position.a) After 4.0 seconds low frequency heating b) After 0.75 seconds dwellc) After 0.45 seconds high frequency heatingFigure 5. Temperature and transformed austenite during heatingFig
48、ure 6. Part surfaces defined for setting up spray quenching model8 11FTM26Figure 7. Tooth surface crown distortion calculation using DANTE modeling resultsThecrowndistortionsofthepitchlinesonbothsidesofthetoothareshowninFigure 8. TheX-axisrepresentstheaxialpositionfrom thebottom endsurfacetothetopen
49、dsurface, withX = 0locatedat apoint 2mm awayfromtheend. Thedisplacementsarecalculatedwitharound2mmawayfromeachendtoavoidthesignificantdistortion on the edge. Without any distortion, all the lines will align perfectly with Y = 0. For the front toothsurface, anegativecrowndistortionvaluemeans bowoutward. For the back tooth surface, a positivecrowndistortionmeansbowoutward. Forquenchingscenario1,thecrowndistortionofthefrontpitchis7.8mm,andthatofthebackpitch5.8mm. Thecrowndistortionofthefrontpitchisreducedbyabout1.0mmforthesecondquenching scenario. However, t
