1、05FTM03Modelling Gear Distortionby: P.C. Clarke, David Brown HeatechTECHNICAL PAPERAmerican Gear Manufacturers AssociationModelling Gear DistortionPhilip C. Clarke, David Brown HeatechThe statements and opinions contained herein are those of the author and should not be construed as anofficial actio
2、n or opinion of the American Gear Manufacturers Association.AbstractDealing with carburize case hardened gear distortion and growth is a challenge for the global gear industry.Attempts started in 1978 with computer programs to calculate distortion and growth, plus residual stressdistributions for a
3、gear and evolved by gathering distortion data for a wide range of sizes, shapes, grindingallowances with trends for different geometries. A spread sheet program with gear dimensional input,calculates the distortions and growths, and then calculates the modified dimensions for requiredprotuberance an
4、d the minimum carburized case depth. Case histories illustrate the consequences of variousgeometries and future developments are discussed.Copyright 2005American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2005ISBN: 1-55589-851-31Modelling Gear D
5、istortionPhilip C. Clarke, David Brown HeatechIntroductionFor high quality carburise case hardened gears apredictive capability combined with close controlover distortion and growth is essential.ASM Handbook Volume 4, ref 1, defines distortionas “An irreversible and usually unpredictablechange of si
6、ze and shape”.This paper seeks to show that there is predictabilityand change of shape is not always irreversible.Initial DevelopmentsOur first driver for a better understanding of distor-tion was dealing with a large face width, double heli-cal gear, ref 2-5. This had 178 x 5.08 module (5DP)teeth,
7、measured 36” on the outside diameter andweighed in at 2.4 tonnes - see Figure 1.Figure 1. Marine Gear Wheel SchematicIn 1978 a research contract was placed by theMOD(N), the British naval procurement agency, onDavid Brown to develop a suite of programs to pre-dict distortion and growth plus residual
8、 stress dis-tributions for the above gear wheel.Partial Success was achieved by:X Modelling CCT diagrams and calculating metal-lurgical transformations during cooling andheating.X Defining a correlation between cast analysisand growth.X Accurately predicting final case and core hard-nesses, ref 6.Fi
9、gure 2 shows the core micro-structural distribu-tions when the tooth roots attain the carburisingtemperature during heating.0% Austenite100% AusteniteFigure 2. Core Microstructural distributionswhen the tooth roots attain the CarburisingTemperatureHowever, attempts to achieve the final objectivewere
10、 thwarted by:X A dearth of theoretical models.X Little data on the mechanical properties of indi-vidual phases at temperature and during trans-formation.X No data for the effect of stress on transforma-tionX Poor computing power.A Pragmatic ApproachDistortion remained a huge problem because wemake l
11、arge numbers of unique large gears and notbeing right first time is unacceptable.A pragmatic approach was adopted starting in theearly 1980s.This required the:Gathering of historical and new data for a widerange of gear geometries and sizes.2Analysis and extraction of trends for specificgeometries.F
12、igure 3 shows the variation of taper with outside di-ameter (OD) for gear wheels. Figure 4 shows howout of roundness (Ovality) varies with outside diam-eter for large ring gears.Figure 3. Gear Wheel OD Taper vs ODWhilst there are clear trends the scatter is large.One clear objective when managing di
13、stortion is toreduce this scatter.As data was collected trends, which depend onshape, emerged. Figure 5 shows the variation ofgrowth rate (thou per inch of outside diameter) withlength/wall thickness ratio. This observation led tothe first classification of shapes as a function ofshape as illustrate
14、d in Figure 6.This classification applies to:1. Gears heat treated with the major axis verticalas illustrated in Figures 2, 7 and 9.2. All gear materials provided that core harden-ability is matched to section size to achieve corehardnesses between 300 and 400 HV.This classification was the key to t
15、he first DavidBrown standard, ref 7, giving distortion and growthallowances for six shapes. Figure 7 is an extractfrom the standard.These allowances were incorporated in 1987 intothe CAD system from which prior and post heattreatment tooth sizes were calculated. Appendix 1shows a sample output page.
16、Figure 4. Ring Gear Ovality vs ODFigure 5. Growth Rate vs Length / WallThicknessFigure 6. Classification of Shapes3Ring ShapeOutside Diam-eter LimitsDistortion andGrowth AllowanceHeat TreatmentProceduresLess than orequal to 20 in1) No growth al-lowance2) Normal grindingallowance1) Axis vertical atea
17、ch stageOver 20 in andless than orequal to 38in(2)1) No growth al-lowance2) Special grindingallowance(3)3) Increased casedepth(3)2) Support at 3points 120Oapart circumfer-entially at eachstage.Over 38 inSubcontractingrequired1) Growth allow-ance .0005 inper in O.D.2) Special grindingallowance3) Incr
18、eased casedepthConsult Metal-lurgy Depart-ment1) Axis vertical ateach stage.(a) Largest O.D.uppermost.(b) Step Heat(c) Support at 3points 120Oapart circumfer-entially.Table Notes1) The minimum wall thickness is a design minimum require-ment except for gears of less than 25 in O.D. and lessthan 50 Kg
19、 in weight which are to be treated as thinwalled tubes.2) 38 in O.D. is the limit for gas carburising at Park Works.3) Until further experience is gained of these sizes.General NoteThe basic helix angle at hobbing is to be reduced by 0o0200”if:(1) The base angle helix exceeds 15oand,(2) The O.D. is
20、greater than 15 in.Figure 7. Extract from Distortion and GrowthStandardManaging Distortion and GrowthHaving defined the trends and identified the scatterthis experience was applied to a specific productrange with the objectives of introducing controlmeasures to reduce both the levels and the scatter
21、of distortion, ref 8.This involved the measurement of all key dimen-sions before and after each stage of heat treatment.For the gear wheels by changing the stacking ar-rangement, increasing spacing between gears andimproving support, see Figure 8, taper and ovality ofoutside diameter, out of flatnes
22、s and cumulativepitch errors were reduced and became more con-sistent. Figures 9 and 10 show the effects of thesemeasures on these distortions.Figure 8. Changing Stacking of Gear WheelsThe significance of cumulative pitch error alsoemerged. Cumulative pitch error is a large elementof gear wheel dist
23、ortion and shows little correlationwith other distortions and growths such as ODtaper, ovality, growth and out of flatness.This means that if a gear wheel is almost round, un-tapered and flat then cumulative pitch remains andcan represent up to 90% of the grinding stock re-moval required to clean up
24、 the teeth.This project also looked at pinions. Measures takenresulted in reductions of out of straightness of up to75%.4Figure 9. Effects of Improved Stacking onMean Gear Wheel DistortionsFigure 10. Effects of Improved Stacking onVariation in Gear Wheel DistortionsLimitationsFrom 1987 to 1998 more
25、data was gradually col-lected, collated and published in 1998, ref 9.Limitations of the standard emerged. These in-cluded: Step changes in allowances when crossingboundaries between shapes. No accurate allowances for cumulative pitch er-ror and lead change. Restricted to tooth sizes and outside diam
26、eters. Maximum gear size.The New TaskIn 1998 the task was to remove these limitations.The first outcome in 2002 was an extended model,SHAPE, in spread sheet form, which: Takes input of tooth and gear dimensions. Calculates the distortions and growths for allthe key dimensions. Calculates the modifie
27、d dimensions to cater forthese distortion and growths. Calculates the minimum carburised case depthand the protuberance required. Outputs warnings for increased grinding times,removal of protuberance and low hardness(due to excessive case depth removal).The size limits for the model were expanded. F
28、orexample the OD limit for gear wheels was increasedfrom 40” to 80”.Figure 11 shows a sample page of the initial calcula-tions with measures including lead corrections andcarburised case depths automatically included.Particular consequences of interest in this exampleare: Unless the protuberance is
29、increased steps willoccur during profile grinding. The minimum case depth at carburizing mustbe increased from 0.044” (1.11 mm) to 0.055”(1.40 mm). The bore growth of 0.066” (1.67 mm) is greaterthan the outside diameter growth of 0.039”(1.00 mm).The second outcome in 2004 was the inclusion ofSHAPE i
30、n a revision of the original distortion andgrowth standard.5Calculation of Grinding Allowances for Carburise Case Hardened GearsPart No : Initial DesignGear Dimensions Teeth Details CommentsOutsideDiameter 800.00 Module 6.0Bore Diameter 300.00 Number 130Facewidth 150.00 Pressure Angle 20Length 150.0
31、0 Helix Angle 25CommentsID/OD 0.38 Length/Wall Thickness 0.60Shape W Shape Code 87OD Growth 1.00 Cumulative Pitch Error 0.24OD Taper 0.60Angular Lead Change inMinutes - 1.31OD Ovality 0.24 Lead Error - 0.057Bore Growth 1.67 Width/Length Shrinkage - 0.90Bore Taper 0.42 Out of Flatness 0.32 *Increase
32、for thin wheelsBore Ovality 0.36Out of Straightness(Pinions)GrindingAllowances Other Allowances CommentsPer Flank 0.292Addition to FinishedCasedepth 0.438 To allow for high spot stock removalOn BoreDiameter 2.29Mod Prior ToothThickness By 0.242 To allow for mean growth and distortionSide Faces 0.44F
33、inished Base Tangent -inches Base Tangent at Hobbing - inchesOutsideDiameter - 0.37 Maximum 9.5020 Maximum 9.5115Minimum 9.5000 Minimum 9.5095Notes Precautions and Actions40% 1. Minimum Recommended 1.40297% Carburised Casedepth to 500HV151%(Standard mincarburisedCasedepth) 1.11Warnings 2. Protuberan
34、ce needed 0.482to avoid steps( Standard Protuberance) 0.290AGMA 2005Calculated Distortions and Growths used to deriveallowancesProfile grinding times will be extendedExtensive removal of standard protuberancewill occurMaximum stock removal as a Percentage of :Minimum Carb CasedepthDB Flank GrindingA
35、llowanceDB Standard ProtuberanceFigure 11. SHAPE Data SheetCase Histories1. Large Ring GearThe shape data sheet for the initial design of thisring gear shown in Figure A of Appendix 2, showsexpected distortions of:Ovality at 0.035” (0.89 mm)Taper at 0.033” (0.84 mm)Out of Flatness at 0.044” (1.12 mm
36、)The consequences of these distortions are:The minimum carburised case depth needs tobe increased from 0.071” to 0.090”.The increase in protuberance from 0.016” to0.030” is unacceptable.Special measures are required to reduce these dis-tortions. These include stress relieving after roughmachining, s
37、upporting the gear on a machinedNickel Chrome plate and step heating to the carbu-rising temperature. By employing these measuresthe distortions, see figure B of Appendix 2, can po-tentially be reduced to:Ovality at 0.012” (0.30 mm)Taper at 0.017” (0.42 mm)Out of Flatness at 0.015” (0.37 mm)This mea
38、ns that:The minimum carburised case depth reducesfrom 0.090” to 0.077”.The required protuberance is restored to0.016”.2. Effects of Cumulative Pitch ErrorWhilst measures can be taken to reduce shape dis-tortions to low levels no method has yet been foundto significantly reduce cumulative pitch error
39、s aris-ing from case hardening.The effects are illustrated in Appendix 3. Calcula-tions for a gear wheel with normal and very low le-vels of OD taper, OD ovality and out of flatness, Fig-ures C and D in Appendix 3, show that the stockremoval per flank required to clean up the gear teethcan only be r
40、educed by 29% from 0.021” (0.523mm) to 0.015” (0.389 mm).3. Consequences of Large Tooth NumbersOne outcome of the model is to show that the grind-ing stock required to clean up gear teeth is6dependent on gear shape and size only and is notdependent on tooth size.This means that, as the number of tee
41、th increases,so do the consequences of distortion together withthe measures needed to control distortion and thecosts of catering for distortion as illustrated in Figure12 for a gear wheel with diameter kept constant.This shows that, without special measures:Localised grinding steps are expected abo
42、ve 70teeth because the predicted maximum grindingstock removal exceeds the protuberance size.Localised loss of surface hardness will occurover 200 teeth because the predicted maximumstock removal exceeds half the minimumeffective case depth.Figure 12. Effect of Gear Wheel ToothNumber4. Hard BoresPas
43、t standards used the bore diameter to specifybore grinding allowances. Unfortunately, unless theratio of outside diameter to bore diameter is con-stant, this method is invalidated by the dependenceof bore diameter growth and distortion on outsidediameter.Figure 13. Effect of Gear Wheel OD on BoreGri
44、nding Allowances.Figure 13 shows the effect of gear wheel O.D. onbore grinding allowance using results calculated us-ing SHAPE. The main consequence is that, whenthe outside diameter exceeds 10.2” for the gears inthis study, case hardened bores are likely to havelocalised soft spots after grinding.
45、Thus above thissize it is recommended that bores are masked toleave soft for turning and grinding after case hard-ening.Conclusions A methodology to calculate distortion andgrowth for wide range of carburised case hard-ened gears has been described. A spreadsheet based model has been devel-oped to c
46、alculate distortion and growth, growthand grinding allowances for all major dimen-sions and minimum carburised case depths.Warnings are generated when criteria such asexcessive case depth reduction and loss of sur-face hardness is predicted. The algorithms can be adapted for changes inheat treatment
47、 practice including: Special techniques to minimise distortion Different quenching systems Specific and generic case histories have beendemonstrated. To date SHAPE has been usedon over 150 different gears for both David7Brown and for sub contract heat treatmentcustomers. While this model is primaril
48、y applicable to gearsheat treated axis vertical, smaller gears (typi-cally 15” OD) treated axis horizontal showsimilar growth trends but with increased ovalityoffset by reduced taper.Future DevelopmentsScope for future development exists in severalareas.1. The results from SHAPE can be correlated an
49、dcompared with theoretical models when theybecome available.2. The database is sufficient to develop statisticalmeasures which can be used to examine worstcase scenarios and develop process capabilityparameters.References1. ASM Handbook Volume 4. Heat Treating. 19912. G.S. HarperThe Distortion and Growth Characteristics ofY205 Primary Wheels.D.B.G.I Report H/M 5837 1979.3. D.W.Ingham, P.C. ClarkeDistortion of Y205 Primary Wheels Changingthe Shape at Heat Treatment.D.B.G.I Report H/P/41.8 1981.4. D.W.Ingham, P.C. ClarkeDistortion of Y205 Primary W
