Niyama Based Taper Optimizations in Steel Alloy Castings

101 Pages·2011·6.58 MB·English

Niyama Based Taper Optimizations in Steel Alloy
Castings
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Science in Engineering
by
Daniel A. Gorsky
B.S.M.E., Purdue University, 2009
2011
Wright State University
Wright StateUniversity
GRADUATESCHOOL
September9,2011
I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPER-
VISION BY Daniel A. Gorsky ENTITLED Niyama Based Taper Optimizations in Steel
AlloyCastingsBEACCEPTEDINPARTIALFULFILLMENTOFTHEREQUIREMENTS
FORTHEDEGREEOFMaster ofScience inEngineering.
RamanaV.Grandhi,Ph.D.
ThesisDirector
GeorgeHuang,Ph.D.
Chair,Mechanicaland
MaterialsEngineering
Committee on
FinalExamination
RamanaV.GrandhiPh.D.
RaghavanSrinivasanPh.D.
ScottK.ThomasPh.D.
AndrewHsu,Ph.D.
Dean,GraduateSchool
ABSTRACT
Gorsky, Daniel. M.S. Egr., Department of Mechanical and Materials Engineering, Wright State
University, 2011.NiyamaBasedTaperOptimizationsinSteelAlloyCastings.
In the casting process, regions of porosity can be reduced or eliminated through the
implementation of taper, or small angled additions of mass on the boundaries of the part
design,beforerisersareplacedonthecasting. Tapersupplementstheeffectofriserssothat
asmallerriservolumeisnecessarytomakeacastingsound. Typically,taperisdetermined
for a casting by using industry guidelines that were developed for simple two-dimensional
simplificationsofacomplexcasting. Thereisnoacceptedmethodofdefiningtaperdirectly
onpartgeometryasidefromusingexpertopinionstomakefinaldecisionsontaperlocations
andsize.
An optimization of taper geometries is performed on two-dimensional casting models
to determine if a Niyama based optimization of taper directly on a part design is possible.
TheNiyamacriterionidentifiessmallregionsofsolidificationshrinkagethatcorrespondto
shrinkageporosityincastingsimulations. Thetaperoptimizationwasperformedonaplate
with riser model and a spindle cross section model to determine the effectiveness of the
optimization methodfor multiple geometries. Thisworkconcludesthattaperoptimization
based on Niyama constraints is possible and effective, but care must be taken when deter-
miningthedesignspaceofthetaper. Itwasfoundthatthesurfacecoolingratesofacasting
can identify effective locations to taper so optimizations can be performed specifically on
thesizeofthetapertoeliminateporosityinacasting.
iii
List of Symbols
Ny Niyamavalue
G Spatialthermalgradient
T˙ Coolingrate
T Niyamaevaluationtemperature
eval
T Solidustemperature
s
T LiquidusTemperature
l
T˙ Coolingratecalculatedanalytically
average
t Solidificationtime
solidification
T˙ Coolingratecalculatedbysimulation
local
Teval−1 Temperatureatthetimeincrement beforeTeval
t IncrementtimewhereT occursinsimulation
solid,inc eval
x Designvariable
m numberofdesignvariables
y˜ Responsesurfaceequation
β Responsesurfacecoefficient
q Numberofresponsesurfacecoefficients
β Vecorofresponsesurfacecoefficients
q
X Matrixofsimulateddesigns
n,q
y Vectorofresponsescorrespondingtosimulateddata
N Numberofsampleresponsesurfaces
p Numberofsampleddatapoints
y Sampledresponsevector
a
y Excludedresponsevector
b
R2 Errorofsampledrespnosesurface
norm
w Weightofsampledresponsesurface
y¯ Mean
σ StandardDeviation
S2 Commonvariance
p
t t-value
S2 Variance
H NullHypothesis
o
α Confidencelevel
L LengthofPlate
T ThicknessofPlate
W WidthofPlate
EZL EndZonelength
RZL RiserZoneLength
CZ CriticalZone
R RiserRadius
R
H RiserHeight
R
A CriticalNiyamaArea
crit,Ny
N¯y AverageCritical NiyamaValue
crit
TG TaperGeometry
iv
Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 DocumentSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 LiteratureReviewandTheory 9
2.1 CastModelingBackground . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 TheNiyamaCriterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 CastOptimization Background . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 ResponseSurfaceMethodology . . . . . . . . . . . . . . . . . . . 15
2.3.2 Weighted-StackResponseSurfaceMethodology . . . . . . . . . . 17
2.3.3 StatisticalComparisons . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.4 CastOptimization Literature . . . . . . . . . . . . . . . . . . . . . 19
2.4 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 SimulationModels 22
3.1 PlatewithRiser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 FiniteElementModel . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.3 ModelResponses . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.4 Critical NiyamaValueforthePlateModel . . . . . . . . . . . . . . 31
3.2 SpindleCasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 FiniteElementModel . . . . . . . . . . . . . . . . . . . . . . . . 34
4 AnalysisandOptimization 37
4.1 PlateTaperGeometryOptimization . . . . . . . . . . . . . . . . . . . . . 37
4.2 SpindleGeometryOptimization . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.1 ParametricInvestigation . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.2 TwoVariableTaperOptimization . . . . . . . . . . . . . . . . . . 41
4.2.3 OneVariableTaperAnalysis . . . . . . . . . . . . . . . . . . . . . 42
v
5 ResultsandDiscussion 44
5.1 PlatewithRiserResultsandDiscussion . . . . . . . . . . . . . . . . . . . 44
5.1.1 TaperAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.1.2 DesignSpaceResponses . . . . . . . . . . . . . . . . . . . . . . . 49
5.1.3 PlateGeometryResponses . . . . . . . . . . . . . . . . . . . . . . 57
5.2 ChoosingaDesignSpacefortheCasting . . . . . . . . . . . . . . . . . . . 61
5.3 SpindleResultsandDiscussion . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3.1 SpindleBaseAnalysis . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3.2 SpindleDesignSpaceDetermination . . . . . . . . . . . . . . . . 64
5.3.3 Two-VariableOptimization . . . . . . . . . . . . . . . . . . . . . . 67
5.3.4 One-VariableOptimization . . . . . . . . . . . . . . . . . . . . . . 73
6 Summary 77
7 FutureWork 79
Bibliography 79
8 Appendix: DataTables 84
vi
List of Figures
1.1 CaterpillarInc. 777OffHighwayTruck[2] . . . . . . . . . . . . . . . . . 2
1.2 High-PressureDie-CastAluminum AlloyEngineBlock[3] . . . . . . . . . 2
1.3 CastingTerminology [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 RadiographViewofSandInclusions[5] . . . . . . . . . . . . . . . . . . . 5
1.5 RadiographViewofSpongyPorosity[5] . . . . . . . . . . . . . . . . . . . 6
3.1 3-DGearapproximated as2-DPlateGeometries[16] . . . . . . . . . . . . 23
3.2 ThreeDimensionalPlatewithRiserModel . . . . . . . . . . . . . . . . . . 24
3.3 Three-DimensionalGeometrywithTwo-DimensionalAssumptions . . . . 26
3.4 TwoDimensionalPlatewithRiserModel . . . . . . . . . . . . . . . . . . 27
3.5 TwoDimensionalPlateModelMesh . . . . . . . . . . . . . . . . . . . . . 28
3.6 CriticalNiyamaAreaMeshRefinement(Ny=0.7) . . . . . . . . . . . . . 30
3.7 CriticalNiyamaArea,Ny≤0.7(◦C-s)1/2/mm . . . . . . . . . . . . . . . . 32
3.8 CriticalNiyamaArea,Ny≤0.2(◦C-s)1/2/mm . . . . . . . . . . . . . . . . 32
3.9 SpindleGeometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.10 NiyamaProfileComparisonofSpindleModels . . . . . . . . . . . . . . . 35
3.11 SpindleFEMesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1 PlateTaperOptimization DesignVariableDefinition . . . . . . . . . . . . 38
4.2 Spindlewith6DesignVariablesforTaperInvestigation . . . . . . . . . . . 40
4.3 SpindleDesignSpacesforTwo-VariableTaperOptimization . . . . . . . . 41
4.4 SpindleDesignSpacesforOne-VariableTaperOptimization . . . . . . . . 43
5.1 PlateAverageNiyamaValue((◦C-s)1/2/mm) ResponseSurface(Eq5.1) . . 45
5.2 PlateCritical NiyamaArea(mm2)ResponseSurface(Eq5.2) . . . . . . . . 47
5.3 RedbookSuggestedTaper . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.4 PadNiyamaValuesEvaluatedatT . . . . . . . . . . . . . . . . . . . . 50
Eval
5.5 PadNiyamaValuesEvaluatedatT (Contour SideView) . . . . . . . . 51
Eval
5.6 PadTemperatureGradientsEvaluatedatT . . . . . . . . . . . . . . . . 52
Eval
5.7 PadTemperatureGradientsEvaluatedatT (Contour SideView) . . . . 52
Eval
5.8 PadCooling RatesEvaluatedatT . . . . . . . . . . . . . . . . . . . . 53
Eval
5.9 PadCooling RatesEvaluatedatT (ContourSideView) . . . . . . . . . 54
Eval
5.10 PadCooling RatesEvaluatedatT (ContourRotatedView) . . . . . . . 54
Eval
vii
5.11 TG10CoolingRatesEvaluatedatT (Contour View) . . . . . . . . . . . 55
Eval
5.12 TG10CoolingRatesEvaluatedatT (Contour RotatedView) . . . . . . 56
Eval
5.13 TG2CoolingRatesEvaluatedatT (Contour View) . . . . . . . . . . . 57
Eval
5.14 TG2CoolingRatesEvaluatedatT (Contour RotatedView) . . . . . . . 57
Eval
5.15 NiyamaValuesofthePlateEvaluatedatT for3TaperGeometries . . . 58
Eval
5.16 CoolingRatesofthePlateEvaluatedatT for3TaperGeometries . . . . 59
Eval
5.17 ThermalGradientsofthePlateEvaluatedatT for3TaperGeometries . 60
Eval
5.18 PlatewithRiserModelEdgeCoolingRates . . . . . . . . . . . . . . . . . 62
5.19 BaseSpindleNiyamaProfile(CriticalNiyamaAreasCircled) . . . . . . . . 63
5.20 SpindleEdgeCoolingRates . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.21 ProposedSpindleTaperLengths . . . . . . . . . . . . . . . . . . . . . . . 66
5.22 AverageNiyamaValue1ResponseSurface . . . . . . . . . . . . . . . . . 68
5.23 CriticalNiyamaArea1ResponseSurface . . . . . . . . . . . . . . . . . . 69
5.24 AverageNiyamaValue3ResponseSurface . . . . . . . . . . . . . . . . . 70
5.25 CriticalNiyamaArea3ResponseSurface . . . . . . . . . . . . . . . . . . 70
5.26 AverageNiyamaValue4ResponseSurface . . . . . . . . . . . . . . . . . 71
5.27 CriticalNiyamaValue4ResponseSurface . . . . . . . . . . . . . . . . . . 72
5.28 One-VariableTaperHeightResults . . . . . . . . . . . . . . . . . . . . . . 76
viii
List of Tables
3.1 RedbookPlateDimensions . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1 ProblemDefinition: FlatPlateTaperOptimization . . . . . . . . . . . . . . 39
4.2 SpindleParametricInvestigation Designs . . . . . . . . . . . . . . . . . . 41
4.3 ProblemDefinition: SpindleTwo-VariableTaperOptimization . . . . . . . 42
5.1 t-TestofPlateAverageNiyamaValues . . . . . . . . . . . . . . . . . . . . 46
5.2 t-TestofPlateCriticalNiyamaAreas . . . . . . . . . . . . . . . . . . . . . 47
5.3 ResponseSurfaceOptimization Results . . . . . . . . . . . . . . . . . . . 49
5.4 PadData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.5 TG10Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.6 TG2Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.7 SpindleCriticalNiyamaArea1Optimization Results . . . . . . . . . . . . 67
5.8 CriticalNiyamaArea1: One-VariableAnalysis(TaperLength=650mm) . 73
5.9 CriticalNiyamaArea3: One-VariableAnalysis(TaperLength=277mm) . 75
5.10 CriticalNiyamaArea4: One-VariableAnalysis(TaperLength=277mm) . 75
8.1 FlatPlateTaperDesignsandResponses . . . . . . . . . . . . . . . . . . . 85
8.2 SpindleParametricInvestigation: AverageNiyamaValues . . . . . . . . . 86
8.3 SpindleParametricInvestigation: CriticalNiyamaNodeTotals . . . . . . . 87
8.4 SpindleParametricInvestigation: CriticalNiyamaAreas . . . . . . . . . . 88
8.5 CriticalRegion1: 2-VariableDesignsandResponses . . . . . . . . . . . . 89
8.6 CriticalRegion3: 2-VariableDesignsandResponses . . . . . . . . . . . . 89
8.7 CriticalRegion4: 2-VariableDesignsandResponses . . . . . . . . . . . . 90
8.8 t-TestofTwo-VariableA ResponseSurface . . . . . . . . . . . . . 90
crit,Ny,1
8.9 t-TestofTwo-VariableN¯y ResponseSurface . . . . . . . . . . . . . . 90
crit,1
8.10 t-TestofTwo-VariableA ResponseSurface . . . . . . . . . . . . . 90
crit,Ny,3
8.11 t-TestofTwo-VariableN¯y ResponseSurface . . . . . . . . . . . . . . 91
crit,3
8.12 t-TestofTwo-VariableA ResponseSurface . . . . . . . . . . . . . 91
crit,Ny,4
8.13 t-TestofTwo-VariableN¯y ResponseSurface . . . . . . . . . . . . . . 91
crit,4
ix
Acknowledgement
IwouldliketothankDr. Grandhiforwelcomingmeintohisresearchgrouptwoyearsago
and for being my advisor. He has given me the opportunity to advance my engineering
skillsandhehaspreparedmeforworkinginindustrytowhichIcannotthankhimenough.
I would also like to thank Dr. Raghavan Srinivasan and Dr. Scott Thomas for being a
part of my final thesis examination. Caterpillar Inc. is the organization that made this
projectpossible,sothankyoufortheacademicopportunity. AlysounTaylor-Hallhasbeen
integral in improving my technical writing skills...which is a reason that many of you are
able to read this document! I would like to thank my parents especially for their constant
moral support throughout the past two years. Thank you to Charles Monroe for his active
presence in my work as well as Rick Huff for keeping my research focused. Last but not
least, thank you to all of my friends and family that kept me motivated and proud of my
work. Youallhavemadethisamemorable experience.
x