choi.pdf

Center for Computer Aided Design

Automotive Research Centerarc

CAD-BASED DESIGN PROCESS FORFATIGUE ANALYSIS, RELIABILITY-

ANALYSIS, AND DESIGN OPTIMIZATION

CAD-BASED DESIGN PROCESS FORFATIGUE ANALYSIS, RELIABILITY-

ANALYSIS, AND DESIGN OPTIMIZATION

K.K. Choi, V. Ogarevic, J. Tang, and Y.H. ParkCenter for Computer-Aided Design

College of EngineeringThe University of Iowa

Iowa City, IA 52242



CONTENTS OF THE PROCESS

l Create a Pro/E CAD Model of a Typical Passenger VehicleSystem and Automatically Translate It Into DADSDynamics Model

l Perform Dynamics Simulation of the Car Model Over aTypical Road Profile

l Create Parameterized CAD Model and FE Models of theFront Right Lower Control Arm

l Perform Fatigue Life Analysis of the Lower Control Arm

l Perform CAD-Based Fatigue Design Sensitivity Analysisand Optimization of the Lower Control Arm

l Reliability-Based Analysis and Design Optimization



Pro/E MODEL OF THE VEHICLE SYSTEM

26 Bodies Model



DADS MODEL OF THE VEHICLE SYSTEM

l Total of 22 Rigid Bodies

l Simulation Parameters:n 7 seconds straight line run

n RMS2 road profile: 0.316in. average peak to valleyheight

n Speed 10 m/sec



FRONT RIGHT SUSPENSION

X

FR_Lower Control Arm



Pro/E MODEL OF THE LOWERCONTROL ARM



JOINT REACTION FORCE HISTORIES(X-Direction at Three Joints)



FE MODEL OF THE LOWERCONTROL ARM

l Total Number of Elements: 297

l Element Type: ANSYS 20-Node Solid

l Total Number of Nodes: 1977

l Total Number of DoF: 5931

l Mesh Generator: MSC/PATRAN



FATIGUE LIFE PREDICTIONAPPROACH

l Obtain and Convert Joint Reaction Forces and InertialForces From Rigid or Flexible Multibody DynamicsSimulation in the Format Readable by DRAW

l Create FE Models That Are Consistent with the CADModel of the Structural Component

l Superimpose Stress Time Histories for All Surface Nodesof the FE Model Using Hybrid Method

l Perform Preliminary Analysis To Identify Critical Regions

l Perform Refined Analysis for Higher Fidelity Fatigue LifePredictions



COMPUTATIONAL FLOW CHART

Pro/EFEA ToolANSYS &NASTRAN

DynamicAnalysisDADS

CADModel(LCA)

GeometryPATRAN orHyperMesh

FE Model

FrameInformation

DADSOutput File

InterfaceDADS_READER

DynamicInformation

Load VectorCalculation Tool

DynamicParameters

Quasi StaticLoad Vectors

StressCoefficients

SuperpositionTool

Dynamic StressTime History

PreliminaryAnalysis Tool

RefinedAnalysis Tool

CriticalRegion

Crack Initiation Life

VehicleSystem

DRAW



STRESS HISTORY AT CRITICAL NODE(Three Principal Stresses)



ALGORITHM FOR FATIGUE LIFEPREDICTIONS IN DRAW

l Compute Stress/strain and Damage Parameter History

l Edit and Rainflow Count Damage Parameter History

l Identify Surface Critical Region Using PreliminaryLife Analysis with von Mises Strain Approach

l Estimate Elastic-plastic Strain at Critical Region

l Refine Life Predictions at Critical Region Using vonMises Strain Approach or More Advanced CriticalPlane Approaches



ESTIMATION OF ELASTIC-PLASTICSTRAINS

l Uniaxial Case:n Neuber’s Rule and Remberg-Osgood Equation

l Multiaxial Case:n Equivalent strain energy density approach

n Assumed elastic-plastic loading paths

n Currently linear kinematic hardening plasticity model(Mroz Model) is being implemented



LIFE PREDICTION METHODS

l Equivalent Strain Methods:n Von Mises equivalent strain approach with Smith-

Watson-Topper theory

n ASME Boiler and Pressure Vessel Code approach

l Critical Plane Methods:n Tensile strain based critical plane approach

(Fatemi-Socie)

n Shear strain based critical plane approach(Fatemi-Kurath)



FATIGUE CRACK INITIATION LIFECONTOUR

(Preliminary Analysis with von Mises Equivalent-Strain Approach)



CRITICAL REGION IDENTIFICATIONPROCEDURE

l User Selected Points

l Preliminary FatigueAnalysisn Calculate linear elastic von

Mises strain

n Calculate fatigue crackinitiation life for all surfacenodes

n Select critical nodes withminimum life

n The procedure is automatedin DRAW

LIST OF CRITICAL NODES



REFINED FATIGUE ANALYSIS AT THECRITICAL NODES(Equivalent Strain Method)

NodeNo.

560

583

590

PreliminaryAnalysis

Cycles Years

Refined Analysis(with Neuber)

Cycles Years

Refined Analysis(with EP)

Cycles Years

2.8901E8

3.2312E8

1.217E10

2.8295E8

3.1671E8

2.7053E8

2.2432E8

3.5239E8

3.9165E8

64 62 50

78

87

70

60

72

2700



CAD-BASED SHAPE OPTIMIZATIONAPPROACH

l Implement CAD-based Shape Design ParameterizationCapability within Pro/E Environment

l Use HyperMesh or PATRAN for Mesh Generation,ANSYS or NASTRAN for FEA, and DRAW for FatigueLife Prediction

l Develop a Design Velocity Field Computation MethodBased on Pro/E Shape Design Parameter

l Hybrid Method Is Used for Sensitivity Computationn Continuum DSA for Sensitivity of the Dynamic Stresses

n Finite Difference for Sensitivity of the Fatigue Life

l DOT Is Used for CAD-based Shape Design Optimization



COMPUTATIONAL FLOW CHART

Pro/ENGINEER

DesignParameterization

Velocity FiledComputation

Pro/EEnvironment

Mesh GeneratorHyperMesh or PATRAN

DRAW

DSA

DOT

DesignUpdate

DesignOptimization

Trade-offDetermination

What-ifStudy

SensitivityDisplay

CADModeler

DesignParameterization

Velocity FieldComputation

Mesh Generator

Life Prediction

DSO

4-StepDesign Process

DesignOptimization

SensitivityAnalysis



CAD-BASED DESIGN PARAMETERIZATION

l CAD Model Must BeWell-Constructed :• Able to regenerate

perturbed models inlarge design space

• Maintain topologywhen regenerating

• Exported geometrymust support meshgeneration byHyperMesh orPATRAN



DESIGN PARAMETERIZATION

l Design Parameters Are Chosen From Pro/E FeatureDimensions Such as Length, Radii, General Surface, etc.

l Design Parameters Selection by Pointing and Clicking atPro/E Display

l Identify FE Nodes on CAD Surfacesn PATRAN generates a file including FE surface node information

n This step is automated if meshes are generated by Pro/E

l Boundary Design Velocity Fields Are Computed UsingFinite Difference Method Based on CAD Regeneration

l Domain Velocity Fields (Velocity of Interior Nodes) AreComputed Using Boundary Displacement Method



SELECTED DESIGN PARAMETERS

s1

s2

s3

s4

s5 s6

d1043d1044d1036d1037d1029d1030d837d838d842d843d854d855

height at s1width at s1height at s2width at s2height at s3width at s3height at s4width at s4height at s5width at s5height at s6width at s6

Design Parameter Description

l Independent Section Dimensions (Heights and Widths) Are Selectedas Design Parameters



OPTIMIZATION PROBLEM

l Objective Function - Minimize Volume

l 66 Constraint Functions - Fatigue LifeLonger Than 11 Years at 66 CriticalNodes

l 12 Shape Design Parameters

l MFD Algorithm Is Used forOptimization

DP Value(mm) Lower Bd Upper Bd

d1043d1044d1036d1037d1029d1030

d837d838d842d843d854d855

12.07.015.07.024.09.0

22.017.026.018.034.019.0

DP Value(mm) Lower Bd Upper Bd

25.025.519.010.019.09.0

35.035.529.020.029.019.0

17.012.020.013.029.014.0

30.030.524.015.024.014.0



DESIGN HISTORY

l Optimal Design Is Obtained in 11 Iterations

Cost Function History Design Parameter History



LIFE CONTOUR AT INITIAL ANDOPTIMAL DESIGNS

Initial Design Optimal Design

Volume(mm ) Initial Optimal3

195786.5 173787.8

DP Initial (mm) Optimal

d1043d1044d1036d1037d1029d1030

d837d838d842d843d854d855

DP Initial (mm) Optimal

17.012.020.013.029.014.0

30.030.524.015.024.014.0

17.39.826.07.031.110.9

25.025.519.013.120.79.0



DESIGN OPTIMIZATION STARTING FROMTWO DIFFERENT INITIAL DESIGNS

Initial Design I Initial Design II

Volume(mm ) Design I Design II3

195786.5 210118.1

DP Design I Design II

d1043

d1044

d1036

d1037

d1029

d1030

d837

d838

d842

d843

d854

d855


17.0

12.0

20.0

13.0

29.0

14.0

30.0

30.5

24.0

15.0

24.0

14.0

17.0

16.0

20.0

17.0

29.0

18.0

30.0

30.5

24.0

15.0

24.0

14.0



COMPARISON OF OPTIMAL DESIGNS OFINITIAL DESIGNS I & II

Optimal Design I Optimal Design II

Volume(mm ) Design I Design II3

173787.8 173809.0


d1043

d1044

d1036

d1037

d1029

d1030

d837

d838

d842

d843

d854

d855


17.3

9.8

26.0

7.0

31.1

10.9

25.0

25.5

19.0

13.1

20.7

9.0

17.4

9.8

26.0

7.0

31.3

10.6

25.0

25.5

19.0

12.7

20.6

9.0



RELIABILITY-BASED DESIGNOPTIMIZATION (RBDO)

l Mathematical Formulation:

Distributional and deterministic designvectors θ=[θ1,θ2,...,θn1]T and b=[b1,b2,...,bn2]

min. W(b,θθ)

s.t.

l Reliability Constraints Are Assumed to beMutually Independent and No CorrelationExists Between Them

Pf i= P(g i(b,θ) ≤ 0) ≤ Pf i

U , i = 1− m

b jL ≤ b j ≤ b j

U , j =1 − n1

θkL ≤ θk ≤ θk

U , k = 1 − n2

Design ModelDefinition

FORM forFailure Functions

Optimum?

Reliability-BasedDSA

UpdateDesignModel

STOPYes

No

OptimizationAlgorithms

(DOT)



RANDOM VARIABLE SPACESl Transformation Matrix T: U = T(X) from a non-normally distributed

random variable space X to a standard normally distributed randomvariable space U where

U i = Φ −1( fXi(x)), i = 1− n

U2

U1

X2

0

0

Pf

β

Failure Regiong(U) < 0

MPP U*

Major Contributionto Failure ProbabilityFrom this Area

(FORM)

Failure Surfaceg(X) = 0 Failure Surface

g(U) = 0

MPP U*

Mean ValuePoint

f (x)X

(SORM)

Cumulative DistributionFunction (CDF)

Φ:

b

X1

Safe Regiong(U) > 0

0

f (u)U

ReliabilityIndex β



NUMERICAL EXAMPLETRACKED VEHICLE ROAD ARM

Roadarm

101

11

12

13

14

15

16

17

X

X

3

2

4

5

6

7

8

9

X

RR

RR

RR

RR

R

R

RR

RR

R

R

12

3

l Multibody Dynamics Model: 17 Rigid Bodies



SHAPE DESIGN PARAMETERIZATION

Intersection 1Intersection 2

Intersection 3

Intersection 4

20 in.

1x'

3x'

2x'

2x'

1x'

Design Parameters:b1, b3, b5, b7 Design Parameters:

b2, b4, b6, b8

Cross Sectional Shape

StraightLines

Cubic Curves

3x'

bi, i = 1,3,5,7

bi, i = 2,4,6,8

1236

12TorsionBar

Center of theRoadwheel

1x'

3x'

2x'

Intersection 1b1, b2 Intersection 2

b3, b4 Intersection 3b5, b6

Intersection 4b7, b8



DETERMINISTIC DESIGN OPTIMIZATION

l Objective Function - Minimize Volume

l Constraint Function - 24 Fatigue Life Greater Than20 Years

1x'3

x'

2x'1x'

3x'

2x'

12271287

1544

1340

11401023

843505547

439

1391

12161311

14331519

926

9221012

1008

918

742

472

1380 1129

Function Description Lower Bound Current Design StatusCost Volume 487.678 in3

Constraint 1 Life at node 1216 9.63E+6 (20 Year) 9.631E+6 blocks ActiveConstraint 2 Life at node 926 9.63E+6 (20 Year) 8.309E+7 blocks InactiveConstraint 3 Life at node 1544 9.63E+6 (20 Year) 8.926E+7 blocks InactiveConstraint 4 Life at node 1519 9.63E+6 (20 Year) 1.447E+8 blocks InactiveConstraint 5 Life at node 1433 9.63E+6 (20 Year) 2.762E+8 blocks Inactive



RANDOM VARIABLES FORRELIABILITY ANALYSIS

Random Variables Mean Value Standard Deviation Distribution

Young’s Modulus E 30.0E+6 0.75E+6 LogNormal

Fatigue Strength Coefficient s'f 1.77E+5 0.885E+4 LogNormal

Fatigue Ductility Coefficient e'f 0.41 0.0205 LogNormal

Fatigue Strength Exponent b -0.07300 0.00365 Normal

Fatigue Ductility Exponent c -0.6 0.003 Normal

Tolerance b1 2.889 in. 0.032450 Normal










FOUR-STEP INTERACTIVE DESIGNl Reliability-Based Design Model Definition

n Objective function - minimize volume

n Constraints - failure probability of fatigue life Š 1%

n Design parameters - mean values of b1 to b8

l Interactive Designn An improved design obtained in two iterations

n 10 FORMs, 2 Reliability-Based DSAs (5 days on HP9000/755)

Function Description Pf = F(-b) Pf = F(-b) Changes

at “Optimum” 2 RB Designs

Cost Volume 436.722 in3 447.691 in3 2.5%

Constraint 1 Life at node 1216 0.476% 0.532% 0.056

Constraint 2 Life at node 926 3.24% 0.992% -2.2






SUMMARY AND CONCLUSIONSl The Connection Between Pro/E and DADS Seems to Be Working

Properly and Efficiently

l DRAW Code Efficiently Identified Fatigue Critical Regions During thePreliminary Analysis

l DRAW Refined Analysis Provided Higher Fidelity Predictions on theFatigue Critical Locations

l DSO Provided Accurate Design Sensitivity Information Very Efficiently

l Very Similar Optimal Designs Are Obtained from Two Different InitialDesigns

l CAD-Based Design Model Is Critical for Multidisciplinary CAE Analysisand Design Optimization

l CAD-Based Design Model Will Allow Connection of CAE to CAD-CAM

l Reliability-Based Design Optimization Provides High Quality DesignsThat Are Cost Effective in Manufacturing Process

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