CAD-BASED DESIGN PROCESS FOR FATIGUE ANALYSIS, RELIABILITY- ANALYSIS, AND DESIGN OPTIMIZATION

CAD-BASED DESIGN PROCESS FOR FATIGUE ANALYSIS, RELIABILITY- ANALYSIS, AND DESIGN OPTIMIZATION K.K. Choi, V. Ogarevic, J. Tang, and Y.H. Park Center for Computer-Aided Design College of Engineering The University of Iowa Iowa City, IA 52242

CONTENTS OF THE PROCESS Create a Pro/E CAD Model of a Typical Passenger Vehicle System and Automatically Translate It Into DADS Dynamics Model Perform Dynamics Simulation of the Car Model Over a Typical Road Profile Create Parameterized CAD Model and FE Models of the Front Right Lower Control Arm Perform Fatigue Life Analysis of the Lower Control Arm Perform CAD-Based Fatigue Design Sensitivity Analysis and Optimization of the Lower Control Arm Reliability-Based Analysis and Design Optimization

Pro/E MODEL OF THE VEHICLE SYSTEM 26 Bodies Model

DADS MODEL OF THE VEHICLE SYSTEM Total of 22 Rigid Bodies Simulation Parameters: 7 seconds straight line run RMS2 road profile: 0.316 in. average peak to valley height Speed 10 m/sec

FRONT RIGHT SUSPENSION X FR_Lower Control Arm

Pro/E MODEL OF THE LOWER CONTROL ARM

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

FE MODEL OF THE LOWER CONTROL ARM Total Number of Elements: 297 Element Type: ANSYS 20-Node Solid Total Number of Nodes: 1977 Total Number of DoF: 5931 Mesh Generator: MSC/PATRAN

FATIGUE LIFE PREDICTION APPROACH Obtain and Convert Joint Reaction Forces and Inertial Forces From Rigid or Flexible Multibody Dynamics Simulation in the Format Readable by DRAW Create FE Models That Are Consistent with the CAD Model of the Structural Component Superimpose Stress Time Histories for All Surface Nodes of the FE Model Using Hybrid Method Perform Preliminary Analysis To Identify Critical Regions Perform Refined Analysis for Higher Fidelity Fatigue Life Predictions

COMPUTATIONAL FLOW CHART Interface DADS_READER Dynamic Information Frame Information DADS Output File Load Vector Calculation Tool Dynamic Parameters Preliminary Analysis Tool Vehicle System Dynamic Analysis DADS Quasi Static Load Vectors Superposition Tool Dynamic Stress Time History Critical Region Pro/E CAD Model (LCA) FEA Tool ANSYS & NASTRAN Stress Coefficients Refined Analysis Tool Crack Initiation Life Geometry PATRAN or HyperMesh FE Model DRAW

STRESS HISTORY AT CRITICAL NODE (Three Principal Stresses)

ALGORITHM FOR FATIGUE LIFE PREDICTIONS IN DRAW Compute Stress/strain and Damage Parameter History Edit and Rainflow Count Damage Parameter History Identify Surface Critical Region Using Preliminary Life Analysis with von Mises Strain Approach Estimate Elastic-plastic Strain at Critical Region Refine Life Predictions at Critical Region Using von Mises Strain Approach or More Advanced Critical Plane Approaches

ESTIMATION OF ELASTIC-PLASTIC STRAINS Uniaxial Case: Neuber s Rule and Remberg-Osgood Equation Multiaxial Case: Equivalent strain energy density approach Assumed elastic-plastic loading paths Currently linear kinematic hardening plasticity model (Mroz Model) is being implemented

LIFE PREDICTION METHODS Equivalent Strain Methods: Von Mises equivalent strain approach with Smith- Watson-Topper theory ASME Boiler and Pressure Vessel Code approach Critical Plane Methods: Tensile strain based critical plane approach (Fatemi-Socie) Shear strain based critical plane approach (Fatemi-Kurath)

FATIGUE CRACK INITIATION LIFE CONTOUR (Preliminary Analysis with von Mises Equivalent-Strain Approach)

CRITICAL REGION IDENTIFICATION PROCEDURE LIST OF CRITICAL NODES User Selected Points Preliminary Fatigue Analysis Calculate linear elastic von Mises strain Calculate fatigue crack initiation life for all surface nodes Select critical nodes with minimum life The procedure is automated in DRAW

REFINED FATIGUE ANALYSIS AT THE CRITICAL NODES (Equivalent Strain Method) Node No. Preliminary Analysis Refined Analysis (with Neuber) Refined Analysis (with EP) Cycles Years Cycles Years Cycles Years 560 2.8901E8 64 2.8295E8 62 2.2432E8 50 583 3.2312E8 72 3.1671E8 70 3.5239E8 78 590 1.217E10 2700 2.7053E8 60 3.9165E8 87

CAD-BASED SHAPE OPTIMIZATION APPROACH Implement CAD-based Shape Design Parameterization Capability within Pro/E Environment Use HyperMesh or PATRAN for Mesh Generation, ANSYS or NASTRAN for FEA, and DRAW for Fatigue Life Prediction Develop a Design Velocity Field Computation Method Based on Pro/E Shape Design Parameter Hybrid Method Is Used for Sensitivity Computation Continuum DSA for Sensitivity of the Dynamic Stresses Finite Difference for Sensitivity of the Fatigue Life DOT Is Used for CAD-based Shape Design Optimization

COMPUTATIONAL FLOW CHART Pro/E Environment Mesh Generator Mesh Generator HyperMesh or PATRAN Pro/ENGINEER CAD Modeler Life Prediction DRAW Design Parameterization Design Parameterization Sensitivity Analysis DSA Velocity Filed Computation Velocity Field Computation 4-Step Design Process Design Optimization Trade-off Determination What-if Study Sensitivity Display Design Optimization DOT Design Update DSO

CAD-BASED DESIGN PARAMETERIZATION CAD Model Must Be Well-Constructed : Able to regenerate perturbed models in large design space Maintain topology when regenerating Exported geometry must support mesh generation by HyperMesh or PATRAN

DESIGN PARAMETERIZATION Design Parameters Are Chosen From Pro/E Feature Dimensions Such as Length, Radii, General Surface, etc. Design Parameters Selection by Pointing and Clicking at Pro/E Display Identify FE Nodes on CAD Surfaces PATRAN generates a file including FE surface node information This step is automated if meshes are generated by Pro/E Boundary Design Velocity Fields Are Computed Using Finite Difference Method Based on CAD Regeneration Domain Velocity Fields (Velocity of Interior Nodes) Are Computed Using Boundary Displacement Method

SELECTED DESIGN PARAMETERS Independent Section Dimensions (Heights and Widths) Are Selected as Design Parameters s5 s6 s4 Design Parameter Description s1 s2 s3 d1043 d1044 d1036 d1037 d1029 d1030 d837 d838 d842 d843 d854 d855 height at s1 width at s1 height at s2 width at s2 height at s3 width at s3 height at s4 width at s4 height at s5 width at s5 height at s6 width at s6

OPTIMIZATION PROBLEM Objective Function - Minimize Volume 66 Constraint Functions - Fatigue Life Longer Than 11 Years at 66 Critical Nodes 12 Shape Design Parameters MFD Algorithm Is Used for Optimization DP Value(mm) Lower Bd Upper Bd DP Value(mm) Lower Bd Upper Bd d1043 d1044 d1036 d1037 d1029 d1030 17.0 12.0 20.0 13.0 29.0 14.0 12.0 7.0 15.0 7.0 24.0 9.0 22.0 17.0 26.0 18.0 34.0 19.0 d837 d838 d842 d843 d854 d855 30.0 30.5 24.0 15.0 24.0 14.0 25.0 25.5 19.0 10.0 19.0 9.0 35.0 35.5 29.0 20.0 29.0 19.0

DESIGN HISTORY Optimal Design Is Obtained in 11 Iterations Cost Function History Design Parameter History

LIFE CONTOUR AT INITIAL AND OPTIMAL DESIGNS Initial Design Optimal Design DP Initial (mm) Optimal DP Initial (mm) Optimal 3 Volume(mm ) Initial Optimal 195786.5 173787.8 d1043 d1044 d1036 d1037 d1029 d1030 17.0 12.0 20.0 13.0 29.0 14.0 17.3 9.8 26.0 7.0 31.1 10.9 d837 d838 d842 d843 d854 d855 30.0 30.5 24.0 15.0 24.0 14.0 25.0 25.5 19.0 13.1 20.7 9.0

DESIGN OPTIMIZATION STARTING FROM TWO DIFFERENT INITIAL DESIGNS Initial Design I Initial Design II DP Design I Design II DP Design I Design II 3 Volume(mm ) Design I Design II 195786.5 210118.1 d1043 d1044 d1036 17.0 12.0 20.0 17.0 16.0 20.0 d837 d838 d842 30.0 30.5 24.0 30.0 30.5 24.0 d1037 13.0 17.0 d843 15.0 15.0 d1029 29.0 29.0 d854 24.0 24.0 d1030 14.0 18.0 d855 14.0 14.0

COMPARISON OF OPTIMAL DESIGNS OF INITIAL DESIGNS I & II Optimal Design I Optimal Design II 3 Volume(mm ) Design I Design II DP Design I Design II DP Design I Design II 173787.8 173809.0 d1043 d1044 d1036 17.3 9.8 26.0 17.4 9.8 26.0 d837 d838 d842 25.0 25.5 19.0 25.0 25.5 19.0 d1037 d1029 d1030 7.0 31.1 10.9 7.0 31.3 10.6 d843 d854 d855 13.1 20.7 9.0 12.7 20.6 9.0

RELIABILITY-BASED DESIGN OPTIMIZATION (RBDO) Mathematical Formulation: Distributional and deterministic design vectors θ=[θ 1,θ 2,...,θ n1 ] T and b=[b 1,b 2,...,b n2 ] min. W(b,θ) s.t. U = P(g i (b,θ) 0) P f i, i = 1 m P f i b j L θ k L U b j b j, j =1 n 1 U θ k θ k, k = 1 n 2 Reliability Constraints Are Assumed to be Mutually Independent and No Correlation Exists Between Them STOP Yes Design Model Definition FORM for Failure Functions Optimum? No Reliability-Based DSA Optimization Algorithms (DOT) Update Design Model

RANDOM VARIABLE SPACES Transformation Matrix T: U = T(X) from a non-normally distributed random variable space X to a standard normally distributed random variable space U where U i = Φ 1 (f Xi (x)), i = 1 n X 2 U 2 Φ: Cumulative Distribution Function (CDF) Failure Region g(u) < 0 MPP U * P f MPP U * 0 f (x) X Mean Value Point Failure Surface g(x) = 0 Safe Region g(u) > 0 X 1 0 b Reliability Index β f (u) U 0 β Major Contribution to Failure Probability From this Area (FORM) (SORM) Failure Surface g(u) = 0 U 1

NUMERICAL EXAMPLE TRACKED VEHICLE ROAD ARM Multibody Dynamics Model: 17 Rigid Bodies Roadarm 10 9 R R 8 7 17 R 16 X R 3 R15 X1 14 1 X R 2 R 13 2 R R R R R R 6 R 3 5 R 4 12 R 11

SHAPE DESIGN PARAMETERIZATION Cubic Curves bi, i = 1,3,5,7 x' 3 Straight Lines bi, i = 2,4,6,8 x' 1 Cross Sectional Shape Design Parameters: b1, b3, b5, b7 Design Parameters: b2, b4, b6, b8 Torsion Bar 1236 12 Intersection 1 b1, b2 Intersection 2 b3, b4 Intersection 3 b5, b6 Intersection 4 b7, b8 x' 3 x' 2 20 in. x' 1 x' 3 x' 2 Center of the Roadwheel Intersection 1 Intersection 3 Intersection 2 Intersection 4 x' 1 x' 2

DETERMINISTIC DESIGN OPTIMIZATION Objective Function - Minimize Volume Constraint Function - 24 Fatigue Life Greater Than 20 Years x' 1 x' 3 1340 x' 2 1544 1227 1287 1140 439 1023 843 505 547 1311 1391 1216 1012 922 1008 1380 1433 1129 1519 918 472 742 926 x' 1 x' 3 x' 2 Function Description Lower Bound Current Design Status Cost Volume 487.678 in 3 Constraint 1 Life at node 1216 9.63E+6 (20 Year) 9.631E+6 blocks Active Constraint 2 Life at node 926 9.63E+6 (20 Year) 8.309E+7 blocks Inactive Constraint 3 Life at node 1544 9.63E+6 (20 Year) 8.926E+7 blocks Inactive Constraint 4 Life at node 1519 9.63E+6 (20 Year) 1.447E+8 blocks Inactive Constraint 5 Life at node 1433 9.63E+6 (20 Year) 2.762E+8 blocks Inactive

RANDOM VARIABLES FOR RELIABILITY 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 Tolerance b2 1.583 in. 0.019675 Normal Tolerance b3 2.911 in. 0.031703 Normal Tolerance b4 1.637 in. 0.019675 Normal Tolerance b5 2.870 in. 0.031703 Normal Tolerance b6 2.420 in. 0.026352 Normal Tolerance b7 2.801 in. 0.032496 Normal Tolerance b8 4.700 in. 0.050568 Normal

FOUR-STEP INTERACTIVE DESIGN Reliability-Based Design Model Definition Objective function - minimize volume Constraints - failure probability of fatigue life Š 1% Design parameters - mean values of b1 to b8 Interactive Design An improved design obtained in two iterations 10 FORMs, 2 Reliability-Based DSAs (5 days on HP9000/755) Function Description P f = F(-b) P f = F(-b) Changes at Optimum 2 RB Designs Cost Volume 436.722 in 3 447.691 in 3 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 Constraint 3 Life at node 1544 3.21% 0.998% -2.2 Constraint 4 Life at node 1519 0.83% 0.721% -0.11 Constraint 5 Life at node 1433 0.023% 0.018% -0.005

SUMMARY AND CONCLUSIONS The Connection Between Pro/E and DADS Seems to Be Working Properly and Efficiently DRAW Code Efficiently Identified Fatigue Critical Regions During the Preliminary Analysis DRAW Refined Analysis Provided Higher Fidelity Predictions on the Fatigue Critical Locations DSO Provided Accurate Design Sensitivity Information Very Efficiently Very Similar Optimal Designs Are Obtained from Two Different Initial Designs CAD-Based Design Model Is Critical for Multidisciplinary CAE Analysis and Design Optimization CAD-Based Design Model Will Allow Connection of CAE to CAD- CAM Reliability-Based Design Optimization Provides High Quality Designs That Are Cost Effective in Manufacturing Process