Chapter 4 Robust Design v9.0

1. Chapter 4Robust Design v9.0

2. Why Robust Design? “Lockheed Martin used to spend an average of 200 work-hours trying to get a part that covers the landing gear to fit. For years employees had brainstorming sessions, which resulted in seemingly logical solutions. None worked. The statistical discipline of Six Sigma discovered a part that deviated by one-thousandth of an inch. Now corrected, the company saves $14,000 a jet.”1 1: Firms aim for Six Sigma efficiency; [FIRST Edition] Del Jones. USA TODAY. McLean, Va.: Jul 21, 1998. pg. 01.B

3. Why Robust Design? “It will keep the company (Allied Signal) from having to build an $85 million plant to fill increasing demand for caprolactam used to make nylon, a total savings of $30 - $40 million a year.”1 “Raytheon figures it spends 25% of each sales dollar fixing problems when it operates at four sigma, a lower level of efficiency. But if it raises its quality and efficiency to Six Sigma, it would reduce spending on fixes to 1%.”1 1: Firms aim for Six Sigma efficiency; [FIRST Edition] Del Jones. USA TODAY. McLean, Va.: Jul 21, 1998. pg. 01.B

4. Why Robust Design? “The reason to do DFSS is ultimately financial. It generates shareholder value based on delivering customer value in the marketplace. Products developed under the discipline and rigor of a DFSS-enabled product development process will generate measurable value against quantitative business goals and customer requirements. DFSS helps fulfill the voice of the business by fulfilling the voice of the customer.”2 2: Design for Six Sigma in Technology and Product Development, C.M. Creveling, J. L. Slutsky, and D. Antis, Jr.

5. Robust DesignOverview • Background of Robust Design • What is Robust Design, DFSS, …? • Design for Quality • Robust Design in Engineering Analysis • Illustration Example • Sources of Uncertainty • Effects of Uncertainty • Compare Deterministic and Probabilistic Approach • Enabling Technologies • Demonstration • Overview of Application Example • Demo • Questions

6. Background of Robust Design What is Robust Design, DFSS, etc.? • Uncertainty Analysis • Quantify the effect of uncertainties on the performance of a product (mean value, standard deviation, etc.) • Reliability Analysis • Quantify the reliability (failure probability, defects per million) • Robust Design or Design For Six Sigma (DFSS) • Optimize the design such that it is insensitive to unavoidable uncertainties (e.g. material,loads,…) • Reliability-based Optimization • Optimize the design such that reliability is maximized or failure probability (defects per million) is minimized Robust Design is often synonymous to “Design for Six Sigma” or “Reliability-based Optimization”

7. Background of Robust DesignDesign for Quality Six Sigma Quality = Only 3.4 out of 1’000’000 parts fail LSL = Lower Specification Limit USL = Upper Specification Limit Six Sigma Quality is inherently a probabilistic statement P.S.: Gaussian distribution is not realistic, but does convey the idea correctly

8. Background of Robust DesignDesign for Quality Six Sigma = Optimize manufacturing processes such that they automatically produce parts conforming with six sigma quality Design For Six Sigma = Optimize the design such that the parts conform with six sigma quality, i.e. quality and reliability are explicit optimization goals • Design for Six Sigma: • Achieve “Designed-In” quality as opposed to letting customers find out about quality problems • Make informed decision that are critical to quality early in the development process

9. Background of Robust DesignDesign for Quality Robust Design is a Paradigm Shift … • FROM: • Reactive Quality Management • Extensive Design Rework • Assess Performance by “build-test-build-test-…” • Fix performance/quality problems after manufacturing • Quality is “Tested-In” • TO: • Predictive Quality Management • Controlled Design Parameters • Estimate likelihood/rate of performance problems in design & development • Address quality problems in design & development • Designed for robust performance and quality • Quality is “Designed-In”

10. Background of Robust DesignRobust Design in Engineering Analysis Purpose of Robust Design Input Output ANSYS • Material Properties • Geometry • Boundary Conditions • Deformation • Stresses / Strains • Fatigue, Creep,... It’s a reality that input parameters are subjected to scatter => automatically the output parameters are uncertain as well!! Uncertain ! Scatter !

11. Background of Robust DesignRobust Design in Engineering Analysis Purpose of Robust Design ANSYS DesignXplorer Uncertain ! Scatter ! • Questions answered with Robust Design: • How large is the scatter of the output parameters? • What is the probability that output parameters do not fulfill design criteria (failure probability – defects per million)? • How much does the scatter of the input parameters contribute to the scatter of the output (sensitivities – critical-to-quality)?

12. Background of Robust DesignSources of Uncertainty Source: Klein, Schueller et.al. Probabilistic Approach to Structural Factors of Safety in Aerospace. Proc. CNES Spacecraft Structures and Mechanical Testing Conf., Paris 1994

13. Background of Robust DesignEffects of Uncertainty Materials, Bound.- Cond., Loads, ... ±5-100% Thermal Analysis CAD FEM CFD LCF ±??% Geometry FEM ± 0.1-10% Materials, Bound.- Cond., ... Structural Analysis Materials Materials, Bound.- Cond., Loads, ... ±30-60% ±5-50% ±5-100%

14. Background of Robust DesignEffects of Uncertainty Influence of Young’s Modulus and Thermal Expansion Coefficient on thermal stresses: thermal = E ·  ·T Deterministic Approach: Mean = EMean · Mean · T Mean = typically used results Probabilistic Approach: Probability that (thermal >= 105% Mean) (thermal >= 110% Mean) ‘E’ scatters ±5% 16% (~1 out of 6) 2.3% (~1 out of 40) ‘E’ and ‘‘ scatter ±5% 25% (~1 out of 4) 8% (~1 out of 12) ‘E’, ‘‘ & ‘T’ scatter ±5% 28% (~1 out of 4) 13% (~1 out of 8)

15. Background of Robust DesignCompare Deterministic/Probabilistic Turbine What-If Analysis Series

16. Background of Robust DesignEnabling Technology: Parameterization • Robust Design for all parameters including: • APDL Parameters CAD Parameters (Workbench) APDL Parameters Parameter value Paramesh db Initial mesh /syp,parabatch.exe,'testpb.rsx','testpb.cdb','location',%value%,'testpb_mod.cdb' /inp,testpb_mod,cdb ! Input the modified geometry Output mesh Parameter name Import Output mesh ParaMesh Parameters

17. Background of Robust DesignEnabling Technology: DesignXplorer DesignXplorer manages the parameters and the uncertainties

18. Robust Design DemonstrationOverview of Application Example FEM Boundary Conditions CAD Geometry FEM Mesh

19. Robust Design DemonstrationOverview of Application Example Results for Maximum Principal Stress Design Variables and Uncertainties Pressure Side Suction Side Axial Leaning Tang. Leaning Material Density (Gaussian) Peak Value ss Peak Value sp Fillet Radius (Lognormal) Dove Tail Width Mass Imbalance: (sp – ss)2 Avg.Stress: 0.5(sp + ss)

20. Robust Design DemonstrationDemonstration Robust Design Demonstration Turbine Blade Workshop

21. DesignXplorer Familyv9.0

22. DX Family 9.0 New Features • DesignXplorer & DesignXplorer VT • Robust Design • GUI Structure • Parameterize DFSS Results • Optimize DFSS results • New Trade-Off Study • Genetic Algorithm for Sample Generation • Variational Technology (DesignXplorer VT) • Support of Discrete Variables in Workbench • RSX File Viewing • Additional Contact Support • Frequency dependent material properties • Support inertial load parameters • 2D Analysis

23. DX Family 9.0 New FeaturesRobust Design - GUI Structure DFSS Charts and Table Pages Measures of robustness Statistics Available CDF Plot Y-Axis can be scaled as Gaussian, Log-Normal, Weibull, Exponential Sigma-Level in Tables Customize Tables (add, delete)

24. DX Family 9.0 New FeaturesParameterize DFSS Results New “Robust Design” View New DFSS Parameters showing up in Parameter View

25. DX Family 9.0 New FeaturesOptimize DFSS results 1) 2) 1) Random Variables: Uncontrollable – used to obtain DFSS results 2) Design Variables: Useable for Robust Design Optimization

26. DX Family 9.0 New FeaturesOptimize DFSS results Same optimization functionality as for GDS

27. DX Family 9.0 New FeaturesTrade-Off Studies Both 2D and 3D Tradeoff Plots are available Conflicting goals lie along the Pareto Front, Tradeoffs Studies occur here Mouse-Over Results

28. DX Family 9.0 New FeaturesTrade-Off Studies Feasible Infeasible Mouse-Over Results Pareto Front for Conflicting Goals Infeasible Points in Pareto Front

29. DX Family 9.0 New FeaturesGenetic Algorithm Sample Generation Choice of Basic (Screening), which is pseudo-random sampling method typically done first, or Advanced (Genetic) Algorithm which is typically done second

30. DX Family 9.0 New FeaturesGenetic Algorithm Sample Generation Advanced sample options Advanced Samples Screening Samples

31. Variational Technology is much faster than DOE for discrete parameters Supports: Spot Welds Solid Bodies Sheet Bodies Line Bodies Parts DesignXplorer VT 9.0Support of Discrete Variables in Workbench

32. DesignXplorer VT 9.0Support of Discrete Variables in Workbench • Efficient Postprocessing • Multi-objective Boolean optimizer based on Bayesian sampling faster optimization of discrete parameters • Boolean scatter chart representing the solution points of all the parameter combinations of the selected parameters.

33. DesignXplorer VT 9.0Support of Discrete Variables in Workbench 6 Supports 4 Suppressed 6 Supports None Suppressed

34. DesignXplorer VT 9.0RSX File Viewing • Allows user to view Variational Technology results from a variety of sources including • DesignXplorer VT (of course) • ANSYS using VT Hoover model solved with VT within the ANSYS Environment

35. DesignXplorer VT 9.0Support for Face-to-Edge Contact

36. DesignXplorer VT 9.0Support for Edge-to-Edge Contact

37. DesignXplorer VT 9.0Support of Frequency Dependent Properties • For harmonic analyses, VT supports frequency dependant modulus and damping

38. DesignXplorer VT 9.0Inertial Load Paramenters & 2D Analysis • Support Inertial Load Parameters • Acceleration (Magnitude and Components) • Rotational Velocity (Magnitude and Components) • Rotational Acceleration (Magnitude and Components) • Allows Variational Technology analysis of 2D Simulation studies to include: • Axisymmetric • Plane Strain • Plane Stress