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Multi-Level Design Process For 3-D Preform Shape Optimization In Metal Forming Using The Reduced Basis Technique

CDOC. Multi-Level Design Process For 3-D Preform Shape Optimization In Metal Forming Using The Reduced Basis Technique. Department of Mechanical and Materials Engineering Wright State University Dayton, OH 45435. CDOC. Presentation Outline. Research objectives

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Multi-Level Design Process For 3-D Preform Shape Optimization In Metal Forming Using The Reduced Basis Technique

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  1. CDOC Multi-Level Design Process For 3-D Preform Shape Optimization In Metal Forming Using The Reduced Basis Technique Department of Mechanical and Materials Engineering Wright State University Dayton, OH 45435

  2. CDOC Presentation Outline • Research objectives • Overview of forging process • Need for preform shape optimization • Research challenges • Reduced basis design approach • Case studies • Summary

  3. CDOC Research Objectives • Develop a methodology for 3-D preform shape optimization in forging • Identify 3-D preform shape parameters • Define optimization design parameters • Define finite element-based objectives and constraints • Establish explicit relationship between design parameters and objectives and constraints • Enable preform design for complex 3-D forging components • Develop a computationally feasible technique • Improve product quality

  4. CDOC Initial billet Trimming Preform Blocker Finisher Tradeoff designs Heat treatment process Rejected Machinable Temperature distribution Introduction to Metal Forming Process Intermediate shapes Forming process Quality check Robust design

  5. CDOC Flash Underfill Reduced underfill Need for Preform Shape Design Initial shape Preform shape Blocker shape Blocker shape • Minimize load • Minimize material waste • More uniform Material flow • Minimize geometric variation • Decrease production cost • Increase die life

  6. CDOC Conventional Preform Design Techniques Preforms for steel finished forgings • Design guidelines • Empirical relations • Computer-aided design • Knowledge-based approach • Finite element approach • Forward simulations • Backward simulations No preform h=b h = 2b Finished forgings Upset stock Preforms h = 3b

  7. Design Issues CDOC • 2D Assumptions for 3D parts • Plane-strain - No deformation in out-of-plane direction • Axisymmetric - Material flow is radial • Practical forgings are neither axisymmetric nor plane-strain • Require large number of parameters • Require large number of simulations • Long computational times Shape parameters Preform shapes

  8. CDOC Shape Optimization Methodology Identify initial preform shape Parameterize preform shape • Reduced basis technique • Obtain basis shapes • Employ design variable linking Determine critical optimization parameters • Generate DOE points using Latin Hypercube sampling techniques • Conduct forging simulations of the DOE billets • Extract FEM output data Construct surrogate models Optimize

  9. CDOC Axisymmetric 3-D metal hub Finite element model of 2-D section Reduced Basis Technique • Innovative technique for defining preform shapes

  10. CDOC Reduced Basis Technique • Innovative technique for defining preform shapes • Generate initial guess preform basis shapes • X and Y co-ordinates of boundary points define basis vectors Metal hub Basis 2[Y2] Basis 3[Y3] Basis 1[Y1] (xi, yi) Basis shape boundary points

  11. CDOC Desired boundary False boundary Basis 2[Y2] Basis 3[Y3] Basis 1[Y1] Basis Vectors • Need large number of boundary points • Increases length of the basis vector • Require no extra computational cost • Define all of the basis shapes similarly

  12. CDOC Basis 2[Y2] Basis 3[Y3] Basis 1[Y1] Basis Vectors • Need large number of boundary points • Increases length of the basis vector • Require no extra computational cost • Perform Gram-Schmidt orthogonalization • Produces independent basis shapes

  13. Basis shapes Forged parts Design Parameters Definition • Weighted combination of orthogonal basis shapes

  14. Y1 a1 × Y2 a2 × Y3 a1 a2 a3 a3 × Forged part 0 ≤ ai ≤ 1 Design Parameters Definition • Weighted combination of orthogonal basis shapes Basis shapes

  15. Y1 a1 × Y2 a2 × Y3 a1 a2 a3 a3 × Forged part 0 ≤ ai ≤ 1 Design Parameters Definition • Weighted combination of orthogonal basis shapes Basis shapes

  16. Y1 a1 × Y2 a2 × Y3 a1 a2 a3 a3 × 0 ≤ ai ≤ 1 Forged part Design Parameters Definition • Weighted combination of orthogonal basis shapes Basis shapes

  17. Y1 a1 × Y2 DOE points a2 × Resultant preform shapes Y3 • Scaling maintains constant volume for resultant preforms • Weights (ai) are the design parameters a3 × 0 ≤ ai ≤ 1 Design Parameters Definition • Weighted combination of orthogonal basis shapes Basis shapes

  18. CDOC Underfill Max Underfill Med Min Strain variance Construction of Surrogate Model • Generate Latin Hypercube sampling points • Perform finite element simulations • Obtain objectives and constraints Variable 2 Variable 1 • Construct response surface model

  19. CDOC Optimization Statement • Design variables • Weighting factors of reduced basis technique (ai) • Cost function • Minimize strain variance f(ai) • Subject to • Underfill g(ai) ≤ 0 • Side bounds on weights • 0 ≤ ai ≤ 1

  20. CDOC Basis 3 [Y3] Basis 2 [Y2] Basis 4 [Y4] Basis 1 [Y1] Design Optimization h1 h1 = 1.25 x b1 h2 = 1.50 x b2 b1 b2 h2 Symmetry axis Cross-sectional view Rail section • Four basis shapes generated Basis shapes Finite element simulations Final forged parts

  21. CDOC Response Iteration number Results Optimized billet Iteration history of objective and constraint functions Final forged part Strain variance : 0.0647 Flash : 3 %

  22. CDOC Basis 3 [Y3] Basis 2 [Y2] Basis 4 [Y4] Basis 1 [Y1] Simple basis shape Inappropriate basis shape Viable basis shapes Need For Multi-Level Design Process • Single level design requires appropriate starting basis shapes • No information available for a new product • Enable design with geometrically simple basis shapes

  23. CDOC Multi-Level Optimization Routine Generate starting guess shapes Define design parameters (Level L) Reduced basis method DOE techniques Obtain design points Build new basis shapes (L=L+1) Conduct FEM analysis using DEFORM-3D Obtain objective and constraints Generate surrogate model using response surface method Redesign using optimization algorithm No Yes Optimum preform Constraint satisfied?

  24. CDOC Basis 2 [Y2] Basis 3 [Y3] Basis 1 [Y1] Basis shapes Final forged part Best shape Best weights Final forged part Case Study – 1 (Level 2) (Level 1) • Multi-Level design optimization Rail section

  25. CDOC Basis 2 [Y2] Basis 3 [Y3] Basis 1 [Y1] Basis shapes Final forged part Best shape Best weights Final forged part Case Study – 1 (Level 3) (Level 2) Rail section

  26. CDOC Basis 3 [Y3] Basis 2 [Y2] Basis 1 [Y1] Optimum shape Optimum weights • Complete die fill • Flash: 3 % Final forged part Case Study – 1(Level 3) Rail section Basis shapes Final forged part

  27. CDOC Multi-level design scheme Single-level design scheme Basis 1 [Y1] Basis 2 [Y2] Basis 3 [Y3] Basis 3 [Y3] Basis 2 [Y2] Basis 4 [Y4] Basis 1 [Y1] Optimum billet Optimum billet Result Comparison Single-level • Multi-level design scheme leads to optimum billet • Computational time increases • Expert knowledge can be used for single-level design scheme Multi-level

  28. CDOC Zone B Zone A h b h = b Case Study - 2 • h/b ratio is one • Three simple billet shapes as basis shapes • All basis shapes give underfill • Flash: 3 % • Quarter model for forging simulation 3-D Metal hub 3xh 2.2xh 1.5xh Basis 1 [Y1] Basis 2 [Y2] Basis 3 [Y3] Forged part • [Y1] and [Y2] give underfill at Zone Aand [Y3] at Zone B

  29. CDOC Results • Three design variables • 15 DOE points generated • None give complete die fill Optimum weights Forged part with complete die fill Preform shape • Achieved optimum shape in single level • Requires multi-level design process for higher h/b ratios

  30. CDOC h b 3-D Metal hub Quarter models with section view (h/b = 2) Case Study - 3 • 3-D Metal hub with h/b = 2 • Allowable flash percentage: 2% • Quarter model assumed for forging simulations

  31. CDOC Basis 3 [Y3] Basis 1 [Y1] Basis 2 [Y2] Basis shapes (quarter models) Level 1 • Three basis shapes selected in Level 1 • Fifteen DOE points for building the RSM

  32. CDOC Level 1 Results Top die profile • Level 1 best shape : Basis 3 Underfill Forged part • No other basis shape combinations give less underfill • Need to satisfy the underfill constraint • Tapering profile of the Basis 3 is crucial

  33. CDOC Level 2 • Basis 1 is the Level 1 best shape • Variation of Basis 1 form Basis 2 and Basis 3 Basis 1 [Y1] Basis 2 [Y2] Basis 3 [Y3] Basis shapes (quarter models) • Basis 2 and Basis 3 have opposing profiles

  34. CDOC Level 2 Results • No underfill • Flash volume: 2% • Basis 2 has the maximum contribution Optimum weights Preform shape Forged part with complete die fill Performance characteristics

  35. CDOC Rear end Steering link Top view Front end Isometric view Side view Case Study - 4 (Steering Link) • High volume forged component • Huge material waste (30%) occurs • Cross-sections vary along all three axes

  36. CDOC Level 1 Basis Shapes Basis 1 • Allowable flash percentage: 5% • Three simple basis shapes • All basis shapes give more underfill at the front end • Each basis vector contains 648 shape co-ordinates (216 points) Basis 2 Basis 3

  37. CDOC Resultant Shapes • Reduced basis technique decreases the number of design variables to three Basis 1 Basis 2 Possible preform shapes Basis 3

  38. CDOC Level 1 Results Level 1 best weights Level 1 best shape Forged part with underfill • Rectangular nature of Basis 3 is most crucial • Contribution of Basis 2 provides the tapering profile • Level 1 best shape becomes the Basis 1 in Level 2

  39. CDOC Level 1 Results Level 1 best shape Forged part showing underfill Performance characteristics Level 1 best shape Level 1 best shape Basis 1 Basis 2 Basis 2 Basis 3 Flash % Strain Variance Required flash percentage Basis 3 Basis 1 Basis shape Basis shape Flash percentage Strain variance

  40. CDOC Level 2 Basis 1 • Four basis shapes in Level 2 • Each basis shape has different cross-section • Number of shape co-ordinates are 1125 (375 points) Basis 2 Basis 3 Basis 4 Basis shapes

  41. CDOC Resultant Shapes Basis 1 • Four deign variables Basis 2 Possible preform shapes Basis 3 • Increasing the number of basis shapes also increases the DOE points to 25 from 15 Basis 4

  42. CDOC Level 2 Results Optimum Weights Optimum Preform Final Forged Part • Complete die fill achieved, Flash volume: 5% • Contribution of Basis 1 reduces the curvature of Basis 2 • Basis 3 Cross-sectional radii reduced • Any contribution of Basis 4 increases the strain variance

  43. CDOC Level 2 Results Optimum Preform Final Forged Part Performance characteristics Basis 2 Preform Basis 1 Basis 4 Basis 2 Basis 4 Strain Variance Flash % Preform Basis 3 Basis 1 Basis 3 Basis shape Basis shape Flash percentage Strain Variance

  44. CDOC Summary • Introduced a novel concept for 3-D preform design • Reduced basis technique • Enables design variable definition for complex 3-D components • Utilized simple basis shapes in multi-level optimization • Knowledge based basis shapes aids faster optimization • Optimum preform shapes can be easily manufactured • Applicable for both 2-D and 3-D forging processes

  45. Any questions ???

  46. Thank you

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