Geometrical optimization of a disc brake

1. Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu

2. Presentation Overview • Optimization Overview • Disc Brake Analysis • Response Surface Optimization

3. Design process • Functional requirements • Initial design • Topologic optimization • Parametric optimization

4. Problem statement objective function state variables bounded domain Given geometry Given parameters

5. Example problem • Variables ? Minimize displacement Bounded volume Bounded stress

6. Parametric optimization • X = thickness of each portion • 5 Variables Minimize displacement Bounded volume Bounded stress

7. Topologic optimization • X = presence of each cell • 27 variables Minimize displacement Bounded volume Bounded stress

8. Parametric with interpolation • X = position of each point • 8 variables Minimize displacement Bounded volume Maximum stress • We use this one!

9. ANSYS Modeling (Reference) 0.28 MPa Linear Elastic, Isotropic 80mm 60mm Symmetry

10. ANSYS Modeling (Optimization) Min total displacement BC & symmetry 0.28 MPa Linear Elastic, Isotropic 80mm 60mm X 1 X 2 Symmetry

11. Ansys Results : Deflection 9.2% Reduction mm mm Optimized Reference

12. Ansys Results : not exceeded 8.35% Reduction MPa MPa Optimized Reference

13. Response Surface Optimization Displacement X 2 X 1

14. Objective Function Formulation Penalty functions for state variables Optimization parameter Penalty functions for design variables Traditional Method ANSYS

15. Design of Experiments Angle 1 Angle 2

16. Kriging Algorithm Displacement x2 x1

17. MISQPMixed Integer Sequential Quadratic Programming Displacement Angle 2 Angle 1

18. Candidate Point Validation Displacement Angle 2 Angle 1

19. Thank you!