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

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) 80mm 60mm Symmetry 0.28 MPa

10. ANSYS Modeling (Optimization) 80mm 60mm 0.28 MPa Symmetry X 1 X 2

11. Ansys Results : Deflection OptimizedReference mm 9.2% Reduction

12. MPa OptimizedReference

13. Response Surface Optimization X 1 X 2 Displacement

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

15. Design of Experiments Angle 1 Angle 2

16. Kriging Algorithm x1 x2 Displacement

17. MISQP Mixed Integer Sequential Quadratic Programming Angle 1 Angle 2 Displacement

18. Candidate Point Validation Angle 1 Angle 2 Displacement

19. Thank you!