Geometrical optimization of a

disc brakeLauren Feinstein lpf24@cornell.edu

Vladimir Kovalevsky vk285@cornell.edu

Nicolas Begasse nb442@cornell.edu

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

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

Problem statement objective function

state variables

bounded domain

Given geometryGiven parameters

Example problem

• Variables ?

Minimize displacement

Bounded volumeBounded stress

Parametric optimization

• X = thickness of each portion• 5 Variables

Minimize displacement

Bounded volumeBounded stress

Topologic optimization

• X = presence of each cell• 27 variables

Minimize displacement

Bounded volumeBounded stress

Parametric with interpolation

• X = position of each point• 8 variables

Minimize displacement

Bounded volumeMaximum stress

• We use this one!

ANSYS Modeling (Reference)

80mm

60mm

Symmetry

0.28 MPa

Linear Elastic, Isotropic

ANSYS Modeling (Optimization)

80mm

60mm

0.28 MPa

Symmetry

X 1

X 2

Min total displacementBC & symmetry

Linear Elastic, Isotropic

Ansys Results : Deflection

Optimized Reference

mm mm

9.2% Reduction

Ansys Results :

not exceeded8.35% Reduction

MPa MPa

Optimized Reference

Response Surface Optimization

X 1 X 2

Disp

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Objective Function Formulation

Optimization parameter

Penalty functions for design variables

Penalty functions for state variables

Traditional Method

ANSYS

Design of ExperimentsAngle 1

Angl

e 2

Kriging Algorithm

180190

200210

220110

120130

140

0.9

1

1.1

1.2

1.3

x 10-4

x1 x2

Disp

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men

t

MISQPMixed Integer Sequential Quadratic Programming

Angle 1Angle 2

Disp

lace

men

t

Candidate Point Validation

Angle 1Angle 2

Disp

lace

men

t

Thank you!