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Geometrical optimization of a
disc brake
Lauren Feinstein [email protected]
Vladimir Kovalevsky [email protected]
Nicolas Begasse [email protected]
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
Dis
plac
emen
t
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
120
130
140
0.9
1
1.1
1.2
1.3
x 10-4
x1 x2
Dis
plac
emen
t
MISQPMixed Integer Sequential Quadratic Programming
Angle 1Angle 2
Dis
plac
emen
t
Candidate Point Validation
Angle 1Angle 2
Dis
plac
emen
t
Thank you!