geometrical optimization of a disc brake lauren feinstein [email protected] vladimir kovalevsky...
TRANSCRIPT
![Page 1: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/1.jpg)
Geometrical optimization of a
disc brake
Lauren Feinstein [email protected]
Vladimir Kovalevsky [email protected]
Nicolas Begasse [email protected]
![Page 2: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/2.jpg)
Presentation Overview
• Optimization Overview• Disc Brake Analysis• Response Surface Optimization
![Page 3: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/3.jpg)
Design process• Functional requirements• Initial design• Topologic optimization• Parametric optimization
![Page 4: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/4.jpg)
Problem statement
objective function
state variables
bounded domain
Given geometryGiven parameters
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Example problem
• Variables ?
Minimize displacement
Bounded volumeBounded stress
![Page 6: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/6.jpg)
Parametric optimization
• X = thickness of each portion• 5 Variables
Minimize displacement
Bounded volumeBounded stress
![Page 7: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/7.jpg)
Topologic optimization
• X = presence of each cell• 27 variables
Minimize displacement
Bounded volumeBounded stress
![Page 8: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/8.jpg)
Parametric with interpolation
• X = position of each point• 8 variables
Minimize displacement
Bounded volumeMaximum stress
• We use this one!
![Page 9: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/9.jpg)
ANSYS Modeling (Reference)
80mm
60mm
Symmetry
0.28 MPa
Linear Elastic, Isotropic
![Page 10: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/10.jpg)
ANSYS Modeling (Optimization)
80mm
60mm
0.28 MPa
Symmetry
X 1
X 2
Min total displacementBC & symmetry
Linear Elastic, Isotropic
![Page 11: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/11.jpg)
Ansys Results : Deflection
Optimized Reference
mm mm
9.2% Reduction
![Page 12: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/12.jpg)
Ansys Results :
not exceeded8.35% Reduction
MPa MPa
Optimized Reference
![Page 13: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/13.jpg)
Response Surface Optimization
X 1 X 2
Dis
plac
emen
t
![Page 14: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/14.jpg)
Objective Function Formulation
Optimization parameter
Penalty functions for design variables
Penalty functions for state variables
Traditional Method
ANSYS
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Design of ExperimentsAngle 1
Angl
e 2
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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
![Page 17: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/17.jpg)
MISQPMixed Integer Sequential Quadratic Programming
Angle 1Angle 2
Dis
plac
emen
t
![Page 18: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/18.jpg)
Candidate Point Validation
Angle 1Angle 2
Dis
plac
emen
t
![Page 19: Geometrical optimization of a disc brake Lauren Feinstein lpf24@cornell.edu Vladimir Kovalevsky vk285@cornell.edu Nicolas Begasse nb442@cornell.edu](https://reader030.vdocument.in/reader030/viewer/2022032703/56649d205503460f949f5278/html5/thumbnails/19.jpg)
Thank you!