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http://nasa.ece.olin.edu/projects/2006/Mirrorhttp://nasa.ece.olin.edu/projects/2006/Mirror
A Distortion Free A Distortion Free SupportSupport
for a Thin X-Ray Mirrorfor a Thin X-Ray Mirror
Team members: Team members: Mark Cavalowsky, Brad Westgate, Peter Massari, Chester Mark Cavalowsky, Brad Westgate, Peter Massari, Chester
Macklin Macklin
Supervising NASA Astrophysicist Dr. William ZhangSupervising NASA Astrophysicist Dr. William ZhangAdvisors Dr. Steve Holt and Dr. Brad MinchAdvisors Dr. Steve Holt and Dr. Brad Minch
Presented byPresented byBennett Chabot and Andy KalcicBennett Chabot and Andy Kalcic
A NASA/Olin Research Project
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
MirrorMirror
The ProblemThe Problem
Create a cradle of Create a cradle of springs to minimize springs to minimize the distorting the distorting effect of gravity on effect of gravity on the mirrorthe mirror
Maximum Maximum distortion: 10 nm distortion: 10 nm or 1e-8 mor 1e-8 m Correlates to 5 arc-Correlates to 5 arc-
second resolutionsecond resolution
Springs must compress Springs must compress springs by an average springs by an average which is orders of which is orders of magnitude greater magnitude greater than combined than combined irregularityirregularity
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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The SolutionThe Solution
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Our ApproachOur Approach
Test configurations with increasing Test configurations with increasing complexitycomplexity
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Virtual ModelVirtual ModelFEMLABFEMLAB
Complete:Complete:““1D” Beam with Solid Supports1D” Beam with Solid Supports““1D” Beam with Spring Supports1D” Beam with Spring SupportsAbility to Automate Ability to Automate
In Progress:In Progress:““1D” Curved Beam1D” Curved BeamFull 3D Curved MirrorFull 3D Curved MirrorAdjust individual spring Adjust individual spring
constants/positionsconstants/positions
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Z Displacement in Virtual Model
Two Solid Supports Case
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Z Displacement in Virtual Model
Eleven Solid Supports Case
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Analytical ModelAnalytical Model
Complete:Complete:1D straight beam, solid supports1D straight beam, solid supports1D straight beam, spring supports1D straight beam, spring supports2D flat plate2D flat plate
In Progress:In Progress:2D flat plate, point support boundary 2D flat plate, point support boundary
conditionsconditions1D Curved beam1D Curved beam
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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2D Plate with Edge Constraints and Point Forces (Analytical Model)
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Comparison of ModelsComparison of Models
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Comparison of Model Data
1D Beam with 11 Solid Supports
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Absolute Error Comparison
1D Beam with 11 Solid Supports
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Comparison of Models
3 Spring Supports
Maximum Absolute Error: 3.57e-9m
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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Their placement has errors: σp~ 0.5mm
http://nasa.ece.olin.edu/projects/2006/Mirrorhttp://nasa.ece.olin.edu/projects/2006/Mirror
http://nasa.ece.olin.edu/projects/2006/http://nasa.ece.olin.edu/projects/2006/
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