1. 4/20/2004s.e.mathews1 Steward Observatory Technical Division Mechanical Engineering Seminar Series Seminar #1 April 20, 2004

2. 4/20/2004s.e.mathews2 Mechanical Engineering Seminar Series  Welcome and Introduction  Purpose  Presenting Ideas  Discuss Methods and Techniques  Review of New Technology  Current Projects  Demonstration of Useful Tools  Sharing what we all know

3. 4/20/2004s.e.mathews3  Who Should Attend?  Anyone with an interest in current Opti- Mechanical Engineering Applications and Projects at UASO/SOML  Who Should be a Presenter?  Anyone who has something useful to share with the technical community. Mechanical Engineering Seminar Series

4. 4/20/2004s.e.mathews4 Scott Mathews Principal Engineer, Steward Observatory smathews@as.arizona.edu 626-8528 This Week’s Topic – April 20, 2004 Design of an Elastomer Bond Layer for Mounting Optics in a Metallic Cell Mechanical Engineering Seminar Series

5. 4/20/2004s.e.mathews5  Bonded or “Potted” Optics  The Optic is attached to its cell using an elastomeric material, epoxy, or glue  Why Bond?  Simplicity  Durability  Repeatability  Compact  Low Cost  Sometimes…nothing else will work! Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

6. 4/20/2004s.e.mathews6  Design Considerations  Static Equilibrium  Strength  Natural Frequency (jitter)  Ease of Assembly  Ease of Dis-assembly!  Deflections!!! Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

7. 4/20/2004s.e.mathews7  Deflections  Rigid Body Displacements  6 DoF motions of optic relative to its cell and to other elements of the optical system.  Allowables – “bore sight” tolerances.  Assumes optics are rigid bodies with respect to their cells, the bond materials, and the support structure.  Initial rigid body motions can be removed during “set-up” alignment.  Subsequent motions can sometimes be re- adjusted using passive or active control. Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

8. 4/20/2004s.e.mathews8  Deflections  Linear Elastic Deformation of Optical Elements  Optical aberrations caused by strain in optical materials.  Total deformation defined by P-V and RMS surface figure error.  Aberrations characterized by “shape” components (Zernike Polynomials).  Certain shapes can also be removed at initial alignment and by applying subsequent control. Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

9. 4/20/2004s.e.mathews9  Minimizing Deflections  Rigid Body  Minimize load path offsets to reduce and eliminate overturning moments.  Use widest possible support “footprints” to lower reaction forces.  Use stiffest possible bond design. Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

10. 4/20/2004s.e.mathews10  Deflections  Surface Figure Error  Unfortunately, the best design to reduce rigid body motion, can increase surface figure error.  Gravity sag between supports  Clear aperture and transmissive elements Lenses have fewer places where support attachments are allowed. Get involved in the lens design early to address mounting features.  Overconstraining – bond cannot be too stiff, needs to be compliant.  Athermalization Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

11. 4/20/2004s.e.mathews11  Analysis of RBE Lens 2 Mount  SF6 Glass lens  SS Cell  Sylgard 184 RTV for bond Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

12. 4/20/2004s.e.mathews12  Lens Dimensions  Ø 300 mm  20 mm center thickness  Surface 1, R = 1332 mm  Surface 2, R = 4350 mm  8.94 mm edge thickness Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

13. 4/20/2004s.e.mathews13  Properties  SF6  E = 7.25 x 10 6 psi  =.244   = 4.5 x 10 -6 in/in/°F  304 S.S.  E = 28.0 x 10 6 psi  =.29   = 9.6 x 10 -6 in/in/°F  Sylgard 184  E = 267 psi (derived from durometer)  =.4995 (derived from bulk modulus 90 ksi)   = 1.5 x 10 -4 in/in/°F Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

14. 4/20/2004s.e.mathews14  Initial Bond dimensions for FEA  Assume elastomer layer is constrained  Thermal expansion of elastomer (h = thickness of elastomer layer) =  e *((1+ )/(1- ))*  T*h = 2.996  e  T*h  Thermal expansion of cell (D = diameter of lens) =  c *  T*(D/2+h)  Thermal expansion of lens =  l *(D/2)*  T  The mounting is athermalized if the expansion of the elastomer equals the cell expansion less the lens expansion: 2.996  e  T*h =  c *  T*(D/2+h) -  l *(D/2)*  T  Solve for h  Adjust for Shape factor! Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

15. 4/20/2004s.e.mathews15  RTV is Nearly Incompressible!  Athermalization and Shape Factors  References  Doyle, et.al., Athermal design of nearly incompressible bonds  Michels, et. al., Finite element modeling of nearly incompressible bonds  Fata, et. al., Design of a cell for the wide-field corrector for the converted MMT Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

16. 4/20/2004s.e.mathews16  FEA Guidelines and Tips  Make sure bond layer has sufficient DoF’s  Edge effects  Mesh density  Mesh layout for rapid prototyping  Coordinate systems (cylindrical,spherical)  Element topography (tets vs. bricks)  Axisymmetric models  Test things out with sample models  Pay Attention to numerical precision Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

17. 4/20/2004s.e.mathews17  FEA of RBE L2 Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

18. 4/20/2004s.e.mathews18  Elastomer Layer Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

19. 4/20/2004s.e.mathews19  Lens Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

20. 4/20/2004s.e.mathews20  Boundary Conditions  Actual DoFs for gravity cases.  Symmetric/kinematic for thermal “rigid body”. Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

21. 4/20/2004s.e.mathews21  Remove Rigid Body Displacements  Gravity Cases  Assume glass’ modulus is 2 to 3 orders of magnitude stiffer than RTV.  Run unit gravity cases.  Displacement vectors for “rigid” lens will be subtracted from cases run with actual glass stiffness. Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

22. 4/20/2004s.e.mathews22 Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell  Remove Rigid Body Displacements  Thermal Cases  Run lens only, allowing it to expand unconstrained through anticipated  T (using symmetric/kinematic B.C.  Subtract lens displacement vector from that for case of lens attached to cell with RTV.

23. 4/20/2004s.e.mathews23  Post Processing  Group nodes that are on the same surfaces and in the clear aperture.  Calculate unit normal vectors.  Calculate orthogonalized shape components.  Remove translations, tilts, and power.  Calculate higher order shapes if necessary  RSS components that are uncorrelated, add components that are. Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

24. 4/20/2004s.e.mathews24  Unit Normal Vector u r = u x cos  + u y sin  u n = u z cos  + u r sin  u z = u z Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

25. 4/20/2004s.e.mathews25 Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell  Orthogonalization

26. 4/20/2004s.e.mathews26  Note that coefficients for unit displacements work out to be the average displacement in any unit vector direction  Zernike Polynomials   = r local /r max  Tilts,  sin ,  cos   Power, 2  2 -1  Higher order shapes, e.g. astigmatism, spherical, trefoil, etc. Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell

27. 4/20/2004s.e.mathews27 Design of an Elastomer Bond Layer for Mounting a Lens in a Metallic Cell  Excel Spreadsheet  E:\Home\RBE Lens 2.xls E:\Home\RBE Lens 2.xls