Steward Observatory Technical Division

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Steward Observatory Technical Division

• Mechanical Engineering
• Seminar Series
• Seminar 1 April 20, 2004

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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

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Mechanical Engineering Seminar Series

• 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.

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Mechanical Engineering Seminar Series

• Scott Mathews
• Principal Engineer,
• Steward Observatory
• smathews_at_as.arizona.edu
• 626-8528
• This Weeks Topic April 20, 2004
• Design of an Elastomer Bond Layer for Mounting
  Optics in a Metallic Cell

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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
• Sometimesnothing else will work!

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Design Considerations
• Static Equilibrium
• Strength
• Natural Frequency (jitter)
• Ease of Assembly
• Ease of Dis-assembly!
• Deflections!!!

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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.

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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.

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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.

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Analysis of RBE Lens 2 Mount
• SF6 Glass lens
• SS Cell
• Sylgard 184
• RTV for bond

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Lens Dimensions
• Ø 300 mm
• 20 mm center thickness
• Surface 1, R 1332 mm
• Surface 2, R 4350 mm
• 8.94 mm edge thickness

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Properties
• SF6
• E 7.25 x 106 psi
• n .244
• a 4.5 x 10-6 in/in/F
• 304 S.S.
• E 28.0 x 106 psi
• n .29
• a 9.6 x 10-6 in/in/F
• Sylgard 184
• E 267 psi (derived from durometer)
• n .4995 (derived from bulk modulus 90 ksi)
• a 1.5 x 10-4 in/in/F

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Initial Bond dimensions for FEA
• Assume elastomer layer is constrained
• Thermal expansion of elastomer (h thickness of
  elastomer layer)
• ?e((1?)/(1- ? ))?Th 2.996 ?e ?Th
• Thermal expansion of cell (D diameter of lens)
  ?c?T(D/2h)
• 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 ?Th ?c?T(D/2h) - ?l(D/2)?T
• Solve for h
• Adjust for Shape factor!

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• FEA Guidelines and Tips
• Make sure bond layer has sufficient DoFs
• 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

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• FEA of RBE L2

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Elastomer Layer

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Lens

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Boundary Conditions
• Actual DoFs for gravity cases.
• Symmetric/kinematic for thermal rigid body.

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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.

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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 DT (using
  symmetric/kinematic B.C.
• Subtract lens displacement vector from that for
  case of lens attached to cell with RTV.

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• 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.

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Unit Normal Vector
• ur uxcosq uysinq un uzcosf ursinf
• uz uz

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Orthogonalization

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Note that coefficients for unit displacements
  work out to be the average displacement in any
  unit vector direction
• Zernike Polynomials
• r rlocal/rmax
• Tilts, r sinq, r cosq
• Power, 2r2-1
• Higher order shapes, e.g. astigmatism, spherical,
  trefoil, etc.

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Design of an Elastomer Bond Layer for Mounting a
Lens in a Metallic Cell

• Excel Spreadsheet
• E\Home\RBE Lens 2.xls