Athermal bond thickness for axisymmetric optical elements - PowerPoint Presentation

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Athermal bond thickness for axisymmetric optical elementsTutorial by Eric Frater

IntroductionMotivationsSurvival of opticsSurvival of bondPerformance of opticsConcernsT

hermal stressRadial stressShear stresses

Glass distortion

r

z

r

𝜃

Example designCell: Aluminum 6061-T6Optic: Schott N-BK7Adhesives:MG chemicals RTV 5663M 2216 B/A (gray)

Design:Bond provides constraintUniform and continuous bond-line

Zero-strain in materials at nominal bonding temp

Material constantsMATERIAL

α(ppm/°C)Poisson ratio, ν

E (Gpa

)

N-BK7

7.1

.21

82

6061-T6

24

.33

69

2216 B/A (

gray)

[1]

102

~.43

69

RTV 566

200~.499

~.003

α

c

r

c

α

b

α

o

r

o

Quick note: 2216 B/A and RTV 566

very

different adhesives. As seen in the table,

RTV compliance highly dependent on aspect ratio of bond.

Subscript notation:

“

c

”:

cell

“

b

”:

bond“o”: optic

Required:αb > αc > αo orαb = αc = αo

[1] Yoder, Paul R.

Mounting Optics in Optical Instruments

Bayar equation

Consider positive

ΔT

in example design

Assume bond only radially constrained Require:

Δ

T

z

r

𝜃

r

Example: h= 2.75mm (2216 B/A), h= 1.22mm (RTV 566)

Δ

T

(Bayar equation

[2]

)

Note: This

vastly over-predicts

thickness, neglects

ν

[2]

Bayar, Mete

. “

Lens Barrel

Optomechanical

Design Principles

”

Radial strain and Hooke’s LawFrom Bayar equation (valid in all cases):

Radial stress from Hooke’s Law:

Athermalizing

:

Define

ε

r

and

ε

θ

Set radial stress equal to zero

(pre-factor drops out)

Solve for

athermal

bond thickness

h

Van

Bezooijen equation

Assume bond is

perfectly constrained in r, z,

θ

Solving for

σ

r

=0,

.

Δ

T

z

r

𝜃

r

Δ

T

Example: h= 1.03mm (2216 B/A), h= 0.40mm (RTV 566)

(van

Bezooijen

equation

[3]

)

Note: This

under-predicts

thickness, neglects axial

bulging of bond

[3]

Van

Bezooijen

,

Roel

. “Soft Retained AST Optics”

Modified van

Bezooijen equation

Assume bond is

perfectly constrained in r,

θ and unconstrained

in z

Solving for

σ

r

=0,

.

Δ

T

z

r

𝜃

r

Δ

T

Example: h= 1.50mm (2216 B/A), h= 0.60mm (RTV 566)

(modified van

Bezooijen

equation

[4]

)

Note: This

over-predicts

thickness, allows excessive axial

bulging

[4]

Monti

,

Christpher

L. “

Athermal

bonded mounts: Incorporating aspect ratio into a closed-form solution”

Aspect ratio Aspect ratio and axial constraint:Part of bond expands freely in zMiddle section is perfectly constrained in zModifies the axial strain

z

r

Varies from 1-2 between limits of van

Bezooijen

eq.’s

Unconstrained in z

if

h=L

Closed-form aspect ratio approximation

Δ

T

z

r

𝜃

r

Δ

T

Example: h= 1.13mm (2216 B/A), h= 0.41mm (RTV 566)

(Aspect ratio approximation

[4]

)

Note: Provides a best-guess for

h

in closed-form

[4]

Monti

,

Christpher

L. “

Athermal

bonded mounts: Incorporating aspect ratio into a closed-form solution”

ConclusionsBayar equationGood conceptual starting pointTends to vastly over-estimate hApplicable to highly segmented bonds

THICKNESS EQUATION

2216 B/A

RTV 566

Bayar

2.75 mm

1.22 mm

van Bezooijen

1.03 mm

0.40 mm

Modified van Bezooijen

1.50 mm

0.60 mm

Aspect ratio approximation

1.13 mm

0.41 mm

Van

Bezooijen

equation

Takes all strains into account

Much more accurate than Bayar eq.

Under-predicts

h

due to bulk effects

Aspect ratio approximation

Approximates varying bulk effects due to aspect ratio of bond

Matches empirical FEA-derived

corrections

to van

Bezooijen

eq. well for

>4

and

ν

[5]

Michels

, Gregory, and Keith Doyle. “Finite Element Modeling of Nearly Incompressible Bonds”

ReferencesYoder, Paul R. Mounting Optics in Optical Instruments, 2nd ed. SPIE Press Monograph Vol. PM181 (2008), p. 732.Bayar, Mete. “Lens Barrel Optomechanical Design Principles”, Optical Engineering. Vol. 20 No. 2 (April 1981)Van

Bezooijen, Roel. “Soft Retained AST Optics” Lockheed Martin Technical MemoMonti

, Christpher L. “Athermal bonded mounts: Incorporating aspect ratio into a closed-form solution”, SPIE 6665, 666503 (2007)

Michels, Gregory, and Keith Doyle. “Finite Element Modeling of Nearly Incompressible Bonds”, SPIE 4771, 287 (2002)