Sag of ZTF components

Callahan9/4/2014

Corrector Trim Plate analysis

Analytic solution using plate model from Roark and Young predicts 1g deflections of 468 microns.

See MathCad model: sag of corrector.

FEA assumptions

• Float glass• Thickness 3/8” [9.525mm]• 1 g vertical (Z-axis) loads

FEA validation. See: sag of correctorFine mesh model: 458 microns

Loads

Mesh density: Fine

Window sag assumptions

• Fused Silica• Outer radius 4406mm• Inner radius flat• Max thickness in center 28mm

Fracture mechanics models determine the factor of safety for any given stress and probability if success.

• See MathCad model: Design Strength- Fused silica by Callahan

• At 99% survival probability the maximum yield strength is 36 MPa. The Factor of Safety, FOS, can now be calculated for any given applied stress.

• The current stress in the ZTF window at 1 atm (14.7psi) is 10.5 MPa with a FOS=3.4

• At an over-pressure of 1.25 x 14.7psi the FOS decreases to 2.7.

Z-deflection max 209 microns

Mesh density

Loads

What is the contribution of gravity loading (opposite direction to the pressure load)

Very small ~1.2 microns

Calculate the sag of the focal plane under 1g

• Assume CCD’s weigh 174 gm each x 27• Force 27.3 N• 1g Z-axis

Analyze final window design

• Fused Silica• Supported on Delrin “cushions”• Apply various pressures (1 atm)

Mesh

Max principal stress

Add line pressure at O-ring center.

• See Parker O-ring handbook to determine the line pressure. I used a typical mid-value of 2 lbs/in.

• See: https://www.parker.com/literature/ORD%205700%20Parker_O-Ring_Handbook.pdf

Loads

Add 2 lb/in line pressure at O-ring center

• Max principal stress increased to 12 psi.

Substitute Delrin support at the outer location.

• Stress decreases to 6.0 Mpa!!!• Use rough contact between outer delrin and

window to allow separation.

Max principal 6.0MPa!Lowest stress yet… very uniform.

May be artifically low due to bonded contracts at cushions.

Deflection under 1 atm~100 microns

Update model3mm thick delrin Gasket model (1/4 model)

8.9MPa Max Principal stressAt 99% probability of survival fused silica has a maximum strength of 36MPa.

Ths means we have a Factor of safety of 4.0.

Change gasket to steel to simulate equal support does not change the stress significantly. Max ~8.91 MPa

Stress due to ends separating from gasket are still high.

To determine the effect of the separeation of the window from the gasket at the corners I fixed the vertical displacement (Z) of the corner.

Stress only reduced to 8.3 Mpa.

Reduce gasket to uniform 0.24” width.Use Delrin. Stress increases to 9.7MPa

Change gasket to steel to see how stiffening effects stress. No change

Increase gasket width to 13.4mm (previously 6.1mm) reduces stress to 8.7MPa

Sag Absolute7.3 microns

Sag under 1g plus weight of CCD package (174gm)

New cable clearance hole size