Statement of Work Deliverables

Statement of Work Deliverables

Deliverable: Action:Update Ansys and Matlab code to enhance model confidence.

Bugs identified and resolved. Matlab data fed back to Ansys.

Model effects of temperature profile for face sheet and truss.

Capability for uniform and gradient temperature loads.

Evaluate the effects of actuator uncertainties.

Two different uncertainty models investigated.

Document model and transfer technology to UF.

Documented Matlab and Ansys GT code integrated in by UF.

• Result: All deliverables successfully completed.

Overview

• Statement of Work Deliverables

• Update of Previous Work – Correction of Matched CTE Cases

• Ansys Verification of Matlab Results– Matlab Actuator Displacements Fed Back to Ansys (closed the loop)

– Thermal Aberration Reproduction vs. Correction

• Actuator Glitch Evaluation– Random Glitch

– Discrete Glitch

• Actuator Forces Evaluation

• Concluding Remarks

Parameters

Facesheet:Diameter (tip to tip) 2mF-number 1.5Thickness mModulus of Elasticity 95 GPaPoisson’s ratio 0.35CTE 13E-6 /°C

Substrate data:Beam diameter 1.16 mmModulus of elasticity 68.3 GpaPoisson’s ratio 0.33CTE 0 /°CActuator stiffness 2N/m

Thermal loads:1) 10°C uniform2) 1°C/m gradient

Actuators cases:1) 152) 1593) 1563

Update of Previous Work – Correction of Matched CTE Cases

• Problem: Similar displacements for matched and unmatched CTEs of the facesheet and truss.

Mismatched CTEs Matched CTEs(incorrect)

Facesheet only

10°C uniform load – 159 actuators

• Solution: Bug fixed in Ansys code so correct CTEs assigned in the matched case.

Update of Previous Work – Correction of Matched CTE Cases

• Problem: Similar displacements for matched and unmatched CTEs of the facesheet and truss.

Mismatched CTEs Matched CTEs(incorrect)

Facesheet only

10°C uniform load – 159 actuators

• Solution: Bug fixed in Ansys code so correct CTEs assigned in the matched case.

Correction of Matched CTE Cases - 10ºC Uniform, 159 Actuators

UpdatedMatched CTEs

PreviousMatched CTEs

• Matched CTE case is now similar to the facesheet only case.

PreviousFacesheet only

Correction of Matched CTE Cases - 1ºC/m Gradient, 159 Actuators

• Matched CTE case is now similar to the facesheet only case.

UpdatedMatched CTEs

PreviousMatched CTEs

PreviousFacesheet only

ANSYS Verification of Matlab Results

• Previously, Ansys provided influence coefficients and the response to thermal loads. These were imported into Matlab to calculate actuator displacements to reproduce the aberration.

• Currently, the Matlab-calculated actuator displacements are fed back into Ansys to either:

– Correct the thermally loaded system.

– Reproduce the thermal aberrations by actuation from an initially unloaded system (similar to previous Matlab work).

• Results: Correct and Reproduce yield similar results.

Summary: Reproduction vs. Correction

15 159 1563

Reproduction uniform x-grad uniform x-grad uniform x-grad

Absolute RMS (nm) 2549 147 2083 93 341 40

RMS (%) 0.926% 0.570% 1.232% 0.992% 0.127% 1.203%

15 159 1563

Correction uniform x-grad uniform x-grad uniform x-grad

Absolute RMS (nm) 2551 147 2084 93 342 40

RMS (%) 0.927% 0.570% 1.232% 0.995% 0.127% 1.204%

• Results: The correction is produced with essentially the same accuracy as the reproduction.

Ansys Plots: Reproduction vs. Correction

• Reproduction vs. Correction Plots:

• 15 actuators, 10ºC Uniform

• 15 actuators, 1ºC/m X-Gradient





10ºC Uniform, 15 Actuators

Absolute RMS 2549 nm

Normalized RMS 0.926 %



Reproduction Correction

Absolute RMS 147 nm


Absolute RMS 147 nm



1ºC/m X-Gradient, 15 Actuators







Absolute RMS 93 nm


Absolute RMS 93 nm





Absolute RMS 341 nm


Absolute RMS 342 nm



Absolute RMS 40 nm


Absolute RMS 40 nm




Actuator Glitch

• Three cases of actuator glitch are compared:

– No Glitch – actuators have infinite resolution.

– Discrete Glitch – actuator displacements are multiples of 50 nm.

– Random Glitch – a random glitch between +/- 50 nm is added to each actuator displacement.

• Results: The RMS errors are not sensitive to small glitches. (Small is relative to maximum actuator strokes).

Glitch Summary

No Glitch 15 159 1563

uniform x-grad uniform x-grad uniform x-grad

Absolute RMS Error (nm) 2551 147 2084 93 342 40

RMS Error (%) 0.926% 0.570% 1.232% 0.995% 0.127% 1.204%

Glitch/Max Stroke (%) 0.07% 1.47% 0.15% 2.00% 0.24% 1.79%

Discrete Glitch 15 159 1563



RMS Error (%) 0.929% 1.813% 1.235% 2.316% 0.129% 2.146%

Additional RMS Error (%) 0.00% 1.24% 0.00% 1.32% 0.00% 0.94%

Random Glitch 15 159 1563



RMS Error (%) 0.942% 1.366% 1.236% 2.871% 0.129% 2.629%

Additional RMS Error (%) 0.02% 0.80% 0.00% 1.88% 0.00% 1.42%

• Result: Glitch Additional RMS Error % Glitch/Maximum Actuator Stroke %.

Ansys Plots: Actuator Glitch

• No Glitch vs. Discrete Glitch vs. Random Glitch:




•15 actuators, 1ºC/m X-Gradient




No Glitch Discrete Glitch Random Glitch

Abs RMS 2551 nm

% RMS 0.927 %

Abs RMS 2556 nm

% RMS 0.929 %

Abs RMS 2593 nm

% RMS 0.942 %



Abs RMS 2084 nm

% RMS 1.232 %

Abs RMS 2089 nm

% RMS 1.235 %

Abs RMS 2089 nm

% RMS 1.236 %



Abs RMS 342 nm

% RMS 0.127 %

Abs RMS 347 nm

% RMS 0.129 %

Abs RMS 346 nm

% RMS 0.129 %



Abs RMS 147 nm

% RMS 0.570%

Abs RMS 468 nm

% RMS 1.813 %

Abs RMS 353 nm

% RMS 1.366 %



Abs RMS 93

% RMS 0.995%

Abs RMS 216 nm

% RMS 2.316 %

Abs RMS 268 nm

% RMS 2.817 %



Abs RMS 40

% RMS 1.204%

Abs RMS 72 nm

% RMS 1.146 %

Abs RMS 88 nm

% RMS 2.629 %

Actuator Forces

• Force Evaluation

– Increasing numbers of actuators, increases required actuator forces.

– 15 actuators case met force specifications (< 0.1N) for both 10ºC Uniform and 1ºC/m X-Gradient loads.

– 159 and 1563 actuators cases exceed force specifications for both loadings.

– (Note: will add 45 and 93 actuator cases.)

Ansys Plots: Actuator Forces

• Force Plots


• 45 actuators, 10°C Uniform

• 93 actuators, 10°C Uniform




• 45 actuators, 1°C/m X-Gradient

• 93 actuators, 1°C/m X-Gradient




• Maximum actuator force within limit (< 0.1N).

aberrationactuator forces

P2V 1419 m



Maximum Force 0.026 N

Maximum Stroke 68.4 m


• Maximum actuator force is exceeded (> 0.1N).


P2V 592 m

Absolute RMS 2,482 nm







P2V 651 m

Absolute RMS 2,329 nm





• Maximum actuator force is exceeded (> 0.1N)

aberration

P2V 661 m





actuator forces



aberration

P2V 654 m

Absolute RMS 342 nm




actuator forces


• Maximum actuator force is within limit (< 0.1N).

aberration

P2V 254 m

Absolute RMS 147 nm




actuator forces


aberration

P2V 283 m

Absolute RMS 121 nm




actuator forces



aberration

P2V 170.7 m

Absolute RMS 106 nm




actuator forces




aberration

P2V 88.1 m

Absolute RMS 93 nm




actuator forces

Concluding Remarks

• Only the 15 actuator case satisfied all specified criteria

– RMS errors for the two thermal loads were low, less than 1%.

– Maximum force levels required only 25% of the holding force.

– Maximum stroke was about 50% of maximum.

– Large P2V amplitudes corrected (1419 m and 254 m).

• Increasing actuators increased actuator forces to unacceptable levels.

Statement of Work Deliverables

Documents

matched case

actuators matched cte

correct ctes

previous matlab work

unmatched ctes

ansys code

matlab code

update ansys