Statement of work deliverables
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Statement of Work Deliverables. Result : All deliverables successfully completed. 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)

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Statement of work deliverables

Statement of Work Deliverables

  • 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

Overview


Parameters

Parameters

Facesheet:

Diameter (tip to tip)2m

F-number1.5

Thickness m

Modulus of Elasticity 95 GPa

Poisson’s ratio 0.35

CTE 13E-6 /°C

Substrate data:

Beam diameter 1.16 mm

Modulus of elasticity 68.3 Gpa

Poisson’s ratio 0.33

CTE 0 /°C

Actuator stiffness 2N/m

Thermal loads:

1) 10°C uniform

2) 1°C/m gradient

Actuators cases:

1) 15

2) 159

3) 1563


Problem similar displacements for matched and unmatched ctes of the facesheet and truss

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

Update of Previous Work – Correction of Matched CTE Cases

10°C uniform load – 159 actuators

Mismatched CTEs

Matched CTEs(incorrect)

Facesheet only

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


Problem similar displacements for matched and unmatched ctes of the facesheet and truss1

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

Update of Previous Work – Correction of Matched CTE Cases

10°C uniform load – 159 actuators

Mismatched CTEs

Matched CTEs(incorrect)

Facesheet only

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


Correction of matched cte cases 10 c uniform 159 actuators

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

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

PreviousFacesheet only

Previous

Matched CTEs

UpdatedMatched CTEs


Correction of matched cte cases 1 c m gradient 159 actuators

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

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

PreviousFacesheet only

Previous

Matched CTEs

UpdatedMatched CTEs


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.

ANSYS Verification of Matlab Results


Summary reproduction vs correction

Summary: Reproduction vs. Correction

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


Ansys plots reproduction vs correction

Ansys Plots: Reproduction vs. Correction

  • Reproduction vs. Correction Plots:

    • 15 actuators, 10ºC Uniform

    • 15 actuators, 1ºC/m X-Gradient

    • 159 actuators, 10ºC Uniform

    • 159 actuators, 1ºC/m X-Gradient

    • 1563 actuators, 10ºC Uniform

    • 1563 actuators, 1ºC/m X-Gradient


10 c uniform 15 actuators

10ºC Uniform, 15 Actuators

Correction

Reproduction


1 c m x gradient 15 actuators

1ºC/m X-Gradient, 15 Actuators

Correction

Reproduction


10 c uniform 159 actuators

10ºC Uniform, 159 Actuators

Correction

Reproduction


1 c m x gradient 159 actuators

1ºC/m X-Gradient, 159 Actuators

Correction

Reproduction


10 c uniform 1563 actuators

10ºC Uniform, 1563 Actuators

Correction

Reproduction


1 c m x gradient 1563 actuators

1ºC/m X-Gradient, 1563 Actuators

Correction

Reproduction


Actuator glitch

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 smallglitches. (Small is relative to maximum actuator strokes).


Glitch summary

Glitch Summary

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


Ansys plots actuator glitch

Ansys Plots: Actuator Glitch

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

    • 15 actuators, 10ºC Uniform

    • 159 actuators, 10ºC Uniform

    • 1563 actuators, 10ºC Uniform

    • 15 actuators, 1ºC/m X-Gradient

    • 159 actuators, 1ºC/m X-Gradient

    • 1563 actuators, 1ºC/m X-Gradient


10 c uniform 15 actuators1

10ºC Uniform, 15 Actuators

No Glitch

Random Glitch

Discrete Glitch


10 c uniform 159 actuators1

10ºC Uniform, 159 Actuators

No Glitch

Random Glitch

Discrete Glitch


10 c uniform 1563 actuators1

10ºC Uniform, 1563 Actuators

No Glitch

Random Glitch

Discrete Glitch


1 c m x gradient 15 actuators1

1ºC/m X-Gradient, 15 Actuators

No Glitch

Random Glitch

Discrete Glitch


1 c m x gradient 159 actuators1

1ºC/m X-Gradient, 159 Actuators

No Glitch

Random Glitch

Discrete Glitch


1 c m x gradient 1563 actuators1

1ºC/m X-Gradient, 1563 Actuators

No Glitch

Random Glitch

Discrete Glitch


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.)

Actuator Forces


Ansys plots actuator forces

Ansys Plots: Actuator Forces

  • Force Plots

    • 15 actuators, 10ºC Uniform

    • 45 actuators, 10°C Uniform

    • 93 actuators, 10°C Uniform

    • 159 actuators, 10ºC Uniform

    • 1563 actuators, 10ºC Uniform

    • 15 actuators, 1ºC/m X-Gradient

    • 45 actuators, 1°C/m X-Gradient

    • 93 actuators, 1°C/m X-Gradient

    • 159 actuators, 1ºC/m X-Gradient

    • 1563 actuators, 1ºC/m X-Gradient


10 c uniform 15 actuators2

10ºC Uniform, 15 Actuators

actuator forces

aberration

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


10 c uniform 45 actuators

10ºC Uniform, 45 Actuators

actuator forces

aberration

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


10 c uniform 93 actuators

10ºC Uniform, 93 Actuators

actuator forces

aberration

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


10 c uniform 159 actuators2

10ºC Uniform, 159 Actuators

actuator forces

aberration

  • Maximum actuator force is exceeded (> 0.1N)


10 c uniform 1563 actuators2

10ºC Uniform, 1563 Actuators

Maximum actuator force is exceeded (> 0.1N)

aberration

actuator forces


1 c m x gradient 15 actuators2

1ºC/m X-Gradient, 15 Actuators

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

actuator forces

aberration


1 c m x gradient 45 actuators

1ºC/m X-Gradient, 45 Actuators

actuator forces

aberration

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


1 c m x gradient 93 actuators

1ºC/m X-Gradient, 93 Actuators

actuator forces

aberration

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


1 c m x gradient 159 actuators2

1ºC/m X-Gradient, 159 Actuators

Maximum actuator force is exceeded (> 0.1N)

actuator forces

aberration


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.

Concluding Remarks


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