design and development of the fsm (fast steering secondary mirror) myung cho, noao-gsmtpo kwijong...

Design and Development of the FSM (Fast steering Secondary Mirror)

Myung Cho, NOAO-GSMTPOKwijong Park, KASI

Young-Soo Kim, KASI

1October 4, 2010 GMT2010: Design and Development of FSM

OUTLINE

1. Prior Work: Magellan Secondary Mirror modeling2. FSM Configuration3. Design and Development (work in progress)4. GMT FSM Performance Predictions

a. Gravity Analysis b. Thermal Analysis c. Natural Frequency analysis d. Lateral support flexure analysis e. Sensitivity analysis f. Zenith Angle effects

5. Summary and Conclusion6. Next Steps


Magellan Heritage

25.4m GMT6.5m Magellan telescope

GMTPrimary: 25.4m (8.4m x 7)Secondary: 3.2m (1.06m x 7)Shape: EllipsoidFocal ratio: F/0.7Final focal ratio: F/8

Magellan telescopePrimary: 6.5mSecondary: 1.3mShape: ParaboloidFocal ratio: F/1.25Final focal ratio: F/11.0

※ Gregorian

Magellan heritage: Magellan secondary mirror


Magellan M2 Assembly

For GMT FSM design and development, take a conservative engineering approach; utilize concepts established from the F/11 M2 of Magellan telescope.

Secondary Mirror Assembly of Magellan telescope


GMT and GMT FSM

Primary: 25.4m (8.4m x 7)Secondary: 3.2m (1.06m x 7)Shape: EllipsoidFocal ratio: F/0.7Final focal ratio: F/8 Gregorian

GMT F/8 Gregorian beamsConjugated M1 and M2


FSM assembly layout


1060mm

17

5m

m

14

0m

m

FSM optical prescription FSM optical prescription (as of 9/2010):

FSM M2 nominal segment Configuration:


FSM Error Budget specification

Error budget: Encircled Energy diameters at 80% (EE80)

Orientation 80% EE Specifications

Zenith 0.020” (arc-seconds)

Horizon 0.030”

Figure error 0.039”


• Finite Element mirror model• 3D solid elements• Center mirror of the FSM array (on-axis)• Clear aperture in the optical surface evaluations:

OD=1060mm

• Solid Zerodur concave lightweight (63%)• Nominal mirror thickness: 140mm• RADCV=4.2m; sag=0.031m• Center of gravity (CG) = 0.0205m (from vertex)• Mass=105 kg; Ixx=6.3 kg-m2, Izz=12.3 kg-m2 at CG• CTE = 20 E-9 /’C

• Support systems• Axial support = 3 point mount with vacuum• Lateral support = single central flexure

Assumptions in FE

X

Y

FSM local coordinates


• Three axial support (defining points) mounted at the mirror back surface

• Axial supports oriented parallel to the optical axis (vertical, Z-axis)

• Axial gravity is fully compensated by a vacuum system at Zenith

• Lateral gravity is held by a flexure at the mirror center position on the M2 CG plane.

FSM Support system

FSM support system


P: Atmosphere pressure(counter-pressure)

W: Weight

Support system – FE modeling

Axial support: Vacuum floating system Atmospheric pressure was applied on the

entire front surface of the FSM from the vacuum

Magnitude of the atmospheric pressure is equivalent to the axial gravity of FSM Reaction force at the three axial supports is

to be zero; therefore, the FSM is floating This floating axial system provides a low

surface error in Zenith. Lateral support: Flexure system

FSM gravity is held by a flexure at the mirror center location Line of action is on the mirror CG plane No axial force is to be induced at Horizon


Mirror Blank Optimization

A. 100mm : 78.8kg

B. 120mm : 84.1kg

C. 140mm : 89.3kg

D. 150mm : 91.9kgE. 150mm (rib = 10mm) : 118.4kg

Four different configurations (depth effect):1. Gravity print-through2. Natural Frequency

Baseline: favorable configuration for stiffness and stress requirements

Depth=140mmFace sheet

thickness=20mm Mass=105kg


FSM: Gravity Print-through

PTT: RMS=6.1 nm surface

RAW (un-corrected))

Optical Surface deformation maps

P.T.T corrected

Lateral Gravity (Gy) Axial Gravity (Gz+vacuum)

PTT: RMS=3.8 nm surface


FSM: thermal gradient, T(z)

Thermal gradients delta T =1oC/0.1m along Z axis (Optical axis)

(CTE = 20 x 10-9 /oC)

Displacement in Z: Max.= 18 nm; PV=35 nm

P.T.T corrected

PV=22nm; RMS=6.3nm surface

Mechanical and Optical surface deformations 14October 4, 2010 GMT2010: Design and Development of FSM

1st Mode Shape: Astigmatism at 720 Hz

Natural Frequency (first mode)

Mirror mass = 105 Kg in the FE model

1st natural frequency mode with free-free condition


3

1412108

641

21191716

Natural mirror mode (low order modes)


Typical Lateral Flexures in trade

15mm 10.16mm

5mm 8.68mm0.7mm

100mm

Thickness of Disk Flexure

Sample: Section Plane of Lateral Flexure17October 4, 2010 GMT2010: Design and Development of FSM

Lateral Flexure Trade study

Typical results during trade study in static, buckling and non-linear analysis

Stress calculation Lateral deformation Buckling analysis

y

x

Stress analysis of lateral flexure was performed initially based on thickness and materials provided by GMTO. Further assumptions were made for parametric study. This work is in progress.


RMS=3.8nm surface

Fully Balanced 97% compensation

RMS=4.1nm surface

Optical Surface deformation maps

Sensitivity: Axial gravity/vacuum

Atmosphere pressure

Gravity

Axial gravity compensated by pressure

3% residual by axial support 10N each

3% residual force by lateral support(work in progress)


RMS=12.2nm surface

10 N/m along optical axis 10 N/m along radial direction

RMS=1.0nm surface

Sensitivity: vacuum sealSeal force applied along the edge of front surface (Flange)(currently assumed a uniform distribution)

RMS=3.9nm RMS=0.4nm

Focus corrected


Zenith Angle Dependence

• Print-through from Zenith variation• Combination of optical surfaces from

Axial and Lateral cases

• Axial support print-through• RMS surface 3.8 nm

• Lateral support print-through• RMS surface 6.1 nm

• RMS calculations based on surface polished out at FSM face-up

Gravity Print-through effects from Zenith angle variations


Optical calculations (AXIAL)

Surface error Slope X Slope Y

EE80 diameter

AXIALRMS surface error 3.8 nm

RMS surface X_slope 0.035 micro_radRMS surface Y_slope 0.035 micro_rad

EE80 diameter 0.007 arcsec


Optical calculations (LATERAL)


LATERALRMS surface error 6.1 nm





Optical calculations (ZA=60o) (polished and tested at FSM face-up)

Zenith Angle at 60RMS surface error 5.6 nm




Structure Function calculations (ZA=60o)

Phase map

RMS WFE: 11.2 nm

Structure function at ZA=60o: sqrt(D) in WFE

Structure function of random variable, P(r)D() = < | P(r+ ) - P(r) |2 >


Summary and Conclusion

FSM mirror blank optimum configuration: D=1.06m; depth=140mm; face plate thickness=20mm;

mass=105kg Lightweight glass or glass ceramic mirror

FSM support system provides adequate optical performances: Gravity print-through effects: – met error budget

Axial gravity: 3.8nm RMS surface; EE80 = 0.007 arcsec (< 0.020) Lateral gravity: 6.1nm RMS surface; EE80 = 0.005 arcsec (< 0.020)

FSM thermal effects were accessed: Thermal soak, thermal gradients

Natural frequency analysis for FSM mirror blank: Lowest mode is at 720 hz (astigmatic mode) – stiff mirror

Optical performances at various Zenith angles: – met error budget Assume: FSM figured and tested at its face up position

At ZA=60 degrees: EE80 = 0.005 arcsec (< 0.039)


Next Step FSM performance evaluations

Support sensitivity Vacuum seals and seal force sensitivity

FSM mirror support system trade study Axial support :

Vacuum support Lateral support :

Lateral support diaphragm/flexure Stiffness of axial and lateral supports

Work with GMTO for Magellan Secondary mirror engineering document: Lateral support flexure and bonding procedure Vacuum


Acknowledgments

The authors gratefully acknowledge the support of the GMT Office, Matt Johns and Stephen Shectman. This work was partially contributed by the scientists and engineers from the KASI and KRISS of Korea. Students of the University of Arizona are also greatly acknowledged.

The individual contributors are:Il Kweon Moon, Andrew Corredor, Christoph Dribusch, Ju-Heon Koh, Eun-Kyung Kim.


design and development of the fsm (fast steering secondary mirror) myung cho, noao-gsmtpo kwijong...

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