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Vibrations And their effect on electro-optical imaging spacecraft

Vibrations And their effect on electro-optical imaging spacecraft. Steve Hearon Applied Math Seminar December 14, 2009 (to fullfill requirements of an optomechanics course). Outline. Material Properties, Stress/Strain and Bending

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Vibrations And their effect on electro-optical imaging spacecraft

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  1. VibrationsAnd their effect on electro-optical imaging spacecraft Steve Hearon Applied Math Seminar December 14, 2009 (to fullfill requirements of an optomechanics course)

  2. Outline • Material Properties, Stress/Strain and Bending • Vibration Transfer Basics (from J. Burge, Univeristy of Arizona) • Electro-optical Spacecraft Examples • Types of Disturbances that cause vibration in optical path • FEA Models • Effects of Vibration on Imaging • Boresight • Primary Mirror Distortion • Conclusions

  3. Material Properties • Materials will deform when subjected to a load • Stress-strain relationship is • where ε is strain (normalized change in length); σ is stress (force/area); and E is Young’s modulus • E = 70 x 10^9 N/m^2 for Aluminum • For an aluminum bar, 1cm x 1cm x 10 cm, 1 Newton force, change of length is : • Stiffness k = F/ΔL = 70,000 N/mm

  4. F Bending example: Bar with force applied at end Max deflection occurs at end. Max deflection for the Aluminum bar As before 1N force, 1cm x 1 cm x 10 cm: Stiffness

  5. Natural Frequency of Vibration • Natural Frequency of Vibration of a mode is • where k is stiffness and m is mass of the moving structure • For previous examples, assuming a 1-pound mass at the end of the aluminum bar: • Bending direction is much more compliant than axial tension

  6. Analysis of Vibrations (J. Burge, University of Arizona) • Each degree of freedom can be represented as a simple mode that has mass, stiffness, and damping • This can be modeled using a simple 2nd-order differential equation • (Charts from J. Burge, University of Arizona) Disturbance Natural Frequency of Vibration

  7. Analysis of Vibrations (J. Burge, University of Arizona) • Critical Damping Ratio is Critical Damping Ratio:

  8. (From J. Burge, University of Arizona)

  9. (From J. Burge, University of Arizona)

  10. Electro-optical Spacecraft Example - Hubble • 2.4m Primary Mirror • Richey-Chretien (2-mirror) • SA and Coma corrected • Staring Arrays • 24 arcminutes Full FOV for • widest sensor • Reaction Wheels for attitude • control • Gyroscopes for stabilization

  11. Electro-optical Spacecraft Example -- IKONOS • 0.7m primary mirror • 10m focal length • Three-Mirror Anastigmat (TMA) • Controls SA, Coma, Astig, FC • Attitude controlled by Reaction Wheels • Pushbroom detector technology • 6500 lines/sec, 12 um pixels PAN • 48 um pixels MSI • Fully steerable, swath 12 km • Resolution 0.8m PAN

  12. Types of Disturbances That Can Affect Optical Path (1) • Reaction Wheel • Electric motor attached to a flywheel • Upon spinup, causes spacecraft to turn other way • Work around a nominal zero rotation rate • IKONOS and Hubble • Control Moment Gyroscope (CMG) • Gyroscope that is always spinning during operation ~ 6000 rpm • Spacecraft attitude controlled by turning axes of CMG’s • S/C rotates in reaction to CMG rotation (ang. mom. conserved) • More energy efficient than Reaction Wheels • Used in WorldView Satellite, International Space Station • Thrusters • Used for orbit adjusts

  13. Types of Disturbances That Can Affect Optical Path (2) • Slewing to acquire a target • s/c decelerates after slewing to begin imaging • Vibration damps out before imaging can begin • Motors • Solar array • Communications antenna • Cryocoolers • Sudden temperature change; thermal snap • Spacecraft enters or exits umbra

  14. Finite Element Analysis • Describes material in terms of small elements connected by nodes • Each element models the compliance of the material (J. Burge, University of Arizona)

  15. Using FEA Tools in Vibration Analysis (1) • FEA Tools allow the natural frequencies of a complex structure to be obtained • Additionally, the shape of the natural mode is obtained, • For a complete dynamical description, the damping ratio is also needed • Damping ratio is difficult to model for space structures • Often a low value is assumed e.g. 0.005 • It is possible to perform a factory test (“modal test”) to obtain this • However, difficult to transform measurements at std pressure and 1 g to vacuum and no gravity

  16. Using FEA Tools in Vibration Analysis (2) • With natural frequencies, mode shapes, damping, and the input disturbance, the time-varying motion of the structure can be obtained • Effect on imaging obtained by importing structure into ASAP or another optical modeling tool • Optionally, can perform an analysis based on analytical calculations

  17. FEA Results from a Study for an 8-Meter space telescope • Shown on next slide is a table of natural modes from following report: • “HST Optics Enhancement, preliminary feasibility study summary report”, 2000 • Note that mode shapes and frequencies have been calculated, and damping ratios have all been set to 0.005

  18. FEA Results from a Study for an 8-Meter space telescope

  19. Trussed Mirror Concept • Following two slides show NASTRAN results for first natural frequency for a trussed-mirror concept

  20. Strutted Mirror - 1st Natural Mode at 73.7 Hz Lockheed Martin

  21. Baseline Petal - 1st Natural Mode at 63.2 Hz Lockheed Martin

  22. Effects of Vibration on Optical Path –Boresight Variation -- Jitter • Vibrational Modes that affect telescope as a whole cause jitter • Jitter is often spec’d as a PSD in units of microrad^2/Hz • On a per-axis basis • Frequencies greater than line rate cause image blur • Frequencies less than line rate cause frame-to-frame jitter (Line-to-line jitter) PSD (urad^2/Hz) With programmed Motion added (pushbroom) Jitter realization Frequency (Hz) Lockheed Martin

  23. Effects of Vibration on Optical Path –Primary Mirror distortions • Distortions of the Mirrors (e.g. primary or secondary mirror) cause spreading of point-spread-function • Results in a decrease of Strehl Ratio • Movie showing time-dependent PM distortions, and resulting variation in Point-Spread Function: • X:\7\7CNO\Hearon\PSFvsTime_2kHz_04.avi Lockheed Martin

  24. Conclusions • Vibrations are an important consideration for EO spacecraft, across their entire lifecycle • Development, build, operation • Vibration analysis tools help designers to understand and mitigate potential vibration issues early in the design process Lockheed Martin

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