VibrationsAnd their effect on electro-optical imaging spacecraft

Steve HearonApplied Math Seminar

December 14, 2009(to fullfill requirements of an optomechanics course)

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

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

E

nmmPaemNL 14)10970/()1.01( 24

Bending example: Bar with force applied at end

F

Max deflection occurs at end. Max deflection for the Aluminum barAs before 1N force, 1cm x 1 cm x 10 cm:

mmPae

mN

EW

FL 1.2)01.0)(970(2

)1.0)(1(3

2

34

3

4

3

StiffnessmmN

L

EWk /467

3

23

4

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

m

kfN 2

1

Hzkg

mNef AXIAL 1880

5.0

/77

2

1

Hz

kg

mNefBENDING 154

5.0

/57.4

2

1

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)

Natural Frequency of Vibration

Disturbance

Analysis of Vibrations (J. Burge, University of Arizona)

• Critical Damping Ratio is

)2/( NR mCC Critical Damping Ratio:

(From J. Burge, University of Arizona)

(From J. Burge, University of Arizona)

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

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

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

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

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)

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

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

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

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

Trussed Mirror Concept

• Following two slides show NASTRAN results for first natural frequency for a trussed-mirror concept

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Strutted Mirror - 1st Natural Mode at 73.7 Hz

Baseline Petal - 1st Natural Mode at 63.2 Hz

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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)

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Frequency (Hz)

PSD (urad^2/Hz)

Jitter realization With programmedMotion added(pushbroom)

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

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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

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