Material Properties, Stress/Strain and Bending


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Material Properties, Stress/Strain and Bending

  • 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



Materials will deform when subjected to a load

  • 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




Natural Frequency of Vibration of a mode is

  • Natural Frequency of Vibration of a mode is

  • For previous examples, assuming a 1-pound mass at the end of the aluminum bar:

  • Bending direction is much more compliant than axial tension



Each degree of freedom can be represented as a simple mode that has mass, stiffness, and damping

  • 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)



Critical Damping Ratio is

  • Critical Damping Ratio is











Reaction Wheel

  • 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


Slewing to acquire a target

  • 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




FEA Tools allow the natural frequencies of a complex structure to be obtained

  • 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


With natural frequencies, mode shapes, damping, and the input disturbance, the time-varying motion of the structure can be obtained

  • 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



Shown on next slide is a table of natural modes from following report:

  • Shown on next slide is a table of natural modes from following report:

  • Note that mode shapes and frequencies have been calculated, and damping ratios have all been set to 0.005





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

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







Vibrational Modes that affect telescope as a whole cause 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

  • Frequencies greater than line rate cause image blur

  • Frequencies less than line rate cause frame-to-frame jitter (Line-to-line jitter)





Vibrations are an important consideration for EO spacecraft, across their entire lifecycle

  • 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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