Material Properties, Stress/Strain and Bending

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

• 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

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:

• “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

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

• 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)

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