Creep Model

1
Creep Model

• Average creep velocity is measured to be 56 pm/s
• Creep lore (from Eric)
• Creep due to atomic dislocations that lower
  stored energy in the spring
• Creep rates vary strongly with temperature
• Suggests dislocations inhibited by potential
  barrier gtgt kT
• Assume that creep takes place due to
  instantaneous steps in the spring constant
• Assume steps are constant in magnitude
• Treat rate of these steps as an unknown parameter
  R
• Assume steps occur randomly in time ? time
  between steps falls exponentially

2
Equation of Motion

• Assume mass m is suspended from a spring extended
  by a length x with damping constant b
• Look at variations in k and x about their nominal
  values
• Forces balance at their nominal position, creep
  velocity is related to rate of change in spring
  constant

3
Creep Simulation

• Start at xk0 at t0
• Let spring creep
• Use equations of motion to determine position,
  velocity at next creep at time ttDt

4
Creep Analysis

• Wait 10 time constants to reach steady-state
• Sample position every 5 ms for 20,000 seconds
• Fourier transform position data to get noise
  spectrum
• Integrate noise power down to 0.1 Hz
• Include effect of mechanical transfer function

5
Creep Noise Spectrum
6
Creep Results

• Integrated creep noise above 0.1 Hz including
  transfer function
• Checks
• Integrated position noise gives RMS noise
• Adding sinusoidal position term gives back
  expected amplitude/freq