john w. conklin, 9 th international lisa symposium, paris, 23 may 2012 1 estimation of the lisa...
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John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 1
Estimation of the LISA TM-to-release tip adhesion force during dynamic separation
John W. ConklinStanford University
Matteo Benedetti, Daniele Bortoluzzi, Carlo ZanoniUniversity of Trento
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Test Mass Caging & Release• LISA GRS Impact factor: 2 kg TM 4 mm gap = 810–3 kg m
Caging required
• GRS electrostatic force (5 μN) << Au adhesion force
• Solution: quick retraction, relying on the TM inertia
*Bortoluzzi et al (2010)
John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 3
LISA Test Mass Release Phase• TM residual velocity must be < 5 μm/s
• Caging & Vent Mechanism final stage designed to minimize the residual velocity and consists of two opposing tips
TestMass
LISA Caging System
Grabbing Positioning and Release Mechanism (GPRM)
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Testing Release Phase in the Lab• Goal: Determine impulse imparted to TM during dynamic rupture of
adhesive bond in representative conditions of the in-orbit environment
• On-orbit no contributions of shear (pre-)stress at the contact patch that may promote the adhesion rupture
adhesion
Release tip Quick retraction of the release tip
Dynamic failure of adhesion
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Transferred Momentum Measurement Facility
On-orbit release(double-sided)
Lab simulation(single-sided)
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Transferred Momentum Measurement Facility
On-orbit release(double-sided)
Lab simulation(single-sided)
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Adhesion Force Data Reduction
• Force-vs-elongation, Fad
(e), function models adhesion
phenomenon
• Can be transformed to on-orbit conditions (mass, release profile, …)
• Experimental results show that systematics dominate
• Statistical approach adopted to bound in-flight release
• Interferometer measures TM (insert) position, xI
• Release tip motion, xS, measured separately
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Adhesion Force Model• Adhesion force modeled as non-linear spring
• Fad = kad x where x = xP – xI
• Initial model was empirical:
• Current model is more general:
M
m
xmmad eAk
1
pxBad Aek
Consistent with single-contact Johnson Kendall Roberts theory extended to multi-contact (rough) surfaces by Fuller & Tabor
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TM Release Data (medium 100 g TM)
Unexpected oscillations
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Parameter Estimation
Model:
Estimation algorithm: Levenberg-Marquardt
A priori used for initial velocity and preload
Measurement noise includes:
Interferometer noise: = 0.9-1.2 nm
Uncertainty in measured positioner motion: = 5.8 nm
Unmodeled non-Gaussian behavior of residuals
xI = h(t, p, x
S) + w
xI = measured TM insert motion
h = nonlinear model
p = 7 parameters to be estimated
xS = measured stage motion
w = measurement noise
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Fit and Residuals
Example best-fit
Post-fit residuals
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In-flight Monte Carlo Simulations• Due to nonlinearities, Monte Carlo method adopted to
estimate confidence interval for in-flight release velocity
• GPRM release dynamics Measured by RUAG Schweiz
• No adhesion present
• Mathematical model ofGPRM fit tomeasurements
• Parameter estimates &covariances feed MonteCarlo simulation ofin-flight scenario
GPRM electro-mechanical model
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Data Set 1 Data Set 2 Data Set 3Estimated max (3) velocity (μm/sec)
1.9 1.1 1.6
Margin of safety w.r.t5 μm/sec requirement
2.6 4.7 3.1
See Poster by Carlo Zanoni
et al
Nu
mb
er
of
tria
ls
Results
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Parameters Estimation
Adhesion force parameters: A, B, p
Time lead/lag between measured insert motion and measured translation stage motion
At time ti, xI = xI(i) and xP = xP(i + ∆t fs)
Initial velocity of TM, insert, plunger: v0
TM/insert transition from stick to slip: xI = xs l i c k
Plunger preload (defines, xT0, xI0, xP0): Fp r e
a priori = 0.5 mN 0.1 mN