John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 1 Estimation of the LISA TM-to-release tip adhesion force during dynamic separation

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


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)


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)


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


Transferred Momentum Measurement Facility

On-orbit release(double-sided)

Lab simulation(single-sided)


Transferred Momentum Measurement Facility

On-orbit release(double-sided)

Lab simulation(single-sided)


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


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


TM Release Data (medium 100 g TM)

Unexpected oscillations


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


Fit and Residuals

Example best-fit

Post-fit residuals


Adhesion Force Estimates


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


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


Backup slides …


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


Documents

John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 1 Estimation of the LISA TM-to-release tip adhesion force during dynamic separation