Test Mass Caging & Release

1. Estimation of the LISA TM-to-release tip adhesion force during dynamic separationJohn W. ConklinStanford UniversityMatteo Benedetti, Daniele Bortoluzzi, Carlo ZanoniUniversity of Trento

2. Test Mass Caging & Release • LISA GRS Impact factor: 2 kg TM  4 mm gap = 810–3 kgm • Caging required • GRS electrostatic force (5 μN) << Au adhesion force • Solution: quick retraction, relying on the TM inertia *Bortoluzzi et al (2010)

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 Grabbing Positioning and Release Mechanism (GPRM) LISA Caging System

4. 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 Release tip Quick retraction of the release tip Dynamic failure of adhesion adhesion

5. Transferred Momentum Measurement Facility On-orbit release(double-sided) Lab simulation(single-sided)

6. Transferred Momentum Measurement Facility On-orbit release(double-sided) Lab simulation(single-sided)

7. 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

8. Adhesion Force Model • Adhesion force modeled as non-linear spring • Fad = kadxwherex = xP – xI • Initial model was empirical: • Current model is more general: Consistent with single-contact Johnson Kendall Roberts theory extended to multi-contact (rough) surfaces by Fuller & Tabor

9. TM Release Data (medium 100 g TM) Unexpected oscillations

10. Parameter Estimation xI = measured TM insert motion h = nonlinear model p = 7 parameters to be estimated xS = measured stage motion w = measurement noise • 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, xS) + w

11. Fit and Residuals Example best-fit Post-fit residuals

12. Adhesion Force Estimates

13. 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

14. Results Number of trials See Poster by Carlo Zanoni et al

15. Backup slides …

16. 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 = xslick • Plunger preload (defines, xT0, xI0, xP0):Fpre • a priori = 0.5 mN  0.1 mN