1. 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 Stanford University Matteo Benedetti, Daniele Bortoluzzi, Carlo Zanoni University of Trento

2. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 2 Test Mass Caging & Release LISA GRS Impact factor: 2 kg TM  4 mm gap = 810 –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)

3. John W. Conklin, 9 th 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 Test Mass LISA Caging System Grabbing Positioning and Release Mechanism (GPRM)

4. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 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 adhesion Release tip Quick retraction of the release tip Dynamic failure of adhesion

5. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 5 Transferred Momentum Measurement Facility On-orbit release (double-sided) Lab simulation (single-sided)

6. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 6 Transferred Momentum Measurement Facility On-orbit release (double-sided) Lab simulation (single-sided)

7. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 7 Adhesion Force Data Reduction Force-vs-elongation, F ad (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, x I Release tip motion, x S, measured separately

8. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 8 Adhesion Force Model Adhesion force modeled as non-linear spring F ad = k ad  x where  x = x P – x I 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. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 9 TM Release Data (medium 100 g TM) Unexpected oscillations

10. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 10 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 x I = h(t, p, x S ) + w x I = measured TM insert motion h = nonlinear model p = 7 parameters to be estimated x S = measured stage motion w = measurement noise

11. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 11 Fit and Residuals Example best-fit Post-fit residuals

12. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 12 Adhesion Force Estimates

13. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 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 of GPRM fit to measurements Parameter estimates & covariances feed Monte Carlo simulation of in-flight scenario GPRM electro-mechanical model

14. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 14 Data Set 1Data Set 2Data Set 3 Estimated max (3) velocity (μm/sec) 1.91.11.6 Margin of safety w.r.t 5 μm/sec requirement 2.64.73.1 See Poster by Carlo Zanoni et al Number of trials Results

15. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 15 Backup slides …

16. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 16 Parameters Estimation Adhesion force parameters: A, B, p Time lead/lag between measured insert motion and measured translation stage motion At time t i, x I = x I (i) and x P = x P (i + ∆t f s ) Initial velocity of TM, insert, plunger: v 0 TM/insert transition from stick to slip: x I = x s l i c k Plunger preload (defines, x T0, x I0, x P0 ): F p r e a priori = 0.5 mN  0.1 mN

17. John W. Conklin, 9 th International LISA Symposium, Paris, 23 May 2012 17