Transcript PPT
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 John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 1 Test Mass Caging & Release • LISA GRS Impact factor: 2 kg TM 4 mm gap = 810–3 kg m Caging required *Bortoluzzi et al (2010) • GRS electrostatic force (5 μN) << Au adhesion force • Solution: quick retraction, relying on the TM inertia John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 2 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) John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 3 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 adhesion Dynamic failure of adhesion John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 4 Transferred Momentum Measurement Facility On-orbit release (double-sided) Lab simulation (single-sided) John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 5 Transferred Momentum Measurement Facility On-orbit release (double-sided) Lab simulation (single-sided) John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 6 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 John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 7 Adhesion Force Model • Adhesion force modeled as non-linear spring • • • Fad = kad x where x = xP – xI Initial model was empirical: k Ae Bx ad Current model is more general: k ad p M m x A e m m 1 Consistent with single-contact Johnson Kendall Roberts theory extended to multi-contact (rough) surfaces by Fuller & Tabor John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 8 TM Release Data (medium 100 g TM) Unexpected oscillations John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 9 Parameter Estimation Model: xI = h(t, p, xS) + w xI = measured TM insert motion h = nonlinear model p = 7 parameters to be estimated xS = measured stage motion w = measurement noise 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 John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 10 Fit and Residuals Example best-fit Post-fit residuals John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 11 Adhesion Force Estimates John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 12 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 John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 13 Number of trials Results Data Set 1 Data Set 2 Data Set 3 Estimated max (3) 1.9 1.1 1.6 velocity (μm/sec) Margin of safety w.r.t 2.6 4.7 3.1 5 μm/sec requirement John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 See Poster by Carlo Zanoni et al 14 Backup slides … John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 15 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 John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 16 John W. Conklin, 9th International LISA Symposium, Paris, 23 May 2012 17