A Simple Nutation Damper Design Mark Woodard May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Background Nutation is commonly encountered when trying to control a spin-stabilized spacecraft Nutation typically occurs after separation from launch vehicle and after maneuvers It is highly desirable to remove any nutation from the system May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Nutation Dynamics Nutation represents an offset between the principal inertia axis (I3) and the angular momentum vector (H) The I3 axis “cones” about the H vector at a constant offset angle, known as the “nutation angle” Dynamics of the spacecraft X, Y, and Z axes is complex Nutation can be controlled either actively or passively A commonly used passive nutation damper uses fluid motion inside a closed ring to dissipate excess nutation energy May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Ring Nutation Dampers Passive ring nutation dampers are typically a closed tube partially or fully filled with fluid (alcohol, oil) These can be mounted in the spin plane or perpendicular to the spin plane Spacecraft nutation (wobble) causes fluid to move inside ring; surface friction forces dissipate nutation energy; (t) = (t0) ·e-·t May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar ST5 Nutation Damper May 18, 2018 Flight Dynamics Seminar

Design Considerations Nutation damper performance depends on several design parameters Ring radius, R, and tubing radius, r Fluid viscosity, , and fluid density,  Fluid surface tension,  Spacecraft Inertia Properties (I1, I2, I3) Spin Rate,  Distance from spacecraft c.m., L May 18, 2018 Flight Dynamics Seminar

Nutation Damper Mounting Mount in Spin plane Pro: Time constant can be reduced by properly tuning design parameters Con: performs only over a limited range of spin rate Mount perpendicular to spin plane Pro: robust performance over variable spin rate Con: longer time constant Option 2 is generally preferred to handle pre- and post- array or boom deployments May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Governing Equations Nutation Frequency  = [(I3-I1)(I3-I2)/(I1I2)]1/2 Damper Time Constant = I22/(R3r2I3) Wobble Reynolds Number (fluid momentum/viscosity)  = r2/ Bond Number (acceleration/surface tension force) NB = r2L2/ Note: IMAGE nutation damper was poorly designed; Bond number was 0.0007 May 18, 2018 Flight Dynamics Seminar

Normalized Energy Curve May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Drawbacks to ST5 Design Since damper is fully filled with fluid during fabrication at 25 C, internal pressure increases dramatically at high end of operating temperature (thousands of psi at 50 C) High pressure required use of titanium and Class A welds Significant fabrication and testing costs May 18, 2018 Flight Dynamics Seminar

Proposed Design Improvement May 18, 2018 Flight Dynamics Seminar

Internal Pressure Comparison May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Damper Improvements Lower cost Lower internal pressure; no bellows device necessary Less mass No titanium – damper will demise on reentry No degradation in performance Testing needs to be performed to prove this May 18, 2018 Flight Dynamics Seminar

Damper Environmental Testing Env. Test Need? Rationale Acoustic NO The launch environment will not be tested for the prototype damper Vibe Shock Thermal YES The effect of thermal cycling on the unit is important Vacuum Since the damper is a sealed unit, external vacuum will have negligible effect Micro-gravity Too difficult to do in a near-Earth environment – will validate with acceleration testing instead Acceleration Needed to validate the Bond equation Performance Needed to validate the time constant equation May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Thermal Testing Procedure: A damper was constructed from standard copper plumbing parts (rated at 735 psi?) from Home Depot. The damper was filled with silicone fluid to within 5” (0.127 m) of the escape tube cap, thus leaving 11.4 cm2 of air in the sealed damper. The damper was placed in an oven and raised from an ambient temperature of 70ºF (21C) to a temperature of 150ºF (66 C) for 1 hour. Results There was no indication of leakage due to increased internal pressure at 66C. Although the internal pressure of the damper was not measured, it is estimated that the air volume decreased by a factor of 2.5 and the internal pressure increased by a factor of 2.5; it was 14.7 psi at 21C and 36.8 psi at 66C. Conclusions: By providing sufficient room in the escape tube for fluid expansion across the survival temperature range, the damper internal pressure can be kept well below the pressure rating of the damper material. May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Acceleration Testing Producing centrifugal accelerations in a micro-gravity environment is difficult to do in a near-Earth environment The prototype damper was validated with acceleration testing instead Bond Number (acceleration/surface tension force) In Space: NB = r2L2/ On Earth: NB = r2g/ May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Acceleration Testing Results: 6 test dampers were constructed from clear PVC tubing. Each section of tubing was formed into an 18” diameter ring, and the tubing ends were joined into a tee fitting. The tubing was nearly filled with water, isopropyl alcohol, or dimethyl silicone fluid in order to provide a range of increasing Bond numbers. The damper was shaken in order to distribute bubbles throughout the fluid; then the damper was laid on a 15º inclined surface to observe the movement of the bubbles under the influence of an acceleration force. Each test was performed 3 times, and the maximum migration time was recorded. The test results are given in Table 2. May 18, 2018 Flight Dynamics Seminar

Acceleration Test Results Bond Number Bubble Migration Time Results 1 0.6 Very long – fluid locked up Poor Bond number 2 1.7 67 seconds Marginal Bond number 3 2.1 57 seconds 4 14.5 16 seconds Good Bond number 5 18.3 45 seconds 6 90.7 11 seconds Excellent Bond number May 18, 2018 Flight Dynamics Seminar

Acceleration Test Conclusions Proper fluid selection and Bond number (Tests 4, 5, 6) will eliminate any potential for damper fluid lockup. In Test 5, large bubbles migrated into the escape tube quickly, but it took a longer time (compared to Test 4) for small bubbles to migrate because of the higher viscosity of silicone relative to alcohol. Small bubbles are not indicative of a fluid lockup, so the Bond number is considered good for Case 5.  A Bond number of ~100 proves to be quite sufficient, so higher Bond numbers were not tested. May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar Performance Testing To Be Performed Procedure: The existing ST5 performance test apparatus at GSFC will be used. The damper will be laid flat (+Z axis up) The spacecraft mass properties and spin rate for ST5 will be used. Expected Results: It is expected that the damper time constant will agree will the modeling equations, with similar performance as ST5 damper. May 18, 2018 Flight Dynamics Seminar

Flight Dynamics Seminar New Technology Status “Disclosure of Invention and New Technology” was provided to Code 504 in 2003. No patent was issued due to limited commercial application Looking for future spin-stabilized mission to apply technology demonstration (SMEX, SmallSat, UniSat, etc.) May 18, 2018 Flight Dynamics Seminar