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

2. 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

3. 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

4. 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

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

6. 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

7. 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

8. 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
May 18, 2018
Flight Dynamics Seminar

9. Normalized Energy Curve
May 18, 2018
Flight Dynamics Seminar

10. 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

11. Proposed Design Improvement
May 18, 2018
Flight Dynamics Seminar

12. Internal Pressure Comparison
May 18, 2018
Flight Dynamics Seminar

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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