Spacecraft Charging Technology Conference Electrodynamic ... · Spacecraft Charging Technology Conference, ESA/ESTEC, Netherlands 04 -08 April 2016 4 Electrodynamic tethers • The

04 -08 April 2016 Spacecraft Charging Technology Conference, ESA/ESTEC, Netherlands

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DIPARTIMENTO DI INGEGNERIA INDUSTRIALE

Spacecraft Charging Technology Conference

Electrodynamic tethers in space: dynamical issues, solutions and performance

Enrico Lorenzini and Riccardo Mantellato

University of Padova, Italy


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Outline

Ø Dynamical issues of electrodynamic tethers (EDT) in space

Ø Solutions to prevent the tether dynamic instability

Ø Use of EDTs for deorbiting spent satellites

Ø The BETs project results

Ø Techniques for stabilization

Ø Deorbiting performance


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Tether missions (Electrodynamic and not) ElectrodynamicMissionsingreen

NAME Date Orbit Length Agency Comments Gemini 11 1967 LEO 30 m NASA spin stable 0.15 rpm Gemini 12 1967 LEO 30 m NASA local vertical, stable

swing H-9M-69 1980 suborbital 500 m NASA partial deployment S-520-2 1981 suborbital 500 m NASA partial deployment Charge-1 1983 suborbital 500 m NASA full deployment Charge-2 1984 suborbital 500 m NASA full deployment

Oedipus-A 1989 suborbital 958 m Canadian NRC/NASA

spin stable 0.7 rpm, magentic field aligned

Charge-2B 1992 suborbital 500 m NASA full deployment TSS-1 1992 LEO <1 km NASA/ASI electrodynamic, partial

deployment & retrieval SEDS-I 1993 LEO 20 km NASA downward full

deployment, swing & cut PMG 1993 LEO 500 m NASA electrodynamic, upward

deployed SEDS-II 1994 LEO 20 km NASA full deployment, local

vertical stable Oedipus-C 1995 suborbital 1 km Canadian

NRC/NASA spin stable 0.7 rpm, magnetic field aligned

TSS-1R 1996 LEO 19.6 km NASA/ASI electrodynamic, close to full deployment, severed

TiPS 1996 LEO 4 km NRL long life tether on-orbit (~12 years)

ATEx 1999 LEO 6 km NRL partial deployment ProSEDS* 2003 LEO 15 km NASA H/W built but not flown

MAST 2004 LEO 1 km NASA Cubesat - did not deploy YES2 2007 LEO 32 km ESA full deployment, swing &

release of reentry capsule T-REX 2010 suborbital 135 m JAXA flat bare-tether

technology

SEDS-II in orbit pictured from the ground in 1994

TSS-1RdeploysfromShu3le,1996


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Electrodynamic tethers

•  The conductive tether moving at speed U in the magnetic field is subjected to an electric field (emf) that displaces charges

•  In a prograde orbit the tether charges positively toward the top and negatively toward the bottom

•  Free electrons in the ionosphere are collected at the top (anode) and re-emitted into the ionosphere at the bottom (cathode)

•  The current I produces the Lorentz force F (drag) without consuming propellant and also power on board if a load is present in the circuit

•  In a more modern and efficient configuration (Ref [1], Sanmartin et al., 1993) the anode is the tether itself left bare

emf =U×B ⋅LF = IL×B Motional

electric field (emf)

cathode -

+ anode

Conventional current

Electron current


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Equilibrium points

Ø  Equilibrium points without tether current: Ø  two stable positions along LV (θe = 0 and π) Ø  two unstable positions along LH (θe = π/2 and 3π/4)

Ø  Tether oscillates in a stable manner about LV within ±π/2 both in-plane θ and out-of-plane φ (not shown here)

Ø Natural oscillation frequencies (rad/s): Ø  In-plane Ø Out-of-plane 2n (with n the orbital rate θ the in-plane and φ the out-of-plane angles of tether w.r.t. LV)

!!θ +3n2 sinθ cosθ = 0 − > sinθe cosθe = 0

3n

LV

LH

θ

Orbital plane (in-plane)

In-plane equilibrium equation


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Tether attitude instability

Ø  The mechanism of tether attitude instability due to Lorentz forces is non-intuitive

Ø Coupling between in-plane and out-of-plane degrees of freedom through the radial component (i.e., LV) of the magnetic field Bx

!!θ +3θ −ΛBxϕ = ΛBy

!!φ + 4φ +ΛBxθ = ΛBz

Ø  Tether libration equations in linearized form

Ø  Bx, By, Bz vary with time and the system has periodic solutions with frequency equal to the orbital frequency


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Trajectories

Ø The coupling gives raise to 8-shaped trajectories when plotted as φ vs. θ (or viewing the tether tip along LV)

Ø The instability grows with the index ε = f(Λ) and depends on the orbit inclination w.r.t. the magnetic equator

ε =32

Immt +3mB

µm

µsin i = out-of-plane ED force

LV gravity gradient force

Ø In the non-linear analysis all periodic solutions are unstable in the absence of damping and even without resonant forcing components


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Energy explanation

Ø  The system with no current will be trapped to librate in the potential well (e.g., at θ = φ = 0) and energy does not exceed Go (if started with kinetic energy w.r.t. LVLH, T0 = 0)

Ø  When the current ≠ 0, the ED force does not produce work over a cycle only if the motion follows the periodic orbit

Ø  In all other cases the ED force increases the system energy over each cycle in the absence of damping

Ø  A trajectory in phase space will eventually surpass the saddle point at G = 3/2 and the system starts rotating

Potential energy vs. θ and φ[Adapted from Ref. 3]


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Techniques/strategies for stabilization

Ø  Expression of ε suggests some of the techniques for stabilization besides the introduction of damping into the system

Ø  Stabilization strategies/techniques Ø  Increase of gravity gradient force along LV

Ø  Increase mass of tip mass Ø  Insert an inert tether in series with ED tether

Ø  Insert a passive damper in-line with tether (in-line shock absorber) Ø Add a passive rotational damper that follows the tether motion Ø Optionally, limit maximum tether current below a selected saturation value Ø Alternatively, modulate tether current to reduce kinetic energy w.r.t. LVLH

(and produce negative work over cycle)


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BETs system configuration

Ø  Strategies adopted Ø  Tip mass (passive) Ø  Inert tether (passive) Ø  In-line damper (passive) Ø Rotational damper (passive) Ø Optional current limitation below max

value irrespective of tether dynamics

Ø  The current modulation (not adopted for BETs) is complex to implement because require knowledge of the tether dynamical status

in-line damper


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Software per la simulazione di sistemi a filo

Ø Deorbiting simulations with flexible tether model and perturbations: Ø Many vibrational modes of tether Ø Models of in-line & rotational dampers Ø  Tether current according to OML model Ø  Evaluation of tether temperature Ø  Electrical tether resistance dependent on

temperature Ø All relevant environmental perturbations

Ø  Extensive simulation campaign carried out for different system parameters

Ø Reference system: 1000-kg satellite from a circular orbit at 1000-km altitude through atmospheric reentry

0 5 10 15 20 25 30 35 40−100

−50

0

50Attitude Motion: In-Plane Angle

θ[◦

]

0 5 10 15 20 25 30 35 40−40

−20

0

20

40Attitude Motion: Out-Of-Plane Angle

Time [day]

ϕ[◦

]


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Deorbiting performance

•  The tether current and deorbiting time depend on orbital inclination

•  Reentry time between 1 and 10 months for all orbital inclinations (time << 25 years specified by the guidelines for satellites in LEO)

FP7 BETs team: UPM, UNIPD-CISAS, Onerá, DLR, Emxys, Tecnalia, CSU

Credit: ESA

Polar

Sun-sync.


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Concluding remarks

Ø  The attitude dynamics of electrodynamic tethers (EDT) is inherently unstable in the absence of damping in the system

Ø  The instability is due to in-plane/out-of-plane coupling and is independent of the presence of resonant forcing components

Ø  The instability is weak if system is started near equilibrium but eventually destabilizes the system over time

Ø  Several strategies/devices were developed for cancelling the effects of the instability

Ø  The BETs team has tested through numerical simulations the effectiveness of those strategies/devices

Ø A suitably designed EDT can deorbit a 1000-kg satellite from a 1000-km circular orbit in 1 to 10 months at all inclinations


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References

1.  Sanmartín, J.R., Martínez-Sanchez, M., and Ahedo, E. (1993), Bare Wire Anodes for Electrodynamic Tether, Journal of Propulsion and Power, Vol. 9, pp. 352–320

2.  Pelaez J., Lopez-Rebollal O., Ruiz M, Lorenzini E.C. (2001), Damping in rigid electrodynamic tethers on inclined orbits, AAS/AIAA Space Flight Mechanics Meeting, Paper AAS 01-190, 11-15 February 2001, Santa Barbara, CA

3.  Pelaez J., Lorenzini E.C., Lopez-Rebollal O., Ruiz M. (2000), A New Kind of Dynamic Instability in Electrodynamic Tethers. The Journal of the Astronautical Sciences, Vol. 48, No. 4, 449-476

4.  Mantellato R., Valmorbida A., Pertile M., Francesconi A., Lorenzini E. C., Sánchez-Arriaga G. (2014), End-of-life Deorbiting Services for Small Satellites Making Use of Bare Electrodynamic Tethers, Procs. of Small Satellites Systems and Services (4S) Symposium, 2014, Mallorca, Spain

5.  Mantellato R., Pertile M., Colombatti G., Lorenzini E. C. (2013), Analysis of Passive System to Damp the Libration of Electrodynamic Tethers for Deorbiting, AIAA Space 2013 Conference & Exposition, 10-12 September 2013, San Diego, CA

6.  Mantellato, R., Pertile, M., Colombatti, G., Valmorbida, A., Lorenzini, E. (2014), Two-bar model for free vibrations damping of space tethers by means of spring-dashpot devices, CEAS Space Journal, Vol. 6, No. 3, 133–143. doi:10.1007/s12567-014-0065-x

7.  Sanmartin J.R., Charro M., Chen X., Lorenzini E.C., Colombatti G., Zanutto D., Roussel J-F, Sarrailh P., Williams J.D., Xie K., Metz, G.E. Carrasco J.A., Garcia-de-Quiros F., Olaf Kroemer O., Rosta R., van Zoest T., Lasa J., Marcos J. (2012), A Universal System to Deorbit Satellites at End of Life, Journal of Space Technology and Science, Vol. 26, No. 1, 21-32. doi: 10.11230/jsts.26.1_21

8.  Zanutto D., Lorenzini E.C., Mantellato R., Colombatti G., Sanchez-Torres A., (2012), Orbital Debris Mitigation Through Deorbiting with Passive Electrodynamic Drag, Procs. of the 6th International Astronautical Congress (IAC2012), Paper IAC-12-D9.2.8, Naples, 2-6 October 2012

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Spacecraft Charging Technology Conference Electrodynamic ... · Spacecraft Charging Technology Conference, ESA/ESTEC, Netherlands 04 -08 April 2016 4 Electrodynamic tethers • The