大 More of How Far apart will they work? With further simplification Force vs Separation Distance F~312(MCR) 10E+02 1.0E+01 一MR=0.1 The graph to the right shows a family of 一MR=03 1.0E+00 curves for various products of mc and Rc g =312 10E02 MR=300 1.0E03 Force vs Separation Distance 1.0E-04 1.0E+03 Separation(m) EMFORCE Testbed 1.0E+02 10E+01 MR=0.1 =312 1.0E+00 1.0E-01 Example 300 kg satellite 2 m across, needs 1.0E-03 10 mN of thrust, want MC< 30 kg 1.0E-04 EMFF effective up to 40 meters Separation(m) DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 More of ‘How Far apart will they work’? More of ‘How Far apart will they work’? Force vs. Separation Distance 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1 10 100 Separation (m) Force (N) MR = 0.1 MR = 0.3 MR = 1 MR = 3 MR = 10 MR = 30 MR = 100 MR = 300 kg-m EMFORCE Testbed Force vs. Separation Distance 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1 10 100 Separation (m) Force (N) MR = 0.1 MR = 0.3 MR = 1 MR = 3 MR = 10 MR = 30 MR = 100 MR = 300 kg-m With further simplification: 2 4 1 ~ 31.2 ( ) F MRC C s The graph to the right shows a family of curves for various products of MC and RC 2 3 -7 C 2 3 m I (10 ) = 31.2 2 kg-s ρ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ 2 3 -7 C 2 3 m I (10 ) = 312 2 kg-s ρ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ Example: • 300 kg satellite, 2 m across, needs 10 mN of thrust, want MC < 30 kg • EMFF effective up to 40 meters
大 Far Field/Near Field Comparison The far field model does not work in the Ex Far Field near field Ex Near Field (Separation/Distance)> 10 to be within 10% B=30 Some configurations are more accurate 1.6F a better model is needed for near-field motion since most mission applications will /1. 4f B=6 B=75° work in or near the edge of the near field For TPF,(s/d)-3-6 Seperate 1.522.533.544.5 Diameter Tz Far Field Tz Near Field E Far Field 阝=10° 2.75 B=30 B=3 B=45° 1.5 4.5 1.522.533.544.5
DII EMFF Final Review Aug. 29, 2003 Far Field/Near Field Comparison Far Field/Near Field Comparison • The far field model does not work in the near field • (Separation/Distance)>10 to be within 10% – Some configurations are more accurate • A better model is needed for near-field motion since most mission applications will work in or near the edge of the near field – For TPF, (s/d) ~ 3 - 6 β =10º β =30º β =45º β =60º β =90º β =15º β =30º β =45º β =60º β =90º
大 Outline Motivation Fundamental principles MIT EMFFORCE Testbed Governing Equations Design Trajectory Mechanics Calibration Stability and Control Movie Mission Applicability Space Hardware Design Issues Sparse Arrays Thermal Control Filled Apertures Power System Design Other Proximity Operations High b-Field Effects Mission Analyses Conclusions Sparse Arrays Filled Apertures Other Proximity Operations DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 Outline Outline • Motivation • Fundamental Principles – Governing Equations – Trajectory Mechanics – Stability and Control • Mission Applicability – Sparse Arrays – Filled Apertures – Other Proximity Operations • Mission Analyses – Sparse Arrays – Filled Apertures – Other Proximity Operations • MIT EMFFORCE Testbed – Design – Calibration – Movie • Space Hardware Design Issues – Thermal Control – Power System Design – High B-Field Effects • Conclusions
大 2-D Dynamics of spin-Up Spin-up/spin-down Spin-up from"static" baseline to rotating cluster for u-v plane filling Spin-down to baseline that can be reoriented to a new target axis Electromagnets exert forces/torques on each other Equal and opposite"shearing forces Torques in the same direction Reaction wheels(RW) are used to counteract EM torques Initial torque caused by perpendicular-dipole orientation Reaction wheels counter-torque to command EM orientation Angular momentum conserved by shearing of the system EM Torque/ RW Torque DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 2-D Dynamics of Spin D Dynamics of Spin-Up • Spin-up/spin-down – Spin-up from “static” baseline to rotating cluster for u-v plane filling – Spin-down to baseline that can be reoriented to a new target axis • Electromagnets exert forces/torques on each other – Equal and opposite “shearing” forces – Torques in the same direction • Reaction wheels (RW) are used to counteract EM torques – Initial torque caused by perpendicular-dipole orientation – Reaction wheels counter-torque to command EM orientation – Angular momentum conserved by shearing of the system EM Torque RW Torque N S S N
大 2-Satellite Spin-up F 104B 2cos a cos B-sin asin B) 4兀a F 104B 4d4 (cos asin B+sin a cos B 04 6 DOF (4 Translational, 2 Rotational (cos a sin B+2sin a cos B 4丌d 4 DOF(2 Translational, 2 Rotational 2 Reaction wheels control 2 rotational DOF F=ma centripical=mor 2 dipole strengths and 2 dipole angles to control 2 translational degrees of F=mor freedom (relative motion) 2 extra degrees of freedom B=0 Allows for many different spin-up figuration Allows for different torque 32mmr3√4i2+0 distribution Become more complex with more satellites Must solve non-linear system of equations a=-cOS 40-+0 DIl EMFF Final review ug.29,2003
DII EMFF Final Review Aug. 29, 2003 2-Satellite Spin Satellite Spin-up 2 Fx centripical = = ma m r ω 0 F mr y ω β = = 0 4 0 4 0 3 3 (2cos cos sin sin ) 4 3 (cos sin sin cos ) 4 1 (cos sin 2sin cos ) 4 A B x A B y A B z F d F d T d µµµ α β αβ π µµµ α β αβ π µµµ α β αβ π = − =− + =− + d N S α N S β xˆ y ˆ 5 24 0 2 1 2 4 32 4 3 cos 4 A B π m r ω ω µ µ µ ω α ω ω − + = ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ + • 6 DOF (4 Translational, 2 Rotational) • 4 DOF (2 Translational, 2 Rotational) • 2 Reaction wheels control 2 Rotational DOF • 2 dipole strengths and 2 dipole angles to control 2 translational degrees of freedom (relative motion) – 2 extra degrees of freedom. – Allows for many different spin-up configurations – Allows for different torque distribution – Become more complex with more satellites – Must solve non-linear system of equations