Sittiporn Channumsin Co-authors

Transcription

1 28 Oct 2014 Space Glasgow Research Conference Sittiporn Channumsin Sittiporn Channumsin Co-authors S. Channumsin

2 Outline Background Objective The model Simulation Results Conclusion and Future work 2

3 Space Debris Space debris - Artificial debris and natural debris. - Orbit with hypervelocity that can threat to active spacecraft leading to catastrophic break-ups generating new space debris - Need to reduce the number of debris. Experiment Gravity movie 3

4 Space debris 4

5 Discover HAMR objects Collision and explosion - Fengyun1-C Discovery in 2004 (GEO) - Iridium 33 and Cosmos 2251 Suspected objects -High area-to-mass ratio (HAMR) objects -Variations of light curves -Variations of area-to-mass ratio (AMR) (Anselmo, L. and C. Pardini, 2010) Experiment - Shot micro satellite model Multi-layer insulation (Murakami, J., et al 2008) 5

6 Objective 1. Develop a model of a thin, highly flexible MLI-type membrane, in terms of multi-body dynamics, and solved by using fundamental Newtonian mechanics 2. Investigate the orbital dynamics under J2 and the lunisolar third body gravitation and solar radiation pressure (SRP) by comparing with rigid body case 3. Investigate a self-shadowing effect to the orbital dynamics of flexible debris 6

7 flexible model 7

8 The flexible model Flat plate y Torsional Damper x Torsional spring Consider deformation in 2 D of x-y plane 8

9 Simplification Flat plate Dimension 1 x 1 square meter l 1 = l 2 = 0.5 (m) Torsional Damper y m 1 m 2 m 3 0.5m 0.5m x Torsional spring 9

10 Simplification Triangular shape Torsional Damper y m 2 m 1 m 3 x Torsional spring 10

11 Multibody dynamics Newtonian equation F T F F m a F k i i s, i d, i i i Where i = mass of each (1,2 and 3) Spring and damper forces s s k s EI Length Fd c c DF Mk s Torsional Damper m 2 m 1 Torsional spring Constrained equation m 3 Where k s = rotational spring constant, θ = angle of deformation θ = angular velocity of the deformation, E = young modulus I = the moment of inertia of thin plate Length = the length of each rod and is c = Coefficient of torsion spring (N.m rad -1 ) DF= dissipation factor of material M = mass of rod (Kg) ( x x ) ( y y ) ( z z ) l i1 i i1 i i1 i i - Length of a rod = 0.5 m 11

12 Simulation of the model 12

13 Initial shape to test the model 13

14 Validation of spring The simulation results without external force and damper by activating torsional spring 14

15 The simulation with torsional spring and damper 15

16 Orbital dynamics and Perturbation 16

17 The modified equinoctial elements p i 2 p w p i, t p fi L w L f h L k L w g i, t i, n [ i, r sin [( 1) cos ] ( sin cos ) ] p gi L w L g h L k L w i, t i, n [ i, r cos [( 1) cos ] ( sin cos ) ] 2 p s hi cos Li, n 2w 2 p s ki cos Li, n 2w w 2 1 p Li p( ) ( hsin L k cos L) p w i, n w f w 2 p a(1 e ) i h tan( )sin 2 g esin( ) f ecos( ) i k tan( )sin 2 L Where = gravitational constant = right ascension of ascending node degree e = eccentricity = true anomaly a = semi-major axis(km) = argument of perigee i = Inclination L = true longitude p = semi-parameter 17

18 J2 Perturbations and Third body J2 perturbations a a a R 3J R x 5x (1 ) I K j2, I 5 2 xi 2x x R 3J R x 5x (1 ) J K j2, J 5 2 xj 2x x R 3J R x 5x (3 ) K K j2, K 5 2 xk 2x x The third body a G M k k1,2 k x x x x x k k 3 3 x k k Where k = 1 and 2 (Sun and Moon) 18

19 Solar radiation pressure force Solar radiation pressure force N psr Ai cos CRd i Frad 2 CRs cos( ) (1 ) i inc n C i Rs s i i1 c 3 Reflection beam n sun s inci A 19

20 S i Average solar radiation pressure = [1,0,0] Rigid body case Average SRP force 2 1 F F d d avg rad, j s s Equivalent area Therefore xi x FAVG Aeq PSP ( R) x x i A eq Where P F SP avg ( ) E PSP R C x ( R) i A 2 x 2 20

21 Self-shadowing d n l p l ( v l) n( v l) or P = Mv P n. l d lxnx lxny lxnz lxd lynx n. l d lyny lynz lyd M lznx lzny n. l d lznz lzd nx ny nz n. l Where p= the projection of vertex v v = Vertex on the plane : n x d 0 l= a location of light source The planar shadow projection, the original technique invented by Blinn [15], allows shadows to be cast on plane surface l v p 21

22 Self-shadowing a) Change position of light source b) Change the geometry of debris 22

23 Simulation 23

24 Material properties Material type AMR [m2/kg] Young s Modulus [N/m2] Cs, Cd, Ca PET coated x Kapton coated x uncoated PET Kapton (Sheldahl, The red book (2012) 24

25 Initial position Geosynchronous Earth orbit (GEO) Six element Semi-major axes(km) Mean anomaly(degree) Argument of perigee(degree) Value 42, Ascending node(degree) Eccentricity Inclination(degree) Propagation in 12 days Start point 28 Oct 2014 S. Channumsin 25

26 J2 and SRP 26

27 Orbital dynamics 12 days PET 27

28 PET without self-shadowing 10 minutes 28

29 PET with self-shadowing 10 minutes 29

30 Comparison PET without self-shadowing PET with self-shadowing 30

31 Orbital dynamics under J2, third body and SRP 31

32 Orbital dynamics 12 days 32

33 PET Euler angles 1 st panel 2 nd panel 33

34 Kapton Euler angles 1 st panel 2 nd panel 34

35 Conclusion and Future work 28 Oct 2014 S. Channumsin 35

36 Conclusion 1. Orbital dynamics of flexible debris is different from that of rigid debris due to the effective area. 2. Direct solar radiation pressure is the most effect to the orbital dynamics of HAMR flexible model. 3. Self-shadowing effect lead to irregular attitude dynamics and deformation 36

37 Future work To set the deformation experiment to validate the flexible model Acknowledge This work was funded by Ministry of Science and Technology of the Thai government and the European Office of Aerospace Research and Development (project award FA ). 28 Oct 2014 S. Channumsin 37

38 Space Glasgow Thank you