1. 1 衛星結構設計 祝飛鴻 5/25/2006

2. 2  What are the main functions of structure subsystem?  Provide support all other subsystems and attach the spacecraft to launch vehicle.  What factors need to be considered for structure design?  Size  Weight  Field-of-view  Interference  Alignment  Loads ARGO Satellite - The first Taiwan designed satellite

3. 3  Size:  Fit into the fairing of candidate launch vehicle.  Provide adequate space for component mounting. 123 cm 135 cm 132 cm 30 cm Falcon-1 Envelope 13mm clearance 11mm clearance

4. 4  Weight:  Not to exceed lift-off weight of the selected launch vehicle.

5. 5  Field-of-view (FOV):  Define by other subsystems, e.g. attitude control sensors, payload instruments, antenna subsystem, etc. X Band Antenna FOV 110 ° 65 ° 110 ° MSI FOV=  6 ° Star Camera FOV=  6.7° on short axis  9.2° on long axis

6. 6  Interference:  With the launch vehicle fairing.  Between components for physical contact and assembly. Falcon-1Envelope Section Y=1219 Solar Panel 19mm clearance X-Band Ant 15.5mm clearance GPS Ant. 8.6mm clearance

7. 7  Alignment:  Define by other subsystems, e.g. attitude control sensors, payload instrument, etc.  Ground alignment.  On-orbit thermal & hydroscopic distortion. Requirement Star Camera Orientation ± 0.5  (TBR) Thruster Orientation ±1.5  (TBR) X-antenna Orientation ±5  (TBR) S-antenna Orientation ±5  (TBR)

8. 8  Loads:  Environmental loads for structure design.  Not-to-exceed loads for components and payloads.

9. 9  What are major tasks to be performed for structure design?:  Configuration design  Environmental loads  Structure design and analysis  Design verification

10. 10  To accommodate all the components in a limited space while satisfying its functional requirements, every spacecraft will end up with a unique configuration. Configuration Design

11. 11 Configuration Design - ARGO

12. 12  To successfully deliver the spacecraft into the orbit, the launcher has to go through several stages of state changes from lift-off to separation. Each stage is called a “flight event” and those events critical to the spacecraft design is called “critical flight events”. Environmental Loads

13. 13 Environmental Loads  Each flight event will introduce loads into the spacecraft. Major types of loads include:  Transient dynamic loads caused by the changes of acceleration state of the launcher, i.e. F = ma.  F will be generated if  a or  m is introduced.  Random vibration loads caused by the launcher engine and aero-induced vibration transmitted through the spacecraft mechanical interface.  Acoustic loads generated from noise in the fairing of the launcher, e.g. at lift-off and during transonic flight.  Shock loads induced from the separation device.

14. 14 Environmental Loads  The above mentioned launcher induced loads are typically defined in the launch vehicle user’s manual. However, these loads are specified at the spacecraft interface except for acoustic environment. The loads to be used for the spacecraft structure design has to be derived.  For picosat design, if P-POD is used, please refer to “The P- POD Payload Planner’s Guide” Revision C – June 5, 2000 for definition of launch loads.

15. 15 Dynamic Coupling  Among all the launch loads, the derivation of transient dynamic loads is most involved and typically is the dominate load for spacecraft primary structure design.  To understand the derivation of transient dynamic loads, the concept of “dynamic coupling” needs to be explained.  Based on the basic vibration theory, the natural frequency of a mass spring system can be expressed as: 1 f = ------ K/M 2   Where f = natural frequency (Hz: cycle/second) M = mass of the system K = spring constant of the system

16. 16 Dynamic Coupling  Based on the above equation, a spring-mass system with K 1 = 654,000 lb/in and weight W 1 = 4,000 lbs will have f 1 = 40Hz (verify it!).  Assume a second system has f 2 = 75Hz. (if this system has 30 lbs weight, what should be the value of K 2 ?)  The forced response of these two systems subjected to 1g sinusoidal force base excitation with 3% damping ratio will have 16.7g response at their natural frequency, i.e. For system 1: 16.7g at 40Hz For system 2: 16.7g at 75Hz (Please refer to any vibration text book for derivation of results) W K 1g a

17. 17 Dynamic Coupling  Suppose we stack these two system together, the response of the system can be derived as: 39.8Hz 75.4Hz a 1 16.6g 0.4g a 2 23.1g 6.4g where 39.8Hz and 75.4Hz are the natural frequencies of the combined system. (Please refer to advanced vibration text book for derivation of results) W2 W1 K2 K1 1g a1a1 a2a2

18. 18 Dynamic Coupling  Now, let’s change the second system to have natural frequency of 40Hz, then the responses will be: 38.3Hz 41.8Hz a 1 9.9g 9.2g a 2 99.2g 83.4g where 38.3Hz and 41.8Hz are the natural frequencies of the combined system. W2 W1 K2 K1 1g a1a1 a2a2

19. 19 Dynamic Coupling  It can be seen that by changing the natural frequency of the second system to be identical to the first system, the maximum response of the second system will increase from 23.2g to 99.2g. This phenomenon is called “dynamic coupling”. The more closer natural frequencies of the two systems, the higher response the system will get. W2 W1 K2 K1 1g a1a1 a2a2

20. 20 Dynamic Coupling  Now you can think the first system as a launcher and the second system as a spacecraft. To minimize response of the spacecraft, the spacecraft should be designed to avoid dynamic coupling with the launcher, i.e. designed above the launch vehicle minimum frequency requirement.  Obviously the launcher and spacecraft are more complicated than the two degrees of freedom system. Coupled loads analysis (CLA) is required to obtain the responses. W2 W1 K2 K1 1g a1a1 a2a2

21. 21 Structure Design & Analysis  Once the mechanical layout is completed, the structural design and analysis can be started. Major items include:  Mass property analysis  Structure member and load path  Material selection  Dynamic and Stress analysis

22. 22 Mass Property Analysis  One of the important factors associated with the mechanical layout is the mass property analysis, i.e. weight and moment of inertia (MOI) of the spacecraft.  Mass property of a spacecraft can be calculated based on the mass property of each individual elements e.g. components, structure, hardness, etc.  The main purpose of mass property analysis is to assure the design satisfies the weight and CG offset constraints from the selected launcher. W1 W2X Y D2 D1 Total Weight ? MOI about Z axis ?

23. 23 0 200 400 600 800 1000 1200 1400 Spacecraft Weight (lb) 2.5 2.0 1.5 1.0 0.5 0.0 Lateral CG centerline offset (in) Falcon-1 Launcher

24. 24 Structure Member and Load Path  The spacecraft is supported by the launcher interface therefore all the loads acting on the spacecraft has to properly transmitted through the internal structure elements to the interface. This load path needs to be checked before spending extensive time on structural analysis.  No matter how complex the structure is, it is always made of basic elements, i.e. bar, beam, plate, shell, etc.

25. 25 Plate Beam Components => Supporting Plate => Beam => Supporting Points Structure Member and Load Path

26. 26 Material Selection  From purely structure design point of view, it is always desirable to use material with high stiffness, high strength, and low density, i.e. high strength/stiffness to weight ratio. However, other factors may affect the material selection, e.g. thermal conductivity, CTE (coefficient of thermal expansion), cost, manufacture, lead time, stability, etc.

27. 27 Material Selection Material Density  (Kg/m ) Young’s Module E (Gpa) Yield Strength S (Mpa) E/  S/  CTE (  m/m K) Aluminum 7075 T6 2700 71 503 26 186.3 23.4 Magnesium AZ31B 1700 45 220 26 129.4 26 Titanium Ti-6Al-4V 4400 110 825 25 187.5 9 Beryllium S 65 A 2000 304 207 152 103.5 11.5 Fiber Composite - Kevlar - Graphite 1380 1640 76 220 1240 760 55 134 898.5 463.4 -4 -11.7 3

28. 28 Dynamic & Stress Analysis  Finite element analysis is the most popular and accurate method to determine the natural frequencies and internal member stresses of a spacecraft. This analysis requires construction of a finite element model.

29. 29 Dynamic & Stress Analysis  Once the environmental loads, configuration and mass distribution have been determined, analysis can be performed to determine sizing of the structure members.  Major analysis required for spacecraft structure design include dynamic (stiffness) and stress (strength) analysis.  Major goal of the dynamic analysis is to determine natural frequencies of the spacecraft in order to avoid dynamic coupling between the structure elements and with the launch vehicle.

30. 30 Dynamic & Stress Analysis  Purpose of the stress analysis is to determine the Margin of Safety (M. S.) of structure elements: Allowable Stress or Loads M. S. = - 1  0 Max. Stress or Loads x Factor of Safety Allowable stresses or loads depends on the material used and can be obtained from handbooks, calculations, or test data. Maximum stress or loads can be derived from the structure analysis. Factor of Safety is a factor to cover uncertainty of the analysis. Typically 1.25 is used for yield stress and 1.4 for ultimate stress.

31. 31  Construction finite element model of a spacecraft is not an easy task. Local models, e.g. panel and beam models, can be used to determine a first approximation sizing of the structure members. Dynamic & Stress Analysis close form solution (Simply supported plate with uniform loading) Finite element solution (Simply supported plate with concentrated mass) close form solution (beam with concentrated force) reaction force

32. 32 Design Verification  Mechanical Layout – Assembly and integration  Mass Property – Mass property measurement  Quasi-static Loads – Static load test  Transient Dynamic Loads – Sine vibration test  Random Vibration Loads – Random vibration test  Acoustic Loads – Acoustic test  Shock Loads – Shock test  On-orbit loads – Thermal vacuum test

33. 33 Future Challenge

34. 34 Homework Problem  Derive a complete structure development process charts. Input Step 1 Output Step 2 Output

35. 35 References  Spacecraft Systems Engineering, 2 nd edition, Chapter 9, Edited by Peter Fortescue and John Stark, Wiley Publishers, 1995.