祝飛鴻

1. 衛星結構設計 祝飛鴻 5/31/2007

2. Pre-Class Assignment What are key constraints for the spacecraft structure design? How the structure design is affected by other subsystems? How the structure design affects the performance of other subsystems? How to distinguish a good and bad spacecraft structure design?

3. Spacecraft Structure Design: • What are the main functions? • What factors need to be satisfied? • What are major tasks? • How to verify the design?

4. Structure subsystem holds all other subsystems together: • Carry Loads - provide support all other subsystems and attach the spacecraft to launch vehicle. • Maintain geometry – alignment, thermal stability, mass center, etc. • Provide radiation shielding Structure design is affected by all the other subsystems The first Taiwan designed satellite

5. Spacecraft structure design has to satisfy the following factors: • Size • Weight • Field-of-view • Interference • Alignment • Loads The first Taiwan designed satellite

6. 13mm clearance 11mm clearance 衛星尺寸限制: • Falcon 1 (Dia. 1371) • Falcon 1E (Dia. 1550) • Taurus-63 (Dia. 1405) 1.Size: • Fit into the fairing of candidate launch vehicle. • Provide adequate space for component mounting. Taurus-63 Falcon 1E Falcon 1 1371 1405 1550

7. 2. Weight: • Not to exceed lift-off weight of the selected launch vehicle to the desired orbit. • Trade will be performed to determine the launch vehicle injection orbit for best weight saving.

8. 110 ° 110 ° 65 ° 65 ° X Band Antenna FOV 3. Field-of-view (FOV): • Define by other subsystems, e.g. attitude control sensors, payload instruments, antenna subsystem, etc. MSI FOV= 6 ° Star Camera FOV= 6.7° on short axis 9.2° on long axis

9. 4.Interference: • With the launch vehicle fairing. • Between components for physical contact and assembly. GPS Ant. 8.6mm clearance Falcon-1Envelope Solar Panel 19mm clearance X-Band Ant 15.5mm clearance

10. 5.Alignment: • Define by other subsystems, e.g. attitude control sensors, payload instrument, etc. • On ground alignment, if necessary. • On-orbit thermal & hydroscopic distortion.

11. 6. Loads: • Environmental loads for structure design. • Loads for components and payloads.

12. The structure design may not be able to satisfy all the design factors. Therefore Factors to be satisfied for structure design is not a one way street Factors to be satisfied Structure Design System Performance

13. Major tasks for spacecraft structure design include: 1. Configuration design 2. Material Selection 3. Environmental loads 4. Structure analysis

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

15. The First Taiwan Designed Satellite

16. 2. Material Selection: Factors to be considered: • Strength-to-weight ratio • Durability • Thermal stability • Thermal conductivity • Outgassing • Cost • Lead time • Manufacture Commonly used material: • Metals – Aluminum, etc. • Composites • Ceramics • Polymers • Semiconductors • Adhesives • Lubricants • Paints • Coating

17. 3. Environmental Loads: 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”.

18. 3. 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.

19. 3. 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.

20. Environmental Loads: • 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. • Unfortunately the transient dynamic loads are structure design dependant, e.g. magnitude of loads depends on the spacecraft structure design (see appendix for explanation). However, loads are required for the design. • Typically spacecraft structure are designed with the quasi-static load factors defined in the launch vehicle user’s manual, e.g. 2g lateral and 7g axial. • These quasi-static loads are only applicable if the stiffness design of the spacecraft is above the minimum frequency requirement as specified in the launch vehicle user’s manual, e.g. >20Hz lateral. These loads may not be applicable for light weight second appendages, e.g. solar panel, antenna, etc. and needs to be verified by the coupled loads analysis.

21. Coupled Loads Analysis: The natural frequencies of a spacecraft can be predicted by mathematical model, e.g. finite element model. This model will be delivered to the launcher supplier for coupling with the launch vehicle model. Dynamic analysis can be performed using this combined model and critical responses of the spacecraft can be derived for the spacecraft structure design. Spacecraft Model Combined Model Dynamic Analysis Spacecraft Responses Launch Vehicle Model Forcing Functions of Critical Flight Events

22. Typical CLA Results

24. Dynamic Coupling

25. Structure Analysis 4. Structure Analysis: 4.1Mass property analysis 4.2 Structure member and load path 4.3 Dynamic and stress analysis

26. 4.1 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 Y W2 X D1 D2

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

28. 4.2 Structure Members 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. Plate Beam Components => Supporting Plate => Beam => Supporting Points

29. 4.3 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. • 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. 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. 4.3 Dynamic & Stress Analysis: • Construction finite element model of a spacecraft is a time consuming task. Local models, e.g. panel and beam models, can be used to determine a first approximation sizing of the structure members. close form solution (Simply supported plate with uniform loading) Finite element solution (Simply supported plate with concentrated mass) reaction force close form solution (beam with concentrated force)

32. Structure design is an iterative process However Major design changes will have significant impact to the program SDR (System Design Review) PDR (Preliminary Design Review) CDR (Critical Design Review)

33. How to verify spacecraft structure design? • Mechanical Layout – Assembly and integration • Alignment – Alignment measurement • 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 Depends on the program constraints and risk assessment not all the tests are required.

34. Homework Problem 1. Revise answer to the pre-assignment problems. 2. Define detailed step by step process for your picosat structure design. Identify sources for the required inputs. Please provide your answer by 6/8 (Fri)

35. What you have learned is:

36. Reference • Spacecraft Systems Engineering, 2nd edition, Chapter 9, Edited by Peter Fortescue and John Stark, Wiley Publishers, 1995.

37. Appendix Phenomena of Dynamic Coupling

38. 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 

39. Dynamic Coupling • Based on the above equation, a spring-mass system with K1 = 654,000 lb/in and weight W1= 4,000 lbs will have f1 = 40Hz (verify it!). • Assume a second system hasf2 = 75Hz. (if this system has 30 lbs weight, what should be the value of K2?) • 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 a K 1g

40. Dynamic Coupling • Suppose we stack these two system together, the response of the system can be derived as: 39.8Hz 75.4Hz a1 16.6g 0.4g a2 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 a1 K2 W1 a2 K1 1g

41. Dynamic Coupling • Now, let’s change the second system to have natural frequency of 40Hz, then the responses will be: 38.3Hz 41.8Hz a1 9.9g 9.2g a2 99.2g 83.4g where 38.3Hz and 41.8Hz are the natural frequencies of the combined system. W2 a1 K2 W1 a2 K1 1g

42. 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 a1 K2 W1 a2 K1 1g

43. 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 a1 K2 W1 a2 K1 1g