1. 1 衛星結構設計 祝飛鴻 10/13/2005

2. 2  Design Considerations  Environmental Loads  Configuration Design  Structure Analysis  Design Verification  Contest Problem #1  Homework Problems

3. 3  Structure exists everyplace in our life; building, bridge, car, airplane, etc. What making the spacecraft structure differs from those structures?  Everybody knows the spacecraft is delivered to space by a launcher. Therefore, the spacecraft structure has to comply with the constraints induced by the selected launcher. In addition, the structure will be useless unless it can serve the intended function. What are the constraints from the launcher and what are the intended functions of spacecraft structure? Design Considerations

4. 4  External loads or so called environmental loads will be induced to the spacecraft during the lift-off and flight of the launcher. Determination of these loads for the structure design is not a straightforward process. As a matter of fact, the loads depend on the design, i.e. changing the design may affect the loads. We will explain this process in more detail later.  Besides environmental loads, the launcher will also introduce weight and size limitation to the spacecraft design. Design Constraints

5. 5  We all know it is expensive to reach space. With today’s technology, the cost is around $10,000 USD per pound although the price varies considerably. Every launcher has weight limitation for a specific orbit height. More costly larger launcher has to be used if the weigh limitation is exceeded. Weight Constraints Falcon-1

6. 6  Besides the launcher limitation, weight saving from the structure can be used to enhance the spacecraft performance by adding more fuel or adopt more powerful components. Therefore, minimizing the structure weight is always a challenge on spacecraft design. Weight Constraints

7. 7  To launch a spacecraft into space, the launcher has to provide a streamline cover, i.e. fairing, in order to protect the spacecraft from the air heating effects. As a consequence, the spacecraft has to fit into the limitation of fairing size. 123 cm 135 cm 132 cm 30 cm Falcon-1 Envelope Size Constraints

8. 8  Just like other structures, the basic function of spacecraft structure is to provide mechanical support to other subsystems and components. However, the spacecraft structure is more complicated in the sense that it has to satisfy the stringent alignment and field of view requirements as well as long term stability under space environment for critical sensors and payload instruments. We will discuss the mechanical layout issue in more detail later. Functional Constraints

9. 9 Design Considerations  Launcher constraints:  Environmental loads  Size  Weight  Others, e.g. CG Offset, mechanical interface, etc.  Functional constraints:  Field of view  Alignment  Stability  Others, e.g. jitter, etc.

10. 10 Environmental Loads  There are two types of loads for spacecraft structure design: loads induced from the launcher and the loads induced from the on-orbit environment.  The major on-orbit environmental load, unless for special mission, mainly due to the temperature variation during mission operation of the spacecraft.  For picosat design, except for composite material, effects of the on-orbit environmental loads can be ignored if material with same thermal expansion coefficient is used.

11. 11 Flight Events  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”.

12. 12 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.

13. 13 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.

14. 14 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

15. 15 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

16. 16 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

17. 17 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

18. 18 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

19. 19 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.  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

20. 20 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 Launch Vehicle Model Combined Model Dynamic Analysis Forcing Functions of Critical Flight Events Spacecraft Responses

21. 21 Quasi-Static Design Loads  As one can see from the above process that a structure model is needed to determine the loads. However, the model can not be constructed without a design and the design can not be started without loads. How can we get out of this loop?  Fortunately, the quasi-static loads defined in launcher user’s manual can be used as a good starting point. These loads were derived by assuming the spacecraft is designed with frequencies higher than a specified minimum frequency to avoid dynamic coupling with the launcher.

22. 22 Spacecraft Preliminary Design Transient Dynamic Loads Quasi-static Loads Spacecraft Model Preliminary CLA Spacecraft Detailed Design Spacecraft Model Final CLA Design Verification

23. 23 Environmental Loads  Transient Dynamic Loads  Quasi-static loads  Sine vibration loads  Random Vibration Loads  Acoustic Loads  Shock Loads  Others, deployment loads, thermal shock, etc.

24. 24 Configuration Design  Typically the spacecraft structure starts with configuration design. This includes mechanical layout and determination of load path.  To serve its function, the structure must accommodate all the components within the launch vehicle fairing size constraint. Major consideration factors include component size, orientation and field-of-view requirements, e.g. sun sensor must able to view the sun, antenna must able to communicate with the earth, etc.

25. 25  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

26. 26 Configuration Design - ARGO

27. 27 Configuration Design - YAMSAT

28. 28 +Y Panel Battery Magnetic Coil -X Panel Magnetometer Magnetic Coil CW Antenna x 1 -Z Panel TT&C Antenna x 1 +X Panel Payload_Micro-Spectrometer CW Antenna x 1 -Y Panel OBMU +Z Panel DRU Antenna x 1 X Y Z Configuration Design - YAMSAT

29. 29 Configuration Design Hardware List Hardware Size Structure Configuration Orientation Requirements FOV Requirements Mechanical Layout Structure Analysis

30. 30 Structure 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

31. 31 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 ?

32. 32 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

33. 33 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.

34. 34 Plate Beam Components => Supporting Plate => Beam => Supporting Points Structure Member and Load Path

35. 35 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.

36. 36 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

37. 37 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.

38. 38 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.

39. 39 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.

40. 40  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

41. 41 Dynamic & Stress Analysis  Besides primary structure members, detailed analysis and design are needed for other parts of the spacecraft structure, e.g. joints between panels and beams, support bracket for components, etc.

42. 42 Yamsat Design - Load Cases & FEM  Load cases from P-POD requirements: 15g acting in any directions  FEM: No. of GRID : 1017 No. of BAR elements: 240 No. of Quad elements : 1040 Material:7075-T6 Total Weight : 0.991Kg

43. 43 Yamsat Design – Stress Contour

44. 44 Lateral mode : 221 Hz >> 25Hz (requirement) Longitudinal mode : 1156Hz >> 40Hz (requirement) Yamsat Design – M. S. & Frequency

45. 45 Bolts used for Yamsat: ultimate stress allowable =700Mpa yield stress allowable = 560Mpa nominal tightening torque = 0.21 Nm Yamsat Design – Bolts Analysis

46. 46 Structure Configuration Dynamic & Stress Analysis Mechanical Layout Load Path Check Quasi-Static Loads Material Selection Approximation Sizing Finite Element Model Preliminary Analysis/Design Preliminary CLA Detailed Analysis/Design Final CLA Design Verification

47. 47 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

48. 48 Description: Design an aluminum cube box of 10cm side and an internal holding mechanism for a raw egg. The weight of the box shall not exceed 500g and shall not be wrapped around by any material. This box will also be used as the thermal box for contest problem no. 3. The team shall generate documents and procedures for the design and test. These documents and procedures will be scored. Contest Problem No. 1

49. 49 Process: 1. Measure the box weight including the internal holding mechanism. Lighter box will get higher score. 2. Remove internal holding mechanism and install material for contest problem no. 3. 3. Conduct contest no. 3 4. Remove the material and install the holding mechanism with the raw egg. 5. Drop the box from a height to the ground covered with a carpet without damaging the box or cracking the egg. The height will be between 50 to 100cm or defined by the team. Higher distance from the ground will get higher score. Contest Problem No. 1

50. 50 Homework Problems An aluminum cube box of 10cm side contains 5 components with the following size (W x L x H) and weight: 1. 47 x 81 x 25 mm 133 gram 2. 23 x 23 x 19 mm 30 gram 3. 70 x 70 x 16 mm 80 gram 4. 85 x 65 x 20 mm 110 gram 5. 94 x 94 x 14 mm 20 gram 6. 17 x 43 x 10mm 35 gram HW #1: Layout the components which will produce the smallest MOI about the Z axis. HW #2: Calculate the CG offset HW #3: Assuming the box is supported at the bottom of the four corners. Describe load path of the design. HW #4: Estimate required panel thickness and column area under 15g loading condition 10cm X Y Z

51. 51 References  Spacecraft Systems Engineering, 2 nd edition, Chapter 9, Edited by Peter Fortescue and John Stark, Wiley Publishers, 1995.