Simplified Dynamic Model Generation and Vibration Analysis, of the International Space Station Mission 12A
Simplified Dynamic Model Generation and Vibration Analysis, of the International Space Station Mission 12A
José J. Granda §, Louis Nguyen†, Montu Raval§ § California State University, Sacramento. Department of Mechanical Engineering Sacramento, California, 95819
† NASA Johnson Space Center Integrated Navigation, Guidance and Control Analysis Branch, Houston, TX 77058
ABSTRACT
The use of computer models to predict the dynamic behavior of Space Vehicles is now a well accepted technique used to understand the natural frequencies and dynamic system responses of a complex flexible multibody system such as the International Space Station. Each new mission of the Space Shuttle after STS114, is destined to build the remaining of the International Space Station (ISS) and each new mission presents new challenges that need to be confronted during flight. One of those is the contingency plan for inspection, repair of the shuttle known as Orbiter Repair Maneuvers. The complete physical system needs to be modeled on a computer to understand the modes of vibration and to design a control system capable of controlling the proposed maneuvers. Building on the theoretical principles and procedures established in Granda, Nguyen1, the authors present the development of a computer model of ISS Mission 12A. As the station is built in space, here on earth, the authors build the components from scratch from generation of each component to assembly and dynamic analysis of ISS Mission12A configuration. The authors propose a simplified modeling technique compared to the actual methods currently in place at NASA and test their model with data from real flights. Such process and results are presented here using a technique that mixes solid modeling and dynamic finite element modeling. Software packages such as SOLIDWORKS, NASTRAN4D, MATLAB and SIMULINK have been incorporated in the process. Since the International Space Station is a combination of rigid and flexible bodies, a dynamic finite element model is appropriate instead of a standard rigid multi body model. Flexible members are analyzed as distributed systems with an infinite set of vibration modes. Once the model has acquired a level of detail in accordance with the actual station, tests are conducted for modal analysis, guidance and control of flight and Orbiter Repair Maneuvers. This research proposes a new method for producing a new generation of simplified computer models while still preserving significant dynamics information.
I. INTRODUCTION The international Space Station is a project supported by twelve nations in which the United States and Russia play a central role. It may be helpful for the reader not familiar with the details of the construction of the Space Station to go over the initial missions already accomplished until we reach Mission 12A which is the objective of this paper. In doing this the authors also familiarize the reader with the assembly of the sequential computer models that had to be generated for prior missions in order to reach Mission 12A. Just as in the building of ISS, the computer models of modules were put together until the configuration reached Mission 12A. Missions have either and A or an R designation in their names, the A stands for American, the R stands for Russian. The following flights and configurations are listed in the order of launch2.
______§ Professor, Department of Mechanical Engineering, email: [email protected] AIAA Member * Integrated Navigation, Guidance and Control Analysis Branch, email:louis.h.nguyen@nasa.gov AIAA Member § Graduate Student, Department of Mechanical Engineering email: [email protected]
1 A. FLIGHT BACKGROUND INFORMATION
1. Flight 1A/R (Russian Proton Rocket). The first element launched was the Control Module named Zarya, the Russian word for “sunrise.” Zarya provides propulsion control capability and power through the early assembly stage. It also provides fuel storage and rendezvous and docking capability to the Service Module. The 18,182- kilogram pressurized spacecraft was launched on a Russian Proton rocket. As assembly continues, Zarya provided orbital control, communications, and power for the U.S.-built Node 1, Unity. During this period, Zarya controlled the motion and maintained the altitude of the Space Station’s orbit. It also generated and distributed electrical power and provides ground communications. In the later stages of ISS assembly, Zarya primarily provide storage capacity. It be used throughout the life of the Space Station.
2.. Flight 2A (Shuttle Flight). On flight 2A, Unity and Pressurized Mating Adapters (PMA) 1 and 2 were launched in 1998. The PMA-1 connects the U.S. and Russian elements. The PMA-2 provides a Shuttle docking location. Unity’s six ports provide connecting points for Zarya, as well as the Z1 truss, airlock, cupola, Node 2, and the Multi-Purpose Logistics Module, to be delivered later. Unity is a connecting passageway to the living and working areas of the ISS—the U.S. Habitation and Laboratory Modules—and airlock. It is the first major U.S.-built component of the ISS. It contains more than 50,000 mechanical items, 216 lines to carry fluids and gases, and 121 internal and external electrical cables using 9.7 kilometers of wire.
3. Flight 1R (Russian Proton Rocket). Flight 1R launched the Russian Service Module, the primary Russian element. The Service Module provided the Environmental Control and Life Support System elements and was the primary docking port for the Progress resupply vehicles. It also provided propulsive attitude control and reboost capabilities, early Space Station living quarters, electrical power distribution, the data processing system, the flight control system, and communications. Although many of these systems will be supplemented or replaced by later U.S. ISS components, the Service Module will always remain the structural and functional center of the Russian segment of the ISS.
4. Flight 2A.1 (Shuttle Flight). The flight element for 2A.1 is the Spacehab Logistics Double Module. The purpose of the double spacehab flight is to provide a logistics flight for the early assembly missions. It carried equipment to further outfit the Service Module and equipment that can be off-loaded from the early U.S. assembly flights. The Double Module has the capacity to hold up to 4,536 kilograms as well as the ability to accommodate powered payloads.
5. Flight 3A (Shuttle Flight). Flight 3A delivered the Integrated Truss Structure (ITS) Z1. The Z1 truss is used as a mounting location for the P6 Truss Segment and Photovoltaic (solar array) Module. This Photovoltaic Module provides power for the early science that will be done on the ISS. Also being delivered on this flight was the third Pressurized Mating Adapter and the Control Moment Gyros (these provide non propulsive attitude control). In addition, the Ku-band communications system was be installed on this flight (and later activated on flight 6A). This system provided video capabilities to support ISS scientific research and television transmissions.
6. Flight 2R (Russian Soyuz Rocket). This launch established the first ISS three-person crew, or Expedition I. The Commander was a U.S. Astronaut and the other two crew members were Russian Cosmonauts. The Soyuz vehicle provided crew return capability without the Shuttle present. The first crew will spend 5 months on the ISS.
7. Flight 4A (Shuttle Flight). The completion of this flight reflects the temporary installation and activation of the P6 truss segment. The P6 Photovoltaic Module is the first of four U.S. solar based power sources. It moved and permanently attached to the P5 truss after flight 13A. Two Photovoltaic Thermal Control System radiators will provide early active thermal control. Also, the S-band communications system will be activated. This will provide radio communications on a specific frequency and the capability of transferring data.
8. Flight 5A (Shuttle Flight). Flight 5A delivered the U.S. Laboratory Module. This lab provided a shirtsleeve environment for research, technology development, and repairs by the on orbit crew. The U.S. Laboratory will distribute several systems, including Life Support, Electrical Power, Command and Data Handling, Thermal Control, Communications, and Flight Crew Systems. There will be a total of 24 racks for experiments in the U.S. Laboratory.
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9. Flight 12A (Shuttle Flight). Space Shuttle mission 12A resumed assembly of the ISS by delivering the P3/P4 truss segment to the port side of the ISS integrated truss assembly. The 17-and-a-half ton truss segment contains a new set of photovoltaic solar array wing, the Solar Alpha Rotary Joint (SARJ), and the Beta Gimbal Assembly to position the solar arrays for electrical power generation. When the solar arrays are unfurled to their full length of 240 feet, they will provide additional power for the station in preparation for the delivery of international science modules.
II PRINCIPLES OF SOLID MODELING-FINITE ELEMENTS DYNAMIC ANALYSIS
The flow chart (Fig.1) 22 shows a brief summary of the proposed procedure to mix Solid Modeling and the Finite Element Method. First Step is to build a solid model using SOLIDWORKS OR PRO ENGINEER. The authors experimented with both of these programs in order to initiate the generation of ISS modules. Both software packages have great capabilities to build the 3D part as well as an Assembly. SOLIDWORKS was found more user friendly. The models generated by SOLIWORKS were saved and an interface to VISUAL NASTRAN4D was investigated. The second step was to translate the *.Prt(*.sdprt) and *.assemb(*.sdassemb) to a standard file format which could be read by another program such as NASTRAN4D. Once in the NASTRAN4D environment, a mesh for FEA was generated. NASTRAN4D joins the best of worlds, the Finite Element Analysis and the Multi Body analysis. After translating the file to the format like *.STEP,*.IGES or any other format which can be recognized by the FEA software, The constraints, which in this case are the joints between modules and the interface with the solar arrays were generated for each body in VISUAL NASTRAN4D. Once the mesh was done, utilizing the capabilities of NASTRAN4D the dynamic analysis for vibration, modal shape analysis and frequencies was conducted. Finally generating a plant model out of this three dimensional dynamic finite element model was investigated in order to analyze the control system. The authors have investigated also other methods to generate state space models for ISS such as those in References 24 and 25 which work with system matrices.
Build a Solid Model Standard SOLIDWORKS File Format visualNASTRA Pro Engineer Translator N 4D Model
FEA Results Assemble
Rigid plus • Mode Shapes Run FEA • Natural Frequencies flexible • State Space Matrices bodies
Figure 1. Flow Chart for Finite Element Analysis
A. Generating Models of Preceding Missions, Configurations and Orbital Elements Using the convention of naming the configuration number, then a step number, and a stage or flight description we can locate the exact building state of ISS. The configuration number is a specific number for each flight, which was agreed upon by NASA and RSC-E during the November 06, 2001 Assembly and Configuration Video conference2. The step number is the sequential order of events specifically for the current assembly sequence Data Book. Table XX provides a list of step number for each configuration. Section XX provides information on nomenclature used in the stage and flight designations. Mission 12A is also called STS-115 flight. The crew of Mission STS-115 will complete another assembly phase of the International Space Station. CSA Astronaut MacLean will become the first Canadian to operate Canadarm2 and its Mobile Base in space as he is handed a new set of solar arrays from his crewmate controlling the original Canadian robotic arm, the Canadarm. Once again, the two Canadian robotic arms will work "hand-in-hand" in space. MacLean will perform two spacewalks during the course of the 10-day mission. The model of Mission 12A presented here was originated from the early missions and assembly. Shown below are a couple of preceding configurations which were used in the development.
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Figure 2. Zvezda Service Module Assembly2
Figure 3. ISS Configuration 053 (RSA Flight ID: 256)2
4 1) Solid Model of Soyuz Module
Using the dimensions published by NASA, such as those in Reference 2, each single module was individually generated. Defining the section of the main body of the Soyuz module by 180 deg. Revolve method as shown in Fig. 4.
Figure 4. Section of Soyuz Module
Details of the actions SOLIDWORKS performs on basic primitive lines and areas. Using the extrude feature (1) generate the solar panel for the Soyuz module. Using the cut extrude feature we generate the necessary holes and generate the solids of revolution for symmetrical objects.
Figure 5. Final Model of Soyuz Module
5 2) Solid Modeling Of Zarya Module.-
The section was defined according to dimension given in mass properties and Data Book2. The Revolve Feature was used on the defined section as shown in Fig. 6.
Figure 6. Section of Zarya Module
The next step was to make the new plane – Plane 1. the plane was made from the reference geometry menu to the new plane. The new plane was made parallel to right plane the distance between right plane and new plane is 0.01 m. as shown in Fig.7.
Figure 7. Creating New Plane on the Zarya Module
6 3) Solid Modeling of Unity Node
The section was made according the dimensions shown in Fig. 8. Then Revolve feature was used and the section was revolved 360 degrees.
Figure 8. Section of Unity Node
Then Plane 1 was made for the section. The section for Loft feature was made on Plane 1. Two sketches were made. One was to make the profile and the other sketch was to make path. Then the loft feature was used to finalize the model as shown in Fig. 9. Using these techniques we modeled the Destiny module.
Figure 9. Loft feature in Unity Node
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4) .Solid Modeling Of Air Lock Assembly
The solid model of the Air Lock Assembly was developed in SOLIDWORKS next. The following steps were used. First the Air Lock Assembly was started with the simple Extrude feature. Circle was extruded with the 3M Diameter up to 1.50M depth. Then Extrude and Cut Extrude features were used as shown in Fig 10.
Figure 10 Extrude, Loft feature for Airlock Assembly
5). Solid modeling of z1 assembly: First step was to make the sketch to extrude. The sketch was made on the TOP plane as shown in Fig. 11. The Z1 Truss was the first permanent latticework structure for the Space Station, very much like a girder, setting the stage for the future addition of the station's major trusses or backbones. The Z1 fixture also serves as the platform on which the huge U.S. solar arrays were mounted on the shuttle assembly flight STS-97. It includes power distribution components, four flat discs that will be used to control the station's attitude, communications equipment, temperature control system hardware, space walks, extravehicular aids and power, data and coolant connections22. Figure 11. Section to Extrude for Z1 Assembly
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The Extrude and cut Extrude features were used to finilize the model shown in Fig. 12. There were three new planes that were created named plane1, plane 2 and plane 3. Plane 1 was created parallel to front plane at 1.38 m distance. Plane 2 was created 45 degree angle to the front plane. And plane 3 was created parallel to top plane at 2.40 m distance. The plane 2 and plane 3 were used with the sweep feature. The plane 4 was also made parallel to plane 3 at 0.50 m distance. Plane 3 and plane 4 were used for loft feature.
Figure 12. Use of Extrude and Cut Extrude Features
6) Solid modeling Of P6 Assembly During shuttle mission STS-97, Space Shuttle Endeavour delivered the first set of U.S.-provided solar arrays and batteries, called the P6 Photovoltaic Module, and temporarily installed the P6 Integrated Truss Structure on the Z1 Truss until it is relocated to its permanent location on the P5 Truss during a later assembly mission. The P6 Integrated Truss Structure contains three discrete elements: the Photovoltaic Array Assembly, the Integrated Equipment Assembly and the Long Spacer. The P6, Fig 13. has four primary functions: the conversion or generation, storage, regulation and distribution of electrical power for the space station. The station derives its power from the conversion of solar energy into electrical power22. Then with the help of different Extrude and Cut Extrude feature the module was finalized. The P6 assembly carries two P6 POA solar arrays. They are about 32 m long and 8 m wide. They are connected with the individual motor so they can rotate in the direction of sun accordingly. It is also important to know the structural dynamics of P6 assembly and to make sure with the help of Finite element analysis that P6 assembly can sustain weight of P6 POA solar array. Figure 13. Finalize Model of Extension
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III ASSEMBLY OF INTERNATIONAL SPACE STATION (MISSION 12A) A. SOLID MODELING OF MISSION 12A The parts used in assembly of Mission 12A were generated using SOLIDWORKS. These are: 1. Zarya 2. Unity Node1 3. Zvezda 4. Z1 Assembly 5. P6 Assembly 6. P6 POA Solar Array 7. Destiny Lab Module PMA on 2 (On destiny lab forward CBM) 8. PMA 3 9. Airlock core with external equipment 10. Airlock Assembly (Airlock core with external equipment plus HPGA and 2 Misse unit) 11. Pirs DC1 Assembly (deployed BPM Ladder & Strela 1 and 2) 12. 4S Soyuz TM-33 (docked to DC1nadir) 13. 7P Progress Figure 14. Assembly of Zarya and Soyuz 14. S0 Assembly (deployed)
1). Assembly of Zarya and Soyuz – The first step was to assemble the Zarya and the Soyuz modules with the help of four constraints (1) Concentric1 – Face<1@Zarya-1> and Face<2@Soyuz1-1>, (2) Concentric2 – Edge<1@Soyuz1-1> and Face<1@Zarya-1>, (3) Coincident1 –
Figure 15. Assembly of Zarya1 and Zarya22
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2). Assembly of Zarya1-1 and Unity Node1- The third step was to assemble fourth module Unity Node1 with the help of three constraints. (1) Concentric12 – Face<1@zarya1-1> and Face<2@unity node-1>, (2) Distance6 – Right@Zarya1-1 and Right@ Unity Node1-1 (9.05M), (3) Angle6 – Front@zarya1-1@mission12A and Front@ Unity Node1-1@mission12A (0.00 Degree). 3). Assembly of Unity Node1 and Z1 Assembly – The fourth step was to assemble the fifth module Z1 assembly with the help of three constraints. (1) Concentric13 – Face<1@Unity Node-1> and Face <1 @ centerofforwardcbinterface> (2) Distance7 –
Figure 16. Assembly of Unity Node1 and Zaria Figure 17. Assembly of Z1 and Unity Node1
Figure 18. Assembly of Extension and Z1 Figure 19. Assembly of Solar Arrays with Extnesion
Top@Unity Node1-1 and Top plane @centerofforwardcbinterface (6.0M), (3) Angle7 – Front @Unity Node1-1 and Right plane@centerofforwardcbinterface (0.00Degree). (As shown in fig. X) 4) Assemble between Z1 assembly and P6 Assembly: The fifth step was to assemble sixth module P6 Assembly with three constraints. (1) coincident20 – face<1@centerforforwardcbinterface> and face<2@ extension- 1>, (2) coincident21 – face<1@centerforforwardcbinterface> and face <2@extension-1>, (3) Coincident22 – face<1@ centerforforwardcbinterface> and face<2@extension-1>.(As shown in fig. X)
11 5). Assemble P6 Assembly and Solar Panel 1 and Solar panel 2 – The sixth step was to assemble P6 Assembly with Solar Panel 1 and 2 with the help of two constraints for solar panel 1 and three constraints for solar panel 2. (1) Concentric15 – Face<1@connection-1> and Face<2@solar panel-1>, (2) Distance9 – Point1@Origin@connection and Face<1@solar Panel-1> (0.0M) (3) Perpendicular2 – Front plane @connection-1 and Top@ solar plane-1, (4) Concentric16 – Face<1@connection> and Face<2@solar panel-2>, (5) Distance10- Point1@origin@connection and Face<1@solar panel-2>, (6) Parallel4 – Right@solar panel-1 and Right@solar Panel-2.. Fig 19. 6) Assemble Unity Node1 and Unity Module : The seventh step was to assemble Unity Node1 and Unity Module with the help of two constraints. (1) Concentric17 – face<1@unity node1> and face<2@unity module>, (2) Distance11 – Right@ unity node1 and Right@ Unity module. (As shown in Fig. 20)
Figure 20. Assembly of Unity Node1 and US Lab Figure 21. Assembly Docking Compartment
Figure 22. Assembly of Soyuz Vehicle Figure 23. Assembly of Soyuz to DC1
7)) Assemble Zarya 1 and Pirs Docking Compartment (DC1) assembly- The eighth step was to assemble Zarya 1 and Pirs1 with the help of two constraints.(1) Concentric19 – Face<1@Zarya-1> and Face<2@Pirs-1-1> , (2) Coincident26 – Face<1@Zarya-1> and Face<2@pirs1-1>. This is shown in Fig. 21. 8). Assemble Zarya1 and Soyuz1 – The ninth step was to assemble Zarya1 and Soyuz1 two constraints. (1) Concentric20 – face<1@zarya1-1> and face<2@soyuz-3> (2) Distance12 – face<1@zarya1-1> and face<2@soyuz- 3> (0.40M). Fig.22 shows this.
12 9). Assemble DC1 and Soyuz3 – The tenth step was to assemble Pirs1 and Soyuz3 with the help of three constraints. (1) Concentric21 – face<1@pirs1> and Edge<1@soyuz1-3>, (2) Distance13 – face<1@pirs1> and face<2@ soyuz1-3> (0.32M), as shown in Fig. 23. 10) Assemble Destiny Lab Forward (Pressurized Mating Adapter - PMA) and Unity Module1- The eleventh step was to assemble Destiny Lab Forward with Unity Module1 with the help of two constraints. (1) Concentric31 – face<1@unity module> and face<2@destinylabforward>, (2) Angle10 – Top@unity module-1 and Top plane @destinylabforward (250.00 deg.). (as shown in Fig. 24) Angle10 constraint was used to define the right position of destiny lab forward.
Figure 24. Assembly of Destiny Lab Forward Figure 25. Assembly of PMA to Unity Node1
11) Assemble Zenith Pin 1 and Unity Module : The twelfth step was to assemble Zenith Pin1 and Unity Module with the of three constraints. (1) Concentric32 – face<1@Unity Module> and face<2 Zenith pin1>, (2) Distance24 – plane3@Unity Module and Top plane @Zenith pin1 ( 4.50M), (3) Angle 11 – Front plane@centerofcbforwardlab and Front plane @Zenith pin1 (180.00 deg). 12) Assemble Unity Node1 and Destiny lab forward. The thirteen step was to assemble Unity Node1 and Destiny Lab forward with three constraints. (1) Concentric35- Face<1@Unity Node1> and Face<2@destinylabforward>, (2) Distance31 – Front@Unity Node1and Front plane@destinylabforward (3.55M), (3) Angle15 – Right@Unity Node1 and Right plane @ destinylabforward (0.00deg). as shown in Fig 24 and Fig 25. 13) Assemble Air lock assembly and Unity module : The last step to complete the Mission 12A assembly was to assemble Air lock assembly and Unity with the help of three constraints. (1) concentric 36 – face<1@Unity Node1> and face<2@Air Lock Assembly>, (2) Distance32 – front@ Unity Node1-1 and front plane@airlock assembly, (4.40M), (3) Angle16 – Right@ Unity Node1-1 and Right plane@airlock assembly, (22.52 deg). The final assembly of Mission 12 A completed by this process is show in Fig 26. This was the end of the solid modeling phase of Mission 12A, Now the next major step on the development he ISS Mission 12 is the transformation to a finite element model to convert the simple solid model into a dynamic system finite element model.
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Fig. 26 Final Solid Model Assembly of Mission 12A
B. DYNAMIC FINITE ELEMENT MODELING OF MISSION 12A In order to transfer the solid model from SOLIDWORKS to Visual NASTRAN4D, STEP standard format was used. There are many other formats which vN4D we tried such as IGES, Parasolid, ACIS and STL. The only problem we encounter using STEP is that the model loses any constraints that were given to it in the solid modeling software, which means some constraints need to be applied to the vN4D model to describe its kinematics movements. Mission12A vN4D model appears as shown in Figure 27 after transferring it from SOLIDWORKS solid model to vN4D, as seen the model loses its constraints. This was a problem we had to resolve to assemble the station in the way it would represent the real systems. Otherwise, simulation of the bodies showed a downward horizontal motion because of gravity and at the same time the bodies detached from each other. The list in the far left of the window is the model tree that includes all parts of which the model is built. The best option to import the model from the SOLIDWORKS is the SOLIDWORKS assembly file or SOLIDWORKS part file. We can open the SOLIDWORKS assembly or part file in visual NASTRAN 4D in order to alleviate the problem with the constrains so that it recognize them from SOLIDWORKS
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1) Importing the STEP file of the mission12A in MSC Visual NASTRAN 4D
Figure 27. Imported STEP file from SOLIDWORKDS to Visual NASTRAN4D 2) Assigning The Simulation Properties To The Models The properties of the simulation were changed according to the requirements. The gravity of the environment is first turned OFF to create the space environment. The values of the coefficient of restitution are assigned to the individual models. We decided to analyze the model under two conditions. (1) All modules with rigid constraints. And (2) All modules with flexible and damping constraints. (1) All modules with the rigid constraints: As we discussed earlier the model brought from SOLIDWORKS as STEP model losses all the constraints or mates as they are called in SOLIDWORKS. We needed to put the constraints in Visual NASTRAN4D. First step was to hide the Soyuz module and Insert the coordinate (coord) on the Zarya1 mating surface. (As shown in Fig. 28)
22 Figure 28. Visual NASTRAN4D15 Coordinates
Figure 29. Visual NASTRAN4D22 Constraints The second step was to put the same coord on the mating surface of the Soyuz module. After putting the coord we can define the constraints between two coord, as shown in Fig. 29. The constraints between all the modules were generated in this maner. . (2) All modules with flexible and damping constraints. The constraints were put in the same way as discussed in the previous section between two modules.
Properties Assigned to the solid model 2: Mass of International Space Station – 106158 Kg Mass of Orbiter – 9173 Kg Co-efficient of restitution of International Space Station – 0.5 Co-efficient of restitution of Orbiter – 0.5 Velocity of approach – 0.05 m/sec
C. DYNAMIC FINITE ELEMENT RESULTS OF MISSION 12A All the modules are then meshed & included in FEA using the “Include FEA & Show Mesh” options in the individual menus of NASTRAN 4D. Tetrahedron elements were used in transforming the solid models into finite elements. The stress analysis is then performed using Finite Element analysis option & selecting the Stress Analysis option. Here the finite element model is a three dimensional dynamic model as opposed to static finite element model. This means that the deformations, the stress and vibration analysis is done as the dynamic load act on the system. This approach has the advantage of being able to produce finite element analysis on this model as the Space Station maneuvers either to change attitude, correct orbits or perform orbiter repair maneuvers. The output of the Finite Element Analysis was exported to Excel or HTML files in order to make it easier to analyze. The modes of vibration were generated from this flexible multi body model. Using the capabilities of NASTRAN4D we can select the number of modes to be generated. The results are excellent, we can obtain plots of each of the selected modes showing the deformations and also we can animate these, giving the user a complete perspective of a vibration mode at a particular frequency. Having the flexibility to specify the number of modes or the frequency range of the modes we are interested in, gives us the ability to investigate the ISS dynamic behavior over a frequency range, a very important consideration when analyzing the capabilities of the guidance and control system. Numerical tabulated results are presented in Reference 22.
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Figure 30. FEA Modes of Vibration with Rigid Constraints
Figure 31. FEA Stress Analysis with Rigid Constraints
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Figure 32. FEA Stress Analysis with Displacement as Output with Damping Constraints
Figure 33. FEA Stress Analysis with Stress as Output with Damping Constraints
18 IV ASSEMBLY OF MISSION12A SRMS, STATION ARM AND MOBILE BASE STATION.
A. MISSION 12A, MOBILE BASE STATION AND STATION ARM:
The first step was to assemble the Mobile base station and station arm separately and then assemble the whole assembly to mission 12A. Mission 12A, Mobile base station and station arm assembly was assembled by three constraints. (1) Parallel 9 – face<1@zenithpin1-extension> and face<2@New master assembly>, (2) Distance 45 – front plane @zenithpin-1-extension and front plane @New Master assembly, (2.00 M), (3) Distance 44 – Top plane@Zenithpin1-extension and right plane @ New Master assembly, (5.30M). This can be seen in Fig 34.
B. MISSION 12A AND SRMS (SHUTTLE REMOTE MANIPULATOR SYSTEM)
The second step was to assemble the arm 1 to the space station. They were assembled with the help of three constraints. (1) Distance 46 – front plane@ destinylabforward and right plane@arm2-1 (0.65M), (2) coincident 32 – top plane@ destinylabforward and top plane @ arm2-1, (3) Distance 47- right plane@destinylabforward and front plane @ arm2-1 (0.90M). See Fig 35.
Figure 34. Station Arm and Mobile Base Station Figure 35. Assembly of Arm1 and Destiny Lab Forward
The third step was to assemble second arm of the shuttle arm with first arm. They were assembled with three constraints. (1) coincident37 – right plane@arm2-1 and Right plane@arm1-1, (2) Distance49 – Top plane@arm2-1 and Top plane@arm1-1, (3) Distance50 – Front plane@arm2-1 and front plane@arm1-1 (As shown in Fig 36)
Figure 36. Assembly of Arm1 and Arm2 Figure 37. Assembly of Arm2 and Arm3
19 The fourth step was to assemble Arm3 to arm 2. they were assembled with the help of three constraints. (1) Distance51 – face<1@Arm1-1> and face<2@Arm3-1> (0.00M), (2) Coincident42 – face<1@Arm1-1> and face<2@Arm3-1>, (3) coincident43 – Face<1@Arm1-1> and Face<2@Arm3-1> (As shown in Fig 37)
The fifth step was to assemble Arm3 and Arm 4. They were assembled with the help of three constraints. (1) Distance 52 – Face1@Arm3-1 and Face2@Arm4-1, (0.00M), (2) Coincident45 – face<1@Arm3-1> and Face<2@Arm4-1>, (3) Distance 53 – Face<1@Arm3-1> and Face<2@Arm4-1> (0.60M). See Fig 38. The assembly was made according to configuration 1. It was very important in the assembly process that they assembled correctly so the constraints imported from SOLIDWORKS would be also fine. Otherwise, the constraints need to be redefined in on the NASTRAN4D side.
Figure 38. Assembly of Arm 3 and Arm4 Figure 39. Assembly of Coupling and Arm4
The sixth step was to assemble the Arm-4 and Coupling which connects to Latching end effectors. They were assembled with the help of two constraints. (1) Distance 57 – Face<1@arm4-1> and Face<2@coupling-2>, (0.00M), (2) Coincident53 – Face<1@arm4-1> and Face<2@coupling-2>. This can be seen in Fig 39. The seventh step was to assemble the Coupling to Latching end effectors. They were assembled with the help of the three constraints. (1) Distance 59 – Face<1@coupling-2> and Face<2@Latching End Effectors>, (0.09M), (2) Distance62 – Right plane@ coupling and Top plane@ Latching end effectors, (0.18M), (3) Distance 61 – Top plane@ Coupling and Front plane @ Latching end effectors, (0.20M). (As shown in Fig 40)
Figure 40. Asssembly of Coupling and Latching End Effector
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Figure 41. Solid Model Assembly of Latching Effector and the Space Shuttle
The eighth and last step was to assemble Space shuttle with latching end effectors. See Fig 41. They were assembled with the help of two constraints. (1) Distance63 – Face<1@Latching end effectors> and Face<2@space shuttle>, (0.00M), (2) Distance 65 – Top plane@ Latching End Effectors and Top plane @space shuttle, (2.40M).
V. ASSEMBLY OF MISSION 12A AND SPACE SHUTTLE
A. DYNAMIC FINITE ELEMENT ANALYSIS OF SRMS AND STATION ARM.
The solid model for Mission 12A with SRMS and the station arm was generated using SOLIDWORKS, following the procedure outlined above. We tried a different approach for importing the model to visual NASTRAN 4D in an effort to have it keep the constraints from SOLIDWORKS
We investigated many ways to import the part or assembly file to visual NASTRAN 4D like IGES, STEP files. The IGES file converts the assembly model to a single continuous model The STEP file convert model to individual parts. In STEP file converting produces a loss of all of the constraints on the NASTRAN4D side. It was necessary to put all the constraints into visual NASTRAN 4D. . We investigated a new interface mode by making Visual NASTRAN4D import interpret the SOLIDWORKS assembly files in order to preserve the constraints. This meant that now NASTRAN4D would interpret the *.sldasm (SOLIDWORKS Assembly file) files. Using this new approach, we were able to preserve most of the constraints from the SOLIDWORKS model. However a careful review of each and adjustments were done before the model could be transformed into a finite element model and dynamically analyzed,
Shown in Fig 42 is the NASTRAN 4D model of the Space Station Mission 12A with the arms and the Orbiter docked to it.
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Figure 42. Finite Element Model of Mission 12A and Space Shuttle
At this stage of the model development we needed to assign the real data for the physical properties of each module from the real Station and Shuttle. The system has a total mass of 290581.71kg or 19911.17 slugs which includes space station, SRMS, space shuttle and station arm with mobile base station. The next step was to change the rigid constraints to revolute constraints accordingly to the actual system. In other words, we had he ability to considered a whole assembly with the modules and arrays locked in place or to consider the actual constrains between each of the modules as in reality exisits.
Other properties besides the mass properties were specified such as the corresponding coefficients of restitution and coefficients of friction and considered the safety factors. Using this model we generated an analysis of the modes of vibration separately, the station, the robotic arms and the orbiter. in order to visualize individually the mode shapes at each frequency The rigid and the flexible modes were able to be observed, analyzed and animated. Shown in Fig 43 and 44 are the first and sixth rigid body modes for the SRMS.
In conducting this investigation of he vibration analysis, we were successful in isolating the systems in order to speed up the computation. We included the shuttle arm in FEA and then choose to include the first 15 modes of vibration. Note that at this stage of our model development the system is represented in its true rigid-flexible configuration which in principle has an infinite number of modes. In this case we chose to examine a finite set of modes of significance. The model was analyzed with gravity turned off in order to simulate the conditions in space. In the following Figures 45-to 50 we can appreciate the vibration modes of the Space Shuttle arm in his configuration.
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Figure 43. First Vibration Mode of SRMS Figure 44. Sixth Vibration Mode of SRMS
Here we have the ability to produce the vibration analysis of a particular section while the whole assembly is included in the model. Therefore a particular configuration of the arms can be analyzed in place. The same is true for any configuration of the station and its solar panels. Therefore we can isolate a section of interest or consider the entire assembly in order to study the modes of vibration.
Fi gure 45. Seventh Vibration Mode of SRMS Figure 46. Eighth Vibration Mode of SRMS
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Figure 47. Ninth Vibration Mode of SRMS Figure 48. Tenth Vibration Mode of SRMS
The vibration analysis results are then summarized below. The different natural frequencies for different modes of vibration results are shown in Table. 1. We were able to make Visual NASTRAN 4D recognize the SRMS as individual linkages and calculate the individual frequencies for each part.
Figure 49. Eleventh Vibration Mode of SRMS Figure 50. Eleventh Vibration Mode of SRMS
24 Table 1. Vibration Analysis of the SRMS Linkages22 Modes Space Coupling Arm4-1 Arm3-1 Arm2-1 Arm1-1 Shuttle
1 3.31E-5 0.000214 0.000214 0.000214 0.000214 0.000214 2 2.56E-5 0.000124 0.000124 0.000124 0.000124 0.000124
3 6.91E-5 8.04E-5 8.04E-5 8.04E-5 8.04E-5 8.04E-5 4 1.19E-5 7.66 7.66 7.66 7.66 7.66
5 1.69E-5 8.43 8.43 8.43 8.43 8.43
6 3.14E-5 15.9 15.9 15.9 15.9 15.9 7 17.1 17.3 17.3 17.3 17.3 17.3
8 21.1 47.9 47.9 47.9 47.9 47.9 9 25.9 49.9 49.9 49.9 49.9 49.9
10 26.5 87.6 87.6 87.6 87.6 87.6 11 42.3 95.9 95.9 95.9 95.9 95.9 12 49 120 120 120 120 120
13 58.8 131 131 131 131 131 14 641 193 193 193 193 193
B. DYNAMIC FINITE ELEMENT ANALYSIS OF ISS MISSION 12A AND SPACE SHUTTLE
Using the same approach as in section A above for the Space Shuttle arms, we generated the vibration analysis concentrated on the attached Orbiter. Figures 51 to 57 show the visual display of the finite set of the first 15 vibration modes chosen for analysis.
Figure 51. Space Shuttle 1st and 2nd Modes
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Figure 52. Space Shuttle 3rd and 4th Modes
Figure 53. Space Shuttle 5th and 6th Modes
Figure 54. Space Shuttle 7th and 8th Modes
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Figure 55. 9th and 10th Space Shuttle Modes
Figure 56. 11th and 12th Space Shuttle Modes
Figure 57. 13th and 14th Space Shuttle Modes
27 The results of the vibration analysis of the modes of the Space Shuttle under this configuration are summarized in Table 2. Table 2. Modes of vibration and Natural Frequency of the Space Shuttle
MODES FREQUENCY 1 2.55E-5 2 2.17E-5 3 2.05E-5
4 2.42E-5 5 3.12E-5 6 3.57E-5 7 17.1
8 21.2 9 25.9 10 28.5 11 42.3
12 45 13 58.9 14 64.1 15 75.6
VI CONCLUSIONS
A new procedure to generate the model of Mission 12A has been developed and presented herein. It demonstrates that a simplified model which significantly keeps the important dynamics of the real system can be used for dynamic analysis of Mission 12A. This is a rigid-flexible model from which a finite number of modes has been presented here but it is able to produce any number of modes of interest. The method presented here can be used to generate models of future missions and future Orbiter Repair Maneuvers with an accuracy that is dependent on how many elements and modes are included.
The method presented here mixes technologies which are separate and distinct in their objectives. First, solid models are intended to produce parts drawings and manufacturing templates in order to produce parts. Here such capability is used to generate the geometry of the modules that build the modules of Mission 12A. The reason for this approach is that solid modeling offers us the ability to produce detailed models with great accuracy and detail as desired. These are used in fact in production of parts and detailed drawings. Now the idea here is to use these precision models and transform them into three dimensional dynamic finite element models. For this reason, the finite element models that are generated from these solid models are accurate and detailed. In this case the transformation of the solid model to a dynamic model was done investigating the best way to use SOLIDWORKS in conjunction with NASTRAN4D. This was done because of the wonderful dynamic and analysis capabilities of this package. Once the solid models are transformed into dynamic finite element models the vibration analysis including frequencies and visual modes of vibration are easily generated using NASTRAN4D.
Future work will include the development of the control system that will be integrated and simulated using a SIMULINK model linked directly with the NASTRAN4D model. The objective is to be able to reproduce the specified Orbiter Repair Maneuvers using the models of the Station Mission 12A configuration, the models of the robotic arms, the model of the Space Shuttle and the model of an astronaut at the end of an arm are the four components necessary to simulate an Orbiter Repair Maneuvers with precision including the complete system in the control loop. This is possible because NASTRAN4D has the ability to generate the system plant which can be used in the simulation and for any position of the rigid-flexible bodies’ action as a complete system. Utilizing this
28 approach the system can be exported to MATLAB/SIMULINK for the analysis and design of the Guidance and Control System. At this point then the Simulink Control System will control the NASTRAN4D mode producing a simulation of a three dimensional dynamic finite element model with its control system in real time. The authors are one step away from doing this and such is reserved for a future publication.
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