Modeling the Completed Space Station a Three Dimensional Rigid-Flexible Dynamic Model to Predict Modes of Vibration and Stress Analysis

MODELING THE COMPLETED SPACE STATION A THREE DIMENSIONAL RIGID-FLEXIBLE DYNAMIC MODEL TO PREDICT MODES OF VIBRATION AND STRESS ANALYSIS

José J. Granda1, Louis Nguyen2, Sukhbir S Hundal3

1, 3 California State University, Sacramento. Department of Mechanical Engineering Sacramento, California, 95819

2NASA 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 the Space Vehicles is used to understand the natural frequencies, dynamic system responses of complex rigid-flexible multi- body system such as the International Space Station (ISS). One of the major problems in assembling the ISS is simulating dynamics and control analysis in orbit. This problem is a challenge that confronts the ISS program and thus computer modeling and simulation becomes a crucial tool for the success of space missions since the Station is being built in Space instead of a lab on earth where dynamic tests could be run. Each new mission of the Space Shuttle is designed to build the ISS and each new mission presents new challenges because the structure changes and thus the model has to change. In this paper, the authors present a model of the ISS assembled after the Space Shuttle STS-133 mission. The objective is that this model can be used to understand the modes of vibration and to design a control system capable of controlling ISS attitude. Once the computer model was assembled in a way that resembles the actual ISS assembly, model data were compared with NASA’s data. This paper proposes an alternative method for producing a new generation of three dimensional simplified computer models while still preserving significant dynamics information. In order to achieve this, the authors used components created in three dimensions via solid modeling and then transformed them into time dependent dynamic finite element models. The idea here is to have a model consisting of rigid-flexible multi-body systems, as this is what ISS is. Such process and results are presented here step by step using a technique that mixes solid modeling and dynamic finite element modeling. Software packages such as SOLIDWORKS, MSC VISUAL NASTRAN4D, MATLAB and SIMULINK were incorporated in the process. The computer model results can provide aerospace engineers with new alternative methods to perform dynamic analysis to study forces, deflections, vibrations, and position of spacecraft. The alternative method can provide aerospace engineers with new simplified methods to quickly get a handle of the forces, deflections, modes of vibration and prediction of dynamic loads during space maneuvers and ultimately crucial information to be used in guidance and control. I. Introduction

Several feasibility studies have been conducted to investigate alternative simplified methods for dynamic modeling and simulation. Several references are presented here with these background studies. For example 8 Granda JJ, Nguyen L studied the possibility of generating simple models of the first modules of ISS such Zvezda and the initial mission assembly up to Mission 3A.

______1 Professor, Department of Mechanical Engineering, email: [email protected] AIAA Member 2 Integrated Navigation, Guidance and Control Analysis Branch, email:louis.h.nguyen@nasa.gov AIAA Member 3 Graduate Student, Department of Mechanical Engineering email: [email protected]

Elramady Alyaa, Granda J.J. 11 investigated the modal analysis of the Zvesda Mission of the Space Station using another altenative method that used bond graph technology. 9 Granda JJ, Nguyen L, Raval M continued this work to create a model for Vibration Analysis using the Mision 12A configuration. On (Ref 10) Bee Tao developed the intermediate modules to assemble the Station in the post STS-124 configuration. The fundametal principle is the solution of the finite element partial differntial equations for time dependent finite element modesl proposed by well known researchers. One of them 12 Segerlind L. explains this is a simple way, which was followed throughout this research. In 13 Singh, R. P., R.J. VanderVoort, and P. W. Likens the studied the Dynamics of Flexible Bodies in Tree Topology and also 14 Montgomery R, Granda J. investigated the basic principles of using bond graphs for articulated, flexible multi-bodies, sensors, actuators, and controllers with Application to the International Space Station. Using all this background work, the authors developed a procedure that allows the building of ISS starting on the simple module level to the STS-133 configuration.

II. Principles of Dynamic Models and Modes of Vibration

The Finite Element Method can be used to simulate a combination of flexible and rigid bodies as discussed in 8 Granda JJ, Nguyen L. For the flexible set, we must consider an internally distributed system whose dynamics are controlled by a set of time dependent partial differential equations Using the equations proposed by 12 Segerlind L. we have:

 2  2  2  D  D  D  G   Q   (1) x x 2 y y 2 z z 2 t

Here  is the field function (solution) and the parameters in the equation are Dx, Dy, Dz, the stiffness in the x, y, and z directions, and λ is time dependant coefficient. These parameters are generally constructed from material and geometric properties and the solution is sought over a domain in x, y, and z and time. Practical solutions of the above are presented by Segerlind 12. A short summary is included here. The partial differential equation is solved for each class of element over its associated sub domain. There are several methods available to implement a practical solution. Two of the most popular are the Galerkin method and the Calculus of Variations. In any case, the objective is the same, to find an approximate solution for the partial differential equations and to do it in such a way as to reduce the finite element problem to a set of linear algebraic equations whose unknowns are called nodal values. In this case, these nodal values are the positions and velocities of points of interest on the different bodies, which make up the International Space Station. Galerkin methods, for example, fall under a general class of methods known as the weighted residuals, Segerlind 12. In these methods, an approximate parametric solution to the partial differential equation is constructed from a linear combination of shape functions. This parametric form is substituted into the governing differential equation, Equation (1), and a measure of the resulting error, or residual, which is integrated and required to vanish over the domain of the solution produces the set of algebraic equations whose unknowns (nodal values) are positions and velocities at points of interest in the ISS structure. In Segerlind 12, it is shown that applying the weighted residual methods, such as Galerkin's method, one can obtain the system of algebraic equations in terms of the time dependent nodal values. Denoting as f(t) the time dependent forcing function and {  } as the nodal values applying Galerkin’s method, the following equation is obtained for each finite element (e).: (e) (e) (e) (e) [c ]{} [k ]{} f {0} (2) Where [c, k and f] are the individual finite element mass, stiffness and load vectors. By means of the direct stiffness method, as explained in Siegerlind 2 these element vectors and matrices can be summed over all the finite elements resulting in global vectors and matrices. Equation (3) represents the Global Vectors and matrices, which define a set of first order differential equations as, follow:

[C ]{} [K ]{} f {0} (3)

Here [C, K, f] are now the global mass, stiffness and input vectors. Granda, Kong 5, 6 demonstrated the relationships between the finite element matrices and those generated by first order differential equations from bond graph models. That research also presented a relationship between the state variable form of systems and the global matrices obtained from the application of Galerkin’s method in finite element models. Such fundamental relation can be summarizes as follows: Using the Finite Element Form of equation (3) we have:

[C]1[C]{} [C]1[K ]{}[C]1 f {0} (4)

Singh, R. P., R.J. Vander Voort, and P. W. Likens13 present the classical approach that has been the basis for development of software used by NASA in the Space Station analysis such as SOMBAT. They discuss the Dynamics of Flexible Bodies in Tree Topology. This approach combined with the NAST RAN program has been the method of choice for the dynamic analysis of the Space Station missions. Such approach has its origins also in the work of Kane, Thomas and D. A. Levinson.15 who wrote on the Formulation of Equations of Motion for Complex Spacecraft. The software program actually used for the Station analysis is SOMBAT (Station Orbiter Multi-body Berthing Analysis Tool) is discussed in more detail in Subramaniam M, Phillips R.26. In this paper, the intent is to study models with alternative methods to these and produce simplified models that still keep the fundamental dynamic information necessary for the analysis of the vibration modes and the guidance and control system.

There are different kinds of finite element analysis such as modal analysis, contact analysis, pre-stress analysis, and vibration analysis. Here the authors concern with the modes that are inherent properties of a structure used in vibration analysis. Resonance frequencies are determined by the material properties such as mass, and damping properties and boundary conditions of the structure. Each mode is described by a natural frequency. The mode changes if the material properties or the boundary conditions of a structure changes. The elements that form a vibratory system are the mass, the spring and the damper, and the excitation elements. These issues have been investigated here with the creation of a dynamic model, which analyzes the ISS in the configuration after the STS- 133 mission.

III. Proposed Procedure to Build 3D Computer Models

Using the principles of (Ref 9 and 25), the flow chart (Fig.1) 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 ‘SOLIDWORKS 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 both 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 11, 14 and 24, 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

Solid models start with ‘SOLIDWORKS or Pro-Engineer. These software packages have great capabilities to build the 3D parts components of ISS. The authors used the data available from NASA and other sources for the basic information necessary to create the details of each modules assembly until reaching the configuration post STS-133. These are explained in more detailed in references 2 National Aeronautics and Space Administration by Lockheed Martin On-Orbit Assembly, Modeling, and Mass Properties Data Book Volume I – II International Space Station Program January 2008, 3 Dunbar, Brian., 7 Catherine A. Jorgensen, Editor and her International Space Station Evolution Data Book Revision, 19. NASA, “On-Orbit Assembly, Modeling and Mass Properties”, 23 National Aeronautics and Space Administration, [1998] Educational brief; EB-1998-07-126-HQ. “Connecting in space docking with the International Space Station”. 1998 and 29 Murugan Subramaniam ISS VAC 12A Flexible Linear Models of Orbiter Repair Maneuver Analysis.

The second step is to import the model into FEA software. After putting the boundary conditions, we can run the FEA analysis and get the FEA results such as Mode Shapes, Natural Frequencies and State Space Matrices. The solid modeling of all the modules and assembly parts were done using ‘SOLIDWORKS 2008. It was very important to be accurate in the dimensions when creating these models because these models must mate with other modules. Engineers are working together with other nations’ top design engineers to build modules that conjoin with other modules in space without major problems. For purposes of this project, the following modules and parts of ISS were built from scratch.

1. Truss Segment S6 with Solar Arrays 2. Kibo Japanese Experiment Module Exposed Facility (JEM EF) 3. Kibo Japanese Experiment Logistics Module - Exposed Section (ELM-ES) 4. Multi-Purpose Logistic Module (MLM) 5. European Robotic Arm (Docked to MLM) 6. Airlock Assembly (Docked to MLM) 7. Mini-Research Module 1 (MRM1) 8. Node 3 9. Cupola (Docked to Node 3) 10. Express Logistics Carriers (ELC1, ELC2, ELC3, ELC4) 32 11. Mini-Research Module 2 (MRM1)

A. Configurations and Orbital Elements

. The figures below are solid model representation of ISS that were designed using 3D computer aided software. The configurations below begin with Stage 15A to 3R after Rendezvous provide from Data Book Volume 1-II. Each figure is titled as a list with a configuration number follow by a stage number, and then with a flight number and description. The following are only representative samples as the actual data used to develop the complete configuration leading to Mission STS-133 is very extensive.

CONFIGURATION 139 CONFIGURATION 205 Stage 15A - Intermediate 2 Stage 1J/A - Intermediate (STS-119 Space Shuttle Discovery) (STS-123 Space Shuttle Endeavour)

S6 Assembly on S5 JEM ELM Pressurized Section

CONFIGURATION 240 CONFIGURATION 241 2J/A - Intermediate 1 Flight 2J/A - Intermediate 2 (STS-127 Space Shuttle Endeavour) (STS-127 Space Shuttle Endeavour)

JEM Exposed Facility JEM-ELM Exposed Section

Fig 2 Mission Components Configuration

CONFIGURATION TBD CONFIGURATION TBD ULF4 - Before Separation ULF4 - Before Separation (STS-STS-131 Space Shuttle Endeavour) (STS-STS-131 Space Shuttle Endeavour)

MRM1 at FGB Nadir SSRMS AT LAB

CONFIGURATION TBD CONFIGURATION TBD 20A - After Rendezvous STEP 108 (STS-STS-132 Space Shuttle Discovery) 3R - After Rendezvous

PMA 3 relocated from Unity Node 1 nadir CBM to Multipurpose Laboratory Module on Service Module Node2 zenith CBM

Fig 3 Mission Components Configuration

B) Sequential Mission Assembly Background Information Since the purpose here is to build a model on the computer as if we were building it in space, each intermediate mission details for assembly from STS-126 to STS-133 are described below:

1) STS 126/Flight ULF2 (Shuttle Flight) STS-126 has been launched on November 15, 2008 on Space Station Endeavour. The purpose of this mission is to service and repair the Solar Alpha Rotary Joints (SARJ) and launch the final flight the Leonardo Multi- Purpose Logistics Module (MPLM) to expand the crew capacity to six astronauts. Leonardo is one of three MPLM that will be used during re-supply missions such as this mission to the ISS. MPLM is approximately 21 feet long, 15 feet in diameter, weighs 4.5 tons, and can deliver up to 10 tons of cargo to the ISS. A MPLM is a large pressurized container used during Space station missions to transfer cargo to and from the ISS.

2) STS 119/Flight 15A (Shuttle Flight) STS-119 is scheduled to be launched no earlier than February 12, 2009 on Space Station Discovery. This mission will complete the construction of the Integrated Truss Structure with the addition of the fourth starboard Integrated Truss Segment (S6) and provide a fourth and final set of solar arrays and radiators to the station. S6 truss will be mounted the on the S5 truss. Astronauts on the STS-119 will be conducting several experiments too. This mission is scheduled to have duration of 14 days in space.

3) STS 127/Flight 2J/A (Shuttle Flight) STS-127 is scheduled to be launched no earlier than May 15, 2009 on Space Station Endeavour. The purpose of this mission is to complete the Japanese Experiment Module with the addition of the Exposed Facility (JEM EF) and the Exposed Section of the Experiment Logistics Module (ELM-ES). The JEM EF will be located outside the port cone of the Pressurized Module (PM). The purpose of the JEM EF is to run experiments when exposed in space. The ELM-ES section will be used as storage and transportation module. ELM-ES is un-pressurized and will serve the JEM EF. The ELM-ES will be brought back to Earth at the end of the mission. In addition, this mission is planned to replace and install six new batteries on the P6 truss and return the old batteries to Earth on the Integrated Cargo Carrier-Vertical Light Deployable (ICC-VLD).

4) STS128/Flight 17A (Shuttle Flight) STS-128 is scheduled to be launched no earlier than July 30, 2009 on Space Station Atlantis. The purpose of this mission is to deliver equipment allowing the station crew to be expanded from three to six astronauts. Leonardo MLPM will be the primary payload on the shuttle in order to expand to six astronauts. The mission will include three space walks to remove and replace a materials processing experiment outside European Space Agency (ESA) Columbus module and return an empty ammonia tank assembly.

5) STS 129/Flight ULF3 (Shuttle Flight) STS-129 is planned to be launched no earlier than October 15, 2009 on Space Station Discovery. This mission primary focus will be preparing spare components outside the station by carrying the EXPRESS Logistics Carrier (ELC1) and the ECL2. These two large External Logistics Carriers are holding two spare gyroscopes, two nitrogen tank assemblies, two pump modules, an ammonia tank assembly, spare latching end effectors for the station's robotic arm, a spare trailing umbilical system for the Mobile Transporter and a high-pressure gas tank.

6) STS 130/Flight 20A (Shuttle Flight) STS-130 is planned to be launched no earlier than December 10, 2009 on Space Station Endeavour. This mission primary purpose is to install the Node 3 and the Cupola. Cupola is a robotic control station with seven windows to provide an astronaut with a 360-degree view of the station as well as offer a window for earth observations. Cupola is approximately 2 meters in diameter and 1.5 meters tall and has a mass of 1,880 kg. Node 3 will recycle wastewater for crew use and generate oxygen the crew to breathe. Node 3 will also provide six berthing locations, data and commanding, thermal and environmental control. Node 3 will be mating with the nadir port of Unity and the Cupola will be attached to the nadir of Node 3.

7) STS 131/Flight 19A (Shuttle Flight) STS-131 is planned to be launched no earlier than February 11, 2010 on Space Station Atlantis. The purpose of this mission is to deliver equipment allowing scheduled to be the final flight of Raffaello MPLM. In addition, the

7 mission will attach a spare ammonia tank assembly outside the station and return a European experiment that has been outside the Columbus module.

8) STS 132/Flight 3R (Russian Proton Rocket and Shuttle Flight) STS-132 is planned to be launched in early 2010 on Russian Proton rocket and Space Station Discovery with different payloads. Discovery launch will deliver and install the Russian Mini-Research Module 1 (MRM1) and the ICC-VLD. A radiator, airlock and European Robotic Arm (ERA), which is attached to the Russian Multipurpose Laboratory Module (MLM), also scheduled to be installed on the mission on the Russian Proton rocket. ERA will be able to installation and deployment of solar arrays, replacement of solar arrays, inspect the station, handling of external payloads, and support astronauts during space walks. The MLM, Russian designed, will be used for experiments, docking and cargo and it will serve as a crew work and rest area. The MLM will be docked onto the Zvezda module nadir docking port. MLM is 13 meters in length, 4.11 meters in diameter and has a mass of 20,300 kg. 9) STS 133/Flight ULF4 (Shuttle Flight) STS-133 is the final mission planned to be launched on May 31, 2010 on Space Station Endeavour. The purpose of this mission will launch the third and fourth EXPRESS Logistics Carrier. In addition, this mission will add spare parts including two S-band communications antennas, a high-pressure gas tank, and additional spare parts for Dextre and micrometeoroid debris shields. Russian Proton rocket delivers Research Module which docks to Zvezda Service Module nadir port.

C) Solid Modeling of ISS Components

Below are some examples of the development of parts of ISS. There are more details in (Ref 27)

1) Solid Modeling of Truss Segment S6 with Solar Array S6 will bridge with S5 Truss Segment.

Using the capabilities of the 3D solid modeling software, starting with simple shapes, the base of P6 truss was generated and next the solar panel connections.

Solar panel base P6 Truss Assembly

Fig 4. P6 Trust Assembly development

2) Solid Modeling of Japanese Experiment Module Exposed Facility (EF)

EF is connected to Kibo. The Exposed Facility is located outside the port cone of the Pressurized Module. Experiments are fully exposed to the space environment. The Extrude feature was used to extrude 1000 mm rectangular, 5000 mm by 5600 mm. Also, extrude feature was used to create four mini-rods on both sides of the exposed facility. The Extrude feature was used to extrude an octagon that will be conjoin with Kibo. As shown in Fig 5.

Fig 5. Extruded Octagons and Small Packages on Top and Fig 6. Final model of Exposed Facility Bottom of EF

Fig 7. Extruded Octagons and Small Packages on Top and Fig. 8 Final model of Exposed Facility Bottom of EF

Fig 9 Four Identical Solar Panels on Each Rectangular Fig 10. Finalize Model of MLM Plate

3) Solid Modeling of Japanese Experiment Module Exposed Section (ES) ES bridges connection with EF. This section is used for experiments fully exposed to the space environment is shown in Fig 7 and Fig 8.

4) Solid Modeling of Multipurpose Laboratory Module (MLM) MLM joined the assembly file. MLM will link to Zarya. Serves as a crew work and rest area. The MLM will be Russia's primary research module. The MLM was designed by two separate part files, main body and two identical solar rays. Shown in Fig 9 and Fig 10.

Fig 11. Final Model of ERA Fig 12. Extrude feature for Airlock Assembly

Fig 13. Loft feature for Airlock Assembly. Fig. 14 Finalize Model of Airlock Assembly

Fig 15 Loft Feature on Top of the Body of MRM1 Fig 16. Extruded and Mated Rectangular Plate

5) Solid Modeling of European Robotic Arm (ERA)

ERA will bridge connection with MLM. (Fig 11)

6) Solid Modeling of Air Lock Assembly

Air lock assembly will bridge connection with MLM. This experiment airlock assembly will be positioned on the side facing ports at the bottom of the MLM. (Fig 12-14).

7) Solid Modeling of Mini-Research Module 1 (MRM1)

MRM1 will link to Zarya. MRM1 will primarily be used for cargo storage and docking with the ISS. It will have two docking units: one to attach to the nadir port of the Zarya module, and one to provide a docking port for the Soyuz, Progress. (Fig 15-16).

8) Solid Modeling of Node 3

Node 3 will be connected to Node 1. Node 3 contains the most advanced life support systems ever flown in space. These systems will recycle wastewater for crew use and generate oxygen for the crew to breathe. Node 3 will provide six berthing locations with power, data and commanding, thermal and environmental control, and crew access for more attached habitable volumes or for crew transportation vehicles. Created a half section of the main body of the Node 3 module by 360 deg. Revolve method. Created a plane to mirror the other half of Node 3. Extruded a circular length of 250 mm to conjoin to Node 1 also called Unity. Used cut extrude feature to finalize the modulus. Four identical cut extrude cut were made. (Fig 17)

9) Solid Modeling of Cupola Module

Cupola will link to a docking port on Node 3. Cupola will provide a pressurized observation and work area for the crew giving visibility to support the control of the space station remote manipulator system and general external viewing of the Earth, space objects and visiting vehicles. The Cupola was created by two separate parts, bottom and top portion. Created a half section of the body for the bottom portion of the Cupola module by 360 deg. Revolve method. Created a one-fourth section of the body of the top portion of the Cupola module by extruding. Copied the one-half cupola with mirror feature to create the top portion of Cupola. Cupola has six windows for astronauts to view the ISS. Mirror method. (Fig 18). Using the Draft feature, created the top portion with a 30-degree compression. Draft Method. (Fig 29). Cupola top and bottom portion were matted together into one model using the Assembly feature. (Fig 20)

10) Solid Modeling of Express Logistics Carriers (ELC 1-4)

ELC 1 will be connected to S3 Truss Segment. ELC 2, ELC 3, and ELC 4 will be connected to P3 Truss Segment. ELCs is an un-pressurized attached payload project that will provide mechanical mounting surfaces, electrical power, and command and data handling services for science experiments on the ISS. Used the extrude feature to created a base for the ELC and then created six identical battery packs using the same feature. Then used the cut extrude feature so the ELCs will mate with S3 truss. All of the ELC are identical to each other so the part was duplicated for simplicity. (Fig 21)

11) Solid Modeling of Mini-Research Module 2 (MLM2)

MRM 2 will be linked to Zvezda module. MRM 2 will provide similar services like MRM 1. Defining the section of the main body of the MRM 2 module by 360 deg. Revolve method (Fig 22)

Fig 17. Final model of Node 3 Fig 18. Completed the Top Portion of Cupola

Fig. 19 Draft feature applied to the Top Portion of Cupola Fig 20 Final model of Cupola

Fig 21. Final model of ELCs Fig 22 Final Model of MRM 2

D) Assembly of Complete ISS using Solid Models.

The different configurations corresponding to each flight of the Space Shuttle were assembled. Using the approach outlined above, Bee Tao 10 contributed to put together each of the complete STS-124 mission and to study the guidance and control of the entire assembly. Then the components described in the eleven subassemblies were assembled together in the same sequence to reach STS-133. The complete International Space Station on the configuration of STS-124 is shown in (Fig 23).

Figure 23. Assembly of STS 124

Fig 24. Assembly of S6 Truss Segment Fig 25. Assembly of STS 119

Fig. 26 Assembly of Exposed Facility, Exposed Section Fig 27 Assembly of STS 127

Fig 28. Assembly of Cupola to Node 3 . Fig 29 Assembly of STS 130

Fig 30 Multi-Purpose Logistic Module (MLM) Fig 31 European Robotic Arm (ERA) to MLM Module

It is worth expanding a bit the explanation about some of the figures above. In Fig 25. The Assembly of STS 119 Is the Assembly of Kibo Japanese Experiment Module Exposed Facility (JEM EF) and Kibo Japanese Experiment

In Fig 27, the Assembly of STS 127 is the Assembly of Express Logistics Carriers (ELC1 and ELC 2) to S3 Segment and P3 Segment.

In Fig 30 the Assembly is of Multi-Purpose Logistic Module (MLM) to the module Zarya

The Final assembly is shown in Fig 34 and corresponds to the ISS configuration as of STS-133, thus completing the assembly of ISS for the entire model of the Station.

Fig 32 Assembly of Mini-Research Module 1 Fig 33 Assembly of STS 132

Fig 34. STS-133 Final Assembly

E. Solid Models Become Dynamic Models. Finite Element Analysis of the Space Station, Space Shuttle and Station Arm

The next procedure once the solid model was created in ‘SOLIDWORKS was to transform the data in a way that could be read in an analysis program. One challenge here is not to lose the constraints defined to put together the assembly and import the model in a software package like NASTRAN4D, which has the capabilities of dynamics and finite element analysis combined. There are several possibilities and formats, which NASTRAN4D can recognize, such as STEP, IGES, Parasolid, ACIS and STL. The problem encountered with the STEP, Parasolid, and

IGES files was that these files do not process constraints, but they only describe rigid bodies. In order to describe the kinetics movements of the ISS in vN4D one has to redefine them inside NASTRAN4D. The best option would be to import the model as a SOLIDWORKS assembly file or SOLIDWORKS part file, but SOLIDWORKS 2008 and vN4D are not compatible software. If the analysis is to be conducted on a fixed configuration, a second possibility is the use the “Combine” command in SOLIDWORKS, which combines multiple solid bodies into a singled-bodied part. Fig 35 and 36 illustrate this.

Fig 35 Imported Parasolid nulti-body model into Fig 36. One Body Created in ‘SOLIDWORKS Nastran4D

III. 3D MODEL VERIFICATION

A. Purpose of Model Verification

One of the most critical aspects of a study is verifying the computer model and comparing it to NASA’s model. In this case, the verification focused on testing the model geometry and properties in order to determine if, the center of mass matches NASA’s data. The center of mass is the average location of the weight of the positions and masses of the particles that comprise the system. Therefore, the location of the center of mass for the entire ISS is largely controlled by the weights and structures of the different modulus and components.

In order to calculate the location of the center of gravity (CG), of the ISS we first calculated the weight of each component and found their relative CG location along the station. The CG location of each component, and their relative distance to the datum point set at center of the “part”. The following equation was used to figure out the central CG. The center of gravity location has been calculated without the Space Shuttle attached. In order to calculate the center of gravity, these values need to be multiplied by their weight with respect to the total weight then summed together. The results will add to the relative center of gravity location. The actual value is gained by multiplying by the total length. The distances were measured using the datum point set by NASA 2,23,30 as the point of origin seen in (Fig. 37).

Wcomponent *(x / L)component C.Glocation  (5) Wtotal

B. ISS Center of Mass Location

The Space Station Analysis Coordinate System (SSACS), illustrated in (Fig. 37), is a right-handed Cartesian, body-fixed coordinate system that corresponds to Local Vertical/Local Horizontal (LVLH) coordinate system. The origin is located at the geometric center of the mid-ship Integrated Truss Segment (ITS) S0. The longitudinal x-axis of multiple core modules, including the Zarya Functional Gruzvoi Blok (FGB) and Unity Node 1, is parallel with the analysis coordinate system axis XA, positive in the direction of the velocity vector. Positive YA axis runs parallel with the starboard truss from the center point at S0. Axis ZA completes the triad, pointing to the nadir.

To make accurate orbital adjustments, thrusts have to be accomplished in a direct line with the station’s center of mass. Pushing out of line of the center of mass will cause unwanted rotation, rather than translation only. When new station elements are added to the structure, the center of mass has to be recomputed for this purpose.

It will also undergo several configuration changes during its lifetime, both due to initial assembly and routine operations such as docking and berthing of vehicles. These changes affect the attitude controller, which must maintain stable operation under these conditions. The configuration of the center of mass after STS 133 is provided by NASA from Data Book Volume I-II. 2,3

Fig 37 ISS Center of Mass

Center of Mass X (m) Y (m) Z (m) -4.18 -0.90 3.02

Table 1 NASA’s Center of Mass Configuration after STS 133

C. Computer Model Center of Mass Location

Before one could calculate the computer model’s center of mass location, we had to use the “Combine” feature in ‘SolidWorks to join the model as one assembly. After combining the ISS station as one part then it was imported into Nastran4D as a Parasolid file. Nastran4D performs the calculation of the mass and inertial properties of the computer model in the FEA using the “Include FEA & Show Mesh” options. The calculation of the center of mass is from the datum point we assigned is not at the same location as NASA datum point2,3 .

Since the computer model and NASA model had a different datum point, we had to calculate the difference in our computer model. It was necessary to calculate the difference in the x- axis and z-axis, but not in the y-axis due to symmetry with NASA2,3 reference point. The differences in the x-axis were 39.58 meters and in the z-axis is 5.29 meters from NASA datum point. The datum point of the computer model was adjusted in the x-axis and z-axis to match the same datum point in the NASA data2,3.

Figure 38 Computer Model’s Center of Mass

Center of Mass X (m) Y (m) Z (m) -4.4 -0.50 4.4

Table 2 Computer Model Center of Mass Configuration after Adjusting Datum Point

Fig 39. Computer model’s difference in x-axis direction Fig 40. Computer model’s difference in z-axis direction

D. Comparison between Computer Model and ISS Center of Mass Location

Since coordinates are values based on a reference system, if one set of coordinates is known along with its reference system, and information is available for a second reference system, we calculated a new set of coordinates relative to the first reference. A set of coordinate values for one reference system such as computer model can be converted to a new set of values based on a different reference such as NASA datum point. Each coordinate indicates the distance rightward or downward from an arbitrary origin.

Center of Mass X (m) Y (m) Z (m) +0.22 +0.40 +1.38

Table 3. Differences of Center of Mass between Computer Model and NASA

The difference in the center of mass location between the computer model and NASA model is less than 1% difference, which accounts for geometric tolerances. It is then demonstrated that even if the model was created independently from many components, the center of mass, and other mass properties, can be adjusted to accurately match NASA's (or real system) data. The evidence supports the validity and gives creditability to the approach presented here.

IV. Dynamic Analysis of International Space Station Models

A. Modes of Vibration of ISS Station

The modes of vibration analysis were studies to test the model against random vibrations, shock, and impact. Each of these incidences may act on the natural vibration frequency of the model, which may cause resonance and subsequent failure. In our study, the modes of vibration were completed under two separate tests. For the first test,

18 we analyzed the ISS station such as the starboard truss and major modulus at 15 modes of vibration. For the second test, we analyzed the Space shuttle and station arm at 25 modes of vibration. Due to complexity and the size of the model, it took a long time to analyze the model. Simplifying the model became an iterative process by modifying the model in ‘SOLIDWORKS in addition, testing the model in NASTRAN4D. Through this iterative process, we figured out the optimum configuration to speed up reaching the ultimate goal to find the modes of vibration of ISS. The first step on this process was to convert the solid model once inside the analysis program into a mesh of finite elements model. During this process, the tetrahedron elements were used. This is illustrated on Fig 41.

Fig 41. ISS Model converted into Finite Element Model to perform calculations to determine the Modes of Vibration Analysis

Using the idea that we can define several bodies as one assembly, we were able to isolate sections of ISS, isolate the robotic arms, the solar panels and the truss as separate sub models of which we wanted to learn more about the modes of vibration of each. The entire assembly was included in the analysis, but we were able to isolate sections to display the individual modes. Fig 43 and Fig 43 illustrate this concept.

Fig 43 Starboard Truss and Solar Rays combined as Body Fig 44 Modulus underneath the truss combined as Body 2

In Nastran4D, a mesh size automatically generated was chosen for the mesh generation. The mesh contains the material and structural properties, which define how the structure will react to certain loading conditions. The mesh acts like a spider web in that from each node, there extends a mesh element to each of the adjacent nodes. This web of vectors is what carries the material properties to the object, creating many elements. This mesh analysis in Nastran4D contains the basic information such as location of corner and boundary nodes, element types, and density of elements, then a typical mesh size is generated. With large finite element, parts such as the starboard truss and solar rays cannot mesh with smaller finite element such as the Kibo, MLM, and Node 3. Nodes are assigned at a certain density throughout the material depending on the anticipated stress levels of a particular area. Regions, which will receive large amounts of stress usually, have a higher node density than those, which experience little or no stress. Points of interest may consist of fracture point of previously tested material, fillets, corners, complex

19 detail, and high stress areas. A mesh analysis for each body is tested and seen that the mesh size for each body was significantly different. Body 1 had a mesh size of zero. Both 1 and Body 2 were meshed and included in the FEA analysis. The modes of vibration can get from the simulation settings. The number of modes was defined, in this case for purposes of this paper 15 modes were investigated with their respective frequencies. The first six modes offered nothing noticeable that can be displayed graphically as they belong to six rigid body modes. Starting at mode 7, we begin seeing the combination effects of the different panels, flexible bodies and the rigid bodies (modules) as a complete assembly. What follows is a summary of those modes of vibration considering the configuration at Mission STS-133.

Fig 45. 7th Mode of Vibration of ISS Fig. 46. 8th Mode of Vibration of ISS

Fig 47. 9th Mode of Vibration of ISS Fig 48. 10th Mode of Vibration of ISS

Fig 49. 12th Mode of Vibration of ISS Fig. 50 13th Mode of Vibration of ISS

Fig 51. 14th Mode of Vibration of ISS Fig. 52 15th Mode of Vibration of ISS

Modes Body 1 Frequency (Hz) Body 2 Frequency (Hz) 1 1.63e-5 2.16e-5 2 9.16e-6 1.80e-5 3 1.95e-6 9.62e-6 4 2.33e-6 1.05e-5 5 9.95e-6 2.06e-5 6 1.53e-5 2.88e-5 7 0.0932 0.115 8 0.0955 0.116 9 0.0965 0.170 10 0.0969 0.172 11 0.0982 0.662 12 0.101 0.662 13 0.102 0.796 14 0.106 0.796 15 0.106 0.931 Table 4 Modes of Vibration and respective Natural Frequency of ISS

B. Modes of Vibration of the Space Shuttle and Station Arm

The second vibration analysis conducted were the modes of vibration of the Space shuttle and the Station arm with 25 modes. The Space shuttle and the station arm were represented detail and even then are not as complex as the ISS station. The “combine” feature in ‘SOLIDWORKS was used again to combine the Space shuttle and Station Arm SSRMS as one part seen in Fig. 53.

For this model the Parasolid file type was chosen for the interface from ‘SOLIDWORKS/ NASTRAN4D. Therefore, it was saved as a Parasolid file in Solidworks and imported into Nastran4D. Two main assemblies were analyzed where Assembly 1 is the ISS station and Assembly 2 is the Space shuttle and station arm seen in Figure 53. In this test, only the modes of Assembly 2 were displayed.

Fig 53. Combined Space Shuttle Station Arm Parasolid file

Second step was to define the mass properties. The total mass of the shuttle and station arm is around 99,000 kg (the orbiter alone is about 210,000 pounds) 2,3. The modes of vibration required mass properties, coefficient of restitution and coefficient of friction. Using Assembly 2 in FEA, we set the analysis at 25 modes. It is important to note that at this point gravity was turned off to simulate the environment in which the Space Shuttle and the Space Station operate. Representative samples of those results are shown below. Just as with the Station vibration analysis the first six modes corresponding to the rigid body modes did not offer much of a contrast as the motion is along each of the axis and with the entre assembly and no other intervening torques. The different natural frequencies for different modes of vibration are shown in Table 5. It is obvious that the vibration frequencies are lower for the arm than for the Space Shuttle because one is a flexible body and the other one is rigid.

Fig 54. 7th Mode of Vibration of Space Shuttle and Fig 55. 10th Mode of Vibration of Space Shuttle and Station Arm Station Arm

Fig 56. 13th Mode of Vibration Space Shuttle and Fig 57. 15th Mode of Vibration of Space Shuttle and Station Arm Station Arm

Fig 58. 16th Mode of Vibration of Space Shuttle and Fig 59. 21st Mode of Vibration of Space Shuttle and Station Arm Station Arm

Fig 60. 22nd Mode of Vibration of Space Shuttle and Fig 61. Zoom-In of the 25th Mode of Vibration of Space Station Arm Shuttle and Station Arm

Modes Body 2 Frequency (Hz) 1 1.51e-5 2 9.57e-6 3 7.31e-6 4 6.81e-6 5 9.22e-6 6 1.10e-5 7 0.989 8 1.04 9 2.60 10 3.25 11 6.10 12 7.54 13 9.19 14 10.1 15 12.1 16 13.8 17 15.2 18 16.0 19 20.7 20 22.8 21 23.0 22 23.7 23 26.8 24 26.9 25 27.5

Table 5 Modes of Vibration and Natural Frequency of Space Shuttle and Station Arm

This detail analysis shows the importance of Modes of Vibration to obtain answers not only in numerical form but also visually as the authors have presented their details from development of the model to the analyzis. This vibration analysis can be used to test a model against random vibrations, shock, and impact. The mode shapes described here show the expected curvature (or displacement) of a surface vibrating at a particular frequency. The natural vibration frequencies are determined by the material properties (like mass, stiffness and damping properties) and boundary conditions of the structure. Using this approach engineers are capable to quickly build and test virtual models for verification or calculations of dynamic loads, deformation and stress and strain tests, a crucial capability for those structures that are not build on earth but they must work with reliability in space..

V. CONCLUSIONS

This paper describes an overview of a new proposed development and analysis procedure to analyze a set of rigid and flexible bodies, which is the computer representation of the physical reality of the International Space Station. Herein the authors describe how to create and how to use computer models, which originally start and were developed with tools not intended for dynamic analysis but rather for design and production purposes. These were converted into intelligent Dynamic Finite Element Models with analysis capabilities in order to predict the dynamics behavior of the ISS station to understand the natural frequencies and dynamics responses of a complex flexible multi-body system.

The objectives of this work were fulfilled. The model developed here can serve as template procedure for the development of models in many areas of research from ground to space vehicle to robotics and autonomous systems. These goals are:

• 3D Model Design Using ‘SOLIDWORKS • Design Verification • Failure Analysis Using Nastran4D • Modes of Vibrations of ISS Station • Modes of Vibration of Space Shuttle and Station Arm • Stress Analysis on the ISS Station • Position Control Using SIMULINK

The complete physical system is modeled to understand the modes of vibration and to design a control system capable of controlling the proposed maneuvers. The modes of vibration of the station arm were studied, obviously the frequencies of vibrations and corresponding configurations and displacement increases as the modes of vibration increased. Damping or controlling these vibrations can be studied next once a model like this is developed. This opens new doors for research in Guidance and Control of large space vehicles such as ISS. Given the flexibility to change the configuration by adding or subtracting components in order to evaluate a new configuration, another use of such model is to revisit previous studies, compare new results, and evaluate improvements.

Study of these vibrations and the stresses caused by them in the structure of space shuttle and ISS are of great importance. The control system to control the rates of the rigid-flexible system can be built with the help of SIMULINK. Control scheme can be developed once the State Space model representation in the form of a vector block diagram compatible with SIMULINK is obtained from the NATRAN4D model. Frequency response and compensation then are possible using this model. The obvious next task is the study to guidance and control of ISS. This model in intended for getting a very quick handle on operations that come up in orbit, some that have not been tried or imagined before, but with the flexibility to change the model as presented here, new mission maneuvers can be simulated and results obtained in a short time compared to the actual calculations using conventional software like SOMBAT26. Several guidance and control schemes can be studies to control the ISS Station about all its degrees of freedom simultaneously. Using SIMULINK and NASTRAN4D simultaneously to study the control of ISS and its different configurations with or without the Orbiter, is something that can make good use of the modeling technique presented here.

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