Development of a Digital Engineering Testing Framework for CUBESAT Applications

This paper presents the development of a comprehensive Digital Engineering (DE) testing framework for CubeSat applications, demonstrated through the SleeperSat-1 (SPST-1) modular small satellite project at the University of Texas at El Paso Aerospace Center. The study emphasizes the integration of Digital Engineering tools, particularly Digital Twins (DT), to enhance the testing and validation processes of CubeSat under diverse environmental conditions. The research outlines the creation and implementation of a high-fidelity Digital Twin model for the SPST-1, incorporating Computer-Aided Design (CAD), Finite Element Method (FEM), and simulation models to ensure accurate representations of the satellite’s physical counterparts. Specifically, this research creates a high-fidelity Digital Twin model of the SleeperSat-1 CubeSat chassis and validates the solution against actual environmental testing, to find discrepancies and optimize the design for enhanced reliability and efficiency. This approach facilitates efficient early-stage testing, reducing the need for extensive physical prototyping and thereby minimizing time and costs. The SPST-1 project showcases the potential of Digital Engineering to improve reliability, scalability, and adaptability in CubeSat development. The findings highlight the transformative impact of Digital Twins in satellite design, offering promising advancements in design, testing, and operational workflows.

1.1 Digital Engineering

This paper presents the development of a comprehensive Digital Engineering (DE) testing framework for CubeSat applications, demonstrated through the SleeperSat-1 (SPST-1) modular small satellite project at the University of Texas at El Paso Aerospace Center. The study emphasizes the integration of Digital Engineering tools, particularly Digital Twins (DT), to enhance the testing and validation processes of CubeSat under diverse environmental conditions. The research outlines the creation and implementation of a high-fidelity Digital Twin model for the SPST-1, incorporating Computer-Aided Design (CAD), Finite Element Method (FEM), and simulation models to ensure accurate representations of the satellite’s physical counterparts. Specifically, this research creates a high-fidelity Digital Twin model of the SleeperSat-1 CubeSat chassis and validates the solution against actual environmental testing, to find discrepancies and optimize the design for enhanced reliability and efficiency. This approach facilitates efficient early-stage testing, reducing the need for extensive physical prototyping and thereby minimizing time and costs. The SPST-1 project showcases the potential of Digital Engineering to improve reliability, scalability, and adaptability in CubeSat development. The findings highlight the transformative impact of Digital Twins in satellite design, offering promising advancements in design, testing, and operational workflows.

Figure 1. Aerospace Center DE Framework (Aerospace Center).

1.2 CubeSat

Space activities are extremely expensive and include a high degree of risk. Building and launching a full-scale satellite platform with instruments for experimental science can cost $200 million or more. A general industry estimate for building and fully testing space instruments is about $1 million per kilogram. CubeSats are a bargain by comparison, with total costs ranging from $200,000 to $2 million each, with much of its cost coming from development and testing (Woellert et al 2011). CubeSat launch expenses can also vary widely from $10,000 to $500,000 depending on the type (Bomani 2021). The term CubeSat is used to describe a small satellite whose base unit form is a 10cm edge cube, namely ‘1U.’ CubeSats units can be put together to form bigger artifacts, like 2U, 3U, 6U, and so forth. CubeSats must follow the standards defined by the CubeSat Design Specification, which includes compliance with flight safety guidelines (Johnstone 2020). CubeSats are considered a competitive solution for space applications as they allow equilibrium among crucial variables of a space project, such as development time, cost, reliability, mission lifetime, and replacement (Villela et al 2019).

The UTEP Aerospace Center is currently developing the SPST-1, a 4U modular CubeSat capable of executing several missions in the same envelope (Figure 2) The SPST-1 will consist of three modules: Core, Artificial Intelligence and Machine Learning (AIML) and Robotic Arm (RA). The core module will serve as the satellite’s communication and control system. The AIML and Robotic Arm modules are the satellite’s secondary missions. Each module will have its own power supply, and its functionalities are independent from each other. Having this modularity requires a flexible chassis design that can accommodate any type of payload desired. The development of the chassis will also be discussed in this article. The SPST-1 will mostly utilize Digital Engineering tools for its design, development, testing, and operational lifecycle with the objective of developing and standardizing a digital workflow to minimize time and cost even further.

Figure 2. 4U SPST-1 Configuration. Robotic Arm (left), AIML and Core (right), the figure is proportioned appropriately for compliance.

2.1 CAD and FEM Model

A Digital Twin is a set of virtual information constructs that fully describes a potential or actual physical manufactured product from the micro atomic level to the macro geometrical level. At its optimum, any information that could be obtained from inspecting a physical manufactured product can be obtained from its Digital Twin. It aims to combine the best of all worlds, namely, twinning, simulation, real-time monitoring, analytics, and optimization (VanDerHorn and Mahadevan 2021). It has been recognized as the next breakthrough in digitization, and as the next wave in simulation. This approach offers potential cost, time, and resource savings by deferring and reducing the need for physical prototyping. It facilitates precise and efficient early-stage testing on virtual prototypes, without disrupting actual operations (Sharma et al 2022). Digital Twins can be divided into three subcategories: Computer Aided Design (CAD) models, Finite Element Method (FEM) models, and Simulation (Sim) models. Each of these models is crucial for the development of a high-fidelity digital twin. The Siemens PLM software is used for the design, analysis, and optimization of the SPST-1 Digital Twin. It is a comprehensive portfolio of software used to design products, realize their potential, and optimize their performance. It utilizes NX for mechanical design, and NX Nastran for simulation and test solutions. An early example illustrating the benefits of multi-disciplinary optimization in CubeSat design is provided by Shi et al. 2018.

A phased approach has been adopted to manage the complexity of the full SPST-1 design, with the initial phase concentrating on the modeling and physical testing of the chassis, while the broader focus is on modeling and validating the Digital Twin. This decision is based on two primary considerations: the chassis is relatively simple to model, manufacture, and test, and repeated testing could pose a risk of damage to sensitive and expensive components within the SPST-1.

The nature of the SPST-1 required a chassis design able to provide flexibility to the desired number of modules in each mission. With this idea in mind, a modular design approach was taken for the development of the SPST-1 chassis. The chassis consists of four separate parts (z-face, y-face, x-face, and rails) that are mechanically connected with the use of screws. The isometric view with the coordinate system used is shown in Figure 3. The material used for the chassis is Aluminum 6016. With NanoRacks being the chosen launch provider, all design specifications and requirements were made by referring to the NanoRacks CubeSat Deployer (NRCSD) Interface Definition Document (IDD) and NanoRacks DoubleWide Deployer (NRDD) Interface Definition Document (IDD) (Prejean 2018).

Figure 3. Isometric View of Assembled Chassis with Coordinate System.

Two types of elements were used to mesh the four chassis parts. The Constrained Tetrahedral (CTETRA) and Conforming Hexahedral (CHEXA) elements, Figures 4 and 5, respectively. The CTETRA element is an isoparametric tetrahedron element with four vertex nodes and up to six additional midside nodes. The CTETRA solid element is used widely to model complicated systems (i.e., extrusions with many sharp turns and fillets, turbine blades). The element offers a distinct advantage over the CHEXA in scenarios involving geometries with sharp corners, as CTETRAs can be more appropriately shaped compared to CHEXAs (Siemens). The CTETRA element was used to mesh the locations of the screws, as well as the radius of the corner rail. The CHEXA has eight corner grid points and up to twenty grid points if you include the twelve optional mid-side grid points. The CHEXA element is recommended for general use, but its accuracy degrades when the element is skewed (Siemens). The CHEXA element was used to mesh the rest of the parts. Each part was meshed separately first, and then combined to create the assembly FEM. An idealized part was created for each part to make any changes needed for the creation of the mesh. The idealized part is a copy of the original part file that can be edited without changing the original part. The idealized part has to be first promoted in order for the software to reference the changes made to the fem file. The idealized part of both the x and y faces were modified similarly. The extensions at the corners, as well as the four screw holes were cut to be meshed separate from the body. Also, the material was added to the middle of the faces, and two screw holes were made. The addition of the material and extra screw holes in the chassis body is to be able to connect the chassis to the vibration table for testing. Figure 6 shows the isometric view of the chassis assembly FEM.

Figure 4. CTETRA element connection (left) and coordinate system (right).

Figure 5. CHEXA elements (left) and coordinate system (right).

Figure 6. Chassis assembly FEM.

Although the parts are now together to create the assembly, there is still no connection between the parts. To create the connections, the use of a Constant Beam Analysis Routine (CBAR) element and spider connected to Rigid Body Element (RBE3) elements will be used at each screw location to simulate the screw connection between the parts. The material applied to the CBAR element is steel. The CBAR element is a general-purpose beam that supports tension and compression, torsion, bending in two perpendicular planes, and shear in two perpendicular planes. The CBAR uses two grid points and can provide stiffness to all six Degree of Freedoms (DOFs) of each grid point. With the CBAR, its elastic axis, gravity axis, and shear center all coincide. The displacement components of the grid points are three translations and three rotations. The RBE3 element is a powerful tool for distributing applied loads and mass in a model. The RBE3 does not add additional stiffness to the structure. Forces and moments applied to reference points are distributed to a set of independent degrees of freedom based on the RBE3 geometry and local weight factors (Siemens). The CBAR and RBE3 elements are shown in Figure 7.

Figure 7. CBAR and RBE3 elements modeling screw connection between chassis parts.

A mesh study was conducted to evaluate the effects of different element sizes; 1 mm, 3 mm, 5 mm, and 8 mm on several critical parameters. The study focused on comparing the maximum deformation observed at an element located at the top of the z-face, the computational time required for each simulation, and the total number of elements involved. Based on these comparisons, the 3 mm element size was selected as the optimal choice for our simulations.

Table 1. Comparisons of deformation and computational time across various element sizes.

Element Size, mm	Element Count	Max. Deformation, mm	Node Deformation, mm	Time, hour
1	251,418	4.258e-03	2.522e-03	2
3	66,820	4.108e-03	2.501e-03	0.67
5	55,057	3.988e-03	2.504e-03	1.5
8	53,823	3.783e-03	2.476e-03	1.2

2.2 Structural Model

The NanoRacks IDD states that “The CubeSat shall be capable of withstanding a force of 1200N across all rails ends in the Z axis” (Prejean 2018). Solution 101 Liner Statics was the chosen solver for this study. The linear static solution type is used to solve small strain and small displacement structural problems, where the loads do not vary with time and the material behavior is linear elastic. Linear static problems can include gaps and contact. The results of a linear static analysis are typically displacements, stresses, strains, and forces (Siemens). The 1200N force can be divided by the four rails for a total force of 300N applied across the top face of each rail. The bottom faces of the rails had a fixed constraint applied to avoid any movement. A surface-to-surface contact was also added to the entire model. The surface-to-surface contact is used when parts are meshed independently but should function as a unified whole. Furthermore, it allows the parts to have sliding and motion between each other. Figure 8 shows the model with the forces and boundary conditions applied.

Figure 8: Isometric view showing forces (red), contacts (yellow), and constraints (blue).

Figure 9 displays the deformation contour of the chassis, indicating the maximum deformation at the walls, measured at 4.1413×10^-3 mm, the deformation at the top of the rail measures 2.327×10^-3 mm. In Figure 10, the stress contour of the chassis is shown, with the peak stress reaching 15.1 MPa, located at the interfaces between the rails and the chassis faces. The chassis maintains a factor of safety of 16. 

Figure 9. Deformation contour of chassis.

Figure 10. Stress contour with inverted spectrum of chassis.

The chassis geometry used for simulation was manufactured for physical testing. The physical testing of the chassis aims to validate simulation results and assess the model’s reliability as additional components are incorporated. The integrated loads environment testing requirement was tested using a compression machine to apply the 1200N force. Two circular plates were attached to the compression machine to apply the load. These plates were not big enough to fit the chassis, so two rectangular plates with rail extensions had to be manufactured to make sure that the loads were being applied directly to the rails. The experimental setup can be seen in Figure 11.

Figure 11. Experimental compression test setup.

The deformation measured at 1200N was 0.6mm compared to the deformation at the rails in the model which was 2.327×10-3 mm. The significant difference between the deformations can be explained by two things: 1) the machine measured the deformation relative to the position of the rod that was moving down. No deformation data was acquired directly from the chassis. 2) The stiffness of the machine is less than the stiffness of the chassis. This can cause the measurements to lose accuracy. To better capture the deformation of the chassis, two options are available. 1) Adding strain gauges to the chassis will measure the deformation at that exact location which can be directly compared with the model. 2) Adding a dial gauge to the experiment to measure the displacement of the rails before and after the force is applied.

2.3 Vibration Model

The NanoRacks IDD states that “The CubeSat shall be capable of withstanding the random vibration environment for flight with appropriate safety margin” (Prejean 2018). Random vibration tests the flight article in the soft-stow (wrapped in bubble wrap and secured in a foam-lined Cargo Transfer Bag) flight configuration to the Maximum Expected Flight Level (MEFL) +3dB, for a duration of 60 seconds in each axis, or Random vibration test the flight article in the hard-mount (directly secured with bolts or clamps) configuration to a combined test profile that envelopes the MEFL+3dB and a minimum workmanship level (MWL) vibration, for a duration of 60 seconds in each axis.” The hard and soft mount test profiles can be seen in Figure 12.

Figure 12. Random Vibration Test Profiles (Prejean 2018).

Solution 103, Response Dynamics (NX Nastran), was selected as the solver for this study due to its capability to evaluate the responses of a structure under various static and dynamic excitations. Response Dynamics is a full-featured add-on for defining complex solution processes with the user interface (Siemens). For this simulation, a remote point connected to the chassis by an RBE2 element has to be added to apply the excitations. Only the z-axis will be excited, and the results used for model validation purposes. Figure 13 shows the remote point added to the FEM.

Figure 13. FEM with remote point connected to chassis.

A user-defined constraint is applied to the remote point to fix all degrees of freedom (DOF) except for the specific one where the excitation is intended to occur. In this case, the z-direction was the only free DOF. An enforced motion location was also added to apply the excitation only in that location. Surface-to-surface contact was again added to the model. First a modal analysis has to be performed to find the natural frequencies of the structure. The natural frequencies are the frequencies at which a structure tends to oscillate without any driving force. The range will be between 20 and 2000 Hz as specified by the NanoRacks requirement in Figure 12 with an evaluation period of 60 seconds. The first four normal modes are shown in Figure 14.

Figure 14. Normal modes response at 49.15 (upper left), 183.74 (upper right), 191.92 (lower left), and 198 (lower right) Hz.

A Response Dynamic solution was created. The total modal effective mass of the direction at which the forces were applied needs to be greater than 80%. Any lower than this and not enough normal modes would have been calculated for an accurate solution. The modal effective mass for the z direction is 80.47%. A 5% damping factor will be added to the modes (Casiano 2016). Sensors will be added around the structure of the chassis. There are three types of sensors available: displacement, velocity, and acceleration. In this case, acceleration sensors were chosen to compare the data from the simulation to the data from an accelerometer in physical testing. The black lines in Figure 15 show the locations of the acceleration sensors.

Figure 15. Locations of acceleration sensors.

A random event was then defined using the hard mount profile from Figure 12. The sensor will be evaluated and the frequency versus acceleration graph results extracted. Also, the RMS Von Mises stresses at the top face will be evaluated (Day et al 2020). Figure 16 presents the frequency versus acceleration graph, which visually illustrates the peak accelerations observed at various frequencies. Figure 17 illustrates Von Mises stresses at the top Z-face.

Figure 16. Frequency vs acceleration evaluation for sensor with applied random profile.

Figure 17. Von Misses stresses at top face.

The random vibration environment was tested using a vibration table to physically excite the chassis with the NanoRacks profile, and an accelerometer was mounted to the chassis at the same location as the sensor in the model. Both sine and random vibration profiles were tested. The sine profile was tested to obtain a smooth Power Spectral Density (PSD) versus acceleration response, and the random to document the pass or fail criteria. The setup of the experiment can be seen in Figure 18.

Figure 18. Vibration test setup.

The sine test allowed us to see the frequencies at which the chassis was being exited and compare them with the results from the simulation. Figure 19 shows the comparison between the test and simulation data. The simulation data does not align with the physical data. This discrepancy is likely due to several uncertainties present in the physical test that are not considered in the simulation. Components such as the accelerometers, plate, vibration table, and screws used to connect different parts are not modeled in the simulation, which can alter the chassis response. To achieve accurate matching between simulation and physical results, either the simulation needs to incorporate these factors, or the physical setup must be adjusted accordingly. Additionally, using a laser vibrometer, which measures acceleration without direct contact with the structure, could help reduce uncertainty introduced by the accelerometers. For more precise and in-depth validation, improved equipment is necessary.

Figure 19. Comparison between simulation and test data showing the Acceleration versus Frequency Response.

The integration of Digital Engineering tools in the development of a digital testing framework for CubeSat, as demonstrated in this study, highlights significant advancements in the field. By creating a high-fidelity Digital Twin for the SleeperSat-1 modular small satellite chassis, this project showcases the potential of Digital Engineering to improve the efficiency and reliability of satellite design, testing, and validation processes. Methodologies such as strength-based design and experimental validation, applied in similar studies on fertilizer spreader chassis and precision planter chassis, underscore the importance of combining computer-aided engineering (CAE) tools with experimental validation. This ensures the reliability and accuracy of designed structures under real-world conditions (Irsel 2021; Irsel 2023). Such approaches confirm that digital models can accurately represent physical systems, enhancing the overall reliability of the DE testing framework. Detailed stress and fatigue analyses using strain gauges and finite element analysis (FEA) further provide valuable methodologies (Agarwal and Mthembu 2022) for assessing the durability of satellite components. The SPST-1 project similarly employed FEA and physical testing to evaluate the chassis’ structural integrity under various load conditions, ensuring thorough examination and mitigation of potential failure modes.

The successful implementation of a Digital Engineering testing framework for the SPST-1 will have significant implications for CubeSat development, including enhanced efficiency, cost reduction, improved accuracy, reliability, scalability, and adaptability. This framework could reduce the need for physical prototypes, enabling early-stage testing and validation through digital simulations. This approach could also accelerate the development process and reduce costs. Validation of digital models with experimental data ensures that Digital Engineering tools provide precise and trustworthy results, further enhancing reliability. Additionally, the modular design approach facilitated by Digital Engineering tools allows for easy scaling and adaptation of CubeSat designs, which is crucial for missions requiring rapid deployment and customization to meet specific objectives.

A Digital Twin model of a CubeSat chassis, justified through rigorous analysis, was presented in this study. Both digital and physical models were subjected to comprehensive environmental testing requirements, including integrated loads and random vibration environments. The physical data obtained were compared with the digital twin’s data to verify the analysis results. While the absence of advanced testing equipment prevented direct one-to-one data comparison, leading to notable discrepancies between simulated and tested data, this does not imply that the models produced erroneous results. On the contrary, the Digital Twin models likely provided more precise and insightful data, offering a deeper understanding of system behavior than physical testing alone could achieve. The primary challenge lies in aligning the model simulation with the physical testing setup and ensuring that the physical setup accurately records the necessary data for comparison with the digital model. Once these conditions are met, the digital and physical data will converge, thereby fully validating the Digital Twin model. Finally, the integration of Digital Engineering tools in the SPST-1 project could represent a significant leap forward in the design, testing, and validation of CubeSat. By leveraging high-fidelity Digital Twin models and robust validation methodologies, this project might highlight the transformative potential of Digital Engineering in satellite industry. Future research could focus on addressing challenges related to interoperability, validation, and complexity management to further refine and expand the capabilities of Digital Engineering tools in the aerospace industry.

Acknowledgement: This material is based on research sponsored by the Air Force Research Laboratory under agreement number FA 8650-20-2-5700. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Air Force Research Laboratory or the U.S. Government.

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