Modeling of composite mesh adapter for Marathon satellite system spacecraft output

Толық мәтін

Introduction

Composite anisogrid shells of revolution have found wide application in spacecraft engineering in recent years. Therefore, close attention is paid to the study of their behavior [1–12]. The adapter design consists of a cylindrical and a conical part, therefore, a comprehensive study was conducted to investigate the influence of the main design parameters of anisogrid cylindrical and conical shells on their rigidity and load-bearing capacity. In this study, the inertial effect of spacecraft on the adapter design was modeled by a set of various force factors on one of the end frames of the shell [13–15]. In the case of a mesh conical shell [14], which is the lower load-bearing element of the adapter, the forces and moments are concentrated on the small base of the cone. The lower base of the conical shell is attached to the launch vehicle frame. Here, the set of force efforts corresponds to the inertial action from the upper cylindrical part of the adapter, to which the satellites are directly attached. The objective of this study is to demonstrate that, for any combination of end-face force factors, there are optimal design parameter values ​​that minimize the adapter's structural mass. The basic design parameters here are the number of helical ribs and their winding angles, as well as the rib cross-sectional dimensions and the mechanical properties of the composite material. The results of a similar study conducted for an anisogrid cylindrical shell, which is the upper structural part of the adapter, are presented in [13] and [15].

This paper examines the influence of key design parameters on the rigidity, strength, and stability of the Marathon system's anisogrid adapter. The actual inertial impact of each spacecraft on the mesh composite structure is taken into account. The algorithm developed in the authors' previous papers [13–15] on the optimal design of anisogrid cylindrical and conical shells of traditional cross-sections is used in constructing the geometric and finite element models.

Finite element modeling

Generation of a finite element (FE) model of a spatial structure is performed in the pre- and postprocessor environment (GEOSTAR module). Traditionally, it begins with the construction of a geometric model using standard geometric primitives: key points (POINTS), lines (CURVE), plane elements, and general surface elements (SURFACE). When modeling structures with a regular system of similar elements, as in the case of an anisogrid adapter (Fig. 1), there is no need to construct a geometric model of the entire structure. It is sufficient to first generate a geometric model of a typical segment, then construct a finite element mesh (of this segment) based on it, and finally, using copy operations, obtain a FE model of the entire structure.

Рис. 1. Сетчатый адаптер: изометрия, вид сбоку и вид сверху

Fig. 1. Mesh adapter: isometry, side view and top view

The central part of the adapter is an octahedral prism consisting of identical mesh panels (Fig. 2). The mesh structure of the panel is formed by two families of ribs inclined (at an angle of ±φ) to the generatrix and a family of horizontal ribs. The inclined rib forms a spiral in space. The horizontal rib has the shape of an octahedral closed ring. The horizontal (annular) ribs are located in the adapter's cross-sections, equidistant from the cross-sections where the inclined (spiral) ribs intersect.

The ribbed structure of the panel is characterized by a typical segment (Fig. 2), consisting of sections of inclined and horizontal ribs. The geometric dimensions of this segment are uniquely determined by the following design parameters: the diameter of the circle circumscribed around the octagonal cross-section of the prism (Fig. 1, top view), the number of inclined ribs per panel width, and the angle (φ) of the spiral ribs to the generatrix.

Рис. 2. Общий вид сетчатой панели и увеличенный фрагмент с типовым сегментом

Fig. 2. General view of the mesh panel and enlarged fragment with a typical segment

To form a geometric model of a typical segment, straight line segments (CURVE) are used, which are then "broken down" into beam finite elements. The approximate FE model of a typical segment (Fig. 3) consists of 12 beam elements (BEAM3D). The geometric parameters of the rib cross-section are defined in the real constants (RC) group. The mechanical properties of the composite are recorded in the material properties (MP) group. In this study, the longitudinal modulus of elasticity (180 GPa) and density (1500 kg/m³) are relevant.

Рис. 3. КЭ модель типового сегмента

Fig. 3. FE model of a typical segment

After forming the finite element mesh of a typical segment, elements are generated on one panel of the octahedral prism using symmetric copying and plane-parallel transfer operations (Fig. 2). The remaining seven faces of the finite element model of the mesh structure of the central part are obtained by copying the elements of the first face by rotating them 45º around the longitudinal axis of the adapter.

The geometric model of the adapter's upper section is also formed by eight faces, four of which are rectangular and four are triangular (Fig. 1, top view). The FE mesh of the rectangular faces of the upper section was obtained using a technique similar to that used for the ribbed faces of the adapter's central section. This technique also involves constructing beam finite elements on geometric primitives (CURVEs) of a typical segment (Fig. 4), followed by their duplication and copying.

Рис. 4. КЭ модель прямоугольных граней верхней части адаптера

Fig. 4. FE model of the rectangular faces of the upper part of the adapter

The mesh structure of the triangular faces of the upper part of the adapter is modeled to connect the inclined edges of the central part and the edges of the upper part into a single frame structure.

The lower part of the adapter (Fig. 5) is a solid octahedral structure in the form of a regularly truncated pyramid. It is modeled using quadrangular finite elements of a thin-walled shell (SHELL4) of constant thickness.

Рис. 5. КЭ модель нижней части адаптера

Fig. 5. FE model of the lower part of the adapter

The adapter's most important elements, influencing its static and dynamic behavior, are the frames. They are intended to be made of the same material (carbon fiber) as the ribs of the lattice structure. The topmost frame (Fig. 6) is square in plan, while the others are regular octagons. All are modeled using beam finite elements (BEAM3D) with a rectangular cross-section. The cross-sectional parameters of each frame can be independently varied.

Рис. 6. Размещение элементов сосредоточенной массы на боковых гранях центральной части (слева) и на верхней части адапетра

Fig. 6. Placement of concentrated mass elements on the side faces of the central part (left) and on the upper part of the adapters

The inertial impact of spacecraft on the adapter's mesh structure is simulated using concentrated mass elements (MASS), which are placed at the attachment points of the spacecraft. Since the mass of a single spacecraft is 100 kg, each MASS element is assigned a mass of 25 kg. Each panel of the adapter's central section contains 20 concentrated mass elements (Fig. 6), and another 16 are located on the top of the adapter.

Numerical study

One of the most relevant design cases is the insertion of spacecraft into orbit. The adapter design must, firstly, have sufficient load-bearing capacity to withstand inertial loads and, secondly, ensure the necessary rigidity to prevent unacceptable movements under the launch vehicle fairing. Therefore, at the beginning of the study, we will focus on the modal analysis of the adapter, namely, stability under inertial loads and the analysis of the frequencies and modes of natural oscillations.

In the adapter calculation model (Fig. 7), fixed (unchangeable) values ​​of design parameters are specified:

• the diameter of the circumscribed circle of the cross-section of an octahedral prism is 2.280 m;
• the height of the central part is 4.5 m;
• the height of the upper part is 1 m;
• height of the lower part – 0.310 m.

Рис. 7. Исходная КЭ модель адаптера

Fig. 7. Initial FE model of the adapter

In the initial version, we will accept the following values ​​of variable design parameters:

• the number of spiral ribs per width of the side face of the central part of the adapter is 10;
• the cross-sectional height of the ribs (ring and spiral) of the mesh structure is 15 mm, the width is 3 mm;
• the angle of inclination of the spiral ribs is 20º;
• thickness of the shell elements of the lower part is 3 mm.

With the given design parameters, the adapter mass (excluding the mass of the spacecraft) was 137 kg.

Let's perform a stability analysis of the structure under vertical overload. To do this, we'll set the vertical acceleration to –9.81 m/s² and calculate the safety factor. The buckling pattern (Fig. 8) indicates that the "weak point" is the skirt—the lower part of the adapter. Since the main focus of the study is optimizing the adapter's mesh structure, it makes sense to make the lower part sufficiently robust so that its load-bearing capacity is beyond doubt in further experiments.

Рис. 8. Форма потери устойчивости исходной модели адаптера

Fig. 8. Shape of the stability loss of the original adapter model

We increased the thickness of the skirt shell elements to 6 mm (the structure's weight increased by almost 10 kg) and repeated the axial overload stability calculation. The stability loss zone shifted into the adapter's mesh structure (Fig. 9) and was localized in its lower section, where the compressive stresses are greatest, as they are caused by the inertial forces from the entire “load”.

Рис. 9. Форма потери устойчивости модели адаптера с усиленной нижней частью

Fig. 9. Shape of stability loss of the adapter model with reinforced bottom part

The structural rigidity can be estimated from the values of the first natural vibration frequencies. A modal calculation performed for the initial adapter model with a spiral rib inclination angle of φ = 20º in the mesh structure yielded the following natural vibration frequencies for the first four modes: f₁ = 9.44 Hz, f₂ = 9.70 Hz, f₃ = 9.70 Hz, and f₄ = 9.90 Hz. The corresponding vibration modes are shown in Figs. 10–12.

Рис. 10. Форма колебаний по первой собственной частоте

Fig. 10. Shape of oscillations at the first natural frequency

Рис. 11. Форма колебаний по второй собственной частоте

Fig. 11. Shape of oscillations at the second natural frequency

Рис. 12. Форма колебаний по четвертой собственной частоте

Fig. 12. Shape of oscillations at the fourth natural frequency

The first three modes are shell-type. They are characterized by oscillations of the panels of the central part of the adapter. The upper square frame, however, exhibits no significant displacements. Note that the second and third modes are symmetrical. The fourth mode (also shell-type) resembles the oscillations of a cantilever beam. The amplitude of the oscillations of the panels of the central part is insignificant, but the overall displacement of the free end (upper frame) can reach unacceptably large values, which could cause contact with the nose cone fairing and its deformation.

The table presents the results of a natural vibration analysis of adapter models with various helical rib inclination angles φ. A range of values from 15 to 45° in 5° increments is considered. Note that the actual φ angle values differ slightly from the nominal values. The angle adjustment was made to accommodate an integral number of standard segments along the height of the adapter's central section. In this case, all frames will be located in those adapter cross-sections where the helical ribs of the mesh structure intersect.

The table (column 3) presents the values of the natural oscillation frequencies of the first four modes, since in all variants of the model the “dangerous” beam frequency (the corresponding value is highlighted in bold) “did not rise” above the fourth mode.

As the angle φ increases, the mesh becomes denser (Fig. 13). At the same time, the mass (see table, column 2) of the mesh structure (and, consequently, the mass of the entire adapter) increases due to the lengthening of the spiral ribs and the increase in the number of annular ribs.

φ = 15º	φ = 20º	φ = 25º	φ = 30º	φ = 35º	φ = 40º	φ = 45º

Рис. 13. Сетчатая структура панели центральной части адаптера при различных углах наклона спиральных ребер

Fig. 13. Mesh structure of the panel of the central part of the adapter at different angles of inclination of spiral ribs

From the analysis of the obtained results (see table), it is clear that the model with the spiral rib inclination angle φ = 30º is optimal in terms of rigidity.

The load-bearing capacity under axial overload was also studied. The stability factor K_cr increases with increasing angle φ, both in absolute value (see table, column 4) and relative (see table, column 4). The specific stability factor (K_cr /m) characterizes the mass efficiency of the model. In our case, this means that a model with a higher specific stability factor (while ensuring the required load-bearing capacity) has a lower mass (compared to a model with a lower stability factor).

Results of the numerical experiment

Let's consider the strength of the adapter's ribbed structure during spacecraft orbital insertion. To simulate the inertial load on a model with a spiral fin inclination angle of φ = 20º, we set the axial acceleration (along the Y-axis, Fig. 14) to 2g and the lateral acceleration (along the X-axis, Fig. 14) to 1g.

Рис. 14. Распределения напряжений в модели (φ = 20º) с первым вариантом направления боковой перегрузки

Fig. 14. Stress distributions in the model (φ = 20º) with the first variant of lateral overload direction

The calculation resulted in a distribution of the maximum von Mises stresses in the rib sections, the highest value of which (183.56 MPa) is localized in the lower region of the central ribbed portion of the adapter (Fig. 14). This value is within the permissible compressive stress limits for carbon fiber reinforced plastics (450 MPa).

One might expect that with a different lateral load direction (Fig. 15), the stresses would be higher due to the reduced bending moment arm in the octagonal prism cross-section. However, calculations showed that the maximum acting stresses actually decreased slightly (183.45 MPa).

Рис. 15. Распределения напряжений в модели (φ = 20º) со вторым вариантом направления боковой перегрузки

Fig. 15. Stress distributions in the model (φ = 20º) with the second variant of lateral overload direction

A similar pattern was revealed in calculations for a model with a more gradual arrangement of inclined (spiral) ribs (Figs. 16 and 17). However, the highest von Mises stress values ​​in the model with a spiral rib inclination angle of φ = 35º were significantly higher (222.66 MPa) than in the model with φ = 20º.

Рис. 16. Распределения напряжений в модели (φ = 35º) с первым вариантом направления боковой перегрузки

Fig. 16. Stress distributions in models (φ = 35°) with the first observance of the overload limiting direction

Рис. 17. Распределения напряжений в модели (φ = 35º) со вторым вариантом направления боковой перегрузки

Fig. 17. Stress distributions in the model (φ = 35º) with the second variant of lateral overload direction

A numerical strength analysis experiment performed for models with different inclinations of the spiral ribs showed that the stress intensity (table, column 6) in the ribs increases with increasing angle φ, since this reduces the longitudinal rigidity of the ribbed structure.

If the inertial overload is doubled (axial – 4g, lateral – 2g), then the stress intensity will also double. The von Mises stress values in the model with a spiral rib inclination angle of φ = 35º (Fig. 18) will almost reach the maximum permissible values. If the overload is set to 3g in both directions, these values will exceed the permissible values.

Рис. 18. Распределения напряжений в модели (φ = 35º) с первым вариантом направления боковой перегрузки: слева – для осевой перегрузки 4g, для боковой перегрузки 2g, справа – для осевой перегрузки 3g, для боковой перегрузки 3g

Fig. 18. Stress distributions in the model (φ = 35º) with the first variant of lateral overload direction: left for axial overload 4g, for lateral overload 2g, right for axial overload 3g, for lateral overload 3g

The intensity of hazardous stresses can be reduced by increasing the rib strength in the area where maximum stress is localized, for example, by winding spiral ribs at the bottom of the mesh structure. However, in this case, it is sufficient to add additional longitudinal ribs along the connection lines of the central prism faces (Fig. 19). The maximum stress will be reduced to acceptable values. It should be noted that the added longitudinal ribs are stronger than the ribs of the main mesh: the cross-sectional height is 30 mm, the width is 6 mm. The total mass of the longitudinal ribs is insignificant (1.331 kg), compared to the mass of the entire adapter (171 kg).

Рис. 19. Распределения напряжений в модели с добавленными продольными ребрами

Fig. 19. Stress distributions in the model with added longitudinal ribs

Conclusion

The results of the numerical experiment demonstrated the high sensitivity of the stiffness and stress-strain state, as well as the critical forces of the spacecraft adapter, to the design parameters of the composite mesh structure. They also reaffirmed the need for a comprehensive study during the design phase of anisogrid composite load-bearing structures to determine the optimal combination of numerous design parameters, which is unique for each new mission, as each corresponds to different characteristics of the inertial impact determined by the masses of the spacecraft. The study also demonstrated that, in some cases, an alternative to optimizing the design parameters may be modifications to the mesh structure's design, for example, by introducing additional vertically oriented ribs.

Авторлар туралы

Vladimir Nesterov

Хат алмасуға жауапты Автор.
Email: nesterov@mail.sibsau.ru
ORCID iD: 0009-0003-6384-3849

Cand. Sc., Associate Professor

Fyodor Sinkovsky

Email: sfk@iss-reshetnev.ru

Cand. Sc., Director of the Industry Center for Large-Scale Transformable Mechanical Systems – Deputy General Designer for Mechanical Systems

Alexander Sukhanov

Email: suhanovas@iss-reshetnev.ru

Group Head

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1. JATS XML

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2. Fig. 1. Mesh adapter: isometry, side view and top view

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3. Fig. 2. General view of the mesh panel and enlarged fragment with a typical segment

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4. Fig. 3. FE model of a typical segment

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5. Fig. 4. FE model of the rectangular faces of the upper part of the adapter

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6. Fig. 5. FE model of the lower part of the adapter

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7. Fig. 6. Placement of concentrated mass elements on the side faces of the central part (left) and on the upper part of the adapters

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8. Fig. 7. Initial FE model of the adapter

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9. Fig. 8. Shape of the stability loss of the original adapter model

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10. Fig. 9. Shape of stability loss of the adapter model with reinforced bottom part

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11. Fig. 10. Shape of oscillations at the first natural frequency

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12. Fig. 11. Shape of oscillations at the second natural frequency

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13. Fig. 12. Shape of oscillations at the fourth natural frequency

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14. Fig. 13. 1

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15. Fig. 13. 2

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16. Fig. 13.3

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17. Fig. 13. 4

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18. Fig. 13. 5

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19. Fig. 13.6

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20. Fig. 13. Mesh structure of the panel of the central part of the adapter at different angles of inclination of spiral ribs

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21. Fig. 14. Stress distributions in the model (φ = 20º) with the first variant of lateral overload direction

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22. Fig. 15. Stress distributions in the model (φ = 20º) with the second variant of lateral overload direction

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23. Fig. 16. Stress distributions in models (φ = 35°) with the first observance of the overload limiting direction

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24. Fig. 17. Stress distributions in the model (φ = 35º) with the second variant of lateral overload direction

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25. Fig. 18. Stress distributions in the model (φ = 35º) with the first variant of lateral overload direction: left for axial overload 4g, for lateral overload 2g, right for axial overload 3g, for lateral overload 3g

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26. Fig. 19. Stress distributions in the model with added longitudinal ribs

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27. Fig. 1. Mesh adapter: isometry, side view and top view

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28. Fig. 2. General view of the mesh panel and enlarged fragment with a typical segment

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29. Fig. 3. FE model of a typical segment

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30. Fig. 4. FE model of the rectangular faces of the upper part of the adapter

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31. Fig. 5. FE model of the lower part of the adapter

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32. Fig. 6. Placement of concentrated mass elements on the side faces of the central part (left) and on the upper part of the adapters

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33. Fig. 7. Initial FE model of the adapter

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34. Fig. 8. Shape of the stability loss of the original adapter model

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35. Fig. 9. Shape of stability loss of the adapter model with reinforced bottom part

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36. Fig. 10. Shape of oscillations at the first natural frequency

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37. Fig. 11. Shape of oscillations at the second natural frequency

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38. Fig. 12. Shape of oscillations at the fourth natural frequency

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39. Fig. 13. 1

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40. Fig. 13. 2

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41. Fig. 13.3

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42. Fig. 13. 4

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43. Fig. 13. 5

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44. Fig. 13.6

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45. Fig. 13. Mesh structure of the panel of the central part of the adapter at different angles of inclination of spiral ribs

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46. Fig. 14. Stress distributions in the model (φ = 20º) with the first variant of lateral overload direction

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47. Fig. 15. Stress distributions in the model (φ = 20º) with the second variant of lateral overload direction

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48. Fig. 16. Stress distributions in models (φ = 35°) with the first observance of the overload limiting direction

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49. Fig. 17. Stress distributions in the model (φ = 35º) with the second variant of lateral overload direction

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50. Fig. 18. Stress distributions in the model (φ = 35º) with the first variant of lateral overload direction: left for axial overload 4g, for lateral overload 2g, right for axial overload 3g, for lateral overload 3g

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51. Fig. 19. Stress distributions in the model with added longitudinal ribs

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