​​​Optimal Design, Dynamic Modeling and Shape Control of Space Deployable Mesh Reflectors

Deployable Mesh Reflectors (DMR), due to their important space applications, have experienced continued R&D interest in the past several decades. A deployable mesh reflector utilizes a spherical or parabolic surface as working shape (a required radio-frequency surface), which is formed by a network or mesh of tensioned facets. To develop a high-accuracy, high-performance large DMR, three tasks are essential. Task 1 defines the topology and geometric configuration for surface accuracy. Task 2 ensures uniform tension across all cable members. In Task 3, the DMR shape is designed to withstand deformations, thermal strains, and fabrication errors. ​This research focuses on optimal design, dynamic modeling and shape control of large DMRs, in order to generate a geometric configuration with high surface accuracy, large effective region (Task 1) and uniform member tension distribution (Task 2), and at the same time, maintain the desired shape under deformation of supporting structure, thermal strain and member length errors (Task 3).

Space deployable mesh reflectors.
An AstroMesh DMR with deployed working surface.
Desired working surface of a deployable mesh reflector.

Surface Accuracy Evaluation

Surface accuracy is crucial in reflector design, typically evaluated using root-mean-square errors. Traditional definitions don’t accurately measure deviations from the desired surface, especially when high precision is needed. This work introduces the direct root-mean-square error, which measures these deviations directly and is suitable for off-surface nodes. Additionally, we propose the effective region root-mean-square error, factoring in both effective region area and mesh geometry accuracy.

Comparison of two types of RMS errors: (a) the best-fit surface RMS error; (b) the direct RMS error.

Generation of Surface Mesh Geometry

To warrant high performance, it is desirable to have a methodology for systematic design of DMR surface geometries that can produce almost uniformity of member lengths and triangular facet sizes while maintaining a relatively small total member length and yield high surface accuracy. This effort is aimed to fill the above-mentioned technical gap in this area by developing a new optimal geometry mesh design method that automatically determines the nodal coordinates and member connectivity for a given DMR with high surface accuracy and almost uniform member lengths, and at the same time, guarantees the pseudo-geodesic property of the generated surface mesh geometry, which in many cases gives a minimum total member length.

Generation of geodesic mesh geometry: (a) generation of subdivision lines; (b) placement of nodes on subdivision lines; (c) generation of ring lines in each subdivision; (d) addition of internal nodes on ring lines; (e) connection of nodes to form facets.

Shape Control

Traditional shape control methods for large high DMRs usually utilize many actuators and are only applicable to predictable shape distortions. To this end, a new method, namely the minimum residual nodal displacement method, for optimal shape adjustment of large DMRs is developed. The new shape adjustment method can significantly reduce shape distortion of a DMR by automatically placing a small number of actuators at optimal locations. This new method is applicable to DMRs under both predictable and unpredictable shape distortions, and can determine the minimum number of actuators needed to satisfy prescribed design requirement for surface accuracy. In this method, a simple linear relationship between nodal displacements, external loads and undeformed member lengths of a DMR is established, and residual nodal displacement of the structure is minimized.

A 3-D view of the center-feed and parabola-shaped DMR.
RMS error versus temperature of the reflector working surface adjusted by 10-40 actuators.

References

  1. Yuan, S. and Yang, B., 2022. A New strategy for form finding and optimal design of space cable network structures. In Nonlinear Approaches in Engineering Application: Design Engineering Problems (pp. 245-285). Cham: Springer International Publishing.
  2. Yuan, S.*, 2022. Review of root-mean-square error calculation methods for large deployable mesh reflectors. International Journal of Aerospace Engineering, 2022. doi: 10.1155/2022/5352146
  3. Yuan, S.* and Jing, W., 2021. Optimal shape adjustment of large high-precision cable network structures. AIAA Journal, 59(4), pp.1441-1456. doi: 10.2514/1.J059989
  4. Yuan, S. and Yang, B., 2021. Shape adjustment of large deployable mesh reflectors under thermal strain. In AIAA SciTech 2021 Forum (p. 1148). doi: 10.2514/6.2021-1148
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