Deployment dynamics of a high strain deployable rolled-up composite SAR antenna

Abstract

The Deployable Rolled-up Composite Antenna - Synthetic Aperture Radar (DERCA-SAR) concept design is proposed for a 12U CubeSat low-power remote sensing application. A SAR reflectarray system is considered to be implemented on a High-Strain Composite (HSC) structure with a shallow “tape-measure” inspired shape. The stiffness required in the deployed state is provided by the cross-sectional curvature of the shell, which will be rigidly maintained at the root during stowage. To provide a low-mass solution for this application, the DERCA-SAR technology considers flattening and coiling the shell tip until it reaches the clamped root and deploys by releasing the elastic strain energy stored in the coiled configuration. In this paper, two analytical models are developed to describe the deployment dynamics of this structure and predict the deployment velocity that may impact the antenna performance. Given an initial coil radius $r$, which is much smaller than the natural radius $R$ to fit a nanosatellite platform, the deployment occurs in two stages that have been revealed through experiments. The first blossoming phase is described as an expanding and uncoiling process based on the Lagrangian approach. The second and more chaotic phase of the deployment is modelled using a Hencky-type model that discretises the shell’s structure in a multi-pendulum system connected by elastic rotational hinges/springs. In this model, the shell’s stiffness is made to locally change based on the characteristic tape springs’ moment–rotation relationship and the implementation of a stiffness function. The analytical results are then compared to experimental data derived from deployment testing on samples of the shells with different material properties. The predictions from the two models capture the significant trends of the data well, and predict the maximum speed with an error of $<$ 10 %.