[Univ of Cambridge] [Dept of Engineering]

 Thin-Walled Elastically Foldable Reflector Structures

Lin Tze Tan


This dissertation is concerned with thin-walled reflector structures that can be folded elastically.  The Spring-Back Reflector which was recently invented by Hughes Space Corporation, is a state-of-the-art flexible paraboloidal deployable reflector based on this approach.  A key feature of this deployable structure is its simplicity;  it is simply folded elastically into half, like a 'taco' shell and stored above the spacecraft, in the normally unused space in the top of the rocket fairing.  To deploy it, the restraining cords are released and the reflector deploys by releasing its stored strain energy, hence it 'springs back' into shape.  This passive deployment sequence means that there are no motors, controls or hinges that could malfunction in orbit.

Due to its inherent flexibility, the Spring-Back Reflector suffers from distortions which result from the residual strains of the manufacturing process.  This is potentially a severe limitation on the applicability of this reflector.  The current remedy is to mechanically adjust the surface in orbit, however, this is neither ideal nor in keeping with the simplicity of the original concept.

The purpose of this research is to develop stiffening methods for this reflector in order to reduce these distortions.  Working within the constraint of a passively deployed system, these methods are required to stiffen the reflector in its deployed configuration, and yet still allow it to be flexible enough to be folded elastically.

An innovative stiffening system is proposed.  This consists of a circular skirt connected to the rim of the original reflector, in effect preventing the original shell from deforming in its lowest stiffness eigenmode.  A key feature of the stiffening systemis a series of cuts and slits in the skirt, which allow it to buckle when the reflector is being packaged, thus reducing the stiffness and hence, enabling the reflector to be folded elastically.

A preliminary study of the effectiveness and viability of this stiffening system, which uses extensive geometrically non-linear finite element simulations, on a simplified 1/10th scale model is presented.  These results are validated with a series of experiments.  The configurations with the greatest potential were optimised, to minimise the packaging strains while maximising the stiffness of the reflector.  This involved hundres of variations of the stiffening system, a procedure to automatically remesh the finite element models was also devised.  Optimized models were found to be many times stiffer than the original structure and to have acceptable peak packaging strains.  It was also demonstrated that configurations with circumferential slits are more effective than those with radial cuts, as the slits are able to reduce the peak strains while the continuous skirt provides higher deployed stiffnesses.

Once a thorough understanding of the behaviour of these small-scale models had been obtained, the effects of stiffening a 4.6 m diameter full-scale Spring-Back Reflector were investigated.  Mathematical expressions for the geometry were derived to describe the complex reflector.  Small-scale optimization results were used as a framework for the optimization of the full-scale reflectors, limiting the search space and also allowing for 'informed guess' starting points.  The resulting optimals exceeded the expected targets and it is now feasible to design reflectors which are nearly 7 times stiffer, with peak stresses half that of the breaking strength of the material.

The ability of the stiffened Spring-Back Reflector to withstand the distortions resulting from the maufacturing process, was examined.  Firstly, a method of replicating the residual stresses and corresponding distortions was devised on the assumption that both stiffened and unstiffened reflectors experience similar residual strains during the manufacturing process.  It was then demonstrated that the stiffening system reduces these distortions by approximately one hundred times.  This results in extremely good shape accuracy and hence, the operating frequency range of the Spring-Back Reflector can potentially be more than doubled.

In conclusion, the new stiffening system has been shown to significantly reduce the distortions caused by the manufacturing process, thus increasing the surface accuracy.  The deployed stiffness has been increased by more than six fold.  This was accomplished by stiffening the reflector in its deployed configuration yet with the help of slits, still allowing it to be folded elastically, i.e. without compromising the simplicity of the original concept.


[Cambridge University | CUED | Structures Group | Geotechnical Group]

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