The stiffness and stability of drum-deployed tape springs
Creators: name: SHORE, JASON LUKE
Publisher: name: University of Surrey
Year: 2021

description: Today's Earth observation telescopes can achieve less than one-metre resolution images, which are used in sectors such as agriculture and defence. The temporal resolution, or the ability to image a location quickly, is one of the remaining challenges faced. A solution to this problem is to use deployable telescopes so that more than one Earth observation satellite can be launched from the same launch fairing to form a constellation of satellites that can patrol the skies. This makes deployable telescopes an attractive prospect, but it must not be at the expense of the image quality, which can be degraded if the supporting deployable structure is not sufficiently stiff.
description: In this thesis the stiffness of a drum-deployed tape spring is investigated for its potential to provide a means to extend and support the optics of a telescope. The characteristics of drum-deployed tape springs are usually such that the root is only partially restrained, so that the tape spring can coil uninhibited, and is partially flattened against the deployment drum. The partial restraint at the root introduces a more compliant boundary condition. The stiffness of isotropic and composite drum-deployed tape springs is quantified using a finite element method and experiment to derive the rotational stiffness. The introduction of the deployment drum at the root is shown to decrease the rotational stiffness of the tape springs by orders of magnitude when compared to a tape spring in a fixed-free configuration. The effects of the deployment drum geometry, tape spring material and tape spring geometry on the rotational stiffness are investigated.
description: The presence of the deployment drum confines deformations to the root. From this observation a drum-deployed tape spring is modelled as a beam restrained at the root using a sprung hinge. The stiffness of the torsion spring is assigned the previously derived rotational stiffness and the natural frequency is calculated. The model correctly predicts power-law trends of the natural frequency against the tape spring length and rotational stiffness. The approach is sufficiently accurate for preliminary design purposes and is validated against experimental results and a finite element model. The sprung-root model is then extended to consider a deployed tape spring that supports a large tip mass. The need for a numerical method to solve for the roots of an Euler-Bernoulli equation is circumnavigated using Dunkerley's method. Dunkerley's method is accurate providing the rotational stiffness is small, which is the case here. The error between the derived Dunkerley equation and experimental results is &lt;13%.
description: The bending moment-rotation behaviour of tape springs is extensively researched, where a solution is obtained using plate or shell theory. Using large-displacement plate theory an analytical model is derived to predict the bending moment-rotation behaviour of strips with a non-uniform cross section. The non-uniform cross section is modelled using a polynomial series, which is an extension from the second order polynomials used in the literature. The analytical model is applied to a tape spring with a flat region at the centre, a bridged tape spring. The analytical model correctly predicts the existence or absence of a structural instability, which is also seen in tape springs, and, using a Maxwell construction, the propagation moment in the post snap-through regime is accurately captured. As the flat width is increased, the flexural behaviour of bridged tape springs converges to the behaviour of a flat plate. All of the analytical model's results are validated against results from a finite element model. Comparing both the snap-through moment and propagation moment predictions of the analytical model with values from the FE model produces an error of &lt;5%. Finally, using the derived analytical model a more accurate prediction of the flexural behaviour of a deep cross section is made when compared to previous literature.