Analysis of Structures Deployed by Tape-Springs

 K A Seffen

Following recent proposals for large deployable structures exploiting the structural simplicity and robustness of such springs as deployment actuators, this dissertation begins by investigating the formation of elastic folds in a tape-spring.

It is shown that the spring deforms by forming an elastically deformed region with zero transverse curvature and uniform longitudinal curvature.

It is also shown that the process of formation and growth of elastic folds belongs to a wide class of propagating instabilities. It is characterised by a high peak moment and a lower propagation moment. A compact characterisation of the moment-rotation relationship for an elastic fold is presented.

A key feature is that the bending moment on either side of a fold located anywhere along a uniform tape-spring, but far away from the ends of the spring, is constant, whereas this moment increases near a rigid support.

Compact and accurate two-dimensional theories are developed to simulate the self-actuated deployment of tape-springs that are either coiled around a circular hub, or folded into a zig-zag pattern. It is shown that conservative energy formulations are appropriate for coiled springs, where the velocity field is smooth, but not for springs with localised folds.

To simulate the motion of such localised folds a non-conservative impulse-momentum formulation is proposed, and it is found that this model can accurately predict both the steady motion of the folds along the tape-spring and their rebound against the end supports.

The use of tape-springs in deploying a panel of similar inertia properties to an actual satellite radar panel is investigated. Deployment of the panel to approximately its intended configuration is governed by the value of the fold propagation moment in the tape-spring, whereas the high peak moment controls ``locking out'' of the panel; the velocity field of the deploying springs is similar to that of self-actuated coiled tapes.

It is demonstrated, by theory and experiment, that mounting tape-springs in pairs, with their centres of curvature in opposite directions, results in an energy well which traps the kinetic energy of the panel on lock-out. The panel does not overshoot its fully deployed configuration and collision with other parts of the spacecraft is thus prevented. Disturbing torques applied by the panel to the spacecraft can also be computed.

Keywords: tape-springs, deployable structures, elastic folds, propagating instability, moment-rotation relationship, rigid support, free deployment, coiled, folded, deployment simulation, conservative, impulse-momentum, lock-out, overshoot, vibration.