Abstract
Tape springs have been previously proposed as a structure for deploying a secondary mirror of a Cassegrain Earth observation telescope in orbit. The stiffness of such a structure would be critically important to avoid image distorts due to on board micro-vibrations. Tape springs have historically been deployed from cylindrical drums where the partially restrained root decreases the stiffness. Additional supporting structure is one solution, but this often increases the size of the stowed volume. In this paper the limitations of clamping a tape spring at the root, to increase stiffness, whilst still being able to coil it are explored. Securing a tape spring in this way induces a transition region when coiled, which produces high stresses. A finite element model is presented that shows a local crinkle forms close to the root of the tape spring during coiling and results in a stress concentration. The same local crinkles have been shown to exist experimentally using beryllium-copper tape springs attached to a 3D printed deployment drums. Decreasing the embrace angle of a tape spring from \ang{180} to \ang{90} yields a reduction of $66\%$ in the maximum Von Mises stress. The deployment drum radius sets the allowable transition length of the tape spring, and if this value is less than a critical length the tape spring crinkles, which compromises the deployed stiffness. The crinkle length is explored via finite element simulations and is shown to decrease with a decrease of the embrace angle.