Stability of fiber trajectories for winding toroidal pressure vessels

In this paper the fiber trajectory stability of filament wound toroidal pressure vessels is evaluated for two most frequently used patterns: single helical winding, helical and hoop winding. The basic equations of equilibrium for fibers on a torus are given based on netting analysis. The governing equations that determine helical winding angles along the meridional direction are derived for the two winding patterns. The slippage coefficients of the obtained fiber trajectories are calculated using the non-geodesic law and differential geometry. The condition between the hoop-to-helical thickness ratio and the relative bend radius of the toroid is also formulated to prevent fiber bridging on the concave surface. The fiber slippage and bridging tendencies are outlined and compared, corresponding to various relative bend radii and hoop-to-helical thickness ratios. The results show that the single helical winding process provides better stability of fiber trajectories, in terms of both fiber slippage and bridging, than the helical and hoop winding. The toroidal vessel with larger relative bend radius requires lower coefficient of friction between the fiber bundle and the supporting surface. The present analysis for fiber trajectory stability affords a useful reference tool for designing filament-wound toroidal pressure vessels.