Mechanics of Woven Fabrics

Abstract

Theoretical maximum weavability relationships of fabrics woven from regular warp ends and variable thickness filling yarns are derived by developing a local geometry where the thick filling place is interlaced with warp ends and where warp yarn is interlaced with thick and thin filling yarns. Geometric relationships are derived from the local geometry, and hence a local weavability limit relationship is deduced. The average warp and filling spacings are calculated by developing an imaginary proba bilistic model of a time scale and relating the geometric parameters at different locations. The final expressions for the weavability limit, which represent the fabric sheet as a whole, relate the average maximum warp and filling cover factors to the ratio of average filling yarn to warp yarn diameters; the ratio of thick place of filling to warp yarn diameters; and the ratio of thick place length of filling to the wave length, warp and average filling densities, thick and thin places of filling yarn densities, number of filling yarns in the pattern repeat, and weave design.