EQUILIBRIUM OF YARNS ON THE SURFACE OF A 2/1 TWILL FABRIC

This study is devoted to the theoretical and practical investigation of the equilibrium state of warp and weft yarns on the surface of a 2/1 twill woven fabric. The equilibrium arrangement of yarns within the fabric structure is one of the key factors determining the geometric parameters, surface topography, mechanical properties, and service performance of woven materials. Therefore, determining the equilibrium state of yarns formed under the influence of yarn tension, bending, mutual compression, and interaction forces at interlacing points during the weaving process is an important scientific challenge in modern textile engineering.

The main objective of this research is to identify the regularities governing the arrangement of yarns on the surface of a 2/1 twill fabric, evaluate the structural and technological factors affecting their equilibrium state, and describe the geometric configuration of the yarns using mathematical modeling approaches. The study comprehensively analyzes fabric geometry, yarn bending radius, yarn crimp, interaction forces at interlacing points, tension distribution, and the spatial configuration of warp and weft yarns. The investigation is based on theoretical analysis, mathematical modeling, and structural analysis of woven fabrics.

The obtained results demonstrate that the equilibrium state of yarns in a 2/1 twill fabric significantly influences the surface topography, fabric thickness, areal density, air permeability, deformation behavior, and mechanical strength of the material. Furthermore, maintaining an optimal ratio between warp and weft yarn tensions ensures a more uniform yarn distribution over the fabric surface, reduces contact stresses, and improves both the appearance and functional performance of the fabric. Conversely, disturbance of yarn equilibrium leads to surface irregularities, localized deformation, increased mechanical stresses, and deterioration of fabric quality.

The findings of this research have considerable scientific and practical significance for the structural design of twill woven fabrics, optimization of weaving process parameters, improvement of mathematical models describing fabric structure, and development of high-quality textile materials. The proposed approaches can be applied in selecting weaving machine operating conditions, controlling yarn tension, and predicting the quality characteristics of finished woven fabrics.