Theoretical study on the bending rigidity of filament yarns with an elliptical cross-section using energy method. II. Numerical evaluation

This is the second part of a series of work investigating on the bending rigidity of filament yarn with an elliptical cross-section. In the present paper, the quantitative error analysis of the earlier simplification of a circular cylindrical of yarn geometry under deformation is evaluated, and the effects of filament properties on yarn bending rigidity are also evaluated. It is highly useful in preciously predicting yarn bending property from filament behaviors for virtual processing of textile materials. So the explicit formula derived in the Part I of this series for the elliptical cylindrical of yarn geometry is used to compute the quantitative error of the earlier model. The four characters, including the eccentricity of elliptical cross-section of yarn, the ratio of bending to torsional rigidity of filament, the helix angle of filament on yarn surface and the number of filaments inside the yarn, are adopted to quantify the bending rigidity relationship between the filaments and yarn. Based on the analytical method, the earlier method in which the circle shape takes place of the elliptical shape of yarn cross-section for simplification is evaluated. The simulation results show that the relative error of the circle assumption is not higher than 10 % when the eccentricity of yarn cross-section is lower than 0. 8. However if the eccentricity is higher than 0. 8 and the helix angle is larger than 30 degrees, it is suggested to conduct the deformation analysis based on the elliptical cross-section of yarn.