Characteristic Features of Building Packages of High Linear Density Glass and Basalt Yarns

We consider the conditions for building packages of high linear density glass and basalt yarns, using a delayed-action laying mechanism. We establish the reasons for the appearance of such defects as wedging of the bobbins in the bobbin holder, slipping of the filled package from the bobbin holder, and also the appearance of nonuniform winding density. We present analytical and graphical relationships letting us select the package building parameters for which the considered defects do not occur.

Appendix

$$ p=Q\frac{1-c}{2{d}_{\mathrm{sp}}^2}\left\{\begin{array}{l}\ln \left[\frac{\left({r}_2^2-{cr}_1^2\right)}{\left({r}_1^2\left(1-c\right)\right)}\right]-\ln \left(\frac{r_2^2}{r_1^2-c}\right)\ln \left[\frac{\left({r}_2^2-{cr}_1^2\right)}{\left({r}_1^2\left(1-c\right)\right)}\right]+\frac{\left(1-\upmu \right){\left[\ln \left(\frac{r_2^2}{r_1^2-c}\right)\right]}^2}{4}\\ {}-\frac{\left(1-c\right){\left[\ln \left(1-c\right)\right]}^2}{4}+\left(1-\upmu \right)\ln \left(\frac{r_2^2}{r_1^2-c}\right)\ln \left(\frac{r_2}{r_1}\right)-\left(1+c\right)\cdot {cr}_1^2\ln \frac{\left(\frac{r_2^2}{r_1^2}\right)}{r_2^2}\end{array}\right\}, $$

(3)

where r₁ is the outer radius of the yarn support, m; r₂ is the outer radius of the take-up (package), m; ì is the Poisson’s ratio of the take-up; c = [μ − 1 + r₁E₂/(δ₁E₁)]/[μ + 1 + r₁E₂/(δ₁E₁)] is the coefficient that takes into account compliance of the yarn support; δ₁ – is the wall thickness for the yarn support, m; E₁ is the modulus of elasticity of the yarn support, MPa; E₂ is the modulus of elasticity of the take-up, MPa; d_sp is the reduced diameter of the yarn, m.