Theoretical study of fiber tension distribution at the spinning triangle

The spinning triangle is a critical region in the spinning process of yarn. Its geometry influences the fiber tension distribution and thus affects the properties of spun yarns. In conventional ring spinning, on the one hand, the spinning triangles are often asymmetric due to the frictional contacts of fibers with the bottom roller, which interferes with the twist propagation into the spinning triangle zone, and thus leads to the migration of the axis fiber at the front roller nip. On the other hand, the yarn spinning tension has an obvious angle with the vertical axis perpendicular to the nip line. Therefore, in this paper, a theoretical model of the fiber tension distributions in the general spinning triangle has been proposed by considering both the inclination angle of the spinning tension and the migration of the axis fiber at the front roller nip according to the principle of minimum potential energy. Two shape parameters were introduced to describe the skew level of the geometry of the spinning triangle in the analysis. The effects of shapes of the spinning triangle on the fiber tension distributions were investigated. The results show that the fiber tension distribution at the spinning triangle tends to more non-uniformity with increasing the asymmetry of the spinning triangle. The effects of both shape parameters on the fiber tension distributions are similar under the assumption that the spinning triangle height H is constant. In addition, a more long-narrow shape of the spinning triangle shows more uniform fiber distributions.