Abstract
The resistance force against the slipping out of fibers from spun yarns has an important bearing on the weavability of yarns, fussing and pilling.
The resistance force against the slipping out of fibers from spun yarns has an important bearing on the weavability of yarns, fuzzing and pilling.
The theoretical relation between this force and the geometrical structure of yarn has been obtained in this study.
The following theoretical equation gives resistance Q against the slipping out of fibers from yarns to estimate the resistance froce against fuzzing : Q=μλF0 / 4π 2Na20 (4π2N2a20+1) {tan-1 2πN2r1a0 / √ 4π2N2a20+N2r21+1 -tan 2πN2r1(a0- r1 θ /2π) / √ 4π 2N2 (a0- r1 θ / 2π)2+N2r21+1 +1/Nr1 · ln 2πNa0+√4π2N2a20+N2r21+1/2πN(a0-r1θ/2π)2+N2r21+1}-μλF0/4π2Na2r1{πa0√4π2N2a20+N2a20+N2r21+1 -π(a0-r1θ/2π)√4π2N2(a0-r1θ/2π)2+N2r21+1 +N2r21+1/2N · ln2πNa0+√4π2N2a20+N2r21+1/2πN(a0-r1θ/2π)+√4π2N2(a0-r1θ/2π)2+N2r21+1}
where,
Q: The resistance force against the slipping out of fibers from spun yarns.
μ: Coefficient of friction of fiber.
λ: Length of circumference of fiber.
F0: Tension of yarn.
N: Number of twists of yarn per unit length.
a0: Radius of yarn.
r1: Migration of fibers per pitch of twist.
θ: Displaced angle of radius of spiral.
