Spinning Systems and Yarn Structure

Yarn twist multiplier calculation

The twist multiplier (TM) is the index that lets yarns of different counts be compared at the same twist intensity. In the English cotton system it is defined as TM = tpi/\sqrt{N_e}, where tpi is turns per inch and N_e is the English cotton count. Rearranging gives tpi = TM \times \sqrt{N_e}, so the required twist follows directly from the count, and the count can be recovered as N_e = (tpi/TM)^2. Calculating TM from a given tpi and count is the most direct use of this definition, so for a 25 Ne yarn with 18 tpi the TM is 18/5 = 3.6. In the direct (metric) system the equivalent measure is the twist factor \alpha = T_{tpm}\sqrt{tex}, with T_{tpm} in turns per metre. Because N_e = 590.5/tex, the two systems are tied by a fixed constant, \alpha = TM\sqrt{590.5}/0.0254 \approx 956.7\,TM, so a TM of 5 corresponds to a metric twist factor of roughly 4780 tpm tex^{0.5}. Yarns with the same twist factor are geometrically similar: they share the same packing density and the same surface-fibre twist angle, although their turns per metre and linear densities differ. At a fixed tpi, making the yarn coarser lowers N_e and therefore raises TM, and the surface twist angle also grows because the yarn diameter is larger. Do not mix the systems: TM uses tpi and Ne, while the twist factor uses tpm and tex, and the constant 590.5 applies only to the cotton hank relation.

Ring spinning draft and count

In ring spinning, the mechanical draft is the ratio of the front-roller delivery speed to the feed-roller speed. Because the drafting zone conserves mass, the linear density of the drafted strand is the roving linear density divided by the draft, so in the Ne system the nominal yarn count equals the roving count multiplied by the draft. Count depends on length as well as mass: Ne is the number of 840-yard hanks per pound, so a shorter delivered length for the same mass gives a lower Ne and a higher tex. When the twisted yarn is shorter than the parallel strand by a given fraction, the Ne falls in the same proportion. The tex rises by the inverse of the length ratio, and this new tex must be used when computing the metric twist factor \alpha = T_{tpm}\sqrt{tex}. The number of cops needed for a roving follows from the mass-to-length relation. For example, 2 kg of 500 tex roving has 2000/500 = 4 km of roving, which after a draft of 25 becomes 100 km of yarn; with 5 km per cop, 20 cops are needed.

Helical model of yarn twist

In the helical model, the yarn is treated as a cylinder whose surface fibres lie on helices making an angle \theta with the yarn axis. The surface twist angle satisfies \tan\theta = \pi d T, where d is the yarn diameter and T is the twist per unit length, so a thicker yarn at the same twist has a larger surface angle. If the yarn diameter is inversely proportional to the twist, the product dT is constant, and the surface twist angle is the same for all such yarns, while packing density, twist multiplier and cross-sectional area still differ. When the diameter is written in terms of linear density and fibre density, the surface angle depends only on the twist factor and fibre density: \tan\theta = \pi\sqrt{4\times10^{-6}/(\pi\rho)}\,\alpha, with \alpha in turns per metre times \sqrt{\text{tex}} and \rho in kg/m^3. The angle is therefore independent of linear density for a given twist factor and fibre density. A single fibre of radius r whose axis makes an angle \alpha with the yarn axis appears in a section cut normal to the yarn as an ellipse with semi-axes r and r/\cos\alpha, so its projected area is \pi r^2/\cos\alpha, which is larger than its own circular section. For example, a fibre of 4 μm radius at a helix angle of 30° projects an area of about 58 μm^2.

Yarn irregularity index (CV%)

Yarn irregularity is measured by the coefficient of variation, CV = \sigma/\bar{x} \times 100\%. The index of irregularity compares the actual CV with the theoretical CV of a yarn made of random fibres with the same number of fibres in its cross-section. The number of fibres is n = \text{yarn tex}/\text{fibre tex}, and the theoretical CV is 100/\sqrt{n}. Denier converts to tex by dividing by 9. An index above 1 means the yarn is more irregular than the random-fibre ideal. For example, a 20 tex yarn of 1.5 denier fibre has n = 20/(1.5/9) = 120 fibres, giving a theoretical CV of about 9.1%. When two single yarns are plied without twist contraction, their linear densities add, and for independent components the variances add, so \sigma_p^2 = \sigma_1^2 + \sigma_2^2 and the plied CV is \sigma_p/\bar{x}_p. For instance, plying a 10 tex yarn with CV 10% and a 15 tex yarn with CV 10% gives \sigma_p = \sqrt{1 + 2.25} = 1.80 tex on 25 tex, a CV of about 7.2%. Dimensionless quantities are ratios of like quantities or pure numbers; packing density, twist contraction and the index of irregularity fall in this class, whereas the twist multiplier carries units of tpi \cdot Ne^{-0.5} and is not dimensionless.

Friction spinning systems

Friction spinning uses two perforated drums rotating in the same direction, with suction inside the drums that holds the fibres on their surfaces. Fibres are fed into the gap between the drums, and the yarn is formed as the fibres are twisted by friction between the drum surfaces and the yarn. The perforated drums are the defining element of this technology, which distinguishes it from ring, rotor and air-jet spinning. In friction spinning the yarn rotates on the drum surface, and because the drum diameter is large compared with the yarn diameter, one revolution of the drum produces several turns of twist. This is different from ring spinning, where one revolution of the traveller inserts one turn, and from rotor spinning, where one rotor revolution inserts one twist.

Classimat yarn fault classification

The Uster Classimat system classifies yarn faults detected by a capacitive sensor on a grid of fault length and thickness. Each class is identified by a letter for the fault family and a number for the size level, so that a higher number indicates a larger deviation within its family. Thick faults occupy the classes with short and medium lengths, while the H class covers thin faults that extend over long lengths. Comparing an H2 fault with a C3 fault therefore shows that H2 is thinner and longer, because H lies in the thin, long-fault region of the grid while C lies in the short, thick region. Electronic yarn clearers on cone winding machines use capacitive or optical sensing to detect deviations in mass and foreign matter. When a deviation exceeds the preset limit, the clearer cuts the yarn, which removes objectionable faults such as thick places, thin places and neps, as well as foreign matter such as vegetable matter. General imperfections are not removed as a class, and long hairs are not removed because they protrude from the surface without a detectable mass change.

Rotor spinning yarn structure

Rotor (open-end) spinning deposits individual opened fibres into the groove of a rotating rotor, where they are twisted into a yarn. The characteristic structure is a core of helically twisted fibres with wrapper or belt fibres laid over the surface, which is why rotor yarn is bulkier than ring yarn of the same count. The main structural contrasts among spun yarns are as follows. Ring yarn is strong and has a uniform helical structure from full twist. Rotor yarn is bulky and has wrapper fibres on a twisted core. Friction (open-end) yarn is bulky with very poor fibre migration, because the fibres lie side by side with little mixing. Air-jet yarn is stiff and has a nearly twistless core of parallel fibres. Matching these features with the spinning system is the usual way the characteristic structure is tested.