# Rieter

### Fiber collection in the rotor groove (back-doubling)

#### Index

The process of yarn formation in rotor spinning involves the separation by an opening roller of a fiber bundle fed in into individual fibers or small groups of fibers (no more than 5 fibers), which are then transported by the air current into the rotor, where they slide down the rotor wall. They are only combined again into fine layers of fibers in the rotor groove. A layer of these individual fibers is deposited in the rotor groove with each revolution of the rotor until the yarn reaches the required thickness. This buildup of fiber layers to the final yarn thickness is described as back-doubling, with the number of fiber layers resulting from the (genuine) yarn twist set and the diameter/circumference of the rotor used. Customary values are in the range of 60 - 90-fold back-doubling. Doubling of linear fiber formations always improves the regularity of the resulting new product, an effect that is, of course, consciously exploited in drawframes. This process is significantly finer and more intensive if it takes place at the level of the finest linear structure, namely the individual fiber. The regularity obtained in this way is of a high degree and is always better than that of ring-spun yarn. However, it must be borne in mind again that improvement in regularity is possible only over a length corresponding to the internal circumference of the rotor. With a currently widely used rotor diameter of 35 mm, the length that can be leveled out is 33 x 3.14 = 103  mm. All eveness in the sliver with a length greater than this pass into the yarn.

The numbers of back-doubled fiber layers is calculated as follows:

$D = \frac {Rotor \varnothing mm \times T/m (yarn) \times \Pi}{1000}$

Example:
Yarn Nm 34/Ne 20, αm 135/αe 4.45;
Rotor ⌀ 35 mm>

$T/m = \sqrt{Nm} \times \alpha_m = \sqrt{34} \times 135 = 787$
$T/'' = \sqrt{Ne} \times /\alpha_e = \sqrt{20} \times 4.45 = 20$

$D = \frac {35 mm \times 787\ T/m \times 3.14}{1000} = 86\ doubled\ fiber\ layers$

$D = \frac {35 mm \times 20\ T/'' \times 30.3 \times 3.14}{1000} = 86\ doubled\ fiber\ layers$

When the required yarn thickness – formed from the individual fiber layers – has been reached, the yarn is withdrawn from the rotor groove. The end of the yarn extending into the rotor groove assumes the form of a fiber wedge due to the continuous take-off process. This fiber wedge is exactly the same length as the rotor groove. The diameter of the fiber wedge is at its largest – the full number of back-doubled fiber layers necessary for the required yarn thickness – at the moment it is withdrawn from the rotor groove, and at its smallest at the end of the fiber layer deposited last (Fig. 93, A). One fiber layer after the other – always the lowest (since it was the first deposited) – is thus removed by the yarn being taken off, followed successively by the subsequent fiber layers in the order they were deposited. When a layer of fibers is completely integrated it is immediately replaced by the fiber layer deposited next in the rotor groove. The wedge-shaped end of the yarn shifts continuously with the unrolling motion of the yarn liftoff point and thus ahead of the peripheral speed of the rotor.

Fig. 93, A - D shows the position of the yarn lift-off point and the corresponding fiber deposit situation in the rotor groove on 4 occasions. The lift-off point moves forward by the distance between the starting points of 2 fiber layers with each revolution of the rotor. For example: with a rotor diameter of 35 mm and 88 layers of fiber, the yarn lift-off point travels 35 mm x 3.14 / 86 = 1.28 mm with one revolution of the rotor. After 86 revolutions of the rotor (86 x 1.28 mm = 110 mm rotor circumference or 35 mm rotor Ø) the yarn lift-off point has therefore returned to its starting position (Fig. 93, A).

Fig. 93 – Illustration of the buildup of the fiber ring in the rotor groove by back-doubling and the corresponding position of the yarn lift-off point