# Rieter

### The winding principle

#### Index

As already mentioned, winding can occur only when there is a difference between the circumferential speed of the bobbin and that of the spindle (flyer). At each instant, this difference must correspond to the delivery speed, since the length delivered and the length wound up must be the same. As roving layers are deposited on the bobbin, however, their diameters increase. Hence, in the absence of intervention, the circumferential speeds (and finally their difference) would increase. There would be a constant increase in the length wound up, and a roving break would occur. To avoid this the bobbin speed must continuously be reduced in a precisely controlled manner in order to maintain the speed difference continually equal to the constant delivered length. The following general principle can therefore be derived. If the circumferential speeds (bo = bobbin, spi = spindle) are given by:

$\nu_{bo} = d_{bo} \times \pi \times n_{bo}$

$\nu_{spi} = d_{spi} \times \pi \times n_{spi}$

then, since delivery is given by:

$L = \nu_{bo} - \nu_{spi}$

$L = d_{bo} \times \pi \times n_{bo} -d_{spi} \times \pi \times n_{spi}$

The bobbin diameter and the spindle diameter are equal, since in this context only the winding point at the press finger is significant. Hence we obtain:

$L = d \times \pi \times n_{bo} -d \times \pi \times n_{spi}$

$L = d \times \pi (n_{bo} -n_{spi})$

By transforming the equation, the bobbin speed corresponding to any given bobbin diameter can be derived:

$(n_{bo} -n_{spi}) \times d \times \pi = L$

which gives

$n_{bo} = \frac {L}{d \times \pi} +n_{spi}$