Computer modelling of yarn winding on conical bobbins

Abstract

The article presents the results of the computer modelling of yarn winding on conical bobbins based on the analytical method of constructing tubular-shaped surfaces as a partial case of channel surfaces using the vector algebra apparatus. It is stated that the guide line takes the shape of a conical spiral line along which the forming moves (in the form of a circle with a diameter equal to the average diameter of the yarn), and is set using the moving Frenet basis. The obtained mathematical models facilitate the building, in MathCAD 3D visualization graphics, of a tubular-shaped surface, which represents the layers of yarn winding on a conical cartridge, and the reinforced yarn, which comprise the core component and the wrapping component, as well as the determination of both the lengths of individual layers of winding and the total length of winding (not including the transition sections). Well-known methods of forming geometric objects and computer modelling were also used in the work. The theoretical studies are based on the basic principles of textile production technology.

V članku so predstavljeni rezultati računalniškega modeliranja navijanja preje na stožčaste navitke, kjer so bile kot primer žlebičastih površin z uporabo analitične metode vektorske algebre konstruirane cevaste površine. Vodilna linija ima obliko stožčaste spirale, vzdolž katere poteka oblikovanje (v obliki kroga s premerom, ki je enak povpreč¬nemu premeru preje) in se nastavi s pomočjo gibljive Frenetove baze. Dobljeni matematični modeli omogočajo vizualizacijo cevaste površine s pomočjo grafičnega orodja MathCad 3D, tj. plasti preje, navitih na cevko stožčaste oblike, ojačitvene preje iz jedra in ovojne komponente in določanje dolžine posameznih plasti navitja kot tudi celot¬ne dolžine navitja (brez prehodnih odsekov). Pri tem so bile uporabljene znane metode oblikovanja geometrijskih objektov in računalniškega modeliranja. Teoretične študije temeljijo na osnovnih principih tehnologije za izdelavo tekstilij.