Mathematical Modeling of Dynamic Yarn Path Considering the Balloon Control Ring and Yarn Elasticity in the Ring Spinning Process Based on the Superconducting Bearing Twisting Element

Abstract

The productivity of the conventional ring spinning process is currently limited by the frictional heat that occurs in the ring/traveler twisting system. In the framework of a fundamental research project from the German Research Foundation (DFG), the levitation principle of superconducting magnetic bearing (SMB) was implemented as a twisting element in order to eliminate the frictional problem and thus aim, at least, to double the productivity. A mathematical model of the dynamic yarn path has already been presented considering the friction free SMB system up to an angular spindle speed of 25,000 r.p.m. In this paper, the existing theoretical model, which was developed up to 25,000 r.p.m, was further modified considering the balloon control ring and yarn elasticity at a higher angular spindle speed, such as 50,000 r.p.m. The model was solved numerically using the RUNGE-KUTTA method. With this model, it is possible to estimate the yarn tension distribution and balloon form considering the above-mentioned parameters. The model established was further validated by comparing the yarn tension and balloon forms predicted with measured ones up to an angular spindle speed of 15,000 r.p.m in a ring spinning tester based on superconducting magnetic bearing.