The yarn tension and balloon form are the most important physical process parameters to characterize the dynamic yarn path in ring spinning. The present research work focuses on the in situ measurement of yarn tension in different regions of the yarn path in a developed turbo ring spinning tester with a friction-free superconducting magnetic bearing (SMB) twisting system and at an angular spindle speed of up to 50,000 rpm. The influence of different parameters, such as angular spindle speeds (15,000–50,000 rpm), yarn counts (15–40 tex) and balloon control ring (one or multiple), were evaluated to identify the influence of acting forces, for example, centrifugal forces. The effects of these process parameters were analyzed statistically using an analysis of variance. The yarn tension between the delivery rollers and the yarn guide was measured using a modified one-roller tensile yarn tension sensor. The yarn tension between the yarn guide and the SMB system was determined with an already existing optical approach at a higher angular spindle speed. As the highest yarn tension theoretically occurs between the SMB system and the cop, it was estimated in this region by measuring the coefficient of friction between the yarn and the yarn guide using the friction module of the constant tension tester equipment. The maximum balloon diameter was determined from the recorded balloon form between the yarn guide and the SMB system with respect to different angular spindle speeds. The results provide valuable information about the highest possible spinnable speed and enable a better understanding of the dynamic yarn path in the SMB spinning system. Keywords

Ziel der Arbeit ist es, die instationären zeitlichen und räumlichen Bewegungsabläufe stark deformierbarer eindimensionaler Kontinua durch ein allgemeines mechanisch-mathematisches Modell unter Berücksichtigung ihrer Biege- und Torsionssteifigkeit zu beschreiben und zu dessen Lösung geeignete numerische Verfahren zu testen und auszuwählen. Die entwickelten Algorithmen werden auf Aufgabenstellungen aus der Raumfahrt-, Meeres- und Textiltechnik angewendet. / It is the aim of this thesis to describe the instationary motion of flexible one-dimensional continua by a general mechanical-mathematical model, when bending and torsional stiffness is not negligible, and to test and select appropriate numerical solution methods. The developed algorithms are used to solve problems from space, marine and textil engineering.

The new concept of a superconducting magnetic bearing (SMB) system can be implemented as a twisting element instead of the existing one in a ring spinning machine, thus overcoming one of its main frictional limitations. In the SMB, a permanent magnet (PM) ring rotates freely above the superconducting ring due to the levitation forces. The revolution of the PM ring imparts twists similarly to the traveler in the existing twisting system. In this paper, the forces acting on the dynamic yarn path resulting from this new technology are investigated and described with a mathematical model. The equation of yarn movement between the delivery rollers and the PM ring is integrated with the Runge-Kutta method using MATLAB. Thus, the developed model can estimate the yarn tension and balloon form according to different spindle speeds considering the dynamic behavior of the permanent magnet of the SMB system. To validate the model, the important relevant process parameters, such as the yarn tension, are measured at different regions of the yarn path, and the balloon forms are recorded during spinning with the SMB system using a high speed camera.

Ziel der Arbeit ist es, die instationären zeitlichen und räumlichen Bewegungsabläufe stark deformierbarer eindimensionaler Kontinua durch ein allgemeines mechanisch-mathematisches Modell unter Berücksichtigung ihrer Biege- und Torsionssteifigkeit zu beschreiben und zu dessen Lösung geeignete numerische Verfahren zu testen und auszuwählen. Die entwickelten Algorithmen werden auf Aufgabenstellungen aus der Raumfahrt-, Meeres- und Textiltechnik angewendet. / It is the aim of this thesis to describe the instationary motion of flexible one-dimensional continua by a general mechanical-mathematical model, when bending and torsional stiffness is not negligible, and to test and select appropriate numerical solution methods. The developed algorithms are used to solve problems from space, marine and textil engineering.

Twist plays an important role to impart tensile strength in yarn during the spinning process. In the most widely used ring-spinning machine for short staple yarn production, a combination of ring and traveler is used for inserting twist and winding the yarn on cops. The main limitation of this twisting mechanism is the friction between the ring and traveler, which generates heat at higher speed and limits the productivity. This limitation can be overcome by the implementation of a magnetic bearing system based on superconducting technology, which replaces completely the existing ring/traveler system of the ring-spinning machine. This superconducting magnet bearing consists of a circular superconductor and permanent magnet ring. After cooling the superconductor below its transition temperature, the permanent magnet ring levitates and is free to rotate above the superconductor ring according to the principles of superconducting levitation and pinning. Thus the superconducting magnetic bearing (SMB) ensures a friction-free operation during spinning and allows one to increase spindle speed and productivity drastically. The yarn properties using the SMB system have also been investigated and they remain nearly identical to those of conventional ring yarns.

This paper presents a mathematical model to predict the distribution of yarn tension and the balloon shape as a function of spindle speed in the ring spinning process. The dynamic yarn path from the delivery rollers to the winding point on the cop has been described with a non-linear differential equation system. These equations have been integrated with a Runge–Kutta method using MATLAB software. Since the numerical solution of the equations strongly depends on initial values, an algorithm of sensitivity analysis has been developed to predict the right choice of initial values in order to find a stable solution. For model validation purposes, the yarn tension has been measured between delivery rollers and yarn guide. Furthermore, a high-speed camera has been used to capture the balloon shape at different spindle angular velocities in order to compare the theoretically determined balloon shape with the one that actually occurs on the machine.