Mathematical modeling, simulation and validation of the dynamic yarn path in a superconducting magnet bearing (SMB) ring spinning system

Abstract

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.Keywords mathematical modeling, yarn tension, balloon form, ring spinning, superconducting magnetic bearingIn the existing ring spinning process, the frictional heat generated in the ring/traveler system causes damage to both the twisting element and the yarn structure. 1 The traveler is not allowed to rotate at more than 50 m/s, especially in the case of man-made fibers, due to their melting, caused by the high friction-induced heating, which limits productivity. 2,3 The friction-free superconducting magnet bearing (SMB) eliminates this restriction and thus allows increase of the spindle speed much higher than with existing spinning machines. In our previous work, different concepts of SMB system have been presented, and a suitable one has been successfully integrated in a ring spinning tester. 4 The SMB system comprises of two rings, a magnetic element of Neodymium Iron Boron (NdFeB) with a yarn guide attached to it, and a high temperature superconductor (SC) from YBCO (YBa 2 Cu 3 O 7-x ) chemical compounds. The superconductor (SC) ring is cooled down below its critical temperature at a fixed distance from the PM ring. The PM ring levitates above the SC ring according to the principle of levitation. During the spinning process, the yarn (wound onto the bobbin) rotates the PM ring, instead of the traveler. The patented concept of the SMB system ensures a smooth running of the spinning process for significantly higher productivity with similar yarn properties to the conventional process. 5

Analysis and measurement of the shape of spinning balloons

“…The second boundary condition at the guide eye of the PM ring can be defined from the equation of motion 14 where T1 is the yarn tension at the bottom of the balloon (into the PM ring contact), μ 1 is the friction coefficient between the yarn and the yarn guide eye on the PM ring, and α is the wrapping angle of the yarn on the PM ring guide eye section. As shown in Figure 2, ϕ is the angle between the tangential and the radial at the beginning of the yarn winding, normalsin⁡ϕ=ba; |normal normal′≡normald()normalds; where b is the radius of the wind-point on the bobbin and dR is the rotational damping coefficient of the PM ring 15 where CdR is a proportional constant and Re is the Reynolds number.…”

Numerical analysis of heat transfer in ring spinning

“…[5][6][7] Superconducting magnetic bearing (SMB) systems have been investigated to provide a contact-free method of yarn winding and twisting to replace the original ring/traveler system in ring spinning machines. [8][9][10][11] While this is a novel method for eliminating frictional heat of the ring/traveler system, it cannot be immediately applied for the reasons of installation and cost. Vibration has also been added to the ring/traveler system, to decrease the contact frequency between traveler and ring, thereby reducing the frictional heat.…”

A dynamic modeling approach to the moving filament during high-speed winding by absolute nodal coordinate formulation

“…Among researches related to textile systems, there are quite a few that focus on the movement and dynamics of textile flexible bodies, such as yarns, filaments, or fabrics. For example, Hossain et al [8][9][10] carried out mathematical modeling research on the yarn movement state in the ring-spinning system. A similar study is Tang et al, 11 which adds a part of the experimental verification.…”

“…For example, Hossain et al. 8–10 carried out mathematical modeling research on the yarn movement state in the ring-spinning system. A similar study is Tang et al., 11 which adds a part of the experimental verification.…”