Modeling the Dynamic Behavior of the Fiber Bundle in a Roll-Drafting Process

Abstract

Roll drafting is a mechanical operation that is indispensable when manufacturing staple yams. However, a fiber bundle throughout this operation has a certain number of defects in its regularity of linear density, causing many problems not only for the quality of the textile product but also for the efficiency of the manufacturing processes. In this research, we attempt to set up a mathematical model for the dynamic behavior of the flowing bundle on the basis of general physical laws. Mass balance and momentum balance are applied under certain assumptions. A constitutive model for relating the surface force and the deformation of the fiber bundle is introduced by considering a representative physical variable that stands for the characteristics of the bundle and its constituent fibers. A fundamental equation system can then be simplified in the steady state of the process, and the mathematical problem is reduced to such an extent that mathematical tools can solve the equations. From a simplified model, the simulation results are confirmed by the experiments. The results show that the mathematical model can be adjusted very easily to the experimental outcomes. The fiber bundle accelerates as the bundle attenuation pro ceeds. But near the front roll, the bundle of fibers might experience a jerk, because a discontinuity of the slope of the velocity profile could take place near the nip line of the front roll, which could cause irregularities in the linear density of the output sliver.