A mathematical account of draught‐induced disturbances in the fibre spinning process

Abstract

This work gives a mathematical account of the propagation of disturbances produced by a sudden draught of air impinging on a cylindrical fibre produced by the melt‐spinning process. Accounting for varying tension and aerodynamic drag, the non‐dimensional wave‐type equation of motion is derived in dimensionless form; the solution of which is sought using the Riemann method of characteristics. Using this procedure, the solutions along the leading forward and reflected characteristics are obtained in closed‐form and enable numerical solutions to be obtained via a finite difference routine along the entire computational domain. The analysis shows how such disturbances may be prevented from penetrating beyond the material crystallisation point (where it is extremely susceptible to disturbances) and discusses the application of these findings by optimising the location of a protective shroud.