No abstract

The manufacturing process of glass fibers used for the reinforcement of composite material consists in drawing a glass melt at high temperature through an array of thousands of small orifices (i.e., the bushing plate) into fibers using a winder. This process is sensitive to numerous disturbances that can cause a fiber to break during the drawing process. This paper analyzes how the stress in the fiber depends on the controlling parameters of the process. The approach relies on numerical simulations and sensitivity analysis. Both a semi-analytical one-dimensional model and a more complex two-dimensional axisymmetric model are used. It is first found that radial variations across the fiber are small compared to changes in the axial direction and that the onedimensional approximation is accurate enough to describe the major trends in the process. Sensitivity analyses on some physical parameters controlling the heat transfers and on process parameters are then performed to identify strategies to reduce the axial stress. In particular, it is shown that, for a given fiber diameter, the stress is minimized if the glass melt temperature and the drawing velocity are increased. This approach is then applied to quantify the effect of inhomogeneous heat patterns on a bushing plate with a large number of fibers.

The draw resonance effect appears in fiber drawing processes when the draw ratio, defined as the ratio between the take-up and the inlet velocities, exceeds a critical value. In many cases, inertia, gravity, and surface tension cannot be neglected, and a model combining all these effects is necessary in order to correctly describe the physics of the phenomenon. Additionally, it is also known that cooling can have a highly stabilizing effect on the draw resonance instability. However, a detailed analysis encompassing the effect of inertia, gravity, surface tension, and temperature is still lacking. Due to a destabilizing effect induced by geometry in the heat equation, we first show that the maximum critical draw ratio for fiber drawing can be two orders of magnitude lower than the one for the film casting problem when the heat transfer coefficient is assumed constant. By introducing a scaling making the fiber aspect ratio an independent parameter, we next show that the high value of the critical draw ratio encountered in industrial applications could be rationalized only if we consider that the heat transfer coefficient is not constant but depends on both the velocity and the cross-section area of the fiber. Within this framework, we show how the practical stability window is affected by the five control parameters: the draw ratio, the fiber aspect ratio, the inlet temperature, the convective heat transfer coefficient, and the stiffness of the non-homogeneous ambient temperature. We finally discuss the influence of radiative heat transfer on the stability.