Abstract
An optical fibre is made by stretching, or `drawing', a glass or polymer preform in a drawing tower. Extrusion through dies has received much recent attention as a suitable method for manufacture of preforms of complex shape and novel material composition. However, the preforms are subject to bending during extrusion, so that the final preform has a bent end that must be removed to yield a straight preform to be drawn into a fibre. Control of bending is needed to improve the efficiency of preform extrusion and reduce wastage of high-cost material. Bending occurs even for simple axisymmetric die geometries and in the absence of heating. Hence, we here examine asymmetry in the applied pressure as a cause of bending. Assuming a linear stress profile, and using a quasi-static approach, we determine the relationship between the magnitude of asymmetry and the amount of bend of the preform, for preforms with circular or annular cross section. We show that significant bend may be caused by an asymmetry that is small relative to the applied pressure. A simple idea for controlling bending is also suggested. Undergraduate university level mathematics is used in the analysis, making this a useful educational illustration of the role of mathematics in understanding engineering problems. References G. Barakos and E. Mitsoulis. Non-isothermal viscoelastic simulations of extrusion through dies and prediction of the bending phenomenon, J. Non-Newtonian Fluid Mech., 62, 1996, 55--79. doi:10.1016/0377-0257(95)01385-7 H. Ebendorff-Heidepriem and T. M. Monro. Extrusion of complex preforms for microstructred optical fibres, Optics Express, 15, 2007, 15086--15092. doi:10.1364/OE.15.015086 H. Ebendorff-Heidepriem, Centre of Excellence in Photonics, The University of Adelaide. Personal communication, 2006--9. A. Karagiannis, A. N. Hrymak and J. Vlachopoulos. Three-dimensional non-isothermal extrusion flows, Rheol. Acta, 28, 1989, 121--133. doi:10.1007/BF01356973 S. C. Warren-Smith, H. Ebendorff-Heidepriem, T. C. Foo, R. Moore, C. Davis and T.M. Monro. Exposed-core microstructured optical fibers for real-time fluorescence sensing, Optics Express, 17, 2009, 18533--18542. doi:10.1364/OE.17.018533
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