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  • Stochastic Model for Fiber Lay-down in Nonwoven Production

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    Nonwovens are technical textiles made of a web of fibers. They find their application in various branches of industry, e.g. in textile, hygiene, automobile and building industry. For the industrial production transversal, rotational and oscillating processes are of main relevance. Differing in details, they have in principal three things in common: spinning, entanglement and lay-down. Thousands of fibers are obtai...
    Tags: fiber_lay-downmodelnonwovenofficialstochastic_processtest
    Added by Martin on 2010-07-22 10:39


    Stochastic Model for Fiber Lay-down in Nonwoven Production Nonwovens are technical textiles made of a web of fibers. They find their application in various branches of industry, e.g. in textile, hygiene, automobile and building industry. For the industrial production transversal, rotational and oscillating processes are of main relevance. Differing in details, they have in principal three things in common: spinning, entanglement and lay-down. Thousands of fibers are obtained by a continuous extrusion of a molten granular through narrow nozzles. Then, they are stretched and entangled by acting turbulent air flows to form a web, while laying down on a moving conveyor belt. The complete production process can in principle be described by a mathematical model that takes into account the entanglement and deposition of all fibers on the conveyor belt under the influence of turbulent air flows. Unfortunately, it turns out that the associated simulations are very time-consuming, storage demanding and not suitable for the computation of huge nonwoven webs. But this high computational effort is not obligatory because huge bundles of fibers are realizations of the same stochastic process. Therefore, it makes sense to introduce a simplified surrogate stochastic process that describes the characteristic image of the fibers on the conveyor belt. This enables the easy and fast computation of a web of thousands of fibers. The surrogate model is characterized by a deterministic reference curve Γ being the projection of the spinning position onto the moving conveyor belt. For example it is a straight line for transversal processes and a cycloid for rotational ones. Oscillating around the reference curve, the actual fiber curve and the angle that specifies its tangent are given by a system of stochastic differential equations. Containing typical parameters 1, 2 and A it can be calibrated by the dynamical full simulation of a single fiber.
  • Improved Stochastic Model for Fiber Lay-down in Nonwoven Production

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    This model is an extension of the "Stochastic Model for Fiber Lay-down in Nonwoven Production". The original model describes the image of a fiber on a conveyor belt by a system of stochastic differential equations for the fiber curve and the angle giving the tangent. Perturbing the angle with white noise a continuous curve is obtained. To improve the regularity to a differential curve the following model...
    Tags: fiberfiber_lay-downmodelnonwovenstochasticstochastic_process
    Added by Martin on 2010-07-20 09:42


    Improved Stochastic Model for Fiber Lay-down in Nonwoven Production This model is an extension of the "Stochastic Model for Fiber Lay-down in Nonwoven Production". The original model describes the image of a fiber on a conveyor belt by a system of stochastic differential equations for the fiber curve and the angle giving the tangent. Perturbing the angle with white noise a continuous curve is obtained. To improve the regularity to a differential curve the following model relaxing to the deterministic behaviour of the original one perturbes the curvature.