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In this work we present the industrial application of fiber lay-down models that enable an efficient simulation of non-woven structures. The models describe the deposition of fibers on a moving conveyor belt with the help of stochastic differential equations on manifolds. The model parameters have to be estimated from more complex models in combination with measurements of the resulting non-woven...
The so‐called fiber lay‐down models arise in the production process of nonwovens. We introduce the generalized version of the basic fiber lay‐down model which can precisely be formulated in abstract form as some manifold‐valued stochastic differential equation. An important criterion for the quality of the nonwoven material is how the solution to the associated Fokker‐Planck equation converges towards...
We present an improved three‐dimensional stochastic model concerning the fiber lay‐down in the production process of nonwoven materials. The model describes the position of the deposited fibers on a conveyor belt, which is determined by a system of stochastic differential equations. Here we remove a drawback of a previous 3D model, that is the non‐smoothness of the fiber paths. Besides the derivation...
We present an improved stochastic model concerning the lay‐down of fibers on a conveyor belt in the production of nonwovens. The model is based on stochastic differential equations describing the resulting position of the fiber on the belt having regard to its motion in the deposition region under influence of turbulent air flow. Our aim is to generalize an existing model to 3D. By introducing a parameter...
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