Approximation Methods for the Uniform Coverage Problem in the Spunbond Process

This thesis analyses a typical class of uniform coverage problems motivated by the spunbond process. Three different models are described. In the asymptotic model, the problem is solved analytically in terms of Abel solutions. The Abel solutions show a desirable approximative behaviour in the semi-asymptotic model and in the complete finite model which is proven in this thesis. Numerical comparisons to Remez solutions justify their benefit.

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The homogeneous deposition of material on complex surfaces, e.g., powder coating, paint spraying, fiber lay-down etc., is a well-known task in industrial production. This thesis introduces a mathematical modeling for a typical process class of such uniform coverage problems motivated by the spunbond process. Three different models are described. In the asymptotic model, a simplified uniform coverage problem is solved analytically in terms of Abel solutions. In the semi-asymptotic model, one of the simplifications is revoked and it is proven that the Abel solutions perform very well. Finally, in the complete finite model, convergence to the first model is proven, which implies that the Abel solutions show a desirable approximative behaviour. In the numerical part, the uniform coverage problem is solved in terms of a modified Remez-Algorithm. The Abel solutions are compared to the Remez solutions and their usage is justified.