A Stochastic Model and Associated Fokker-Planck Equation for the Fiber Lay-down Process in Nonwoven Production Processes

In this paper we present and investigate a stochastic model and its associated Fokker-Planck equation for the lay-down of fibers on a conveyor belt in the production process of nonwoven materials. The model is based on a stochastic differential equation taking into account the motion of the fiber under the influence of turbulence. A reformulation as a stochastic Hamiltonian system and an application of the stochastic averaging theorem lead to further simplifications of the model. Finally, the model is used to compute the distribution of functionals of the process that are important for the quality assessment of industrial fabrics.