MATHEMATICAL MODEL OF A ROLLER PAIR FOR APPLICATION OF POLYMER COATING

Abstract

The article considers the process of applying a polymer coating to a textile material by a pair of rollers, which is characterized by the presence of a thin layer of viscous liquid, which, under the action of the relative motion of the rollers and the deformation of the textile base, forms a pressure distribution that directly determines the thickness and uniformity of the coating.

The mathematical description of such a process is complicated by the interconnected influence of the geometry of the rollers, the rheological properties of the polymer, the permeability and deformability of the textile, as well as possible cavitation phenomena in the zone of the divergence of the rollers. The purpose of numerical modeling is to determine the pressure distribution and the gap profile between the rollers, taking into account the specified factors, as well as to establish the regularities of the influence of structural and technological parameters on the efficiency of the coating process.

A generalized mathematical model of the polymer coating process has been developed, based on the Reynolds equation, taking into account the deformation of the textile material and its permeability. The proposed model allows for an adequate description of the hydrodynamic processes in a thin layer of polymer between the rollers.

The transition to the dimensionless form of the equations was made, as a result of which it was established that the behavior of the system is determined by three main dimensionless parameters: the geometric parameter of the curvature of the roll, the parameter of the deformability of the textile and the parameter of the permeability of the material. The obtained numerical results are consistent with classical analytical models of calendering in the corresponding limiting cases, which confirms the correctness and reliability of the proposed methodology.