Dynamic model of closure the liner

Abstract

Annotation Purpose. Develop analytical dependences for modeling the speed and dynamics of deformation of liner depending on its design parameters and physical and mechanical characteristics, taking into account the technological parameters of the process. Methods. Based on the system of geometric equilibrium equations for a cylindrical shell, taking into account the isotropy of the medium and the momentless stress state, the spatial action of forces and pre-tension of the liner, developed analytical equations that allow modeling the dynamics of deformation of liner in time, which allows to determine the time constant of the system “liner – milking cup”. Results. Analytical dependences of the dynamics of deformation of liner in time in the radial plane and the rate of deformation depending on its design parameters and physical and mechanical characteristics of the material are developed. Parameters for deformation simulation are: R – radius of liner, Е – modulus of elasticity, ρ – the density of the rubber material, h – thickness of liner, рн – vacuum pressure, l – the length of the active part of liner, ν – Poisson's coefficient for rubber, Fн – force of tension of liner. Depending on the central angle in the radial plane of the section, the shape of the deformation of the liner is modeled along its entire working length during the closing and opening stroke. Conclusions. The obtained dependences allow to model the dynamics of deformation of liner in the radial plane depending on its design parameters and physical and mechanical characteristics of the material. The developed analytical dependences take into account the pre-tension of the liner, vacuum pressure and allows modeling depending on the central angle in the radial plane of the rubber section. The use of the developed analytical dependences makes it possible to substantiate the main parameters that affect the process of closing and opening of the liner. The characteristic of the deformation in the cross section of the largest deformation is that the tension of the liner does not affect the deformation characteristic. This is due to the isotropy property of the cylindrical shell and the elastic isotropic properties. Keywords: liner, vacuum pressure, modulus of elasticity, radial deformation, coordinate system, tension of rubber, the cylindrical shell, the isotropic medium.