Analytical model of liner with previous loads

Abstract

Purpose. Development analytical model of the liner, taking into account its previous tension, structural and technological parameters and physical-mechanical characteristics of the rubber material, for modeling its deformations in the radial, longitudinal and circular planes. Methods. Analytical, mathematical modeling. Results. On the basis of the equilibrium equations for a cylindrical shell, taking into account the isotropy of the medium and the without momentary stress state, the spatial of forces and the preliminary tension of the liner, a system of analytic equations is developed that enables modelling of the deformations of the liner, which is the factor of its closure. The analytical dependences of the deformation of the liner in the longitudinal, circular and radial planes, depending on its structural parameters and physical and mechanical characteristics of the material, are developed. Parameters for deformation simulation are: R – radius of liner, Е – modulus of elasticity, 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 simulated along its entire working length. Conclusions. The obtained dependences allow simulating the deformation of the liner in the longitudinal, circular and radial planes, depending on its structural parameters and physical-mechanical characteristics of the material. The developed analytical dependences take into account the preliminary tension of the liner, the vacuum pressure and makes it possible to model, depending on the central angle in the radial plane of the cross-section of rubber. The use of developed analytical dependencies makes it possible to substantiate the basic parameters that influence the technological process of milk yield cows Keywords: liner, vacuum pressure, modulus of elasticity, radial deformation, coordinate system, tension of rubber, the cylindrical shell, the isotropic medium.