Mathematical modelling of contact pressure distribution between conical sealing inner surface and cylinder wall

In some cases, sealing the cylindrical surface of the pipe is necessary to carry out by a sealing element having frustoconical shape. This occurs due to the difference of the outer diameters of the pipe and the coupling which passes through the apertures of the sealing element, thereby increasing the gap between the inner surface of the sealing element and the sealed wall of the cylinder. And this in turn leads to a complication to achieve tightness of the cylinder surface. Then, to achieve tightness of the cylinder wall at a low axial load and improve the sealing ability of the sealing element, it is performed in the form of truncated cone. Upon application of an axial load the truncated cone with outer surface sliding along the body, tapers inward thus reducing its inner diameter. This results in a more uniform deformation of the inner cylindrical surface of the sealing element that strongly influences the character of the contact pressure distribution between the cylinder wall and the inner surface of the sealing.The tightness of the body surface of the cylinder wall is achieved by unilateral axial compression of the sealing element. The solution to the problem is performed in two stages. The first step - the compression of the sealing element to its contact with outer surface of the cylinder wall, and the second stage - achieving tightness.Вasing on the Euler equation we obtain the differential equation of equilibrium of the sealing element. The resulting equation is a differential equation with variable coefficients. Its solution is implemented by Ritz approximation method. The contact pressure between the outer surface of the sealing element and the cylinder wall after their complete contact is determined by analogy of beam on elastic base.The magnitude of the axial load to achieve tightness was defined. The dependence between the value of the axial load required for tightness and geometricdimensions was determined. It is shown that the higher the sealing element, the higher is the axial load required to achieve tightness. Besides, the contact pressure distribution between the inner surface of the conical sealing and the cylinder wall was defined.