The sucker-rod string is the most important element to transmit movement to a deep-barrel pump’s plunger. Apart of regular loading, sucker-rod pump plant usage is accompanied by a wide range of oscillations, inertial and shock loadings, causing possible accidents. Therefore, sucker rod protection is an urgent problem; its solution will increase sucker-rod pump plant’s efficiency and save on additional costs. To solve these, the authors propose to use shock absorbers for sucker rod strings, which designed based on packages of annular plates. Such elastic elements are technological and simple to manufacture and operate. The work presents the main concepts of mechanical and mathematical modeling of such shock absorbers and studying the most important performance – the strength and rigidity of the shock absorber.

To describe the deformation of a shock absorber we construct a mechanical and mathematical model of the plate package. We assume that in the package of two plates (Fig. 1) there are no cross-links and friction between the plates. Each of them is deformed as the separate plate, which has its own neutral surface. The load on the package of plates is distributed between the plates in proportion to their stiffness in bending. A package of thin plates was modeled as an equivalent solid plate with a cylindrical rigidity providing equal properties of the solid model and the plate package [1, 2]. To find the submersion of the shock absorber we solve equation for the axisymmetric bend of the circular plate and obtain

,

where D is the cylindrical stiffness,  is Poisson's coefficient. It should be noted, at time of bending the working links, it is appear the tangential stresses due to the shear strain which can be neglected for thin plates, while the accuracy of calculations is still high. The process of loading can be assumed as quasi-static and the calculation of the strength and the submersion of the device does not require the correction.

To illustrate obtained results we choose a plate spring with parameters , , , , which correspond to the real device. There is the diagram of the submersion of the shock absorber from the external load at different thicknesses of the working plate package (Fig. 2). It should be noted that the flexibility of the elastic suspension can be easily adjusted, to change the number of working links, or to vary the thickness of the plate package. To extend the load range at which the device works efficiently, the working links of different thicknesses can be used, and if it is necessary for increasing the working capacity, it is a constructive possibility to include the working links in parallel operation.

Thus, it is proposed the new design of the plate shock absorber and studied its performance characteristics and obtained simple engineering formulas in this work.