ANALYTICAL SOLUTION OF THE PROBLEM OF DETERMINING RESIDUAL STRESSES IN SHAFTS AFTER STRENGTHENING TREATMENT BY PPD METHODS

Abstract

The article is devoted to the analytical solution of the problem of determining residual stresses in shafts after strengthening treatment by surface plastic deformation (SPD) methods. A shaft is an important component in mechanical engineering. Its durability depends on the condition of the surface layer. Surface plastic deformation is an effective method of finishing. The essence of the method is to compact the metal structure with a tool without removing a layer of material. As a result, hardness increases, compressive residual stresses are formed, and fatigue resistance increases. Among the SPF methods, roller burnishing is particularly widespread. For low-stiffness shafts, this method requires precise calculation of parameters. The aim of the study is to obtain analytical expressions for axial, tangential, and radial residual stresses at any depth of the plastically deformed layer. The solution is based on the differential equation of equilibrium, taking into account the replacement of the radial coordinate. The parameter λ(z) of the residual shear modulus of the hardened layer is introduced. It describes the nonlinear behavior of the material in the deformation zone. It has been established that the radial residual stresses have a positive sign. They are zero at the surface and increase with depth to a maximum at the boundary of the plastically deformed layer. Tangential and axial stresses are negative and correspond to compression throughout the entire thickness of the hardened zone. It has been found that a single static load does not reproduce real running-in conditions. During hardening, shear deformations occur in the directions of roller feed and rolling. They increase the hardness gradient and reduce radial deformation by 15–20% compared to the calculated data. Taking these effects into account significantly improves the correspondence of theoretical diagrams to experimental results. The proposed approach is presented in a form convenient for practical application. Based on it, it is possible to reasonably assign PPD modes such as rolling force, tool parameters, and feed. This allows the formation of a system of compressive stresses of the required intensity in the surface layer of the shafts.