The paper discusses the process of normal friction and wear as a result of fretting corrosion, as well as measures to reduce its level. There are considered the issues of reliability and accuracy of the connection of “shaft - sleeve with key” type, which is of particular danger. The disadvantages of the considered connections are shown, namely the relative complexity of the disassembly-assembly processes; high level of stress concentration; the tendency to corrosion at contact. There has been proposed a physically based mathematical model of the wear process for the strengthened surfaces of the flexible coupling parts on the friction conditions. By using the friction work value, the model allows determining the wear expressed through the change in the surface roughness. A method has been developed for determining the constant of the wear equation for various materials of friction pairs. Using the energy and economic criteria, the technique of the integral description of the method for achieving the required quality of the surface layers of the elastic coupling parts is given. A mathematical model has been developed to reliably allow predicting the wear amount for the surfaces of the elastic coupling parts whose surface layers are formed in various ways. It is proposed a system for the directed choice of the technologies to produce the surface layers of the flexible coupling parts taking into account all the stages of their life cycles. In doing so, both economic and environmental requirements are also taken into consideration. The use of the system for the direct choice of the technology to ensure the required quality of the flexible coupling parts at the repair stage allows more economically solving the problem of restoring their performance. As practice shows, at this stage, the application of the results of the scientific research gives a significant economic effect.