The relevance of this study lies in the need to research the wear process of the elements of dynamic systems and to establish the dependence of the geometric and structural characteristics of wheels restored by plasma surfacing with a coating of 15Cr17Ni12V3F on dynamic, cyclically varying loads. The study was aimed to establish the dependencies between the deviation of the wear area, the formation of contact and fatigue stresses, and the change in the phase structure of the wheel defect. It is important to justify the permissible limits of wear of the transverse profile in the contact zone of a wheel and ridge. The object of the study was the dynamic interaction of the “wheel–ridge–rail contact surface” system. To achieve the goal, the following methodology was adopted: kinematic analysis, strength calculation, the use of mathematical analysis in dynamic system modelling, virtual modelling in the SOLIDWORKS software environment of the GearTrax application, experiment planning, and model correction through the results of metallographic studies. The results of the study are presented as reasonable prediction criteria that consider contact cycles during the formation of fatigue stresses at the stage of defect origin. The process of the dynamic interaction of the contact worn profile of a wheel with a railway rail is explored. Polynomial equations are proposed to substantiate the optimal design and technological parameters of designing a railway carriage wheel. The permissible limits of wear of the transverse profile in the contact zone of the wheel and the ridge are justified while taking the coefficient of the reduction of contact stresses in the metal into account. The dependences of the change in static load on the utilization factor of the railway carriage load capacity are established. The dependences of changes in fatigue stresses on the design deviation of the contact area of wheel wear are established. It is confirmed that the stress concentration under cyclic loads is formed in the ferritic layers of the material structure before the appearance of wear.