The disadvantage of the geometry of thin-walled parts, in terms of processing, is the low ability to resist static and dynamic loads. It is caused by the elastic deformation of elements with a low stiffness. Modelling approaches for the evaluation of deflections during machining are presented. Mathematical models of deflections, cutting forces and harmonic response are proposed. The processes of material removal and deflection of a thin-walled sample at the critical points are modelled. A frequency analysis was performed, consisting of a modal analysis of natural frequencies and a harmonic response analysis. As a result, a graph of the deflections amplitude from the frequency of driven harmonic oscillations is generated. The analysis of the obtained values was performed. As a result, the resonance frequency and maximum amplitude of oscillations for the operating parameters are determined.

Ensuring the vibration reliability of power equipment is one of the fundamental problems in modern power machinery. This problem has become more critical due to a permanent increase in the machining performance of high-speed milling of axial turbine blades. This article aims to identify reliable vibration parameters for high-speed milling of turbine blades to increase the energy efficiency of gas and steam turbines. For this purpose, mathematical models of free and forced oscillations of turbine blades during machining were developed. As a result of considering experimental and finite element analysis data, critical frequencies and corresponding mode shapes of free oscillations were identified using regression procedures by the best fit of analytical and empirical approaches. Additionally, after considering the forced oscillations of blades during high-speed machining, the magnitude of the specific cutting force and external damping ratio in the system ‘axial turbine blade and milling head’ were evaluated. The resulting magnitude of forced oscillations during machining was calculated. Finally, the amplitude–frequency response was also assessed, considering the machining parameters. Overall, the proposed methodology increases energy efficiency due to a decrease in the obtained machining quality of turbine blades.