Increasing the durability of the cutting tool when restoring the profile of the rolling surface of railway wheels by controlling the vibrations of the machine-tool-part system. Vibrations arising during the turning of the rolling surface of wagon wheels under various cutting modes were studied. To do this, a matrix of experimental planning was built using the Box-Wilson method, according to which all factors change in turn (cutting depth, cutting speed, feed). After the experiment, a mathematical model is selected and the numerical values of the coefficients of this equation are estimated. In accordance with the power dependences accepted in the theory of cutting, a mathematical model was constructed for the experiments in the form of a logarithmic polynomial of the first degree series. Mathematical processing of measurement results using fractal dimension was carried out. The fractal dimension was determined by the normalized span method. A correspondence has been established between the durability of the he cutter and the intensity of its vibrations when turning railway wheels. A mathematical dependence of the fractal dimension on the cutting modes is obtained, which makes it possible to adjust the cutting speed or feed during the restoration of the rolling surface of the wheel in the presence of defects. Optimal cutting modes, which allow to achieve a given quality of the rolling surface of the wheel in the shortest possible time, give the highest value of fractal dimension. Defects in railway wheels such as sliders, bumps, and gouges lead to a decrease in fractal dimension. The determination of the fractal dimension in the process of turning wheelsets makes it possible to automatically adjust the cutting modes to ensure a given quality of the rolling surface of the wheel and the required durability of the cutting tool.
