Problem. The studies on preparation and application of Ti–Cr–N coating on the surface of the 38Х2МЮА steel have been conducted. Goal. The purpose of the work is to investigate the feasibility of using a fractal approach to evaluate the effect of plasma coatings to increase the wear resistance of parts of a volumetric hydraulic drive. Methodology. Cr was chosen as the material for ion bombardment, since it makes it possible to reduce the temperature of the substrate before applying the coating and avoid the risk of surface softening. After heat treatment of the 38Х2МЮА steel, its hardness ranges from 40 to 45 HRC. The thickness of the applied coating varied from 3 to 6 microns, which corresponds to good adhesion, a smaller thickness does not significantly affect the properties of the product, and in the case of a thickness of more than 6 microns, peeling is observed due to poor adhesion to the substrate. Results. Five series of experiments with HRC hardness values of 42, 43, 44, 45, 46 were performed. Fractal analysis was used to assess the effect of the Ti–Cr–N coating structure of the working surface of volumetric hydraulic drive parts on its wear indicators. The relative error in calculating wear indicators for fractal models ranged from 0.04 to 8.96. The correlation coefficient of Y(X2) model without using indicators of the surface fractal dimension was only 0.73. Experiments proved that the lowest wear value of 2.11 g*10-3 was obtained at a coating thickness of 6 µm and hardness of 45 HRC. At the same time, a roughness coefficient was 0.16. To confirm this hypothesis, an experiment to determine wear resistance at a hardness of 45, roughness of 0.16, and coating thickness of 6 was conducted. Conclusions. Results of the studies of wear indicators of Ti–Cr–N coated samples at the substrate material hardness values from 42 to 46 HRC, surface roughness and coating thickness showed feasibility of the fractal structure estimation approach.