Plain bearings are usually used in internal combustion engines and reciprocating compressors. These bearings have thin-walled liners and are multilayer. When calculating the bearing assembly of an engine, it is rational to use a hierarchical approach, from simple to complex, when choosing a mathematical model at certain stages of bearing design. A one-dimensional mathematical model is often used as a first step. This article uses the results of approximating the graphs by analytical dependencies, in particular, the relative eccentricity on the load factor of the plain bearing at different values of the ratio of the bearing length to its diameter, and the volumetric oil flow rate on the relative eccentricity for different bushing girth angles. The approximation of graphical values using exponential functions was performed using the pwrfit functions built into Mathcad. The estimation of the quality of the approximation was assessed statistically - the correlation index, which was more than 0.999. Using approximations, a refinement calculation of the sleeve bearing for a high-speed small-size air-cooled diesel engine 1h 8.0/7.5 was carried out. The results obtained have confirmed that the labor intensity has significantly decreased, the calculation can be automated by connecting the corresponding module to the previously developed diesel engine automatic design system. © 2022 American Institute of Physics Inc.. All rights reserved.