Calculations of strength, forecasting the residual operation life for repairing traction gears (TG) is carried out on the results of modeling their motion characteristic, which is based on the determined coordinates of the contact points of the gear and wheel profile for the period of engagement (engagement line). This article presents results of a study aimed at developing mathematical dependencies for a refined determination of TG engagement line with the established wear of gear teeth. Adequacy verification of proposed mathematical descriptions was carried out based on the results of the study of new TG of ER-2 electric train series. Their comparison with the coordinates of the engagement line, calculated by the traditional method, showed that modelling uncertainty does not exceed 0.06%. As an example of practical use of the received mathematical descriptions, results of research of motion characteristic of new TG of ER-2 electric train series with the established degrees of wear of gear and wheel teeth are presented.