## 2 Materials and Methods
A certain disadvantage of the existing methods of profile modification is that the shape of the profile modification line is selected for both wheels independently of each other. For this reason, solving this problem is a complex procedure that requires multiple calculations and bench experiments, and this approach does not lead to a consistent improvement in the quality of engagement, since the elimination of stress peaks for one section of the gear profile can lead to peak loads in other sections of the profile. Errors in determining the shape of the profile modification line can also lead to increased vibration due to a violation of the conjugacy of the engagement of gears under load. When two modified teeth contact, a position error occurs, the contact point shifts from the theoretical engagement line, which leads to a deviation from the specified gear ratio. This error is characterizedas the difference in the positions of the ideal driven link (without errors) and the real one (with an error). The magnitude of contact and bending stresses, as well as the vibration activity of the gear transmission, is also determined by the reduced radii of curvature at each point of contact of the moving tooth profiles [5, 6]. To determine the position error and the reduced radii of curvature, it is necessary to solve the inverse problem of the theory of gear engagement, i.e., to determine the law of their motion based on the given shape of the tooth profiles. The currently existing methods allow finding a solution only for profiles specified by a theoretical function, and they allow finding only one contact point. This solution is not sufficient for practical purposes, as when the profile shape is specified using the results of gear measurement, it can lead to a solution error, especially for the double-sided helical traction transmission of electric locomotives [7]. The analysis showed that in order to improve the quality of designing gears with the required strength and vibration indicators, it is necessary to develop and apply a comprehensive method for calculating and selecting the geometric parameters of double-sided helical traction transmission of electric locomotives, ensuring the required stress state of the teeth. The initial data in the new design method are module, number of teeth, angle of the original contour, thickness or thickness coefficient of the tooth at the top, radial clearance coefficient, offset coefficient, and angle of inclination of the teeth. Although the design is independent of the tool, and various gear cutting methods can be used to obtain the required profile shape, in each individual case, it is necessary to determine the parameters of the tool selected for shaping. In previous works and methods [1, 2, 3, 4, 5, 6, 7], the tooth thickness was not included in the initial parameters of gear wheels, although this parameter determines many design and technological indicators of gear transmissions and the kinematic characteristics of the gear wheel, the resulting transfer functions from dynamic loads were not taken into account, and a dynamic calculation of the bending and contact rigidity of the teeth of the gear and wheel of the double-sided helical traction transmission of the VL-80s electric locomotive was not carried out, as well as the development of a new method for calculating the strength of teeth based on bending and torsional stresses, taking into account diagnostic parameters according to operating data. In this regard, in this article proposed by us, the subject of the study is the dynamic calculations of the bending and contact rigidity of the teeth of the pinion and wheel of the double-sided helical traction transmission of the VL-80s electric locomotive, as well as the development of a new method for calculating the strength of the teeth based on bending and torsion stresses, taking into account the diagnostic parameters according to the operating data.