A MATHEMATICAL METHOD FOR EVALUATING THE GEOMETRIC CONFORMITY OF TOOTH SURFACES IN BEVEL AND HYPOID GEAR TRANSMISSIONS

This paper proposes a method for evaluating the geometric conformity of tooth surfaces in bevel and hypoid gear transmissions. The study determines the mutual geometric deviations between theoretical and actual (conjugate) tooth surfaces based on their spatial mathematical models. The deviations between the tooth surfaces are calculated in the normal direction for discretely selected grid points along the axial section, and the obtained values are approximated using a second-order surface. The conformity coefficients are determined using the least squares method, enabling a quantitative characterization of the spatial mismatch of the tooth surfaces.