Gear surfaces three-dimensional slope deviation evaluation method

Addressing the limitation of traditional gear slope deviation evaluation methods confined to two-dimensional (2D) characteristic line analysis, this paper proposes a new three-dimensional (3D) slope deviation evaluation index based on the normal vectors of discrete points on the tooth flank. A 3D point cloud average deviation plane is established based on the least squares method. The normal vector of this plane is extracted and decomposed into the profile and helix directions to construct the evaluation index. The relationship between the 3D slope deviation evaluation index and the 2D slope deviation indicators is analytically derived, thereby achieving a quantitative characterization of the degree of inclination of the entire tooth flank. The effectiveness of the proposed 3D tooth flank slope deviation evaluation method is verified through simulation and experiment. Under complex deviation conditions such as twist, the new method can more comprehensively reflect the 3D topographic characteristics of the tooth flank. This research provides a theoretical foundation for the 3D gear accuracy evaluation system and significantly enhances the completeness of tooth flank quality control.