Research on reverse design method of small-modulus offset face gears based on modified surface optimization

Aiming at the problem of high-precision reconstruction of the tooth face of small-modulus offset face gears, a reverse design method based on three-coordinate measurement and optimization of modified surfaces is proposed. Initially, a coordinate system of tooth face conjugate expansion is established, and the theoretical tooth face radial vector equation and normal vector equation of the small-modulus offset face gear are derived; subsequently, the measurement coordinate system and measurement path are designed and planned, and the tooth face data of the sample gear are obtained by the high-precision coordinate measuring machine; thereafter, a comprehensive modified surface design method for the small-modulus face gear is given, and precise optimal modification parameters that closely approximate the tooth surface of the sample gear are solved through optimization iterations, enabling the reverse design of smooth tooth surface. Finally, comparative analysis and meshing experiments were conducted for the sample gear, the reverse-designed gear and other conventionally designed gears. The results show that the error in the range of working tooth surface between the optimized reverse-designed tooth surface and the original sample gear tooth surface is less than 2 μm, and the contact patterns are highly consistent, which is significantly better than that of the tooth surface designed by other methods, confirming the practicality and effectiveness of the proposed reverse-design method.