Design Method of Conjugate Tooth Profile of the Harmonic Gear Drive Based on the Numerical Envelope Method

In response to the optimization problem of meshing regions caused by the S-shaped tooth profile in the harmonic gear drive, a method for effective edge-conjugate tooth profile design was proposed. This method effectively avoids the difficulties of solving the complex S-shaped tooth profile equation. The convex tooth profile of the S-shaped tooth profile was taken as the base tooth profile. Tooth profiles of the flexspline and circular spline were designed using both the traditional backlash adjustment method and the effective edge-conjugate method. The meshing characteristics and contact stress of the tooth profiles designed by the two design methods were compared and analyzed through the plane numerical analysis and the finite element modeling. The research results show that the effective edge-conjugate tooth profile design method can achieve both quadratic and two-point meshing, increasing the gear's meshing angle and meshing arc length. The total number of meshing teeth per revolution is increased by 15.78%, with 55% of the flexspline teeth participating in the meshing, thereby enhancing the load capacity of the harmonic gear drive. Moreover, the effective edge-conjugate method leads to an enlargement of the contact area, reducing the maximum contact stress between the tooth profiles by 24.36%, which effectively decreases wear between the flexspline and circular spline tooth surfaces.