Existing research on harmonic drive gears mainly focuses on two-dimensional tooth profile design and simple modification along the tooth direction. Three-dimensional redesign of the tooth profile can effectively reduce the influence of flexspline deformation on meshing characteristics. However, current three-dimensional design methods often overlook the combined effects of the actual hobbing process and addendum modification. In this paper, a three-dimensional tooth profile design method considering the actual hobbing process and addendum modification is proposed. The basic tooth profile of the harmonic drive is constructed by adopting the approximate rack method considering the scaling factor. A design method incorporating the hobbing process is proposed by analyzing the deformation of the flexspline, and the influence of the design parameters on tooth profile deviation is analyzed. The tooth profile after addendum modification is calculated iteratively based on the envelope curve generated by the motion trajectory of the flexspline. Multiple cross sections are combined to form the three-dimensional tooth profile. The final design solution is evaluated in terms of assembly situation, motion trajectory, meshing backlash and tooth contact characteristics. The results show that the addendum-modified tooth profile exhibits a significant torsional effect, while the circumferential deviation is minimized when the radial deformation coefficient is 1 and the scaling factor is 0.5. About 68.75% of the tooth pairs maintain continuous meshing. Backlash ranges smoothly from 0.015 μm to 1.88 μm with an average of 0.93 μm over the 0° to 59.5° conjugate range, and is uniformly distributed along the tooth direction. At a torque of 63 N·m the three-dimensional tooth profile reduces the peak contact stress by 59.3% to 623.488 MPa compared with the straight tooth profile and achieves a more uniform stress distribution. This study proposes a three-dimensional tooth profile design method for harmonic drive to achieve good meshing characteristics and improved tooth contact stress distribution.
Xiao et al. (Sun,) studied this question.