Modeling harmonic drive with small deformation of flexspline and assessment of tooth wear by sliding coefficient

Reducing the flexspline (FS) deformation is important for decreasing the alternating stress, flare angle in the axial direction, spatial deformation of teeth, and tube length. However, it may increase the probability of insufficient engagement depth and nonexistent conjugate tooth profiles. In this study, a mathematical model of the harmonic drive (HD) with a new tooth profile is proposed to reduce the FS deformation while satisfying the engagement depth and existence of a conjugated tooth profile. First, the generation mechanism of the new tooth profile is discussed in detail and the connection method of the circular arc tooth profile and transition tooth profile in the FS were presented. Then, two key parameters of the model, the translation distance and offset distance were studied to design the ideal tooth profile. Finally, a tooth root chamfer method was proposed to achieve smooth operation of the HD. Additionally, owing to the lack of a wear assessment of the new tooth profile, a sliding coefficient calculation model was presented. To verify the feasibility of the models, a prototype with a radial deformation coefficient of 0.8 was designed, processed, and tested. The experimental results were consistent with the theoretical analyzes.