Study on tooth profile design of harmonic drive with deformation model of flexspline

The neutral curve of a flexspline (FS) is usually represented by the function curve of cam-shape curve in the traditional harmonic drive (HD) model. This representation may induce tooth tip interference and excessive deformation. In this study, a novel mathematical model of the FS deformation is established to accurately depict the neutral curve. Then, a tooth profile design method is proposed based on this model, which can obtain an exact conjugate tooth profile when giving an initial tooth profile. In addition, another design method that does not demand the initial tooth profile is proposed for simplicity of design. The HD designed by this method has a larger number of meshing teeth and a larger depth of engagement compared to traditional HDs. Moreover, a meshing model of a tooth pair is employed to verify the feasibility of the two design methods. Next, one of them is used to investigate the effect of the wave generator shape on the engagement of a couple tooth profiles, and the results show that the wave generator shapes with different parallel distances have no effect on the continuous engagement. Furthermore, an instantaneous transmission ratio calculation method of a tooth pair is developed for future calculations of the instantaneous transmission ratio between the input and output shafts of the HD. The calculation results manifest that the instantaneous transmission ratio of the tooth pair belongs to a variable transmission ratio.