A novel method based on mechanical analysis for the stretch of the neutral line of the flexspline cup of a harmonic drive

• A novel method is proposed to calculate the stretch based on mechanical analysis.
• The relationship of internal forces and the location angle of the roller is analyzed.
• The lowest bending stress in the FS under this WG is discussed.
• The influence of the location angle of roller on circumferential strain is analyzed.
• FEA simulation results show that the developed model produces accurate results.

The traditional harmonic drive (HD) model is often simplified by assuming that the neutral line in a flexspline (FS) tooth rim is inextensible. The circumferential strain induced by the circumferential force is also always neglected. These simplifications may induce interference between the teeth and excessive deformation or may even require clearance to overcome the jamming resulting from the interference. In this study, a novel method based on mechanical analysis is developed for the stretch of the neutral line of the FS of an HD. First, the internal forces and the deformation of the neutral line of FS are formulated as a set of differential equations with a geometric constraint and equilibrium equations with continuous conditions. Next, the circumferential strain is calculated using Hooke's law for the circumferential force in the assembly state. The stretch between two adjacent teeth of the tooth rim is calculated by solving an integral equation for the circumferential strain. Finally, FEA models are constructed to verify the theoretical results and to determine the circumferential strains in the tooth rim on the FS. The simulation results demonstrate that the method developed is highly accurate.