A method to estimate minimum tooth number for flexspline in harmonic drive

Selection of the tooth number is a challenging problem for engineers in designing harmonic drive, since the tooth number cannot be lower than a certain limit because of the gear strength. However, there is no equation to calculate the minimum tooth number for flexspline. In the present work a mathematical relation has been established to estimate the minimum tooth number for flexspline in harmonic drive based on the theory analyses in radial deformation, section stress, fatigue strength and safety factor on the flexspline, which changes the present situation that little research is done on the relationship between the strength of flexspline and its tooth number in open technical literature. The derived mathematical relation enables one to select a suitable tooth number for practical purposes in designing new harmonic drive; it could also be used to verify the fatigue strength in existing harmonic gear assembly.