Double-arc Tooth Profile Design And Analysis Of Harmonic Gear Drive

A new type of double-arc tooth profile of harmonic drive is designed by using the elliptical cam as wave generator and the cup flexspline in the no-load condition as the object, calculating the instantaneous transmission ratio of harmonic drive and analyzing the spatial mesh motion. And the genetic algorithm is used to optimize and analyze the parameters of double-arc tooth profile.Since the nominal transmission ratio of harmonic drive can’t accurately characterize the actual transmission situation at the engagement portion, and the problem that the instantaneous transmission ratio at the engagement portion has not been clearly defined, this paper establishes a more comprehensive spatial mesh model of harmonic drive to analyzes the actual relative movement at the meshing portion based on the Willis theory and deduces the calculation formula of the instantaneous transmission ratio. The result of the calculating example shows that the instantaneous transmission ratio changes periodically. And the characteristic curve as well as the radial deformation is the key impact factors for the stability of harmonic drive compared with the nominal transmission ratio.To avoid the complex and error-prone drawbacks of the conventional kinematics method, an improved kinematics method is used to analyze the spatial mesh motion of harmonic drive and deduce no deformation matrix of the spatial mesh motion of harmonic drive. A new type of double-arc tooth profile is designed which can be correctly expressed by using fewer parameters. According to the segmented characteristics of double-arc tooth profile, this paper proposes a way to express the tooth profile equation by using polar angle and pressure angle.Selecting the tooth profile parameters and the radial deformation as optimal variables, and the maximum conjugate range and the maximum engagement depth as optimization objectives, the genetic algorithms are used in the process of multi-objective optimization of the designed double-arc tooth profile. And the features of double-arc tooth profile are analyzed. Based on the interference principle, it is described in detail how to choose conjugate profile. An algorithm for data approximation with optimal arc spline is used and the fitting parameters are used to be the basis of Circular Spline. The relationship between optimization objectives is explored based on weight coefficient method, and the performance of optimization objectives of different weights is evaluated by the changes of the instantaneous transmission ratio. The performance of the designed profile at the different forms of wave generator is also explored. Optimization variables how to change tooth profile and affect the transmission performance are explored in this paper. A comparison between the parameters of the foreign circular arc tooth profile and the optimum parameters is to verify the reasonableness of the designed tooth profile.