Nonlinear Dynamic Modeling And Analysis Of Harmonic Drive

As the core of intelligent robot joints,harmonic drives have a series of unique advantages such as small size,large transmission ratio,small gap,and light weight.They have been widely used in aerospace,industrial logistics,medical health,life services and other important fields.However,the microscopic transmission mechanism inside the harmonic drive is complicated and unknown,and it will be adversely affected by nonlinear transmission attributes such as hysteresis,friction,and kinematic error during operation.In view of this,this article respectively carries out nonlinear dynamic modeling and analysis of the hysteresis,friction,kinematic error of the harmonic drive,and builds a harmonic dive dynamic model that comprehensively considers the three nonlinear transmission attributes and the stiffness of the wave generator,which lays the foundation for the design of the intelligent robot controller of the harmonic drive.The main research work and research results of the thesis are as follows:(1)Analyze and model the hysteresis of the harmonic drive.Through the analysis and comparison of the hysteresis generation mechanism,the conclusion that the hysteresis of the harmonic drive is caused by the nonlinear elastic deformation of the flexspline and the pre-slip friction between the meshing tooth surfaces is obtained.Aiming at the existing models' problems of the unclear physical meaning,the large number of identification parameters required,and the unsmooth hysteresis curve obtained,a hysteresis model of harmonic drive combining a "cubic polynomial" and a "Dahl pre-sliding friction model" is proposed.Through simulation experiments,the rationality and simplicity of the model are verified;(2)Analyze and model the nonlinear friction of the harmonic drive.Focusing on the problem that “the position and mechanism of the internal friction of the harmonic drive are not uniform”,the friction is divided into “sliding friction between the outer rim of the flexible bearing of the input end wave generator and the inner wall of the flexspline” and “pre-sliding meshing friction that occurs between tooth surfaces of the flexspline and circular spline”.Considering the effect of lubrication on the former,a calculation model of friction torque between the outer rim of the flexible bearing of the wave generator and the inner wall of the flexspline under the condition of mixed elastohydrodynamic lubrication is proposed,and therefore the friction torque of the input end of the harmonic drive is theoretically calculated under different input speeds and different loads;.Through simulation experiments,the correctness of the calculation model is proved;(3)Analyze and model the kinematic error of the harmonic drive.This paper analyzes and discusses the generating mechanism of the two major components of kinematic error(that is,"pure kinematic error" and "flexible kinematic error"),and clarifies the different effects of the kinematic error components of each part on the transmission performance of the drive.A simple measurement method of kinematic error is determined after the comparison and argument from the two aspects of "single flexible body" and "double flexible body"(that is,both the flexspline and the wave generator are regarded as deformed bodies).Based on the Fourier series as the theoretical basis,the mathematical model of the kinematic error is obtained;(4)Nonlinear dynamic modeling and analysis of harmonic drive robot joints.Based on the above research results,a nonlinear transmission model of harmonic drive,named STL(Serial Transmission Lag)model,which can quantitatively describe the hysteresis,friction,kinematic error,wave generator stiffness and their coupling relationships is proposed.Taking the STL model as the core and under the premise of knowing the input and output angular position of the drive,the "multi-factor coupled harmonic drive joint robot dynamic model" is derived.Through the analysis of the experimental results of step response,the effectiveness and correctness of the dynamic model are verified.