Nonlinear Dynamic Modeling And Controller Design Of Harmonic Reducer Considering Meshing Relationship

As a new type of transmission,harmonic drive has been widely used in industrial robots,aerospace,medical robots and other fields.Harmonic reducer has the advantages of small size,light weight,high transmission ratio,high transmission accuracy,etc.However,due to its unique transmission form relying on elastic deformation for transmission,it has caused its mechanical characteristics and complex meshing characteristics.Due to the existence of these problems,the design and innovation capabilities of domestic harmonic reducer manufacturers are greatly restricted.Therefore,exploring the internal meshing and friction mechanism of the harmonic reducer and establishing a dynamic model based on the physical relationship have great research significance for guiding the design and manufacturing of the harmonic reducer.This paper takes the common tangent double-arc double-arc tooth profile harmonic reducer as the research object,and proposes a method to calculate the stiffness and load distribution of the harmonic reducer.On the basis of this method,the time of the harmonic reducer is measured.The variable meshing stiffness was calculated;a method for modeling the nonlinear friction of the harmonic reducer based on the generation mechanism was proposed,and the model was verified;the dynamic model of the harmonic reducer was established,and the test data Make comparisons,analyze dynamic characteristics,and design controllers.This paper presents the derivation process of the tooth profile equation in the Cartesian coordinate system of the harmonic reducer with double arc tangent tooth profile,the calculation method of the minimum backlash between different tooth pairs,and the harmonics are obtained by calculating the stiffness of the single tooth The load of the reducer is distributed between the pairs of meshing teeth,and the overall meshing stiffness is integrated.The results show that the time-varying meshing stiffness of the harmonic reducer is very stable under no-load or full-load conditions;its time-varying meshing stiffness will fluctuate significantly under medium load.By considering various nonlinear factors,the contact friction torque,viscous friction torque and elastic deformation equivalent dissipative friction torque in the harmonic reducer are modeled,and the genetic algorithm is used for parameter identification,and the friction model of the harmonic reducer is established.Through the analysis of the model parameters,it is found that the elastic deformation energy dissipation of the harmonic reducer may account for as much as 30%-50% of the total energy loss.After modeling the dynamics of the harmonic reducer,the dynamic performance and speed error characteristics are analyzed;the inversion method is used to design the controller,which effectively suppresses the speed error and improves the dynamic performance of the system.The research in this paper can provide a more perfect theoretical basis for the tooth profile and structure design of the harmonic reducer,and has certain guiding value for production practice.