| Cycloid pin wheel transmission system is widely used in precision manufacturing fields such as aerospace,medical equipment,and industrial robots.In particular,the RV reducer developed by the principle of cycloid pinwheel transmission has been listed as one of the three core technologies of industrial robots due to its advantages of large transmission ratio range,high transmission accuracy and strong impact resistance.However,the structure of the cycloidal pinwheel transmission system is complex,and its dynamic behavior is affected by many factors in the actual working process.Therefore,the cycloidal pinwheel transmission system is more prone to vibration and noise problems than ordinary mechanical systems.In order to improve the vibration problem of the cycloid pin-wheel transmission system and improve its stability and reliability in the working process,it is necessary to conduct an in-depth study on its nonlinear dynamic behavior.This paper takes the cycloidal pinwheel transmission system as the research object,and uses the concentrated mass method to establish a 21-degree-of-freedom coupled bending-torsion nonlinear dynamic model.The model considers factors such as time-varying meshing stiffness,tooth flank clearance and transmission error,and considers the eccentric rotation of the cycloid and the orbital movement of the crankshaft according to the actual transmission situation.The Lagrange method is used to derive the differential equations of motion of the system.Aiming at the characteristics of positive semi-definite,variable parameters and strong nonlinearity of the differential equations of the system,the relative meshing displacement of the cycloid and pin gear is used as the generalized coordinates of the system,and linear transformation is used to transform the equations into a unified matrix form to eliminate the influence of rigid body displacement.The dimensionless processing of the equation reduces the order of magnitude in the equation and lays a foundation for subsequent solutions.Determine the calculation method of each parameter in the model,and solve for each parameter.By analyzing the natural frequency results,the rationality and correctness of the model are verified.By summarizing the mode shape,the analysis shows that the first-order natural frequency has the greatest influence on the dynamic performance of the system.The analysis of the influencing factors of the first-order natural frequency of the system provides a certain reference for the selection of the structural parameters of the cycloid pin-wheel transmission system.According to the characteristics of the model,Fourier transform and harmonic function are used to derive the specific form of excitation force,select the appropriate initial value conditions,use the row and column method to solve the static deformation of the system,and finally reduce the price of the differential equation to prepare for further solution.The variable step length Runge-Kutta method is used to solve the differential equations of the system,combined with the global analysis method and the local analysis method to study the influence of the tooth backlash,dimensionless frequency,meshing stiffness,external load and damping ratio on the response characteristics of the system,and obtain The path of the system from bifurcation to chaos.The research in this article reveals the dynamic characteristics of the cycloidal pinwheel transmission system,and provides a theoretical basis for improving the vibration and noise problems of the system during operation. |
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