Three-dimensional Nonlinear Modal Study Of A 3-RRCPR Mechanism Considering Kinematic Pair Clearance

Pointing mechanism is widely used in aerospace field,and its pointing accuracy and stability have great influence on the working performance of applied equipment.Vibrations can affect the pointing accuracy and stability of the mechanism,and considering factors such as clearance and posture changes can cause nonlinear characteristics to appear in the modal properties of the mechanism.Therefore,studying the modal properties of the mechanism under various nonlinear factors is of great significance.This paper focuses on a new type of spatial parallel pointing mechanism and establishes a three-dimensional nonlinear vibration model considering clearance.The theoretical model is verified through simulation and experimentation to understand the dynamic characteristics of the mechanism.The main research content is as follows:Firstly,a three-dimensional vibration model incorporating elastic springs and dampers was established for a parallel mechanism with three rotating pairs,a moving pair and a cylindrical pair,short for 3-RRCPR parallel mechanism.The velocity and acceleration equations were established using the link recursive method,and the dynamic equations of the mechanism were derived based on the virtual work principle method,considering the elastic strain energy of hinges and links.The vibration differential equation for the parallel pointing mechanism was derived,and the inherent frequency of the mechanism was obtained by using the mass matrix and stiffness matrix calculated during the modeling process.Finite element simulation was employed to validate the model.This modeling method enables rapid determination of the overall stiffness and vibration characteristics of the mechanism during posture changes.Next,a clearance model was established for the rotational pairs of the pointing mechanism.The clearance was simplified using the massless rod method,and the dynamic equations were established using the Newton-Euler method.The range of clearance parameters was obtained using the Runge-Kutta method.Based on the ideal mechanism’s vibration model,a modeling method was proposed for the vibration differential equation of a mechanism with clearance.The inherent frequency of the mechanism with clearance was calculated using MATLAB,and the effects of different clearance and posture parameters on the modal characteristics of the mechanism were analyzed.The model was verified using finite element simulation.Finally,based on the modal analysis results of the 3-RRCPR parallel mechanism,the natural frequencies and corresponding vibration modes were obtained.The locations with significant deformation were selected as the excitation and measurement points for experimental testing.ANSYS was used to conduct pre-experimental analysis of the pointing mechanism,and the optimal excitation and measurement points were identified.Based on the pre-experimental analysis,a mechanism testing platform was constructed,and the natural frequencies of the mechanism were measured to validate the theoretical and simulation analyses.