Elastic Dynamics Analysis And Optimization Design Of Parallel Mechanism Based On Finite Element Method

Parallel mechanisms have outstanding performance in terms of load-bearing capacity and working accuracy,and it is a research hotspot in advanced manufacturing.With the advancement of technology,the requirements for parallel mechanisms in various industries are becoming higher and higher.Lightweight and efficient are the current parallel mechanisms development trend.Due to the decrease in mass,the flexibility of its components will inevitably increase.It is no longer possible to meet the performance requirements of theoretical research as a traditional rigid body system.Therefore,it is necessary to consider the impact of the elastic deformation of its flexible components on the performance of the mechanism.In this paper,the 3-UPU parallel manipulator in the model grasping mechanism is studied in terms of kinematics,rigid body dynamics,elastic dynamics considering flexible deformation of components,sensitivity analysis of elastic dynamics and optimization of structural parameters.First,the kinematics analysis of the parallel mechanism.This paper uses the vector method to analyze the location of the organization,combined with the constraint conditions,the limit boundary search method is used to determine the reachable working space at the end of the mechanism;the derivative method is used to determine the Jacobian matrix of the mechanism,and the singularity of the mechanism is analyzed;The acceleration and inverse solution models are modeled,analyzed and verified with Matlab and Adams.Then,the rigid mechanism dynamic analysis of the parallel mechanism is carried out,and the virtual work principle is used as the theoretical basis for modeling.After the force analysis of each component in the mechanism is completed,the mechanism inverse dynamic model is established,and the model is solved and verified by Matlab and Adams;In the analysis of the elastic dynamics of the parallel mechanism,the finite element method is used to treat the flexible telescopic rod in the parallel mechanism as a beam element.The elastic dynamic model of the unit is established in accordance with the Lagrange equation,and the parallel mechanism is finally established according to the coordinate transformation relationship and the constraints And verify the elastic dynamics model.Then on the basis of the elastic dynamic modeling of the parallel mechanism,the expressions of the stress on the flexible telescopic rod and the natural frequency of the system are derived,and the direct integration method is used to program the elastic dynamic model of the mechanism to obtain the kinematic error of the end of the parallel mechanism,Variation of stress and flexible system natural frequency on flexible telescopic rod.Finally,by analyzing the change law of the elastic dynamics-related parameters of the mechanism,the dynamic platform mass of the parallel mechanism and the cross-sectional area of the flexible telescopic rod are determined as design variables,and the elastic dynamics model is processed by the direct differential method to obtain the system elastic dynamics parameters For the sensitivity model of design variables,through the analysis of calculation examples,the kinematic errors of the end of the parallel mechanism,the stress on the flexible telescopic rod and the natural frequency of the system to the sensitivity of the design variables are obtained to determine the optimization variables,goals and constraints in the optimization problem.The NSGA-? algorithm is used for optimization,and the optimized parallel mechanism model is analyzed for elastic dynamics behavior.The comparative analysis determines that the optimized mechanism's kinematics,stress characteristics,and frequency characteristics are actually improved,proving the rationality of the optimization results.