Study On Static And Dynamic Error Analysis And Compensation Algorithm Of A Kind Of Parallel Mechanism

In order to meet the major demand for efficient polishing equipment of aircraft composite skin in the field of aviation maintenance in China,our research group has developed a five DOF(degree-of-freedom)composite drive parallel mechanism.In order to analyze the working accuracy of the mechanism,the static and dynamic error modeling and error compensation algorithm are studied.In order to improve the working accuracy of the mechanism,this thesis deeply studies the inverse solution and positive solution of the mechanism,elastic dynamics modeling,static and dynamic error modeling and error compensation algorithm.The main contents and conclusions are as follows:The kinematic analysis of the mechanism is completed,and the geometric relationship between each component of the mechanism is obtained.The inverse position solution and the forward position solution of the mechanism are analyzed.Through the geometric relationship operation,the inverse position solution operation is completed,and the number of parameters of the forward solution equations is reduced to two.A simplified semi analytical forward position solution model is obtained,which improves the efficiency of the forward solution operation.Then,through the simulation comparison,the accuracy of the inverse position solution and the forward solution is verified,which provides a kinematic basis for the subsequent analysis.The dynamic equation is established based on Newton Euler method.Combined with the finite element method and substructure idea,the elastic dynamics analysis of the mechanism is completed,and the dynamic error of the mechanism is obtained.The parallel mechanism is divided into elements.The element stiffness matrix and mass matrix of the complex model are extracted by using the simulation software.The element stiffness matrix is transformed to obtain the equivalent stiffness matrix.Considering the coupling effect of deformation in each direction of elastic element,a more accurate elastic dynamic model is established.According to the constraints of moving platform and mechanism geometry,the elastic dynamic model of the system is obtained by combining the element elastic dynamic model,and then the response of the elastic dynamic model is solved by Newmark-β method,the dynamic characteristics of the mechanism are analyzed,and the dynamic error model is obtained.Considering the static and dynamic error sources of the mechanism,based on the total error model,the static and dynamic error sources are superimposed at the nodes to obtain the static and dynamic error model,and the error compensation algorithm is given.The mapping from the six dimensional error source of each node to the error of the end moving platform is derived by matrix method,and the total error model of the mechanism is obtained.Considering the coupling between static error and dynamic error,the static error and dynamic error are substituted into the full error model to obtain the static and dynamic error model,which improves the accuracy of the error model.Particle swarm optimization algorithm is used to compensate static and dynamic errors in joint space.Aiming at the defect that particle swarm optimization algorithm is easy to fall into local convergence,the concept of aggregation degree is introduced into particle swarm optimization algorithm.Finally,an example is given to verify the effectiveness of the compensation algorithm in greatly reducing the end error.