Study On Coupling Characteristics And Stability Of Parallel Module Of Large Mirror Machining Equipment

With the advent of the information age,modern optical systems are moving toward high precision,high resolution,and high power.In order to achieve better performance,the accuracy of optical mirrors in optical systems has become higher and higher,which puts higher demands on large mirror machining equipment.The parallel manipulator has the characteristics of high rigidity,high precision and no cumulative error.Combined with the series manipulator,the manipulator is very suitable as a large-scale mirror machining equipment,which can greatly improve the precision of mirror processing.In this thesis,a large mirror machining equipment with two rotational degrees of freedom and three translational degrees of freedom is studied.The coupling characteristics and stability of the parallel module are analyzed,and the relevant conclusions are verified by numerical simulations and virtual prototype experiments.The main research content of this thesis is divided into four chapters: dynamic modeling,analysis of coupling characteristic,analysis of static stiffness and stability analysis.The main contents are as follows:1)The dynamic modeling is studied and the dynamic analysis is carried out.Firstly,the connected coordinate system of each component is established in the parallel module and the series module respectively.The kinematic of the parallel module is analyzed by the vector method,the coordinate system of the tool system is linked with the fixed coordinate system by the rotation matrix,and according to the torque balance,the centroid position of each branch is obtained.Secondly,the "contact-separation" two-state model and the L-N contact force model are selected to describe the contact force in the composite hinge,and the modified Coulomb friction model is selected to describe the frictional force in the Hook hinge.Thirdly,the Newton-Euler method is used to establish the dynamic equilibrium equations of the driving branch,the constrained branch and the moving platform,and the force and moment generated by the series module are equivalently converted into the external load acting on the center point of the moving platform.The dynamic model that considers the composite hinge contact force and the Hook hinge friction force is established.Finally,on the basis of the dynamics model,the external force and external torque generated by the series module are numerically simulated by MATLAB,and the contact force and friction force during the movement are analyzed.The dynamics model is verified by comparing the changes in driving force in both cases with and without consideration of the force of the motion pair.2)The coupling characteristic of parallel module of machining equipment is studied and the influence of the tool system on the coupling characteristics is studied through virtual prototype experiment.Firstly,based on the decomposition of the parallel module kinematic chain,the manipulator coupling degree of the parallel module is calculated,and the complete decoupling and line decoupling of the parallel module are analyzed by the Jacobian matrix.Secondly,according to the coupling degree evaluation matrix,the relationship between the angle of the Jacobian matrix vector and the coupling is used to establish the mathematical model of the evaluation index of the coupling degree and the evaluation index of the global coupling degree,and use MATLAB to analyze the coupling of parallel module in different positions.Finally,the virtual prototype is established by ANSYS Workbench,and the coordinate values of the center point of the moving platform are collected and compared with the ideal values to obtain the influence of the tool system on the coupling characteristics of the parallel modules.3)The static stiffness characteristics of the parallel module of machining equipment are studied and the conclusions are verified by simulation experiments.Firstly,according to the mechanical structure characteristics of the parallel module,the stiffness calculation method is used to establish the driving stiffness matrix of the driving branch and the constrained stiffness matrix of the constrained branch respectively.According to the principle of virtual work,the stiffness model of parallel module is established.Secondly,the stiffness performance indexes,the minimum singular value of the stiffness matrix and the isotropic index,are defined.The finite element analysis and the mechanical manual are used to calculate the element values of the stiffness matrix.The distribution of the line stiffness and angular stiffness of the parallel module is numerically calculated and the stiffness performance of the driving branches is analyzed by MATLAB.Finally,Solidworks is used to establish the 3D model of the machining equipment,which is imported into ANSYS.The displacement cloud maps of the parallel module in different positions are obtained and analyzed.The calculated values of the displacement are compared with the simulation to verify the static stiffness model of the parallel module.4)The stability of the parallel module of the machining equipment is studied and the virtual prototype experiment is carried out.Firstly,according to the definition of Lyapunov exponent,the whole manipulator dynamics equation is transformed to obtain the state equation of the parallel module,so as to obtain the Lyapunov exponent and determine the structural parameters and kinetic parameters affecting the Lyapunov exponent.Secondly,based on the Lyapunov exponent,MATLAB is used to analyze the changes of the Lyapunov exponent in ?,? and L under the original parameters,and the influence of driving force,intermediate branch mass and centroid position on the Lyapunov exponent is analyzed.Thirdly,the influence of the tool system on the Lyapunov exponent is analyzed,and the influence of the tool system on the stability of the parallel module is determined.Finally,the virtual prototype experiment is carried out,and the actual pose parameters of the moving platform are collected in both cases with and without consideration of the tool system.The two sets of parameters are compared and analyzed,so the changes of the parallel module stability in ?,? and L are obtained in two cases and the conclusion of the influence of the tool system on the stability is verified.