| With the rapid development of astronomy,the demand for optical telescopes is increasing.The main mirror in the telescope,as the core component that affects the imaging quality,is increasing in size while its surface accuracy is also improving,which puts forward higher requirements for the processing equipment of optical mirror.In the working process,the mechanical system will vibrate because of the elastic deformation of each component,so that there is a deviation between the actual running track and the theoretical track of the mechanism,which ultimately affects the kinematic accuracy of the mechanism.In this paper,the research object is the optical mirror polishing robot.The kinematics and dynamics of the polishing system and the serial module,the elasticity dynamics of the parallel module,the kinematics and elasticity dynamics of the parallel module under the influence of joint clearance,and the vibration suppression of the parallel module are analyzed.The main research contents can be summarized as follows:(1)The kinematics and dynamics of the serial module and the polishing system are studied,and the elastic dynamics equations of the parallel module are established.Based on the D-H parameter method and the principle of angular velocity superposition,and considering the rotation and revolution of the two rotor polishing system,the kinematics of the series module and the polishing system is analyzed,and the angular velocity and angular acceleration of each component are calculated.By using Newton Euler method,the expressions of force and moment acting on parallel module by series module and polishing system are obtained.Considering the elasticity of each branch of the parallel module and the influence of the composite spherical hinge,a spatial beam element is used to discretize three active branches and one constrained branch.The constraint relationship between the moving platform and each branch chain is analyzed,and the motion coordination equation of the moving platform is established.Based on the KED method,the elastic dynamic equations of parallel modules are established.Using MATLAB to realize the numerical simulation analysis of force and moment,and get the elastic displacement curve at the center of the moving platform.(2)The influence of joint clearance on the kinematics and dynamics of parallel module is studied.Firstly,the joint coordinate system is established at the rotating joint with clearance,and the change model of joint clearance is established by using probability density function.The geometric relationship between the members under the influence of joint clearance is analyzed,and the kinematic model of three active branches and one driven branch under the action of clearance is established.Based on the Lankarani-Nikravesh collision force model,the impact of joint collision is considered,and the impact of friction in collision is considered based on the Coulomb friction model.On this basis,the generalized force model of joint in collision is established.Considering the change of the position of the branch chain under the action of the joint clearance,the density change model of the member is established.Combined with the influence of the generalized collision force,the elastic dynamic equation of the joint space is established.Finally,the influence of joint clearance on the elastic displacement of parallel module is analyzed by MATLAB software.(3)The dynamic performance of parallel module is studied,and its structure size is optimized.The transformation relationship between the unit coordinate vector and the generalized coordinate vector of the system is established,and the distribution of the generalized force on the generalized coordinates of the branch chain is analyzed.Based on the elastic dynamic model of parallel module,the elastic displacement vector is solved,and the binding force and constraint moment of each branch chain are analyzed.The relationship among normal stress,shear stress and interpolation function are established.Based on the fourth strength theory and combined with the influence of normal stress and shear stress,the equivalent stress of each branch chain is analyzed.The natural frequency of the parallel module is calculated by the elastic dynamic equation,and the influence of the operating position of the mechanism,the material used in the structure,the internal and external diameter of the branch chain and the mass of the moving platform on the natural frequency of the parallel module is analyzed by using MATLAB.On this basis,considering the system mass,natural frequency,the elastic displacement of the mechanism with joint clearance and the equivalent stress of the branch chain,the particle swarm optimization algorithm is used to optimize the section size of each branch chain of the parallel module.Finally,it is proved that the optimized section size improves the contribution rate of unit mass to the natural frequency of the system.(4)Based on the piezoelectric control technology,the residual vibration suppression of the system is studied.By combining PZT actuator,sensor theory and modal theory,the motion equation of the controlled beam element is established.Through the elastic dynamic model of the system,the state space model of the system under the action of PZT actuator and sensor is analyzed.On this basis,the state space model is simplified into the controlled modal equation and the residual modal equation by using the modal truncation technique.In addition,the strain rate feedback controller and the linear quadratic optimal controller are designed,and the controlled equation and the controller of the system are analyzed by numerical simulation using MATLAB software.Under the action of PZT actuator and PZT sensor,the control and suppression curves of the two controllers for the vibration of the system.Finally,the feasibility of using PZT technology to suppress the vibration of the system and the effectiveness of the two controllers are verified.In this thesis,there are 39 pictures,6 tables and 94 references. |
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