Research On Geometric Error Analysis And Compensation Of Surface Polishing Platform

Optical surface parts are widely used in many fields,such as national defense science and technology,biological medicine and ship.Due to its special geometric properties and hard and brittle material properties,the processing precision of the processing equipment and equipment is improved.How to realize the high precision,high efficiency and low cost of free-form surface has been studied by many scholars both at home and abroad.The geometric error is the main error source of machine tool error,so it is important to analyze and compensate the geometric error of the surface polishing platform.This dissertation is supported by the Chinese National Program on Key Basic Research Project(973 Program),"Basic Research on the Fabrication of the Optical Freeform Surface—Project 2:Physical Analysis and Reconstruction Strategy for the Generation of the Optical Freeform Surface "(Project No.2011CB706702).This study focused on theory of geometric error detection,modeling and compensation system of the four axis polishing platform including rotation axes,respectively,by using multi-body system theory and differential transformation matrix modeling and compensation of geometric error,finally get the surface machining trajectory considering geometric error.Under the influence of geometric error,the relative position relationship between the moving parts of the moving axis and the original parts is expressed,and the homogeneous coordinate transformation matrix of the moving parts and the theoretical positions of the moving axes are obtained.The Four Axis Polishing Platform's geometric errors is measurement by using the Renishaw laser Interferometer,the interaxis error,positioning error,straightness error,pitch and yaw error of the linear axis and rotation axis positioning were obtained.Based on the theory of multi-body system,the geometric error model is establishedThe thermal errors and geometric errors are separated by several measurements and polynomial fitting methods.The geometric error distribution after separation is studied,and the mathematical expectation method is used to eliminate the random error.Finally,the real geometric error measurement data is obtained.The NURBS curve is used to express the discrete measurement data,and then the NURBS error curve which can meet the precision requirement and the amount of data is optimized.The NURBS error curve can be used in the error analysis and compensation.The multi-body system theory and Newton iteration method are used to study the error compensation algorithm of Four Axis Polishing Platform.The kinematics model of the experimental platform considering the geometry error is established.The nonlinear coupling characteristics of the transformation matrix between the tool coordinate system and the workpiece coordinate system are analyzed.And then the nonlinear equations are solved by Newton iteration method.Because of the instability of the Newton iterative error compensation method based on the multi body system theory,it is not convenient for online real-time error compensation.Therefore,this paper presents an integrated error modeling and compensation method based on differential transformation matrix,established the differential transformation matrix of the movement axis with respect to of the workpiece coordinate system,the path under the influence of the geometry error is obtained.By using the pseudo inverse of the Jacobian matrix to calculate the geometric error compensation value,compared with the Newton iterative method,the proposed error compensation method based on differential transformation matrix to facilitate the realization of real-time error compensation.