Research On Key Technologies Of Figure Error Correction Of Ultrasonic-magnetorheological Compound Finishing

For more superior performance, people apply more and more precision andultra-precision curved optical components in design and fabrication of opticalobservation system, laser system，lithography system and other high-tech opticalsystems. Many novel processing methods have been developed by the requirementfor high quality optical curved surface, and computer controlled polishing(CCP) isengendered by combination of these processing methods and computer numericallycontrolled(CNC)) technology. However，concave surface with small curvature radiusis difficult to fabricate by most of existing technologies for the restriction of theirmachining conditions. Ultrasonic-magnetorheological compound finishing (UMCF)is a new kind of polishing technology for ultraprecision machining of concavesurfaces with small curvature radius and has broad application prospects.The theoretical and technical problems in UMCF figure correction technologyhave been studied in the dissertation. The figure correction of the plane and spherewith small curvature radius is realized by the combination of UMCFmethod and computer controlled technology. The study in the dissertation carrythrough technical preparations for the practical application for figure correction ofoptical curved surface by UMFC, and the dwell time algorithms and polishing pathplanning algorithms developed in the study can be applied in computer controlledpolishing by manifold other polishing technologies. The study has importantsignificance for promotion of figure correction technology for optical curvedsurface.The main aspects of the study are including:An experimental set-up of UMCF has been developed based on the principle ofUMCF, and it is the basis for figure correction study. The study on UMCF removalfunction has been conducted, and the material removal mathematical model isestablished based on the study of the principle of UMCF. The theoretical models areachieved by the analysis of the ultrasonic stress, the magnetic stress and thehydrokinetic stress on the workpiece surface in the polishing zone. The validity of thetheoretical models is examined by the experimental results.The dwell time solution problem is a key issue in the figure correction and,consequently, two dwell time algorithms have been developed. Themethod to determine dwell time initial value and to overcome the edge effect hasbeen studied. The effect of removal functions with different characteristics on surfaceaccuracy after polishing and processing time has been studied by dwell timealgorithm simulation analysis. The figure correction method for axisymmetric figure error and its dwell time algorithm have been studied. The figure correction problemwas solved as a constrained optimization problem, and Thikhonov regularization hasbeen used to achieve small expected residual error and overcome ill-conditioning.The equal dwell unit area method has been developed to solve the problem, howto determine the dwell points on non-parallel polishing path. This method makes thedwell unit areas of the adjacent points equal; thereby dwell points of thepolishing path homogeneous distribution on the workpiece surface can be obtained.In order to solve the problem of the calculation of the dwell time on the non-parallellines polishing path, the dwell time error proportional algorithm fornon-parallel paths has been developed, and the dwell time of the dwell points on thepolishing path can be solved by the algorithm directly. The pseudo-random polishingpath has been developed to remove the mid and high-frequency errors after small toolpolishing. The boundary optimization algorithm has been developed to optimizepseudo-random path, thereby it can be used in polishing workpiece surface of anyboundary shape efficiently. The power spectral density (PSD) of surface before andafter polishing with pseudo-random path has been analyzed and the result indicatedthat the high frequency error can be reduced by the application of pseudo-randompath. Workpiece and the experimental device modeling, preprocessing andpost-processing have been achieved, and the integrated simulation, and verification(IS&V) has been developed. The generation of NC code for UMCF figure correctionand process simulation verification have been achieved.The analysis of error source in the UMCF figure correction process has beenconducted. A dwell time algorithm was used as a tool for simulation study, and theeffect of the positioning error and removal function error on material removal andresidual error has been studied.Figure correction experiments on planar and spherical surfaces have beenconducted by UMCF figure correction technology, and it validate the effectiveness ofthe dwell time algorithms and polishing path planning algorithms. The security ofUMCF in fabrication of high quality optical components is proved by figurecorrection experimental results.