| The advancement of precision manufacturing technology has promoted the development of optical systems in the direction of off-axis and aspherical surfaces,and at the same time put forward higher requirements for the manufacturing accuracy of optical systems.High-precision optical components are widely used in various fields such as aerospace,national defense and military industry,and national economic production.They have an extremely important strategic position.At present,there is still a big gap between my country and developed countries.Therefore,it is of great significance to study ultra-precision polishing technology of optical components.In most deterministic optical polishing processes,because the processing tool is much smaller than the size of the processed surface,the processed surface has a certain medium-to-high frequency error in addition to the low-frequency surface error.In this paper,aiming at the suppression of medium-to-high frequency errors in the magnetorheological polishing process of small-aperture optical elements,a tool system is developed and a theoretical removal model is established,and a pseudo-random programming method on a three-dimensional surface is proposed.The main contents of the study are summarized as follows:1.Establish a theoretical model of deterministic polishing removal.Magnetorheological polishing mainly relies on shear stress to remove materials.According to the bearing lubrication model of Bingham media,dynamic pressure analysis is performed on the magnetorheological polishing area to obtain the shear stress distribution;the fixed-point polishing experiment determines the polishing coefficient;Finally,the theoretical removal model of magnetorheological polishing was established based on the flow velocity distribution of the polishing area.2.A pseudo-random planning method for curved surfaces based on parametric grids is proposed.Aiming at the parameterization process of the curved surface,based on the angle-based flattening method(ABF algorithm),the constraint conditions are transformed,the objective equation is optimized,and the MABF algorithm in matrix form is proposed.After many simulation analyses,the MABF algorithm is better than the ABF algorithm in terms of operating efficiency and calculation accuracy.Due to the different magnitudes of the deformation of the parametric grid mapping,it will cause the uneven distribution of the pseudo-random trajectory of the curved surface.Simulation analysis shows that the amount of deformation and uneven deformation in the mapping process are reduced to a certain extent3.Nurbus interpolation algorithm smoothes the trajectory.Due to the frequent bending of the pseudo-random trajectory,the processing trajectory will produce greater speed and acceleration shocks during the polishing process;In order to solve this problem,the pseudo-random trajectory point is used as the control point,Nurbus algorithm interpolation is applied,the chord length error and normal acceleration are strictly restricted,and the planned pseudo-random trajectory is smoothed..4.In order to verify the correctness of the theory,the scan trajectory is compared with the pseudo-random trajectory based on the parameter grid.By analyzing the measurement data and drawing the PSD curve,the results show that the pseudo-random trajectory can suppress the medium and high frequency error to a certain extent. |
