Research On Key Technology Of Deterministic Polishing Of Optical Surface

Due to the excellent performance of optical surface in lighting and imaging,optical surface has a large number of applications in lighting equipment,camera lens,astronomical telescope and even military equipment.In order to obtain the surface that meets the performance requirements,surface is usually polished in the last step.With the continuous improvement of equipment performance requirements,the requirements for the quality of optical surfaces are no longer limited to lower roughness,but to obtain lower mid-spatial frequency error(MSF error)and profile tolerence while reducing roughness.This process is called deterministic polishing.In this paper,bonnet polishing method is taken as the research object and the deterministic polishing of optical surface is studied.The realization of deterministic polishing relies on the tool influence function(TIF),polishing path planning and dwell time planning.These three main factors are studied in this paper,including the modeling method of TIF of bonnet polishing tool on free-form surface,generation method of polishing path that can achieve physical uniform coverage on a rotationally symmetric surface,generation method of polishing path that can suppress the MSF error of the surface,and dwell time algorithm of the polishing tool at dwell point.In this paper,the main factors involved in deterministic polishing are discussed and a certain theoretical system is formed,which has theoretical value and industrial application value.The main research contents and achievements are as follows:1.The TIF model of bonnet polishing tool on free-form surface is proposed.In previous research,modeling of TIF is mostly based on flat surface and spherical surface.When the target workpiece is an aspheric surface or a more complex free-form surface,the contact area,pressure distribution,and sliding velocity distribution between the polishing tool and the workpiece are more complicated than flat and spherical surface.In this paper,differential geometry is used to solve the theoretical contact area between the polishing tool and the surface,and the 3-dimensional profile of the corresponding contact area is derived.The effectiveness of the proposed method is verified by comparing with traditional contact area modeling method.The contact between the polishing tool and the workpiece is analyzed by finite element analysis software,and the theoretical contact area and pressure distribution were modified according to the fitting results.When solving the distribution of sliding velocity within the contact area,the projection of the rotational angular velocity of the spindle on the tangent plane is proposed as the actual sliding velocity.Finally,the TIF is derived according to Preston formula.2.A polishing path that can realize physical uniform coverage on a rotationally symmetric surface is proposed.In previous research on spiral polishing path,the change of contact area is not considered,thus the traditional Archimedes spiral polishing path will lead to unpolished area and over-polished area.In this paper,a revised Archimedes spiral polishing path is proposed.This path is generated based on the modified tool-workpiece contact model and the pointwise searching algorithm.The contact edge of the polishing path can maintain the same overlapping length and realize the uniform physical coverage on a rotationally symmetrical surface.The effectiveness of the proposed path is proved by comparing with the traditional Archimedes spiral polishing path in experiment.3.A six direction pseudo-random consecutive unicursal polishing path that can suppress the MSF error and cover the surface continuously and evenly is proposed.Compared with the traditional path,this path has the following characteristics:multi-directionality,high randomness,smoothness,and consecutiveness.The proposed path is generated by searching the valid points in the preset point set and connecting them in turn.Therefore,the path can be applied to complex surface.When dead point occurs in the search process and the search cannot be continued,three dead point processing methods and three add point methods proposed in this paper are used to help generate a complete path according to the path generation situation.In order to verify that the proposed path has the ability to suppress the MSF error,a group of contrast experiments were conducted between the proposed path and the revised spiral path.The results show that the six direction pseudo-random consecutive unicursal polishing path has the ability to suppress the MSF error.4.A continuous tool influence function(cTIF)based on polishing path is proposed and combined with the optimized grouping LSQR method to solve the dwell time distribution.In previous research,single-point TIF(sTIF)is usually used in calculation,but it is not consistent with the TIF in the actual polishing process.In addition,when using the linear equation to solve the dwell time,a large TIF matrix results in a normal computer not having enough memory for calculation.To solve these problems,the continuous tool influence function(cTIF)based on the sTIF is proposed,cTIF is generated by the discretization method to simulate the continuous movement of the polishing tool in actual polishing.Compared with the sTIF,the cTIF can improve the modeling accuracy while keeping the size of the TIF matrix(H)unchanged.Then,the dwell time is calculated by grouping the TIF matrix H,and the dwell time of the connected area of the two adajacent group is optimized by the misalignment grouping method and the weight coefficient to obtain the final dwell time distribution.Finally,simulation experiments verify the effectiveness of the solution method.