Research On Aspheric Surface Machining Based On Elastic Deformation Molding Method

The high efficiency,low cost and ultra-precision machining of aspherical surfaces is one of the research hotspots in ultra-precision machining area.Today’s ultra-precision aspheric surface fabricating methods based on material removal mechanics rely on high precision and high rigidity machining systems,which leads to high machining cost.Ultra-precision machining methods based on form replication mechanics belong to hot machining process,thus result in the change of optical properties(e.g.refractive index)of workpiece materials.In this thesis,a new aspheric surface fabricating method-elastic deformation molding method is proposed:In the range of workpiece material strength,make a workpiece linearly elastically deformed and contact with a negative mold until the workpiece closely attached with the mold.The profile of mold is opposite with the target machining aspherical profile.Then the unattached side of workpiece is machined to flat surface.After the workpiece is elastically recovered,the machined surface will deform to be target aspherical profile,thus the rapid and ultra-precision machining of thin axisymmetric aspherical surface is realized by plane machining.Aiming at establishing a comprehensive fabrication process with high efficiency,low cost,with ultra-precision for targeted aspheric surfaces,and centering on two key problems including workpiece strength evaluation and machining profile accuracy,key technologies in this new method are explored.Machining theory system and processing flow of elastic deformation molding method is built.Specific studies include the following aspects:(1)Machining mechanism of elastic deformation molding method is studied.The maininfluencing factors of the machining process are analyzed,and the effecticeness of the machining mechanism is verified by numerical simulation.Elastic behavior of workpiece in machining mechanism is theroretically analyzed based on thin plate theory and energy method,which provides the theoretical foundation of the research on contact state between workpiece and mold.(2)Contact state between workpiece and mold under uniform pressure is researched.A numerical simulation model of static contact between workpiece and mold is established,and a measuring experiment of workpiece deflection when contact with the mold is carried out.The effectiveness of the established numerical simulation model is verified by comparing the results of numerical simulation with those from theoretical analysis and experimental testing.The effects of the overhanging arm’s width and the diameter-thickness ratio on the contact state between workpiece and mold are investigated.The varying trend of the contacting state between workpiece and mold as a function of material removal depth during machining process is investigated using Python software combined with re-mesh and element creation-annihilation technology.(3)The first key problem during machining process,the fracture strength of workpiece,is studied.Permissible stress is utilized as the strength criterion in static contact process between workpiece and mold and a ball load strength test is carried out.Considering workpiece surface micro-crack distribution,coupled with fracture mechanics and weakest-link theories,a theoretical fracture probability model based on micro-cells for thin workpiece of brittle material is proposed and established for lapping process after the workpiece is attached to the mold.The effectiveness of the model is verified through experiments.The effects of abrasive grain size and crack distribution density on the fracture probability model are discussed.Evaluation method of workpiece fracture strength is then built,and the established evaluation method is actually applied in the aspherical surface machining process of elastic deformation machining method.(4)Machining experimental platform for elastic deformation molding method is studied.A workpiece elastic deformation control system based on vacuum suction is established.The effectiveness of the workpiece elastic deformation control system is verified through experimental testing.Through combining the workpiece elastic deformation control system with normal plane polishing machine,the machining experimental platform is then built.Porous ceramic vacuum sucking fixtures are designed and fabricated.Fixture parameters are optimized using numerical simulation.Surface form fitting,peak removing,and low-pass filtering are employed in measuring form errors of a mold surface.To remove the peaks in mold form error measurement,a peak filtering method that is based on a three-pixel shifting window assisted with pixel slope-distance judging is proposed.(5)The second key problem during machining process,the machining profile precision,is studied.Factors that affect profile precision of machined workpiece are analyzed with numerical simulations.Related machining processes are investigated through experiments with consideration of initial flatness of workpiece contact surface,contact fit between a workpiece and a mold,flatness machining accuracy,and lapping residual stress.A complete machining process with elastic deformation molding method for aspheric surface has been established.A convex parabolic surface with its diameter of 45 mm and its apex radius of 3107 mm is set as a fabricating goal for testing machining,and the achieved final form accuracy reached PV 0.68 μm,center and edge surface roughness reached Ra 0.75 nm and Ra 1.12 nm respectively.Research results prove that the proposed elastic deformation molding method can realize high efficiency,low cost and ultra-precision machining of thin axisymmetric aspherical surfaces by plane machining.Comparing with aspherical grinding method,when under the equivalent machining profile accuracy,the proposed method has better surface quality,lower cost and equivalent efficiency.Due to the brittle properties of workpiece materials and limitation in machining means and equipments,the proposed method is mainly suitable for machining of thin axisymmetric aspherical surface with large curvature radius.The research results presented in this thesis possess practical importance and scientific values for realizing high efficiency fabrication of thin axisymmetrical aspheric components and for enriching the theories of aspheric optical precision machining.