| Optical part surface is the key component for an optical system. In recent years, withthe improving requirement of the optical properties, the requests of accuracy, relativeaperture, weight reduction, production efficiency and cost of the optical part surfaces aregetting higher and higher. Nowadays, the production cost and efficiency of the optical partsurface has become one of the signs for a country reflecting the modern level of the opticalindustry and even the whole manufacturing ability. The polishing process is usually used asthe final step to fabricate the optical part surface, which has large effect on the accuracy andduration of the surface. This dissertation is supported by the Chinese National Program onKey Basic Research Project (973Program)[Grant number2011CB706702],“BasicResearch on the Fabrication of the Optical Freeform Surface—Project2: Physical Analysisand Accuracy Control Strategy for the Generation of the Optical Freeform Surface”. Thisstudy focused on the technical architecture of the deterministic polishing process and the keytechnologies of the deterministic polishing. The prediction of the local and glocal polishedprofiles, polishing force control, control strategy of the surface form, et al. are explored indepth both theoretically and experimentally.The core issues in the deterministic polishing process include modelling of the unitmaterial removal function, dwell time calculation, planning of the polishing path, predictionof the material removal depth, et al. For the fundamental principle of the polishing processcorrecting the surface form, the global removal depth is modelled as the convolution of theunit material removal function and the dwell time. It is assumed that the polishing process istime-invariant, which means the unit material removal function does not vary with themovement of the polishing tool. For the spherical optical surfaces and aspherical surfaceswith low gradient, this assumption is reasonable. However, for the high gradient asphericalsurfaces and the freeform surfaces, the surface curvature, tool path and polishing posture arevarying during the polishing, thus the unit material removal function is time variant. Thisdissertation addresses the problem of material removal in the polishing process. The effectsof some polishing conditions upon the material removal are analyzed, including not only theprocess parameters, which refer to the normal force, angular spindle velocity and angularfeed rate, but also the abrasive grain size, polishing slurry properties, topographicalparameters of the sub-aperture pad, as well as tool path curvature. Based on the analysis, anew control strategy to improve the surface form accuracy is proposed. The main researchcontents in this dissertation are as follows:(1) A new material removal model for the velocity-dwell-mode polishing process isproposed. The material removal index, which means the material removal depth at unitlength of polishing path, is defined and derived based on the Preston equation. Thedistribution of material remval index in the polishing contact is affected by the contact pressure and relative sliding velocity between the tool and the surface. The material removalprofile during the polishing can be obtained by intergrating the material removal index alongthe polishing path in the contact region. Based on the fundamental theory, the materialremoval models of the spherical tool and sub-aperture tool are proposed in this dissertation.Accordign to the models and experimental results, the polishing material removal is affectedby the polishing normal force, spindle velocity, polishing attitude, geometrical/physicalpropertities of the tool/surface, et al.(2) The effect of polishing path on the polishing material removal is modelled andanalyzed. Especially, the polished profiles as the sub-aperture polishes at the path corner andalong the trochoidal path were modeled by integrating the material removal index along thetool path in the contact region. The effects of the parameters of the polishing path on thepolished profile were considered in different cases. The theory in this paper is potentiallyuseful for the planning of tool path and processing parameters in the deterministic polishingprocess.(3) A novel mathematical model of the material removal profile for the free abrasivepolishing (FAP) is developed, which successfully explains the effects of the properties ofabrasive grains/slurry and topographical parameters of sub-aperture pad on the profile. Byanalyzing the interations among polishing pad, abrasive grain and workpiece surface in themicro level, the material removal for a single abrasive and the critical condition of materialremoval for the abrasives are modelled. On the basis of above, the material removal indexconsidering the removal mechanism of FAP is proposed to facilitate more accurate polishing.According to the simulation and experimental results, the removal depth is proportional to(normal polishing force)0.65,(volume concentration)2/3and the radius of abrasive grains, andinversely proportional to (deviation of pad asperity height)0.3.(4) The control system of polishing force composed by the pneumatic cylinder andpressure propotional valve is developed. The software platform of the control system isbased on the NI PCIe6321DAQ card and the real time module. The transfer function of thepolishing force control system is derived theoretically. Pseudo Random Binary Sequence(PRBS) signals were applied at the control input, and the output date was caputured. Withthe input and output data, the model of the system is identification by least square method.An integral sliding mode controller (ISMC) is proposed to control the polishing force inorder to improve the performace. Root locus is used to find an appropriate value of ki, theintergral control coefficient, to ensure the closed-loop stability. By compared with the RSTand PID controller, the robustness of the ISMC to the disturbance and model uncertainties isensured by the implementation of an integral sliding control action. The force controlexperiments show that the proposed algorithm is effective in improving the control accuracyof the polishing force.(5) By extending the theory of removal profile orthogonal to the tool path, the localpolished profile, which is defined as the polished depth in the measuring direction, ismodeled. According to the model, the local polished profile is determined not only by the process parameters, the tool attitude, the geometrical/mechanical properties of workpieceand tool, but also the measuring angle. The linear algebraic expression of the2D/3D globalpolished profile is derived by convoluting the local polished depth at each dwell point of thepolishing process. In this model, the matrix of the global polished depth equals to theproduct of influential matrix and feed rate matrix. On the basis of above, the errorcompensation method for the polishing process is developed as an optimition problem of thefeed velocity in polishing. The nonnegative least square method is used to solve this problem.The polishing experiments composed by polihsing of a flat surface and a spherical surfaceare conducted to verify the proposed model. After polishing for a cycle, the Wvvalue of theflat surface was improved from1.8989μm to0.4251, and Wtvalue from28.4896μm to9.3351μm respectively. The spherical surface was polished with the uniform materialremoval control method. For every polishing cycle, the global polished depth is3μm. Afterpolishing, the roughness of the spherical surface reduced from135.8nm to14.7nm, and theuniformity of the whole surface was guaranteed. |
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