Tool Influence Function Research Articles

Restraint of the mid-spatial frequency error on optical surfaces by multi-jet polishing.

Nowadays, the mid-spatial frequency (MSF) error existing in the optical surface after polishing is still a great challenge for the ultra-precision manufacturing of optical components. MSF error severely deteriorates the performances of optical components such as causing small-angle scattering and reducing imaging contrast. In this paper, multi-jet polishing (MJP) was proposed to restrain the MSF error, whose tool influence function (TIF) was relatively more complicated and adjustable than the TIFs of other tools. The results demonstrated that MJP had a superior ability to reduce the ripple error, and the path spacing and nozzle orientation angle both had a significant effect on the MSF error of the polished surface. The optimization of nozzle orientation angle under different path spacings was conducted to achieve a high surface quality. This study contributes to the ultra-precision manufacturing of optical components, achieving a low MSF error together with high finishing efficiency.

Modelling of surface morphology and roughness in fluid jet polishing

Fluid jet polishing (FJP) has been extensively used in various kinds of fields such as precision molding, optical components, etc. However, previous works mainly focused on the material removal process on the macro-scale (e.g., tool influence function, surface generation) to improve the form accuracy, the understanding of surface morphology evolution of FJP on the micro-scale is still far from complete, which makes it difficult to predict the surface quality under certain polishing conditions. Time-consuming and high-cost trial and error are usually needed to obtain suitable polishing conditions for specific surface quality requirements. In this paper, a physical model was developed to predict the surface morphology and roughness after FJP, by combining the computational fluid dynamics (CFD) simulation and kinetic analysis of the abrasives. The single abrasive erosion process including indentation action, ploughing action, and cutting action was analyzed by kinetic analysis. Besides, the overlap of single abrasive erosion pits was modeled to simulate the surface morphology evolution in FJP and determine the surface roughness after polishing. Different parameters were considered in the model including jet pressure, jet angle, and abrasive size. A series of polishing experiments were conducted to validate this model and the effect of different polishing parameters on surface quality was elucidated by the impact velocity distribution and erosion morphologies. It is found that the simulation results agree well with the experimental results. This paper not only provides a deeper understanding of the microscale material removal in FJP, but also provides an effective method for the prediction of surface roughness in FJP.

Towards understanding and restraining the mechanical relaxation effect in polishing silicon carbide with a detachable bonnet tool

Bonnet polishing has shown promising shape adaptability and processing quality in the surface finishing of glass-ceramic optical components with complex surfaces. This study proposed a new robotic bonnet polishing device with a detachable polishing cloth to realize relatively high polishing accuracy on sintered silicon carbide (S-SiC) with low cost and pollution. During polishing, the contact state between the secondary-thermoformed polishing cloth and workpiece was found to follow a complex force curve, including a short-term force drop caused by quasi-stress relaxation and a long-term force rise caused by creep. Therefore, a predictive model was established to modify the removal efficiency error induced by force fluctuation and to estimate the remaining service time. On this basis, a new approach was proposed to accelerate the initial-stage creep and restrain the force drop during polishing via temperature control. The results obtained in tool influence function and form correction experiments proved that the temperature threshold to suppress the stress relaxation effect of the polishing pad is around 45 °C. Meanwhile, the pre-treatment time of the pad can be compressed by more than half at this temperature to maintain the high determinacy and efficiency of the polishing process. After polishing, almost no subsurface damage was detected near the surface of the S-SiC block. However, due to the impact of original micropores and the scratches caused by the abrasive aggregation effect, the roughness is challenging to continue decreasing after Ra reaches 3∼4 nm.

3D-printed functionally-graded lattice structure with tunable removal characteristics for precision polishing

Functionally-graded lattice structure (FGLS) has fascinating properties such as lightweight, tunable stiffness, minimized stress concentration, and excellent energy absorption. The advent of 3D printing has provided feasible and reliable manufacturing solutions for FGLS, which has been boosting wider applications of FGLS. In this paper, 3D-printed polishing tools with tunable removal characteristics are developed based on FGLS. The gradient in stiffness is achieved by varying the strut thickness of different cells. Four FGLS with different gradients are designed and printed. The normal contact pressure between the tools and a rigid plate is modelled by the finite element method and experimentally validated with a pressure mapping system. The polishing performance of the developed polishing tools is investigated on both ductile and brittle materials in a machining centre. Results demonstrate that the removal profiles of the polishing tools strictly follow the change of the lattice gradient regardless of the workpiece materials, which mainly affect the depth of the polished footprints. Besides, the surface roughness Sa after polishing reaches as low as 26 nm for the optical glass, indicating a drastic improvement of more than 90%. These findings enable the fabrication of polishing tools with desired tool influence functions on-demand for form error figuring in the computer-controlled optical surface finishing. Besides, the design strategy presented in this paper will open a new realm of producing functional tools in the field of ultraprecision manufacturing. • Functionally-graded lattice structure (FGLS) is designed for polishing. • Contact pressure of FGLS wheel is studied by FEA and validated by experiments. • The FGLS-based polishing tools can produce desired tool influence functions. • The surface finish of optical glass has been improved by > 90% after polishing. • The wear rate of polishing pads is material-dependent.

Random adaptive tool path for zonal optics fabrication.

Deterministic optics fabrication using sub-aperture tools has been vital for manufacturing precision optical surfaces. The fabrication process requires the tool influence function and the tool path to calculate the dwell time that guides the tool to bring surface quality within tight design tolerances. Widely used spiral and raster paths may leave excess waviness from the tool path, and the unavoidable constant removal layer is added to obtain positive dwell time. This waviness can be removed by either using smaller tools sequentially or randomizing the tool path. However, the existing tool-path solutions can hardly adapt to different surface aperture shapes and localized surface errors. Process efficiency and accuracy are also not well considered in tool-path planning. We propose an innovative zonal Random Adaptive Path (RAP) to solve these problems in this study. Firstly, RAP can be flexibly adapted to different surface aperture shapes by introducing part boundary. Secondly, an average threshold strategy is used in the RAP planning to improve efficiency, enabling the surface errors to be selectively corrected. Finally, the threshold is performed in several passes within one processing cycle, each with its RAP, until the desired residual is achieved. The performance of the proposed RAP is studied by comparing it with the conventional tool paths. The results demonstrated that RAP takes the least processing time and achieves the best surface quality, which verifies the effectiveness of RAP in deterministic optics fabrication.

Surface Quality Control Strategy of Aspherical Mold Based on Screw Feed Polishing of Small Polishing Tool.

For small aspherical molds, it is difficult for the existing polishing method to take into account the correction of the surface error and the control of the uniformity of the surface roughness (SR) distribution, because the polishing tool is always larger than the small mold. Therefore, we used viscoelastic polyester fiber cloth to wrap the small steel ball as a polishing tool to adapt to the surface shape change of the aspherical mold, and designed a semi-flexible small polishing disc tool with microstructure, which can better adapt to the curvature change of aspherical surface and obtain better SR Ra. At the same time, a combined polishing method of constant speed and variable speed for screw feed was proposed to improve the uniformity of SR distribution in the paper. Then, a series of theoretical analysis and experimental verification were carried out in this paper to predict the tool influence function (TIF) of the two polishing tools and the effectiveness of the combined polishing method. In the experiment, a TIF bandwidth of about 0.46 mm was obtained with a small spherical polishing tool, which favors the surface shape correction of the small aspherical mold. The experiment of uniform removal with a small polishing disc tool was carried out to quickly reduce the Ra. Finally, the surface quality of the aspherical mold was effectively improved, combined with the constant speed and variable speed polishing modes of screw feed of the small spherical polishing tool and the smoothing effect of the small polishing disc tool. The peak valley (PV) of two small aspherical molds with an optical effective diameter less than 13 mm converged from 0.3572 μm and 0.2075 μm to 0.1282 μm and 0.071 μm, respectively. At the same time, the SR dispersion coefficient was reduced from 27.9% and 41.6% to 14.2% and 12.7%, respectively. The study provides a good solution for the surface quality control of small aspherical molds.

Finishing of micro-aspheric tungsten carbide mold using small viscoelastic tool

Tungsten carbide is widely used as the material of replication mold to produce small aspheric optics, and the polishing process determines the precision of these molds. However, for micro-aspheric tungsten carbide mold, the existing polishing methods are difficult to realize the form error modification during a polishing process due to the polishing tool is always larger than small mold. Therefore, a polishing tool using polyester fiber cloth to wrap small-size rigid ball is used in this paper. In order to predict the tool influence function (TIF) of this polishing tool, a series of theoretical analysis and experimental verification are carried out in this paper. Firstly, by analyzing the structural and viscoelastic characteristics of the fiber cloth, the pressure distribution in the polishing contact area is determined. And the polishing speed distribution is obtained by analyzing the kinematic movement of polishing tool; Then, combined with Preston equation, the TIF is derived; Afterward, through a series of single point polishing experiments, it is verified that the volume error between the theoretical removal model and the experimental removal is less than 6.9% when the polishing pressure is low; Finally, the TIF is applied to the form error corrective polishing of small size symmetric aspheric tungsten carbide mold. After a form error corrective polishing test, the PV value (peak to valley) of form error is decreased from 0.268 to 0.083 μm, which verifies the effectiveness of this polishing method for small size tungsten carbide mold in form error correction.

Modeling the hydrodynamic impact on the tool influence function during hemispherical subaperture optical polishing

To fabricate high-precision and accurate optics relative to the optical design surface, a high level of deterministic control of material removal (i.e., the tool influence function, TIF) during subaperture tool polishing is required. In this study, a detailed analysis of the pressure distribution, which is a key component of the TIF, has been performed using finite element analysis to couple together solid mechanics and fluid dynamics. Modeling experimental parameters of recently published work reveals that, when considering tool deformation, which in turn influences the fluid film thickness between the tool and workpiece, the effective pressure profile has a flat-top distribution. This flat-top pressure profile differs from the parabolic pressure distributions predicted by Hertzian mechanics. Moreover, the shear contribution is shown here to be a key contributor to material removal, inducing the removal at the periphery of the contact edge and even outside the generally accepted contact area. Finally, the simulated fluid velocities provide evidence of mixed-mode contact polishing, supporting recent experimental findings that also suggest that onset of hydroplaning contributions lead to material removal drop-off.

Morphology characterization of polishing spot and process parameters optimization in magnetorheological finishing

Magnetorheological finishing (MRF) has become the mainstream method for ultra-precision manufacturing of optics due to its high certainty and low damage. However, there are still some gaps in the research on the characteristics of the tool influence function for the MRF method, which makes the parameter optimization and quality improvement lack effective theoretical support. To solve this problem, this paper demonstrates the mapping relationship between various process parameters and the evaluation indexes of the influence function based on the orthogonal test. A characteristic length coefficient is proposed to characterize the suppression effect of the tool influence function on the ripple errors. The uniform removal experiment shows that selecting reasonable characteristic length coefficient and line spacing can significantly suppress the generation of ripple errors and obtain the optimal parameters under a comprehensive consideration. Finally, a component with a size of 400 mm × 280 mm is deterministically finished and a high-quality optical surface is obtained. The theoretical analysis and experiment data carried out in this work can effectively improve the final quality of components and provide certain theoretical support for parameter optimization.

Modification of tool influence function for bonnet polishing tool based on analysis of interfacial contact state

Modification of tool influence function for bonnet polishing tool based on analysis of interfacial contact state

Nonlinear dwell-time algorithm for freeform surface generation by atmospheric-pressure plasma processing.

Based on deterministic chemical etching, atmospheric pressure plasma processing (APPP) with a high material removal rate and spatial machining resolution, is a promising computer-controlled optical surfacing (CCOS) technique for freeform surface generation. However, the time-variant removal characteristics of APPP induce nonlinearity in the CCOS process, which requires more consideration in the dwell-time calculation. In this paper, the nonlinear dwell-time algorithm based on the concept of controlling volumetric removal is studied. The freeform surface generation by controlling volumetric removal is modeled to provide the theoretical basis for the algorithm. The applicability of the algorithm in freeform generation by APPP with time-varying characteristics is explored through numerical simulations. Finally, a freeform surface is successfully created based on the algorithm and relevant analysis results, which validates the applicability of the algorithm in freeform generation using time-variant tool influence functions.

Genetic algorithm-powered non-sequential dwell time optimization for large optics fabrication.

Computer Controlled Optical Surfacing (CCOS) is widely applied for fabricating large aspheric optical surfaces. For large optics fabrication, various sizes of polishing tools are used sequentially. This raises the importance of efficient and globally optimized dwell time map of each tool. In this study, we propose a GEnetic Algorithm-powered Non-Sequential (GEANS) optimization technique to improve the feasibility of the conventional non-sequential optimization technique. GEANS consists of two interdependent parts: i) compose an influence matrix by imposing constraints on adjacent dwell points and ii) induce the desired dwell time map through the genetic algorithm. CCOS simulation results show that GEANS generates a preferable dwell time map that provides high figuring efficiency and structural similarity with the shape of target removal map, while improving computational efficiency more than 1000 times over the conventional non-sequential optimization method. The practicability of GEANS is demonstrated through error analyses. Random tool positioning error and tool influence function errors are imposed on dwell time maps. Compared to the conventional non-sequential optimization method, the power spectral density values of residual surface error from GEANS remain stable. GEANS also shows superior applicability when the maximum acceleration of a tool is applied.

Understanding and reducing mid-spatial frequency ripples during hemispherical sub-aperture tool glass polishing

During sub-aperture tool polishing of glass optics, mid-spatial surface ripples are generated because of material removal non-uniformities during tool linear translation (resulting in feed ripples) and tool pathway step overlaps (resulting in pitch ripples). A variety of tool influence function (TIF) spots, trenches, and patches were created to understand and minimize such ripples on fused silica workpieces after polishing with cerium oxide slurry using a rotating hemispherical pad-foam tool. The feed ripple amplitude can be decreased by reducing the non-uniformities in the pad texture and/or by minimizing a derived feed ripple metric (rf=Vmax0.5Vf/Rt) via adjustments in processing parameters. Pitch ripples can be minimized by reducing relative step distance to spot radius ratio (xs/at) and by achieving a flat bottom trench shape cross section or by reducing the material removal per pass. Using the combined methods, an overall ripple error of ∼1.2nm rms has been achieved.

Investigation of an Influence Function Model as a Self-Rotating Wheel Polishing Tool and Its Application in High-Precision Optical Fabrication

A new and patented polishing tool (ZL2020102387137) called a Self-rotating Wheel Polishing Tool (SWPT) was built, and its tool influence function (TIF) was investigated in this study. The polishing wheel is an innovative two-layer structure: a rigid hub inside and a flexible polishing pad outside. By using finite element analysis, the dynamic contact characteristics between the polishing wheel and the workpiece were studied, and the theoretical TIF was modeled. Due to the influence of friction resistance, the TIF is not circular, but oval. We then ran material removal experiment, and it was found that the experimental TIF and the theoretical TIF are very close and both are close to the Gaussian shape. Finally, optical fabrication was performed. After four times of about 3 h fabrication, the form error converged from PV-1.434λ (λ = 632 nm), RMS-0.308λ to PV-0.144λ, RMS-0.009λ, and PV and RMS converged by 90% and 97%, respectively. The form accuracy achieved the expected target of RMS-0.02λ, which proves that the SWPT has the characteristics of high convergence rate and high fabrication accuracy. The SWPT has a broad application prospect in the field of high-precision optical fabrication.

Generalized large optics fabrication multiplexing

High precision astronomical optics are manufactured through deterministic computer controlled optical surfacing processes, such as subaperture small tool polishing, magnetorheological finishing, bonnet tool polishing, and ion beam figuring. Due to the small tool size and the corresponding tool influence function, large optics fabrication is a highly time-consuming process. The framework of multiplexed figuring runs for the simultaneous use of two or more tools is presented. This multiplexing process increases the manufacturing efficiency and reduces the overall cost using parallelized subaperture tools.

Effect of material removal characteristics with varying incident angle in fluid jet polishing process

Fluid jet polishing process is a non-contact type polishing process which is used to manufacture different kind of precise components in various engineering sectors. Such processes require more deterministic material removal distribution to better understand the position of the workpiece material and impingement angle. In this paper attempt is made to simulate the three dimensional Fluid Jet Polishing (FJP) model at vertical and oblique impingement mode. It was observed from the simulation that the shape of Tool Influence Function (TIF) is unsymmetrical and achieve more material removal when jet strikes at oblique impingement mode. Also, concluded that material removal rate becomes more when impingement angle increases from normal axis of rotation.

Investigation of the tool influence function neighborhood effect in atmospheric pressure plasma processing based on an innovative reverse analysis method.

Ultra precision optical surfaces can be efficiently manufactured using a computer-controlled optical surfacing (CCOS) process. Based on the chemical reaction, atmospheric pressure plasma processing (APPP) is a promising deterministic CCOS technique and has great application prospect for the figuring processing as well as freeform generation. However, the plasma jet also works as the heat source, leading to the variation of substrate temperature field. This way, the tool influence function (TIF) is continuously changed, which leads to the nonlinear removal characteristic. Especially, it becomes much more complex when considering the neighboring dwell points, because they are thermally interacted. The conventional time-variant TIF model cannot accurately describe the practical TIF changes. In this paper, an innovative reverse analysis method is proposed to derive the practical TIF changes in APPP. First, the special problem of the TIF neighborhood effect is pointed out. The limitation of the conventional TIF model is analyzed with the assisted thermal model. Then, an innovative reverse analysis method is presented to derive the TIF changes from the practical removal, which is demonstrated with the simulation. Further, the proposed method is applied to the analysis of the TIF changes in APPP. To verify its feasibility, the experimental validation is undertaken, which proves its capability of deriving complex TIF changes.

Generic model of time-variant tool influence function and dwell-time algorithm for deterministic polishing

In computer-controlled optical surfacing (CCOS) techniques, the tool influence function (TIF) is generally assumed to be time-invariant; thus, two-dimensional convolution can be employed to compute the dwell time. However, the material removal rate is time-variant in some CCOS processes. This time-variant material removal rate makes it difficult to accurately model the TIF and leads to impracticality of the two-dimensional convolution algorithm. We herein establish a novel modelling framework of the TIF considering the time-variant material removal rate in CCOS based on a partial differential equation. An updated dwell-time algorithm is also proposed to address the inverse problem of freeform surface generation by using the established TIF. The proposed modelling technique is well demonstrated in magnetically driven internal finishing and abrasive jet machining. The results demonstrate that the model can precisely predict the polished profile against the polishing time, and the novel dwell-time algorithm outperforms the conventional convolution algorithm in terms of efficiency and accuracy. The modelling framework enables localised freeform surface generation and corrective polishing on internal surfaces. The proposed TIF model and dwell-time algorithm may be extended to other CCOS techniques to achieve better figuring accuracy, such as bonnet polishing, ion beam figuring, and plasma jet machining.

Investigation of the polishing mechanism of magnetorheological elastic polishing composites

Computer-controlled ultra-precision polishing technology is widely used for high-quality surface processing. However, its polishing tool has some shortcomings, such as limited adaptability and more surface damage to the complex surface. Therefore, a new smart material-based abrasive tool named magnetorheological elastic polishing composites (MREPCs) and its flexible polishing method is proposed. This study first prepared MREPCs and developed a polishing tool for MREPCs. Then, the material properties of MREPCs were obtained by theoretical and experimental analysis, and the tool influence function (TIF) of the hemispherical MRPECs was established according to the Hertz contact theory, the variable rheological theory, and the Preston equation. Finally, the TIF and the polishing performance of MREPCs were verified by polishing experiments. The results show that the theoretical and the experimentally measured TIF models have a high coincidence, and the developed MREPCs can remove surface material with high precision. The above preliminary study indicates that MREPCs are promising for ultra-precision machining of small-sized parts with complex profiles.

Modeling and prediction of tool influence function under complex edge in sub-aperture optical polishing.

Edge mis-figures are regarded as one of the most difficult technical issues in optical fabrication. At present, only the near straight-line edge tool influence function (TIF) can be fitted by a polynomial function, but it is difficult to unify a 2-D analytical model suitable for complex edge workpieces and various tools, due to the lack of the scientific understanding of the edge removal behavior. In this paper, a comprehensive mathematical model is proposed to reveal the mechanism of the edge effect and accurately predict the complex edge TIF. The concept of a nonlinear edge kernel is first proposed and verified that the nonlinear pressure can be characterized by convoluting the kernel with the edge contour, which can be easily adapted to complex edge cases; besides, the edge kernel obtaining algorithm is established. The linear pressure part is verified to be constrained by the moment balance formula, which occurs in universal joint tool. Besides, the basic pressure distribution is presented to compensate the pressure distortion caused by the uneven form of the tool pad. The introducing of these three parts makes the complex edge pressure modeled efficiently and matched perfectly with the FEA results. In addition, a series of TIF experiments were carried out on various complex edge workpieces and different tools, which could be well predicted by the proposed model in 2-D view.