Computer-controlled Optical Surfacing Process Research Articles

Effect of Robot Motion Accuracy on Surface Form during Computer-Controlled Optical Surfacing Process

Nowadays, large-aperture optical components are increasingly used in high-power laser systems, remote-sensing satellites, and space-based astronomical telescopes. Fabricating these surfaces with submicron-scale shape accuracy and a nanoscale surface finish has been a great challenge for the optical industry, especially for hard and difficult-to-machine materials. Thus, to achieve the high-efficiency and high-precision polishing of large-aperture aspherical optical parts, this study combined robotic machining technology with computer-controlled optical surfacing (CCOS) technology and investigated the effect of robot motion accuracy on the surface topography of workpieces during polishing. First, a material removal model considering the normal error of the polishing tool was developed based on contact mechanics, kinematic theory, and the abrasion mechanism. Next, in combination with the polishing trajectory, the surface morphology and form accuracy after polishing were predicted under different normal-error conditions. Then, preliminary experiments were conducted to verify the model. The experimental data agreed with the simulation results, showing that as the normal error increased from 0° to 0.5° and 1°, the peak-to-valley (PV) values of the surface profile of the optical element decreased from 5.42, 5.28, and 4.68 μm to 3.97, 4.09, and 4.43 μm, respectively. The corresponding convergence rates were 26.8%, 22.5%, and 5.3%. The root mean square (RMS) values decreased from 0.754, 0.895, and 0.678 μm to 0.593, 0.620, and 0.583 μm, with corresponding convergence rates of 21.4%, 30.7% and 14.0%, respectively. Moreover, a higher motion accuracy enabled the polishing robot to reduce the mid- and high-frequency errors of the optical element.

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.

Multi-tool optimization for computer controlled optical surfacing.

With the rapid development of precision technologies, the demand of high-precision optical surfaces has drastically increased. These optical surfaces are mainly fabricated with computer controlled optical surfacing (CCOS). In a CCOS process, a target surface removal profile is achieved by scheduling the dwell time for a set of machine tools. The optimized dwell time should be positive and smooth to ensure convergence to the target while considering CNC dynamics. The total run time of each machine tool is also expected to be balanced to improve the overall processing efficiency. In the past few decades, dwell time optimization for a single machine tool has been extensively developed. While the methods are applicable to multi-tool scenarios, they fail to consider the overall contributions of multiple tools simultaneously. In this paper, we conduct a systematic study on the strategies for multi-tool dwell time optimization and propose an innovative method for simultaneously scheduling dwell time for multiple tools for the first time. First, the influential factors to the positiveness and smoothness of dwell time solutions for a single machine tool are analyzed. The compensation strategies that minimize the residual while considering the CNC dynamics limit are then proposed. Afterwards, these strategies are extended to the proposed multi-tool optimization that further balances the run time of machine tools. Finally, the superiority of each strategy is carefully studied via simulation and experiment. The experiment is performed by bonnet polishing a 60 mm × 60 mm mirror with three tools of different diameters (i.e., 12 mm, 8 mm, and 5 mm). The figure error of the mirror is reduced from 45.42 nm to 11.18 nm root mean square in 13.28 min. Moreover, the measured polishing result well coincides with the estimation, which proves the effectiveness of the proposed method.

Modeling and experimentation of dynamic material removal characteristics in dual-axis wheel polishing

CCOS (computer-controlled optical surfacing) approach is widely used in different optical polishing processes for making ultra-precision components with high surface form accuracy requirements. Under the polishing mode using complex tool motions, middle-spatial-frequency errors (MSF, i.e., residual ripples) tend to be generated on the workpiece surface, which would deteriorate the functional performance of the parts. In this paper, a dynamical removal model (DRM) based on the spatial kinematic analysis and polishing material removal theory is proposed, to investigate the actual material removal characteristics in dual-axis wheel polishing (DAWP). The model is developed to calculate the overall material removal profile (low-spatial-frequency error, LSF) and the middle-spatial-frequency errors, simultaneously. The shape and the stability of the tool influence function (TIF) are firstly investigated. A series of straight line path polishing tests on BK7 glass are carried out to investigate the effects of process parameters on the generated MSF errors and also check the validity of the proposed DRM. Uniform polishing tests on 50 × 50 mm BK7 samples are conducted, under different polishing parameters, the power spectral density (PSD) characteristics of the surface are also analyzed. The results show that the proposed model can effectively predict the material removal profile and especially the ripple characteristics generated on the surface, which are not reflected when using the conventional convolution algorithm typically used in a CCOS process. When increasing the ratio of feed velocity to co-rotating speed, the wavelength and amplitude of the residual ripples increase, and the ratio of ripple amplitude to total material removal depth also increases. The level of residual ripples can be effectively restrained by the appropriate setting of the speed ratio (reducing the feed velocity or increasing the co-rotating speed).

Modeling of pad surface topography and material removal characteristics for computer-controlled optical surfacing process

Computer-controlled optical surfacing (CCOS) technology is an advantageous polishing process for producing optical surfaces with high convergence rates and high form accuracy, especially for fabricating hard and brittle materials. However, the optimum control of polishing parameters depends critically on the understanding of polishing mechanisms and modeling of material removal characteristics to achieve a deterministic process with high polishing efficiency. Removal analysis still requires further enhancement due to the multi-disciplinary, multi-scale complexity of the material removal mechanism involved in CCOS. Thus, this study presents a novel statistical asperity model and a material removal model to provide scientific and quantitative knowledge of the material removal mechanisms in CCOS. The model is developed on the basis of the research on statistical method, contact mechanics, iterative algorithm, abrasive wear mechanism, and cumulative removal process in CCOS. Practical experiments with different polishing parameters are performed to verify the theoretical model. Simulation results reasonably agree with measured data. Simulation experiments also show that the proposed model helps clarify the effect of pad surface topography on the micro-contact behavior and the material removal characteristics in CCOS and thus forms the theoretical basis for optimizing the polishing process.

Optimization technique for rolled edge control process based on the acentric tool influence functions.

In the process of computer controlled optical surfacing (CCOS), the uncontrollable rolled edge restricts further improvements of the machining accuracy and efficiency. Two reasons are responsible for the rolled edge problem during small tool polishing. One is that the edge areas cannot be processed because of the orbit movement. The other is that changing the tool influence function (TIF) is difficult to compensate for in algorithms, since pressure step appears in the local pressure distribution at the surface edge. In this paper, an acentric tool influence function (A-TIF) is designed to remove the rolled edge after CCOS polishing. The model of A-TIF is analyzed theoretically, and a control point translation dwell time algorithm is used to verify that the full aperture of the workpiece can be covered by the peak removal point of the tool influence functions. Thus, surface residual error in the full aperture can be effectively corrected. Finally, the experiments are carried out. Two fused silica glass samples of 100 mm×100 mm are polished by traditional CCOS and the A-TIF method, respectively. The rolled edge was clearly produced in the sample polished by the traditional CCOS, while residual errors do not show this problem the sample polished by the A-TIF method. Therefore, the rolled edge caused by the traditional CCOS process is successfully suppressed during the A-TIF process. The ability to suppress the rolled edge of the designed A-TIF has been confirmed.

Distortion of removal function based on the local asphericity of aspheric surface and the viscoelasticity of polishing tool in computer-controlled optical surfacing

In the process of large aspheric optical surfaces fabrication, the distortion of the removal function is a big problem that affects the producing efficiency and accuracy, due to the misfit between the tool and the aspheric surface in the contact region. Consequently, this paper aims to find out the influence factors and the distortion rule of aspheric removal function in the computer-controlled optical surfacing. Firstly, based on the analysis of the sub-aperture polishing technology for the large aspheric optical surfaces, the local asphericity of aspheric surface and the viscoelasticity of polishing tool are supposed to be the main sources. After that, a method to calculate the local asphericity considering the misfit between the tool and the aspheric surface is proposed based on the least square method, and the viscoelasticity of the polishing tool is obtained through viscoelastic experiment. Subsequently, combining the results of the local asphericity of aspheric surface and the viscoelasticity of polishing tool, the prediction of the distortion rule of aspheric removal function is presented. Finally, the comparative experiment is carried out, and the removal function on different regions of the aspheric surface is obtained. The experimental result indicated that the distortion of the removal function is consistent with the theoretical result. Through this study, the distortion rule of aspheric removal function in the computer-controlled optical surfacing with pitch tool is finally mastered, which provides a theoretical guidance for the computer-controlled optical surfacing process optimization.

컴퓨터 제어를 통한 광학 가공에서의 다양한 툴 영향 함수의 모델링

The computer controlled optical surfacing (CCOS) technique provides superior fabrication performance for optical mirrors when compared to the conventional method, which relies heavily on the skill of the optician. The CCOS technique provides improvements in terms of mass production, low cost, and short polishing time, and are achieved by estimating and controlling the moving speed of the tool and toolpath through a numerical analysis of the tool influence function (TIF). Hence, the exact estimation of various TIFs is critical for high convergence rates and high form accuracy in the CCOS process. In this paper, we suggest a new model for TIFs, which can be applied for various tool shapes, different velocity distributions, and non-uniform tool pressure distributions. Our proposed TIFs were also verified by comparisons with experimental results. We anticipate that these new TIFs will have a major role in improving the form accuracy and shortening the polishing time by increasing the accuracy of the material removal rate.

Unicursal random maze tool path for computer-controlled optical surfacing.

A novel unicursal random maze tool path is proposed in this paper, which can not only implement uniform coverage of the polishing surfaces, but also possesses randomness and multidirectionality. The simulation experiments along with the practical polishing experiments are conducted to make the comparison of three kinds of paths, including maze path, raster path, and Hilbert path. The experimental results validate that the maze path can warrant uniform polishing and avoid the appearance of the periodical structures in the polished surface. It is also more effective than the Hilbert path in restraining the mid-spatial frequency error in computer-controlled optical surfacing process.

Optimization of parameters for bonnet polishing based on the minimum residual error method

For extremely high accuracy optical elements, the residual error induced by the superposition of the tool influence function cannot be ignored and leads to medium-high frequency errors. Even though the continuous computer-controlled optical surfacing process is better than the discrete one, which can decrease this error to a certain degree, the error still exists in scanning directions when adopting the raster path. The purpose of this paper is to optimize the parameters used in bonnet polishing to restrain this error. The formation of this error was theoretically demonstrated and will also be further experimentally presented using our newly designed prototype. Orthogonal simulation experiments were designed for the following five major operating parameters (some of them are normalized) at four levels: inner pressure, z offset, raster distance, H-axis speed, and precession angle. The minimum residual error method was used to evaluate the simulations. The results showed the impact of the evaluated parameters on the residual error. The parameters in descending order of impact are as follows: raster distance, z offset, inner pressure, H-axis speed, and precession angle. An optimal combination of these five parameters among the four levels considered, based on the minimum residual error method, was determined.

Method to calculate the error correction ability of tool influence function in certain polishing conditions

Tool influence function (TIF) is quite important for computer-controlled optical surfacing (CCOS) technology. Quantitatively investigating the error correction ability of TIF in frequency domain is essential for CCOS to restrain different spatial frequency errors. The smoothing spectral function (SSF) is a newly proposed parameter to evaluate the error correction ability of CCOS process. Based on the SSF, a new method to calculate the error correction ability of TIF in certain polishing conditions will be proposed. The basic mathematical model for this method will be established in theory. A set of polishing experiments with rigid conformal (RC) tool are performed to calculate the error correction ability of TIF. The calculated results can quantitatively indicate the error correction ability of TIF for different spatial frequency errors in certain polishing conditions.

A method to evaluate error correction ability of computer controlled optical surfacing process

Quantitatively investigating error correction ability in frequency domain is important for computer controlled optical surfacing (CCOS) process to correct different spatial frequency errors. Based on the mathematical model coherence between filtering and material removal process of CCOS, a method is proposed to quantitatively evaluate the correction ability of CCOS process. A generalized model named normalized smoothing spectral function (SSF) will be established combine convolution model of CCOS and power spectral density (PSD) function. A set of polishing experiments are performed to calculate SSF curves and validate SSF model. By comparing the results of SSF curve with PSD curve and surface figure, it reveals that SSF curve can quantitatively indicate the correction ability of CCOS process for different spatial frequency errors.

Frequency-domain analysis of computer-controlled optical surfacing processes

Mid-high spatial frequency errors are often induced on optical surfaces polished by computer-controlled optical surfacing (CCOS) processes. In order to efficiently remove these errors, which would degrade the performances of optical systems, the ability of a CCOS process to correct the errors have been investigated based on the convolution integral model in view of the availability of material removal. To quantify the ability, some conceptions, such as figure correcting ability and material removal availability (MRA), have been proposed. The research result reveals that the MRA of the CCOS process to correct a single spatial frequency error is determined by its tool removal function (TRF), and it equals the normalized amplitude spectrum of the Fourier transform of its TRF. Finally, three sine surfaces were etched using ion beam figuring (IBF), which is a typical CCOS process. The experimental results have verified the theoretical analysis. The employed method and the conclusions of this work provide a useful mathematical basis to analyze and optimize CCOS processes.