Chunjin Wang

Dwell-time algorithm for polishing large optics

The calculation of the dwell time plays a crucial role in polishing precision large optics. Although some studies have taken place, it remains a challenge to develop a calculation algorithm which is absolutely stable, together with a high convergence ratio and fast solution speed even for extremely large mirrors. For this aim, we introduced a self-adaptive iterative algorithm to calculate the dwell time in this paper. Simulations were conducted in bonnet polishing (BP) to test the performance of this method on a real 430  mm × 430  mm fused silica part with the initial surface error PV=1741.29  nm, RMS=433.204  nm. The final surface residual error in the clear aperture after two simulation steps turned out to be PV=11.7  nm, RMS=0.5  nm. The results confirm that this method is stable and has a high convergence ratio and fast solution speed even with an ordinary computer. It is notable that the solution time is usually just a few seconds even on a 1000  mm × 1000  mm part. Hence, we believe that this method is perfectly suitable for polishing large optics. And not only can it be applied to BP, but it can also be applied to other subaperture deterministic polishing processes.

Highly efficient deterministic polishing using a semirigid bonnet

Abstract. This paper presents a semirigid (SR) bonnet tool which has the advantages of high efficiency and determinacy for material removal on optical elements and also has the potential to be used on aspheric optics. It consists of three layers: a metal sheet, a rubber membrane, and a polishing pad, from inside to outside. It inherits the flexibility of a normal bonnet but has a higher stiffness. Finite element analysis was performed to determine that the stainless steel is the best-suited material for use as the metal sheet. An SR bonnet with a stainless-steel metal sheet was fabricated and tested. Its tool influence function (TIF) is Gaussian-like, and the TIF stability is more than 90%. The peak-to-valley of its uniform removal area is less than 0.1λ. Tool ripples are highly depressed and the surface profile is well preserved in the prepolishing test. In 12 min, ∼36  mm3 of material is removed.

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.

Analysis of corrective characteristics of various polishing methods for mid-frequency errors

The theoretical analysis of corrective characteristics of three kinds of polishing methods for mid-frequency errors was studied, which was aimed to confirm the possibility that computer control optical surfacing and computer control active-lap can be replaced by bonnet polishing in the machining process. The first step was to calculate the removal functions of three kinds of polishing technologies and use fast Fourier transform to figure out the frequency spectrum of each method. After that, according to the frequency spectra, curves of cut-off frequencies related to the working ranges of spatial frequencies errors were obtained. It revealed that the affected scope of spatial frequencies is determined by the polishing method, diameter size of polishing tool and shape of removal function. Moreover, only low-frequency errors could be modified and mid-frequency errors could not be corrected or created by computer control active-lap, and computer control optical surfacing can correct part of the mid-frequency errors and low-frequency errors in the polishing process, but at the same time can produce some new mid-frequency errors; as for bonnet polishing, it can be computer control active-lap-like in smoothing which only modified and created the low-frequency errors or computer control optical surfacing-like which corrected and created the mid-frequency errors in local polishing. Otherwise, the efficiency of bonnet polishing is higher than the other two methods. As a result, seen from the point of correction ability of mid-frequency or polishing efficiency, bonnet polishing could replace computer control active-lap and computer control optical surfacing for finishing two polishing stages by only one tool, which is significant to extending the application of bonnet polishing in optical manufacturing.

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

Abstract. 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.

Dynamic removal function modeling of bonnet tool polishing on optics elements

The dwell time function of the bonnet tool polishing on optics elements is achieved based on static removal function in recent studies.But the polishing tool keeps moving during the process,its necessary to do the research on dynamic removal function.The static and dynamic contact zone is acquired through finite element simulation analysis,and so is the contact pressure.Both of the contact zones are circle and the size of them are almost the same.The peak point of the dynamic contact pressure has an offset contrary to the direction of the tool movement compared to the static contact pressure.The dynamic contact pressure distribution function is deduced by using the least square method based on the theory that the static pressure distribution function is a modified Gaussian function.The device which can extract both the dynamic and static contact zone is set up to capture them on the condition of different offset.Then the simulation results are verified.The dynamic removal function is deduced and numerical simulated based on the forward simulation and experiment results.The removal rate of the dynamic removal function is smaller than the static removal function and its nadir has a deflection compared to the latter.

Movement modeling and control of precession mechanism for bonnet tool polishing large aixsymmetrical aspheric lenses

Movement modeling and control for bonnet tool polishing large axisymmetrical aspheric lenses is present.The intersection point of the spin axis and the bonnet is selected to be object,after analyzing the structure of bonnet tool and process feature of large axisymmetrical aspheric lenses polishing;a base coordinate is set up with the centre of bonnet to be its origin point.As the included angle of the spin axis of bonnet tool and the local normal is fixed in continuous precession polishing,a corresponding coordinate is set up to get the position parameters of the intersection point of the spin axis and the bonnet when polishing a random point,the position parameters of the intersection point of the spin axis and the bonnet in base coordinate are got according to space coordinate conversion;Movement model is obtained by space matrix transformation,based on the surface equation of large axisymmetrix aspheric lenses,processing control model and the position parameters got in last step;Finally,most efficiency algorithm is added to the movement model,and precession motion curve is got by simulation.The correctness of movement model and control algorithm is confirmed through simulating the trend of spin axis of bonnet follows the local normal and comparing the simulated value of precession angle with the actual value of precession angle.

Effect of the tool influence function shape of the semirigid bonnet to the tool path ripple error

Abstract. To suppress the medium-high spatial frequency, error on optical surfaces is still a challenging work to date, and the tool path ripple (TPR) error is the main reason for these errors. With this in view, the effect of the tool influence function (TIF) shape of the semirigid (SR) bonnet to the TPR error is analyzed. The SR bonnet is a recently developed bonnet tool for high efficiency polishing. This tool can generate three kinds of TIF including Gaussian-like shape, trapezoidal shape, and “M” shape. Experimental studies have been conducted to analyze their effect to the root mean square/peak-to-valley value of the TPR error, and discussions have been made on those results. It is found that different shapes of TIF can be implemented through controlling its inflated pressure. The Gaussian-like shape has the highest probability to generate lower TPR error than the trapezoidal shape and “M” shape TIFs, which have been proven by the verification experiments.

Effect of the inflated-pressure to the tool influence function for polishing using SR bonnet

The purpose of this paper is to study the effect of the inner pressure to the tool influence function (TIF) for polishing using a semi-rigid (SR) bonnet tool. The simulation model of a Semi-rigid (SR) bonnet polishing tool polishing BK7 is demonstrated and the pressure distribution data under different inflated-pressures in the contact area has been extracted. It’s observed that the inflated-pressure has few effects to the polishing pressure, and their shapes are also Gaussian-like. Hence, we made a hypothesis that the effect of inflated-pressure to the TIF is rather small. To verify this hypothesis, a group of experiments to generate TIFs under different inflated-pressure are conducted, and the hypothesis has been proved to be correct through comparing these TIFs.

Analysis of Effects of precession mechanism error on polishing spot for bonnet polishing

In this article, a research was conducted on the effects of the precession mechanism error on polishing spot, and it is helpful for optimizing the mechanism. In the research, an error model was built to analyze the error caused by gravity and polishing force on the accuracy of the mechanism, finite element analysis and MATLAB simulation were carried out based on the error model to estimate the effects, and, finally, an experiment was conducted to test the simulation result. It was found that the precession mechanism error mainly has an influence on the position of polishing spot in x and y directions. Simulation results show the position error up to −698.7 µm in y direction and −88.5 µm in z direction under free condition, while in polishing process, the error decreased 588.4 µm in y direction and 26.7 µm in z direction. The size of single polishing spot decreased 2.67%, while the size of four-step tilted polishing spot and continuous polishing spot increased 0.66% and 6.78%, respectively. Through experiment, it can be seen that the size of the polishing spot is also affected by the inflation pressure in bonnet tool, rigidity of bonnet tool, tool clamping error, and mechanism processing error.