Free-form Surface Polishing Research Articles

Comprehensive error modelling and error compensation for complex optical free-form surface polishing platform

Four-axis polishing platform plays an important role in machining a complex optical free-form surface and the kinematic error generally determine the accuracy of the optical free-form surface fabricated by this platform. This paper analyses kinematics of the polishing platform based on the homogeneous coordinate transformation theory and the error of kinematics synthesis model is established. Based on minimum error assumption, transition matrix is obtained from machine tool coordinate system to the cutting tool coordinate system and changing rule of comprehensive error in different position and direction is gained in two-axis motion worktable. Laser interferometer is used to measure the geometric error of polishing platform, it is found that different feed rate and measured spacing had no significant effect on the positioning error of moving axis and positioning error rather than the straightness and angle error has more significant influence on the accuracy of machine tool. Compensation experiment was conducted based on integrated error model, the x-axis and z-axis positioning error was reduced by 87.37% and 90.32% after compensation and the compensation result is remarkable.

Comprehensive error modelling and error compensation for complex optical free-form surface polishing platform

Four-axis polishing platform plays an important role in machining a complex optical free-form surface and the kinematic error generally determine the accuracy of the optical free-form surface fabricated by this platform. This paper analyses kinematics of the polishing platform based on the homogeneous coordinate transformation theory and the error of kinematics synthesis model is established. Based on minimum error assumption, transition matrix is obtained from machine tool coordinate system to the cutting tool coordinate system and changing rule of comprehensive error in different position and direction is gained in two-axis motion worktable. Laser interferometer is used to measure the geometric error of polishing platform, it is found that different feed rate and measured spacing had no significant effect on the positioning error of moving axis and positioning error rather than the straightness and angle error has more significant influence on the accuracy of machine tool. Compensation experiment was conducted based on integrated error model, the x-axis and z-axis positioning error was reduced by 87.37% and 90.32% after compensation and the compensation result is remarkable.

Deterministic polishing of freeform optical surface by iterative intersection tool path in an off-axial three-mirror anastigmat imaging system

Deterministic polishing as the final step of freeform surface machining can acquire preferable form accuracy. In this article, a deterministic polishing model based on iterative intersection tool path is presented to meet the requirement of high-form accuracy in freeform surface. In the polishing process, on-machine measurement and point set registration method are adopted for installation error extraction and form error calculation. The iterative polishing can be finished without discharging of workpiece by on-machine measurement strategy, which will reduce the processing time and improve the machining efficiency. In addition, a boundary extension method is employed to diminish the surface edge collapse generated by edge effect. Finally, the polishing experiment of freeform optical surface in an off-axial three-mirror anastigmat imaging system is conducted to verify the effectiveness of the proposed model.

Corrective polishing of freeform optical surfaces in an off-axis three-mirror imaging system

The application of freeform surface in the off-axis three-mirror imaging system can greatly improve its optical performance. However, it is difficult for fabrication of freeform optical surface to high precision by traditional machining technology. This paper focuses on the corrective polishing of the primary mirror and tertiary mirror, which are fabricated on one monolithic substrate and described by NURBS-based freeform surfaces, in an off-axis three-mirror imaging system. The integrated polishing process system is proposed for polishing the two mirrors on the 4-axis CNC polishing machine by use of spherical polishing tool. The tool influence function (TIF) module, polishing path generation and dwell time calculation module included in the integrated polishing process system are described respectively. The material removal on the measurement line of part surface is predicted to validate the dwell time calculation algorithm. The polishing experiments of the primary mirror and tertiary mirror are performed to verify the proposed integrated polishing process system.

Conformal polishing approach: Tool footprint analysis

Polishing process is one of the most critical manufacturing processes during a metal part production because it determines the final quality of the product. Free-form surface polishing is a handmade process with lots of rejected parts, scrap generation and time and energy consumption. Two different research lines are being developed: prediction models of the final surface quality parameters and an analysis of the amount of material removed depending on the polishing parameters to predict the tool footprint during the polishing task. This research lays the foundations for a future automatic conformal polishing system. It is based on rotational and translational tool with dry abrasive in the front mounted at the end of a robot. A tool to part concept is used, useful for large or heavy workpieces. Results are applied on different curved parts typically used in tooling industry, aeronautics or automotive. A mathematical model has been developed to predict the amount of material removed in function of polishing parameters. Model has been fitted for different abrasives and raw materials. Results have shown deviations under 20% that implies a reliable and controllable process. Smaller amount of material can be removed in controlled areas of a three-dimensional workpiece.

Tool path generation for ultra-precision polishing of freeform optical surfaces in an off-axis three-mirror imaging system

The optical performance of the off-axis three-mirror imaging system can be greatly improved using freeform surfaces. This article focuses on the polishing of the primary mirror and tertiary mirror in an off-axis three-mirror imaging system. The primary mirror and tertiary mirror are fabricated on one monolithic substrate and described by non-uniform rational B-spline–based freeform surfaces. The separated and integrated polishing strategies are presented for polishing the two mirrors on the four-axis computer numerical control polishing platform. A tool path generation approach is proposed for polishing of the non-uniform rational B-spline–based freeform surface. Three kinds of the tool paths are given for ultra-precision polishing of the primary mirror and tertiary mirror with the freeform surfaces. The concentric circle path and the approximately concentric circle path are generated for polishing two mirrors separately, while the spiral path is calculated for integrated polishing of two mirrors simultaneously. The polishing tool posture along the planned tool paths is also analyzed. The ultra-precision polishing experiments of the primary mirror and tertiary mirror on the four-axis computer numerical control polishing platform are performed to verify the proposed approach for tool path generation.

光学自由曲面研抛机床的综合误差建模与补偿

To improve the machining accuracy of an optical free-form surface,an integrated error model for five-axis polishing machine tool was established based on multi-body system theory.The movement error and rotation error of every axis were measured and analyzed by direct and repetitive measurement model,and it shows that the feed speed and measurement spacing have no significant influence on the movement and rotation errors.By taking the error data into the integrated error model,the variation rule of movement and rotation errors which are the components in the three axes of x,yand zfrom the integrated error of polishing machine tool was obtained.According to the above analysis,the main influence factor of integrated error is linear displacement errors.The compensation experiment was conducted based on integrated error model.The linear displacement errors of the three axes of x,yand z have been compensated obviously and they are decreased by 88%,89% and84%respectively.The experiment results indicate that the integrated error model and compensationmethod have high accuracy and excellent robustness.

Uniform scanning path generation for abrasive waterjet polishing of free-form surfaces modeled by triangulated meshes

In this paper, a method is proposed to generate scanning paths to be used in automated abrasive waterjet polishing of free-form surfaces. This method is able to produce trajectories with constant offset distance between curves on surfaces with holes and complex boundaries without reconfiguration of their triangular mesh model. For this, the particular requirements of this polishing technique to be kept along the path are investigated. Next, a reference curve is obtained and using geodesic distances in specific directions, the adjacent offset curves are found. Finally, if needed, the main trajectory is divided into a set of continuous sub-trajectories. By defining two indices, the effect of the shape of the surface and the configuration of the generated path on the uniformity of the distribution of the waterjet is evaluated. Through several examples, it is shown that the method can effectively generate scanning paths adapted to the requirements of this technique.

A material removal and surface roughness evolution model for loose abrasive polishing of free form surfaces

We report on the development of a simple process model, motivated by a need to predict the evolution of surface roughness and geometrical change over external, three dimensional free form surfaces undergoing a loose abrasive polishing process. To this end, the process model was derived from tribological wear laws and cast in terms of the point sliding velocity and apparent pressure and then benchmarked against data drawn from experiments in three disparate loose abrasive finishing techniques, namely, vibratory finishing, abrasive flow machining and magnetorheological finishing. We conclude with a brief discussion on the potential and limitations of the model in analysing loose abrasive finishing processes.

Predictive models of the local and the global polished profiles in deterministic polishing of free-form surfaces

The deterministic polishing process is usually used as the final step to produce part surfaces of high surface finish and form accuracy. This article presents the models of the local and the global polished profiles for the deterministic polishing process when a surface is polished by a spherical polisher. The local polished profile is modeled by integrating the index of material removal, which is defined as the polished depth at unit length of the polishing path, at each tool–surface contact region. According to the model, the local polished profile is determined by the process parameters, the tool attitude, the measuring angle and the geometrical/mechanical properties of workpiece and tool. The linear algebraic expression of the global polished profile is derived by convoluting the local polished depth at each dwell point of the polishing process. The polishing experiments are conducted to verify the proposed model in the different polishing conditions. Moreover, simulation results are given to illustrate the application of the proposed model in optimizing the feed rate to minimize the surface form error in the deterministic polishing process.

Improving tool wear and surface covering in polishing via toolpath optimization

Polishing operations are commonly carried out manually, thus inducing variability on the surface quality. The aim of this paper is to automate the polishing of free-form surfaces in order to obtain high quality surfaces. Tool wear and toolpath surface covering have a great impact on surface properties. The current work proposes therefore a toolpath which optimizes both tool wear and surface covering. This toolpath is composed of an optimized elementary pattern repeated along a 5-axis carrier trajectory. Usually, trochoid patterns are used. Non uniform wear of the tool and uneven probability density function of the surface covering are the main inconvenients of such pattern. So, this paper proposes two optimized patterns: Spade and Triangular. Both of them lead to uniform tool wear. Our paper also demonstrates that the second solution provides a uniform probability density function. All presented computations are validated experimentally.

MR Fluid Jet Polishing 시스템을 위한 분사노즐 및 전자석 모듈 개발

Generally, abrasive fluid jet polishing system has been used for polishing of complex shape or freeform surface which has steep local slopes. In the system, abrasive fluid jet is injected through a nozzle at high pressure; however, it is inevitable to lose its coherence as the jet exits a nozzle. This problem causes incorrect polishing results because of unstable and unpredictable workpiece material removal at the impact zone. In order to solve this problem, MR fluid jet polishing method has been developed using a mixture of abrasive and MR fluid which can maintain highly collimated and coherent jet by applied magnetic field. Thus, in this study, an injection nozzle and an electromagnetic module, most important parts in the MR polishing system, were designed and verified by magnetic field and flow analysis. As the results of experiments, it can be confirmed that stable fluid jets for polishing were generated since smooth W-shapes and uniform spot size were observed regardless of standoff distance changes.

Stability Analysis of the MRT-Based Compliant Polishing Tool System

In order to meet the needs for the precise polishing of free-form surfaces, a new compliant polishing tool system was designed based on a magnetorheological torque servo (MRT), and integrated into a CNC milling machine. Through analysis, it was pointed out that the key factor affecting the polishing quality of this system is the stability of the system. By means of the 3D geometric modeling software ProE, the finite element analysis software ANSYS, and the dynamic simulation software ADAMS, the rigid-flexible mixed model of the system was established and the stability of the polishing pressure and tool position was numerically analyzed.

Comparative Study of Magnetic Abrasive Finishing in Free-Form Surface Based on Different Polishing Head

Nowadays, researches concerned magnetic abrasive finishing (MAF) are becoming increasingly popular. Polishing head is one of the most important factors in the whole polishing system in which magnetic abrasive act directly on the workpiece. In this paper, two kinds of polishing heads applied in the polishing of free form surface are proposed. They are hard polishing head and soft polishing head, respectively. And some important factors are contrasted such as selfsharpening capacity, morphology distribution, and removal uniformity. Moreover, the finishing force is the key factor which is different between the two polishing heads having a great influence on polishing effect. Through comparison and analysis, the soft polishing head is better to finish free form surface. And the experimental results reflect its superiority in polishing free form surface.

Study on Profile-Adaptive Tool System for Small Robots in Large Freeform Surface Polishing

An adaptive tool system of polishing robots for large freeform surface which is installed discoid tool is proposed. To improve processing efficiency, the mechanical of adaptive tool system adjust to curvature changing of large freeform surface is designed. Adaptability of the processing is analyzed and simulated, and kinematic equation of tool system is established. The polishing process of large freeform surfaces with tool system is analyzed.

Freeform optical surface polishing machine helps optical designers

Freeform optical surface polishing machine helps optical designers

Analysis of surface generation in the ultraprecision polishing of freeform surfaces

The use of freeform designs in engineering surfaces has become increasingly popular over the last decade. Applications of freeform shapes range from aesthetics of components to the bending of light rays through advanced optic designs. The fabrication of the components for these applications requires submicrometre form accuracy, in some cases with surface roughness at nanometric levels. Ultraprecision polishing is an emerging technology for the fabrication of high-precision and high-quality freeform surfaces. However, the factors affecting nanosurface generation in ultraprecision polishing have received relatively little attention. Moreover, the quality of the polished surface relies heavily on appropriate selection of process conditions and polishing strategies. This paper presents an analytical study of the factors affecting surface generation in ultraprecision polishing. A series of polishing experiments have been designed and undertaken, allowing the relationships between various factors and the surface quality of the workpiece to be determined. The results of the study provide a better understanding of nanosurface generation, as well as the strategy for optimizing surface quality, in the ultraprecision polishing of freeform surfaces.

RESEARCH ON POLISHING PROCESS OF A SPECIAL POLISHING MACHINE TOOL

In this paper, a serial-parallel hybrid special polishing machine tool based on the elastic polishing theory is developed, which is used for polishing mould surface by using bound abrasives. This machine tool mostly consists of parallel mechanism of three-dimensional moving platform, series rotational mechanism of two degrees of freedom and elastic polishing tool device. The parallel mechanism controls the spatial position of the polishing tool. The series mechanism controls the pose of the polishing tool. The elastic polishing tool system can realize active control by a pneumatic servo system and passive conformity by a spring. The main process parameters that have influence on surface roughness and polishing efficiency are tool speed, feed rate, force, pose angle and polishing number of times. Optimal combination of process parameters is presented by the Taguchi and grey relational analysis, which provide a choice of parameters as a basis for free-form surface polishing in practice.

Fractal Tool-Path Planning for Free-Form Surface Polishing System

This paper presents a reasonable method for generating the tool-path of free-form surface polishing using the fractal curves. Free-form surface polishing processes as a finishing process are used to reduce the roughness of surfaces and smooth the surface form by eliminating the surface waviness left by tool marks, EDM spark erosion and so on. In the interest of realizing this aim without introducing undesirable surface waviness and time efficiency, a tool-path should provide even coverage of free-form surface during polishing. A fractal curve is suitable to cover the free-form surface uniformly at any complexity due to its plane-filling and self-similar characteristics. A method of generating the fractal path for free-form surface polishing is presented, and also an automatic polishing system is installed to confirm the path planning method’s validity.

314 GCによる曲面研磨に関する研究(OS 材料加工・精密加工(その2))

314 GCによる曲面研磨に関する研究(OS 材料加工・精密加工(その2))