Shape control and removal footprint characteristics of a novel wheel bonnet polishing tool

NIAOT has made a stressed lap polishing machine and finished a φ910mm, F/2.0 paraboloid. In the process we found shape control strategy is an important technology for stressed lap polishing tool and this kind of content has not been discussed systematically before. So this paper mainly dedicates to the method of lap shape control. Firstly a mathematical model of stressed lap is introduced. Then three shape control methods are put forward one by one concerning aspects as shape accuracy and deformation hysteresis. The fundamental method is least square algorithm. On the base of it we put forward its reformation form: least square algorithm with damping factor. To get more satisfied performance a new algorithm using optimization under constrains of linear inequalities is proposed. Through theoretical analysis and computer simulation some comparisons are made among three methods. Finally we have done experiments using stressed lap polishing machine in NIAOT and the results obtained substantiate the feasibility and efficiency of our method.

As a new polishing method, bonnet polishing is suitable for polishing the curved surface due to its advantages in flexibility and adaptability of the polishing tool. In the polishing process, the contact state between the bonnet and the curved surface always changes. The traditional polishing tool path with equal interval will inevitably lead to over-polished areas and unpolished areas. In this article, a new tool path for bonnet polishing, which is called the revised Archimedes spiral polishing path, is proposed to ensure the physical uniform coverage of the curved surface in bonnet polishing. The path generation method is based on the modified tool–workpiece contact model and the pointwise searching algorithm. To prove the effectiveness of the revised path, two aspheric workpieces were polished along the traditional Archimedes spiral polishing path and the revised path, respectively. The roughnesses of the two workpieces are 10.94 and 10 nm, and the profile tolerances are 0.4097 and 0.2037 μm, respectively. The experimental results show that the revised path achieves lower roughness and surface tolerance than the traditional Archimedes path, which indicates that the revised path can achieve uniform physical coverage on the surface.

A new optical manufacturing technology called bonnet polishing has been developed over last decade. During bonnet polishing, the puffed bonnet is flexible and self-reacting against the surface configuration of optical parts. So the same polishing tool can be used in machining the optical parts with different curvature. The mechanism of the bonnet polishing is described in this paper firstly. Since the optical workpiece has been polished in the “polishing spot”, the bonnet polishing experiments have been accomplished on the trial-manufacturing machine to study the effect of technological parameters on the size and shape of “polishing spot” and the material removal rate of optical workpiece. At last, the material removal rules of the bonnet polishing have been given in the paper.

A new optical manufacturing technology called bonnet polishing has been developed over last decade. During bonnet polishing, the puffed bonnet is flexible and self-reacting against the surface configuration of optical parts. So the same polishing tool can be used in machining the optical parts with different curvature. The mechanism of the bonnet polishing is described in this paper firstly. Since the optical workpiece has been polished in the “polishing spot”, the bonnet polishing experiments have been accomplished on the trial-manufacturing machine to study the effect of technological parameters on the size and shape of “polishing spot” and the material removal rate of optical workpiece. At last, the material removal rules of the bonnet polishing have been given in the paper.

The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.

Compliant machining processes, such as bonnet polishing, can be used on hard and brittle ceramic materials such as alumina and silicon carbide, to produce ultra-precise surfaces with sub-micron form accuracy and nanometric surface roughness. However, a comprehensive understanding of the removal mechanism in such process is lacking. In this paper, an analytical model is proposed that is based on the existence of “three zones” in compliant machining process, namely elastic recovery, plastic removal and brittle fracture. The inherent relationships of the three critical pressures with actual pressure, due to compression of the elastic bonnet tool and asperity effect, are established and analyzed in association with different material removal behaviors. Analysis indicates that pad asperity plays an important role in material removal and that lower material hardness combined with higher tensile strength contributes to enlarged plastic removal zone, and thus higher manufacturability. Removal footprints and polishing tests were then generated to verify accurate prediction of the material removal rate under different conditions and demonstrate effectiveness of the proposed model.

This study proposes and develops a novel polishing system for micro molds which need high precision polishing, high aspect ratio of micro channel structure, or further miniaturization for micro channel structure. The proposed system has been named a “low contact force polishing system for micro mold utilizing 2-dimensional low frequency vibrations (2DLFV) with piezoelectric actuators (PZTs) and a mechanical transformer mechanism.” The system consists of 2DLFV with PZTs incorporated into the mechanical transformer structure, a low contact force loader, and a polishing tool. The shape of the polishing tool is flexible and can be changed depending on the complicatedness of the shape of the work. Several experiments are conducted to evaluate the performance of the polishing system. The evaluation reveals that a convex removal footprint can be easily achieved with the polishing system. The fact that the relationship between the removal depth and the polishing time suit Preston’s law well shows a stable polishing process is realized with the system. The polishing performances remains the same even if the shape of the polishing tool is changed. This indicates that the system can use polishing tools of a wide selection of shapes, which allows the system to polish a large variety of materials and most of the complicated shapes of metal structures, achieving a dramatic reduction in surface roughness. The plano raster polishing results also show the system to be well suited to the dwell time control polishing because the results show the removal footprint to be proportional to the dwell time and the defined raster path. All in all, the system is a versatile polishing system capable of achieving the intended objectives.

Movement modeling and control of a ‘bonnet tool’ polishing machine, based on a strategy of static highest-stiffness, are presented. The aim is to achieve polishing controllability as the bonnet tool executes a precessive motion trajectory. Taking an aspheric optical surface, e.g. lens or mirror, as the workpiece, the precessive polishing tool trajectory is designed as if the moving parts were rigid bodies connected by ideal articulations. Then by establishing the Jacobian stiffness matrix of the bonnet tool machine, the static stiffness of the machine is derived taking into account tool loading along its path. To minimize deformation, the control algorithm that achieves a maximum static stiffness strategy is superposed on the rigid body system tool trajectory model. This combined bonnet tool trajectory is produced by numerical simulation. Finally suitability of the rigid body movement model, compensated for desired static, but not inertial, load deflection, is assessed by simulating the trajectory of the tool’s rotational axis to determine how much angular deviation it sustains from the local surface normal. It was found that this bonnet polishing tool compensation method, based on a greatest static stiffness strategy, will produce satisfactory results.

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.

Bonnet tool polishing is one kind of methods that can obtain higher surface quality of the ultra precision processing for producing flat, aspheric and other mould free surface, etc. The latest development and research results on bonnet polishing technology at home and abroad were reviewed. The core technologies of bonnet polishing were analyzed, including polishing principles, polishing tool, the rate of material removal, edge control, dwell time, path planning etc. The results show that the bonnet polishing method is an economic, efficient, practical and high precision polishing technology.

Residual error evaluation method for deterministic polishing of aspheric optics is studied. Two residual error evaluation methods, which are axis-direction error method and normal error method respectively, are researched theoretically. It's inferred that the residual error of aspheric surface should be evaluated by normal error method. A new approach is proposed to calculate normal direction residual error on the basis of the axis-direction residual error of the aspheric surface. There exists difference between these two kinds of error which increases from the center of the aspheric optic to the edge through the comparison of them. Taking bonnet polishing and numerical controlled small tool polishing as examples, experiments are made to quantitatively prove that using axis-direction error method to evaluate residual error in deterministic polishing would introduce different degrees of processing error. It's found that the processing error is positively correlated with the relative aperture of aspheric optics, which is the ratio of the optic's aperture and vertex's curvature radius. Therefore, it is recommended to use axis-direction error method instead of normal error method as the evaluation method of the residual error during deterministic polishing aspheric optics with relatively small relative aperture; the opposite is the other way around.

Virtual pivot alignment method and its influence to profile error in bonnet polishing

Non-Newtonian fluid based contactless sub-aperture polishing

The objectives of this project are to develop, evaluate, and optimize novel designs for a polishing tool intended for ultra-precise figure corrections on aspheric optics with tolerances typical of those required for use in extreme ultraviolet (EUV) projection lithography. This work may lead to an enhanced US industrial capability for producing optics for EUV, x-ray and, other high precision applications. LLNL benefits from developments in computer-controlled polishing and the insertion of fluid mechanics modeling into the precision manufacturing area. Our accomplishments include the numerical estimation of the hydrodynamic shear stress distribution for a new polishing tool that directs and controls the interaction of an abrasive slurry with an optical surface. A key milestone is in establishing a correlation between the shear stress predicted using our fluid mechanics model and the observed removal footprint created by a prototype tool. In addition, we demonstrate the ability to remove 25 nm layers of optical glass in a manner qualitatively similar to macroscopic milling operations using a numerically- controlled machine tool. Other accomplishments include the development of computer control software for directing the polishing tool and the construction of a polishing testbed.

Bonnet polishing is a practical and economical polishing technology for the fabrication of precision optical components. Its removal function is controlled by many parameters, and much research has been performed on them in the past few years. However, most of the previous research has been focused on the inner pressure of the bonnet, the rotation speed of the spindle, the precession angle, the bonnet decrement, etc. The deformation of the bonnet under the inner pressure has received relatively little attention. This paper demonstrates the deformation of the bonnet under the inner pressure and its effect to the contact area and the bonnet decrement. It also proposes two solutions, one is to add an enhancement layer on the bonnet; the other is to design a novel bonnet contour which is aspheric but turns to spherical under the effect of the inner pressure. The latter one is proved that it’s effective to reduce the deformation to the polishing process.