論文

Surface finishing with compliant tools is a widely used technology that still relies heavily on the trial-and-error approach. To predict surface evolution, one should ideally consider the tool as a set of grains and take into account the cutting action of each grain. In practice, the small size of abrasives renders this approach unpractical for industrial application. In this paper, the various aspects playing a role in surface generation, from micro-scale abrasives to macro-scale tool deformation as well as the time-dependent nature of compliant processes, are rationalized and modelled in a Folding Space (FS) rather than a classic geometrical space. This approach drastically reduces the computation time, and is found to be quite realistic as in each position the tool shape is distorted, taking into account the compliance level between the tool and local surface topography. Firstly, the concept of FS and methodology for physical representation of surfaces and processing by compliant tools in the FS are detailed. Next, predictions from the finishing model are analyzed for a variety of compliant grinding and polishing tools typically used in industry. Experimental testing confirms the accuracy and usefulness of the proposed method. To conclude, the model is exploited to offer a better understanding of finishing operations with compliant tools, while the limits and future possibilities of FS simulation method are discussed.

Silicon carbide is a ceramic material with a desirable combination of high thermal and mechanical stability, making it ideal for optical application in aerospace and next generation lithography. It is however notoriously difficult to machine down to super-fine finish when the shape is other than flat or spherical. In this paper, we describe the application of a “semi-elastic” machining method called shape adaptive grinding (SAG), in which an elastic tool is combined with rigid pellets made of nickel or resin, to which super abrasives are bonded. A comprehensive model of the physical interaction between SAG tool and workpiece is proposed, and used to understand the mechanics driving brittle-ductile transition on ceramic materials such as SiC. Machining parameters adequate for optical finishing are then derived from the model and demonstrated on an aspheric silicon carbide workpiece, which was manufactured by reaction bonding and coated with a layer of pure SiC by chemical vapour deposition (CVD). Through SAG processing and final polishing, this aspheric mirror was improved from an initial form error of 40 µm down to 112 nm Peak-to-Valley, with no residual damage visible on the surface.

Free form surfaces have for some time played a part in the latest developments in the exploitation of new products in optics, from micro lenses up to ELT telescopes. The demands of the required tolerance on these "new" optics have led to significant improvements in manufacturing and metrology, as the capability to produce form in the tens of nanometre range coupled with nanometre surface roughness have become the critical enabler the their use. Free form surfaces are not limited to optics, and other product developments such as bio-implant surfaces in the prosthetics industry are utilising free form surfaces to make significant strides implant life. The prosthetic industry, have for some time, known from research into hip replacements, that significant reductions in the production of biologically damaging wear debris could be achieved by implementing hard on hard bearing couples rather than the traditional metal on polymer bearing couples. In these "new" knee joints the bearing couples comprise free form alumina on alumina or CoCr alloy on CoCr alloy surfaces. Unfortunately the application of these new materials for knee implants has been largely halted by the inability of manufacturers to polish their knee surfaces to the more demanding tolerances placed on free form hard on hard bearings of both form and roughness. These tolerances require micron level form deviation combined with nanometre surface finish in order to maintain full fluid film lubrication during in vivo functioning of the joint. This paper discusses the development of the capability to machine biomaterials for use as hard on hard knee joints. The surfaces are machined utilising a 7 axis CNC optics polishing machine, the Zeeko IRP200. The machine uses a novel precision technique to correctively polish components [1].

We summarise the reasons why aspheric surfaces, including non-rotationally-symmetric surfaces, are increasingly important to ground and space-based astronomical instruments, yet challenging to produce. We mainly consider the generic problem of producing aspheres, and then lightweight segments for the primary mirror of an Extremely Large Telescope. We remark on the tension between manufacturability of spherical segments, and performance with aspheric segments. This provides the context for our presentation of the novel Precessions process for rapid polishing and form-correction of aspheric surfaces. We outline why this is a significant step beyond previous methods to automate aspheric production, and how it has resulted in a generalized, scaleable technology that does not require high capital-value tooling customized to particular types of optical form. We summarise implementation in the first two automated CNC machines of 200 mm capacity, followed by the first 600 mm machine, and the current status of the process-development programme. We review quantitative results of polishing trials, including materials relevant to large and instrumentation optics. Finally, we comment on the potential of the technology for space optics and for removing quilting in honeycomb substrates.

Modeling of grinding process, especially the grinding forces, has been studied extensively. Most previous work concerns the conventional grinding process using a rigid wheel, where the forces are generally based on the preset depth of grinding. However, for compliant grinding such as Shape Adaptive Grinding (SAG) that adopts an elastic tool covered with abrasive pellets, the penetration depth of individual abrasive grains is not simply equal to the preset value. As elastic contact occurs between the tool and workpiece, previous models are not able to estimate the material removal mechanism. Besides, the progressive transitions in grain-workpiece interaction for compliant cutting tools have not been reported yet. To fill these gaps and to offer a fundamental understanding of the compliant grinding process, we propose in this study a new multi-scale model spanning from macroscopic tool-workpiece contact to microscopic grain-workpiece interaction in the unique conditions of using a compliant grinding tool, i.e. SAG tool. Based on the spring-grain model and considering the stochastic nature of grain size and wear flat area, the static penetration and dynamic removal of individual grain can be predicted. Particularly, the removal mechanism is clarified with a new consideration of the transition between rubbing, plowing and cutting stages for each individual grain of the compliant tool. Experiments including scratch tests and removal footprints were carried out, and the high consistency with theoretical predictions validates the proposed model. Finally, considering the progressive abrasive wear in grinding, in-process wear compensation was conducted to enable consistent material removal on aspheric steel molds. The proposed method is not only meaningful to reveal the mechanism of SAG process, but also offers a new foundation for studying other compliant grinding processes in future.

In the technology of computer-controlled optical surfacing (CCOS), the convergence of surface form error has a close relationship with the distribution of surface form error, the calculation of dwell time, tool influence function (TIF) and path planning. The distribution of surface form error directly reflects the difference in bulk material removal depth across a to-be-polished surface in subsequent corrective polishing. In this paper, the effect of path spacing and bulk material removal depth on the residual error have been deeply investigated based on basic simulation experiments excluding the interference factors in the actual polishing process. With the relationship among the critical evaluation parameters of the residual error (root-mean-square (RMS) and peak-to-valley (PV)), the path spacing and bulk material removal depth are mathematically characterized by the proposed RMS and PV maps, respectively. Moreover, a variable pitch path self-planning strategy based on the distribution of surface form error is proposed to optimize the residual error distribution. In the proposed strategy, the influence of different bulk material removal depths caused by the distribution of surface form error on residual error is compensated by fine adjustment of the path spacing according to the obtained path spacing optimization models. The simulated experimental results demonstrate that the residual error optimization strategy proposed in this paper can significantly optimize the overall residual error distribution without compromising the convergence speed. The optimized residual error distribution obtained in sub-regions of the polished surface is more uniform than that without optimization and is almost unaffected by the distribution of parent surface form error.

The fabrication of precision optical surfaces has undergone a revolution in recent years. The first purpose of this paper is to present case studies of novel optical designs not previously published, that utilize complex, or 'freeform', surfaces. These designs are described both for their own merits, and as pointers towards the types of adventurous designs for ground or space-based astronomy that might now be envisaged. The potential benefits are enhanced optical performance in more compact, lower mass, and rugged packages. Such designs would, until recently, have been impossible to fabricate, and so we also describe some of the recent technical advances that have materially changed this position.

Advanced ceramics have many attractive features such as high stability and wear resistance that find broad applications in various fields, e.g. optics, aerospace, etc. However, the accompanying difficult-to-machine property with complex geometry brings great challenges to the commonly used laser machining and rigid wheel based grinding in industry. To achieve optical surface quality with surface roughness below 10 nm Ra, three promising ultra-precision compliant machining technologies using adaptive elastic tools are presented in this paper, including bonnet polishing, compliant pitch polishing and shape adaptive grinding with fine grain size. A comparative study was conducted by machining three different low thermal expansion ceramics while continuously increasing attack angle, spindle speed and tool offset across rectangular regions. Material removal rate (MRR) and surface roughness (Ra) with respect to different process conditions are compared. With sufficient data, the processing ability using above three compliant machining technologies is summarized based on the MRR-Ra plots for different ceramics. In addition, microscopic observation and X-ray diffraction analysis are conducted to characterize differences in material behavior.

A study of automation of hard X-Ray molding dies polishing by FJP and BP was carried out. The following conclusions were drawn: 1. Surface roughness in the range 0.6-0.8nm rms can be obtained on electroless nickel samples by a combination of Fluid Jet polishing with micro-particles followed by Bonnet polishing with nano-particles. 2. Automated corrective polishing was demonstrated on a borosilicate cylindrical sample, with form error improvement from PV 3.2um down to 0.18um. 3. By using the automated process to get surface texture down to circa 0.6-0.8nm rms, it is possible to reduce the time of final hand polishing to 0.3nm by as much as 75% [3].

Electroless nickel is one of the best materials for making optical molding dies, because of its machinability with both single-point diamond turning and polishing, as well as its suitable hardness and durability. This paper deals with the ultra-precision polishing of aspheric molding dies for next-generation hard X-ray telescope mirrors, which require a super smooth surface with a roughness below 0.3 nm root-mean-square (rms). The material was machined using various methods, and a surface roughness of 0.23 nm rms was obtained on aspheric molding dies of 300 mm in diameter. A surface roughness of 0.16 nm rms was achieved on platinum/carbon multilayer mirrors, replicated from plano dies. © 2008.

The Precessions™ process polishes complex surfaces from the ground state preserving the ground-in form, and subsequently rectifies measured form errors. Our first paper introduced the technology and focused on the novel tooling. In this paper we describe the unique CNC machine tools and how they operate in polishing and correcting form. Experimental results demonstrate both the '2D' and '21/2D' form-correction modes, as applied to aspheres with rotationally-symmetric target-form. © 2006 Optical Society of America.

This paper proposes a measurement and adjustment procedure for virtual pivot errors using the R-test and investigates the influence of virtual pivot errors to the surface profile in bonnet polishing. Initially, kinematic modeling is carried out for describing the location errors of rotary axes and defining overall errors of the virtual pivot arm. Then, the R-test is introduced to measure the three-dimensional displacement of a sphere located at the virtual pivot point and identify location errors. The adjustment procedure for virtual pivot errors is developed by means of mathematical analysis. The measurement and adjustment approach is applied to an ultra-precision polishing machine, on which an adjustment experiment was conducted to validate the proposed method. Based on this, a contrastive polishing experiment on a concave lens is carried out under good and poor virtual pivot errors. The experiment result shows that the maximum form deviation of the polished surface profile is reduced from 241.0 nm to 89.6 nm when good alignment of virtual error is achieved. Analytical simulation based on a material removal model of the bonnet polishing tool and machine is implemented to reveal the influence of virtual pivot errors to polishing quality.

In optics fabrication technologies such as computer controlled optical surfacing (CCOS), accurate computation of the dwell time map plays an essential role in the deterministic performance of the fabrication process. However, it is still difficult for existing methods to derive smooth dwell time maps that reduce dynamic stressing on the machine especially at the aperture edge region, while retaining fine correction capability on freeform optics. To answer these challenges, we propose a new method based on Zernike decomposition and improved differential evolution optimization of the dwell time map, which can be applied to time-dependent optics fabrication processes such as fluid jet machining. Simulations and experiments based on a bi-sinusoidal freeform design were carried out to assess the feasibility of the proposed methodology. With appropriate fluid jet pressure, a bi-sinusoidal optical surface with demanding form error target of sub-100 nm in peak-to-valley was achieved, showing a remarkable improvement on the state-of-the-art, while keeping a good average surface roughness of 2.6 nm Ra on the optical glass.

The novel Shape Adaptive Grinding (SAG) process, which uses diamond abrasives bonded in nickel or resin pellets attached to an elastic tool, has been previously demonstrated in finishing freeform ceramic molding dies with surface roughness below 1 nm Ra. In this paper, a dynamometer was used to characterize grinding forces and the results show that contrary to conventional grinding, in SAG the grinding force increases proportionally to the diamond grit size. The chip thickness was derived statistically, and the grinding mechanism was correlated with previous observations of the ductile to fracture grinding mode transition.

This research introduces abrasive nano-blasting using fine abrasive particles. Fine abrasive particles are difficult to use in abrasive blasting due to tendency of forming agglomerates caused by prevalent surface forces. The pressure gradient and streaming effect of ultrasonic vibration is utilized to break the abrasive agglomerates before impacting the workpiece for polishing. It could be observed through simulations that the pressure gradient to overcome the adhesive forces and breaking the agglomerates can be theoretically achieved. Polishing experiments revealed that acoustic streaming inside the ultrasonic cavity also improved uniform surface generation with up to 67 % reduction in surface roughness Sa.

Compliant finishing (e.g. shape adaptive grinding) can routinely achieve nanoscale roughness on diverse metal and ceramic materials. However, when processing multiphase materials consisting of distinct phases with different mechanical properties, non-uniform material removal often occurs and the inherent mechanism remains unclear. Here, a deterministic and stochastic model to predict processed surface topography is derived from the different material removal behaviours across phases. Experimental topographies, profiles and roughness on three selected Si-SiC samples show high consistency with theoretical predictions. Both model and experiments indicate that improved and stable surface finish can be achieved on metal matrix composites with small grain size.