論文

Pseudo-random paths are a useful tool to reduce mid-spatial frequency errors created in the processing of optical surfaces by sub-aperture polishing tools. Several types of patterns have been proposed, including hexagonal, square and circular, but prior literature has largely focused on flat and gently curved surfaces. Here, an extension of the circular-random path to strongly curved aspheric and freeform surfaces is proposed. The main feature of the algorithm is to cover the entire surface to be polished with a uniformly distributed tool path. Aspheric condenser lenses are then polished with a regular raster and circular-random path. Analysis of the optical performance shows that the random path can reduce the amplitude of mid-spatial frequency errors and relative intensity of satellite images. These features are particularly desirable in short wavelength applications, such as mirrors for EUV and X-ray.

Abrasive wire cutting (AWC) and wire electric discharge machining (WEDM) are efficient and econom-ical processes for the fabrication of precision parts from bulk material. Operating costs and manufacturing lead times are low compared to more general methods such as 5-axis CNC milling, turning, or electro-discharge machining. In this paper, an algorithm based on differential geometry in Euclidean space is proposed for reverse engineering of ruled geometries. The algorithm can determine whether a given geometry is producible by wire cutting, and can also de-rive the associated wire trajectories. Implementation is demonstrated by producing complex turbine blade geometries on 4-axis wire cutting machines with an overall shape accuracy of 20–40 μm peak-to-valley.

The Precessions process for producing aspheric and other optical surfaces is undergoing rapid development. In this paper, we summarise the considerable success achieved in controlling the repeatability of the process on both the 200mm and 600mm machines, and illustrate this with examples of aspherics that have been produced. We particularly describe our approach to fine form-control. This has required the development of various strategies to moderate the volumetric removal rates, in order to give the required sensitivity of removal. We conclude with a discussion of the scaling laws that apply when adapting the process to smaller and larger sized parts. This is illustrated by predicting the process-parameters for mass-producing segments for extremely large telescopes.

Shape adaptive grinding (SAG) is a novel process for freeform machining of difficult materials such as ceramics and hard metals. Despite low stiffness requirement from the machining equipment, due to the "semi-elasticity" of the process (achieved by a combination of elastic tool with rigid pellets), ductile mode grinding can be achieved with high surface finish. In this paper, the SAG process mechanism is investigated by studying how the size and shape of the pellet bonded abrasives evolve over time, measuring grinding forces for various process parameters, and comparing the equivalent chip thickness and specific energy with the observed grinding modes.

Material removal rate in fluid jet polishing is significantly enhanced when ultrasonic cavitation bubbles are introduced at the nozzle outlet. In this paper, two theories are put forward to explain the process mechanism: a micro-scale hypothesis in which the surface is micro-jetted by collapsing bubbles, and a macro-scale hypothesis in which vibration of the fluid in the impingement region increases abrasive particle erosive action. Experimental investigation suggests the higher likelihood of the macro-scale phenomenon, and a material removal model is proposed accordingly. Process footprints simulated by this model were found to agree well with experimental measurements.

The recent upsurge in the demand for off-axis and complex "freeform" optical surfaces is driving the development of novel processes for their fabrication. This paper focuses on recent developments of the Precessions CNC polishing process for freeform surfaces, including off-axis as a special case. First, the surface-prescription and metrology-data, and their relation to the data-input for the polishing machines, are considered. The relevance of consistent coordinate frames is emphasised. An outline of how the process can 'polish' a ground freeform part (improve the texture), and then 'figure' the part (reduce the form errors) is given. Specific experimental case-studies are then presented, illustrating the versatility of the process on different materials and forms. Recent work is included in which the process-speed has been moderated in order to remove tens of nanometres of stock material, rather then the more usual hundreds of nanometres to tens of microns as in the standard Precessions process. The relevance of this to improving the ultimate surface-precision that should be achievable by this method is described. As a final illustration, the potential of the process to the rapid fabrication of the hundreds to thousands of 1-2 metre class mirror segments required for extremely large telescopes is considered.

Since the 2003 Annual Meeting, the Precessions process has become accepted as an efficient method for polishing and figuring moderate-sized axially-symmetric aspheric parts in industry. In this paper, we report on some very significant new advances beyond this capability. The first is the demonstration of the process on substantially larger diameter parts than worked hitherto - in particular, a precision-ground 500mm diameter deeply-concave aspheric mirror. We describe the consequences of polishing large parts with the axis of the part vertical, in contrast to the horizontal axis of the smaller machines. Issues include slurry puddling and settlement in concave forms, process-uniformity, adequate support of the part and handling. We then report on recent work developing the Precessions process for non axially-symmetric surfaces including free-form. The correct relationship of the process with metrology has proved to be complex on several fronts, one example being differing descriptions of form either along a surface or its projection. We present our experience using profilometry and interferometry on precision-ground and polished surfaces, and in achieving absolute form with known base radius. Finally, we remark on the potential power of a priori predictions of achievable surface quality when optimizing optical system designs.

In time-dependent processes, such as bonnet and fluid jet polishing, surface quality and accurate processing critically depend on careful planning of the tool feed. CNC feedrate commands are usually generated from a dwell time map calculated by deconvolution or numerical iteration. These methods are time-consuming, numerically unstable, and fail to consider dynamic stressing of the machine tool. In this research, Gaussian mixture model (GMM) is proposed to model experimental tool influence functions (TIF). This leads to a general analytical convolution model integrating processing depth, volumetric removal rate of TIF, path spacing and feedrate. Based on this model, a novel direct feedrate scheduling method is proposed, which is suitable for any kind of smooth time-dependent processing beam. Optimal feedrate scheduling within dynamic constraints of the machine tool is achieved by establishing acceptable path spacing and feed ranges, whilst dynamic stressing of the machine tool is optimized concurrently through adaptive path spacing. Simulations and experiments demonstrate the enhanced stability and usefulness of the proposed feedrate model in deterministic material removal. It also verifies that path adaptability allows for improved machine tool dynamics, without incurring a process accuracy penalty.

This paper describes a major advance in the post-treatment of diamond-turned surfaces to remove repetitive micro-structure; a result which could have a major beneficial impact on fabrication of Walter-type X-ray mandrels, and metal mirrors. Diamond-turning is highly deterministic and versatile in producing axially-symmetric forms, and through fast-tool servos, non-axially symmetric, free-form and micro-structured surfaces. However, the fine turning marks left in the metal surface limit performance. In this paper, we describe how fluid-jet polishing under CNC control can be used to eliminate these structures, without significantly degrading the surface roughness or form produced by the prior turning operation.

Background: We have developed edge-control for the Precessions TM process suitable for fast fabrication of large mirror segments, and other applications sensitive to edge mis-figure. This has been applied to processing of European extremely large telescope (E-ELT) prototype mirror-segments, meeting the specification on maximum edge mis-figure. However we have observed residuals that have proved impossible to correct with this approach, being in part the legacy of asymmetries in the input edge-profiles. Methods: We have therefore compared different proposed methods experimentally and theoretically and report here on a new edge-rectification step, which operates locally on edges, does not disturb the completed bulk area. Results: A new toolpath has been developed and experiments have been carried out to demonstrate that local edge rectification can be carried out. Conclusions: With this method, the residue error on edges can be removed separately and has potential to reduce total process time.

Shape Adaptive Grinding (SAG) is a new process for freeform finishing of difficult materials such as ceramics and high-performance alloys. The basic principle of SAG can be described as "semi-elasticity": compliance is achieved with freeform workpieces by an elastic spherical tool, while hard contact is simultaneously achieved by small rigid pellets covering this elastic tool (diamond or cubic boron nitride super-abrasives are embedded in these pellets). In this paper, we present recent developments in the application of SAG to (1) corrective grinding of aspheric silicon carbide optics, and (2) smoothing of high-performance titanium alloy components produced by additive manufacturing.

Because of the direct relationship between removal rate and surface roughness in conventional grinding, ultra-precision finishing of hard coatings produced by chemical vapour deposition (CVD) usually involves several process steps with fixed and loose abrasives. In this paper, an innovative shape adaptive grinding (SAG) tool is introduced that allows finishing of CVD silicon carbide with roughness below 0.4 nm Ra and high removal rates up-to 100 mm 3/min. The SAG tool elastically complies with freeform surfaces, while rigidity at small scales allows grinding to occur. Since material removal is time dependent, this process can improve form error iteratively through feed moderation. © 2014 CIRP.

Shape Adaptive Grinding (SAG) is a new process capable of producing optical mirror quality surfaces (Ra <0.5nm) on CVD silicon carbide coatings. The methodology and capability of the SAG process are presented in this paper.

Shape Adaptive Grinding (SAG) is a novel finishing process capable of achieving optical surface finish on silicon carbide. In this paper, we report on the application of SAG to grinding of an aspheric optic.

Preston's law is a widely used equation that expresses time-dependency of material removal in polishing process. In this research, it is experimentally found that Preston's law does not hold at the tool rotational center in glass polishing. Material removal observations point to a mechanical phenomenon accelerated by chemical reaction. To identify the underlying phenomenon, experiments are conducted that isolate the contribution from each constituent factor in Preston's law. By observing the motion of loose-abrasive particles during polishing, it is found that they travel as expected on concentric trajectories around the tool rotational center. By measuring the pressure distribution in static situation as well as the contact force during polishing, it can be concluded that no hydrodynamic increase in pressure occurs at the tool rotational center. Finally, experiments are performed to investigate the relationship between distance from tool rotational center and removal depth by a single abrasive particle. The depth of removal is observed to reach a maximum value at the tool rotational center in all polishing conditions tested, from which a modified expression of Preston's law is derived. Finally, hypotheses based on fracture and material mechanics are proposed to explain abrasion mode transitions in single particle abrasion.

Fabricating super-smooth aspheric optics for future hard X-ray telescopes will require a new process chain. Whilst diamond turning of electroless nickel plating can generate ~100 nm P-V aspheric molding dies, associated turning marks must be removed before replication. An innovative two-step freeform finishing method is presented, that combines fluid jet and precessed bonnet polishing on a common 7-axis CNC platform. The removal rate and surface texture relationship of fluid jet with abrasive type and pressure is documented, and form correction demonstrated down to 27 nm P-V. A novel bonnet tool-pathing method called "continuous precessing" is then applied, which delivers super-smooth anisotropic surface texture of 0.28 nm rms. © 2013 CIRP.

Recent efforts at NASA's Goddard Space Flight Centre aim to produce X-ray telescopes that deflect X-ray beams into an observatory's instruments at an extremely shallow angle, yielding high-resolution images. This necessitates exceptional surface slope precision on each individual aspheric mirror. Typical industrial robotic polishing accuracy remains well below the practical specifications of X-ray optics, due to undesired equipment vibrations that induce waviness in the polishing contact zone. It is therefore necessary to develop a method that can ensure consistent contact and accommodate for undesirable vibrational effects in the polishing equipment. This work presents a study on contact pressure fluctuations in the contact zone, validated by a statistical approach to counteract the imprinted vibration. A passive error compensator is introduced thereby maintaining uniform pressure, adhering to the planned material removal rate. Analysis of the experimental results verified the elimination of force overshoot, bringing us closer to the practical applicability of robot polishing to produce performance standard X-ray mirror segments.