Abstract

In the context of industry 4.0, building data clouds in manufacturing technologies is the fundamental step to approach intelligent automatic process. This new technology has proved to efficiently and effectively monitor five important responses (removal rate, texture, surface accuracy, edge-profiles and mid-spatial frequencies) with more than 95% repeatability in real time. This faster and inexpensive process can serve for the nowadays high-quality segmented telescopes. We illustrate the underlying problem by reference to a case-study – the challenge of an average manufacturing rate of 11.4 segments per month for the 39.3m optical/infrared European Extremely Large Telescope (E-ELT) project.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

1. Introduction

The 39.3m aperture European Extremely Large Telescope (E-ELT), when completed circa 2025, will be the largest optical/infrared telescope in the world. The project requires 798 hexagonal mirror segments, each 1.45m across-corners, and comprising off-axis aspheric sections of the near-parabolic form of the overall mirror. Although the hexagonal segments needed comprise 133 different surface shapes, it will still be a challenge to complete all the segments before 2024. Not only is the E-ELT testing the boundaries of current manufacturing technology, therefore, it also requires innovative methods in order significantly to reduce the processing time. This presents an unprecedented manufacturing challenge, given the required surface precisions in the ~10nm RMS regime, accompanied by stringent constraints on segment-matching and edge mis-figure, and a total segment-number over 20 times that of state-of-the-art segmented telescopes in operation today.

Our team has successfully completed a contract from the European Southern Observatory (ESO) [1]. This primarily involved manufacturing prototype segments for the E-ELT, corresponding to the most extreme off-axis aspheres near the edge of the parent primary. The basic process-chain involved CNC grinding, followed by CNC polishing using Zeeko’s PrecessionsTM process [2], for this project.

Mid spatial frequencies (MSFs) at 0.02~1mm−1, produced in the surface during grinding, proved slow to remove by polishing [3]. This arose because the compliant polishing tools, which very effectively adapt to conform to the local asphere, also adapt to the MSF content. This has led us to consider a possible intermediate smoothing-step between grinding and polishing, which could potentially be applicable to segments, but also to a wide range of other optical and precision mechanical surfaces. We have previously adopted the term “grolishing” for a family of such intermediate processes.

The specific type of grolishing considered here is the use of a rotating, rigid, hard, smoothing-tool, loaded onto the work-piece surface by its own weight. Such a tool, as it progresses along the tool-path, rides over the MSF-peaks, preferentially suppressing them. However, on an asphere, the misfit of the tool’s surface with the local topography tends to introduce new MSFs. We have found that it is possible to mitigate this by using an abrasive grit size sufficient to fill the misfit gaps between tool and surface [4,5].

The Zeeko CNC polishing machines are designed to deliver the precise positioning required for corrective local-polishing, including the use of small spot-sizes to target individual surface-defects and edges. We have previously reported on implementing grolishing on a Zeeko machine [6–9]. However, in comparison with the equivalent Cartesian machine, robots can offer advantages using processes which i) benefit from the robot’s circa ten-times higher speeds and accelerations and ii) where their lower resonant frequencies and circa ten-times inferior positional-accuracies are not deleterious. Grolishing is such a case, specifically when i) the tool-diameter is much larger than the robot lateral positional accuracy, and ii) when the tool is ‘floating’ on the surface of the part by virtue of its mass, as this desensitizes the process from robot errors in Z and tip/tilt.

Furthermore, the capital costs of robots are much lower than equivalent CNC platforms, making the robot an attractive proposition for an intermediate process-step. Using different platforms to separate grolishing from precision polishing also helps to avoid the risk of cross-contamination between the coarser grolishing abrasives and the polishing machine.

To establish the grolishing process, we consider some indicative targets for production of a smoothed, aspheric surface. This is clearly a trade-off, as achieving a superior surface in step ‘n’ will take longer, but will reduce the time for step ‘n + 1’, as shown in Fig 1. Also, as robots are substantially less expensive, robots can be ‘doubled up’ in a process chain [10]. Taking such issues into account, we set realistic targets for control of five responses, as follows:

 

Fig. 1 Potential role of grolishing in a process-chain.

Download Full Size | PPT Slide | PDF

  • 1. Required volumetric removal rate (VRR). The BoX grinder performance has been reported grinding samples of a 1.45m E-ELT segment [11,12]. Measured performance of the ground segment was quoted as 100–200 nm RMS texture, sub surface damage < 10μm, and form error <5.5µm PV. In practice there appears to be some relaxation of such segments when removed from their grinding fixtures which degraded form error. In order to remove the damaged layer, we allow a total removal depth in grolishing of 10 microns plus a 50% contingency i.e. 15 microns. This also gives some scope to improve form in grolishing. For the area of an E-ELT segment, and a realistic smoothing time of 14 hours, the required VRR should be > 16.3mm3/min.
  • 2. Texture. A smoothed output texture < 400nm Sa gives an input- surface well-matched to CNC polishing. This allows some degradation of the BoX delivered texture, but with the considerable benefit of reduced MSFs.
  • 3. Form. The smoothing process should not materially degrade the overall form delivered by CNC grinding. We take as a target, the preservation of form error smaller than the 3 µm PV, or 0.4µm RMS, level.
  • 4. Edges. CNC grinding gives straight edges. Hard-tool smoothing will in general turn edges up, or roll them down, depending on process parameters. A gently turned-up edge is preferred by CNC polishing as otherwise, the entire surface has to be polished down to the level of edge-roll.
  • 5. Mid spatial frequencies. The E-ELT prototype segment specification gives a maximum wavefront error for a segment of 30nm RMS, after removing defined percentages of the Zernike 3,4,5,8,9 terms [13,14]. This translates to 15nm RMS surface, and approximately 70nm PV. Ideally, the grolishing process should not inject new mid spatials into the surface well within this tolerance, and we adopt 40nm PV as a target.

The influence function (IF) is a three-dimensional footprint of the tool on the surface. It can be numerically integrated to calculate VRR, and thus global processing times. However, it is less useful predicting removal-effects at local-level, particularly on scales smaller than the width of the IF. This encompasses most MSFs – indicating that IF-modelling is not particularly relevant to smoothing.

Our goal is to ultimately build intelligent automatic manufacturing cells in each processing step so that the precise surface can be manufactured automatically with an optimized flow from design to manufacture and to measurement, in order to speed up the process [15]. One important aspect to realize in the automation is the need to build data-cloud-based reproducible empirical experiments so that a process can choose optimized parameters to complete a manufacturing task automatically. This idea is facilitated by statistical experimental designs, statistical data analysis and statistical inference.

Conducting series of experiments and controlling all the 5 responses would be a tedious approach, however. The solution adopted was to apply statistical design of experiment and analysis to accelerate experiments and increase model accuracy for automatic selection of grolishing parameters. The results presented show that the repeatability of all responses achieves > 95%. All the researches are the fundamental to approach industrial 4.0.

2. Methods and potential variables to control the 5 response variables

2.1 Volumetric removal rate (VRR)

VRR is a response relevant to evaluating grolishing process-speed. Selection of potentially significant variables can be usefully referred to the Box CNC-grinding parameters for the final cut: 50μm depth with a 25μm diamond grit size, 2600rpm spindle speed, 18000mm/min tool travel feed and a < 100N loading force [11,16]. To mitigate artifacts of sub-surface damage, texture and MSFs, the plausible variables for grolishing could be 9~20μm abrasive sizes, 600~1000rpm spindle speed, 1500~4500 mm/min tool travel feed, and ~10N loads. Other potentially significant variables were also considered, such as raster track spacing of 2~10mm and slurry density (abrasive: water = 3:9 ~4:9, measured by weight).

2.2 Texture

The resulting texture is also a response relevant to evaluating process efficiency, since a grey grolished surface has to be polished to a sufficient quality to enable interferometry, and so provide metrology data to close the corrective polishing loop. We target this ‘pre-polish’ as being conducted in a single polishing run of 14 hours per m2 of a surface, to facilitate an efficient grolishing – to – corrective-polishing transition.

2.3 Surface accuracy and edge-profiles

Surface form accuracy is a response that determines output image-quality. Edge-misfigure is a response that predominantly determines stray light, diffraction-effects and IR-emissivity, which degrade signal-to-noise ratio. The total area was divided into i) a 100mm wide edge-zone and ii) the bulk area within this, as shown in Fig. 2.

 

Fig. 2 Definition of edge and bulk areas for a 1.45m segment.

Download Full Size | PPT Slide | PDF

In our approach, all processes were conducted on pre-machined hexagonal mirror blanks. CNC-grinding with a stiff machine such as BoX [12,19], delivers sharp edges that must be preserved or controlled in subsequent grolishing or polishing process-steps. The key parameter available is the overhang of the tool at the edges of the part, corresponding to the ends of the tool-path.

2.4 Mid-spatial frequencies (MSFs)

MSFs exhibit characteristic waviness with different spatial frequency components and contribute stray light, diffraction effects, flares or ghosts into an optical system. The errors are the consequence of various effects, such as print-through from prior grinding, the influence-functions of sub-aperture tools, and periodicity of tool-paths. These all conspire to generate both periodic and non-periodic surface features. In current high-resolution imaging systems, such as x-ray optics, laser optics, lithography, remote sensing, as well as telescopes [17,18], controlling MSFs is considered a key criterion to assess a high-quality system. Grolishing is a potential process-step to mitigate one important contributor – grinding print-through.

Figures 3(a)–3(c) shows an example of two 632.8nm wavelength interferograms of real surfaces that have MSFs of 90 and 40nm PV respectively. The corresponding computed point-spread functions, which represent image quality, are also shown, as is the modulation transfer function for the 40nm surface. This data demonstrates that, for PVs ≤ 40nm in the 0.02~1mm−1 spatial frequency domain, the theoretical limit of diffraction-limited imaging can be obtained in the visible.

 

Fig. 3 To demonstrate MSFs PV < 40nm is diffraction limit. (a) Two different input surfaces with their respective MSFs. (b) The respective outputs surface by using PSF. (c) The MTF from the PV = 40nm surface.

Download Full Size | PPT Slide | PDF

Since grolishing is an intermediate step between hard grinding and soft polishing, control of MSFs in these processes is usefully reviewed. For the grinding process, Franse [20] and Cheung et al. [20] found that the tool spindle speed was the most important variable with respect to introducing MSFs. Takasu et al. [21], Sata et al. [22], and Tonnellier [23], meanwhile, investigated the relationship between the MSFs and the removal depth, showing that the removal is affected by vibrations, tool-wear instability, overlap in the tool paths of the used tools, increase in temperature in relation to the spindle speed, as well as thermal errors.

For the polishing process, Dunn and Walker [24] reported on pseudo-random zero-crossing tool paths to remove periodic MSF structure. Yu et al. [3,7] used a Zeeko IRP machine to attenuate MSFs by using loose abrasive rigid hard tools. Song et al. [25], meanwhile, discussed the relationship between MSF and tool misfits. These studies all provide useful information on how to control residual MSF in rigid tool grolishing.

In summary, the significant variables potentially contributing to MSFs on the bulk surface comprise (i) abrasive grit size, (ii) spindle speed, (iii) tool-path raster-spacing, (iv) tool-path traverse-speed, and (5) tool-load.

3. Experimental preparation

3.1 Tool design for grolishing

When CNC hard-grinding with a machine such as the BoX [11], the part is rotated and the tool traverses a diameter, giving a spiral tool-path in part-coordinates. This naturally leaves a signature of regular cusps on the surface, separated by the in-feed per rotation. A hard grolishing tool used with loose abrasives would need to span several cusp wavelengths to attenuate these features. Combined with the need for pad diameter to be much larger than robot XY positional accuracy, we have used 50mm, 100mm and 280mm diameter pads – this paper focusses on the intermediate size.

Figure 4 shows the 100mm diameter grolishing tool, which can be separated into three parts:-

 

Fig. 4 Mechanism of the grolishing tool.

Download Full Size | PPT Slide | PDF

  • 1. A spigot to interface the tooling assembly to the rotary-spindle end-effector on the robot
  • 2. The holder, which contains the gimble arrangement allowing the tooling to float on the surface, whilst being driven in rotation
  • 3. The pad, comprising a hard brass disk with central hole and grooves, to aid slurry mobility

3.2 Processing and measurements

The hard brass pad can be supplied with Al2O3 loose abrasive to grolish a surface, as shown in Fig. 5(a). The load is determined by the tool weight. This type of tooling can control MSFs in a range of continuous surfaces [4,5]. A 280mm diameter grolishing tool based on this design has also been shown to remove MSFs on a 1m part [9].

 

Fig. 5 (a) The hard grolishing tool used to process 400mm hexagonal segment. (b) Bonnet pre-polishing on a Zeeko machine.

Download Full Size | PPT Slide | PDF

A borosilicate hexagonal glass blank of 400mm corner-to-corner was used for the work reported in this paper. VRR, removal depth and edge-profiles were measured by an extended range Talysurf stylus profilometer (Fig. 7(a)). Since the maximum traverse range for the Talysurf is 300mm, when examining the removal depth, a sub-area for grolishing was defined as per Fig. 6. This gave un-grolished areas that were used as a datum to establish absolute removal depths.

 

Fig. 6 Process for removal measurement.

Download Full Size | PPT Slide | PDF

Textures of grolished surfaces were measured by an ADE phase shift MicoAXM white light interferometer (Fig. 7(b)). Attempts were made to measure MSFs using a Talysurf IntraTM stylus profilometer, but difficulties were experienced disentangling MSFs from surface noise. Therefore, the sample part was uniformly pre-polished on a Zeeko IRP600 machine. A raster toolpath orthogonal to the grolishing raster was used to decouple grolishing from polishing effects (Fig. 5(b)). Then, a 4D simultaneous-phase interferometer at 632.8nm (Fig. 7(c)) was used for MSFs measurement.

 

Fig. 7 Measurement equipment (a) extended range Talysurf for measuring surface profile; (b) white light interferometer for texture; (c) 4D interferometer for MSFs measurement.

Download Full Size | PPT Slide | PDF

4. Building data cloud for the automatic grolishing process

4.1 Screening experiment to evaluate significant variables

The purpose of ‘screening experiments’ is to determine significant variables for each response variable. As discussed in section 2, the 6 potentially significant variables (AS, L, S, SD, TS and TF, as shown in Table 1) need to be evaluated. To reduce unnecessary experimental trials, an L8 experimental design of Taguchi method was used. Please note that defects can be reduced to arbitrarily low values simply using arbitrarily low removal-depths. Therefore, edge and MSF results were scaled by their respective removal depths in order to provide a sound basis for comparison.

Tables Icon

Table 1. The L8 of the Taguchi method for screening experiment to determine significant variables. Note that edge and MSFs were scaled by their respective removal depths to merit the comparison of each variable effect.

The analysis of variance (ANOVA) was the statistical method used to analyze Table 1, with the conclusion summarized in Table 2. For the edge, however, the 6 testing variables were insignificant, meaning that manipulating overhang (OH) can be the method for edge control.

Tables Icon

Table 2. Summary of significant variables from ANOVA.

4.2 Confirmation experiments of significant variables

This section is to further evaluate the significant variables in Table 2 and further models the results by using regression analysis for parameter optimization.

4.2.1 VRR and texture

For VRR, 3 significant variables were evaluated through a 23 full factorial design. Each trial was repeated 3 times so as to check the repeatability of the experiment and to improve model accuracy. The measuring time for texture was short so as to examine with VRR in Table 3.

Tables Icon

Table 3. 23 full factorial design to evaluate significant variables for VRR and texture.

The repeatability was about ± 2.4% for VRR and ± 1.3% for texture. According to our ANOVA calculation, R2 for VRR and texture are 99.1% and 99.7% respectively, showing significant variables can be determined by the design in Table 3. To this end, regression analysis was used to model the empirical data into resolution space for variables optimization effectively, yielding:

VRR=-16.7+2.84×AS-0.0181×L+0.0113×S+0.00122×AS×L+0.000025×L×S+0.00000017×AS×L×S
Texture=7.34+34.8×AS+0.133×L+0.191×S0.00444×L×S
where 9 < AS (abrasive size) < 20, 1000 < L (load) < 1350, and 600 < S (spindle speed) < 1000.

Equations (1) and (2) were then examined by another confirmation experiment and the consideration is described as follows: the 9μm abrasive was controlled because the specification of both VRR and texture in Fig. 1 is achievable. Since spindle speed was the second most significant variable, 5 different spindle speeds (600 rpm, 700 rpm, 800 rpm, 900 rpm and 1000 rpm) were chosen to examine the Eqs. (1) and (2).

As shown in Table 4, the data confirms a 95% confidence interval for the predicted data, indicating that both data-cloud of Eqs. (1) and (2) are accurate.

Tables Icon

Table 4. Comparison of the predicted data and experimental data.

4.2.2 Edge-profiles

Two objectives are studied in this section. Firstly, as demonstrated in section 4.2.1, abrasive size, spindle speed and load were the significant variables for the control of VRR, and also appear to have a significant influence on edges. In order to verify this, these three variables were studied. Secondly, it is known that OH is a significant variable, and therefore the next step was to determine the optimized OH value.

One aspect is to minimize edge-misfigure. As shown in Fig. 8, when using a parallel raster tool path along an edge, the traverse-speed is constant. In contrast, when the tool-path cuts an edge or corner, the tool-path reversal implies the more complex case of a variable speed. In order to examine this effect, two measurements were conducted: edge-to-edge (EF) and corner-to-corner (CD), as shown in Fig. 9.

 

Fig. 8 A tool has a constant speed at the edge but decelerates and then accelerates at the corner when changing processing direction.

Download Full Size | PPT Slide | PDF

 

Fig. 9 The 400mm hexagon with two orthogonal directions measurement.

Download Full Size | PPT Slide | PDF

4.2.2.1 Evaluating abrasive sizes, spindle speeds and loads

Three levels were selected for each testing variable: 9μm, 15μm and 20μm abrasives; 600rpm, 800rpm and 1000rpm for spindle speeds; 1000g, 1175g and 1350g for loads. Note that the edges were normalized with removal depth to achieve the same comparison basis. Results shown in Figs. 10(a)–10(c) demonstrated that abrasive size, spindle speed and load were insignificant variables, confirming the conclusion in Table 2.

 

Fig. 10 Evaluating the 3 variables (data were offset for comparison). (a) testing: abrasive size (1175g load and 800rpm spindle speed); (b) testing: spindle speed (1175g load and 9μm abrasive; (c) testing: load (1175g load and 800rpm spindle speed).

Download Full Size | PPT Slide | PDF

4.2.2.2 Evaluating bulk area and overhang (OH)

If the center of the tool moves beyond the edge of the workpiece, it will tip. A positive value of OH is defined as the distance that the center of the tool falls short of the workpiece-edge, at the extreme of the tool-path. Note that to simplify the problem, the bulk area, which is smooth and more easily controlled than the edges, will be temporarily omitted until section 5.

Five levels (9.6mm, 11.6mm 13.6mm 15.6mm and 17.5mm) were varied to examine the optimized edge-profiles. As shown in Fig. 11(a), a huge gap is obvious between an OH of 11.6mm and 9.6mm, which can be caused by the pressure of the tool significantly increasing at the boundary. Hence, another experiment was conducted and presented in Fig. 11(b). Since the 2mm track space limited the raster path, OH with 11.6mm was selected for edge control. It is also important to note that using 11.6mm OH with 2mm raster path would effectively produce smooth and upstanding edge-profiles that are well-matched to subsequent rectification by subsequent automatic CNC polishing [7].

 

Fig. 11 Evaluating the method of overhang for edge control with 9μm abrasive, 800rpm spindle speed and 1150g load (data were offset for comparison. (a) 5 levels of testing variables: OH; (b) further testing the OH between 11.6mm and 9.6mm.

Download Full Size | PPT Slide | PDF

4.2.3 Mid-spatial frequencies (MSFs)

The aim of this section was to investigate how to achieve an MSF amplitude below the nominal specification (PV < 40nm) in one grolishing run. Although it is obvious that lower spindle speeds and loads can achieve shallower MSF amplitudes, it was necessary to balance the MSFs with VRR in order to maximize the grolishing efficiency.

According to our ANOVA (analysis of variance) calculation from Table 1, abrasive size and raster space overwhelm the remaining variables, 9μm abrasive and 2mm raster space was determined to minimize MSF amplitudes. Another reason for choosing the 9μm abrasive in our algorism was because this size could achieve the required VRR, texture and edges. For this reason, an evaluation of the load, spindle speed and tool feed values that can control MSFs were investigated. As shown in Table 5, Taguchi’s experimental design (L9) was used to reduce the total of 27 trials to 9.

Tables Icon

Table 5. L9 experimental design to control MSFs.

The result is reasonable since it confirms that decreasing removal depth indeed leads to lower MSFs. Moreover, the MSFs recorded in trial 9 are observable, but unmeasurable because the MSF amplitudes were too low and masked by the background noises. Hence, when the MSFs become small and close to the diffraction limit, continuing to attempt to remove MSFs can increase the overall processing time and add unnecessary cost. This conclusion again indicates the requirement to define the MSF tolerance in Fig. 1 and Figs. 3(a)–3(c).

According to our ANOVA calculation, the 3 testing variables were significant variables, and up to 99.7% of the variation in the data could be explained by this analysis. The regression analysis was used to model the results, yielding the data-cloud of the MSF:

MSF=16.3+0.0675×S0.0173×TF+0.0259×L
where 600 < S < 1000, 1500 < TF < 4500, 1000 < L < 1350.

5. Optimization of automatic-grolishing parameters

This section further demonstrates that automatic-grolishing process can optimize parameters to achieve the specification shown in Fig. 1. Another task was to demonstrate that the repeatability of each response >95% to show a statistically robust grolishing process.

The next task was to determine a set of optimized parameters. Our algorism is showing as following, 4 significant variables that can affect the response were decided at the beginning. (1) An 11.6mm OH was set because this was the only significant variable to control the edge. (2) A 4500mm/min tool feed and a 2mm raster space were selected because these values could control required MSFs in one grolishing run. (3) A 9μm abrasive was chosen so that the grey grolished surface could be polished into a specular one removing 1-2 microns depth of the grolished surface (compatible with a modest pre-polishing run).

In addition, using resolution spaces can help to understand our algorism decide spindle speed and load values, as shown in Figs. 12(a) and 12(b). Since the opposite requirements of MSFs and VRR can meet specification in Fig. 1, the weighting of the both response variables are equal to choose the middle level of the two significant variables: 800rpm and 1175g respectively. From this, all the values for optimized variables were determined automatically without human intervention and the next step was to evaluate the repeatability.

 

Fig. 12 Resolutions spaces from Eqs. (1) and (2) respectively. (a) resolution space of VRR; (b) resolution space of MSFs.

Download Full Size | PPT Slide | PDF

Five repeat experiments were conducted automatically to evaluate each response, with repeatability larger than 95% in order to demonstrate that the grolishing is a robust process. The results are shown in Figs. 13(a)–13(d). Statistics for the experiments are summarized in Table 6. Repeatability for all responses was 95.88%, indicating that the process can provide acceptably uniform outputs.

 

Fig. 13 Optimization experiments. (a) removal depth; (b) one example of texture; (c) edge zone and bulk area; (d) one example of MSFs examination. There were 3 supports underneath the segment for interferometry.

Download Full Size | PPT Slide | PDF

Tables Icon

Table 6. Optimization experiment-statistics for each response; repeatability R > 95%.

6. Error maps for the subsequence automatic polishing process

This section is to demonstrate the smoothing connection from grolishing to polishing. In order to increase overall efficiency, Zeeko’s Metrology ToolkitTM software was used to stitch grolished measurements into a surface topography map to create an error map. Based on this, corrective polishing could be conducted automatically [15]. Figure 14 is an example of stitching a grolished surface, showing the progressive edge-upstand.

 

Fig. 14 Error map of a grolishing surface by using the optimized parameters in section 5. The software can calculate the error of the grolished surface was PV = 0.81μm and RMS = 0.17μm.

Download Full Size | PPT Slide | PDF

7. Conclusion

The grolishing process is an advance on the state-of-the-art. It offers several advantages over classical lapping machines using big tools, loose abrasives, and a motorized orbital mechanism to move the tool over the part. Compared to conventional methods, the process is faster, able to control the VRR, surface accuracy, edges, surface texture and MSFs predictably. Hence, grolishing truly blurs the lines between grinding and polishing to increase the overall efficiency.

The results have shown the complementarity of fast-moving, less precise robots for grolishing, and slower-moving, high-precision Cartesian machines for corrective polishing. In summary:- (i) robot deliver six degrees of freedom, accommodating different part sizes, shapes and forms, (ii) the specification listed in Fig. 1 is achievable, (iii) robots are much cheaper than comparable-reach Cartesian machines, (iv) implementation on a robot avoids risk of cross-contamination between grolishing and polishing. These indicate that a robot grolishing is well-matched to complement a Zeeko or similar polishing machine, for a wide range of complex optical and engineering surfaces.

For the E-ELT project, the ultimate objective is to build data clouds in each processing steps so that the machine can choose parameters without human intervention. From that, a surface can be fabricated automatically across the stages of designing, manufacturing and measuring in order to speed up the process. In this regard, resolution spaces for each process can be successfully built, indicating that the machine is able to choose optimized parameters in a cost-effective fabricating chain so as to realize the next-generation automatic process.

Funding

RCUK Basic Technology Translation Grant (‘Ultra Precision Surfaces: A New Paradigm’); an R&D project funded under the EPSRC Integrated Knowledge Centre in Ultra Precision and Structured Surfaces; an STFC IPS grant; Fundamental Research Project, System Manufacturing Center, National Chung-Shan Institute of Science & Technology, Taiwan and the MOE Technologies Incubation Scholarship from the Ministry of Education, Taiwan.

Acknowledgments

We thank Dr Wu Pei Jung for her algorism of optimization for the automatic process, and Dr Christina Reynolds for her work developing the robot control software within the Zeeko environment. We also thank Dr Chunliang Kuo for his knowledge of statistical method Particular thanks are also due to Glyndŵr University, and to the Vice Chancellor Prof. Mike Scott, in regard to their substantial commitment and financial support of the segment project.

References

1. D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014). [CrossRef]  

2. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S.-W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003). [CrossRef]   [PubMed]  

3. G. Yu, H. Li, and D. D. Walker, “Removal of mid spatial-frequency features in mirror segment,” Journal of the European Optical Society 6, 11044 (2011). [CrossRef]  

4. G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016). [CrossRef]  

5. D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017). [CrossRef]  

6. D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007). [CrossRef]  

7. G. Yu, D. Walker, and H. Li, “Implementing a grolishing process in Zeeko IRP machines,” Appl. Opt. 51(27), 6637–6640 (2012). [CrossRef]   [PubMed]  

8. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef]   [PubMed]  

9. D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

10. D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

11. X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010). [CrossRef]  

12. P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011). [CrossRef]  

13. M. Cayrel, “E-ELT optomechanics: overview,” Proc. SPIE 8444, 84441X (2012). [CrossRef]  

14. “The E-ELT Construction Proposal,” ESO, 1–263 (2011).

15. D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017). [CrossRef]  

16. X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008). [CrossRef]  

17. A. Beaucamp and Y. Namba, “Super-smooth finishing of diamond turned hard x-ray molding dies by combined fluid jet and bonnet polishing,” CIRP Ann. 62(1), 315–318 (2013). [CrossRef]  

18. F. Tinker and K. Xin, “Fabrication of SiC aspheric mirrors with low mid-spatial error,” Proc. SPIE 8837, 88370M (2013). [CrossRef]  

19. J. Franse, “Manufacturing techniques for complex shapes with submicron accuracy,” Rep. Prog. Phys. 53(8), 1049–1094 (1990). [CrossRef]  

20. C. F. Cheung and W. B. Lee, “Modelling and simulation of surface topography in ultra-precision diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 214(6), 463–480 (2000). [CrossRef]  

21. S. Takasu, M. Masuda, T. Nishiguchi, and A. Kobayashi, “Influence of study vibration with small amplitude upon surface roughness in diamond machining,” CIRP Annals, 34, 1), 463–467 (1985).

22. T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985). [CrossRef]  

23. X. Tonnellier, “Precision Grinding for Rapid Manufacturing of Large Optics,” PhD Thesis (2009).

24. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008). [CrossRef]   [PubMed]  

25. C. Song, D. D. Walker, and G. Yu, “Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments,” Opt. Eng. 50(7), 073401 (2011). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
    [Crossref]
  2. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S.-W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003).
    [Crossref] [PubMed]
  3. G. Yu, H. Li, and D. D. Walker, “Removal of mid spatial-frequency features in mirror segment,” Journal of the European Optical Society 6, 11044 (2011).
    [Crossref]
  4. G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
    [Crossref]
  5. D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
    [Crossref]
  6. D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
    [Crossref]
  7. G. Yu, D. Walker, and H. Li, “Implementing a grolishing process in Zeeko IRP machines,” Appl. Opt. 51(27), 6637–6640 (2012).
    [Crossref] [PubMed]
  8. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012).
    [Crossref] [PubMed]
  9. D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).
  10. D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).
  11. X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010).
    [Crossref]
  12. P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011).
    [Crossref]
  13. M. Cayrel, “E-ELT optomechanics: overview,” Proc. SPIE 8444, 84441X (2012).
    [Crossref]
  14. “The E-ELT Construction Proposal,” ESO, 1–263 (2011).
  15. D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
    [Crossref]
  16. X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008).
    [Crossref]
  17. A. Beaucamp and Y. Namba, “Super-smooth finishing of diamond turned hard x-ray molding dies by combined fluid jet and bonnet polishing,” CIRP Ann. 62(1), 315–318 (2013).
    [Crossref]
  18. F. Tinker and K. Xin, “Fabrication of SiC aspheric mirrors with low mid-spatial error,” Proc. SPIE 8837, 88370M (2013).
    [Crossref]
  19. J. Franse, “Manufacturing techniques for complex shapes with submicron accuracy,” Rep. Prog. Phys. 53(8), 1049–1094 (1990).
    [Crossref]
  20. C. F. Cheung and W. B. Lee, “Modelling and simulation of surface topography in ultra-precision diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 214(6), 463–480 (2000).
    [Crossref]
  21. S. Takasu, M. Masuda, T. Nishiguchi, and A. Kobayashi, “Influence of study vibration with small amplitude upon surface roughness in diamond machining,” CIRP Annals, 34, 1), 463–467 (1985).
  22. T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
    [Crossref]
  23. X. Tonnellier, “Precision Grinding for Rapid Manufacturing of Large Optics,” PhD Thesis (2009).
  24. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
    [Crossref] [PubMed]
  25. C. Song, D. D. Walker, and G. Yu, “Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments,” Opt. Eng. 50(7), 073401 (2011).
    [Crossref]

2017 (2)

D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

2016 (2)

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

2015 (1)

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

2014 (1)

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

2013 (2)

A. Beaucamp and Y. Namba, “Super-smooth finishing of diamond turned hard x-ray molding dies by combined fluid jet and bonnet polishing,” CIRP Ann. 62(1), 315–318 (2013).
[Crossref]

F. Tinker and K. Xin, “Fabrication of SiC aspheric mirrors with low mid-spatial error,” Proc. SPIE 8837, 88370M (2013).
[Crossref]

2012 (3)

2011 (3)

C. Song, D. D. Walker, and G. Yu, “Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments,” Opt. Eng. 50(7), 073401 (2011).
[Crossref]

G. Yu, H. Li, and D. D. Walker, “Removal of mid spatial-frequency features in mirror segment,” Journal of the European Optical Society 6, 11044 (2011).
[Crossref]

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011).
[Crossref]

2010 (1)

X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010).
[Crossref]

2008 (2)

X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008).
[Crossref]

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
[Crossref] [PubMed]

2007 (1)

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

2003 (1)

2000 (1)

C. F. Cheung and W. B. Lee, “Modelling and simulation of surface topography in ultra-precision diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 214(6), 463–480 (2000).
[Crossref]

1990 (1)

J. Franse, “Manufacturing techniques for complex shapes with submicron accuracy,” Rep. Prog. Phys. 53(8), 1049–1094 (1990).
[Crossref]

1985 (1)

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Baldwin, A.

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Beaucamp, A.

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

A. Beaucamp and Y. Namba, “Super-smooth finishing of diamond turned hard x-ray molding dies by combined fluid jet and bonnet polishing,” CIRP Ann. 62(1), 315–318 (2013).
[Crossref]

D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012).
[Crossref] [PubMed]

Bibby, M.

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

Brooks, D.

Cayrel, M.

M. Cayrel, “E-ELT optomechanics: overview,” Proc. SPIE 8444, 84441X (2012).
[Crossref]

Cheung, C. F.

C. F. Cheung and W. B. Lee, “Modelling and simulation of surface topography in ultra-precision diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 214(6), 463–480 (2000).
[Crossref]

Comley, P.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011).
[Crossref]

X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010).
[Crossref]

Davies, G.

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Dunn, C.

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

Dunn, C. R.

Evans, R.

D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012).
[Crossref] [PubMed]

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Fox-Leonard, T.

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Franse, J.

J. Franse, “Manufacturing techniques for complex shapes with submicron accuracy,” Rep. Prog. Phys. 53(8), 1049–1094 (1990).
[Crossref]

Freeman, R.

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S.-W. Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11(8), 958–964 (2003).
[Crossref] [PubMed]

Gray, C.

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Hamidi, S.

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Hiraoka, H.

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Kim, S.-W.

King, A.

Lee, W. B.

C. F. Cheung and W. B. Lee, “Modelling and simulation of surface topography in ultra-precision diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 214(6), 463–480 (2000).
[Crossref]

Li, C. Q.

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Li, H.

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

G. Yu, D. Walker, and H. Li, “Implementing a grolishing process in Zeeko IRP machines,” Appl. Opt. 51(27), 6637–6640 (2012).
[Crossref] [PubMed]

D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012).
[Crossref] [PubMed]

G. Yu, H. Li, and D. D. Walker, “Removal of mid spatial-frequency features in mirror segment,” Journal of the European Optical Society 6, 11044 (2011).
[Crossref]

Li, M.

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Lu, C.

D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

McCavana, G.

McCluskey, L.

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

Messelink, W.

Mitchell, J.

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Morantz, P.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011).
[Crossref]

X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010).
[Crossref]

X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008).
[Crossref]

Morton, R.

Namba, Y.

A. Beaucamp and Y. Namba, “Super-smooth finishing of diamond turned hard x-ray molding dies by combined fluid jet and bonnet polishing,” CIRP Ann. 62(1), 315–318 (2013).
[Crossref]

Orton, D.

X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008).
[Crossref]

Petrovic, S.

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

Rees, P.

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Reynolds, C.

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

Sata, T.

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Shore, P.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011).
[Crossref]

X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010).
[Crossref]

X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008).
[Crossref]

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Song, C.

C. Song, D. D. Walker, and G. Yu, “Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments,” Opt. Eng. 50(7), 073401 (2011).
[Crossref]

Takata, S.

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Tinker, F.

F. Tinker and K. Xin, “Fabrication of SiC aspheric mirrors with low mid-spatial error,” Proc. SPIE 8837, 88370M (2013).
[Crossref]

Tonnellier, X.

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011).
[Crossref]

X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010).
[Crossref]

X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008).
[Crossref]

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Volkov, A.

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Walker, D.

Walker, D. D.

D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

G. Yu, H. Li, and D. D. Walker, “Removal of mid spatial-frequency features in mirror segment,” Journal of the European Optical Society 6, 11044 (2011).
[Crossref]

C. Song, D. D. Walker, and G. Yu, “Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments,” Opt. Eng. 50(7), 073401 (2011).
[Crossref]

C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008).
[Crossref] [PubMed]

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Wang, Z.

Wei, S.

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Williams, C.

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Wu, H.-Y.

D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Xiao, X. G.

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Xin, K.

F. Tinker and K. Xin, “Fabrication of SiC aspheric mirrors with low mid-spatial error,” Proc. SPIE 8837, 88370M (2013).
[Crossref]

Xing, X. Z.

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Yu, G.

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

D. D. Walker, H.-Y. Wu, G. Yu, H. Li, Z. Wang, and C. Lu, “Insight into aspheric misfit with hard tools: mapping the island of low mid-spatial frequencies,” Appl. Opt. 56(36), 9925–9931 (2017).
[Crossref]

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012).
[Crossref] [PubMed]

G. Yu, D. Walker, and H. Li, “Implementing a grolishing process in Zeeko IRP machines,” Appl. Opt. 51(27), 6637–6640 (2012).
[Crossref] [PubMed]

G. Yu, H. Li, and D. D. Walker, “Removal of mid spatial-frequency features in mirror segment,” Journal of the European Optical Society 6, 11044 (2011).
[Crossref]

C. Song, D. D. Walker, and G. Yu, “Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments,” Opt. Eng. 50(7), 073401 (2011).
[Crossref]

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Zhang, P.

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

Zheng, X.

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

Adv. Mat. Res. (1)

D. D. Walker, G. Davies, T. Fox-Leonard, C. Gray, J. Mitchell, P. Rees, H.-Y. Wu, A. Volkov, and G. Yu, “Advanced abrasive processes for manufacturing prototype mirror segments for the world’s largest telescope,” Adv. Mat. Res. 1017, 532–538 (2014).
[Crossref]

Appl. Opt. (2)

CIRP Ann. (3)

P. Comley, P. Morantz, P. Shore, and X. Tonnellier, “Grinding metre scale mirror segments for the E-ELT ground based telescope,” CIRP Ann. 60(1), 379–382 (2011).
[Crossref]

A. Beaucamp and Y. Namba, “Super-smooth finishing of diamond turned hard x-ray molding dies by combined fluid jet and bonnet polishing,” CIRP Ann. 62(1), 315–318 (2013).
[Crossref]

T. Sata, M. Li, S. Takata, H. Hiraoka, C. Q. Li, X. Z. Xing, and X. G. Xiao, “Analysis of surface roughness generation in turning operation and its applications,” CIRP Ann. 34(1), 473–476 (1985).
[Crossref]

Journal of the European Optical Society (1)

G. Yu, H. Li, and D. D. Walker, “Removal of mid spatial-frequency features in mirror segment,” Journal of the European Optical Society 6, 11044 (2011).
[Crossref]

Opt. Eng. (1)

C. Song, D. D. Walker, and G. Yu, “Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments,” Opt. Eng. 50(7), 073401 (2011).
[Crossref]

Opt. Express (3)

Proc. Inst. Mech. Eng., B J. Eng. Manuf. (1)

C. F. Cheung and W. B. Lee, “Modelling and simulation of surface topography in ultra-precision diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 214(6), 463–480 (2000).
[Crossref]

Proc. SPIE (8)

X. Tonnellier, P. Morantz, P. Shore, and P. Comley, “Precision grinding for rapid fabrication of segments for extremely large telescopes using the Cranfield BoX,” Proc. SPIE 7739, 773905 (2010).
[Crossref]

D. D. Walker, C. Dunn, G. Yu, M. Bibby, X. Zheng, H.-Y. Wu, H. Li, and C. Lu, “The role of robotics in computer controlled polishing of large and small optics,” Proc. SPIE 9575, 95750B (2015).

G. Yu, H.-Y. Wu, D. D. Walker, X. Zheng, H. Li, C. Dunn, and C. Gray, “Optimisation of grolishing freeform surfaces with rigid and semi-rigid tools,” Proc. SPIE 9912, 99123Q (2016).
[Crossref]

F. Tinker and K. Xin, “Fabrication of SiC aspheric mirrors with low mid-spatial error,” Proc. SPIE 8837, 88370M (2013).
[Crossref]

D. D. Walker, G. Yu, A. Beaucamp, M. Bibby, H. Li, L. McCluskey, S. Petrovic, and C. Reynolds, “More steps towards process automation for optical fabrication,” Proc. SPIE 10326, 103260S (2017).
[Crossref]

X. Tonnellier, P. Shore, P. Morantz, and D. Orton, “Surface quality of a 1m zerodur part using an effective grinding mode,” Proc. SPIE 7102, 71020B (2008).
[Crossref]

M. Cayrel, “E-ELT optomechanics: overview,” Proc. SPIE 8444, 84441X (2012).
[Crossref]

D. D. Walker, A. Baldwin, R. Evans, R. Freeman, S. Hamidi, P. Shore, X. Tonnellier, S. Wei, C. Williams, and G. Yu, “A quantitative comparison of three grolishing techniques for the Precessions process,” Proc. SPIE 6671, 66711H (2007).
[Crossref]

Rep. Prog. Phys. (1)

J. Franse, “Manufacturing techniques for complex shapes with submicron accuracy,” Rep. Prog. Phys. 53(8), 1049–1094 (1990).
[Crossref]

Society (1)

D. D. Walker, G. Yu, M. Bibby, C. Dunn, H. Li, H.-Y. Wu, X. Zheng, and P. Zhang, “Robotic automation in computer controlled polishing,” Journal of the European Opt,” Society 11, 16005 (2016).

Other (3)

“The E-ELT Construction Proposal,” ESO, 1–263 (2011).

S. Takasu, M. Masuda, T. Nishiguchi, and A. Kobayashi, “Influence of study vibration with small amplitude upon surface roughness in diamond machining,” CIRP Annals, 34, 1), 463–467 (1985).

X. Tonnellier, “Precision Grinding for Rapid Manufacturing of Large Optics,” PhD Thesis (2009).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1 Potential role of grolishing in a process-chain.
Fig. 2
Fig. 2 Definition of edge and bulk areas for a 1.45m segment.
Fig. 3
Fig. 3 To demonstrate MSFs PV < 40nm is diffraction limit. (a) Two different input surfaces with their respective MSFs. (b) The respective outputs surface by using PSF. (c) The MTF from the PV = 40nm surface.
Fig. 4
Fig. 4 Mechanism of the grolishing tool.
Fig. 5
Fig. 5 (a) The hard grolishing tool used to process 400mm hexagonal segment. (b) Bonnet pre-polishing on a Zeeko machine.
Fig. 6
Fig. 6 Process for removal measurement.
Fig. 7
Fig. 7 Measurement equipment (a) extended range Talysurf for measuring surface profile; (b) white light interferometer for texture; (c) 4D interferometer for MSFs measurement.
Fig. 8
Fig. 8 A tool has a constant speed at the edge but decelerates and then accelerates at the corner when changing processing direction.
Fig. 9
Fig. 9 The 400mm hexagon with two orthogonal directions measurement.
Fig. 10
Fig. 10 Evaluating the 3 variables (data were offset for comparison). (a) testing: abrasive size (1175g load and 800rpm spindle speed); (b) testing: spindle speed (1175g load and 9μm abrasive; (c) testing: load (1175g load and 800rpm spindle speed).
Fig. 11
Fig. 11 Evaluating the method of overhang for edge control with 9μm abrasive, 800rpm spindle speed and 1150g load (data were offset for comparison. (a) 5 levels of testing variables: OH; (b) further testing the OH between 11.6mm and 9.6mm.
Fig. 12
Fig. 12 Resolutions spaces from Eqs. (1) and (2) respectively. (a) resolution space of VRR; (b) resolution space of MSFs.
Fig. 13
Fig. 13 Optimization experiments. (a) removal depth; (b) one example of texture; (c) edge zone and bulk area; (d) one example of MSFs examination. There were 3 supports underneath the segment for interferometry.
Fig. 14
Fig. 14 Error map of a grolishing surface by using the optimized parameters in section 5. The software can calculate the error of the grolished surface was PV = 0.81μm and RMS = 0.17μm.

Tables (6)

Tables Icon

Table 1 The L8 of the Taguchi method for screening experiment to determine significant variables. Note that edge and MSFs were scaled by their respective removal depths to merit the comparison of each variable effect.

Tables Icon

Table 2 Summary of significant variables from ANOVA.

Tables Icon

Table 3 23 full factorial design to evaluate significant variables for VRR and texture.

Tables Icon

Table 4 Comparison of the predicted data and experimental data.

Tables Icon

Table 5 L9 experimental design to control MSFs.

Tables Icon

Table 6 Optimization experiment-statistics for each response; repeatability R > 95%.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

VRR=-16.7+2.84×AS-0.0181×L+0.0113×S+0.00122×AS×L+0.000025×L×S+ 0.00000017×AS×L×S
Texture=7.34+34.8×AS+0.133×L+0.191×S0.00444×L×S
MSF=16.3+0.0675× S0.0173×TF+0.0259×L

Metrics