Mid-spatial frequency (MSF) errors challenge freeform manufacture, not in the least due to tool-misfit. This can compromise the performance of functional surfaces and is difficult to remove by post-processing. Our previously reported work on an effective process-chain for aluminum polishing demonstrated the ability to remove MSFs by hard-tool grolishing. In this paper, we describe MSF removal on an aluminum mirror, deformed to a saddle-like freeform shape, using power spectral density (PSD) as a diagnostic. CNC Precessions bonnet polishing was optimized to minimize output MSFs, then a non-Newtonian (n-N) tool was used to attenuate the residual MSFs that were present. Our approach was distinct from the approach pioneered by University of Arizona, in that we adopted small-tool polishing on the saddle-like part, with removal rate restored by rotating the n-N tool. In order to define the optimum window of rotation speeds, the dynamic behavior of the n-N material was explored by modelling and experiments. The tool was deployed on an industrial robot, and we describe a novel ‘hyper-crossing’ tool-path with wide sweeping paths, which is the logical opposite of the unicursal zero-crossing paths we have previously reported. This new path has proved ideally suited to robots, given their high velocity/acceleration capabilities. Detailed results are presented from the PSD viewpoint.
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A successful optical design requires a careful balance of performance, cost, schedule and risk, which is influenced by system configuration, mirror material and manufacturability. Utilizing a freeform in the optical system can significantly reduce the size and mass of the system e.g. for lightweight space systems, and enhance optical performance. This is because freeforms offer additional degrees-of-freedom in the optical design, providing enhanced control of optical aberrations at each surface [1–4]. However, due to the complexity of freeform-signatures, these surfaces are extremely difficult to manufacture and measure. One of the most challenging manufacturing issues is tool-misfit. Given a CNC-machined part, a spherical surface is the simplest to polish, because a rigid polishing tool pressed into intimate contact at one location, can maintain contact anywhere else. For freeforms, this is not the case, as tool-misfit tends to create surface artefacts, especially mid-spatial frequency (MSF) errors . In optical applications, MSFs can produce diffractive side-lobes to images, scatter light, and reduce detected signal-to-noise ratio [6,7]. Misfit is most severe for full-size tools but can still be evident with small tool (‘sub-aperture’) polishing.
As a mirror material, bare aluminum alloys have approximately the same Young’s Modulus and density as glasses, but offer several advantages [8–10]:
- • Low material cost
- • High ductility, leading to immunity to fracture during manufacture, or under vibration or shock loads (e.g. during launch)
- • Suitability for extreme light-weighting for space or mobile applications
- • Suitability to incorporate cooling channels for high energy applications
- • High reflectivity over a wide spectral range, especially for multispectral imaging
- • An all-aluminum telescope (mirrors and structure) can be essentially athermal
- • Emerging potential for additive manufacturing of complex structures and integrated support
- • Bare aluminum avoids the bimetallic effect with electroless nickel coated aluminum
Single point diamond turning (SPDT) with tool-servoing is the usual approach to imprinting the base freeform topography . However, SPDT tends to leave MSF turning marks on the surface , which in principle can be removed by post-polishing. Traditional polishing methods have been applied in many applications to improve surface roughness and form - mainly plano optics and some aspheric surfaces. However, the results have been limited by the material alloy and slurry properties . Many research groups have attempted to develop modern freeform fabrication techniques to improve surface quality. X. Guo et al have developed a pseudorandom orbiting stroke computer numerical control (CNC) post-processing technique which is suitable for aluminium freeform processing for diameters ranging from 30 mm to 100 mm . OPTIMAX Ltd has developed a robust freeform optical fabrication CNC process. This technology has been successfully applied and demonstrated on a glass sample . The modern sub-aperture and deterministic optical processing techniques are prone to residual periodic surface errors (MSFs), especially for aluminum due to its ductility and sensitivity to oxidization. In our previous research, we have demonstrated the potential of industrial robots to automate manual interventions with CNC polishing machines, and to provide surface-processing capabilities in their own right . We also have investigated several specialized aluminum polishing slurries, both on small spherical mirrors, and a 490 mm diameter aspheric mirror. Through this work, we have developed an effective process chain for aluminum polishing, demonstrating MSF removal after hard-tool grolishing .
In this paper, we focus on important diagnostic information in the spatial frequency domain (power spectral density, PSD) at different stages of manufacture. Using this information, we have optimized CNC Precessions bonnet polishing to minimize MSFs. We have then gone on to develop sub-aperture non-Newtonian tools, where, unlike the work of the University of Arizona , the tools are rotated to recover volumetric removal rate. Finally, recognizing MSFs that originate in repetitive tool-paths, we have demonstrated a new hyper-crossing tool-path algorithm, providing surface-randomization.
2. Preparation of the freeform surface
The part in this research is a 3 mm thick, 400 mm × 400 mm square, grade 1050A aluminum, known for its good corrosion resistance, high ductility and high reflective finish. To create a freeform surface, a flat aluminum plate was deformed on a bending rig, as shown in Fig. 1. The aluminum bending-plate was mounted spanning two stainless steel support-rails. The deformation was applied by an adjustable screw pulling down on a metal pull-bar attached across the center of the plate. In order for the deformed surface to resist polishing forces with negligible additional deformation, ISOPON P38 car-body filler was inserted to fill the gap under the bending-plate, with thin isolating plastic sheets above and below to prevent adhesion. The ISOPON P38 hardens after the ~30 minutes curing time, facilitating rapid turnaround of experiments. After processing the deformed part, it was returned to the unstressed, nominally-flat state, to facilitate surface measurement and interpretation. The deformation of the surface was measured by a portable coordinate measuring arm (Hexagon Absolute 7512) as shown in Fig. 2(a), with an uncertainty of measurement 10 μm. This measurement provided the information of the actual shape of the surface for tool path generation in Z direction. Figure 2(b) shows the strong saddle shape surface with PV~1.3 mm achieved. The saddle shape surface can be described mathematically by Eq. (1).
Using the bending-rig to create such saddle shape surface has certain advantages i) deformable during setup, ii) stiff under polishing-forces, iii) then deformable to a different figure. In this paper, the saddle shape surface of 1.3 mm PV has proven an effective demonstration for investigating effects of tool misfit, MSFs etc.
3. MSFs after raster tool path polishing
The 400 mm square freeform surface was first processed on the IRP1200 Precessions CNC polishing machine, using an R80 bonnet tool with polyurethane pad, as shown in Fig. 3(a). The abrasive was the standard re-circulated Cerox1663 cerium oxide with a specific gravity of 1.02 g/mL and temperature at 21 °C. This slurry is not normally the first choice for aluminum but is used in this case since it conveniently delivered a uniform grey surface with attenuated diamond-turning marks. This process also provided a similar removal rate to fine colloidal silica slurry with a Uninap pad . The Cerox process parameters are shown in Table 1.
To identify and compare the raster signature with different track space and tool offset, the entire surface was divided into 4 regions. The schematic raster tool path is shown in Fig. 3(b). Each of the four regions was rastered first using a 1 mm track spacing and then increased to 2 mm in order to leave two spatial frequencies on the surface. The four different regions were processed with different tool Z-offsets (bonnet compressions): 0.5 mm, 0.7 mm, 1.0 mm and 1.2 mm, which corresponded to polishing spot-size of 17 mm, 21 mm, 24 mm and 27 mm respectively. After 100 minutes of polishing per region, it was observed that the surface was gray, with periodic raster features visible, as shown in Fig. 4(a). The depth of the mid-spatial stripes at different regions was measured with a Talysurf Intra profilometer. The profilometer stylus was not a spherical ball, but a pointed tip with radius of curvature of 2 µm with Gaussian filter 2.5 mm Lc and 0.08 mm Ls. This high-frequency cut-off was selected to discriminate mid spatial frequencies from texture. The depths varied between ~1.0 μm and ~2.0 μm, as shown in Fig. 4(b). These provided the MSF signatures for the next stage of experiments, the objective of which was to remove these features. The details are described in the next section.
The MSFs from raster-polishing with different spot-sizes were characterized by PSD analysis, as shown in Fig. 5. Two peaks can be clearly seen, corresponding to the 1 mm and 2 mm raster spacing. The area under the curve is the square of the RMS surface error. These PSD plots indicate that an R80 mm bonnet with a 24 mm spot-size, resulted minima in the PSD amplitudes at spatial wavelengths corresponding to 1 mm and 2 mm track spacing. The quantitative discrepancy between precise spatial-wavelength and raster spacing can be attributed to the projection effect on flattening the part for measurement. The results indicate that process parameters such as variable spot-size and track spacing can be optimized to minimize MSFs.
4. Design and modelling of rotating non-Newtonian(n-N) tools
4.1. Young’s Modulus test of the Silly Putty material
Unlike spherical surfaces, it’s not possible for a rigid tool to conform to an aspherical or freeform surface. Specially for processing a deep aspheric or freeform surface, a rigid tool tents to produce significant MSFs due to large misfit. The magnitude of misfit will vary as the tool is driven along the surface of the part. In processing a large part (for example >1 m diameter), in order to speed up whole process, the size of the tool inevitably needs to be increased. The misfit however will increase significantly. Therefore, a compliant tool is needed to conform to the local surface contours of the part, but which can then contradict the ability to smooth MSFs. In order to resolve this, n-N material -Silly Putty was adopted in the tool design, building on the work of the University of Arizona Mirror Lab  polishing 8.4 m off-axis paraboloids. Unlike U-of-A, we are using such tools in rotation to increase the volumetric removal rate.
As an n-N material, the Young’s Modulus of the Silly Putty varies depending on the frequencies of the external force applied. For a processing tool, the upper-limit of spindle speed needs to be set by the transition of the Silly Putty from its n-N behavior to fully-hard to balance the tool misfit and rigidity. To investigate the n-N effect of the Young’s Modulus of the Silly Putty, the stress-strain curve has been measured on universal compression and tensile test instrument 5900 , as shown in Fig. 6(a). The Silly Putty material samples were prepared as 40 mm × 40 mm square shape, but with different heights of 20 mm, 40 mm and 80 mm. The stress-strain curves were tested with different stain rates, as 0.5%·s−1, 1%·s−1, 5%·s−1 and 10%·s−1. The Young’s Modulus was then calculated by averaging the slop of the curves, as plotted in Fig. 6(b). These plots reveal the relationship between the Young’s Modulus of the Silly Putty material and the frequencies of the external forces applied. Based on these plots, the dynamic FEA of the Silly Putty was carried out to optimize the tool design, which is described in next section.
The design of the polish tool is shown in Fig. 7(a), in which a 10 mm thick Silly Putty material was sandwiched between a rigid back plate and a flexible Bellofram diaphragm. Then, a polishing cloth (polyurethane or Uni-nap) was glued to the diaphragm. The diameter of the tool is 100 mm. The weight of the Silly Putty material filling in the tool is about 125 g. As shown in Fig. 7(b), the back plate of the tool was mounted onto an adaptor attached with an ABB motorized spindle as an end-effector to a robot arm. The setup of the tooling onto an industrial robot arm is introduced in following section.
4.2. FEA of a rotating n-N tool
The n-N behavior of the tool enables it to conform to the local surface of an aspherical or freeform part. The more rigid the tool, the more capable it is to remove input-MSFs, but local high-pressure variations tend to produce new MSFs. At lower spindle speeds, the n-N material has sufficient time to conform to the local surface of the part, while at higher speeds, its response is too slow. COMSOL5.3 dynamic FEA was used to predict the pressure distributions between the tool and the freeform surface to optimize the tool spindle speed. Figure 8 shows the CAD mesh model. The 400 mm × 400 mm freeform surface created in Fig. 2 was input into this model. Figure 9 shows that a 124 µm misfit is produced between a 100 mm diameter flat tool and the saddle-shaped surface. In this simulation, the polishing force was applied by the 10 kg self-weight of the tool. This has been set as a uniform load in the model. The side wall of the tool was assigned as spring foundation, which was used to restrict the movement in the radial direction. The fixed constraint was added onto the back plate which connected with an ABB spindle motor during the polishing. To simulate the contact process, the contact interface was assigned on the upper surface of the part and the bottom surface of the tool. The meshing type was free tetrahedral with a total number of mesh elements of 15800. The two contact surfaces are the region of interest. In this region, a mesh size of 0.2 mm was used to control the simulation resolution.
The simulation results with different spindle speeds are shown in Fig. 10, and the 2D plots in Fig. 11. It can be seen that: i) A nominally uniform pressure distribution on the bulk area was achieved due to the flexibility of the n-N material, even with a 124 µm misfit; ii) The pressure distribution on the bulk area increased when the spindle speed increased from 30 rpm to 150 rpm, as the tool became more rigid; iii) The pressure distribution in the vicinity of the periphery of the tool increased compared with the bulk, attributed to centrifugal force redistributing the material within the tool. From the simulation results, higher spindle speeds were more attractive in terms of higher removal rates and more uniform pressure distribution. 100 rpm was adopted as the best compromise, due to the onset of dynamic instability at faster speeds.
To simulate the ability of MSF removal using an n-N tool, a second FEA was performed to calculate the pressure distribution on a surface having an MSF signature. This FEA model was based on the model in Fig. 8, in which the surface of the part was a saddle-like freeform with PV~1.3 mm, created by the bending rig, with the tool rotating at 100 rpm. A 2 mm track-spacing periodic raster MSF signature of ~2.0 μm PV was imprinted onto the modelled surface. As shown in Fig. 12, the model predicted a periodic pressure distribution which corresponded to the input MSF signature. According to the theoretical basis of prediction of material removal in optical surface polishing presented by Preston, the material removal rate ∆h(x, y) at each point on the surface is proportional to the local contact pressure p(x, y) and relative velocity v(x, y) between the tool and surface of the part, as described as follows:
5. A novel hyper-crossing tool path
5.1. The hyper-crossing tool path generation algorithm
The modern sub-aperture and deterministic optical processing techniques are prone to residual periodic surface errors (MSFs). A regular tool path inevitably leaves repetitive signature in the surface, resulting from the superposition of the near-Gaussian influence functions over a range of parallel tracks in a spiral or raster. To achieve randomized residual errors, an algorithm for generating pseudo-random unicursal tool path has previously been developed . This path travels over the entire surface of the part without ever crossing itself. This avoids localized double-removal and has many qualities that lend it to sub-aperture polishing techniques. However, a drawback is that a unicursal path contains many sharp turns, and the resulting accelerations are challenging for a CNC machine-tool to execute. The alternative strategy is a tool-path which crosses itself essentially everywhere – which we call a ‘hyper-crossing’ tool path. Several variants have been explored , and in this paper we report on the combination of an epicyclic-based variant, executed by a robot, using an n-N tool.
The seed for the epicyclic tool path is the unicursal random tool path, as shown in Fig. 13. The first step in creating an epicyclic tool path is generating a unicursal random tool path. The MATLAB function curvspace is then used to extrapolate this tool path to 10,000 points. For each point along the path, the closest point on the part boundary is located. The distance to this boundary point is calculated and saved in an array. Epicycles are then calculated which are centered on the points along the unicursal random tool path. The coordinates of the epicyclic path are calculated using the Eqs. (3) and (4):Fig. 14 with two different epicycles of t = 50 π and t = 1,000 π. It can be seen that the tool path with t = 50 π has randomly covered entire surface, although the coverage is not uniform, as shown in on the left of Fig. 14. As t increased to 1,000 π, the coverage of the tool has become uniform. The tool path can be used with any continuous region, including those with one or more interior holes. The density of the pattern can be changed, which is analogous to increasing or decreasing the spacing of a raster or spiral. The tool path can be configured to give different randomized paths with almost identical input parameters. This tool path has been implemented onto an industrial robot and trialed in the polishing process chain, as introduced in following section.
5.2. Implementation of the hyper-crossing tool path on an industrial robot arm
We have previously demonstrated the potential of industrial robots to automate manual interventions with CNC polishing machines . We have also proved the capabilities of surface processing on glass parts using the FANUC R-2000iB industrial robot . To investigate the feasibilities of surface processing on freeform aluminum parts, the n-N Silly Putty tool driven by the novel epicyclic tool path were implemented onto the FANUC R-2000iB industrial robot, as shown in Fig. 15. This robot has a reach of 3.05 m and maximum-payload of 125 kg. It is capable to reach its maximum speed of 5.1 m/s in 100 ms. An ABB motorized spindle with a detachable gearbox is mounted as an end-effector to the robot arm, enabling tool rotation with options of high speed and low torque, or high-torque and low-speed, as shown in Fig. 7. A 100 mm diameter n-N Silly Putty tool was attached to the ABB spindle. The weight of the tool is 10 kg. Tooling ‘floats’ in the Z-axis perpendicular to the surface of the part under its self-weight and is driven in the X-Y plane by a gimbal-type coupling. The polishing pads were grooved before cementing to the tool. This allows the slurry to flow adequately into the polishing area. The slurry was delivered by a digitally-controlled peristaltic pump with an accuracy of 0.1 mL/min.
MATLAB functions were added to the Zeeko-TPG to allow for the testing of generalized tool paths. These functions take the Cartesian coordinates as generated by the Zeeko-TPG and format them correctly for the robot. For the Fanuc robot, the tool path is output as an LS file; a text file which is converted to a binary TP file readable by the robot. LS files consist of definitions of positions and motions. The position definitions are given in six axes: x, y, z, w, p, and r. The angles w, p, and r are computed with respect to the surface normal of the workpiece, which is obtained from the Zeeko-TPG. The position definition also includes information about the frame-of-reference of the coordinates. The epicyclic tool path was recently developed and implemented into the Zeeko-TPG.
6. Experimental results and analysis
The objective of these experiments is to quantify MSF removal using n-N polishing tools on the Fanuc 2000iB robot, following hyper-crossing tool paths. The input part was the part previously raster-polished in quadrants on the IRP1200 machine with different spot sizes (as reported in section 3). Two different hyper-crossing tool paths were generated with different track-densities with the aim of removing the raster MSF signature by changing the distance r in Eqs. (3) and (4) is between each point (x, y) and the nearest boundary. Figure 16 shows tool path patterns with a) 5mm, and b) 2mm track−1 nominal densities.
Two sets of surface profiles were measured using the Talysurf Intra stylus profilometer after robotic polishing, as shown in Fig. 17. The MSF depths in the input part after IRP1200 polishing (as per section 3) varied between ~1.0 μm and ~2.0 μm. After 95 minutes of robotic polishing with 5 mm track spacing, MSF depths were reduced to roughly 100 nm - 200 nm. Finally, after 120 minutes of robotic polishing with 2 mm track spacing, MSF depths were further reduced to between 30 nm ~50 nm. The results show that the input MSFs (shown in Fig. 4) have been attenuated by the robotic process. The surface quality was then measured under the ADE MicroXAM white light interferometer. The objective used is × 50. This provides an 86 µm × 64 µm measurement area. The texture of Sa ~2.9 nm (after removing the low order Zernike terms) was achieved, as shown in Fig. 18. The PSD for the final stage is shown in Fig. 19.
To better understand and quantify the MSFs at different stages of the process, PSD analyses after bonnet and robotic polishing are plotted together for different spot-sizes, as shown in Fig. 20. The quantitative results of PSD analysis are shown in Table 2. The conclusions are summarized below:
- 1. Two peaks corresponded to the periodic features input by raster polishing with 1 mm and 2 mm track spacing, as shown in Fig. 5. This provided two MSF regions, with the objective of removing them using robotic processing.
- 2. From PSD analyses, MSFs arising from Precessions bonnet raster-polishing can be minimized by adopting 1 mm track spacing and 24 mm spot-size (1.0 mm Z-offset, 80 mm tool radius). The results show the minimum PSD is 2.6 × 10−3 μm2·mm in a 1mm region, and 4.5 × 10−3 μm2·mm in a 2 mm region. The maximum PSD is 1.2 × 10−2 μm2·mm from a 17 mm spot-size (0.5 mm Z-offset), as shown in Table 2.
- 3. After the first robotic polishing, MSFs were reduced significantly. The maximum PSD is 1.6 × 10−3 μm2·mm for the 1 mm region and 9.0 × 10−4 μm2·mm for 2 mm, corresponding to a 17 mm spot-size (0.5 mm Z-offset).
- 4. After the second robotic polishing process, the MSFs were removed effectively. This is due to the very nature of the epicyclic-based tool-path, it avoids all of the repetitive parallel signature of a traditional raster tool-path. With the assistance of PSD analysis, the results show that 99% of MSFs arising from raster tool path polishing were reduced by epicyclic tool path polishing. The PSD was reduced to ~10−5 μm2·mm for all spot-size, as shown in Fig. 19.
In this paper, we focused on one of the most challenging issues – MSF error-removal in freeform aluminum mirror fabrication. To quantify and diagnose the MSF information at different stages of the process, PSD analyses were adopted, rather than peak-to-value and RMS as we have previously reported. In order to minimize the MSFs in CNC Precessions bonnet polishing, parameters such as spot-size and track spacing have been optimized experimentally, with the assistance of PSD analysis. To address the issue of tool misfit using a rigid tool, a non-Newtonian tool has been designed to conform to an aspherical or freeform surface. A distinguishing feature of our work is that we rotate the n-N tool to recover removal-rate, and that has led us to explore the dynamic performance of the material through experiment and FEA in this special mode of operation.
Furthermore, a novel ‘hyper-crossing’ tool-path has been reported, where the new algorithm generates a different pseudo-random path every time it is run. The large sweeping motions produced are ideally suited to remove MSFs, as demonstrated on a 400 mm square aluminum freeform surface. As pointed out, the path (unlike the unicursal path) crosses itself, and for uniform removal many cross-overs are essential. Implementation on an industrial robot has proved particularly effective, given the high velocities and accelerations that such robots routinely deliver.
Science and Technology Facilities Council (ST/L001950/2); Engineering and Physical Sciences Research Council (EP/F031416/1).
We wish to acknowledge financial support from the STFC and EPSRC UK research councils for funding different aspects of the work reported. The help and advice of Kemet Ltd regarding their polishing products for aluminum was greatly appreciated. The Fanuc robot used for the project was kindly provided to the laboratory on extended loan by Zeeko Ltd, and the tool-path was implemented within the Zeeko TPG software environment. Hongyu Li acknowledges financial support from the EPSRC-funded Future Metrology Hub at the University of Huddersfield.
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