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A new and patented polishing tool called Orthogonal Velocity field Tool (OVT) was built and its material removal characteristics from Chemical Vapor Deposition Silicon Carbide (CVD SiC) mirror surfaces were investigated in this study. The velocity field of OVT is produced by rotating the bicycle type tool in the two orthogonal axes, and this concept is capable of producing a material removal foot print of pseudo Gaussian shapes. First for the OVT characterization, we derived a theoretical material removal model using distributions of pressure exerted onto the workpiece surface, relative speed between the tool and workpiece surface, and dwell time inside the tool- workpiece contact area. Second, using two flat CVD SiC mirrors that are 150 mm in diameter, we ran material removal experiments over machine run parameter ranging from 12.901 to 25.867 psi in pressure, from 0.086 m/sec to 0.147 m/sec tool in the relative speed, and 5 to 15 sec in dwell time. Material removal coefficients are obtained by using the in-house developed data analysis program. The resulting material removal coefficient varies from 3.35 to 9.46 um/psi hour m/sec with a mean value of 5.90 ± 1.26(standard deviation). We describe the technical details of the new OVT machine, the data analysis program, the experiments, and the results together with the implications to the future development of the machine.
© 2016 Optical Society of America
1. Introduction
Traditionally, precision optical polishing and figuring have been regarded as a `black art’ rather than a quantitatively controllable engineering process. However, over the last few decades, a number of new optical fabrication techniques have been developed and they bring some degree of controllability to the large optics fabrication process. Examples include, but are not limited to, computer controlled optical surfacing from ITEK [1,2], stressed-lap polishing from University of Arizona [3], active lap polishing from University College London [4], the ion figuring method from Kodak [5], magnetorheological finishing (MRF) from QED [6], and the intelligent robotic polisher (IRP) from Zeeko [7,8].
Typically, these techniques attempt to bring high repeatability to material removal characteristics from the workpiece surface by controlling an array of polishing parameters including polishing pressure, tool-surface contact speed, tool path, and dwell time optimized for given material removal methods. Clear improvement in fabrication process efficiency has been achieved for a number of small, medium, and large precision optical surfaces. With this technical evolution, we are now stepping toward the ultimate goal of a ‘deterministic process’ applicable to the optical fabrication shop floor. However, the optimum control of such parameters depends critically on workpiece material characteristics and defined surface specifications, and each optics fabrication shop uses its own know-how and techniques that are normally blocked from community access under commercial confidentiality.
In the meantime, SiC is a relatively new material for precision optical surfaces. Because of its excellent material characteristics, it has been a preferred choice for light weight mirror surfaces for space optical instruments. A notable example is the primary mirror segment for the Herschel telescope [9]. Techniques used for fabricating SiC mirror surfaces may include 1) use of Si cladding on top of the SiC mirror substrate [10], 2) computer-controlled polishing (CCP) together with ion beam figuring (IBF) utilizing a polishing database [11], 3) advanced flow polishing [12,13], and 4) diamond turning followed by traditional polishing performed by an optician [14]. With such techniques used today, small and medium size SiC mirrors are readily available in the market, although meter class SiC mirrors have not reached the mass production stage. Nevertheless, the material removal characteristics of the SiC mirror surface under a wide range of polishing and figuring variables are still poorly understood and have never been reported clearly to the optics fabrication community in sufficient detail.
Regarding the material removal characteristics of the polishing tool from the workpiece surface, circularly non-symmetric foot prints have been reported by previous studies [15–17]. One example is called Ultra-Form Finishing (UFF) process where a tool rotating about an axis is in contact with a spinning workpiece that rotates about an axis perpendicular to the tool rotation axis. In this configuration, the tool rotation axis is parallel to the workpiece surface. When the workpiece is stationary, the rotating tool tends to generate circularly non-symmetric material removal footprints. When the workpiece rotates, such a tool tends to generate a circularly symmetric footprint at the center of the workpiece surface and a donut-shaped groove pattern of the material removal footprint is produced at other locations on the workpiece surface. The existence of such different footprints on the same work piece surface tends to produce a slower convergence of the tool path optimization in the actual polishing run.
In order to overcome the aforementioned shortcomings, we developed a new patented polishing tool called the Orthogonal Velocity field Tool (OVT) [18,19]. As mentioned in Section 2.1, OVT produces tool rotations at about two independent axes simultaneously. This is in contrast to other existing techniques [15–17]. The OVT is also capable of producing a pseudo Gaussian foot print of the material removal from the workpiece by either rotating or non-rotating ways.
The development of the OVT [18,19] and initial experiment results were introduced to the community elsewhere in an earlier study without a detailed description of the technical and theoretical elements [19]. We address this shortcoming with a detailed description of the theoretical model of the OVT and experiments conducted in the study. Section 2 deals with the OVT polishing machine, followed by theoretical model of the OVT polishing run described in Section 3. Section 4 shows details of the experiment and the data analysis, after that Section 5 presents the measurement results and an interpretation of the results. The issue of removal coefficients is discussed in Section 6 before concluding remarks in Section 7.
2. Polishing and figuring with OVT
2.1 Concept
As shown in Fig. 1 [19], OVT uses a patented concept of a bicycle type rotating tool rubbing the workpiece surface. The tool is configured such that it rotates about two orthogonal axes (e.g. azimuth axis and radial axis) simultaneously by means of two independent motors. The tool radial rotation generates a map of the tool velocity field for one direction and the tool azimuth rotation is again used to rotate the above mentioned directional velocity field in the other direction. This simultaneous operation results in a combined speed map that is randomized and circularly symmetric when viewed from above the workpiece surface. When the tool is in contact with the workpiece surface together with an abrasive slurry, it removes the workpiece material mostly by radial rotation. The azimuth tool rotation also serves as a means to rotate the footprint so that the resulting material removal shape is pseudo Gaussian. To such extent that the rotation produces circularly symmetric pseudo Gaussian TIF while other existing methods [15–17] produce circularly non-symmetric TIF, the OVT method is in striking contrast to the other methods such as UFF process.
The OVT wheel can be made with polishing cloths of various materials attached to a wheel substrate made of polyurethane, PVT or alternatively an inflatable rubber bag. The OVT is capable of using an array of different wheel shapes. Examples include a flat disk, elliptical oval, and spherical shapes. It is mounted to a spindle that carries it to and from the workpiece surface. For a typical configuration where the workpiece sits on top of a rotating table in the XY plane, the spindle moves the OVT up and down in the Z axis. Alternatively, the OVT can be mounted to a Z axis spindle with an interface capable of moving the OVT to two angular directions. In this case, the machine configuration becomes similar to the OVT mounted to a 5 axis CNC machine base.
2.2 Polishing machine with OVT
As shown in Fig. 2, an in-house developed polishing machine was constructed for a SiC polishing experiment using the OVT. A fixed Z axis spindle holds the OVT oriented down to the workpiece holding table. The OVT can be moved up ( + Z) and down (-Z) by manually turning the top handle and its location in the XY plane is fixed. Once it is at the desired location, its vertical position can be locked by operating a locking handle. One load cell is installed inside the OVT frame and the second load cell just underneath the table. By reading the force level from the load cell electronics, one can determine when the wheel is in touch with the workpiece. If higher polishing pressure is required, the OVT position with respect to the table can be lowered further until the load cell reading has reached the desired level. The machine is also equipped with a slurry feeding sub-system so that the polishing slurry can be supplied at a constant rate during machine run. The machine characteristics are summarized in Table 1 [19].
Table 1. Polishing machine characteristics
3. Theory of material removal using the OVT
3.1 Material removal equation
Material removal from a specific location on the workpiece can be expressed by the well-known relationship called the Preston’s equation [20], given as Eq. (1).
Here Δz is the depth of the material removal, κ the material removal coefficient, P the polishing pressure exerted onto the workpiece, V the relative speed between the tool and workpiece surface, and ΔT the dwell time for which the tool surface is in touch with the workpiece surface at a specific location.3.2 Pressure distribution
In order to understand the pressure exerted unto the workpiece by the OVT, the OVT wheel with a cerium oxide polishing pad was pressed onto the workpiece over a force range from 0.05 kgf to 0.13 kgf at an incremental force step of 0.02 kgf. Then, at each force level, the tool and workpiece contact area was measured. The average pressure was subsequently obtained from the exerted force reading divided by the tool-workpiece contact area, which has the shape of an ellipse. Figure 3 [19] shows the resulting relationship between the polishing pressure and the exerted force, and the least square linear fitting produced Eq. (2) [19] as its mathematical expression.
When pressed against the workpiece, the tool and workpiece surface contact area appears as an ellipse. This is because the “bicycle type” wheel has a larger radius of curvature in one direction, e.g. the X axis, and a smaller radius of curvature in the other direction, e.g. the Y direction. Figure 4 shows that the semi major and semi minor axis of the ellipse increase with the polishing pressure (i.e. exerted force), and they can be expressed as Eqs. (3) and (4). When the tool gives pressure to the workpiece surface, the instantaneous pressure distribution inside the tool-workpiece contact area can be defined as Eq. (5) [19] using the modified form of a bivariate normal Gaussian distribution. Here P(x,y) is the pressure exerted to the workpiece surface, a the semi major axis of the tool-workpiece contact area, e.g. an ellipse, b the semi minor axis, c a coefficient influencing the maximum pressure value, and σx, σy define the width of the Gaussian distribution along the axis. Figure 5 [19] is an example of a pressure distribution computed using Eq. (5). The derivation of Eq. (5) is described in Seo et al (2015) [19].
Fig. 5 Example of pressure distribution inside the tool-workpiece contact area, i.e. ellipse; 3D (a) and 2D color contour map (b).
We next integrate the aforementioned instantaneous pressure distribution over the time period for which the tool-workpiece contact area (i.e. ellipse) rotates along the azimuth angle. Equation (6) below expresses the integrated pressure distribution over the time period t. Here ωa is the angular speed in the azimuth direction. Figure 6 shows the integrated pressure distribution over the time period t. Note that the pressure map in Fig. 6 is no longer an ellipse but rather it looks circular.
Fig. 6 Integrated pressure map over time period t. (a) t = 0.2 sec (b) t = 0.4 sec (c) t = 0.6 sec (d) t = 0.84 sec.
3.3 Velocity field
Figure 7 shows a schematic diagram of two velocity fields generated from operating the OVT wheel. Here vector Va is generated from the tool azimuth rotation and Vw from the tool radial rotation. The instantaneous tool speed experienced by the (X,Y) coordinate on the workpiece surface at any given time t can be written as Eq. (7) below. Here wa and wb are the angular speed along the azimuth angle and radial angle, respectively. Integrating this over the time period t for which the machine run takes place gives the total accumulation of the velocity field map expressed in Eq. (8). An example of a computed integrated velocity field is presented in Fig. 8.
Fig. 8 Integrated velocity map over time period t. (a) t = 0.2 sec (b) t = 0.4 sec (c) t = 0.6 sec (d) t = 0.84 sec.
3.4 Dwell time
The tool dwell time on the workpiece surface can be derived using the schematic diagram presented in Fig. 9. Here, a black ellipse is the contact area between the tool and workpiece surface. “a” and “b” are the semi-major and minor axes. “r” is the distance from the center of the contact area and θ is the angle between r and a. One can imagine that when the OVT runs in polishing, the tool-workpiece contact area (i.e., black ellipse) rotates following the tool azimuth rotation. The blue dotted circle is then a circle with the radius r and it forms a subset of the resulting tool-workpiece contact area that is circularly symmetric. The red dashed arc represents the instantaneous tool-work piece contact length of 4rθ at r.
Fig. 9 Instantaneous tool – Workpiece contact area (i.e., black ellipse) and resulting instantaneous contact length (i.e., red arcs) at r. The red arc tends to form a blue dotted circle when a full rotation is made.
Figure 10 is a graphical representation of Eq. (9), which is the equation of an ellipse in a polar coordinate (r, θ). For the tool azimuth rotation speed of 36 rpm, the dwell time at r inside the tool-work piece contact area can be defined as Eq. (10). Here, 4rθ/2πr is the ratio of the instantaneous tool-workpiece contact length (red dashed arc) to the length of the blue dotted circle. The dwell time of the tool per each azimuth tool rotation at r can then be obtained by the ratio multiplied by 60/36. Figure 11 is the resulting dwell time map for one tool azimuth rotation.
3.5 Verification of theoretical material removal
Using the aforementioned equations substituted to Preston’s equation, the material removal footprint (hereafter the tool influence function TIF) was computed for a wheel rotation speed of 17 rpm, a polishing pressure of 15.65 psi, and a machine operating time of 5 seconds, and we then made a trial machine run on CVD SiC. Figure 12 shows that the theoretically predicted TIF agrees well with the experimental material removal footprint for the given set of machine run parameters.
4. SiC TIF generation experiment
4.1 SiC sample preparation
Two samples of 150 mm diameter were prepared with a flat surface with an Oscar type traditional polishing machine and a laser interferometer for this phase. First, CVD SiC of about 70 μm was added to the top of the reaction bonded (RB) SiC surface. The flat surface used in the experiment was then polished and figured to 0.254 μm and 0.356 μm in pv form accuracy, respectively. The rms form accuracy was 0.039 μm and 0.043 μm, respectively. Once completed, the sample was then installed onto the workpiece table of the OVT polishing machine firmly with a number of mechanical brackets. The OVT was then lowered to be in contact with the workpiece at a desirable force (i.e. pressure) level. Once the target force level was achieved, the slurry feeding system was turned on and the sample surface was made wet with the slurry. The OVT was turned on to generate two orthogonal velocity fields lasting for the set time duration, while it stays at the fixed location in XYZ coordinates.
4.2 SiC TIF generation machine run and measurement
A TIF generation machine run was performed following the parameter ranges listed in Table 2 [19]. Other parameters that were fixed for the experiment are summarized in Table 3 [19]. According to Table 2, the combination of force, machine run time, and wheel speed provides 27 TIF generation cases in total. For each case, the machine run was performed 5 times and the sample surface was measured using an Aspheric Stitching Interferometer (ASI) from QED. The final sample surface form that has TIFs generated was obtained by averaging the surface measurement data from 10 independent ASI measurements.
Table 2. Parameter ranges for TIF generation experiment
Table 3. Fixed parameters for TIF generation experiment
4.3 Data processing
In-house developed data processing software was used to extract TIFs from the measured surface form data. First, the surface form data obtained from ASI were converted so that they can be processed in the SAGUARO [21,22] environment developed and publically released by University of Arizona. Second, once converted, the surface data from multiple measurements for each machine run case were aligned using fiducial points and averaged to produce a single surface form data representing the machine run case. In this way, two surface form data were produced for each machine run; one is “surface before the machine run” and the other is “surface after the machine run”. Third, once again, these “before” and “after” surfaces were aligned and then subtracted from each other to product the final surface data from which the TIF was extracted. Fourth, a surface area containing the TIF that is to be extracted was then selected, and the TIF was then obtained by removing the piston, tip/tilt, and power from the selected area.
As an example of data processing, Fig. 13 below shows the aforementioned fourth step. The surface form data (a) contain a number of TIFs. An area is selected as in (b) that includes the surface data surrounding the TIF. Using Zernike polynomial fitting to the surrounding area, piston, tip/tilt and power terms can be removed as shown in (d) and the final TIF was extracted as in (e).
5. Resulting TIFs
The detailed characteristics of resulting SiC TIFs are listed in Table 4 and 5 from Appendix 1 and some interesting features from the resulting TIF data are shown in Fig. 14. Some TIF examples are shown in Fig. 16, Fig. 17 and Fig. 18 from Appendix 2. The maximum TIF depth from the experiment is drawn in (a) [19] and its theoretical prediction appears in (b). We note that they agree with each other very well and their differences fall within +/− 1 nm in height, as in (c). In the meantime, the material removal coefficient from the experiment is shown in (d) [19] and from the theoretical model (e). Mean values of the removal coefficient are 5.90 ± 1.26 (standard deviation) for the experiment and 5.82 ± 1.23 (standard deviation) for the theoretical model. The differences in the material removal coefficient between (d) and (e) are presented in (f) and they are extremely low.
Fig. 14 Experimental maximum TIF depth (a), theoretical maximum TIF depth (b), Difference in maximum TIF depth (c), Experimental material removal coefficient (d), Theoretical material removal coefficient corresponding to the experiment conditions (e), Difference in material removal coefficient (f)
Such results, as appeared in Fig. 14, Table 4, Table 5, Fig. 16, Fig. 17 and in Fig. 18, confirm a high repeatability reaching 89.7% on average for the material removal depth and 85.6% on average for the material removal coefficient, when we repeat the TIF generation run with the experiment parameters fixed. The average difference between the theoretical prediction and the experiment is 0.68% for maximum TIF depth and 1.78% for the material removal coefficient.
6. Discussion
During the experiment and data processing, we noted that the determined material removal coefficient can vary depending on the method used. Two methods can be used to determine the material removal coefficient. First, it can be derived from the total material removal depth at the TIF center. The data presented in Appendix 1 and 2 are produced from this method. However, alternatively, the coefficient can be estimated by using the total volume of a TIF. Figure 15 shows the difference between the two removal coefficients. The red broken line represents the theoretical prediction that the material removal coefficient should have a linear relationship between depth based and volume based methods. However, it is noted that the blue solid line from the experiment deviates sharply from the theoretical prediction for the low removal coefficient range.
This difference might indicate that the material removal does not take place in a uniform manner inside the tool-workpiece contact area. When we consider the tool-workpiece contact area (i.e. ellipse) rotating about the TIF center axis, it is clear that the central part of the contact area on the workpiece surface is in contact with the tool surface all the time. The peripheral part of the contact area produces intermittent contact between the tool and workpiece surfaces. This leads to two separate areas even within the single TIF; one area that is rubbed continuously and another area rubbed that is intermittently. This may cause two different material removal characteristics even within a single TIF. Alternatively, the difference in the removal coefficient shown in Fig. 15 could be caused by the discrepancy in the polishing pressure distribution between the theoretical model and the actual tool. We also note that such a discrepancy is entirely plausible, especially when the polishing force used is light compared to larger forces. When a spherical surface is compressed, the shape can change depending on the force and material displacement. Nevertheless, at the time of this writing, we acknowledge that the causes of this difference are an interesting avenue to explore further in a separate study.
7. Conclusion
We built a new and patented polishing and figuring tool called “orthogonal velocity field tool (OVT)” that we introduce to the optics fabrication field. The bicycle wheel type tool rotates about two orthogonal axes simultaneously with respect to the workpiece center axis and generates the pseudo Gaussian TIF. This method of generating a pseudo Gaussian TIF is markedly different from the existing methods such as precession tool motion from the IRP polishing tool from Zeeko. We then installed it onto a simple polishing machine with a customized slurry feed subsystem. The machine and the tool OVT were then used to study the material removal characteristics from a CVD SiC mirror surface. A total of 27 TIFs were produced while three polishing parameters were changed. The resulting TIFs show very high repeatability up to about almost 90% and there was good agreement between the theoretical TIF model and experiment results.
From the obtained results we conclude that 1) OVT is a good candidate for the ultimate goal of deterministic polishing and figuring, to which the world optics fabrication technology is evolving, 2) OVT can be used to polish and figure a CVD SiC mirror surface, and 3) our study provides the optics fabrication community with useful material removal characteristics of CVD SiC.
While studying the cause of the difference in the material removal coefficients between two analysis methods from TIF depth and TIF volume, we discovered that the effects from continuous and intermittent tool workpiece surface contact may play an important role in producing non-uniform material removal characteristics inside a single TIF. These characteristics are an interesting avenue for further study that will be presented in a separate paper where appropriate.
Appendix 1 Characteristics of SiC TIFs using OVT
Table 4. Maximum material removal depth of each TIF
Table 5. Material removal rate (removal coefficient) of each TIF
Appendix 2 Representative figures of SiC TIF using OVT
Fig. 16 2D profile (a) and 3D shape (b) of TIF for case 1 that each input parameter is minimum value.
Fig. 17 2D profile (a) and 3D shape (b) of TIF for case 14 that each input parameter is intermediate value.
Acknowledgments
This study is supported by the Development of All-SiC Reflected Optical System Project, and, in part, through the CGER SRC program from the NRF research program. We thank Dr. Dae Wook Kim for informative discussions.
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