Sloan Digital Sky Survey Telescope Technical Note 19941206
The plug-plates of SDSS project are responsible for locating the optical-fiber plugs spatially and for defining the plug tilts normal to the fiber axis. The plates are 787 mm (31") in diameter and 3.2 mm (0.125") thick. Approximately 700 holes will be drilled in each plate. For drilling, the plate is held by a drilling fixture that that deforms it elastically so that its upper surface is convex. The center of the drilling region is about 10 mm higher than the edge. The hole axes are drilled vertical. In the telescope, the plate is deformed to match the surface of best focus. When this is done, the hole axes are aligned with the principal rays from the optics.
Two plates were drilled at the University of Washington Physics Instrument Shop on Wednesday, November 9, 1994. A vertical spindle machine, a Dahlih Machining Center, was used. This machine did not have enough memory to store the entire program for one plate. It was necessary to load the program for half of the holes and then load the program for the other half. The machine has a travel of 610 mm (24") in x and 460 mm (18") in y. This is not adequate to reach the entire drilling region. Consequently, 460 of 680 holes were drilled in plate100 and 453 of 680 holes were drilled in plate102.
Fig. 1. Histogram of the x location error for plate100. The histograms for the y error and for plate102 are very similar. The distribution is very nearly normal.
Plate100 took 28:00 minutes and plate102, 28:23 minutes. (There was no plate101.) This was the drilling time only and did not include the time required to load either portion of the program (about 5 minutes each portion). A machine suitable for producing the survey plates would have enough memory to store the entire program.
The drilling time was 3.65 and 3.76 seconds/hole for plate100 and plate102 respectively. The hole drilling order for plate102 was not well optimized whereas the order for plate100 was optimized using the simulated annealing travelling salesman algorithm (from Numerical Recipes, William H Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Cambridge, New York, 1994). It is likely that this accounts for the difference, 3%. However, since the drilling region was truncated as compared to the region that was optimized, the current test may not give all of the improvement that might be expected.
The drilling time is comparable to that reported in Technical Report SDSS19930430, i.e., 5.76 seconds/hole. For the current test, the CNC software was carefully optimized to maximize the fraction of time spent drilling. The time spent approaching the work-piece and clearing chips was minimized and this resulted in a decrease in the time per hole.
Scaling the number for plate102 linearly to 700 holes gives 43.9 minutes. Allowing 10 minutes for set-up and removal (from Ron Musgrave) gives a total of 54 minutes per plate. This is our best estimate of machine time required per plate.
A program in C was used to generate the CNC program from the table of hole locations and depths. The resulting program worked well with one exception. The machine hit the clamping ring during the drilling of Plate 102. This was because during rapid moves between holes, the table moves at 45 degrees (equal x and y velocities) until it reaches the desired x or y coordinate (whichever occurs first). Then it moves in the remaining axis until it reaches the hole location. The path associated with the collision was near the boundary of the drilling region and the angle was about 30 degrees CCW from the x axis. The 45 degree path segment moved the spindle far enough outside the drilling region that the collision occurred.
Fig. 2. Histogram of the hole diameter for plate100. The tail on the left side of the distribution may be due to contamination in the holes.
Fig. 3. Histogram of the hole diameter for plate102. The standard deviation of the distribution is half that for plate100.
Musgrave described the collision as gentle since a hard collision causes the machine to shut down and this did not occur. The fix is to modify the CNC program for such paths so an initial move in the direction of the largest displacement occurs followed by a 45 degree move to the desired location. A new plate102 was drilled after the CNC program was modified manually to eliminate the collision. Subsequently, the C program was modified to detect paths extending beyond the drilling region and to modify them as above. Only one such path was found on each of the two plates. The path on plate100 did not cause a collision.
The plates were drilled at 3500 rpm. A different 9.5 mm long spade drill bit was used to drill each plate. The diameter of each bit was specified to be 0.0867+0/-0.000,50" (2.202 +0/-0.001 mm). The bits were made of carbide steel by Johnson Carbide Produces, Inc., Saginaw, Mich. The drill bit holder is described in Technical Report SDSS19940412-01.
The temperature of the coolant was measured at 15 minute intervals during the drilling. For plate100, the temperature was 21.5 deg C. For plate102, the temperature was 21.0 deg C. The temperature did not change during drilling. The plates were drilled Wednesday. Plate 100 was drilled about 11:00 am. Plate 102 was drilled about 9:30 pm. The small temperature change in the 10.5 hours between the two plates and the short time necessary to drill a plate suggests that control of the plate temperature will not be a significant problem, at least for the UW Physics instrument shop, a heated and air conditioned environment. The only exterior wall faces west and contains a modest amount of glazing. The weather was as partly cloudy.
Musgrave reported light chip build-up next to the collet during the drilling of Plate 100. No such build-up occurred during the drilling of Plate 102. The drill bits were inspected with a low-power stereo microscope after use. The drill for Plate 100 has considerable aluminum/aluminum oxide contamination adjacent to both cutting edges. The drill for Plate 102 has a minor amount of aluminum/aluminum oxide contamination adjacent to one cutting edge. No wear was apparent.
Before shipping the plates to Fermi National Accelerator Laboratory (FNAL), one plate was sanded to remove burrs on the drill exit side. The plates were cleaned by immersing them in an ultrasonic bath containing water and mild detergent for several minutes. Subsequently, they were hosed off with tap water. The plates were dried with filtered compressed air.
The plug-plates were measured on December 2, 1994 at FNAL. The measurement technique is described in SDSS Technical Report 19930430 and SDSS Technical Report 19940412-01. A Giddings & Lewis-Sheffield Measurement, Inc., Apollo RS-50 coordinate measuring machine (CMM) with an accuracy specified at +/-2.5 µm (0.0001") was used for the measurements. During the measurement, the temperature of the plates was estimated to be 20 +/-1.0 deg C.
The plates held flat using suction cups to the bed of the CMM. The suction cups were distributed over theback of the plate at hole-free locations. Surrounding each suction cup was a hard plastic annulus that defined the spacing of the part from the CMM bed. The two 4.76 mm (0.1875") locating pin holes that are at a radius of 349.3 mm (13.750") and define the x-axis were used to center and orient the plate. Twenty points were measured on the top of the plate and the average of these became z = 0. The flatness across the top for both plates was 0.4 mm (0.015").
The CMM extracts hole location, diameter and non-circularity from measurements at eight points equally spaced in angle at the same value of z. Non-circularity is defined as the difference in radius between the points closest to and farthest from the center of the hole. Consequently, non-circularity is quite sensitive to contamination of the hole.These parameters were recorded at three different heights; -2.5375, -1.5875 and -0.3810 mm (-0.1000", -0.0622" and -0.0148").
The hole locations at the three heights were averaged to obtain a mean hole location, x and y. The desired hole locations (the drilling machine coordinates) were subtracted from these values to get hole location errors. The functions f(x,y) = (a1 + a3*r^2 + a5*r^4)*x + dx + b1*y and g(x,y) = (a1 + a3*r^2 + a5*r^4)*y + dy - b1*x were fit to the x and y errors respectively. The coefficient a1 includes the effect of thermal expansion between drilling and measurement and the lowest order effect of bending the plate for drilling. The coefficients a3 and a5 account for higher order effects due to the drilling fixture. The coefficients dx and dy are the offset of the plate center between drilling and measurement. The coefficient b1 is the rotation of the plate between drilling and measurement.
During operation, guide stars on 5 arc-second diameter coherent fiber-optic bundles will be used to determine the actual value of a1, dx and b1 and the telescope scale, pointing and rotator angle will be adjusted accordingly. The telescope scale is adjusted by moving the primary axially and refocussing. Consequently, errors in these coefficients may affect the initial acquisition of the guide stars, but will not affect the ability of the telescope to center the targets in the spectrograph fibers.
We should point out that the holes for the coherent fiber-optic guide bundles are the same diameter as the holes for the spectrograph fibers. In fact, they will be drilled intermingled with the spectrograph fiber holes. Consequently, we expect that the coherent fiber-optic guide bundles will share the same mean location and orientation statistics as the spectrograph fibers.
The fit coefficients are given in Table 1. The a3 and a5 coefficients cannot be determined separately for each plate during operations without measuring each plate. Since this is not envisioned, these coefficient were set using finite element model results. The a1 coefficients can be interpreted as due to a decrease of 0.7 deg C in the drilling temperature between plate100 and plate102, i.e., good agreement with the 0.5 deg C measured. The values for b1 and dy for plate102 are larger than anticipated. They may be due to a problem with drilling or measurement setup. In the worst part of the field of view, the displacement corresponding to these coefficients is 1.4 arc-seconds. Since the same locating surfaces are used to position the plate for drilling and in the telescope, it is likely that some cancellation of errors will occur.
Table 1: Hole location least-squares-fit coefficients
Plate a1 a3 a5 b1 dx dy (µm/mm) (µm/mm^3) (µm/mm^5) (rad) (µm) (µm) 100 -0.303 9.26E-06 -4.65E-11 0.016 23.2 16.2 102 -0.275 9.26E-06 -4.65E-11 0.129 23.3 36.8
Table 2 summarizes the results of the hole measurements. The histogram of Figure 1 showing the distribution of residual hole location error in x for plate100 is typical of the results in both axes and plates. The distribution is adequately described as normal. Histograms of the hole diameters are shown in Figure 2 and Figure 3. The standard deviation of hole diameter for plate102 is half that for plate100. Figure 4 shows that small hole diameters are correlated with large noncircularity. This graph (for the top level of plate100) is typical of all three levels and both plates. This is consistent with the observations of Robert Riley, who performed the measurements. He comments: "As you can see, there is some amount of variation on the roundness of the holes. Some of this is probably caused by dust or dirt in the holes. Occasionally this stuff can stick to the probe and is carried along. I tried to watch and if it seemed too bad ( > .0005 ), I stopped the machine and wiped the tip off. Often this seemed to help, but not always. Obviously with this many holes it's impossible to catch them all. In glancing at the data, it seems to me that the deviation of the hole diameter from nominal correlates with greater roundness deviation. So the smaller hole diameters may just be the result of 'stuff' in the holes."
Fig. 4. Non-circularity is plotted vs. diameter for the mid-level data for plate100. These data are typical of those for other levels and for plate102 although the range in both axes is smaller for plate102.
The radial components of the hole location at the top and bottom of the each hole in combination with the separation of the two measurements were used to calculate the tilt of each hole. The hole tilt as a function of radius is compared to the ideal tilt from the optical design (kent005) and to the finite element model of the plug-plate in its drilling fixture (drl42) is shown in Figure 5 and Figure 6.
Table 2: Summary of results
Plate Pos Error Diameter Error Non-Circ Tilt RMS mean std dev RMS RMS std dev RMS (µm) (µm) (µm) (µm) (µm) (mrad) (mrad) 100 8.7 0.8 5.7 5.7 14.1 1.6 2.6 102 8.9 2.2 3.7 4.3 10.6 1.3 2.1
A minor objective of this study was to learn a bit about how many holes could be drilled with each drill bit. The hole diameter data was divided into quartiles. The first quartile is the first quarter of the holes drilled, and so on. The diameter data for all three levels is averaged and plotted for each quartile (Figure 7). Since the diameter of a given hole is likely to be correlated along its length, the error bars are calculated by dividing the standard deviation for each quartile by the square root of the number of holes in each quartile, not by the square root of the number of measurements. These data indicate no strong trend in hole diameter, nor in the standard deviation of the hole diameter. A similar plot of non-circularity shows a decrease of non-circularity with time. However, if non-circularity is due to contamination, this tells us nothing about drill bit performance.
Fig. 5. Hole tilt is plotted as a function of radius for plate100 (open circles). The filled squares are the optimal tilts from the optical design. The filled diamonds are the tilts calculated from the finite element model.
Fig. 6. Hole tilt is plotted as a function of radius for plate102 (open circles). The other symbols have the same meaning as in Figure 5.
Fig. 7. Mean hole diameter is plotted vs. time-ordered quartiles for each plate. The error-bars are one standard deviation in the means. These data do not show a significant trend, e.g., due to drill bit wear.
The error budget that we proposed in SDSS Technical Report 19930430 allows 9 µm root-mean-square (RMS) for hole location and 8 µm RMS for plug/hole concentricity. The position error measured is consistent with our error budget although worse that that measured for the 89 mm (3.5") diameter plates. We should point out that a detailed look at the position error data indicates that considerable large scale structure (e.g., shear) remains in the data after the fits described above.
It is encouraging that the RMS diameter error is not much larger than the standard deviation of the diameter error, i.e., the mean hole diameter is very close to the nominal diameter. This was identified as a concern in SDSS Technical Report 19940412-01 where the RMS diameter error for the spade bits was 9.8 µm. Our colleagues at FNAL are working with the manufacturer to understand the factors that influence the mean hole diameter drilled by a bit.
The error budget includes 10 mrad RMS for principal ray misalignment due to errors in the deformation in the plug-plate. This item actually has two components. One is the deformation during drilling and the other is deformation in the telescope. It is pleasant to see that the measured tilt error associated with drilling deformation uses so little of the budget. Indeed, it is little more than that for hole drilling alone which was allotted 2 mrad RMS in the budget. Plug/hole alignment is allocated separately at 5 mrad RMS. This item is associated with the clearance needed for reliable plug insertion. Again, good control over hole diameter is the key to minimizing this item. However, the diameter values reported above are consistent with this number.
We are grateful to our colleagues at FNAL, Paul Mantsch, Robert Riley and Charles Mathews for their help with the measurement of the plates and their interest in and assistance with various aspects of plug-plate drilling. We thank Ron Musgrave and Dan Skow of the UW Physics Instrument Shop for their interest, expertise and enthusiasm. Siriluk Limmongkol of the UW helped with temperature measurement and took excellent photographs that we have not yet digitized.
Date created: 12/6/94 Last modified: 6/16/99 Copyright © 1994-1999, Walter A. Siegmund Walter A. Siegmund
siegmund@astro.washington.edu
