Sloan Digital Sky Survey Telescope Technical Note 19960526
The plug-plates of SDSS project are responsible for locating the optical-fiber plugs spatially and for defining the plug tilt with respect to the surface of best focus. The plates are 795 mm (31.3") in diameter and 3.2 mm (0.125") thick. Approximately 670 holes will be drilled in each plate. For drilling, the plate is held by a drilling fixture 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 parallel. 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.
Once the plug-plate is assembled and installed on the telescope, guide stars on ø8.25 arc-second coherent fiber-optic bundles plugged into the ten ø2.1666 mm (ø0.0853") guide holes, are used to determine the errors in telescope pointing, image scale and rotator angle. A low-bandwidth servo loop acts to minimize the position errors of the guide stars on the guide fiber bundles. (The telescope scale is adjusted by moving the primary axially and refocusing.) Consequently, it is important that the guide holes be drilled in the same operation and intermingled with the object holes to minimize any offset between the two hole patterns.
Two plates were drilled at Karsten Engineering. Plates ke0111 and ke0112 were drilled on May 10, 1996. A horizontal milling machine, a Dixi 420TPA, was used (Figure 1). Its travel limits were 1.40 m x 1.22 m x 1.02 m, i.e., more than adequate to reach the entire drilling region. Facing the machine and referenced to the part, the machine +x is right, +y is toward the machine, and +z is up.
The hole drilling order for both plates 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). This algorithm minimizes the total distance travelled to drill the holes assuming that the path between holes is a straight line. Actually, the travel time between each pair of holes is proportional to the greater of the x or y separation. Consequently, this would be a better optimization criterion. However, the improvement would be small since the travel time between holes is already a small part of the total. The drilling order for the light-trap holes is optimized separately from that for the object, guide and quality holes since an intervening tool change is required. (No quality holes were included on these plates since they had not been specified when the plug-plate drilling files were produced.)
A second program converts the list of hole types and coordinates into a CNC program. This program converts the coordinates to English units, compensates for the distortion of the plate between drilling and the focal plane, and adjusts for the anticipated temperature difference between drilling and use.
The drilling order was object, guide and quality holes, followed by light-trap holes, followed by the sky hole, followed by locating holes. The locating holes were drilled in the same operation as the other holes. In earlier tests, these holes were drilled in a separate setup with the plate flat prior to clamping the plate in the bending fixture and drilling the other holes. Also, the number of locating holes was changed from two to three. The locating holes consist of three ø6.35 mm (ø0.250") equally spaced on a ø731.5 mm (ø28.8") circle.
The small holes were drilled at 2500 rpm. A different spade drill bit was used to drill each plate. Each bit is specified to be ø0.0853+0/-0.000,50" (ø2.1666 +0/-0.001 mm). The bits are made of carbide by Johnson Carbide Products, Inc., Saginaw, Mich. The bits have a ø0.1250" shank. The tip extends 9.5 mm from the shank. The shank was fully inserted into the collet. In a departure from earlier tests, a standard drill bit collet was used to hold the these bits.
The temperature of the coolant was logged at 20 to 40 minute intervals during the drilling. For ke0111, the initial temperature reading was 21.8°C. Subsequent readings (eight) were 21.1 to 21.6°C. For ke0112, the initial temperature reading was 21.1°C. Subsequent readings (three) were 21.1 to 21.2°C. Plate ke0111 took 6.7 hours to drill all holes. This included time to debug the CNC program. Plate ke0112 took 2.3 hours to drill. The 650 ø2.1666 mm holes took 150 and 85 minutes on ke0111 and ke0112 respectively.
The coefficient of thermal expansion for aluminum alloy 6061 is 24.3 µm/m·°C. The drilling temperature range for ke0111 corresponds to 5.5 µm on the radius. The drilling temperature range for ke0112 corresponds to 0.8 µm on the radius. A new bit was used for each plate. Drill runout was measured prior to drilling and was 2.5 µm (0.0001") total indicated runout for both plates.
Before shipping the plates to Fermi National Accelerator Laboratory (FNAL), both surfaces of each plate were sanded with 120 grit sand paper to remove burrs and to eliminate specular reflections from the front surface. Then they were vapor degreased and sprayed with clean solvent. Robert Riley (FNAL) reports as follows on the quality of the plates.
"Plate ke0112 appeared to be very clean. Plate ke0111 was not as clean. I checked some of the holes that had bad form on plate ke0111 and found what appeared to be aluminum powder in these holes. I could not find any of this on plate ke0112."
The plug-plates were measured on May 23 and 24, 1996 at FNAL. 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. The CMM was checked by Giddings & Lewis technicians on April 11, 1996 and found to be within calibration.
The plates were measured flat on the CMM. The x and y coordinates were set using the locating holes. The z coordinate was measured relative to a plane fit to 19 evenly-spaced measurements of the upper surface of each plate (Table 1). Since the maximum hole tilt is about 30 mrad at a radius of 230 mm, the maximum hole location measurement error due to the lack of flatness of the plates is less than 8 µm or 0.13 arcseconds (the image scale is 60 µm/arcsecond). This would correspond to about 3 µm root-mean-square (RMS), i.e., negligible when added in quadrature to other errors.
Table 1: Departure of upper surface from a best-fit plane. Plate ke0111 ke0112 (µm) (µm) Points 19 19 Minimum -264.2 -111.8 Maximum 119.4 76.2 Mean 0.3 -0.3 Std Deviation 104.6 43.8
The temperature of each plate was monitored during measurement by taping a thermocouple probe to the plate. The temperature was measured with an Omega 872A digital thermometer with a thermocouple. Thermally conductive grease was used to couple the thermocouple to the plate.
The coefficient of thermal expansion for aluminum alloy 6061 is 24.3 µm/m·°C. The measurement temperature range for ke0111 corresponds to 1.3 µm on the radius. The measurement temperature range for ke0111 corresponds to 4.4 µm on the radius. Temperature effects corresponding to the variation of temperature during drilling and measurement were not detected in the data. It is likely that such effects were present but overwhelmed by other effects (see below).
As a CMM stability check, hole #1 was remeasured after all the other holes were measured. Its location repeated to 5 µm or better in each axis on both plates.
Each plate took about 70 minutes to measure. The CMM extracts hole location, diameter and non-circularity from measurements at eight points equally spaced in angle at the same value of z. Since the hole diameters determined in this manner are not consistent with diameters determined using plug gauges, the hole diameter and non-circularity measurements were not used.
The locations, x and y, of each hole, were measured at the z = -0.0625 (middle of plate). The desired hole locations (the drilling machine coordinates) were subtracted from these values to get hole location errors.
During operation, guide stars on ø8.25 arc-second coherent fiber-optic bundles will be used to determine the values of a1, b1, dx and dy and the telescope scale, pointing and rotator angle will be adjusted accordingly. The errors in these coefficients, as long as they are small enough that the guide stars can be acquired, do not affect the ability of the telescope to center the targets in the object fibers. Only the residual errors, after these effects are removed, are important.
To remove these effects, the functions f(x) = dx + b1*y + (a1 + a3*r^2 + a5*r^4)*x and g(x) = dy - b1*x + (a1 + a3*r^2 + a5*r^4)*y were fit to the x and y errors respectively of the object, guide and quality holes. 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 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.
The coefficients a3 and a5 account for higher order effects due to the drilling fixture. Unlike the other coefficients, these cannot be determined separately for each plate during operation of the telescope without measuring each plate. Since this is not envisioned, these coefficients were set to the mean of the coefficients found separately from least squares solutions for uw0111 and uw0112, the two University of Washington plates (a3 = 1.46E-05 µm/mm^3, and a5 = -8.29E-11 µm/mm^5). Once the coefficients were determined, the residual errors in x and y were calculated (Table 2).
Table 2: Hole location fit. Plate a1 dx RMS dy RMS (µm/mm) (µm) (µm) ke0111 -0.131 7.2 11.6 ke0112 -0.104 6.7 11.0
The locating holes are used to position the plate within the cartridge and, ultimately, with respect to the focal surface. Consequently, their errors affect the open-loop acquisition of the desired field of galaxies. The statistics of their locations were reduced to the same coordinate system as the object, guide and quality holes (Table 3). The holes will be engaged by floating locating pins that float radially but constrain the plate in the tangential direction. Consequently, the mean radial error is irrelevant and is not tabulated. The tangential error is the hole location error in the tangential direction, i.e., perpendicular to the radial error. The plate center and rotation offsets correspond to less than 0.5 arc seconds (the scale is 60 µm/arc second). As expected, this is considerably better than was found in the earlier tests.
Table 3: Locating holes. Plate ke0111 ke0112 (µm) (µm) Points 3 3 Mean x -1.0 11.7 Mean y 11.6 -23.4 Mean t -0.2 -1.5 Std Deviation r 7.8 30.8 Std Deviation t 13.9 14.9
The light-trap holes are drilled at the locations of bright stars to prevent light scattering off the plate from contaminating the spectra of targets. They are non-precision holes. However, they represent an opportunity to understand how a tool change and a different drill bit affect position accuracy. Their locations were reduced to the same coordinate system as the object, guide and quality holes (Table 4). The standard deviations of the hole locations are worse than for the object, guide and quality holes. This is as expected since the precision spade drill bits used for the object, guide and quality holes are much more expensive than the standard high-speed steel twist drill bits used for the light-trap holes. Hole diameter is expected to be better for the precision spade drill bits, too. The offset in the mean of y is interesting and will be discussed below.
Table 4: Light-trap holes. Plate ke0111 ke0112 (µm) (µm) Points 15 23 Mean x -2.7 12.7 Mean y -19.0 -15.9 Std Deviation x 11.9 14.9 Std Deviation y 16.8 14.2
Figure 2: Hole location error in y is plotted v. drilling order. Standard deviations after trend removal are given.
Figure 2:
Hole location error in y is plotted v. drilling order. Standard deviations after trend removal are given.
Figure 3a: Hole drilling order for plate ke0111. Holes are drilled in a serpentine spiral pattern as shown both in stereo and color. Plate axis +x is right, plate axis +y is up and hole number increases out of the page. White is color of the first holes drilled, followed by red, yellow, green, cyan, blue and purple, the last holes drilled.
Figure 3a:
Hole drilling order for plate ke0111. Holes are drilled in a serpentine spiral pattern as shown both in stereo and color. Plate axis +x is right, plate axis +y is up and hole number increases out of the page. White is color of the first holes drilled, followed by red, yellow, green, cyan, blue and purple, the last holes drilled.
Figure 3b: Stereo pair showing hole location errors dx (stereo z) and dy (color) v. position on plate ke0111. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
Figure 3b:
Stereo pair showing hole location errors dx (stereo z) and dy (color) v. position on plate ke0111. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
Figure 3c: Stereo pair showing hole location errors dy (stereo z) and dx (color) v. position on plate ke0111. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
Figure 3c:
Stereo pair showing hole location errors dy (stereo z) and dx (color) v. position on plate ke0111. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
Figure 4a: Hole drilling order for plate ke0112. Holes are drilled in a serpentine spiral pattern as shown both in stereo and color. Plate axis +x is right, plate axis +y is up and hole number increases out of the page. White is the color of the first holes drilled, followed by red, yellow, green, cyan, blue and purple, the last holes drilled.
Figure 4a:
Hole drilling order for plate ke0112. Holes are drilled in a serpentine spiral pattern as shown both in stereo and color. Plate axis +x is right, plate axis +y is up and hole number increases out of the page. White is the color of the first holes drilled, followed by red, yellow, green, cyan, blue and purple, the last holes drilled.
Figure 4b: Stereo pair showing hole location errors dx (stereo z) and dy (color) v. position on plate ke0112. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
Figure 4b:
Stereo pair showing hole location errors dx (stereo z) and dy (color) v. position on plate ke0112. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
Figure 4c: Stereo pair showing hole location errors dy (stereo z) and dx (color) v. position on plate ke0112. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
Figure 4c:
Stereo pair showing hole location errors dy (stereo z) and dx (color) v. position on plate ke0112. Plate axis +x is right, plate axis +y is up and +z is out of the page. White is the most negative, followed by red, yellow, green, cyan, blue and purple, the most positive.
The residual errors in x are dominated by a positive trend with hole number (Figure 2). The spiral serpentine travelling-salesman-optimized drilling order is apparent in Figure 3c and Figure 4c because of this trend. No correlation is seen when plotted against x, y, r or theta. The trend is also seen as an offset in the mean x of the light-trap hole data (Table 4) that were drilled after the object, guide and quality holes. With a linear trend in hole number removed, the residual error in x is 6.2 and 6.5 µm RMS for ke0111 and ke0112 respectively. The residual errors in y do not show this correlation (Figure 3b and Figure 4b).
No higher order correlations of the residual error in r with r are apparent. This indicates that the model of plate distortion on the drilling fixture is adequate.
The errors in both x and y are highly correlated between pairs of holes adjacent in the drilling sequence. The standard deviation of the differences of the residual errors of adjacent holes is 4 µm or less for each axis for ke0111 and less than 4 µm for each axis for ke0112. These numbers represent the small-scale (20 mm) repositioning error of the machine and drill bit wander.
The holes in ke0111 and ke0112 were gauged with pin gauges (Table 5) on May 23, 1996. Each hole was assigned the diameter of the largest gauge that could be inserted in the hole. All holes were larger than the smallest pin gauge (2.167 mm). For ke0111, the mean was 2.172 mm (0.08549"). For ke0112, the mean was 2.170 mm (0.08545"). The project goal for hole diameter is 2.167 +0.010 -0.000 mm.
Table 5: Pin gauges. Diameter(mm) Diameter(inches) 2.167 0.0853 2.169 0.0854 2.172 0.0855 2.174 0.0856
Figure 5: Hole size distribution for plate ke0111. If the fit of the largest pin gauge was judged loose, it was assigned to the right-most bin.
Figure 5:
Hole size distribution for plate ke0111. If the fit of the largest pin gauge was judged loose, it was assigned to the right-most bin.
Figure 6: Hole size distribution for plate ke0112. If the fit of the largest pin gauge was judged loose, it was assigned to the right-most bin.
Figure 6:
Hole size distribution for plate ke0112. If the fit of the largest pin gauge was judged loose, it was assigned to the right-most bin.
The large-scale feature seen in the residual error hole location errors from earlier tests ("19941206 Full-scale Plug-plate Drilling Tests I", "19950130 Full-scale Plug-plate Drilling Tests II" and "Full-scale Plug-plate Drilling Tests III") is no longer present. Subsequent to writing those reports, interference between the locating pins and their holes was suspected of introducing strain into the plates during the drilling operation. When this strain was relaxed after drilling, the hole location errors due to the strain were apparent. To avoid this perceived problem (and to simplify plate fabrication), the locating pins were removed from the drilling fixtures and three locating holes were drilled as part of the object hole drilling process. The current data indicate that this modification was successful.
Residual error hole location errors are dominated by a linear trend in hole number of the residual error in y. The error budget that we proposed in SDSS Technical Note 19930430 allows 9 µm root-mean-square (RMS). The 2-d position errors measured, 13.6 and 12.9 µm RMS for ke0111 and ke0112 respectively, are not consistent with this error budget. However, if the linear trend in hole number of the residual error in y were corrected or compensated, the results would be very nearly consistent with the budgeted amount, i.e., 9.5 and 9.4 µm RMS for ke0111 and ke0112 respectively.
The linear trend in hole number of the residual error in y may be due to a temperature increase of some portion of the machine. In a milling machine made by another manufacturer, friction in spindle bearings has been observed to cause a 4°C temperature rise in the housing supporting the spindle from the vertical ways (Holes, Contours and Surfaces: Located, Machined, Ground and Inspected by Precision Methods, Richard F. Moore and Fredrick C. Victory, Bridgeport, CT, 1955). A similar effect was seen in the data for uw0111 and uw0112 drilled at the University of Washington.
The same reference describes the use of a resistive heater located near the spindle that is turned on when the spindle is off. The resistance of the heater is chosen so that the power input into the spindle housing is constant whether the spindle is off or on. The authors report that this design results in no discernible movement of the spindle axis during down-time.
We are grateful to our colleagues at FNAL, Paul Mantsch, Robert Riley, Barb Sizemore 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. It is a pleasure to thank John Russell and Meridith Gower of the Karsten Engineering for their help and advice on the plate drilling process. Finally, we thank Charlie Hull, Siriluk Limmongkol, Ed Mannery, Jeff Morgan, and Pat Waddell for their interest and comments.
Date created: 5/27/96 Last modified: 3/27/97 Copyright © 1996, 1997 Walter A. Siegmund Walter A. Siegmund
