Sloan Digital Sky Survey Telescope Technical Note 19960408
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 the University of Washington Physics Instrument Shop by Larry Stark, Instrument Maker. The current version of the plug-plate drilling drawing is available in .dxf format. Plate uw0111 was drilled on April 5 and plate uw0112 was drilled on April 7, 1996. A vertical milling machine, a Dahlih MCV-2100, was used (Figure 1). Its travel limits are 2100 mm (82.67") in x, 850 mm (33.5") in y, and 760 mm (29.9") in z. This was more than adequate to reach the entire drilling region. However, the plate was rotated to prevent interference of the tooling support plate with the vertical machine way. This had the effect of making the plate +x axis the machine -y, and the plate +y axis the machine +x. Facing the machine and referenced to the part, the machine +x is right, +y is toward the machine, and +z is up.
Figure 1: The plug-plate is clamped in drilling fixture mounted on the Dahlih vertical milling machine. Larry Stark, Instrument Maker, verifies the computer numerically controlled (CNC) program used to control the machine.
Figure 1:
The plug-plate is clamped in drilling fixture mounted on the Dahlih vertical milling machine. Larry Stark, Instrument Maker, verifies the computer numerically controlled (CNC) program used to control the machine.
Plate uw0111 took 105 minutes and plate uw0112, 60 minutes. The time difference reflects the increased confidence in the computer numerically controlled (CNC) program used to control the milling machine. This did not include the time required to set up the plate for drilling. In production, Larry Stark estimates that 20 minutes will be required between plates.
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. Since the travel time between holes is proportional to the greater of the x or y separation, 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 drill 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 3000 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 measured at ~20 minute intervals during the drilling. For uw0111, the initial temperature reading was 19.5°C. Subsequent readings (four) were 18.5°C. For uw0112, the initial temperature reading was 21.0°C. Subsequent readings (three) were 20.5°C.
The coefficient of thermal expansion for aluminum alloy 6061 is 24.3 µm/m·°C. The drilling temperature range for uw0111 corresponds to 7.9 µm on the radius. The drilling temperature range for uw0112 corresponds to 4.0 µm on the radius. These systematic effects were too small to be apparent in the plate measurements.
A new bit was used for each plate. Drill runout was measured prior to drilling and was 6.4 µm (0.000250") total indicated runout for uw0111 and was less than 1.3 µm (0.000050") for uw0112.
Before shipping the plates to Fermi National Accelerator Laboratory (FNAL), the rear surface of each plate was sanded with 400 grit sand paper to remove burrs. Then they were vapor degreased and flushed with clean solvent (ASKO, Seattle, WA). Robert Riley (FNAL) reports as follows on the shipping package and the quality of the plates. The burrs on the ø0.250" holes were due to a minor error in the CNC program, i.e., the boring tool went too deep.
"The plates were wrapped in paper, then bubble wrap, and then 2 large sheets of flexible cardboard. The plates were deburred on the bottom side. The holes .250 and larger were chamfered on both sides. The chamfer on the top side of the .250 holes on plate uw0111 has a large burr. The parts were very clean with no apparent dirt left in the holes. The holes that show a bad form did seem to have a little burr inside. For example: On holes 487 & 498 I lightly tried a .085 pin gage which would not go through. I then tried a .084 which with a little wiggling went through. I went back to the .085 pin and it easily went through, so there appears to be a little burr in the middle of the hole somewhere."
The plug-plates were measured on April 19, 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 5 µm or 0.08 arcseconds (the image scale is 60 µm/arcsecond). This would correspond to about 2 µm root-mean-square (RMS). This is negligible when added in quadrature to other sources.
Table 1: Departure of upper surface from a best-fit plane.
Plate uw0111 uw0112 (µm) (µm) Points 19 19 Minimum -109.2 -86.4 Maximum 157.5 114.3 Mean -0.3 0.1 Std Deviation 69.0 55.1
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.
The coefficient of thermal expansion for aluminum alloy 6061 is 24.3 µm/m·°C. The measurement temperature range for uw0111 corresponds to 1.8 µm on the radius. The measurement temperature range for uw0111 corresponds to 4.8 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 another systematic effect (see below).
Each plate took about 70 minutes to measure. Light-trap hole 663 on uw0111 and 658 on uw0112 were not drilled because they were very close to the clamping ring and a suitable tool-holder was not available. The diameters of holes uw0111/665 and uw0112/673 were given incorrectly in the CNC input files.
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 have been shown to be inconsistent 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 the two 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) uw0111 0.074 8.4 4.5 uw0112 0.052 10.6 5.3
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 radial error is irrelevant and is not tabulated although the radial standard deviation is tabulated. 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 uw0111 uw0112 (µm) (µm) Points 3 3 Mean x 28.3 21.5 Mean y -2.5 -3.4 Mean t 8.9 22.7 Std Deviation r 26.4 17.2 Std Deviation t 23.4 20.4
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 somewhat worse than for the object, guide and quality holes. This is reasonable 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. Of course, location is not the only important parameter. Hole diameter is expected to be better for the precision spade drill bits, too. The offset in the mean of x is interesting and will be discussed below.
Table 4: Light-trap holes.
Plate uw0111 uw0112 (µm) (µm) Points 14 20 Mean x 19.8 15.5 Mean y -4.0 1.4 Std Deviation x 7.2 13.0 Std Deviation y 10.2 12.5
Figure 2: Hole location error in x is plotted v. drilling order. The outliers for plate uw0112 are the most non-circular holes and are likely due to remnant burrs or contamination. Standard deviations after trend removal are given. For clarity, 40 µm has been subtracted from the data for uw01.
Figure 2:
Hole location error in x is plotted v. drilling order. The outliers for plate uw0112 are the most non-circular holes and are likely due to remnant burrs or contamination. Standard deviations after trend removal are given. For clarity, 40 µm has been subtracted from the data for uw01.
Figure 3a: Stereo pair showing hole location errors dx (stereo z) and dy (color) v. position on plate uw0111. 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 3a:
Stereo pair showing hole location errors dx (stereo z) and dy (color) v. position on plate uw0111. 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 dy (stereo z) and dx (color) v. position on plate uw0111. 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 dy (stereo z) and dx (color) v. position on plate uw0111. 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 dx (stereo z) and dy (color) v. position on plate uw0112. 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 dx (stereo z) and dy (color) v. position on plate uw0112. 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 3d: Stereo pair showing hole location errors dy (stereo z) and dx (color) v. position on plate uw0112. 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 3d:
Stereo pair showing hole location errors dy (stereo z) and dx (color) v. position on plate uw0112. 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 3 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 4.4 µm RMS for both uw0111 and uw0112. The residual errors in y do not show this correlation (Figure 3).
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 about 4 µm for each axis for uw0111 and 3 µm for each axis for uw0112. These numbers represent the small-scale (20 mm) repositioning error of the machine and drill bit wander.
The linear trend in hole number of the residual error in x 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). In the case of the Dahlih vertical milling machine, the spindle motor as well as the spindle are contained in the same housing. Thus, this effect may be even stronger in this machine.
Consequently, on Monday, June 3, 1996, the spindle was run at 3500 RPM for 3 hours beginning at 0700 Pacific Daylight Time. The machine had been idle the previous weekend and was presumably in thermal equilibrium with the shop air. A bolt was removed from the lower left corner of the front surface of the spindle housing and a temperature sensor was inserted into the bolt hole. Thermally conductive grease was used to couple the sensor to the casting.
A dial indicator with a resolution of 2.5 µm, supported by the table, measured the motion of the front surface of the spindle housing with respect to the vertical ways of the machine. The front surface of the spindle house is 0.843 m from the vertical ways. The spindle axis is 0.643 m from the vertical ways. Temperature and displacement were recorded about every 20 minutes although the exact time of each measurement was not recorded and may include noncumulative errors estimated to be as large as 10 minutes. Data were recorded for 4 hours and included 3 hours of heating and 1 hour of cooling after the spindle was turned off.
Exponential functions were fit to these data. Thermal time constants in the range of 3 to 6 hours were determined. (After one thermal time constant, the temperature is at 63% of its final value with a constant heat input. After two thermal time constants, the temperature is at 86% of its final value.) The asymptotic temperature rise is 26+/-6 °C above ambient, much larger than that reported by Moore and Victory.
To compare these data with the measurements of uw0112, the errors in x from uw0112 were plotted against time by assuming the drilling rate was uniform over the 45 minutes used to drill the ø2.1666 mm holes. The indicator-sensed displacement of the front surface of the spindle housing was scaled by 0.76, the ratio of the distance of the spindle axis to the vertical ways and the distance of the front surface to the vertical ways. The housing temperature measurements were converted to an estimate of the displacement of the spindle axis by multiplying by the estimated coefficient of thermal expansion of the spindle housing (assumed to be grey iron at 11 µm/m-°C) times the distance of the spindle axis from the vertical ways (0.643 m).
The resulting graph is shown below. The agreement of the indicator-sensed displacement data with the drilling errors is excellent. Also, it is clear that much of the indicator-sensed displacement can be accounted for by uniform heating of the spindle housing from the vertical ways to the front of the housing. Better sampling of the temperature distribution in the machine might well lead to better agreement.
Figure 4: Temperature measurements of the spindle housing, dial indicator measurements of the displacement of the front of the spindle housing and CMM measurements of the location error of plug-plate holes for uw0112 are used to infer the motion of the spindle axis v. time.
The holes in uw0111 and uw0112 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 uw0111, the mean was 2.169 mm (0.08538"). For uw0112, the mean was 2.168 mm (0.08535"). 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 uw0111. 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 uw0112. If the fit of the largest pin gauge was judged loose, it was assigned to the right-most bin.
The drill bits used to drill these holes were measured. Plate uw0111 was drilled with a bit measuring ø2.1576 mm. Plate uw0112 was drilled with a bit measuring ø2.1582mm. These numbers are somewhat smaller than the ø2.1666+0/-0.0013 mm (0.0853+0/-0.00005") specified.
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 x. The error budget that we proposed in SDSS Technical Note 19930430 allows 9 µm root-mean-square (RMS). The 2-d position errors measured, 9.5 µm RMS and 11.9 µm RMS for uw0111 and uw0112 respectively, are not quite consistent with this error budget. However, if the linear trend in hole number of the residual error in x were corrected or compensated, the results would be well within the budgeted amount.
The linear trend in hole number of the residual error in x is very likely due to a temperature increase of the spindle housing due to bearing friction and motor heat dissipation. If this is true, it can be corrected rather simply. A oil chiller option is available from the manufacturer of the CNC milling machine. This system circulates temperature controlled oil through the spindle bearings to remove heat from the bearings and control the temperature of the spindle housing. This option costs approximately $10,000.
Moore and Victory describe 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 approach results in no discernible movement of the spindle axis during down-time.
The measured diameters of the drill bits indicate that they do not meet their specifications. However, the measurements of the hole diameters are consistent with the specified diameters of the drill bits. The 6.4 µm of TIR of the bit used to drill uw0111 does not seem to result in a 3 µm increase in the mean hole diameter of that plate. It seems inescapable that the relationship of drill diameter and runout to the diameter of hole drilled is not yet understood.
The measurements of hole diameters suggest a large-diameter tail in the distribution. Since only 1 or 2% of the holes are involved, this appears to be inconsequential. Otherwise, the hole diameters satisfy the project goal. This is despite the fact that the drill bits used appear to be somewhat out of tolerance.
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. It is a pleasure to thank Charlie Hull, Siriluk Limmongkol, Ed Mannery, Jeff Morgan, and Pat Waddell for their interest and comments.
Date created: 4/24/96 Last modified: 6/11/96 Copyright © 1996, Walter A. Siegmund Walter A. Siegmund
