Full-scale plug-plate drilling tests V
Sloan Digital Sky Survey Telescope Technical Note
19960526
Walter
Siegmund and Russell
Owen
Contents
Introduction
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.
Plate drilling
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.
Plate measurements
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.
Analysis
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 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 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 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.
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.
Hole diameters
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 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.
Conclusions
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.
Acknowledgments
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
siegmund@astro.washington.edu