Full-scale plug-plate drilling tests IV
Sloan Digital Sky Survey Telescope Technical Note
19960408
Walter
Siegmund , Russell
Owen , Paul Mantsch, Larry Stark and Dan Skow
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 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.
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.
Plate measurements
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.
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 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 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 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.
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.
Spindle heating experiment
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.
Hole diameters
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.
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 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.
Acknowledgments
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
siegmund@astro.washington.edu