Results of the 1/92 Fermilab Drilling Tests
Sloan Digital Sky Survey Telescope Technical Note
19920916-02
Russell
Owen and Walter
A. Siegmund
Charles Matthews and Christopher Stoughton
Fermi National Accelerator Laboratory
matthews@fnal.fnal.gov
stoughto@fnal.fnal.gov
Introduction
Holes in the plug plates for the Sloan Digital Sky Survey must be
positioned and sized accurately. We tested several techniques by
drilling holes in a number of test plates and measuring the
characteristics of each hole. The results of that experiment are
reported here.
Plates and Drilling
The test plates were 1/4" thick disks of aluminum with conically
concave top surfaces (where the drill entered). The concave surface
was an attempt to simulate drilling into the curved surface of a plug
plate. 50 holes were drilled in each test plate, 10 each in five
concentric circles. The target diameter for the holes was 2.5 mm.
Four different kinds of drill bit were used, two plates per type of
bit, for a total of eight test plates. Each plate was drilled using a
fresh bit. The drilling techniques are described below and are
summarized in table 1.
In all cases: the nominal diameter of each hole was 2.5 mm, a
fresh drill bit (but not necessarily reamer) was used for each test
plate, the tool was held by a double-angle collet (for maximum
accuracy), the collet was cleaned before a tool was inserted and the
tool was flooded with coolant (water-soluble oil) during cutting.
Unless otherwise noted: the feed rate was 5"/min, the spindle
speed was 4000 rpm and the hole was drilled in three pecks, each
0.080" long. The spindle speed was too low, but was the fastest that
the machine could go. The ideal speed for drilling a 2.5 mm diameter
hole is over 10,000 rpm. Drilling too slowly reduces the accuracy of
the hole, especially for small holes such as these, so these results
should represent a worst case.
The plate below the test plate was not changed between some or all
plates. This allowed burrs to form on the bottom of the test plates,
but probably was not a serious problem; the bottom plate was not
moved between test plates, so the holes should have lined up properly
each time.
- Plate 1: Speed Test
- This plate was drilled with a high-speed spindle adapter.
Since this adapter increases error, the holes were not measured.
The plate was drilled used to measure how long it would take to
drill a plate using the proper spindle speed and feed rate.
Results of this test are not yet available.
- Plates 2 and 3: Drill With a Carbide Bit
- The holes were drilled with a carbide helical-point drill bit,
with two flats on each point. Manufacturer and model are unknown.
The bit extended out of the collet 3/4", which is about as short
as practical because room must be left for chip removal. The bit
was driven 0.050" past the bottom face. The run-out (difference in
the transverse position of the flutes) was 0.0005" for both
plates. There were some chips clinging to the bit. This could pose
a problem for large numbers of holes. However, chips should be
less of a problem at the proper spindle speed.
- Plates 4 and 5: Carbide Drill followed by Reaming
- The holes were made in two operations: drilling followed by
reaming. The drill bit was carbide, 2.235 mm (0.088") in diameter,
of unknown point type, manufacturer and model number. Nothing is
known about the reaming bit. For reaming, the feed rate was
2"/min, the spindle speed was 1000 rpm and the hole was reamed in
one peck. The same reaming bit was used for both plates.
- Plates 6 and 8: High-Speed Steel Drill
- The holes were made with a high-speed steel drill bit with one
flat on each point. It was made by Precision Twist Drill Co., 1
Precision Plaza, Crystal Lake, IL 60014, and is type 4ASM, stock
number 46250. It was a standard accuracy bit, but this company can
supply especially accurate bits on demand.
- Plates 7 and 9: Carbide Combination Drill and Reamer
- The holes were made in one operation using a carbide
combination drill and reamer. The drill depth was 0.090", reamer
length was 0.535", and overall length (including shank) was 1.5".
The bit was made by Custanite Corp.; 1200 Utica Ave; Brooklyn, NY
11203 and bought from Reynolds Machine Tool, at $27 each. The
point type and model number are unknown. The spindle speed (4000
rpm) was too low for optimal drilling, as explained above, and too
fast for optimal reaming. The hole was drilled in only one
peck.
Table 1: Summary of Drilling Techniques
Plates Technique
1 speed test; plate not measured
2, 3 carbide drill
4, 5 carbide drill followed by high speed steel reamer
6, 8 high speed steel drill
7, 9 carbide combination drill and reamer
Measurement
The test plates were measured with a coordinate measuring machine.
Each hole was measured at 24 points, 8 each at three depths (one near
the top surface, one near the middle, one near the bottom surface).
At each depth the 8 data points were processed to give four numbers:
x position, y position, diameter and non-circularity. Non-circularity
is computed as the difference in radius between the point closest to
the hole's center and the point farthest from the hole's center.
Analysis
The x-y position data for each plate was corrected for overall
errors in offset, scale and rotation. This corresponds to correcting
for offset, scale, and angle errors when the plate is inserted in the
telescope. The correction was applied as follows: the mid-level x-y
position errors were fit using a model which had coefficients for
offset, scale, and rotation. The model was linear but the fitting
technique was non-linear because that's all the analysis program
offered for fitting to user-defined models. The resulting model was
applied to the measured x-y positions at all three levels for that
plate to obtain residual x-y errors. The scale factors were all less
than one, but most were only a few tenths of a percent under. The
angles and offsets were also very small.
The mid-level depth was used to fit the model because I felt it
was probably the best data set (less likely affected by minor damage
to the holes) and it was a good compromise. The bottom or top of the
holes will actually determine the position of the optical fiber, of
course, but it has not yet been determined whether plates will be
drilled from the sky side or fiber side.
The average and standard deviation of the residual radial position
error was compared to the average and standard deviation of the
un-modelled radial position error, and in all cases there was
improvement, in many cases by more than a factor of two.
The residual x-y position errors of each hole at top and bottom,
combined with the z distance between the upper and lower
measurements, were used to generate the tilt of that hole.
Results
The results are shown in table 2. Position error is the radial
distance of the measured hole from the desired hole. Diameter error
is the measured diameter minus the nominal diameter. Non-circularity
and tilt are described above. The mean and standard deviation of the
diameter error are given in addition to the RMS because the RMS
includes error in the diameter of the bit, an error which can be
greatly reduced by custom-grinding the bit. The mean error shows the
error in diameter of the bit and the standard deviation shows the
error had the bit been made to the correct diameter. The final
expected RMS error presumably lies somewhere between the standard
deviation and RMS error, but just where must be determined by further
tests performed on a number of custom-ground bits.
Table 2: Results
Plate Pos. Err. Diameter Error Non-Circ. Tilt
RMS mean std. dev. RMS RMS RMS
(µm) (µm) (µm) (µm) (µm) (mrad)
2 7 9 13 15 21 4
3 5 11 10 15 16 3
4 9 19 10 21 21 3
5 12 19 12 23 25 5
6 17 4 12 13 22 8
8 13 12 13 18 15 6
7 5 33 10 34 14 2
9 7 20 10 23 17 4
Error Budget
We have revised the error budget based on these drilling
measurements. The new error budget is shown in table 3.
Table 3 New Error Budget
Transverse Error µm RMS
Astrometry 17 (from Steve Kent 9/10/92)
Transformation to focal plane 1
Scale, rotation and guiding 2
Hole location 10 (down from 14)
Temperature gradients 5
Plate deformation 5
Plug/fiber concentricity 8
Plug/hole concentricity 24 (up from 10)
Total transverse error 33 (up from 27)
Axial Error µm RMS
Focus monitor 15
Registering surface 8
Temperature gradients 10
Plate deformation 25
Plug/fiber location 10
Plug/hole registration 12
Total axial error 35
Principal Ray Alignment Error mrad RMS
Hole drilling 4 (up from 1)
Plate deformation 10
Plug/fiber alignment 5
Plug/hole alignment 8 (up from 5 )
Total alignment error 14 (up from 12)
The plug/hole concentricity error was derived from hole diameter
error using gaussian statistics, as follows. Based on the drilling
tests, we can hold hole diameter error to 15 µm RMS (likely
better if we can get bit-to-bit variation down). The plugs we are
planning to buy have a diameter error of 1.3 µm RMS, which is
negligible compared to the holes. Assume normally distributed error
in hole diameter, and that we wish approximately 1 hole in 1000 to
require reaming. Then the nominal hole diameter must be 47 µm
greater than the nominal plug diameter, and the resulting plug/hole
concentricity error is 24 µm RMS.
Conclusions
All bits worked about equally well, except that the high-speed
steel drill bit (plates 6 and 8) had unacceptable position error. The
most significant source of error is diameter error, and in this none
of the bits was a clear winner. The carbide combination drill and
reamer had the largest RMS diameter error but the lowest standard
deviation, so it is not clear how good the bit can be with custom
grinding to control its diameter.
Based on these results, it appears that we can drill plug plates
using any of the tested techniques except drilling with a high-speed
steel bit. Of the remaining techniques, there is no clear winner
based on accuracy, but the plain carbide drill bit is fastest and
simplest. The two-step process of drilling followed by reaming does
not appear to be necessary or even useful. The combination drill and
reamer makes holes about as quickly as a simple drill, but is
custom-made and so will be trickier to obtain. Hence the best
technique for drilling plug plates, based on these tests, is to use a
simple carbide bit, custom-ground if this improves bit to bit
diameter uniformity.
We propose to conduct a new set of tests to study sample-to-sample
variation between bits and to see if using the optimum spindle speed
helps. We propose restricting these tests to carbide drill bits and
carbide combination drills and reamers, and drilling 10 to 20 test
plates.