Sloan Digital Sky Survey Telescope Technical Note 19920916-02
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.
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.
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
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.
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.
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
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.
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.
