Plug-Plate Bending in an Assembled Spectrograph
Cartridge
Sloan Digital Sky Survey Telescope Technical Note
19961230
Jessica Granderson
University of Washington
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 are
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 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.
Matching the Surface of Best Focus
Previous
attempts to match the SDSS plug-plates to the surface of best
focus were conducted using only the bending fixture. The analyses
performed indicated that by adding a central constraint to the
plug-plate deformation process, the plates could be made to match the
surface of best focus within an acceptable range of error. Since the
time that the last tests were performed, the
cartridge that will hold the plug-plates and
the bending fixture on the telescope has been fabricated. Inside of
the cartridge is a thin rod that serves as the central constraint.
The height of the rod, and thus the magnitude of the
central constraint can be adjusted using a
threaded nut. A second series of tests has been performed in order to
determine the accuracy with which the plug-plates can be deformed
using the cartridge.
A set of five indicators supported by tooling balls was used to
measure the deflection of two plates (uw0111 and ke0111). Data was
taken at five points along the radius of the plate, at four different
angular locations. The deformation was recorded and plotted against a
curve of the focal surface, kmg001. The results are shown in
Figure 3 and Figure 4.
The central constraint was adjusted to displace the plate centers
approximately 0.72mm and 0.68mm from their unconstrained positions
for plates uw0111 and ke0111, respectively.
Figure 1: Pictured here is the
cartridge, with bending fixture and plug-plate installed. The
profilometer atop the plug-plate was used to measure the deflection
of the plug-plate. The central constraint is located underneath the
bending fixture. Data was taken at five points along the radius,
using the five indicators pictured. The profilometer is supported by
tooling balls, and calibrated on a granite straight edge that is flat
to 1 micron. The right tooling ball provides a sixth measuring
point.
Figure 2: A close-up view of the
mechanism that is used to impose the central constraint.
Figure 3: This plot shows the
shape of plug-plate uw0111 versus kmg001, the desired shape of the
plate.
Figure 4: This plot shows the
shape of plate ke0111 versus kmg001. Plate ke0111 deformed
differently than plate uw0111, resulting in a slightly closer match
to the best focal surface.
Analysis
It can be seen from the graphs that by bending the plates and
adding a central support, the curvature of the plug-plates can be
made to match the surface of best focus quite closely. The two plates
tested deformed into two different shapes. Since they were fabricated
by two different groups, the 3.175mm aluminum plates differed in
thickness by approximately 0.076mm. This difference in thickness is
the most likely cause of the difference in deformation of the two
plates. The ke0111 plug-plate was the thicker of the two, and
correspondingly it did not vary as much in deflection along the inner
radius.
While the average deformation of the two plug-plates tested
provided quite a close matches to the desired focal surface, there is
a large degree of scatter among data points taken at a given radius
at different points about the plates. The plug-plates deformed into a
saddle-like shape; the deflection at 0° and 180° was
approximately 0.10mm less than the deflection at 90° and
270°. The total variance between largest and smallest
deflections at a given radius was approximately 0.19mm. This is far
greater than the amount of scatter seen in previous bending tests,
which was approximately 0.04mm.
Conclusion
The results of this set of plate bending trials confirm that the
cartridge, into which the plug-plates and bending fixture are to be
installed, provides a suitable mechanism for imposing the central
constraint upon the plug-plates. The average deflection of both
plates tested could be well matched to that of the surface of best
focus. The experimental data indicate that the magnitude of the
constraint should be 0.72mm or 0.68mm, depending upon whether plate
uw0111 or ke0111 is to be used. Variations in the thickness of the
plate, such as those that appear when different manufacturers are
used, do affect the shape of the plate.
The slightly thicker plate, ke0111, matched the desired curve most
closely with a standard deviation of 0.025 mm; the thinner plate,
uw0111, was fit with a deviation of 0.035 mm. The tolerated deviance
of the plates from the target curve is 0.025 mm. An area-weighted
standard deviation was also calculated, to account for the radial
spread in data points that is obscured in a point by point,
unwieghted calculation. The area weighted deviation for plates uw0111
and ke0111 were worse than the allowed deviation of 0.025mm, at
0.043mm and 0.031mm, respectively. The deviation would have been much
the same had the central constraint had not been adjusted between
plates.
The most probable cause for the increase in scatter between data
points at a given radius, is out-of-flatness of the mating surfaces
of the bending rings. Previous deflection tests were conducted using
a different set of bending rings, which could account for the better
results that were obtained. In machining the second set of rings,
more variance of the ring surfaces may have been introduced.
Date created: 12/30/96
Last modified: 12/31/96
Jessica Granderson