Sloan Digital Sky Survey Telescope Technical Note 19940306
The 2.5-m telescope azimuth drive disk is 2.54 m in diameter. It serves as a component in the upper bearing in the telescope azimuth axis and the quality of its outer cylindrical surface is crucial to the pointing and tracking performance of the telescope. In this report we describe measurements of this surface.
The disk was ground on a vertical lathe at Stadco, a subcontractor to L&F Industries. The lathe turntable has rolling element bearings but no documentation was obtained. The lathe has two tool posts. The left tool post was used to hold a single point cutter for initial rough cutting. The right tool post supports the grinder (Figure 1). The grinding wheel was about 0.1 m radius and 0.025 m thick. For a grinding pass, after the wheel is dressed, the grinding wheel is lowered until it just clears the table and is mostly below the level of the disk. It is moved toward the disk, with the vertical feed engaged, until sparks appear. Once the machinist is satisfied with the depth of cut (judged by the amount of spark) the machine is left to finish a pass. A pass takes about one hour.
Fig. 1: Grinding of the altitude drive segments. The azimuth drive disk was ground in a similar manner.
Two Mitutoyo 519-332 cartridge head probe electronic indicators were used with 101205 probe tips (7.65 mm radius). The indicators are half bridge type and specified to be linear to 0.5%. Mitutoyo 519-404a Mu-checkers were used to drive the indicators and produce analog signals. These signals were digitized and logged by a 12-bit A/D card in a Macintosh.
One indicator was mounted on the right tool post of the lathe with its axis along a radius so that it measures runout of the cylindrical surface. To subtract turntable runout, a grade 5 (125 nm sphericity, 20 nm surface finish) 440 stainless steel ball was mounted at the center of the turntable (to 5 microns). A second indicator was mounted on the left tool post so that it measured the ball surface in the plane containing the turntable axis of rotation and the other indicator contact point. The estimated error of the actual contact point relative to the ideal contact point was about 0.5 mm. This was adequate to insure that the indicator was mainly sensitive to runout in the direction of the other indicator (by a factor of 25). Magnetic bases were used to hold the indicators.
To get good repeatability at the sub-micron level, it was essential to couple the indicators as directly and as rigidly as possible to the tool posts. Also, contamination was much more of a problem than with conventional measurements. Wiping the surface continuously in front of the indicator improved repeatability.
System noise was measured by placing both indicators along a diameter of the ball and calculating the diameter variation of the ball as the table rotated. The result was 45 nm RMS. The excess above root(2) x 20 nm was attributed to electrical and quantization noise but was more than adequate for the purpose.
Measurements were made by rotating the turntable counter-clockwise (viewed from above) at a constant angular rate. Two rates and three different sampling intervals were used. Data were repeatable at the sub-micron level. An angular fiducial was established by applying a vertical strip of transparent tape to the location where one of three clearance holes is on the same radius as one of 32 threaded holes. This worked well and also served as a check on the sign of the data. The disk was mounted right side up and "UP" is stamped on the top surface at this location.
A first harmonic was fit to the ball data and removed. This removed the decentering of the ball and gave the table runout. The table runout was removed from the data for the outer surface. These data were plotted against the angle of the disk by using two encounters of the tape fiducial to set scale and zero (the tape fiducial was defined to be at 20°).
Figure 2 is a plot of the ball surface after a best-fit first harmonic was removed. We interpret this as the table runout with a small contribution from the asphericity of the ball. The runout of the turntable is 2.86 µm P-V, assuming that the ball is perfect. The large scale features were quite repeatable. If the lower azimuth bearing of the 2.5-m telescope had this accuracy, it would contribute less than 0.05 arc sec RMS pointing error.
Fig. 2: Runout measurement of the turntable. The runout of a grade 5 ball mounted at the center of the turntable was measured. The lowest harmonic (decenter) was fit to these data and removed.
Figure 3 shows a profile taken at the middle of the disk surface. The rotation rate was 45°/s. The spikes at 20° and 380° are due to the transparent tape on the surface. The spike at ~37° is contamination. It appears only once in these data and does not appear in other data taken at the same location at different times. The valley at 120° is at the location where flame hardening of the surface ended. A strip about 10 mm wide of low hardness occurs at this location. The flat portion from 170° to 195° has an error of 114 nm RMS and appears typical of most of the surface.
Fig. 3: Runout of the middle of the drive disk. The spikes at 20° and 380° are due to transparent tape applied to the surface that serves as an angular scale calibrator.
Some residual surface roughness is present at approximately +25 mm. (Zero is at the middle of the disk. The direction of the feed is positive, i.e., downward.) Several spikes appear as well as general roughness (Figure 4). A blow up of one region measured at three different locations shows that the spikes are quite localized vertically (Figure 5). The spike at 251.3° is apparently contamination since it does not appear in other data taken at this location. Other spikes, such as the 2.7 µm one near 255.5° are repeatable.
Fig. 4: Runout of the drive disk near its lower edge. The surface is not as smooth as at the middle of the disk but is similar in shape.
Fig. 5: Details from a small region of the disk. Files disk44, disk43 and disk45 contain data taken at z equals 22.9, 25.4 and 29.2 mm respectively. Features seem to be localized on the disk surface.
Our report, 19920608, suggested a budget of 200 nm RMS on scales of 1° for this surface. (In a separate analysis, Steve Kent suggested a somewhat larger error over larger scales.) Revisiting the problem, we think that this requirement can be relaxed a bit.
The disk is guided by 4 trucks each containing two rollers, 0.10 and 0.05 m in diameter. The trucks are supported by a square frame that provides a preload of about 5000 N to each truck and transfers lateral loads from the telescope to the pier. Adequate compliance is present to limit forces on the roller/disk contacts to a safe level in the presence of differential thermal expansion without the need for explicit springs.
The trucks are mounted asymmetrically so that most of the preload is applied to the drive roller. Consequently, little averaging of disk error occurs between the two wheels within the truck.
If the disk and rollers were perfect, the contact width would be about 0.49 mm wide and the disk would be deformed elastically 240 nm perpendicular to the center of the contact region. High points on an imperfect surface will be deformed by the extremely high stresses until the stress is reduced to the yield strength of the material. This will make the surface more smooth, although the effect is difficult to quantify.
However, it is the case that some averaging must occur over the line contact between the roller and the surface. This likely will reduce the accuracy requirement by sqrt(2) to about 280 nm RMS. The surface quality at the middle of the surface meets this requirement by a factor of 2 or more. However, in the rough zone near 25 mm, this is not quite met.
The worst spike measured is about 2.7 µm high. If it is not deformed by the contact stress, it will cause a peak tracking error of about 0.05 arc seconds after averaging along the line contact and across the disk.
It is likely that better smoothness and large-scale accuracy could be achieved with a bit more work. The surface we report on here was the second surface we measured. The original surface quality was similar or better than that of Figure 2 at the five locations measured. However, the flame hardening region was not ground smooth at -25 mm and the current surface is the result of an attempt to correct that.
A final comment: in the manufacture of similar disks in the future, consideration should be given to flame hardening on a diagonal to allow better averaging of any feature associated with it.
NOTE: A couple of light grinding passes occurred after these measurements to improve the smoothness of the disk. Measurements of the final surface are reported in "2.5-m Telescope Drive Measurements III", SDSS Telescope Technical Note 19941130.
Date created: 03/06/94 Last modified: 03/28/97 Walter A. Siegmund
siegmund@astro.washington.edu
