Sloan Digital Sky Survey Telescope Technical Note 19940919_01
The proposed drive assemblies for the Sloan Digital Sky Survey 2.5-m telescope are very similar to those manufactured for the Wisconsin-Indiana-Yale-NOAO (WIYN) 3.5-m telescope. Although well-engineered, these drives have not been thoroughly tested on a telescope. Consequently, we contracted with L&F Industries (Huntington Park, California) to manufacture two azimuth drive assemblies. These were delivered to Apache Point Observatory in August, 1994, and will be installed and tested on the 3.5-m telescope. As a first step in validating the performance of these drives, we recently made measurements of the runout of the drive and idler roller surfaces.
Each drive consist of a drive capstan and an idler roller mounted in a common housing. These are preloaded against the 2.5 m diameter azimuth drive disk with sufficient force to prevent slippage when the capstan drives the telescope in azimuth. The preload pivot is located so that 80% of the preload force is applied to the drive capstan. Cam followers mounted on the drive assembly capture the 64 mm thick drive disk.
Each capstan is housed in a cylindrical sub-assembly and supported by a duplex pair of preloaded angular contact ball bearings at either end. This allows access so that the capstan can be ground assembled with and rotating on its bearings. Two 18 mm wide tracks were ground separated by a 18 mm relieved gap. Subsequently, the sub-assembly is pressed into a cylindrical socket in the drive housing. The idler rollers are treated similarly.
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. Most measurements were made concurrently with one probe on each ground track. A narrow (~2 mm) strip of transparent plastic tape was applied to at least one track (at an arbitrary location) to encode a angular reference in the data. A shaded pole gear-head motor was used to drive the rollers. One revolution took 47.5 seconds. Most data were digitized at 10 ms intervals.
The runout of the drive capstans was measured concurrently on the lower and upper tracks (the upper track is the one closest to the motor). Neglecting high frequency error, for drive #1, the peak-valley error was 2.16 µm on the lower track and 1.15 µm on the upper track (Figure 1). For drive #2, the peak-valley error was 0.75 µm on the lower track and 1.20 µm on the upper track (Figure 2).
Figure 1: Runout of the lower and upper tracks of the capstan of drive #1. The spikes at 0° and 360° are due to a narrow strip of transparent tape used as an angle fiducial. The largest positive spikes are likely due to contamination and do not seem to be repeatable.
Figure 2: Runout of the lower and upper tracks of the capstan of drive #2. Some zero-point drift is apparent, particularly in the data for the upper track. We attribute this to drift in the Mu-checker electronics. The standard deviation of each data set (with outliers removed) is given. Note that the scales are the same as for Figure 1 and that the quality of this capstan is considerably higher.
In SDSS Technical Report 19920608, "Telescope Tracking Smoothness", we proposed an error budget of 50 nm RMS for the drive rollers with low frequencies removed. Consequently, we fit a second order harmonic to the data for the lower track shown in Figure 2. Since the reduction ratio is 1/25, this would correspond to removing sine and cosine of 25 and 50 theta on the sky (Figure 3). With this function subtracted, the root-mean-square (RMS) is 64 nm. The residuals for a 3rd order harmonic fit (not shown) have an RMS of 50 nm. The capstan of drive #1 appears to be a factor of two or three worse than this, mostly due to high frequency error.
Figure 3: These are the data for the lower track of Figure 2 with the outliers removed. The smooth curve is the equation, y = a*sin(c3) + b*cos(x) + c*sin(2*x) + d*cos(2*x) + e + f*x, which was fit to these data. The coefficients are given in Table 1. The residuals have an RMS of 64 nm.
Table 1: Coefficients of the fitted equation shown in Figure 3.
Value Error a -0.072176 0.0013052 b -0.064897 0.0012296 c 0.15995 0.0012111 d 0.21665 0.0012116 e 0.63068 0.0017055 f 0.00055944 6.9197e-06 Chisq 24.132 R 0.95416
The runouts of the idler rollers were measured. For drive #1, the lower track had a peak-valley of 1.83 µm and the upper track, 4.14 µm. The idler of drive #2 could not be turned with the gear-head motor since it was fabricated without a threaded hole for the coupling. It was turned manually and digitized at 20 ms intervals. Only the lower track was measured. It had a peak-valley of 3.40 µm.
The peak-valley runouts of the rollers in the old 3.5-m telescope drive boxes were measured (Table 2). The measurements were taken at one location on each roller. The rollers were rotated manually. These data were not digitized.
Table 2: Peak-valley runout of old drive box rollers.
Drive # Roller P-V runout (µm) 1 Capstan 4.5 1 Idler 5 2 Capstan 3 2 Idler 3
These results confirm our conjecture in SDSS Technical Report 19920608, "Telescope Tracking Smoothness", i.e., that it is possible but difficult to achieve runouts of 50 nm RMS on scales on the order 25° for these rollers. Of the rollers we measured, only the capstan of drive #2 satisfied this criterion. However, this conclusion must be taken with a grain of salt. The probe tip was spherical and contacted only a small part of the roller at low pressure. In operation, a line contact between the drive disk and each roller will exist. The pressure will be much higher. This will average uncorrelated noise across the line contact. Furthermore, the high pressure will cause cold flow of locally high features making the roller surface smoother. On the other hand, our measurements sampled only a small portion of the width of each track so that we may have missed features that might increase the error.
We do not understand why the smaller idler rollers should appear to have larger runouts than the capstans. Their influence on telescope tracking is a 1/4 that of the capstans because of the location of the preload pivot, so their errors should be divided by this factor before comparing with the capstan results. Still, had their quality been the same as that of the capstans, their contribution to tracking error would have been negligible.
We plan to discuss these results with the personnel of L&F Industries in an attempt to understand what factors may account for the variations observed. We should emphasize again that our goal for runout is very demanding and it is an impressive achievement that L&F Industries was able to approach our goal so closely on their first attempt.
Also, we intend to perform similar measurements on the 2.5-m drives in conjunction with the testing of the assembled azimuth drive system by the end of the year. Hopefully, the assembled tests will help us better understand the averaging that occurs over the line contact between the rollers and the drive disk. This may allow us to adjust our criteria based on indicator measurements of roller surfaces. In any case, these measurements will provide an excellent indication of the performance to be expected of the telescope azimuth axis.
