Sloan Digital Sky Survey Telescope Technical Note 19950608_01
The tracking uniformity goals for the SDSS 2.5-m telescope are quite demanding ("Telescope Tracking Smoothness", Sloan Digital Sky Survey Telescope Technical Note 19920608-03). They are a consequence of the desire to obtain astrometric accuracy approaching 50 milliarcseconds root-mean-square (mas RMS). Consequently, during the interval of May 22 to June 9, 1995, measurements of various critical components were measured as a part of telescope acceptance testing in the assembly shop of the manufacturer, L&F Industries, Huntington Park, California. At the beginning of the interval, the telescope was assembled and progressively disassembled as testing progressed.
The azimuth disk was positioned by four equally-spaced roller assemblies (Figure 1). Two diagonally opposite assemblies are motor driven and were connected to a variable DC power supply for our tests. This allowed the azimuth structure to be rotated.
The data acquisition system is described in SDSS Technical Report 19940306. The telescope design includes 24 magnets located at 15°intervals on the azimuth disk. During telescope operation, these magnets are sensed by a Sony Magnesensor. For runout measurements, it was more convenient to digitize the output of a Hall-effect switch in order to calibrate the data in angle. Since the Sony magnets are not sensed by the Hall-effect switch, high-energy rare earth magnets were placed next to each Hall-effect magnet. During data analysis, it was discovered that 25 Sony magnets had been installed rather than the 24 that were anticipated. The actual locations of the magnets was recovered from the data by assuming uniform rotation of the axis. Also calculated is the standard deviation of locations from several runs in different directions and speeds (Table 1). Zero azimuth occurs when the "UP" mark is due south of the azimuth axis. Angle increases with clockwise rotation viewed from above (Figure 1). The data were taken at uniform intervals in time, usually 10 msec. A spline interpolator was used to transform time to azimuth angle.
Table 1: Magnet fiducial locations. Although it was intended that there be 24 magnets at 15°intervals, it was discovered during the analysis of the data that 25 magnets are present. They are at 11 intervals of 13.60 +/- 0.11 degrees and 14 intervals of 15.04 +/- 0.04 degrees.
Table 1:
Magnet fiducial locations. Although it was intended that there be 24 magnets at 15°intervals, it was discovered during the analysis of the data that 25 magnets are present. They are at 11 intervals of 13.60 +/- 0.11 degrees and 14 intervals of 15.04 +/- 0.04 degrees.
Location Interval (deg) (deg) -19.3 15.0 -4.3 15.0 10.8 15.1 25.9 15.1 40.9 15.0 55.9 14.9 70.8 15.1 85.9 15.0 100.9 15.0 115.9 13.6 129.5 13.5 143.0 13.6 156.6 13.6 170.2 13.4 183.6 13.8 197.5 13.6 211.1 13.6 224.7 13.7 238.3 13.5 251.8 13.7 265.5 15.0 280.5 15.1 295.6 15.0 310.6 15.0 325.7 15.0
Fig. 1: Lower azimuth bearing measurements. The azimuth disk is shown at 0°(the mark "UP" is due south). The lower azimuth bearing indicator locations and the direction of positive rotation are shown, also.
Fig. 1:
Lower azimuth bearing measurements. The azimuth disk is shown at 0°(the mark "UP" is due south). The lower azimuth bearing indicator locations and the direction of positive rotation are shown, also.
The altitude axis was encoded in a manner similar to the elevation axis. In this case, the magnets were spaced much more uniformly. The altitude angles corresponding to the magnets are as follows: { 0.2, 14.9, 28.8, 45.5, 60.0, 75.3, 89.9 }. The telescope altitude was adjusted until each magnet was aligned with the Hall-effect switch and then measured to a precision of about 0.2°using an electronic tilt meter. The data were taken at 10 msec intervals. A spline interpolator was used to transform time to altitude angle.
The instrument rotator, guide rollers, and encoder rollers were encoded by placing a magnet at one location near the circumference of each. Uniform rotation was assumed. This is reasonable since these components were driven through a large gear reduction ratio. The effect of varying friction on the speed of the motor should be minimal.
It is difficult to obtain repeatable sub-micron measurements unless the indicator is mounted in a very rigid and direct manner to the part to be measured. We found that ordinary magnetic bases were very satisfactory as long as the supporting part was flat. However, the rods and clamps that are normally used with mechanical indicators are not suitable for higher precision measurements. Instead, we found that using hot-melt glue to attach the body of the indicator directly to the magnetic base, or its post (Figure 3), gave excellent results in most cases. However, in a few cases the quality of the data was compromised at the sub-micron level by inadequate mounting of the indicators.
The lower azimuth bearing is a standard precision SKF spherical roller bearing (Table 2). (A higher precision model is available but offers no improvement in the parameters that concern us.) One of the bearing races is spherical, hence the name. This bearing design accommodates a modest amount of angular misalignment ("Detail design problems and their solutions: Apache Point Observatory 3.5 Meter Telescope", Steven M. Gunnels, Proc. SPIE, 1236, 1990, p.854-864). It contains a single row of rollers. The angle of contact is 45°. The roller diameters are matched by the manufacturer to 0.5 µm.
Table 2: Large telescope bearings.
Table 2:
Large telescope bearings.
Lower azimuth Altitude Instrument rotator Manufacturer SKF Kaydon Rotek Type spherical roller 30° angular contact 4 point contact Part number 29292 KG100BR6M A8-37P3 Bore 0.460 m 0.25400 m 0.851 m O.D. 0.620 0.30480 1.0160 Ball pitch dia. 0.56939 0.27940 0.9340 Ball/roller dia. 36 mm 12.7 mm 25.4 mm No. balls/rollers 42 44 - Runout radial - 10 µm max - Runout axial - 10 µm max 13 µm goal
For most measurements, two mutually perpendicular electronic indicators measured the runout of a 25.4 mm diameter steel ball located on the azimuth rotation axis approximately co-planar with the lower azimuth bearing. The grade 5 ball was specified to have 125 nm sphericity and 20 nm surface finish, i.e., almost negligible error. The runout perpendicular to the azimuth axis was measured. The indicators were fixed in angle. The x1 indicator was located at 12°(Figure 1). The x2 indicator was at 105.6°. The uncertainty in these angles is 1 or 2°.
The lower azimuth bearing lateral total indicated runout (TIR) is 6 µm. TIR is an industry term equivalent to peak-valley. Most of the runout is low frequency. Indeed, about 1.6 µm TIR occurs at one-half cycle/revolution. This is the frequency that the roller set orbit the bearing. About 305 nm RMS runout remains after the half harmonic and lowest eight harmonic terms have been removed (Figure 2). Most of this high-frequency runout is due to the 23rd harmonic. The phase of the 23rd harmonic drifts about 15°per revolution of the azimuth axis.
The axial runout of the lower azimuth bearing has no particular effect on tracking accuracy but helps to fully characterize the bearing. The lower azimuth bearing axial TIR is 5 µm. It is dominated by the second harmonic in azimuth.
Fig. 2: Residual lateral runout of the lower azimuth bearing. The lowest 8 harmonics have been removed from the data. The runout in two perpendicular directions is shown and is 303 and 307 nm RMS for x1 and x2 respectively. Most of the residual runout is due to the 23rd harmonic. Curves throughout this note have been separated vertically for clarity.
Fig. 2:
Residual lateral runout of the lower azimuth bearing. The lowest 8 harmonics have been removed from the data. The runout in two perpendicular directions is shown and is 303 and 307 nm RMS for x1 and x2 respectively. Most of the residual runout is due to the 23rd harmonic. Curves throughout this note have been separated vertically for clarity.
Fig. 3: Upper azimuth bearing measurement. This view from the northeast shows a grade 5 steel ball supported on a precision x-y stage that is supported in turn by a steel tube that spans the diameter of the azimuth drive disk. The indicators are attached to the posts of magnetic bases using hot-melt adhesive. The magnetic bases are supported by a wide-flange beam mounted to the stationary azimuth frame.
Fig. 3:
Upper azimuth bearing measurement. This view from the northeast shows a grade 5 steel ball supported on a precision x-y stage that is supported in turn by a steel tube that spans the diameter of the azimuth drive disk. The indicators are attached to the posts of magnetic bases using hot-melt adhesive. The magnetic bases are supported by a wide-flange beam mounted to the stationary azimuth frame.
The upper azimuth bearing consists of a ø2.54 m disk guided by a pair of drive roller assemblies (labelled 3 and 6 in Figure 1) and a pair of idler roller assemblies (labelled 2 and 4). The runout of the azimuth axis at the level of the drive disk was measured by indicators mounted northeast and northwest of the 25.4 mm steel ball mounted on the azimuth axis (Figure 3). The indicator angles were 124°and 214°for x1 and x2 respectively. (The coordinate system is defined in the introduction.)
After uaz14, the indicators were swapped at the inputs to the indicator electronics boxes because the data from x1 contained up to a factor of 10 more power at high frequencies (above 2 cycles/degree or 20 Hz) than that from x2. The effect did not move with the indicators. This indicated that the effect was not associated with the indicators or the axis itself. Since the amplitude of the effect was small, no further effort was made to isolate it.
With the first harmonic (decentering of the ball) removed, the runout was 7.0 µm peak-valley northeast and 4.9 µm peak-valley northwest or 1.52 µm and 1.03 µm root-mean-square (RMS) respectively. With the lowest eight harmonics removed, the median runouts were 259 and 286 nm RMS northeast and northwest respectively (Figure 4). About half of the residual runout (assuming quadrature addition) occurred at the frequencies of lowest four harmonics of the ø100 mm guide rollers, i.e., 25, 50, 75 and 100 cycles/revolution of the azimuth axis.
Fig. 4: Runout of the upper azimuth axis. The lowest eight harmonics have been removed. The upper curve is the northeast runout. The lower is the northwest runout. Perhaps half of the residual runout occurs at the frequency of the 25th harmonic in azimuth, i.e., the fundamental frequency of the ø102 mm guide rollers, or its harmonics.
Fig. 4:
Runout of the upper azimuth axis. The lowest eight harmonics have been removed. The upper curve is the northeast runout. The lower is the northwest runout. Perhaps half of the residual runout occurs at the frequency of the 25th harmonic in azimuth, i.e., the fundamental frequency of the ø102 mm guide rollers, or its harmonics.
Two tracks on the guide rollers were measured at two locations approximately 55.8°apart (Figure 5). Indicator x1 always measured upper track in the as-assembled orientation of the guide roller assembly. One magnet was placed between the tracks to indicate zero angle. After measuring the rollers, the magnet location was transferred to a location on the end of the roller that will be accessible with the telescope assembled. The Hall-effect switch was located approximately 12.5°from x1.
Fig. 5: Measurement of guide roller runout. Indicator x1 is on the left. The Hall-effect switch is in the middle (below the 9 V battery). A shaded-pole AC gearhead motor rotates the roller with a rotation period of 47 seconds, counter-clockwise viewed from the gearhead. The squat black cylinder on the left contains a telescope drive motor.
Fig. 5:
Measurement of guide roller runout. Indicator x1 is on the left. The Hall-effect switch is in the middle (below the 9 V battery). A shaded-pole AC gearhead motor rotates the roller with a rotation period of 47 seconds, counter-clockwise viewed from the gearhead. The squat black cylinder on the left contains a telescope drive motor.
The results show considerable variation from track to track (Table 3). Together with our earlier result (SDSS Technical Report 19941104) that the two tracks are similar at the same angle, these data suggest that the harmonic amplitude is dependent on the angle at which the roller is measured. It seems likely that this is the solution to the puzzle described in SDSS Technical Report 19941130, "2.5-m Telescope Drive Measurements III", Table 2, i.e., that the amplitude of the 25th harmonic of the upper azimuth axis was not consistent with that predicted from the measured guide roller runout. Quantitatively, the 25th harmonic amplitude should be half the vector sum of the amplitudes of the roller first harmonics. The vector sum must be used to account for the phase difference of the two rollers. The maximum amplitude of the 25th harmonic occurs when diagonally opposite rollers are in phase. This number appears in the last column of Table 4 and is computed from the maximum values listed in Table 3. Much of the discrepancy noticed earlier is no longer apparent in the current results and might well disappear if measurements were made at the contact location with the drive disk.
Table 3: Coefficients of harmonic fits to assembled drive/idler roller runout. The coefficients of the first 6 harmonics are given. The RMS is calculated from the coefficients. The two entries for each roller are for locations about 56°apart on the roller surface (Figure 5). The 1st and 2nd harmonics dominate the other terms and depend on the location of the measurement.
Table 3:
Coefficients of harmonic fits to assembled drive/idler roller runout. The coefficients of the first 6 harmonics are given. The RMS is calculated from the coefficients. The two entries for each roller are for locations about 56°apart on the roller surface (
Figure 5
). The 1st and 2nd harmonics dominate the other terms and depend on the location of the measurement.
drive indi 1 2 3 4 5 6 RMS /idler -cator (nm) (nm) (nm) (nm) (nm) (nm) (nm) 2 1 252 36 20 29 6 10 182 2 2 267 94 11 13 15 20 201 3 1 249 13 14 17 13 14 178 3 2 141 109 27 8 19 21 129 4 1 358 40 13 32 18 19 257 4 2 185 136 14 11 17 37 165 6 1 210 29 15 8 21 20 152 6 2 122 69 22 20 21 18 103
Table 4: Correlation of 25th harmonic of upper azimuth axis runout with the 1st harmonic of guide roller runout. Along each diagonal, we expect that the amplitude of the 25th harmonic of the axis will be the average of the effect of the fundamental of the guide rollers along that same diagonal. The last column gives the maximum amplitude of the 25th harmonic expected based on measurements of the guide rollers (Table 3). The drive guide roller assemblies are 3 and 6. The idler guide roller assemblies are 2 and 4.
Table 4:
Correlation of 25th harmonic of upper azimuth axis runout with the 1st harmonic of guide roller runout. Along each diagonal, we expect that the amplitude of the 25th harmonic of the axis will be the average of the effect of the fundamental of the guide rollers along that same diagonal. The last column gives the maximum amplitude of the 25th harmonic expected based on measurements of the guide rollers (
Table 3
). The drive guide roller assemblies are 3 and 6. The idler guide roller assemblies are 2 and 4.
Amplitudes (nm) axis 25th harmonic roller direction min median max max drive 81 185 289 230 idler 101 187 248 312
The altitude axis is defined by angular contact ball bearings. Short axles extend from the inside faces of the fork into the primary support structure (PSS). A preloaded duplex pair of bearings is used at each fork. The bearings are Kaydon Corporation (Muskegon, MI) Reali-Slim bearings, KG100BR6M, precision class 6, with a 254 mm bore and a 305 mm outside diameter (Table 2). The balls were same diameter to better than 1.25 µm.
A ø25 mm ball supported by an x-y stage was mounted to the end of the axle (Figure 6). Two indicators were mounted at 90°to each other and to the altitude axis. They were supported by magnetic indicator bases attached to the inside surface of the PSS. One indicator was parallel to the telescope optical axis. The other indicator was perpendicular to the optical axis. Motion sensed by the latter indicator does not directly affect telescope tracking. However, it contributes to the axis encoding error.
Since accurate astrometry will not be expected with the telescope altitude below 30°, the range of 30°to 90°altitude is discussed. Both the left (Figure 7) and right (Figure 8) bearings were measured. Some stick-slip (~20 - 30 nm) is present (the residual data varies smoothly after harmonics were removed). We believe that this is in the mounting of the indicators. Also, digital-to-analog converter quantization is quite apparent. It would have been better to digitize with higher resolution. Data for one indicator on the right bearing (alt34x1r) includes 60 Hz interference aliased to 40 Hz by the 100 Hz sampling rate. The residual runout with low frequencies removed was excellent (Table 5).
For the range of 0°to 90°altitude, the axial runout was approximately 11 µm for the left bearing and 6 µm for the right bearing. These numbers should be treated with some caution since the indicator mounting may not have been adequately stiff. The runout was mostly due to the first or second harmonic in altitude.
Fig. 6: Runout measurement of the right altitude bearing. A ø25 mm ball is supported by a precision x-y stage that is supported in turn by a bar bolted across the end of the right altitude axle. Two indicators are supported by magnetic bases attached to the inner surface of the primary support structure. The vertical bar was used to support an indicator to measure axial runout.
Fig. 6:
Runout measurement of the right altitude bearing. A ø25 mm ball is supported by a precision x-y stage that is supported in turn by a bar bolted across the end of the right altitude axle. Two indicators are supported by magnetic bases attached to the inner surface of the primary support structure. The vertical bar was used to support an indicator to measure axial runout.
Fig. 7: Runout of the left altitude bearing. The lowest 8 harmonics have been removed. The upper curve is the runout perpendicular to the optical axis while the lower curve is the runout parallel to the optical axis.
Fig. 7:
Runout of the left altitude bearing. The lowest 8 harmonics have been removed. The upper curve is the runout perpendicular to the optical axis while the lower curve is the runout parallel to the optical axis.
Fig. 8: Runout of the right altitude bearing. The lowest 8 harmonics have been removed. The upper curve is the runout perpendicular to the optical axis while the lower curve is the runout parallel to the optical axis.
Fig. 8:
Runout of the right altitude bearing. The lowest 8 harmonics have been removed. The upper curve is the runout perpendicular to the optical axis while the lower curve is the runout parallel to the optical axis.
Table 5: Runout of the altitude bearings. The files alt15x1 and alt15x2 are for the left bearing. The files alt34x1 and alt34x2 are for the right bearing. For both bearings, x1 is measured in the direction perpendicular to the optical axis and x2 is parallel to the optical axis. The second column is the runout with only the mean and first harmonic (decentering) removed. The third column is the residual runout with the mean and lowest 8 harmonics removed.
Table 5:
Runout of the altitude bearings. The files alt15x1 and alt15x2 are for the left bearing. The files alt34x1 and alt34x2 are for the right bearing. For both bearings, x1 is measured in the direction perpendicular to the optical axis and x2 is parallel to the optical axis. The second column is the runout with only the mean and first harmonic (decentering) removed. The third column is the residual runout with the mean and lowest 8 harmonics removed.
RMS runout (nm) file w/low freq. w/out low freq. alt15x1 52 31 alt15x2 92 60 alt34x1 72 52 alt34x2 131 39
To measure the runout of the altitude drive disks, an indicator was placed adjacent to the altitude encoder assembly at an angle of 39.9°from the vertical (Figure 9). The runout of the altitude bearing should be subtracted from such measurements to obtain the disk runout. However, this was not done since the altitude bearing runout was so small to be almost negligible.
The first harmonic in altitude was fit to the data to determine disk decenter. The left disk was decentered by 4.7 µm and the right by 45.5 µm. The centering of the left disk is a remarkable achievement of the L&F Industries assembly personnel, Dan Childs and Conrad (Corky) Guerru, since the disk was centered manually using adjustment screws. The residual runouts with the lowest 8 harmonics removed from the data and between 30°and 90°altitude was calculated (Figure 10). Residual runout was 87 nm RMS for the left disk and 98 nm RMS for the right disk.
Fig. 9: Runout of the left altitude disk. The indicator is supported by a magnetic base adjacent to the altitude encoder (the black cylinder).
Fig. 9:
Runout of the left altitude disk. The indicator is supported by a magnetic base adjacent to the altitude encoder (the black cylinder).
Fig. 10: Runout of the altitude disks. The lowest 8 harmonics have been removed. The upper curve is for the left disk while the lower curve is for the right disk. The runout of the altitude bearings has not been subtracted from these data.
Fig. 10:
Runout of the altitude disks. The lowest 8 harmonics have been removed. The upper curve is for the left disk while the lower curve is for the right disk. The runout of the altitude bearings has not been subtracted from these data.
The instrument rotator is supported by a Rotek four-point contact ball bearing (Table 2). Dicronite dry-film lubricant was applied to the balls and raceways. The maximum frictional torque was specified to be 474 N-m. The frictional torque, measured at L&F Industries prior to assembly in the telescope, was 260 N-m. After installation of the telescope, in October 1996, the frictional torque was measured by Jon Davis of APO to be a mean of 434 N-m. The telescope was assembled at APO and the dummy camera and spectrograph weights were mounted. Measurements were made with the axial cam followers in contact and not in contact. Little difference was observed. The axial runout was specified to be 25 µm and the goal was 13 µm.
To measure the lateral runout of the instrument rotator bearing, a ø25 mm ball supported by an x-y stage was mounted on the rotator axis. Two indicators were mounted at 90°to each other and to the rotator axis. They were supported by magnetic indicator bases attached to a bar spanning the hole in the dummy primary mirror (Figure 13).
The tests of the instrument rotator were performed with masses that represented the photometric camera and two spectrographs attached to the rotator. These masses were mounted so that they applied the same moments and weights that the actual camera and spectrographs will apply.
The lateral runout of the bearing is about 6 µm peak-valley per axis at an altitude of 0°(Figure 11) and 4 µm peak-valley per axis at 90°. With the lowest 8 harmonics removed, the lateral runout was about 170 nm RMS per axis at an altitude of 0°.
Axial runout is 8 µm peak-valley for both 0°and 90°. Axial runout, although interesting, is of little practical consequence in this application. It should be detected by the focus CCD's and removed.
Fig. 11: Lateral runout of the instrument rotator bearing. Only decentering of the ball has been removed. The upper curve is for runout in the direction of the left fork while the lower curve is for vertical runout. The telescope was pointed at the horizon.
Fig. 11:
Lateral runout of the instrument rotator bearing. Only decentering of the ball has been removed. The upper curve is for runout in the direction of the left fork while the lower curve is for vertical runout. The telescope was pointed at the horizon.
To measure the runout of the rotator drive disk, an indicator was placed in contact to the disk surface near the left altitude drive segment (Figure 12). The runout of the rotator bearing along the same radius was measured and subtracted from the disk runout. The disk runout, with ball decentering removed, was 25 µm peak-valley (Figure 13a). The lowest 8 harmonics were fit and removed from these data. Most of the residual runout, 1.0 µm RMS, occurs at a frequency of 10 cycles per revolution (Figure 13b). It is likely that this is due to the variation in radial stiffness of the rotator disk that is associated with 10 access holes in the disk.
Fig. 12: Runout of the instrument rotator drive disk. The indicator is supported by a magnetic base attached to the back surface of the mirror cell. The indicator measures the outer cylindrical surface of the disk.
Fig. 12:
Runout of the instrument rotator drive disk. The indicator is supported by a magnetic base attached to the back surface of the mirror cell. The indicator measures the outer cylindrical surface of the disk.
Fig. 13a: Raw runout of the instrument rotator drive disk. No harmonics have been removed. The residual runout is 17 µm and 25 µm peak-valley for altitude angles of 0°(rot17) and 90°(rot19 and rot20) respectively. The sharp positive going features appear to be contamination on the surface. They disappear when the surface was cleaned between rot19 and rot20.
Fig. 13a:
Raw runout of the instrument rotator drive disk. No harmonics have been removed. The residual runout is 17 µm and 25 µm peak-valley for altitude angles of 0°(rot17) and 90°(rot19 and rot20) respectively. The sharp positive going features appear to be contamination on the surface. They disappear when the surface was cleaned between rot19 and rot20.
Fig. 13b: Runout of the instrument rotator drive disk. The lowest eight harmonics have been removed. The residual runout is 1.0 µm RMS and is dominated by the 10 cycle/revolution frequency that is apparently associated with the 10 openings in the disk, two of which are partially visible in Figure 12.
Fig. 13b:
Runout of the instrument rotator drive disk. The lowest eight harmonics have been removed. The residual runout is 1.0 µm RMS and is dominated by the 10 cycle/revolution frequency that is apparently associated with the 10 openings in the disk, two of which are partially visible in
Figure 12
.
It was difficult to mount indicators with adequate stiffness to measure the tilt of the rotator axis as a function of altitude angle. Consequently, measurements were made with a borescope (a small special purpose telescope) inserted in a cylindrical hole at the center of an adapter plate bolted to the instrument rotator. The borescope was focused on a target attached to the dummy secondary. The displacement of the target with respect to the axis of the borescope was measured (Figure 14). These data (Figure 15) are well-described by the function y = a + b*cos(a). From 0°to 90°altitude, a deflection of less than x = 25 µm and y = 610 µm was measured over the 4.4 meter separation of the instrument rotator and the dummy secondary. These are the lateral displacements that are necessary in the secondary actuators to maintain collimation and coalignment of the telescope optical axis with the rotator axis of rotation. The latter condition is necessary so that the optical axis remains perpendicular to the photometric camera at all telescope altitudes.
Finite element modeling of the telescope was performed during the design of the telescope by Terry King. The model predicted a deflection of y = 483 µm of the secondary with respect to the instrument rotator.
Fig. 14: Terry King of L&F Industries uses a borescope to measure the displacement of a target mounted on the dummy secondary with respect to the normal to the instrument rotator photometric camera mounting surface. The telescope altitude is 0°.
Fig. 14:
Terry King of L&F Industries uses a borescope to measure the displacement of a target mounted on the dummy secondary with respect to the normal to the instrument rotator photometric camera mounting surface. The telescope altitude is 0°.
Fig. 15: Displacement of the secondary with respect to the normal to the instrument rotator photometric camera mounting surface. These data describe the lateral motion of the secondary needed to keep the secondary centered on the rotator axis.
Fig. 15:
Displacement of the secondary with respect to the normal to the instrument rotator photometric camera mounting surface. These data describe the lateral motion of the secondary needed to keep the secondary centered on the rotator axis.
Wobble of the instrument rotator axis causes a variation in focus across the field of view of the photometric camera. Consequently, this effect was specified to be such to cause no more than 25 µm of displacement at the field edge relative to the nominal focal surface. To measure this parameter, a ø50.8 mm shaft was mounted approximately coaxial with the instrument rotator axis (Figure 16). It extended from the rotator toward the secondary. Two pairs of indicators were used. One set was located 0.10 m from the rotator bearing plane. The second set was located 0.42 m from the bearing plane. (The separation of the indicators, 0.32 m, is approximately equal to the telescope field radius, i.e, within 3%. Thus, the differential deflection of the shaft between the indicators, to the extent that it represents the tilt of the focal plane, is the expected defocus from field center to edge.) At each location, one indicator was on the left side of the shaft and one was on the top (as viewed with the telescope at an altitude of 0°). The indicator electronics (muCheckers) were used in differential mode so that the first muChecker was sensitive to wobble about the altitude axis (y) and the second was sensitive to wobble sideways (x). The wobble was measured continuously during a rotation of about 450°of the rotator. Measurements were made at altitudes of 0°, 60°and 90°.
Fig. 16: Indicators measure the diameter variation of a ø50.8 mm shaft in this view through the dummy primary center hole. The shaft is supported by a bore in a plate that is attached to the photometric camera mounting surface. (The same bore was used to support the borescope in Figure 14.) To measure the wobble of the instrument rotator axis, the right pair of indicators was mounted on top of the shaft.
Fig. 16:
Indicators measure the diameter variation of a ø50.8 mm shaft in this view through the dummy primary center hole. The shaft is supported by a bore in a plate that is attached to the photometric camera mounting surface. (The same bore was used to support the borescope in
Figure 14
.) To measure the wobble of the instrument rotator axis, the right pair of indicators was mounted on top of the shaft.
Fig. 17: Wobble of the instrument rotator axis. Only the mean tilt of the shaft with respect to the rotator axis has been removed. The upper curve is the y-wobble at 0°telescope altitude. The lower curve is the y-wobble at 90°. The amplitude of the displacement in the plot is the same as the expected defocus at the edge of the focal plane relative to the center. It is less than one-fourth the 51 µm peak-valley specified.
Fig. 17:
Wobble of the instrument rotator axis. Only the mean tilt of the shaft with respect to the rotator axis has been removed. The upper curve is the y-wobble at 0°telescope altitude. The lower curve is the y-wobble at 90°. The amplitude of the displacement in the plot is the same as the expected defocus at the edge of the focal plane relative to the center. It is less than one-fourth the 51 µm peak-valley specified.
The deflection of the shaft due to gravity is less than 30 µm at the separation of the indicators (using the shaft weight and measured differential spring rate, 0.6 µm/N applied to the end of the shaft). This deflection is constant at any particular telescope altitude and does not affect the differential displacement measured by the two pairs of indicators as a function of rotator angle.
The first and higher harmonics in the indicator data describe the wobble of the instrument rotator. To compare data at 0°and 90°, y = 1.05 + 45.64*cos(theta) - 46.66*sin(theta), was subtracted from the data thereby removing most of the misalignment of the shaft with the rotator axis (Figure 17). The differential displacement of the two indicators sensitive to y-wobble is plotted. The trend apparent in these data is due to drift in the muChecker electronics. The y-wobble is 9 µm peak-valley at 0°altitude and 11 µm peak-valley at 90°. Processing the x-wobble data in a similar manner gives 8 µm peak-valley. Repeatability appears to be 2 µm or so (about as good as can be expected given the mounting of the indicators). The shaft diameter is uniform to better than 4 µm peak-valley (see Figure 16 for the measurement setup).
Five of the six encoder rollers were measured. Most of the runout occurred at either 1.0 or 11.0 cycles per revolution, except for roller 4 where both frequencies were present.
Table 6: Runout of the encoder rollers. The runout for rollers 3 and 5 mostly occurred at 1.0 cycles/revolution. For rollers 2 and 6, 11.0 cycles/revolution dominated. For roller 4, both 1.0 and 11.0 cycles/revolution were important.
Table 6:
Runout of the encoder rollers. The runout for rollers 3 and 5 mostly occurred at 1.0 cycles/revolution. For rollers 2 and 6, 11.0 cycles/revolution dominated. For roller 4, both 1.0 and 11.0 cycles/revolution were important.
RMS runout (nm) encoder runout file 01 - - 02 401 enc06x1 03 602 enc13x1 04 924 enc07x1 05 875 enc12x1 06 479 enc02x1
The power spectral density (PSD) as a function of angular frequency was calculated for the main telescope bearings, i.e., the lower azimuth, left and right altitude, and instrument rotator bearings (Figure 18). Prior to the calculation of the PSD, a least-squares fit of the lowest eight harmonics was performed. The fit was removed from the data. The PSD is normalized so that twice the integral of a spectral feature is the mean square amplitude of the data at that frequency.
The results show that the lower azimuth bearing is inferior to the altitude bearings only at frequencies below 0.2 cycles/degree. This is in contrast with the rotator bearing that has about one order of magnitude higher runout power than the altitude bearings throughout the frequency range that was measured.
Fig. 18: Runout power spectral distribution (PSD) of telescope bearings. The lowest eight harmonics were removed prior to the calculation of the PSD's. The lower azimuth (laz27), left and right altitude (alt15 and alt34), and instrument rotator (rot16) bearing runout PSD's are inversely proportional to the square of the frequency below 3 cycles/degree. The higher runout of the lower azimuth bearing, as compared to the altitude bearings, occurs below 0.2 cycles/degree. The peaks at frequencies above 1 cycle/degree are believed due to vibration in the test environment.
Fig. 18:
Runout power spectral distribution (PSD) of telescope bearings. The lowest eight harmonics were removed prior to the calculation of the PSD's. The lower azimuth (laz27), left and right altitude (alt15 and alt34), and instrument rotator (rot16) bearing runout PSD's are inversely proportional to the square of the frequency below 3 cycles/degree. The higher runout of the lower azimuth bearing, as compared to the altitude bearings, occurs below 0.2 cycles/degree. The peaks at frequencies above 1 cycle/degree are believed due to vibration in the test environment.
In a similar manner, the power spectral density (PSD) as a function of angular frequency was calculated for the large telescope drive disks, i.e., the azimuth, left and right altitude, and instrument rotator disks (Figure 19). The PSD falls off as one over the frequency squared. This behaviour is discussed by R.S. Sayles and T. R. Thomas (Nature 271, 431-434, 1978) who show that it applies to surfaces such as runways and motorways as well as machined surfaces.
The results show that the instrument rotator disk has larger runout at all frequencies. This disk was the only one not hardened prior to grinding. The disk contains ten large openings and it was feared that the hardening process would cause unacceptable distortion of the part. We suspect that the lack of hardening accounts for its higher runout.
Fig. 19: Runout power spectral distribution (PSD) of the telescope drive disks. The lowest eight harmonics were removed prior to the calculation of the PSD's. The azimuth (drive227), left and right altitude (alt13 and alt29), and instrument rotator (rot19) disk runout PSD's are inversely proportional to the square of the frequency. The rotator disk was the only one that was not hardened before grinding. This apparently accounts for its higher runout. The peaks at frequencies above 1 cycle/degree are believed due to vibration in the test environment.
Fig. 19:
Runout power spectral distribution (PSD) of the telescope drive disks. The lowest eight harmonics were removed prior to the calculation of the PSD's. The azimuth (drive227), left and right altitude (alt13 and alt29), and instrument rotator (rot19) disk runout PSD's are inversely proportional to the square of the frequency. The rotator disk was the only one that was not hardened before grinding. This apparently accounts for its higher runout. The peaks at frequencies above 1 cycle/degree are believed due to vibration in the test environment.
The static torque needed to move the wind baffle with the drives attached but not powered was measured with a spring scale. A force of 670 N at 1.1 m was necessary to move the altitude axis to a higher altitude. However, 1560 N was necessary to move it to a lower altitude (presumably because it was unbalanced). The altitude torque is 1200 N•m. A force of 4500 N at 2.7 m was necessary to move the azimuth axis. The azimuth torque is 12 kN•m.
Fig. 20: Measurements of the static torque required to move the wind baffle with the drives connected but not powered. The building hoist applies a torque via the spring scale (just left of center) to the wind baffle altitude axis (left image). A block (near Corky's foot) is used to apply a tangential force near the perimeter of the circular floor panel structure (right image).
The specification of 70 milliarcseconds (mas) RMS and the goal of 28 mas RMS for telescope tracking performance was given in "Telescope Tracking Smoothness" (Sloan Digital Sky Survey Telescope Technical Note 19920608-03). A tracking error budget corresponding to the goal is given in that Technical Note. That table has been revised to include the measurements described herein (Table 7).
The results show that neither the specification nor goal are satisfied. Although many of the components have excellent performance, e.g., the altitude and azimuth drive disks, and the altitude and rotator bearings, the error budget is dominated by the contributions from the azimuth and altitude encoder rollers.
In an attempt to understand the relatively large encoder roller runouts, on or about June 8 we visited the shop of the subcontractor that was responsible for grinding the encoder rollers. The rollers were ground assembled with their bearings. To rotate the rollers without applying excessive moments to the roller shaft, the contractor had coupled the roller shaft to a motor using a 0.15 m length of flexible hose. While this had the desired effect of limiting unwanted moments, it is unlikely that it was very rigid in torsion. We suspect that this torsional compliance, together with forces between the grinding wheel and the roller, modulated the rotation rate and consequently the material removal rate as a function of angle.
The encoder roller assemblies are relatively small and simple components that are relatively easy to grind using an improved procedure. That this action is likely to lead to conformance with the specification is suggested by the performance of the guide rollers that is more than a factor of three better than that of the encoder rollers. However, reaching the tracking performance goal will be considerably more difficult and will require significant reductions of azimuth axis wobble and secondary actuator error.
Table 7: Tracking error budget
Table 7:
Tracking error budget
Component Measured error (nm RMS) (mas RMS) Az axis wobble Drive disk high freq. error 216 20.5 Guide roller error 178 20.5 Lower bearing high freq error 305 22.9 Alt axis wobble Bearing high freq error 51 5.4 Az encoding error Drive disk high freq error 216 5.0 Encoder capstan error 602 69.0 Encoder error 5.5 Az servo error 9.8 Alt encoding error Drive disk high freq error 92 2.1 Encoder capstan error 602 69.0 Encoder error 5.5 Alt servo error 9.8 Rotator bearing error 240 4.0 Rotator encoding error Drive disk error 1000 3.9 Encoder capstan error 602 2.3 Encoder error 0.2 Rotator servo error 0.2 2ry actuator high freq. error 310 20.0 Total 107.9
The results of the instrument rotator bearing tests were excellent. They indicate that proper collimation and alignment of the telescope optics should insure uniform focus across the charge-coupled devices (CCD's) of the photometric camera independent of rotator or altitude angles.
Date created: 06/08/95 Last modified: 10/25/96 Copyright © 1995, Walter A. Siegmund Walter A. Siegmund
