Ultra-Lightweight Telescope Mount

Transcription

1 PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 121: , 2009 March The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. Ultra-Lightweight Telescope Mount M. KURITA, 1 AND S. SATO Department of Physics, Nagoya University Furo-cho, Chikusa-ku, Nagoya , Japan AND N. NODA Taiyo Kogyo Corp , Kigawa Higashi, Yodogawa-ku, Osaka , Japan Received 2008 October 27; accepted 2009 February 12; published 2009 March 31 ABSTRACT. We have developed a transportable, lightweight telescope mount. It is capable of carrying a primary mirror of up to 2.5 m in diameter, but is only 7 m high and weighs 5 tons, approximately one-fifth the weight of a conventional telescope. We measured the pointing and the tracking accuracies to be better than 3 and 0.5 for 10 minutes, for pointing and tracking, respectively. We have demonstrated that the telescope is readily transportable while retaining sufficient accuracy for astronomical observations. 1. INTRODUCTION A light and compact telescope has many advantages: economy of fabrication; ease of transportation to, and erection on, high and dry sites such as Atacama and Antarctica; and low thermal inertia and low air resistance, which are important for good image quality. In order to design light telescopes, we considered the mechanical structures of a telescope in which a large stiffness/weight ratio is achieved by transferring the weight of a mirror as directly and efficiently as possible through the structure. To reduce telescope weight, many techniques relating to mirror blanks and optical systems have been invented, such as the ribbed-back mirror on the Hale Telescope (Anderson 1948; King 1955); the thin mirror on the Keck Telescopes (Nelson 1979); and the multiple ribbed mirrors on the MMT (Meinel 1979). These approaches successfully reduced the mirror weight by 50 90% from that of a classical solid mirror. Techniques for figuring and measuring mirrors have also achieved f ratios as fast as f/2, resulting in weight reduction. On the other hand, not so much attention has been paid to the mechanical aspects. As for the optical support structure (OSS), the Serrurier truss had been employed in many telescopes since 1948 at the Hale Telescope (Rule 1948; King 1955). In the Serrurier truss, a mirror cell is supported with truss pipes from each end of a center section. Because the supporting span is larger than the aperture, large bending forces act on the mirror cell, and therefore both the mirror cell and the center section tend to be heavier to stiffen the OSS. When a Serrurier truss is employed, an OSS is required to be five to 10 times heavier than a primary mirror. 1 mikio@z.phys.nagoya u.ac.jp To achieve lightness, we introduce an innovative arc-shaped bearing system, using s for both the mirror support system and the bearing system. By using them, we are able to support a primary mirror and a turntable from directly beneath. Thus, we are able to eliminate a heavy center section. Furthermore, an azimuth (hereafter, Az-) structure can be shortened. Departing from a Serrurier concept, we can produce a stiff but light mirror cell and a compact mount, eventually. In 2, the design of the will be described. In 3, the drive mechanisms will be presented. In 4, we will deal with structural analyses and experiments. In 5 and 6, the performance of the mount will be described. 2. BASIC STRUCTURE OF MOUNT 2.1. Outline A photo of the mount is shown in Figure 1, and the features are illustrated in Figures 2 and 3. The mount can be divided into three sections: (1) the OSS; (2) the altitude (hereafter; Alt-) structure; and (3) the Az- structure. The OSS holds the primary and the secondary mirrors and an observational instrument at the Cassegrain focus. The secondary mirror is held in the hub, which is supported within the top-end hexagon via 12 beams. The 12 pipe pillars hold the secondary mirror in the top-end hexagon. Because the OSS is composed of a truss structure without a heavy center section, the total mass of the OSS without mirrors is only 1.4 ton. Figure 2 includes a drawing of the telescope carrying a planned mirror of 2.5 m in diameter with f/1.6 and an instrument at the Cassegrain focus. The OSS is already well balanced at this configuration, lacking a primary mirror. Mirror location is close to the Alt-axis. Therefore, it does not lose balance and does not increase the moment of inertia of the OSS as much as when a 266

2 ULTRA-LIGHTWEIGHT TELESCOPE MOUNT 267 Bed B Bed A rails blocks Pedestals Motor Motor Encoder rail & blocks FIG. 1. View of the telescope and temporary control room (blue plastic tent), placed in an open area on the campus of Nagoya University. mirror is located there. This configuration can accommodate an observational instrument of 900 mm in diameter and 1200 mm in length. As for the structures and rotations around the Alt- and Azaxes, we employed the arc-shaped bearing systems 3m Top-end hexagon FIG. 3. Details of the Alt- and Az- structures. The mirror cell is bolted to Beds A and B, and is rotated by the motor. The turntable is rotated by the motor and the position is sensed by an encoder encircling the turntable. (THK Co., LTD), which allowed us to reduce both the width and height of the telescope, as well as its weight. The parallel s provide Alt-rotation, interfacing between the mirror cell and the pedestals (Figs. 3 and 4). The in the Az- structure provides Az- rotation for the base, interfacing between the turntable and the base. The base is placed on the ground via six leveling blocks along a circle of 1.8 m in diameter. Furthermore, the truss members are separable because they are bolted to each other rather than welded. The mount can be easily disassembled and transferred. Hub 12-beams 2.2. Bearings for Main Axes 12-pipes 7m Elevation Axis Optical Support Structure (OSS) Mirror cell 2.5m Turntable Base Leveling block Altitude structure Azimuth structure FIG. 2. Views of the whole telescope (left: side view; lower right: front view; upper right: top view). The whole telescope is composed of (1) OSS, (2) altitude structure, (3) azimuth structure. False primary (diameter 2.5 m, f/1.6) and secondary mirrors and their light ray are described. A box inside the mirror cell is also a false instrument. The height of the elevation axis is 2.5 m. We note that the dimensions of the OSS depend on the optical design. We employed three s for a rotation mechanism of the Alt- and Az- axes; two for Alt-, and one for Az- rotation. The is composed of an arc-shaped rail and bearing blocks. The bearing blocks move only along the rail, being capable of receiving loads in all directions except in the traveling direction. Further details were described by Kurita (2004) Altitude Axis Two s are set in parallel on the beds, A and B (Fig 3). The beds are the foundation of the rails and serve as interface between the mirror cell and the Alt-structure. Bed A is also used for torque transfer to an OSS from a motor, while

3 268 KURITA, SATO, & NODA TABLE 1 Rail Rail DRIVE AND ENCODER PARAMETERS Alt Az Bed B Block EncoderTape Pedestal Pedestal Block Bed A Friction Surface Driven radius (mm) Deceleration :1 16:1 Drive resolution ( ) Drive torque (Nm) Moment of inertia a (kg m 2 ) b Encoder resolution ( ) Curvature radius (mm)... 1,551 1,110 a The moment of inertia for the moving mass without mirrors and instrument. b The maximum moment of inertia for the azimuth rotation; in the OSS, elevation is 30. FIG. 4. Cross section of the Alt- bearing system. In the blocks, caged metal balls guide the rail from four directions. The moving part of the system: the rails, together with the beds, slide around the Alt-axis. The six (3 2 sides) blocks are bolted onto the pedestals. The six R- guide blocks (three for each side) allow Alt- movement. Position sensing is on the Bed A side by the encoder; Alt- driving is on the Bed B side, through surface friction by the motor. bed B is also used for position sensing of an OSS location from a tape encoder. The separation between beds A and B, equivalent to that of the pedestals, is only 1.5 m. Therefore, the total width of the telescope becomes less than 3 m, even for a 2.5 m primary mirror. The diameter of each arc of the beds is 3.0 m with a central angle of 120 (Fig. 2). The center of the arc coincides with the Alt-axis, around which the OSS rotates in the elevation range from 90, i.e., zenith, to 30 above the horizon Azimuth Axis The OSS and Alt-structure, together with the turntable, are rotated around the Az-axis. The rail is located below the turntable. The diameter is 1600 mm, comparable to the 1.5 m span of the pedestals. Because the supports the weight directly beneath the bottom of the turntable, minimal bending forces arise. Therefore, a turntable as thin as 40 mm is thick enough to sustain the loads, and the height of the Azstructure (below the turntable) is only 0.5 m. Thus, we can achieve considerable compactness in both width and height, compared to conventional telescopes with primary mirrors of similar size. 3. DRIVE AND POSITION SENSING 3.1. Drive We used two AC servo motors (DM1A, Yokogawa Electric Corporation) separately to drive the Alt- and Az- rotations. The motors drive the Alt- and Az- rotations by a friction gear using gear ratios of 22:1, and of 16:1, respectively. The motor shafts are pressed onto the friction wheel with dish springs. The motor torque is transferred to the friction wheel (Figs. 2 and 3). Each motor contains a built-in encoder with a resolution of The resolution is given by dividing the resolution of the built-in encoder by the gear ratio. The parameters of the driving systems are summarized in Table Position Sensing For position sensing of the telescope axes, we employed incremental linear tape encoders (LIDA 487, Heidenhain) for both the Alt- and the Az- axes, with one reading head for each. The tape encoders are adhered with double-sided sticky tape to the side of bed B for the Alt-rotation (Figs. 3 and 4), and to the turntable (Fig. 3) for the Az- rotation. The reading head outputs analog signals, which are continuous sine and cosine waves with a wavelength of 20 μm. The resolutions attain 0:02 μm by conversion of the analog signal to digital by 10 bits, or 1024, through the interface card (IK121, Heidenhain). The linear distances along the arcs are converted to rotation angles; for Az- rotation, the conversion factor from the distance to the angle is obtained by dividing 360 degrees by the actual total pulse number 3: For the Alt-rotation, bed B is not a full circle but an arc. By measuring positions of stars and counting the pulses from the encoders, we calibrated the conversion factor for the Alt-rotation. We show the angular resolutions of both axes in Table 1. Note that an angular error due to thermal expansion should not arise, because the turntable, bed B, and the tape-encoder all are made of iron. 4. ANALYSIS OF THE STRUCTURE We employed the truss network cage (Fig. 2) instead of the traditional mirror cell to reduce the supporting span; here we describe the stiffness of the structure. We note a possible problem caused by the omission of the center section: the primary mirror is placed on the top plane of the truss network, while the secondary mirror is fixed at the top layer of the cage with long

4 ULTRA-LIGHTWEIGHT TELESCOPE MOUNT 269 pillars. We anticipate that the secondary mirror could sag, largely relative to the primary one, compared to the Serrurier truss. We ran an analysis of the truss using software (ADAM/ SII-GENE TIS Inc.), to estimate the amount of the deformation and the natural frequencies. We also performed simple experiments to confirm the analysis Static Analyses and Experiments We conducted both analyses and experiments at telescope elevations of 90 (zenith), 75, 60, 45, and 30 (Fig. 5). Analysis conditions are assumed, for simplicity: (1) The mass of each member is concentrated equally at each end of the trusses, so each of the trusses exerts half of the weight on each node. (2) The load exerted on the truss member (pipes and beams) is purely axial force. The truss members behave as a linear spring with a spring constant, k ¼ ES=L, where E, S, and L are Young s modulus, a cross section, and a length of the truss member, respectively. The material is steel with properties E of 205 GPa and a density of 7: kg m 3. (3) Constraint points are the truss nodes nearest to the blocks in each altitude (Fig. 5, upper panel). This analysis showed that the hub displaces perpendicularly to the optical axis. The lateral shifts of the hub relative to the mirror cell are shown in Figure 5. We measured the deflections at the same positions in the analysis (Fig. 5, upper panel) by using a theodolite at five orientations. The error bars are 30 to 40 μm due to tilts of the theodolite and/or the target mirror in Displacement [ µ m] Elevation angle [degree] Experiment Analysis FIG.5. Lateral displacements of the secondary mirror relative to the primary mirror. Ordinate: displacement; abscissa: elevation (degree). Vertical bars on solid line: the experiment; crosses on dashed line: the analysis. Upper figures: the fixed points assumed in this analysis are indicated by filled circles relation to the OSS. Data deviate substantially from the analysis. This discrepancy of 50 μm, however, should be regarded as being in good agreement, and is small enough to allow the optics to be adjusted by a mechanism on the secondary mirror, referring to the analysis results (Fig. 5) Dynamical Analyses and Experiments In controlling telescope motions, a servo loop between a command and a response is crucial for quick and accurate pointing and/or tracking: a computer sends commands to the motors to move to the programmed position, and receives the positional information from the encoders. The time interval between the command and the positioning is limited by the lowest of the natural frequencies inherent to the telescope structure. In the analysis, we found the lowest frequency to lie in the confined range of 16 to 19 Hz, after searching various cross sections of pipes without changing the truss configuration. All of these frequencies are in lateral displacement modes of the hub and the top-end hexagon. They are predominantly determined by the length of the 12 pipes and the weight of the top-end hexagon. Then, we measured the oscillation experimentally: we attached six accelerometers; two at the top-end hexagon, two at the 12 pipes, and two at the base. The OSS was struck with a hammer, and the signals from the sensors were put into a fast Fourier transform (FFT) analyzer. The most dominant mode appeared at 16 Hz, and the next one at 10 Hz. Our analysis simulated only 16 Hz, but the 10 Hz was unexpected. The latter mode probably was due to the boundary condition that the whole telescope was simply placed on the ground via the six leveling blocks, not fixed to the ground in this test. The 16 Hz oscillation arises from two modes: the lateral displacement of the entire structure, and the string vibration of each component of the 12 pipes. The latter is not derived in our truss analysis, because the bending mode of the members is not taken into consideration. We executed another FEM analysis on one piece of the 12 pipes (diameter 60.5 mm, thickness 3.2 mm, length 3750 mm). The result showed a natural frequency of 15.7 Hz, which agrees well with the experimental value. We conclude that the lowest frequency satisfies the requirements for the pointing/tracking accuracies. 5. INSTALLATION OF THE MOUNT 5.1. Assembly of the Mount We here demonstrate the transportability of this telescope mount. We first assembled the entire telescope, except for the primary and secondary mirrors, in the laboratory. In the morning of 2005 October 31, we disassembled it into three parts: (1) the 12-pipes; (2) the Alt-structure with the mirror cell; and (3) the Az- structure. We transported these parts to an open area on the campus, together with the telescope controller and an electric power generator on a truck equipped with a small

5 270 KURITA, SATO, & NODA crane. We placed the Az- structure on the six leveling blocks arranged horizontally, and then adjusted the Az-axis so as to point to the zenith. We mounted the Alt-structure on the Azstructure, and roughly checked the perpendicularity of the Alt-axis relative to the Az-axis, using a theodolite. Next we joined the 12 pipes and the top-end hexagon onto the mirror cell at the six nodes, and balanced the OSS with dummy loads. Finally, we set the motors and the encoder heads for both the Alt- and Az- axes, and wired them in the telescope controller. This sequence of activity took six hours and was finished in the afternoon. That night, we started the telescope analysis for the whole assembly, and continued experiments in the open air for three weeks. Note that the primary and secondary mirrors, as well as the enclosure, were not included in this experiment, as shown in Figure 1. Alt Error [arcsecond] Pointing Error 5.2. Mechanical Adjustments and Software Corrections We measured the misalignment of the assembly and corrected them. This is telescope analysis, an analysis tool to detect misalignments and flexure of the telescope mount. The misalignment and flexure are expressed with seven parameters: (1) an offset of a zero-point for the Alt- encoder; (2) an offset of a zero-point for the Az- encoder; (3) a tilt for the Az-axis to north; (4) a tilt for the Az-axis to west; (5) nonperpendicularity of the Az-axis relative to the Alt-axis; (6) nonperpendicularity of the optical axis to the Alt-axis; and (7) flexure of the OSS. We used T-Point software (Software Bisque, Inc.) to detect errors by observing 30 stars distributed uniformly over the sky with a small refracting telescope attached to the mirror cell. After the analysis, we first adjusted the errors mechanically for parameters 3 and 4 by using the leveling blocks, for 5 by inserting thin metal plates with various thicknesses between the turntable and the pedestals, and for 6 by aligning the attitude of the refracting telescope. Then we repeated the telescope analysis using 70 stars, and corrected the residual errors for each parameter. Final values from parameters 1 to 7 were input to the controller at 24, 20, 7, 7, 40, 25, and 22, respectively. Eventually, a pointing accuracy of 3 was achieved at the end of the night (see Fig. 6) 6. EVALUATION OF THE PERFORMANCE In an imaging observation, pointing error of several arcseconds is required to expedite the data analysis, combining and tiling images with matching point sources. Tracking error of 0 :5, which is similar to or less than typical seeing size on an astronomical site, is required for sufficient image quality. A usual continuous exposure time is less than one minute in infrared, and 10 minutes in optical range. In a spectroscopic observation, which needs long exposure time, tracking accuracy for longer times is not required because such an instrument is usually equipped with an autoguider to correct the tracking error Az Error [arcsecond] FIG. 6. Pointing accuracy: distribution of errors after telescope analysis using 62 stars. Dashed circle shows the standard deviation of Pointing Accuracy Following the telescope procedures, we tested the pointing and tracking accuracies. We defined pointing error as the angular separation between the image center of the small refractor and the position sensed by the encoder. We defined pointing accuracy as a root mean square of the pointing errors for 62 stars. We obtained a pointing as accurate as 3.0. Figure 6 shows the distribution of the pointing errors along the Alt- and Azaxes. The errors may arise predominantly from the loose ground. The pointing accuracy could be improved if the telescope were placed on more solid ground Tracking Accuracy We measured the tracking errors for 64 stars at various altitudes 30 above the horizon. We took 100 images of an object for 10 minutes during tracking. Tracking error was defined as the deviation of the object from the cross-wire of the refracting telescope; we obtained a tracking accuracy of better than 0.5 (Fig. 7). Figure 7 shows the tracking error against the altitude, together with the measurement limit by seeing. The tracking error increases with altitude. This is because the speeds of both the azimuth and the image rotation increase toward infinity at the zenith for the altitude-azimuth mount. These accuracies of pointing and tracking are sufficient for short-exposure observations of a few minutes for imaging without an autoguide system. In these experiments, a primary mirror and an instrument were not loaded. If the loads are assumed to be 2.5 tons and

6 ULTRA-LIGHTWEIGHT TELESCOPE MOUNT 271 Tracking error [arcsecond] /cos(h) fit measurement limit 11/16 11/17 11/18 Tracking error - Al Altitude angle (h) [degree] FIG. 7. Tracking accuracy: errors for 64 stars from the center of the crosswire. Ordinate: tracking error for target; abscissa: altitude h in degrees. Dashed line: measurement limit due to seeing of 1. Solid curve: 1= cosðhþ is the bestfit for the 64 data points, taken for three nights. 0.5 tons for the mirror and the instrument, respectively, the deformation of the mirror cell increases to 60 μm by 40 μm. However, they can be compensated well by the telescope analysis. On the other hand, the tracking accuracy is severely affected by the moment of inertia around the OSS and the natural frequency. The moment of inertia of the OSS is 5000 kg m 2, without the mirror and the instrument (see Table 1). When the mirror and the instrument are located at distances of 0.2 m and 1.0 m, respectively, from the Alt-axis, as shown in Figure 2, the moment of inertia is increased by 2000 kg m 2. Although a load of 3 tons was added, i.e., two times the load of the OSS, this is only 40% of the value 5000 kg m 2 without the loads, due to the proximity of the distance between the mirror and the Alt-axis. The natural frequency falls to 15 Hz, only 1 Hz from the value 16 Hz estimated in SUMMARY We developed a lightweight and compact telescope mount using s for both the Alt- and the Az- axes. The compact bearing system for the Alt-axis supports the mirror cell underneath and provides a stiff but lightweight structure and a short Az- structure of only 500 mm. The mount is able to support a mirror of up to 2.5 m in diameter, but weighs only 5 tons without mirrors, and is 7 m in height. For the optical support structure, we used a truss structure. We disassembled, transported, and reassembled the mount within one day. Subsequently, we carried out pointing and tracking tests for three weeks. Finally, we obtained acceptable accuracy, 3 for the pointing error and 0.5 over 10 minutes for the tracking error. We would like to express thanks to H. Achiwa and R. Nagase for their assistance in construction and data analysis. We would also like to thank Drs. H. Kunieda, H. Kimura, H. Okuda, and J. Storey, whose suggestions and comments helped us to improve the paper. REFERENCES Anderson, J. A. 1948, PASP, 60, 221 King, H. C. 1955, The History of the Telescope, (London: Griffin) Kurita, M., Sato, S., Morishima, K., Achiwa, H., Ito, H., Nagata, T., Noda, N., & Koiso, N. 2004, SPIE, 5495, 518 Meinel, A. B SAO Special Report, 385, 9 Nelson, J., 1979, SPIE, 172, 31 Rule, B. 1948, PASP, 60, 355, 225