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Structure

Structure

Introduction

The overall image size budget is given in MILT Description. The line item which applies to the telescope structure is tracking. Since the control system makes use of a portion of this item we propose the following sub-budget which separates the control system allowance from that of the structure.

Item                            Allowance (arc sec)
Wind loading
      Structure                 0.05 rms
      Control system            0.02

Misc control system error
      Uncorrelated with wind    0.04

Total tracking error            0.08

In this budget the first and second items are assumed to be correlated and to add algebraically. The third item is summed in quadrature.

The above budget applies for a mean wind speed of 5 m/s. While it is a simple problem to calculate structural deflections due to a constant velocity wind, it is much more difficult to calculate the image degradation due to realistic (dynamic) wind loading. One could imagine doing a full dynamic finite element structural analysis using a sample of experimentally measured wind loading vs. time as the driving function, calculate the image position at each time step and thereby derive a rms spot size. While this would be laborious and would require a lot of computer time, the results would only apply to the particular driving function which was chosen and would not be generally applicable unless an impractically long time history was calculated.

For now we take the simple approach of assuming the rms image motion due to amean wind speed of 5 m/s is equal to the image displacement due to a constant wind velocity of 5 m/s. This is a crude approximation and will no doubt be replaced later with a more satisfactory way of relating mean wind speed to image motion.

Optical Support Structure

Purpose

The optical support structure (OSS also referred to as the tube) supports the optical elements of the telescope, maintains their co-alignment, and provides pathways for cables and ventilating air.

Constraints

Ideally the OSS should always maintain perfect alignment and pointing of the optics. This is impossible due to gravity, temperature gradients and wind. Gravity is the largest force on the OSS and produces up to 250 micron deflection of the structure. It is the least troublesome since its effects are predictable and can be corrected. Gravity does excite hysteresis in the structure which cannot be predicted but can be minimized in the OSS by design and appropriate fabrication.

A uniform temperature change causes defocusing of the image due to the difference in the coefficients of expansion of glass and steel. Refocusing compensates for this effect. Temperature gradients cause the OSS to distort slightly causing pointing uncertainties. This effect can be largely prevented by designing the OSS to have a high degree of symmetry, by making the wall thicknesses of members equal where appropriate so that cooling rates will be uniform, and by insuring that the members have low infrared emissivity to prevent asymmetries in the IR radiation field from coupling into the OSS.

Wind loading is by far the most troublesome effect, both quasi-static loading which elastically deforms the structure and dynamic effects which tend to excite the natural vibration modes of the structure. Nelson (1983) has summarized the effects of wind loading on image motion.

The effects are the rotation of the optical axis (defined by the primary mirror), the tilt of the secondary with respect to the optical axis, and the translation of the secondary with respect to the optical axis. To this list could be added the displacement of the detector, which is usually ignored since it is very small in reasonable designs.

These motions of the optical elements are very small so their effect on telescope collimation is negligible. Instead the motions produce time varying motion of the stellar image as the wind changes direction and speed. This results in image enlargement for integrating imaging detectors and the loss of light hitting the slit in the case of a slit spectrograph. Nelson gives formulas relating image motion to the motions of the optical elements.

Measurements by Forbes (1983) at the MMT indicate that the top end of the telescope is only slightly protected from wind loading by the MMT building when the telescope is pointed into the wind. Our enclosure is likely to be "efficient" in the same sense as the MMT (it will fit the telescope closely for reasons of economy) and is not likely to provide much shielding either. The wind problem is aggravated because the telescope is likely to be pointed toward the west and southwest preferentially as astronomers chase objects toward the horizon. This is the direction of the prevailing winds at SPO.

Traditionally wind screens have been used to protect telescopes from wind loading. Beckers and Williams (1982) have reported that the MMT wind screens degrade the image quality by preventing the flushing of heat out of the telescope chamber. For this reason the wind screens at the MMT are not normally used.

If use of wind screens must be avoided to preserve image quality then wind loading effects will be very difficult to overcome. (The MMT side steps the problem by essentially building a large telescope out of a number of small and therefore stiff telescopes.)

The problem is compounded by relatively new realization that ground based image quality can be very good and that ground based telescopes should be designed to take advantage of exquisite seeing (Woolf 1982). As a result the overall error budget for image quality is tight and the portion allotted to wind loading is meager.

Our response is to use wind screens to shield the telescope when the mean wind speed is higher than 5 m/s (11 mph). The enclosure design minimizes the amount of heat generated and stored in and around the telescope. We expect to have a greatly reduced need for air flushing as compared with the MMT and the higher wind speeds will provide effective forced ventilation even with wind screens in use.

Meeting the structure performance requirement still means dealing with wind loading effects beyond what is needed in the design of traditional well-protected large telescopes. The top end (including its supporting truss) will have minimal effective area for wind loading constrained by the requirement that the lowest natural frequency of the structure be greater than 10 hertz.

The design of a sufficiently stiff OSS is eased greatly by the choice of a very fast f/ratio for the primary mirror. A still faster f/ratio would be desirable from the standpoint of the structural design but is much more difficult from the optical fabrication point of view. It is likely that f/1.75 is a good compromise between the optical and structural constraints.

New requirements may demand new solutions. Novel approaches under consideration include shielding the members of the upper structure with with close fitting shields attached to the OSS center section thereby greatly reducing the wind loads applied to the truss and the secondary support structure. Alternatively the state variable tracking control system we propose to implement (see section 4-2) can be modified fairly easily compared to a classical control system to accept more inputs. This suggests that wind loads could be sensed with appropriate transducers and pointing errors could be corrected by the control system. Clearly a novel approach is justified only if there is no other cost effective solution, the risk is reasonable, and the requirements cannot be relaxed.

Description

Figure 3.1 is a perspective view of the telescope. The box-like center section of the optical support structure near the middle of the figure couples the OSS to the fork via bearings in the two fork arms. The primary mirror cell is attached to the underside of the center section. The altitude drive disk is mounted on the centerline of the primary mirror cell so that its center of curvature is at the altitude axis. The secondary is mounted at the top end of the truss. The secondary assembly consists of a square frame (referred to below as the "top ring") and 8 tension members which support the secondary backup structure.

A number of elements of this design require additional explanation. The secondary support vanes are tensioned to a strain of about 0.0002. Though their cross-section is only 150 mm^2 the natural frequency of vibration is high. The vane tension insures that the forces in the vanes always remains tensional. The vanes act to stiffen the peripheral square frame. The vanes extend nonradially from the secondary backup structure; the attachment points are not 90 degrees apart. This adds torsional stiffness to the secondary cell. The MMT secondaries are supported in this manner. Note that the diffraction pattern produced by the four sets of vanes will be degenerate producing four spikes as in traditional telescopes. The spikes will not be at right angles to one another however.

Each axis of the telescope will be driven by a small roller friction coupled to a large (2 m radius) drive disk attached to the driven structure (section 3-4). Friction roller drives are supplanting the traditional large diameter precision spur gears for drive purposes because of the high cost of the latter (~$300k each for the RGO 4.2 m).

The square frame at the top end is also a departure from tradition though the 1.8 meter Steward transit telescope also will have a square top end (McGraw et al. 1982). A square frame is cheaper to fabricate and is a more efficient structure than the traditional circular front ends since the members act as truss elements rather than beams.

The attachment of the truss to the OSS center sections also requires comment. The truss attachment points are at the midpoints of the sides of the center section instead of at the traditional four corners. This change results in very short and direct load paths from the truss to the altitude bearings and drive disk (if the drive disk is mounted at the midline of the back of the mirror cell).

The more traditional geometry with the drive disk mounted near one axle and with the truss mounted at the four corners of the center section was also investigated. In this configuration the center section required much more mass to prevent wind loading on the truss from causing objectionable torsion near the axle opposite the drive disk. In the current design the deformation of the truss is the dominant cause of image motion due to wind induced OSS deformations.

Clearly when the telescope points at the zenith the center section will sag under the static load. Early in our analysis we were concerned that this deformation would propagate to the top end and cause degradation of the performance of the secondary support assembly; the deformation could be sufficient to cause some of the vanes to go into compression where upon they would buckle. Fortunately finite element modeling indicated that in a typical model the tension in the vanes changed by less than 30% in going from the horizon to the zenith, and this is perfectly acceptable.

The present attachment points for the truss results in an efficient envelope for the OSS motion; if the truss were rotated 45 degrees the corners of the square top end would extend well beyond their current positions.

The sag of the primary cell is small; the drive disk can be mounted to partially compensate for the sag in order to minimize the compliance required in the drive and encoding mechanisms.

Traditionally (since the design of the 200 inch) the secondary and primary mirrors of large telescopes have been mounted at opposite ends of a Serrurier truss designed to sag equally at both ends thereby keeping the two mirrors collimated.

For modern fast primaries this strategy is neither practical nor necessary since the center of gravity of the OSS lies very close to the primary mirror. In the case of short telescopes, tube deflection can be kept so small that simply retilting the secondary mirror restores high image quality (Barr et al. 1979).

Finite Element Model

Figure 3.2 shows a finite element model of the optical support structure. All elements have been shrunk 20 % in this figure so that interior elements would be visible. Only half of the OSS was modeled to reduce the required computer time and the effort needed to define the model. (All analysis was performed using software supplied to us under an educational agreement by Swanson Analysis Systems, Inc., Houston, Pennsylvania 15342). The symmetry of the model about the y-z plane and the symmetry or antisymmetry of the loading cases was used to define appropriate constraints on displacements and rotations of nodes on the symmetry planes.

The following table lists the element types used in the construction of the model. The center section is built of quadrilateral membrane shell elements. It is a honeycomb-like structure with the large inside and outside surfaces separated by orthogonal sets of elements forming six-sided cells. The actual structure would be fabricated in a somewhat different way but a welded plate structure with appropriate stiffeners and webbing should have approximately the behavior predicted by the model. The mirror cell is constructed in a manner similar to the center section. Membrane shell elements were also used to construct the drive disk. Membrane shell elements have no bending stiffness. In the analysis described below the performance of the center section, mirror cell and drive disk should be dominated by the in plane properties of the elements so membrane elements should be appropriate.

        OSS Subsection          Element Type

        Mirror cell             membrane shell
        Drive disk              membrane shell
        Center section          membrane shell
        Truss                   3-D spar
        Top ring                3-D beam
        Secondary vanes         3-D spar
        Secondary supports      membrane shell

The mass of the primary and its support structure is modeled by mass elements at the nodes of the front surface of the mirror cell. Similarly the secondary mass is modeled by a mass element at the central node on the appropriate surface of the secondary mirror support structure. The model includes only the weight of the mirrors. In the real structure the mirror weight also applies a torque to the structure since the mirror CG is well in front of the surface of the mirror cell. A better model would explicitly include these torques but should not change the results described here very much.

Constraints due to bearings are infinitely stiff in the model. These will be replaced by springs of the appropriate stiffness as parameter values become available.

The tertiary supporting structure has not yet been included in the model; consequently all analysis of image motion due to wind loading assumes no motion of the tertiary.

All plates are 6.35 mm (0.25 inch) thick steel except for the drive disk which is 12.7 mm (0.5 inch) thick. The truss elements are 76 mm (3 inch) steel tubes with 12.7 mm (0.5 inch) walls. The top ring elements are 76 mm (3 inch) steel tube with 6.35 mm (0.25 inch) walls. The spider vanes have across-sectional area of 150 mm^2 (0.23 square inches) each. The mass of the primary mirror and its supports is astatic supports is 3150 kg and the secondary mirror mass is 44 kg.

The mass of the half model including mirrors is 4980 kg and its moment of inertia about the altitude axis is 17400 kg m^2.

Three loading cases are described below.

1. Static loading with the OSS pointed at the zenith.
Figure 3.3 shows (greatly exaggerated) the deformation due to this loading.
2. Static loading with the OSS pointed at the horizon.
Figure 3.4
3. Wind loading with the OSS pointed at the zenith and wind coming straight in from the slit
Figure 3.5

Symmetric boundary conditions at the symmetry plane were used for all three cases. The results are summarized below.

1. Gravity in the -Z direction (pointed at zenith)
Sag near the center of primary mirror cell is 75 microns. If the tertiary is attached here this will be its displacement as well.
Drive disk sag is 75 microns.
Secondary mirror cell sag is 460 microns.
2. Gravity in the -Y direction (pointed at horizon)
Sag of primary is 26 microns (this will be the displacement of the tertiary as well).
Tilt at tertiary attachment point is 1.1 arc seconds.
The drive disk sags 23 microns.
The secondary sags 268 microns. Rotation is almost zero.
3. Wind loading on top end in the Y direction: Wind loading corresponds to a 5 m/s wind speed.

	Raw values

	Secondary displacement           1.711  microns
	Secondary rotation               0.0
	Primary rotation                -0.0397 microrads
	Primary displacement            -0.0113 microns


	Relative to primary optical axis              Image motion

	Secondary displacement   1.481 microns        0.041 arc sec
	Secondary rotation      -0.0397 microrads    -0.004 arc sec
	Primary rotation         0.0397 microrads     0.008 arc sec
	total                                         0.045 arc sec

The static displacement of the secondary mirror with respect to the optical axis is within the range of motion which can be optically compensated by retilting the secondary.

We have not yet done a modal analysis (calculation of the lowest natural frequencies of a structure), though the static analysis indicates that all modes should be well above 10 Hz. Hand calculations have shown that the truss elements and vanes have natural frequencies above 10 Hz.

No temperature loading has been applied to the structure as of this writing. These calculations will indicate the sensitivity of focus and collimation to temperature gradients in the OSS. The effect of temperature gradients on pointing will be explored also.

Bearings

Requirements

To be practical, altitude bearings should be low friction, tolerant of misalignment and capable of moderate axial thrust forces to allow preloading across the fork tines. Inner race diameter is set by Nasmyth field diameter requirements and will be on the order of 0.5 meter.

Description

For discussion purposes we propose using a spherical roller bearing at each Nasmyth position. The bearing candidates are selected Torrington Series 239 self-aligning spherical roller bearings. Models in stock cover the range from 140 mm to over a meter bore diameter.

Specifications of radial runout, smoothness and friction, repeatability of errors, axial loading, etc are only available for off-the-shelf versions. Substantial improvements in all specifications can be achieved at moderate cost by selection and remanufacture.

Primary Mirror Support

Purpose

Ideally the primary would be supported as if suspended totally immersed in afluid whose density matched that of the glass. In practice such a condition can at best be approximated and with the added constraint that the mirror orientation must remain fixed with respect to the telescope OSS.

Description

Two classes of mirror supports are now in common use. These are the pneumatic 'air bag' support and the counterbalanced mechanical lever mechanism. Mechanical linkage supports are clearly more complex than air bags, being especially challenging in the case of equatorially mounted telescope in which the primary mirror both pitches and rolls and thus requires full omnidirectional radial support.

For an altitude-azimuth telescope the support geometry need only handle pitch in a vertical plane. A very elegant concept which satisfies this requirement has been suggested by Roger Angel (see Figure 2.9) and is currently under development by Larry Barr and colleagues at Kitt Peak for use with a 1.8 meter honeycomb mirror to be tested in the MMT late next year.

The mechanism consists of links forming a pantograph type geometry. The position of one parallelogram pivot is fixed with respect to the mirror cell and serves as a fulcrum for an effective lever whose loads are the counterweight at one end and the mirror at the other. The pantograph geometry preserves a constant lever ratio despite changes in the shape of the parallelogram. In this way the mechanisms may accommodate themselves individually to each mirror load point for all angles in an altitude quadrant between 0 and 90 degrees while applying at all times a constant reaction to gravity.

The airbag alternative support is mechanically less complex and somewhat less massive than mechanical lever supports but requires an actively regulated air supply. Since it inherently provides only axial support some supplementary in-plane support would be required.

The number and positions of such 'astatic' supports necessary to preserve the optical mirror figure at all operating orientations is determined by finite element structural analysis and depends on mirror geometry, thickness, and optical performance constraints. Such an effort will be needed for the MILT 3.5 meter honeycomb mirror and will be commissioned in early 1984.

Secondary Support

Purpose

The mechanism connecting the secondary mirror to its backup structure allows positioning adjustments for initial optical alignment at installation time. It also provides for active real time collimation and focus.

Description

It is intended that the computer controlled motions will be determined by an iterative type algorithm which optimizes collimation and focus automatically using data from the analysis of CCD camera images. Information generated by this algorithm, run off-line during engineering time, will then be used to implement static open loop collimation and focus correction. This capability will be exploited during initial telescope installation and setup as well.

Mirror Supports

The secondary suspension is designed to provide generalized microprocessor control of piston, tilt and offset in any position angle. A link geometry which fully determines the mirror orientation is shown in Figure 3.6. Five degrees of freedom are provided by five actuators (TBD) to control the lengths of 5 of the 6 links.

The mirror is a Pyrex honeycomb structure 80 cm in diameter attached at the three corners of the triangle labeled A, B, and C. The mirror and the structure represented by the triangle then move as a rigid unit.

Two of the three links lying in the plane normal to the optical axis just behind the mirror provide roughly orthogonal mirror offsets by virtue of their length control actuators. In Figure 3.7 the triangle is shown offset as a result of changing a single link length. Notice that even over this exaggerated range of motion, the link end and the triangle (ie. mirror) center follow roughly parallel paths of roughly equal lengths.

Length control of one additional link provides roughly orthogonal freedom of positioning. The third link has a fixed length.

The three remaining links lying parallel to the optical axis provide piston and tilt. Piston is converted by the linkage geometry into harmless secondary revolution about its optical axis, allowing the offset links to freely move out of a plane without any tension or compression buildup.

Obviously all motions interact and one would hesitate to construct such a mechanism were it to be adjusted by hand. Modern microprocessor control technology happily allows full exploitation of the mechanical simplicity of this arrangement. Its control firmware will synthesize the combined link motions necessary to allow effective orthogonality of control commands from ahost computer.

Stiffness

All links act as truss elements carrying all loads in tension or compression. There will be no static or dynamic load reversals in practice. Link pivots will be implemented by omnidirectional flexures since all angles will be small. Flexures have the advantages of low cost, simplicity, high axial rigidity, high reproducibility and zero backlash.

Moreover since the secondary and its mechanism will at all times be shielded from wind, the dynamic performance requirements are comfortably minimal.

Motion Resolution

Since we can use the motion system to actively keep the telescope in collimation and focus, image motion resolution must be no larger than 0.05 arc sec per step.

Linear offset is given by

where f1 is the primary focal length, f is the telescope focal length, and is the image angular offset.

For the 3.5 meter f/1.75 - f/10 telescope secondary mirror tilt is given by

where D2 is the secondary diameter and D1 is the primary diameter. For the same telescope this value is

Motion Ranges

Piston range will be +- 3 mm. This corresponds to approximately +-100 mm at the Nasmyth focus. This is a much smaller range than is provided at most current Cassegrain foci. It is more than adequate in this case since we will enforce parfocality of all instruments.

The 6 mm range will help simplify initial focus at telescope assembly time, allow sufficient range to actively compensate differential sag of primary and secondary supports, and compensate thermal extension and contraction of the telescope OSS (partially compensated by changes in the optics with temperature). The piston range required for tilting is negligible by comparison.

A radial offset range of +- 3 mm min will also be provided, again to facilitate initial telescope collimation and relax some manufacturing and assembly tolerances.

The offset range necessary to compensate gravity deflection is only about 0.25 mm.

Actuators

Stepper motors will probably be used since motion rates need not be high and they offer the simplicity of self encoding (after a reference has been identified) and can be completely powered down during nonoperation to eliminate heat dissipation in the optical path. A mechanical method of converting a motor step to the required link length increment will be required.

Orientation reference

Sensors to provide known actuator position references will be needed. This requirement is currently being studied to identify possible design alternatives.

Secondary removal

The secondary will be removable along with the rest of the secondary assembly including the top ring to allow installation of an IR secondary assembly or the removal of the primary mirror. The details of the attachment of the secondary to the OSS truss are yet to be determined.

Tertiary Support

Purpose

The tertiary support includes all suspensions, actuators, shrouds and structure that transfers tertiary loads to the telescope structure. In provides structural support for the tertiary mirror, adjustments for its position and angle, adequate stiffness and/or compensation for structural deflections with altitude, and rotation about the tube optical axis to direct images to detectors at both Nasmyth positions and perhaps some additional positions in between.

Description

The tertiary is essentially hanging from the end of a cantilever beam attached to the primary mirror cell. To maximize the beam depth and thereby maximize its stiffness, all possible use is made of the secondary shadow area and the corresponding large primary perforation. To minimize the beam length, and again maximize its stiffness the tertiary is located as close to the primary surface as Nasmyth extraction clearances and altitude balance will allow.

Bearings

At the sky end a large diameter Kaydon ball bearing is used and a smaller diameter pilot bearing is used at the other end. The geometry is similar to the telescope azimuth axis.

Actuator and Detents

The tertiary rotation is powered by a 360 degree rotary air actuator. Mechanical stop bars, each individually adjustable, can be deployed against which a dog on the mirror rotator presses. The stop bars are held in place with electrical solenoids until engaged by the rotator dog. Actuator pressure is maintained to hold a preload on the selected stop bar allowing the solenoid current to be cut off. When another tertiary move is required, preload pneumatic pressure is vented allowing a return spring to retract the selected stop bar.

This mechanism is highly repeatable, has few and simple moving parts, uses all standard industrial components (actuator, solenoid, etc.), and dissipates no heat. More glamorous servo technology was considered but was rejected because it costs more, and servo deadband jitter adds to the image size.

Tertiary Mirror

Since there is ample room in the secondary shadow, a circular rather than elliptical flat will be used since it is a more straightforward blank to manufacture, and correspondingly easier to figure. According to Woon-Yin Wong (personal communication) it is likely that a simple three point suspension will be adequate to preserve the optical figure of a honeycomb flat this size (about 65 cm).

Removal and Handling

A top segment of the tertiary baffle cone will be made removable at a joint just safely above the highest extent of the tertiary mirror. The remaining portion of the tertiary baffle will be a heavier structure.

Before removing the primary mirror it will be simple to replace the baffle top segment with a stiff plate having a lifting eye at its center. The entire tertiary structure including structural baffle, rotation mechanism and mirror can lifted away vertically with complete safety.

Azimuth Turntable and Fork

Purpose

The azimuth turntable directly supports the Nasmyth instrument loads, provides azimuth rotation, and by means of vertical fork tines couples to the telescope OSS allowing altitude rotation. Hollow altitude bearings allow passage of the Nasmyth beam. All connections between the telescope and the outside world ultimately pass through this structure.

Description

Cone

The entire moving mass of the telescope is carried on a rotating vertical axis turntable resembling a cone, apex down. A single spherical roller thrust bearing at the apex allows azimuth rotation and carries the entire moving telescope weight.

A rolled or segmented shell with a conical outline connects this bearing with the large diameter friction drive disk about 4 meters above. The rim of the drive disk is ground cylindrical and constrained by guide rollers around its periphery, at least one of which transfers azimuth drive motion from a DC servo motor via a friction reduction drive train.

Platform, Forks, and Nasmyth Platforms

The azimuth cone supports a large welded plate beam which supports the fork tines and extends beyond the tines thereby providing the Nasmyth platforms.

Finite Element Performance

We have done preliminary finite element calculations for the fork. Only one quarter of the fork was modeled to reduce the required computer time and the effort in defining the model. The symmetry of the model about both the x-z and y-z planes and the symmetry or antisymmetry of the loading cases was used to define appropriate constraints on displacements and rotations of nodes on the symmetry planes.

Finite Element Model

Figure 3.8 shows the finite element model of this structure with the elements shrunk 20% to make it easier to see the interior elements. The cone is a conical shell with an interior drive disk near the top. The platform consists of large top and bottom plates with orthogonal elements separating the two surfaces thus forming a honeycomb with quadrilateral cells. The fork tine is a similar structure with the two sides connected together with webbing. While the structure would not be fabricated in precisely this manner a more realistic welded plate structure with appropriate stiffeners and webbing would have approximately the performance of the model. The cone is modeled rather roughly with 30 degree segments; abetter model would have 15 degree or smaller segments.

The cone and drive disks were modeled using quadrilateral shell elements which have both bending and membrane capabilities while the platform and forks were modeled by quadrilateral membrane shell elements which have no bending stiffness. The performance of the forks and platform should be dominated completely by the in plane properties of the elements so membrane elements should be appropriate.

The displacements of the nodes at the base of the cone were constrained vertically and radially. The two nodes on the outer diameter of the drive disk which were on the x-z and y-z symmetry planes were constrained radially. In addition one of these nodes was constrained tangentially. These constraints will be replaced by springs as the stiffness of bearings and guide rollers are determined.

All plates were 12.7 mm (0.5 inches) thick steel except the azimuth cone where the plates were 25.4 mm (1.0 inch) thick. Only a minor attempt was made to optimize thickness of members. No attempt was made to optimize the geometry of the structure. The mass of the 1/4 fork was 4762 kg and its moment of inertia about the vertical axis was 18100 kg m^2.

Wind Loading and Image Motion

Wind loading was modeled using two cases:

1) With the telescope pointed at the zenith, we consider wind blowing in the y direction. This results in forces in the y direction at the tops of the fork tines due to wind loads on the OSS. This is presumably the worse-case wind loading since it corresponds to the wind blowing straight in through the slit and on to the telescope. Figure 3.9 shows (greatly exaggerated) the deformation due to this loading; the undistorted structure is shown by the dashed lines.

2) With the telescope pointing at the zenith, wind blowing the x direction causes x loading at the tops of the fork tines as well as anti-symmetric z loading across the yz plane on the fork tines. The effect of both the x loading and the z loading is to to twist the fork about the y axis. Distortion due to this load case should not be as serious as for case 1 since the enclosure should be effective in shielding the telescope from much of the x component of the wind. Figure 3.10 shows the deformation of the fork due to x loading.

The results of the finite element calculation are given below. The applied forces refer to full model forces rather than those applied to the 1/4 model.

	Case 1: Force on fork tines
	Applied y force                      200 N
	Resultant fork y displacement        0.77 microns

	Case 2: Force on fork tines
	Applied x force                      200 N
	Resultant fork z displacement        0.65 microns
	Applied y torque                     514 N m
	Resultant fork z displacement        0.27 microns

From these results it is straightforward to calculate pointing errors due to wind loading.

	Air density (2800 meters altitude)         0.90 kg/cubic meter
	Wind loading (5 m/s with drag coef = 1)   11 N/square meter
	Fork tine separation                       3.8 meters
	Drive disk radius of curvature             1.8 meters

We consider wind loading on the upper end of the OSS including the truss and secondary baffling.

	Effective area of upper end of OSS         3 square meters
	Moment arm                                 5 meters
	Wind force on upper end of OSS            33 N
	Wind moment                              170 N m

For case 1 the force on the fork ends is 38 N which results in a y displacement of 0.15 microns. Due to the encoder location on the drive disk and its reference to the apex of the azimuth code the control system prevents telescope motion other than rotation about the apex of the azimuth cone (see Figure 4.5 for the geometry). This results in an angular motion of 0.004 arc sec.

For case 2 the x force on the fork arms is 33 N giving a z displacement of 0.11 microns. The moment applied to the tops of the fork arms is 170 N m giving a z displacement of 0.09 microns. Superposition of the two deformations results in a pointing error of 0.008 arc sec.

The fork errors will be correlated to a large extent with the errors due to the deformation of the OSS and the error in the control system due to wind loading and will add algebraically rather than in quadrature.

In both cases the largest stresses were in the short beam section of the platform between the top of the azimuth cone and the base of the fork tine suggesting that the performance of the structure could be substantially improved by adding some material in this region. Also the webbing thickness in the platform and the fork is probably much thicker than it needs to be and it is likely that the webbing weight could be reduced.

Modal Analysis

A modal analysis (a calculation of the lowest vibrational modes and their frequencies) has not been done yet. Based on the static deflection analysis the natural frequencies of the fork are estimated to all be well above 10 Hz.

Thermal Performance

We plan to analyse the behavior of the model under thermal loading in order to calculate how sensitively pointing errors and Nasmyth platform tilts and displacements depend on temperature gradients in the fork.

Bearings

Main Load Bearing

The pilot and load bearing at the cone apex is a stock model selected and possibly reground at the factory for guaranteed smoothness and low friction. It is a spherical thrust bearing tolerant of several degrees misalignment, a feature we hope to exploit to simplify the cone design, fabrication and installation.

Thrust Loading

Surface denting or 'Brinelling' can occur if the bearing surfaces are overstressed. The bearing chosen for the final telescope weight will be derated to guarantee no permanent Brinell deformation.

Radial Loading

Radial load limitations which normally apply to spherical thrust bearings in combined load applications will not apply since radial loads are essentially zero. The only minor exception is a radial load of about 450 N (100 lbs) under maximum operating wind loads. Since the roller tilt is approximately 45 deg, this resolves into no greater than 450 N of lift, a negligible amount.

Accuracy

About 1 arc sec of azimuth tilt is contributed by 10 microns of runout. This is a typical value for selected production bearings. It is not necessarily important that this value be small, but it should be repeatable. The fraction of this error which is random represents an uncompensatable contribution to rms telescope pointing error.

Random errors in radial definition arise typically from nonuniformities in roller dimensions and poor dynamic roller alignment. These errors can be minimized by factory selection of stock bearing with these performance requirements in mind and by selecting a brand with the best roller retainer design.

The extent to which radial runout under the telescope load is repeatable in amplitude and phase will be studied with help from factory engineers before acommitment to this azimuth cone design is made.

Alignment

Spherical roller thrust bearings are designed to be tolerant of up to 2 degrees or more of misalignment with no performance degradation in normal service. This feature should allow very relaxed design dimension tolerances where the bearing mounting ultimately joins to its pier. The self-aligning bearing is a good match to this application since this is an area where holding very tight tolerances would be essentially hopeless.

Friction

Factory stock bearings can be selected and/or reworked for smoothness and low friction. The large ratio of drive disk diameter to bearing diameter (about 15:1) helps reduce tangential force necessary to rotate the telescope at the drive disk periphery. For a friction coefficient of 0.0001 and a telescope total mass of 30,000 kg this force is about 2 N. More information on the actual expected friction and its variability is needed as input to the servo design.

Mounting

To create a convenient absolute encoder mounting topology the preferred bearing orientation is inner race fixed, and outer race rotating (see Figure 4.4). A more detailed consideration of the bearing geometry and the application may suggest some refinement of this choice. Final configuration optimization has not been attempted at this time.

(Note that two types of encoders are referred to in this paper; an absolute encoder generates a signal indicating the position angle of its shaft. An incremental encoder indicates only changes in position angle of its shaft but not the absolute position.)

Very stiff and close fitting seats for the bearing race rings are necessary to prevent bearing distortion under load. No serious design difficulty is apparent here since there are essentially no space limitations that would prevent using components of the required dimensions.

Lubrication

Lubrication and sealing will be provided primarily to protect bearing surfaces from contamination and corrosion. At the very low telescope rotation speeds the bearing operates at all times in metal to metal contact.

Contamination

Sealing method is TBD.

Service Life

At the near zero telescope speeds bearing life will be essentially infinite with no lubrication and all dynamically induced internal forces will be negligible. Essentially static design conditions apply.

Disk Guide-Roller Bearings

A minimum (and perhaps a maximum) of four rollers fixed with respect to the telescope azimuth pier will be used to define the azimuth drive disk center of rotation. One pair of rollers will preload the disk against the other pair which will be fixed. A plan view is shown in Figure 3.11.

Since Nasmyth instrument loads will be balanced at all times there will be no azimuth overturning loads except for some small residuals and those caused by wind loading on the exposed parts of the telescope.

Wind loads resolve into worst case radial loads of less than 1000 N. A balanced radial preload of 10000 N will be applied to the guide rollers. This will increase stiffness since one also serves as drive roller and will provide sufficient tangential friction to resist slipping due to wind load induced torques. The method of preloading the guide and drive rollers is TBD.

Figure 3.12 shows a proposed drive roller mechanism. The driven roller is cylindrical and contacts the drive tire on a line parallel to the rotation axis of both. To optimize drive stiffness its design enforces the condition that the axis of the tangent column pass through the drive contact point and through the flex-hinge at the base point. The mechanical design of this mechanism will undergo a thorough stiffness analysis and optimization.

Guide rollers will contact the ground edges on the drive tire. This arrangement simplifies the alignment of the drive roller with respect to the drive tire, and also localizes stick-slip effects associated with residual misalignment of the drive disk and drive roller axes.

Drive contact preload is applied precisely toward the drive disk axis to guarantee zero moments about the contact line. The preload also establishes uniform pressure along the contact line automatically establishing parallelism of the roller and disk axes. A sufficient degree of torsional compliance in the flex hinge allows this freedom.

Given that the entire mechanism can be manufactured to precision tolerances it can easily be adjusted in place before final locking down of the flex hinge fixed point. This will leave the hinge essentially free of strain other than pure compression and tension along a tangent to the contact point.

Drive Disks

Purpose

Large wheels or disks serve to transfer drive torque and positioning to each axis and also provide an accurate surface from which to derive incrementally encoded position.

Description

Azimuth rotation drive and encoding both make use of the ground cylindrical surface of a TBD diameter disk structure (Figure 3.11). Altitude drive and encoding make use of a segment of a similar disk attached across the back of the primary mirror cell as shown in Figure 4.5.

The azimuth disk is a continuous 360 degree cylinder and along with a number of defining rollers serves as the upper defining bearing for azimuth rotation.

In each case there is a 'track' which is never contacted by the friction drive roller. This clean track is utilized exclusively for friction roller incremental encoding.

Azimuth disk

Figure 3.13 shows a cross section of the azimuth disk. It consists of a shell of outer plates and inner stiffeners designed so as to be assemblable without inaccessible traps. A thick steel tire is welded on to form the cylindrical driving surface. It is flame hardened to Rockwell TBD and ground to a cylindrical surface with TBD finish. The two opposing edges are ground flat and parallel to TBD and serve as surfaces along which the drive mechanism is guided by rollers. Welded joints in the tire (almost certainly unavoidable) will lie at a slant with respect to the drive roller line of contact to minimize unstable development of bumps due to discontinuities in hardness across the welds.

The disk must be radially stiff to minimize 'flower' distortion due to guide roller preload. It must also be torsionally stiff to preserve high torsion mode frequency. In the direction through the disk sufficient stiffness is required to preserve high fundamental mode frequencies and control static sag under gravity. The disk contributes significantly to the azimuth moment of inertia so it deserves to be structurally optimized.

At its center is a reference bore and face concentric with the drive tire to which the absolute encoder driveshaft hub attaches. Loads due to the telescope OSS, fork and instruments are transferred through the disk and distributed around the top rim of the conical shell structure below.

Fabrication

Both azimuth disk and altitude sector will have radii of about 2 meters. A large lathe is required. Such machines exist in Seattle, Portland and Los Angeles.

Tolerances

The azimuth disk is a simple shape and can have all faces, bores and the cylindrical drive surface finished in one setup. Overall accuracy can be held to 0.002 inch under good conditions and 0.005 inch worst case.

The effects of stresses stored as a result of welding is TBD. Some advice from shop experts here is needed.

The effects of a 0.005 inch range in different diameters across the disk amounts to a maximum absolute pointing error of about +- 20 arc sec, most of which repeats in phase with absolute encoder angle and sums to zero after one complete rotation. It is expected therefore that any 'machined in' effects will be largely computer-correctable.

Temperature effects

For isothermal disk and roller, the effects of different temperature should to first order cancel as long as the disk and roller have about the same CTE.

In the presence of thermal gradients across the disk, scale errors will exist whose amplitude and azimuth dependence will be difficult to impossible to predict and correct. For a steel disk (CTE=12 ppm/deg C) a 1 arc sec pointing error over a 180 degree interval would be contributed by a uniform thermal gradient across the diameter of about 0.15 deg C max.

Since the absolute encoder is small, and thermally compensated, azimuth pointing need not be limited by thermal gradients in the drive disk any more than by thermal gradients elsewhere in the mount. Therefore unusual measures to control disk gradients seem unnecessary. Moreover, when offset pointing is appropriate, the allowable thermal gradient budget is increased far beyond anything likely to exist under the worst possible conditions.

Design Lifetime

Surface Hardness

The lifetime of a bearing surface is dramatically extended by hardening. Since the disk is awkward and expensive to replace a hard surface is valuable added protection against accidental damage.

Because of its large size the large disk will be flame hardened. We will exert considerable effort to ensure that the fabricator achieves a minimum specified uniformity. An experienced consultant will be employed for this job.

In case of an accidental skid at the drive contact point it may be possible to confine potential surface damage to the drive roller by making it intentionally softer than the main disk. Damaged drive rollers are easier to replace.

Cleanliness of the disk/roller assembly is essential; a suitable housing and dust seal system will be provided.

The drive disk/roller design task is essentially identical to the design of any rolling antifriction bearing. This is an exceedingly well developed technology and we will thus not need to take any risks. Relatively small loads and large dimensions will mean small stresses, much less than in a typical ball bearing at its rated load. An essentially infinite lifetime design should not be a problem.

Failure Modes

Surface failure can occur over time in the same way ball bearings wear out, by repetitive load cycling. Failure is delayed by hardening and by achieving smooth surfaces.

Surface failure can also occur slowly due to corrosion. This calls for either the use of corrosion resistant steel or surface protection by active means such as by continuously wiping an oil film onto the surface.

Surface denting or 'Brinelling' can occur if the bearing surfaces are overstressed. Shock loading is a common cause for this type of failure. This type of damage is most likely to occur during assembly, disassembly and shipping.

Accidental surface wounds may be inflicted by encounters with sharp tools, etc. Since the drive roller comes into contact along a line many centimeters in length, some insensitivity of performance to this type is damage is available. Appropriate precaution and oversight will occur during manufacture, packing, shipping, and installation, however.

Motion Limits

Purpose

Limits to motion must be established for each axis to prevent damage to the telescope. The architecture of the telescope control system (TCS) will be designed to detect faults and to shut down the telescope drives. Still if the TCS fails passive measures will safely stop the telescope.

Description

For the altitude axis the horizon mechanical limit will be at 90 degrees from the zenith. The other limit will be 5 degrees from the zenith in the opposite direction allowing full access to the zenith plus some leeway to allow for deceleration to occur. Limit switches will indicate the 86 degree and -1 degree positions and will directly cut power to the drive motors. The actual stops will be mechanical shock absorbers. Deceleration will occur over 4 degrees; the moment of inertia of the OSS is 36000 kg m^2 and the required average deceleration force at a distance of 2 meters from the altitude axis is 3200 N. The acceleration at the secondary mirror is 0.09 g. Clearly stresses on the telescope will be very modest. The motion range plus seismic accelerations set constraints on the primary cell; the mirror must not fall out of its cell under a worse case combination of altitude and seismic acceleration.

The situation with the azimuth axis is much simpler. Since the enclosure and the telescope are co-rotating clearances between the telescope and mechanical stops affixed to the enclosure can be made small. Relative angular velocities will be low; a stop will be encountered almost immediately in the event of a failure. The azimuth drive train will be backdrivable by the building without damage. Limit switches will cut power to the drive motors when a fault occurs. Mechanical stops will be shock absorbers. This system is implemented on the MMT.

Instrument Services

Nasmyth platform

At each instrument mounting location the following utilities will be provided:

Coolant lines for detectors are also contemplated. It is expected that detector cooling will be self contained wherever possible. A very compact Joule-Thompson type cooler using nitrogen as the expanding gas has recently been introduced by the MMR Technologies corporation and is being used to cool CCD's at Lick Observatory. The nitrogen gas circuit mentioned above anticipates routine use of these devices.

Where self contained cooling is not practical, cooling equipment will be supported by the enclosure floor near the instrument and rejected heat ducted away from the telescope (Ulich et al. 1983).

Fiber optic data channels

The 10 Mbaud data port will be one or more fiber optic connections to a bus type communications system. The same system will be used to pass instrument control information as well as data.

Instrument changer

Part of INSTRUMENTATION task (section 1.2).

Instrument Rotator

Purpose

For any non-equatorially mounted telescope, images will rotate with respect to the telescope structure during siderial tracking. For non-stellar objects a method of de-rotation is necessary to maintain fixed image orientation on the detector.

Description

In addition to those utilities mentioned above, one Nasmyth position will provide instrument rotation for instruments weighing up to TBD kg at TBD meters away from the mounting surface. The instrument changers will also have instrument rotation capability.

Instrument rotation resolution will be in ~1 micron increments measured at 20 cm from the center of rotation. This will accommodate the most extreme possible case requiring 0.1 pixel guiding precision for a CCD being used at the extreme field margin. This is equivalent to rotator angular resolution of 1 arc sec. This can be conveniently accomplished using a stepper driven worm gear. The exact angle per step is thus determined and since only rate information is required for de-rotation no additional absolute encoders are needed save for a single fiducial position marker arranged for detection by the microprocessor controller.

Field Cameras

Purpose

The field cameras will be used for object acquisition and guiding.

Location

A field camera will be mounted on each fork arm and will be shared by all instruments mounted in the instrument changer on that side of the telescope. It will remain fixed while the instrument changer moves a different instrument into position.

Description

A rotating guide/acquisition TV camera will be provided for use by all parfocal instruments and will rotate with the instrument though no mechanical coupling will exist (Figure 3.14). Its use depends on a flat in the instrument focal plane tilted to direct a field view toward the camera. Without the use of any field optics (the in-focus flat needn't be aconcave field mirror) a 5 arc minute field is viewable with about 50% vignetting near the edges. This arrangement can be elaborated to allow use of a larger field of view for finding guide stars, etc.

Cabling

Cabling for the telescope consists of two types; cables which are part of the telescope control system implementation and which evolve very slowly and cabling for the instruments which must be changed more often. Obviously since the intelligence of the TCS is distributed throughout the telescope permanent cabling for MILT will be greatly reduced compared to a centralized system. Instrument cabling will be simplified since none of the instruments will be mounted on the telescope OSS; cables need only extend to the Nasmyth platforms. Instrument cables will run in exposed surface mounted cable trays and the threading of cables will be minimized.

The azimuth cable windup will be somewhat more complicated than that of the MMT. The bearing diameter at the apex of the azimuth cone will be too small for the cabling. It must be a self aligning thrust bearing and a reference for the absolute azimuth encoder will take much of the space available. Still it is evident that there is room both vertically and horizontally for cable windup exterior to the azimuth cone and reasonably close to the rotation axis. Figure 3.15 shows a conceptual design for the cable wrapup. This appears to be a workable concept; we present it as an example of a solution to the problem, not as the final design.

The altitude windup is a simple problem in comparison. Not only is the range of motion much smaller (90 degrees rather than 540) but the amount of cabling is much less. A simple drape between the fork and the OSS will suffice.

Telescope Protection

Collisions

The need to protect the telescope and its components from damage is obvious. We have already discussed the prevention of collisions with the enclosure. It is also necessary to prevent collisions with obstacles left by personnel in the telescope chamber. The co-rotating design of the enclosure is helpful in preventing this sort of accident since the telescope moves only in altitude with respect to the floor. The portion of the floor which is directly under the telescope OSS when it is pointed at the horizon is 3 by 4 meters. Compared to a conventional telescope and enclosure the potential for collisions is very much reduced; there is only one small region on the floor where an object could potentially cause a collision and this area is invariant.

Earthquakes

The telescope must be protected from seismic accelerations. Positive means of securing mirrors in their cells will be provided. Strength analysis of the structure under seismic loading will be performed. Bearings capacities will take into account seismic loads.

Corrosion

The structure of the telescope must be protected against corrosion. We anticipate dip coating all non-corrosion-resistant steel surfaces with zinc. All fasteners will be stainless steel or number 2 cadmium plated. Ozone and ultraviolet light attack organic polymers much more quickly at the 2800 meter elevation of the site than at sea level. Electrical insulation and seals which are exposed to the air will be made of ozone and uv resistant polymers such as teflon and neoprene where practical.

Mirror Protection

Dust

Covers

During intervals of non-operation the mirror will be completely enclosed by the altitude bearing yoke and a front cover in the form of two facing baby pram type hoods which retract symmetrically for observing. This arrangement has the advantage of completely protecting the tertiary as well and has a low effective area for wind loading when open (Figure 3.16). Remotely deployable covers (TBD) will also be provided for the Nasmyth bearing openings.

Positive Pressurization with Clean Air

With all covers closed a moderately well sealed compartment is formed and will be kept pressurized positively with clean air to prevent entry of dust. With no added complexity the mirror ventilation system becomes the pressurization system when the covers are closed.

Falling Objects

To provide optimal protection from falling objects such as hand tools, sandwiches and combs a tough material such as aluminum or Lexan plastic (used for safety helmets) will be used. Very compact rotary air actuators (Flo-Tork) are available in the torque range required for worst case operating conditions with 30 degree segments of 0.080 aluminum.

Predictability of Structure

Hysteresis

Hysteresis, or the failure to reproduce a structural configuration for successive identical loading conditions, will be dominated largely by slippage at bolted joints or by material yielding in highly stressed (poorly annealed) welded joints when subjected to cyclic service loads.

This means there will be a standing design goal to weld and anneal all structural connections wherever possible. This may include some joints which are welded only after final installation at the site. On site welds will need to be kept small and confined to cases where annealing is not crucial. Joints where bolts must be used will be designed and fabricated to have low hysteresis.

(Hysteresis in the MMT structure is now well controlled and known to contribute no more than 0.3 arc sec to overall pointing error.)

Temperature Effects

Predictability of an isothermal stress-relieved structure as a function of temperature should be very good. Predictability of a non-isothermal structure needn't in principle be any worse as long as a complete temperature map is available. A three-dimensional temperature sensing system would be very complex and expensive. Instead we will exploit passive design opportunities as fully as possible, attempting to keep thermal gradients as small as possible.

Ventilation and Heat Extraction

Ducting in the OSS and azimuth structure will supply clean ventilation air for back of the primary mirror and for other subsystems which require a clean environment. Other ducting will carry exhausted air from primary mirror ventilation, from the interior of the truss tubes, and any other portion of the structure which requires active ventilation. The ducting will also exhaust any heat generated by the instruments.