Figure 1:Honeycomb Mirror with Load spreader Hardware] {6.5 m mirror blank showing honeycomb structure attached with triple, double and single load spreaders and pucks.
P. M. Gray, J. M. Hill & W. B. Davison
Steward Observatory
University of Arizona
and
S. P. Callahan & J. T. Williams
Multiple Mirror Telescope Observatory
University of Arizona
Proceedings of SPIE conference on Advanced Technology Optical Telescopes V, 2199, p. 691 (1994)
The support of large telescope mirrors to the level of accuracy for the tight specifications required for the next generation of telescopes needs an actuator system which must apply a controlled set of forces in a precise, repeatable and controllable way. SOML's large, lightweighted borosilicate mirrors have excellent stiffness combined with low weight by virtue of their honeycomb structure. However, the tight specifications required to hold a high tolerance surface figure mean that the support design remains an important area for both polishing and in the telescope. In all cases the final requirement is to apply precise forces to predetermined positions on the back of the mirror. On the telescope this must be achieved in a variable, semi-controlled environment under such influences as wind loading and telescope orientation. While less severe, the requirements for polishing test support are also critical in order for a high surface figure accuracy to be achieved which can be realised in the final telescope.
The design of the sub-structure and attachment points which are used to spread the support load in an optimum way to the underlying honeycomb structure is one important area. Another is the design of the pneumatic force actuators; their sensing and control; and the way in which they are decoupled from the support structure to minimize any extraneous loads and moments.
In this technique, to prevent the glass bending under gravity, its weight is carried by many distributed reaction forces, which should change with orientation to mimic the buoyant force felt if the mirror were floated in liquid of its own density. Because the distributed actuators apply forces to counteract gravity rather than holding a position, the mirror maintains its figure even as the telescope structure bends or flexes under the load. The position of the mirror is determined by three (six) hardpoints which hold the location of the floating mirror without carrying the gravity load.
The benefit of honeycomb mirrors is that they combine low weight with high stiffness. The faceplates and ribs of the honeycomb act like the flanges and webs of an I-beam to provide stiffness against bending. The deformation of the honeycomb under gravity is similar to that of a solid blank of the same dimensions, but the honeycomb has only one-fifth the mass of a solid blank.
FEA analysis is a valuable tool during the on--going development and refinement of the honeycomb mirrors and their support hardware. Results and existing modeling work can be built upon during the final design process to quickly and efficiently analyze and optimize new components and loadings.
Telescope mirrors are required to operate at all orientations from zenith to the horizon. Support of a mirror away from the zenith requires lateral forces in addition to the axial support. Ideally these lateral forces should be applied at points in the center of mass (CofM) plane of the mirror. Attachment to the relatively thin ribs of the honeycomb at this position within the mirror would have been difficult. Traditionally, lateral support in smaller solid mirrors has been achieved with a ring of lateral supports around the mirror circumference, but for large, fast f--ratio mirrors this method proves difficult. FEA analysis has shown that the 8 m honeycomb mirrors could however have been supported in this manner.
To avoid the additional complexity and poorer performance of edge supports it was decided to provide lateral support at the backplate of the honeycomb mirror. Additional actuators angled at 45 ° combined with push/pull axial actuators provide a net thrust aligned with the gravity vector direction. Since the thrust line is displaced from the CofM plane of the mirror, there is an overturning moment which must be compensated for by the axial supports. A small number of ``cross--lateral'' supports are also included orthogonal to the main laterals to provide resistance against side loads caused by telescope azimuthal acceleration and wind loading.
Like any lightweighted structure, honeycomb mirrors require careful consideration in designing and positioning attachment points. A natural arrangement of load spreaders for a honeycomb is to position the individual pads of the load spreader frame above the rib junctions where the structure has the greatest strength and the most resistance to print-through of deflection. The repetitive hexagonal geometry of the honeycomb permits one size of equilateral triangle load spreader to be used for the majority of the supports. A some locations on the mirror perimeter where the hexagonal symmetry breaks down and at a couple of specific locations within the mirror area, two pad double load spreaders are required. A small number of single pad actuators are also used to fill in the gaps. Figure 1 shows a 6.5 m honeycomb mirror equipped with load spreaders.
Figure 1:Honeycomb Mirror with Load spreader Hardware] {6.5 m mirror blank showing honeycomb structure attached with triple, double and single load spreaders and pucks.
Since the load spreaders are the main attachment points, they must perform a number of functions including:
The design of the load spreaders must take into consideration:
The 100mm diameter pucks are a two
Further information on the design and prototyping investigations of the load spreaders can be found in Callahan (1993) and Callahan (1994).
Figure 2:Detailed assemblies of the triple and double load spreaders with flex pivot pucks and actuator attachment block. Also shown in position in the assembly are the rubber static supports.
A silicone rubber, Dow--Corning Aerospace Sealant, Type 93--076-2 was chosen as the adhesive. This silicone rubber has been used extensively as an optical support adhesive and has a proven track record in this application.
To obtain accurate FEA results for the load spreader, it was necessary to know the precise material properties (Young's modulus, shear modulus and Poisson's ratio) of the silicone material. Joints of rubbery elastomer materials like silicone display stiffness behavior which is critically dependent on a shape factor. A series of laboratory tests were undertaken to measure these properties using test samples with dimensions, shape factors and loads similar to those encountered in the mirror support. A hydraulic ram applied loads (tension, compression and shear) up to 4,000N to 100mm diameter test samples. The deflections were measured with linear variable differential transformers (LVDT) displacement transducers with a resolution of 1.5 microns. Various types of silicone rubber, joint thicknesses and composite geometries (see below) were tested. Some of the test results are given in reference Gray (1993).
Most silicone rubbers are specified as sealants or encapsulants rather than as adhesives. Silicones such as 93--076 have excellent adhesive properties to properly prepared glass and metal surfaces however no specifications are available to quantify this. The test apparatus was also used to proof--test--to--failure the samples under a number of different loading conditions including tensile, pure shear and shear plus bending. These tests showed that with proper surface preparation and curing, the 93-076 silicone had material and adhesive properties which met the operating requirements of the mirror support with sufficient safety margin.
As with any rubber--like material, silicone layers of a shape used for the pucks (100 mm diameter x 2 mm thick) display much greater compressive/tensile stiffness than shear stiffness. For the load spreaders, it was desired to use the silicone layer as a semi-flexible joint to decouple load spreader twist--induced moments from the glass while at the same time achieving good shear stiffness for lateral mirror location. A scheme was developed to construct composite silicone rubber layers using soft foam strips to break up the flat uniform pancake into a number of smaller pads which have shape factors with better axial to shear relative stiffness. A radial pattern of foam ``spokes'' was most successful and achieved a substantial decrease in axial stiffness for a relatively small change in shear stiffness. The radial pattern also assisted in obtaining a more optimum pressure footprint under a puck. However, none of the designs for a composite silicone layer decoupling joint were sufficiently successful to warrant this additional complexity. A metal flex pivot was therefore included in the design of the puck.
The design of the static supports uses commercially available rubber engine mounts. They consist of a rubber ``donut'' bonded around a steel sleeve. As well as axial compression, shear and axial tension are restrained using a shoulder bolt attached to the corner of the load spreader. Tests on these components show that they provide the correct amount of progressive spring rate in all directions.
Study of the tolerances allowed in supporting the large honeycomb mirrors suggests that passive supports are possible. For errors in amplitudes or locations of support forces, precision is typically required at the one percent level. This is the precision that could be obtained from an astatic lever system or other passive systems by paying careful attention to the geometry. The problem comes with astigmatic bending which is the most flexible mode of the mirror. Systematic force errors at the edge of the mirror must now be controlled at the one-tenth percent level. This drives us to consider independently adjustable support forces, if only to remove these systematic errors.
Another problem that arises for a passive system of predetermined forces is that neither the mirror geometry nor the finite element calculations will ever be known better than a few percent. This suggests that any support system will need at least some ``factory adjustment'' or ``field adjustment'' to support the mirror properly. These adjustments can be easily made with a system that allows variable force values.
We also must consider the location of the mirror support actuators. Lateral support patterns could be independent of the axial forces, for example using midplane lateral supports or lateral supports around the edge of the mirror faceplates. Alternately, all of the forces can be applied to the backplate of the mirror
Once the need to adjust the mirror support forces is accepted, the question that remains is whether to use fully active forces or whether to provide tweak-up forces on top of a basically passive system. The passive system provides a fairly soft failure mode with arcsecond quality images, but requires an additional layer of hardware and maintenance. We have selected fully adjustable forces under computer control. Modular design should make such a system very reliable, in fact limited by mechanical rather than electronic reliability. No part of the telescope drive system or the instrument is likely to be functional without computer control. A single actuator failure can be automatically compensated by other actuators with a small loss in surface figure quality. All of the actuator subsystems are modular and can be easily replaced.
We have selected a mirror support system which includes active adjustments of all support forces under computer control. This system is capable of adjusting the mirror figure on-line if suitable wavefront information is available. However, most of the time we expect to operate in an open-loop or internal-loop mode where the loads on the hardpoints are used to scale predetermined support force values. This makes the entire process of mirror support self-contained inside the mirror cell.
A preliminary design for the telescope actuators is shown in Figure 3. This shows a double actuator with a pair of double
Figure 3: Assembly showing preliminary design of double support actuator with double-acting pneumatic cylinders, ball decouplers, load cells and load spreader (old version).
For maximum resistance to wind forces bending the mirror over the hardpoints, the hardpoint supports should be equispaced around the mirror at roughly 70% of the radius from the center of the mirror. Lateral hardpoint locations are less critical, so they may be located near the axial hardpoints for convenience. In fact, the hardpoints may be mounted angled in pairs which have neither pure axial nor pure lateral components.
In order to avoid placing 1/3 of the mirror weight on each hardpoint when the air pressure fails, the hardpoints are required to breakaway from their normal position before the force they exert exceeds 5000 N. The mirror support servo system will normally hold the hardpoint loads near zero force (20 N). This makes the breakaway system simpler than if full axial or lateral support forces were required. The hardpoints need to maintain stiffness up to a few hundred Newtons to resist the high frequency forces in the wind. After the hardpoints breakaway, the rubber earthquake pads hold the mirror before it exceeds the hard range of travel of the mirror support actuators. As with the other actuators, each hardpoint must be decoupled in the directions normal to its line of action. The decoupling will apply to both push and pull forces. The positions of the hardpoints will be motorized and encoded to allow collimation and alignment of the telescope without the need for access inside the mirror cell.
In the simplest system, the actuator forces can be adjusted open-loop based on some measurement of the telescope attitude. This passive system does not account for wind or other unexpected forces.
The next level of complexity is a self-calibrating system. The actuators can be grouped into three segments, each segment centered on one of the three hardpoint pairs. The load cell signal can then be used to scale the forces on all the actuators in that segment. This scheme does not require any knowledge of the telescope orientation since it uses the mirror to measure the local gravity vector. The mirror is automatically floated against any force to produce zero load on all the hardpoints. This allows all mirror support calculations to remain within the mirror cell after the initial calibration is done.
In practice, the forces on all the hardpoints can be compared to estimate linear force gradients (e.g. wind) across the mirror in addition to the simple gravity load. A matrix transformation is used to translate the hardpoint load readings into their axial and lateral force components. These differential force components are added to the axial and lateral loads being applied to the mirror. The load on each actuator is calculated by dividing the total load by the predetermined scaling factors. These scaling factors use a linear combination (another matrix) of the hardpoint readings to account for linear force gradients. As the lateral forces are calculated, the axial correction forces are rescaled to balance the moments. The details of this algorithm are described below.
Rather than use an analog servo loop to generate the actuator support force, we will use the forces on each actuator digitally. The central mirror cell computer will read the hardpoint loads and calculate the force required on each actuator (outer loop). Then the computer will adjust pneumatic regulators to generate the desired forces (inner loop). The system will check itself by reading back the force on each actuator. These forces will be compared to the commanded forces as well as the sum which appears on the hardpoints. Closing the loop digitally allows software adjustment of the forces as well as resistance to long term drifts and noise immunity. The servo loops are illustrated in Figure 4.
Figure 4: Schematic of mirror support control system.
During polishing, the lap moves across the surface applying axial and shear forces unlike anything which is encountered in telescope operation. The small size of the polishing lap relative to the mirror means that global bending is of little consequence. Local bumps caused by inadequate mirror support are important since the lap will attempt to smooth these out. Studies have shown that support forces within 50\% of the ideal telescope forces are adequate for polishing.
For optical testing on the polishing cell must accurately reproduce the force distribution that the mirror will see in the telescope. The support problem is somewhat simplified however since the mirror remains zenith pointing during testing and only axial support is required. The major problem is to control astigmatic bending of the mirror. A certain amount of astigmatic deformation is acceptable in the polishing support since the telescope actuators can be used for active correction, however this is limited by the operational force range of the telescope actuators. Whilst some systematic inaccuracy can be tolerated, the requirement for repeatability is tighter in order to achieve the run--run stability necessary for convergence in the polish--test cycle.
The approach which was adopted for the honeycomb mirror polishing at the SOML is to use the traditional three sector hydraulic support. This has the advantage of being relatively cheap, reliable and providing a good stiff system during polishing. The polishing support mimics as closely as possible the telescope. The same load spreaders and actuator support force optimizations are used. The range of support forces is achieved for a uniform hydraulic sector fluid pressure by using a number of different cylinder diameters and adding quantities of trim weights. The details of a polishing support actuator are shown in Figure 5.
For axial loads, the incompressible fluid support provides sufficient positional stiffness. To resist the lateral loads generated during polishing, a set of tangent rods are used which attach to pairs of load spreaders.
Figure 5:Cross section of polishing cell showing hydraulic axial supports with trim weights, ball decoupler, load cell and load spreader.
