LBT primary mirrors: the final design of the supporting system

G. Parodi(1), G.C. Cerra(1), J.M. Hill(2) ,W.B. Davison(2), P. Salinari(3)

(1) BCV Progetti s.r.l. - via S. Orsola, 1 - Milan - Italy
(2) Steward Observatory Mirror Lab (SOML) - Tucson - USA
(3) Osservatorio Astrofisico di Arcetri - Florence - Italy

http://medusa.as.arizona.edu/lbtwww/tech/parodi.htm

Proceedings of SPIE conference on Optical Telescopes of Today and Tomorrow, 2871 (1996)

2. Supporting the mirror in the furnace

3. Supporting the mirror during the handling

4. Supporiting the mirror in operative condition

The main final results in terms of stresses and optical performances are reported for the Large Binocular Telescope (LBT) primary mirrors. The two borosilicate LBT primary mirrors F/1.14 have 8.4m diameter and are produced at the Steward Observatory Mirror Lab (SOML). They are honeycomb shaped in order to achieve light weight, short thermal constant and high stiffness. The back plate is flat and the upper is paraboloid shaped. Each elementary cell has, in the lower plate, one circular hole permitting the ventilation of cell itself. The material used is the borosilicate Ohara E6. Different supporting systems have been analysed from the mirror casting to the operative conditions,i.e.:

Supporting system during the cooling of the casting phase;
Supporting system for the handling after the casting phase and before the optical surface grinding and polishing;
Supporting system for the handling after the optical surface polishing and for maintenance;
Passive support system in non-operative condition;
Supporting system in operative condition.
The stress checks carried out show that the values of the maximum principal tensile stresses are below 0.7 MPa for long times and/or stresses affecting large volumes, and are below 1.05 MPa for short times and small volumes. Optical performances in operative condition respect the specification.

Keywords: borosilicate - honeycomb - mirror - telescope

BOROSILICATE OHARA E6: MECHANICAL PROPERTIES

Specific gravity = 2.18

Young Modulous = 57500 MPa

Poisson Ratio = 0.195

Linear Thermal Expansion Coefficient =25x10-7

View Figure 1 here

1. PRELIMINARIES

1.1 Mirror geometry

The main mirror dimensions 1 are reported in figures 1. This design permits to achieve a global mass of "only" 15600 kg so that the lightening ratio, i.e. the ratio between the real mirror weight and the weight of a solid mirror having the same shape, is 0.2.

1.2 Approach used

Our structural analyses of LBT primary mirrors or, more general, of some honeycomb mirrors produced at SOML, are dated from 1986 ^2,3. The complexity of the structure to be analysed and the accuracy required, suggested to us, from the beginning of our activities, to use a numerical approach to the problem. The Finite Element Method (FEM) implemented on general purpose codes for structural analysis (SAPV2 and ADINA) has been used.

One "global" FE mesh, relevant to one mirror quarter, modelled by shell elements, having 41300 degrees of freedom has been carried out (fig.2). Many local refined models have been used in order to face particular tasks. Local models are mainly devoted to the check of local stresses in the zones where due to the geometry (i.e. the presence of the ventilation holes) or due to the applied loads, some stress concentration with higher stress gradients occurs.

View Figure 2 here

2. SUPPORTING THE MIRROR IN THE FURNACE

The need to properly support the mirror arises as the borosilicate, during the cooling of the casting phase, becomes sufficiently stiff so that the honeycomb can be considered as a solid. In fact during the casting the furnace changes shape due to the temperature gradient between the top and the bottom of the steel beams supporting the floor of the furnace. This gives the floor a convex shape, 1mm high, which gets "frozen" into the glass. As the furnace cools the floor returns flat causing the mirror to be supported only at the outer perimeter. It is a loading producing not allowable tensile stresses so intermediate supports, the flotation supports, have been added. In this phase, due to the presence of the refractory and to the extra thickness of the lower and upper faceplates the mirror weight is approximately 330 kN.

Two different concepts of flotation supports have been considered: in both the cases some intermediate pushers apply the forces by means of a system of levers and rods inserted in the furnace through proper holes, but in the first case a SiC plate 38mm thick spreads the forces to more honeycomb cells, while in the second case each force is applied directly to an hexagonal tile involving only one cell. Moreover the influence of one layer of soft material, the fiber board layer, placed imediately above the back plate has been taken into account. This soft material obviously helps the force spreading in the case where the hearth plate is used.

Numerical analyses carried out at BCV were devoted:

To state the minimum number, the location and the force values of flotation supports in order to don't overstress the borosilicate.
To check the capability of the system composed by the pushers, the SiC hearth plates and the fiber board layer to sufficiently distribute the pusher forces on the mirror back plate.
In the evaluation of the contact stresses on the mirror some non linearities have been taken into account as:
- I. the gap (non flatness) at the interface between the SiC plates and the mirror,
- II. the non elastic behaviour of fiber board layer.
To check the stresses in the SiC hearth plates. The allowable stresses being stated equal to 16.8 MPa for the principal tensile stresses and 33.6 MPa for the compressive ones.
To check the amount of flow deformation occurring in the mirror due to the viscosity during the borosilicate cooling (to be maintained under 200µm).

View Figure 3 here

The analyses carried out showed that in order to not overstress the mirror, two pusher rings are necessary. The final solution, without SiC plates but with pushers directly applied to the hexagonal SiC plates, came from a trade off between many patterns. Totally it requires 72 pushers (fig. 3 ). 24 pushers are placed along an inner ring around the Cassegrain hole, they exert 2.4 kN each so that they sustain the 15% of the whole weight. 48 pushers are placed along an intermediate ring and they exert 3.5kN each, globally they sustain the 45% of the whole weight. The remainder 40% weight loads the outer mirror wall.

3. SUPPORTING THE MIRROR DURING THE HANDLING

There are two main concepts in the mirror handling:

the handling in the laboratory by means of the front plate fixture,
the handling of the mirror in its telescope cell fixed to the passive/active supports glued to the mirror lower plate.

3.1 The handling by the front plate fixture

The front plate fixture, designed at SOML, is essentially composed by an outer stiff steel frame properly fixed to the mirror blank by means of steel subframes and pads (fig.4). The pads, directly connected to the upper faceplate of the mirror, trasmit the honeycomb weight to the steel structure. The handling is performed moving the outer steel frame.

Being the steel fixture a passive structure the design has been focused on the need to decouple as much as possible the stiff steel frame from the pads connected to the mirror, so that the forces exerted on the mirror by each pad are well known, ruled only by the global equilibrium and they aren't significantly affected by the steel structure deformations or by thermal gradients and differential CTE.

So the front plate fixture is composed by 36 pads divided in six groups having six pads each. A layer of soft material is placed between the metallic pad and the borosilicate. Each group is connected to one steel subframe through a flexible joint permitting movements and rotations. Each subframe is connected to the outer steel frame by means of ball joints.

Two kind of pads are forecast. The first one is a steel circular pad glued to the mirror by means of a 12mm thick RTV layer. The pad has an outer diameter of 610mm and it has an inner central hole of 305mm. It is used to lift out the casting from the furnace and to move the mirror during the first manufacturing phases. Since the RTV transmit both axial and shear stresses this pad permits the rotation of the system mirror+steel frame around the elevation axis and the handling in any elevation angle.

When the optical surface has been polished a vacuum pad is used in place of the pad glued to the mirror surface. It is an Aluminium pad having outer diameter 437mm, the face in contact to the mirror is shaped as a sphere having 17780mm radius. A soft rubber layer, with a square groove pattern in order to reduce the shape factor, permits to compensate without excessive contact stresses the gap between the pad and the mirror shapes. At the outer edge a rubber seal ring permits to obtain the vacuum in the cavity between the mirror and the pad itself.

View Figure 4 here

During the handling by means of the vacuum pad the mirror is zenith pointing so in principle the vacuum pad has to transmit only axial forces, possible small lateral forces are transmitted by the friction. Experimental tests confirmed by numerical ones showed that, lacking lateral force components, the safety factor against the start of pad separation at an elevation of 3300 m is 2.5 and the safety factor against the whole detach is 2.79. The pad location has been stated minimizing the stresses in the honeycomb. The stress analyses take into account the effects of :

stress peaks due to the presence of holes in the back plate (ventilation holes) and holes in the ribs (due to the presence of pins connecting the haxagonal refractories during the casting)
stress peaks due to the local bending at the upper plate of the loaded cells,
non-homogeneity of the contact stress at the interface between pad and mirror due to gap and manufacturing tolerances of the surfaces in contact.

When glued pads are used the mirror weight is considerably greater because of the presence of the refractories. The total weight is equal to 330 kN. In this condition the maximum stress peaks occurs around the cross pin holes in the ribs for the mirror horizon pointing . They are worth 1.16MPa but they can be reduced to the allowable value (1.05MPa) by reducing the lateral stiffness of the joints connecting the innermost pads to the subframe.

When the vacuum pads are used the mirror is free from the refractories and it has its final shape, so its weight is approximately 153 kN. In this condition the maximum stress peaks, equal to 0.73 and 0.67 MPa, occur respectively in the upper plate of the loaded cell and in the ribs in correspondence to the cross pin holes.

3.2 The handling of the mirror on passive supports

When the mirror is in the telescope cell it is supported by 114 triple loadspreaders, by 38 double loadspreaders and by 8 single pucks (fig.5). Triple loadspreaders apply lateral and axial forces, while the double ones and the single pucks exert axial forces only (push-pull). Four lateral crossing loadspreaders sustain the small lateral forces, as the wind loads, in direction perpendicular to the gravity.

View Figure 5 here

Each loadspreader is connected to the mirror by means of three or two pucks glued by RTV 2mm thick to the mirror lower plate. The pucks, having 100mm diameter, are shaped in order to give a flexure decoupling 4 reducing the local bending moments transmitted to the mirror. In fact numerical analyses show that these local bending moments are the main cause of the local stress peaks. The RTV thickness and stiffness have been calibrated, by means of numerical analyses and proofs, minimizing the maximum contact stress values at the RTV-borosilicate interface.

In operative conditions the lateral and axial forces exerted by each loadpspreader are optimized in order to minimize the RMS of the elastic deflections, but when the telescope is not operative the mirror rests, at any elevation angle, on the same loadspreaders. In this case each one of the 426 pucks, after a free travel 3mm long in radial direction and 4mm long in axial direction, engages an elastic fixture fixed to the mirror cell. The compliance of the fixture has been computed in order to fulfill two opposite requirements:

it has to be quite stiff in order to prevent any contact between the mirror edges and the telescope cell.
it has to be quite soft in order to avoid that only a few pucks come in contact, compensating puck location and manufacturing tolerances and differential thermal displacements.

For the worst elevation angle, i.e. when the mirror is horizon pointing, if all the lateral supports sustain the same load and the overturning moment is balanced only by push-pull forces on the two loadspreaders #37 and #38 in figure 5, the maximum tensile stress peaks is 0.77 MPa. Starting from these first results it has been possible to compute the stiffness of the elasticfixtures.

View Figure 6 here

4. SUPPORTING THE MIRROR IN OPERATIVE CONDITION

The pattern of the loadspreaders sustaining the mirror is the same as in figure 5. It has been obtained minimizing the RMS of the elastic deflection of the mirror in order to optimize the optical performances. The axial forces also come from the RMS minimization. Lateral force values don't affect significantly the optical performances, provided that the axial force correction is optimized as function of the elevation angle, so lateral force values come essentially from stress considerations. The force values at one puck, for the two extreme mirror positions, are in the range:

MIRROR ZENITH POINTING: axial force =224 / 620 N

MIRROR HORIZON POINTING: lateral force = 482 / 516 N

axial force = +143 N (push) / -477 N (pull)

The maximum tensile stress peak (0.44 MPa), obtained for mirror horizon pointing, occurs at the puck location.

View Figure 7 here

The value of parameters directly related to the optical performances are:

MIRROR ZENITH POINTING MIRROR HORIZON POINTING

RMS respect to the bestfit paraboloid 5.7 nm 8.2 nm

Peak to Valley of the residual displacements after the bestfit paraboloid removal 54.3 nm 64 nm

Strehl ratio (at 500 nm) 0.98 0.959

In figures 6-7 the isocontour plots of the residual displacements, after the bestfit paraboloid removal, are plotted respectively for the mirror zenith and horizon pointing.

5. REFERENCES

J.M.Hill, "Dimensions for Large Borosilicate Honeycomb Mirrors", Steward Observatory Mirror Laboratory, April 19, 1994.
G.Ballio, G.Parodi, P.Salinari, L.Fini, O.Citterio, R.Angel, L.Goble and J.M.Hill, "Finite Element Analysis of Honeycomb Mirrors", Proceedings of ESO Conference on Very Large Telescopes and their Instrumentation, p.451-466, Garching, 1988.
G.Parodi, J.M.Hill and P.Salinari, "Supporting the 8.4m Honeycomb Mirrors of Columbus", Proceedings of ESO Conference on Progress in Telescopes and Instrumentation Technologies, p.301-306, Garching, 1992.
S.P.Callahan, "Analysis and Design of Glued Joint, Pucks, and Loadspreader Used in the 6.5m Mirror Support System", MMT Conversion Technical Memorandum #93-1, 1993