Circular Arch Isolators as Static Supports

Warren Davison, Steward Observatory

John Hill, Steward Observatory

Bruce Hille, Steward Observatory

Large Binocular Telescope Project

Technical Memo

UA-96-01

April 11, 1996


http://medusa.as.arizona.edu/lbtwww/tech/ua9601.htm

Abstract

The static supports for the telescope mirror are there to rest the mirror on when it is not operating. They have to take the full weight of the mirror at any telescope angle including horizon pointing. They also take upward push, and random earthquake forces. They must have a clear band where they do not touch the mirror during operations. They must have a low spring constant so they provide equal forces on the mirror, and a high spring constant to limit the travel so the mirror or its components do not touch solid objects when excess force is applied. This paper describes circular arch isolators which we have selected as static supports for 6.5 and 8.4 m borosilicate honeycomb mirrors. The circular arch isolators we tested met all of our requirements but did have an annoying feature, that is a dead band in the loading that requires you to set them carefully at installation. Their best feature however is that it is very hard to overload them in a manner that hurts the mirror.

Description

The circular arch isolator is made from a base plate with eight 1/4" stainless aircraft cables that arch to a top plate (figure 1).

It has several desirable characteristics for static supports and a couple undesirable ones. The desirable properties are: it is made of materials that will last the life of the telescope, it is very nonlinear so it uses up a small portion of our travel budget and is nearly impossible to overload to a dangerous stress level, the axial and lateral spring constants are in the correct range, it has a lot of damping, it is low cost, and it fits in the space available. Its faults are: it has an initial hysteresis curve with lost motion of 0.5 mm axial and 1 mm lateral, it work hardens when subjected to the same loading (it however partially resets this hardening when a different load is applied). It meets all of our requirements for a static support and the faults can be overcome.

The top of the basic unit is usually bolted down so in our application the stiffness properties are different from the catalog values. The axial stiffness is lower because the top can twist as it is compressed. For the 100 lb gravity load we anticipate the axial deflection for the first cycle is 1.6 mm and for repetitive cycles is 0.9 mm. In the free state the lateral stiffness is a function of where you press on it. If you press at the height of the plate it pivots up as it translates and the spring constant is too low. If you press at 20 mm higher the plate is nearly flat as it translates and the spring constant is appropriate. The height we require to match our cell is this elevated height. The hysteresis is a classic loop and is a result of the friction in the cables, for repeated loads it is very repeatable and predictable. There does not appear to be any jumps or discontinuities in any of the data. When we subjected the unit to repetitive cycles there was a distinctive hardening, where the maximum deflection was reduced and the zero load position was increased. The slope at load was increased by almost a factor of two. Figures 2 and 3 show some test results.

Requirements

Based on Parodi's analyses of local stresses in the glass (BCV Report #160), the maximum allowable lateral force from a static support is 850 N and the maximum axial force is 1130 N. The mean gravity load on each static support is 422 N for the 6.5m. The difference between the mean load and the maximum allowable force is what gives us tolerances on positions, spring constants, etc..

We have reconstructed the historical division of force tolerances in the following tables: (these apply to all types of static supports)

Lateral force errors:

Total lateral force errors (1.2x1.3x1.3=2) and (2x422=850) Axial force errors: Total axial force errors (1.01x2.0x1.3=2.6) and (2.6x422=1100) We can now combine these force tolerances with the maximum allowable travel in the actuators to generate position tolerances for the static supports and load spreaders. (Or, we are going to calculate the spring constant of the static supports given certain assumptions about the position tolerances.) If the deflection of the static supports under a 1g load is 3 mm, and we want no more than 30% variation in the force, then the tolerance on the positioning stack-up from one support to the next is 1 mm. Given the allocation of travel in Table 4 of "Mirror Support II/R" (UA-95-02) 3 mm is the largest 1G deflection that the actuators can handle. If the deflection of the static supports under a 1G load is 1 mm, and we want no more than 30% variation in the force, then the tolerance on the positioning stack-up is 0.3 mm. This is why you want soft static supports --- to avoid very tight positioning tolerances in the lateral direction. Even if you had perfect positioning, the CTE mismatches drive you to soft supports. We also note that since the allowable axial forces are higher, we are allowed an x2 variation in the axial force; that is from zero to twice the nominal load (provided that the variations are random across the mirror so as not to make global stresses).

Now, to allow for devices with non-linear spring constants, let us define a pseudo spring constant which tells us the deflection under a 1G load. We'll adopt the units of millimeters/100# of load. Let's call this value D --- remember, this is the deflection at 100# regardless of how you got there. The maximum value of D is 3 mm since that's all the travel we have allocated for the compression of the static supports. In the lateral case, the minimum value of D is also 3 mm since less compression gets into stress problems from CTE mismatch (20% variations around the nominal 3 mm value are permitted). In the axial case, smaller values of D are permitted, where the minimum is set by the range of distance over which all the static supports contact the mirror as the mirror is raised or lowered. The historical contact allocation is 1.5 mm, thus Dmin is 1.5 mm.

Let's also define a more traditional spring constant K, which is the slope of the force vs. deflection curves at a loading of 100 pounds. (We'll be tricky and express it as the linear deflection caused by a 100# load so it has the same units as D.)

Properties of the Circular Arch Isolators

Now let us look at the measured properties of the circular arch isolators based on the measurements Bruce has done.

Condition D K
Axial First cycle 2.1 mm
Axial New after 4 cycles 1.7 mm 3.5 mm
Axial after 20K cycles 0.95 mm 1.3 mm
Exercised 20000 lateral cycles
Axial first cycle 1.3 mm
Axial after 4 cycles 0.9 mm 1.6 mm
Axial then 100 more cycles 0.8 mm 1.3 mm
Axial after 40K total cycles
then 200# load 7.1 mm 30 mm
Lateral New 2.8 mm
Lateral after 20K cycles 2.4 mm

The lateral deflection matches our 3 mm ± 20% even after 20000 cycles, so no problem there. The tricky part is that the axial deflection is low so there is potentially a problem relative to the contact distance allocation. The nice thing is that the isolators apparently continue to soften so that a deflection or order 10 mm is needed to get the force up to 200# (love those mixed units!). To control global stresses, we just want to be sure that the deflection of the mirror cell is not more than half of D_axial (< 0.5 mm), and the discussion is easy so long as the total contact stack-up is less than D_axial (< 1 mm). The decreasing D with lifetime seems to be due to lack of rebound caused by increasing friction rather than a continued sagging of the device. This means that the devices compensate for initial position errors as the age --- quite a convenient property.

Mounting

The mounting holes in the baseplate (as delivered from the factory) do not allow enough translation to meet our requirements. The desire to adjust from the bottom of the cell would be greatly facilitated if we had captive nuts in the unit. To solve both problems we have designed a large captive washer shaped piece with six .25-28UNF-2b tapped holes on a 2" bolt circle. This will clamp down the base of the static support with an adjustment range of plus or minus 3 mm. The top of the Isolator will have a 1.06" hole to receive a specially machined "chase nipple". This will allow vertical adjustment. We will need to accommodate the vertical hysteresis by compressing the unit and then adjusting the height. The horizontal hysteresis can be taken care of in the cell by shoving it over with a bar at the time of alignment.

View Figure 2 here

View Figure 3 here