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By Dr. Frank Melsheimer, President,
DFM Engineering, Inc.
The choice of what material to use
for the structural components of a telescope needs to be based
upon both performance and cost. The performance of the telescope
is improved by reducing the weight (and resulting moment of
inertia) and increasing the stiffness of the moving parts.
A high stiffness to weight material of adequate strength is
the best choice for performance. The high stiffness requirement
usually results in more than enough material to provide the
needed load carrying ability. Material strength considerations
are only of a secondary concern. Cost constraints are more
difficult to evaluate because they are intimately tied into
the manufacturing process which is a function of the material
and how the material is used.
The stiffness to weight ratio of common materials used for
telescope parts can be expressed as the ratio of the materials
modulus of elasticity (Young's Modulus) divided by its density.
If we then scale the resulting stiffness to weight ratio by
dividing by the stiffness to weight ratio for steel, we find
that most metals (with the exception of beryllium) have almost
the same stiffness to weight ratio. Aluminum and titanium
are 5% stiffer than steel per unit weight for example. If
all of the structural elements of a telescope were made from
aluminum, the telescope structure (for the same stiffness
telescope) would weigh only 5% less.
The "Figure of Merit" for the material including cost of
the raw material, can be expressed as the stiffness to weight
ratio divided by the cost per unit weight. Steel is 3.8 times
more efficient than aluminum based upon this highly simplified
analysis. A more detailed analysis must take into account
the manufacturing process and the resulting labor costs associated
with that process. Typically, the raw material cost for the
telescope structure is only 20% of the total cost of the structure.
The labor cost is the remaining 80%.
The cost of fabricating the telescope structure is type of
material and telescope size dependent. Small telescopes can
be made more inexpensively by using aluminum castings, particularly
in quantities greater than 4 or 5. Moderate and large telescopes
tend to be made in quantities of 1 or 2 so the cost of the
patterns for the castings becomes prohibitive.
A casting eliminates much of the labor of transforming the
raw material into the desired shape. Machining of mating surfaces
and cosmetic finishing are still required and require about
the same amount of labor as other fabrication techniques.
The minimum wall thickness of castings provides an additional
constraint. Thin sections will still have to be fabricated
from flat sheet stock.
Large telescopes have been traditionally fabricated using
flat steel plate which is cut out and welded into the desired
shape. Round shapes, such as the polar axle, are either made
up from available sized tubing, or the flat stock is rolled
and seam welded. Presently, many of the steel suppliers have
automatic flame cutting or laser cutting equipment for steel
which can cut out the desired shapes very inexpensively. The
practical minimum thickness plate for flame cutting is .25
inches (6 mm) while laser cutting can cut out shapes in much
thinner stock. Cutting shapes out of aluminum plate is much
more expensive.
Welding aluminum is much more expensive than welding steel,
particularly when the aluminum plates are nearly 3 times thicker
as is required to obtain the same stiffness. Welding a DFM
0.5 M telescope fork out of aluminum would require much heavier
equipment and would cost about 3 to 5 times as much as the
steel fork. The material cost would also be 4 times as much
as steel.
Aluminum has many advantages for smaller parts and particularly
for parts which require extensive machining. The best performance
when considering cost is achieved when the proper balance
between steel parts and aluminum parts is reached. This balance
requires considerable knowledge and experience with the various
fabrication techniques available to the telescope manufacturer.
Also, quantity plays a significant part in determining the
manufacturing process and the resulting cost. An "All Aluminum"
moderate to large telescope of the same performance as a predominantly
steel telescope will cost considerably more.
In the next DFM Engineering Article, we will discuss the
effect of geometry on the telescope structure. The geometrical
shape of the structural elements, and the details of how loads
are applied and removed are far more important than the 5%
difference between the stiffness to weight ratio of the commonly
used materials.
Engineering
Articles Summary
Steel
& Aluminum
Geometry
Deflections
Pointing
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