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By
Dr. Frank Melsheimer, President, DFM Engineering, Inc.
In the last Engineering News article, we discussed how the
geometry or shape of a part effects the stiffness or the deflection
of the part. We found that the proper choice of the cross
section can greatly improve the stiffness to weight ratio.
But deflections are unavoidable because we must support the
weight of the telescope structure (static loads). There are
also dynamic loads applied by wind and accelerations. Now
we will discuss how we can minimize the effect of the static
load deflections.
The polar axle of a fork mounted equatorial telescope is
supported by two bearings, one at the south end and another
at the north end. The fork is attached to the north end (for
a telescope in the northern hemisphere) and applies a combination
of bending, thrust (a load along the length of the polar axle
directed towards the south bearing), and shear (a load perpendicular
to the lengthwise axis of the polar axle). Generally, materials
are very stiff in thrust (tension-compression) and in shear,
but the bending load causes the polar axle to assume a curved
shape. The amount of curvature (measured in degrees from one
end to the other for example) causes the telescope to rotate
about a point lower than the undeflected case resulting in
a polar axle alignment error. This error may be removed by
adjusting the elevation alignment of the telescope IF the
polar axle has the same curvature at all hour angles. Axial
symmetry will produce a structural element which has constant
angular deflection as a function of rotation angle. This symmetry
defines a surface of revolution such as a cylinder or a cone.
DFM uses a conical polar axle for our 0.4 meter telescope
and a cylindrical polar axle for the larger sizes.
The fork also needs to have the same angular deflection for
all hour angles, but it doesn't have axial symmetry to simplify
the design. We have developed the characteristic DFM Engineering
fork shape to minimize the changes in angular deflection as
a function of hour angle. Both the polar axle and the fork
need to have high stiffness to minimize dynamic deflections
due to wind loads and other dynamic loads. We will further
explore these requirements in the next Engineering News article.
Engineering
Articles Summary
Steel
& Aluminum
Geometry
Deflections
Pointing
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