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