lunedì, novembre 12, 2007

Sensitivity analysis of a 16" 1.6" thick mirror

Fig.1 perfect piano wire support.

Here is a study of a 16" mirror, 1.6" thick, with two-point lateral support (+/- 45°). The first picture is the perfect case (support at CoG, no friction). The colour scale is magnified 4 times compared to the case of the 30" 2" thick mirror below. Nevertheless the surface deformations, with piston, tilt and defocus removed, is merely 0.85 nm rms (times two for the wavefront).
The effect of misplacement on the contact point is shown in figure 2. It is the case of the contact point standing 1 mm above the CoG. The surface error this time is 2.2 nm rms.
In plane friction is not important. As shown in figure 3 even a large amount of friction (friction coefficent 1) produces a mere 1.18 nm rms. In this case the direction of forces is 45° from the radius, i.e. exactly in the vertical direction.
The last figure depicts the most critical case: a small amount of friction, 0.01 of the radial force, is big enough to cause the largest deformation, which is 3.25 nm rms.
The conclusion is that a simple roller bearing, which cancels out-of-plane forces, and placed at the CoG is perhaps the most effective choice. The small amount of in plane friction is not critical. Conversely the simpler mechanical design maybe allows to better control the location and direction of reaction forces.
N.B. the cases of figure 2 and 4 use a simplified back restraining system (3 points not the complete 18 or 9 or 6 points) and thus the deformations are somewhat overestimated.

Fig.2 support 1 mm above centre of gravity.

Fig.3 support with in-plane friction (friction coefficient 1).

Fig.4 support with out of plane friction (friction coefficient 0.01),