The themo-mechanical calculations for CIRCE in two steps: the first calculations concerned the feasability study using estimated values for the position and weight of the mechanical elements; the second step uses values from the final mechanical CAD design. The system is considered a cemented cantilever beam with null deflection or bending in the fixation. Two different loads are applied to the system: the internal and the external loads. The superposition theorem is used for each load and the total bent due to loads is equal to the sum of each one. The bent of the bench is due to torsion, tension and bending. All these effects are assumed no coupled and thus the coupled-flexure coefficients were neglected. When the instrument moves the gravity angle in relation with the bench changes and the variation in the flexure of the bench creates a shift of the image into the detector.



Deflections, shear and moments were calculated using standard analytical solutions implemented in ITMAS. The feasability assumed that the bench is attached to the front of the instrument. This study showed deflections lower is in the order of the tolerances (25um) in the worth case of the bench parallel to the ground. The shift between mirrors is in the order of some microns.



We study the influence of the thickness of the bench in order to optimize the dimensions of the instrument. An increase of the thickness of the bench increases its stiffness but also its distributed weight participating in the deflection of the system. The study with ITMAS showed that the optimum value is about 40mm.



The second study the mechanical CAD design that consider the physical limitations from the telescope specifications. Values of the elements used for the thermo-mechanical calculations are shown in the following table.

Mechanical Element X(cm) Y(cm) Z(cm) Volume(liters) Weight(kg)
F1 17.53561314 0 -15.6409 2.297628 6.226572
F2 -89.99548219 0.000001016 286.3503 2.78953 7.559625
C1 703.0348439 -0.013157454 283.372 4.836717 13.1075
C2 140.9170908 -0.01840738 93.41091 0.436713 1.183491
IM1 1062.68148 -0.132106416 -211.091 2.843016 7.704575
IM2 878.9555294 0.037731446 -12.0942 0.191266 0.518332
IM3 1051.71924 -0.018615152 11.00891 0.172181 0.46661
IM4 876.0236838 -0.026206704 326.8984 3.065712 8.30808
Filt Wheels 405.1460889 1.09913928 -66.6649 1.193636 3.234755
Filt Box 477.6064936 -33.46281293 -116.289 1.518762 4.115844
Detector 1175.882949 -42.89849078 2.539152 0.275213 0.745828
Bracket 1 64.23266732 -56.26286944 -52.1246 1.032358 2.79769
Bracket 2 -128.4971514 -49.37481489 324.3209 0.944301 2.559056
Bracket 3 679.0453993 -49.53429819 291.7184 2.234331 6.055038
Bracket 4 118.1489204 -84.52582003 95.34327 0.611058 1.655966
Bracket 5 1146.165147 -56.88742801 -210.863 0.981754 2.660553
Bracket 6 854.6161028 -88.1876156 -6.04431 0.538064 1.458153
Bracket 7 1071.206688 -88.43974032 -1.83525 0.481806 1.305695
Bracket 8 886.7877801 -74.98995365 319.3113 1.837902 4.980715


The deflection of the beam at X is given by

and the the resulting shifts of the mirrors are



We show the deflection of the bench(pink) and the deflection due to mirrors and distributed loads(Orange) and bracket (bleu) independently. Analytical results are over plotted with yellow. Using reinforced structures and lightning of the bench improve deflection by about 20-30%.
DIMENTIONNING
ITMAS
Bench Flexures
Thermal Calculations
Assembling
Testing

CAD DESIGN
Bench
Opto-mechanics
Filter Box
Focal Plane
Other