Description: UZ deformation 200Kg , Filename: plot10.eps
Report on Preliminary calculations for detector support structure for E614
by Jan Soukup
The collaboration with Naimat Khan proved very fruitful. We used
Ansys Finite Element Stress Analysis software to check the maximum
deflections at the end of a reasonably realistic cantilevered
cage as well as maximum stresses at critical locations.
The model consisted of three horizontal round rods, of 90mm diameter
spaced evenly around the cylindrical circumference of the cage,
fixed at their upstream end and joined together at their downstream
end by a 30mm thick vertical round plate with a 380mm hole in its center.
the load of 1/2 of 400kg was evenly divided into four locations in a
circle on the plate, corresponding to the protrusions of the four
wire chamber assembly tie rods through this plate.
The results of the calculation are encouraging in the sense, that no
unpredictable behaviour of the rods or any surprise end plate buckling
occurred. Even though the end plate was just simple its deformation alone
was negligible (15 micron axial buckling for aluminum).
All the deformation rested in the sagging of the three rods and although
it was more than an order of magnitude larger than my hand calculations,
(about .5 mm at the end of 870mm length for aluminum) everything else
scaled pretty well exactly as predicted by the hand calculations,
such as:
1) delta y is inversely proportional to the modulus of elasticity E
of the material, i.e. delta y(steel)=1/3 delta y(aluminum)
delta y(titanium)=1/1.7 delta y(aluminum)
etc.
2) delta y is proportional to the cube of the Length of the bars,
i.e. delta y(2L)= 8 delta y(L), etc.
3) it is inversely proportional to the moment of inertia of the
beam representing rod assembly cross section, i.e.
a) it goes with inverse of square of the radial distance of rods from
the central beam axis
b) it goes with inverse of square of the size of each rod (diameter,
width and height of flanges of a "T" bar, etc.
In view of the fact, that the deflection is of the order of .5mm for Al
to .15mm for steel and for the already relatively hefty size rods
(90mm dia) , we will have to resort to profiles with more efficient
cross section shape ("T"). As expected, the top rod is stressed in
tension, the two bottom rods are stressed in compression. The tension
in the top bar is twice as high as the compression in each of the bottom
ones. Thus, rather than adding more rods into the bottom part of the
cage/basket we should try equalizing the rod cross section area between
the top and the bottom. The top bar should be perhaps larger (thicker
flanges, deeper height, wider top flange, etc.) The angular space at the
top is limited, but we may have to compromise. This will also compromise
the desire to have symmetrical distribution of material around the
target area, but the fact, that we want more bars at the bottom and only
one bar at the top is already doing that anyway.
More rods at the bottom half of the cage are then still desirable to
stabilize the rigidity of the cage against squishiness. We will have to
design the attachments of the rods to the end plates very carefully to
make sure, that the joints behave as fixed (I have some good ideas in
this regard).
We have to come to a consensus in what is the acceptable deflection.
This, of course, can be compensated for by the x-y positioning and tilt
adjustments, but the deflection is still an indicator of the rigidity
and stability of the assembly.
Attached are three selected encapsulated postscript files of the stress
analysis of the three-rod detector cage.
plot13.eps shows vertical deformation of the loaded cantilevered
end plate.
plot10.eps shows the axial buckling of the end plate.
plot6.eps shows so called von Mises stress in the end plate
which is the maximum stress (not just in x,y,z directions)
--
Jan Soukup Office: P131A
Physicist/Engineer Phone:(403)492-3095 Fax:492-3408
Center for Subatomic Research E-mail: jsou@Phys.UAlberta.Ca
University of Alberta, CANADA, T6G 2N5
Description: vertical sag 200Kg , Filename: plot13.eps
Description: UZ deformation 200Kg , Filename: plot10.eps
Description: von Mises stress 200Kg , Filename: plot6.eps