ANALYSIS OF THIN BEAM
PIPE CARRYING VACUUM LOAD
H. Wieman
A thin beryllium beam pipe has been proposed for STAR to be used with the HFT detector. This analysis checks the ability to support the vacuum load.
The proposed central thin section of the beam pipe:
29 mm diameter
400 mm long
0.5 mm wall thickness
material beryllium
ends terminated with rigid support rings
The finite element work was done using COMOSWorks/SolidWorks with shell elements.
The critical buckling load was found to be 49 atm.
An analysis with elliptical deviation from a true cylinder increased rather than decreased the critical buckling pressure.
A check was made to verify that this analysis was independent of the angle of the ellipse.
Pure cylinder COSMOS results were compared and found to agree with NASA formula.
The increase in stress with elliptical deviation was quantified. Limiting out of roundness to a major/minor axis difference of 1 mm provides a 21 to 1 safety factor for material failure. This, not buckling sets the performance limit.
Recheck of buckling comparing elliptical cylinder (2:1) and round cylinder with same conditions:
Poisson’s ratio for beryllium set to 0.032
One end fixed, other end fixed in x and y not z
Reinforced with end rings
Note, third mode for elliptical cylinder looks more intuitively reasonable. Buckling still has higher load factor for ellipse. Again the earlier stress analysis with an elliptical pipe is still the limiting issue.