MUON Collaboration meeting at Mission Inn, Riverside, California January 27 - 30, 2004. Development of the curved beryllium window. Stephanie Yang & Wing Lau – Oxford Steve Virostek & Derun Li -- LBL. A short summary of the FEA work carried out on the Beryllium Window. Summary
January 27 - 30, 2004
Development of the curved beryllium window
Stephanie Yang & Wing Lau– Oxford
Steve Virostek & Derun Li -- LBL
A short summary of the FEA work California
carried out on the Beryllium Window
A new window geometry has been developed with the aim to
reduce the thermal stresses which were considered to be on the high side in the previous window geometry although they are still below the allowable stress limit.
The new window has its intersection between the concave and
the convex region shifted away from the edges, thereby making
it slightly more flexible to allow freer thermal expansion.
The pre-bow, before any thermal deformation, is kept to within
30mm which is considered to be acceptable to the cavity as far
as space is concerned
The new window geometry is shown in the next page. Three
window thickness have been studied and all found to have
achieved acceptable thermal stresses.
Zoom in on high stress area California
Stress distribution: Max. approx 150 MPa
Deflection due to thermal load. Max 1.72mm
Linear static runs
Diameter: 16cm; Thickness: 0.25mm
Prescribed temp profile along window
1 Californiast mode shape of the 3-D model
2nd mode shape of the 3-D model
3rd mode shape of the 3-D model
4th mode shape of the 3-D model
5th mode shape of the 3-D model
1st mode shape of the 2-D model
2nd mode shape of the 2-D model
3rd mode shape of the 2-D model
4th mode shape of the 2-D model
Summary of the natural frequency runs
5th mode shape of the 2-D model
Summary Conclusion: California
By shifting the junction between the concave and the convex surface away from the rim, the revised geometry makes the window more flexible than the previous design. This is good news if the loading is purely thermal as it allows expansion to develop more freely, hence less thermal stresses;
Comparing with the results shown in the previous window design which has concave radius larger than the convex radius, the current window has an increased bow and the reduced natural frequency. This indicates that the current window is more flexible;
On a like with like comparison, the current window geometry has its peak stress almost halved, and if one opts for the 0.5mm thick window which expects a peak temperature of only 50C at the Window centre (See Steve Virostek’s memo), the peak thermal stress is less than 100 MPa which is well below the stress limit for this material;
The natural frequencies are in general well below those obtained from the previous window geometry. This may or may not be acceptable for the physics requirement.
Uni-directional bowing is expected even if the inner surface is at a higher temperature than the outer surface.