MUON Collaboration meeting at Mission Inn, Riverside, California
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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

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MUON Collaboration meeting at Mission Inn, Riverside, California January 27 - 30, 2004

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Muon collaboration meeting at mission inn riverside california january 27 30 2004

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


Muon collaboration meeting at mission inn riverside california january 27 30 2004

A short summary of the FEA work

carried out on the Beryllium Window


Muon collaboration meeting at mission inn riverside california january 27 30 2004

Summary

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.


Muon collaboration meeting at mission inn riverside california january 27 30 2004

Zoom in on high stress area

Stress distribution: Max. approx 150 MPa

Deflection due to thermal load. Max 1.72mm

Linear static runs

Window geometry:

Diameter: 16cm; Thickness: 0.25mm

Prescribed temp profile along window


Muon collaboration meeting at mission inn riverside california january 27 30 2004

1st 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


Muon collaboration meeting at mission inn riverside california january 27 30 2004

Summary Conclusion:

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.


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