# Presentation: 745966

## Development of the curved beryllium window

**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 

**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.**

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## Linear static runs

**Prescribed temp profile along window**

**Linear static runs**

**Window geometry:**
**Diameter: 16cm;      Thickness: 0.25mm**

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## Summary of the natural frequency runs

|  | 0.25mm  thk |  | 0.38mm thk |  | 0.5mm thk |  |
| --- | --- | --- | --- | --- | --- | --- |
|  | 2-D axisymodel | 3-D plate model | 2-D axisy model | 3-D plate model | 2-D axisy model | 3-D plate model |
| 1st freq. | 463 Hz. | 482 Hz | 559 Hz | 582 Hz | 635 Hz | 660 Hz |
| 2nd freq. | 1878 Hz | 586 Hz | 2190 Hz | 703 Hz | 2449 Hz | 793 Hz |
| 3rd freq. | 2343 Hz | 586 Hz | 2782 Hz | 704 Hz | 3140 Hz | 793 Hz |
| 4th freq. | 3254 Hz | 820 Hz | 3890 Hz | 1050 Hz | 4423 Hz | 1250 Hz |
| 5th freq. | 3849 Hz | 820 Hz | 4690 Hz | 1050 Hz | 5433 Hz | 1250 Hz |

**1****st**** mode shape of the 3-D model**

**2****nd**** mode shape of the 3-D model**

**3****rd**** mode shape of the 3-D model**

**4****th**** mode shape of the 3-D model**

**5****th**** mode shape of the 3-D model**

**1****st**** 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**

**5th mode shape of the 2-D model**

**Summary of the natural frequency runs**

## 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.**