BTEV PIXEL TEST BEAM

CRYO-VESSEL VACUUM WINDOW

Vacuum Window Engineering Note

(per Fermilab ES&H Manual Chapter 5033.1)

Identification and Verification of Compliance:

Prepared By Date Div/Sec: *Herman Cease, 06/06/2003, PPD/MECH*

Reviewed By Date Div/Sec:

Div/Sec Head Date Div/Sec:

Director's Signature not required (no exception needed).

Vacuum Vessel Title: *BTeV; Pixel Detector Cryo Assembly*

> Vacuum Vessel Number:
>
> *N/A, The vessel volume is small and does not meet the requirements
> for a vacuum vessel.*

Vacuum Window Drawing Number: *8918.120-MB-407456*

Assembly Drawing No.: *8918.120-ME-407399Rev A*

Laboratory location code: Meson Test Beam Facility MT6A

Purpose of vacuum vessel and vacuum window:

*Testing of pixel detector modules for BTeV.*

Internal MAWP: *14.7 psi*

External MAWP: *0 psig*

Working Temperature Range: *Room Temperature*

1 Design Verification calculations included.

2\. Fabrication: Is this vacuum window fabricated in house? *Yes*

If "Yes", attach the written fabrication procedure in the Note Appendix.

*Aluminum sheet metal window, 8918.120-MC-407456*

3\. Inspection: Attach inspection reports and Travelers in the Note
Appendix. Include date(s) of manufacture.

Window shall be inspected during fabrication and installation by a
Qualified Person. Once a year the window should be re-inspected for
damage.

4\. Testing: Attach acceptance testing procedure and results in the Note
Appendix. Include date of testing.

5\. System Venting Verification:

> Is the relieving system of the vacuum vessel to which this vacuum
> window is attached sufficiently sized such that if the vessel is
> pressurized, the maximum differential across the window cannot exceed
> the design differential pressure of the vacuum window? *Yes*

6\. Operating Procedure Section:

Is an operating procedure necessary for the safe operation of this
vessel? *No*

If "Yes", the operating procedure must be attached to the Note Appendix.

7\. Hazard Analysis: Is the safety factor on this vacuum window less
than 2.0? *No*

If "Yes", a hazard analysis must be prepared and attached to the Note
Appendix.

Design Verification Calculations

*Calculating Window Stresses and Deflections:*

> Using TM-1380: Section 4.1 Guidelines for Flexible Material Windows.
> Held not Fixed.

Circular 3.375" diameter by .012" thickness aluminum window under
vacuum.

> t = 0.012" : thickness of window (inch)
>
> a = 1.688" : radius of window measured at O-ring on flange (inch)
>
> q = 14.7 psi : uniform pressure on window (psi)
>
> v = .33 : poisson's ratio
>
> E = 1e7 psi : Young's modulus of window material (Alum. 6061-T6) (psi)

Deflection y, out of plane window deflection :

> y = 0.662 a (qa/Et)\^1/3 (equation 4.1a)
>
> y = 0.662 \* 1.688 \* (14.7 \* 1.688 /1e7 \* 0.012)\^1/3
>
> y = 0.066 inches
>
> Stress S, internal window stress:
>
> S = 0.423 (Eq\^2a\^2/t\^2)\^1/3 (equation 4.1b)

S = 0.423 (1e7 \* 14.7\^2 \* 1.688\^2 /0.012\^2)\^1/3

S = 14,800 psi

> Fu = 45,000 psi, the ultimate tensile stress for 6061-T6

So, to find allowable stress, S = .5 F~u~ = .5 \* 45000 = 22,500 psi

> 22,500 psi \> 14,800 psi. The stress on the window is less than the
> allowable stress, and has a factor of safety of 3 based on the
> ultimate strength of the window.

Design Verification Calculations

*Calculating the Relief Device:*

Orifice Size:

The area of the relief opening is larger than the areas of any potential
inlet path, so the rate of relief would always exceed the rate at which
the gas enters the vessel. The diameter of the opening is 3.375 inches
which has a circumference of 10.6 inches. The relief plate would have to
open 0.14 inches to exceed the area of a 1 ½ inch diameter opening.

Cracking Pressure:

The cracking pressure should be no more than ¼ of the maximum pressure
on the window. The window is rated for 14.7 psi vacuum. The maximum
allowable positive cracking pressure for the relief is then:

¼ \* 14.7 = 3.7 psig

Twelve shoulder bolts and six compressed springs hold the window in
place against the o-ring. The shoulder bolt length is 3/8 inch and the
spring length is ½ inch, causing a 1/8 inch spring compression against
the window.

> The spring used is McMaster Carr #9435K115, which has a spring rate of
> 30.44 lb/inch. The initial spring compression at 1/8 inch is:

1/8 \* 30.44 = 3.8 lbs per spring.

The cracking pressure for the valve is then:

> 3.8 lbs spring force\* 6 springs / (1.688\^2 \*3.14) = 2.5 psi
>
> The actual valve cracking pressure is 2.5 psig, which is below the
> maximum allowable cracking pressure of 3.7 psi.

Design Verification Calculations

*Verification Testing and Procedures:*

> A vacuum pressure of 14.7 psi will be applied to the window. The
> window will be inspected by a Qualified Person and the date will be
> recorded.