Transcript Lau1-8-12-02

MuCool Absorber Review meeting
Fermi Lab, 11 – 12 August 2002
Window design and calculations
by
Wing Lau & Stephanie Yang
A brief review on the design and
development of the absorber window
to date
The first stage development -- a quest for a
better design
A torispherical Window with a tapered section was developed by
Ed Black. This window was considerably thinner than that
suggested by ASME VIII Div.1 which requires that window
thickness be uniform;
The tapered window design is out with that governed by the ASME
code “design by rule” guidelines, and hence a “design by analysis”
method was adopted;
Finite Element method, in particularly the non-linear step loading
technique was used to allow the structure to respond to the
material and geometrical changes up to its bursting pressure;
We were able to demonstrate the close relationship between the
FEA results and the pressure test results;
Both results demonstrated that the 30cm torispherical window would
sustain a pressure load of around 120 psi before it bursts at room
temperature. Taking the design pressure as 25psi, this represent a
safety factor of 4.8
To reach 120 psi burst pressure, the torispherical window requires a
minimum thickness of 0.33mm;
Both results show that the burst pressure would increase to around
156 psi when tested at 80K due to the increase in material properties
at low temperature. This would lead to a safety factor of 6.24;
Similar Finite element analyses were also carried out on windows of
various other sizes, notably the 22cm Absorber windows and the
34cm Vacuum windows for the Lab G experiment;
It shows that a minimum thickness of 0.24mm was required for the
absorber window to sustain a 120 psi bursting pressure;
Similarly, a minimum thickness of the same was required for the
Vacuum window to sustain a bursting pressure of 75 psi.
The stage 2 development – optimising thickness
by reshaping:
The shape of the window was changed to a “bellow” shape to make it
behave more in line with that expected from a sphere, thereby
eliminating most of the bending stresses which were dominant in the
torispherical window when it is subjected to a pressure load;
The revised window shape gave a marked improvement in thickness
reduction. The new window is generally thinner than the old design
for an area of up to 60mm circle radius. The comparison is 45% in
favour of the new design at the window centre;
As the dominant stresses in the new window design are in the
membrane direction, linear scaling is now possible. This allows us to
establish a linear relationship between the minimum pressure
thickness and the window sizes and its pressure rating without any
further elaborate FEA calculations ;
For the Lab G windows, the new window thickness could be as low as
0.13mm for both the 22cm Absorber window and the 34cm Vacuum
window;
The substantiation of the 22cm bellow shape Absorber window was
straight forward. In that the FEA result showed that at 0.13mm thick
(no machining allowance), it burst at just above 120 psi.
The substantiation of the 34cm Vacuum Window requires the
justification of its buckling capacity. In that the window is required to
withstand an external pressure of 25 psi.
The linear buckling analysis (eigenvalue solution) indicates a buckling
pressure of only 5.3 psi.
This approach always lead to very low buckling load because it does
not reflect the change in stiffness due to the geometry changes. A
better approach is to perform the non-linear analysis of the structure
under an incremental external load
A non-linear 2-D axisymmetrical model with incremental external load
No buckling at 52 psi
Local buckling detected at 54 psi
The 0.13mm thick window
General buckling developed at about 55
psi
Stage 3 development -- optimising by using tougher
materials
FEA were carried out on both the 22cm Absorber Window and the
34cm Vacuum Window using the Aluminium Lithium Alloy to see how
much improvement could be achieved.
A comparison of the mechanical properties for the two material is
shown below
Young's
Modulus, E
(N/mm2)
Yield stress
(N/mm2)
Ultimate
stress
(N/mm2)
Elongation
at rupture
(%)
T- 6061
69,500
273
310
17
Aluminium
Lithium Alloy
76,000
558
593
8
Material:
With the Aluminium Lithium Alloy and at 0.07mm thick, the
22cm Absorber Window can withstand a burst pressure of 125
psi. This could be visualised in the following avi file:
For the 34cm Vacuum Window – internal pressure consideration
At 0.07mm thick, the bursting pressure reaches 77 psi
34cm Vacuum Window – external pressure consideration
At 0.07mm thick, the buckling pressure was detected at
around 34 psi:
At 34 psi – prior to buckling
Buckling occurs at 34.3 psi
Comparison of the buckling shape of the 34cm Vacuum
Window with different thickness
0.07mm thick window, P = 34psi
0.13mm thick window, P = 54psi
0.18mm thick window, P = 75 psi
0.23mm thick window, P = 104psi
Evidence so far indicates that Aluminium Lithium Alloy offers another
significant reduction in Window thickness. This is what it offers:
Minimum thickness
for 120 psi burst
pressure (mm)
Maximum sustainable
buckling pressure
(psi)
Aluminium T-6061
0.130
54
Aluminium Lithium
Alloy
0.07
34
From 0.13mm to 0.07mm, it seems that there is everything going for it.
At this thickness, there is doubt if the window, with its bellow shape,
could be manufactured with consistent tolerances.
In order to take advantage of this tougher material, it seems that the next
step in our window development is not to try to optimise its thickness
further, but to look for a simpler geometry that allows an easy and
repeatable production.
Stage 4 development -- the new journey to a thinner
& simpler window!
The simplest window geometry is a flat window, and the most consistent
tolerance is that offered by a foil or a pre-pressed flat plate. Instead of
having a duplex contour, like our bellow window, the window could be
just a flat plate made out of a foil etc;
But a flat plate requires a thickness many times thicker than a curved
shell for the same load.
If we examine the stress formation of a flat plate, we notice that the
dominant stress is that caused by bending. If we could somehow
suppress the bending, in other words, its out of plane deflection, we
would be able to eliminate most of the bending stress
Our next window development is based on this principle:
Imagine a disk (circular plate), if we can somehow tension it to such an
extent that any further out of plane deflection are being “resisted” by
these tension forces, like a tightly strung guitar string, or more to the
point, like a trampoline.
The Creation of a pre-tensioned Window
Burst Pressure
Can’t go anymore,
already stretched to
the limit, like Dan’s
budget!!
Pre-tension
Pre-tension
How does it work?
The window is referred hereafter as the thin foil;
The foil is pre-tensioned to the exact tension level. This reduces the
amount of bending deformation when the window is subjected to an
internal pressure afterwards;
With no room for developing any further out of plane movement, the foil
will “convert” any additional stresses into membrane stress.
The amount of pre-tension must be exact – too little will promote further
bending stresses, and too much will damage the foil by tear.
FEA so far suggests that a foil of 0.1mm will sustain a burst pressure of
100 psi (4 times the design pressure) by using Aluminium Lithium Alloy.
But it requires some detail restraining at its perimeter in order to
achieve the require pressure rating. As we only had the first set of
results a few days ago, we would like to conduct further analyses to
ensure that the proposed scheme is valid for all boundary conditions
before we confirm its general acceptance.
We shall explain our results with further plots and figures at our next
meeting
What next?
The evidence so far suggests that we could continue to thin
the window using higher and higher strength materials. But
there is doubt that the ultra thin window, if the present shape
is to be maintained, may not be possible to produce.
Our next development phase should concentrate more on
making windows that, on one hand, utilises the advantages
offered by the higher strength materials, and on the other
hand, doesn’t involve complicated manufacturing procedures.
Naturally, we want a design the guarantees consistent
accuracy
From an engineering point of view, we should continue to
develop the pre-tension foil window.