# Acrylic Stress and Prices

Everything is paid for and ready for the vacuum chamber to start its journey up here on Monday next week with an ETA of October 8th.

I spent today talking to acrylic vendors about pricing for a large acrylic sheet to cover the 25″ dia. opening at one end the of vacuum chamber and got prices listed below:

The sheets come 48″ wide, and for a 28″ length of, it would cost:

• 2″ thick – \$1200
• 1.5″ thick – \$900
• 1″ thick – \$265

Clearly the 1″ Acrylic sheet is the best price, but the question is, does it have enough strength to hold back the air pressure vacuum over a diameter of 25″?

I found a handy power point slide (attached and zipped), which shows how to calculate the safety factor for a given strength versus diameter for a vacuum chamber window.  It turns out that for an acrylic window with 25″ diameter of unsupported space and 1″ thick, it has a safety margin of 6.8x.  In other words, the window can handle over six times more air pressure before breaking.  For a 1.5″ thick window, it has a safety factor of 15 times and for 2″ thick piece, 27 times.

Here are the calculations I carried out:

First, calculate the stress on the window for a known thickness versus radius (from the power point slide):

Sm=k(wR^2/t^2) where
Sm – the stress on the window in PSI
k – is the coefficient for circular plate, I used 1.1 which is a conservative estimate.  This constant is described in the power point presentation.
w – the uniform pressure across the window, which because Edmonton is ~2300ft above sea level, means our air pressure is 13.66psi.
R – is the radius of the unsupported part of the window, in our case 12.5″ or half of the 25″ diameter (this was reported by the vendor)
t – is the thickness of the window which in our case is 1″, 1.5″ or 2″

The stress for a 1″ thick acrylic window is 2300psi, for 1.5″ thick window it is 1043psi and for 2″, 587psi.

The safety factor of cast acrylic is then calculated by:

S.F. = Modulus of Rupture / Max Stress

where the Modulus of Rupture for Acrylic is typically 16,000psi.

Clearly the 1″ thick acrylic is thick enough to handle the air pressure.  (Please check my assumptions and calculations!)  I don’t plan to buy the acrylic until I can measure the inside dimensions of the vacuum chamber.  The good news is that it cutting the acrylic with a water jet shouldn’t cost me more then \$100 and I can use the extra acrylic to cut 8″ windows for the ports if necessary.

My next step is to model the cavity with a 3D modeling program and then build a plastic replica before cutting any copper.  The replica is not really important, but the process by which the tolerances are assured is and may include jigs if necessary.

I also plan to add the following to the wiki:

There is a method used to make sure the cavity is resonating in the right mode, TE0,1 at the right frequency, 2.45Ghz.  Typically when the cavity is out of tune, it means that the TE0,1,n mode is resonating at a frequency other then the desired 2.45Ghz.  The problem is that there are a lot of resonant frequencies, as shown by each dip in figure XX (to be attached) and it is first necessary to determine which one is the TE0,1 mode before moving the tuning plate. The method is simple.  First, with an S-parameter plot, locate the frequency of the nearby dips and add a “field monitor” in the simulator, then rerun the simulator which will calculate fields for those frequencies.  After looking at the field configuration and determining which one is the TE0,1,n mode, then determine if it higher or lower then the desired 2.45Ghz.  If it is higher, then make the chamber longer, if it is lower then make the chamber shorter (check this!).  It make take a few iterations before the appropriate mode is resonating at 2.45Ghz.

On the lab bench, it will be critical to setup the cavity tuning as closely as possible to the simulated cavity, and then move it just enough to bring the resonance into focus.  The problem with a real cavity is that there is no method to tell which mode the cavity is resonating in.  It might be possible to use the expected S1,1 value… (hmm)