Calculating the Properties of the MiniBooNE Vacuum Window Immediately Upstream of the Target
Larry Bartoszek, 4/25/02
Using the FNAL standard, TM-1380, "Mechanical Safety Subcommittee Guidelines for Design of Thin Windows for Vacuum Vessels," we calculate the minimum thickness required of the beam pipe window immediately upstream of the MiniBooNE target.
The first step is to calculate the allowable stress for the material that the window is made from, Grade 2 unalloyed titanium, .002" thick.
(This is a definition for MathCAD)
Ultimate strength of this titanium
.2% Yield strength for titanium
Allowable stress based on ultimate strength
Allowable stress based on yield strength
The allowable stress is the lower of S1 and S2, or in this case S1, 25,000 psi. Next, we give more constants needed for the next calculation.
The thickness of the window
The radius of the window
Atmospheric pressure on the window
Young's modulus of titanium
Equation for calculated stress in a circular window
The calculated stress is not less than the allowable stress for grade 2 titanium. What would the ultimate strength have to be for this size window?
This would correspond to grade 4 titanium, Fu = 80 ksi.
As a check assuming the material was strong enough, what would be the deflection?
This is a reasonable number, maybe even small for typical windows