HADES Piston Selection and Development

6556K377 on McMaster was selected as the piston. The relevant dimensions and properties of 6556K377 are enumerated in the table below:

Given a 4.5" coupling section, this gives us a 1" margin on separation distance.

¹ Specs for 303 stainless steel used below as estimate.

Buckling Calculation

We need to ensure that the rod of the piston will not buckle when it transfers load to the diaphragm. To perform these calculations we know that the tensile modulus of steel is 28000 ksi:

$//<![CDATA[ \begin{array}{l}P_{cr} = \frac{4 \pi^2 E I}{L^2}\end{array} //]]>$

Given the area moment of inertia for a circular cross section is: $//<![CDATA[ \begin{array}{l}I = \frac{1}{4}\pi r^4\end{array} //]]>$

P_cr,steel = 12,789 lbs

As you can see, there is approximately a 35x factor of safety on rod buckling.

Burst Factor of Safety

Here we calculate the precise burst factor of safety on our piston. Some details:

• • Aluminum 6061-T6 has a tensile yield strength of approximately 276 MPa = 40.03 ksi
  • The inner radius of the piston bore is 0.625"
  • The wall thickness is approximately 0.125"

  $//<![CDATA[ \begin{array}{l}\sigma_{hoop} = \frac{pR}{t} = \frac{p*0.625in}{0.125 in} = 40030 \frac{lb}{in^2}\end{array} //]]>$
P_burst = 8006 lb/in²

The necessary pressure for a separation of 360 pounds is calculated as follows:

$//<![CDATA[ \begin{array}{l}P_{sep} = \frac{F_{sep}}{A_{inner}} = \frac{360 lb}{\pi*(0.5625 in)^2}\end{array} //]]>$

P_sep = 362.17 lb/in²

This gives a ~22x factor of safety on burst.

Premature Separation Factor of Safety

Next we check the factor of safety on premature separation, knowing that as previously calculated the pressure difference for flight will be approximately 12.56 psi (it will actually be much less due to a much lower expected altitude as of 2/2/2018):

$//<![CDATA[ \begin{array}{l}F_{sep} = P_{diff}*\pi*r_{bore}^2\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}F_{sep} = 12.56 psi*\pi*(0.625 in)^2 = 15.4 lb\end{array} //]]>$

Given that we plan to use 180lb of shear pins, this provides a minimum of ~11.7 factor of safety on premature separation due to internal pressure buildup.

Resources:

The following resources are useful materials for learning about pressure vessel and piston theory:

[1] Jeff Hanson, Texas Tech: Intro to Thin Walled Pressure Vessels

[2] University of Colorado, Boulder: Thin-Walled Pressure Vessel Theory

[3] NASA Aerospace Pressure Vessel Safety Standard, 1974: NSS/HP-1740.1

Note that this standard was cancelled in July, 2002.

[4] Aerospace Corporation, Operational Guidelines for Spaceflight Pressure Vessels

[5] NASA, Structural Design Requirements and Factors of Safety for Spaceflight Hardware