Overview

The HADES Cup transfers load from the piston and diaphragm to the booster section, breaking the shear pins and initiating the Recovery deployment sequence.

v1.0: Pathfinder

The first edition of the cup is a simple aluminum cylinder that accepts the Diaphragm at one end via grub screws. It is a simple aluminum cylinder with measured dimensions:

Ground testing has shown that the cup does not buckle under normal piston operating loads, even those as high as 3500 lbs (an order of magnitude greater than normal operating loads) as we predict we saw in Ground Test November 10, 2017.

v2.0: Hermes Dimensions

Development

In addition to a change in outer diameter to accommodate the switch from a 6" ID to 6" OD rocket body, v2.0 of the Hermes cup involves making mass saving cuts.

To quickly determine structural integrity, we can perform a buckling calculation, assuming long vertical cuts are made:

Given some amount of aluminum from the cup on both ends of the column, this scenario is best approximated as a double-wall-mount buckling problem. Only first order buckling is possible, because the mission package tube constrains the cup in one direction. Thus the critical buckling load is:

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

From Matweb, the Young's Modulus of aluminum is 68.9 GPa = 1.00e+7 psi. The area moment of inertia for a rectangle under buckling is $//<![CDATA[ \begin{array}{l}\frac{bh^3}{12}\end{array} //]]>$. Given a 0.1" cup thickness, h, we can solve for the minimum width of each column, b. We apply a 2x factor of safety on the piston load (360 lbs) and generalize the number of columns as n_c. Assuming evenly spaced columns, each column will endure an equal amount of load. An additional factor of safety is applied when we set L = 14", the total height of the cup:

$//<![CDATA[ \begin{array}{l}\frac{720 lb}{n_{c}} = \frac{4*\pi ^2 *10^7 psi * b *(0.1 in)^3}{12*(14in)^2}\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}b = \frac{4.3 in}{n_{c}}\end{array} //]]>$

So if, for example, 8 evenly-spaced columns are used, the minimum necessary width of each column is 0.54 inches.

Dimensions

The dimensions for the Hermes cup were chosen in part due to an investigation on Hermes Packing Procedures and Volumes. Here, we found that pathfinder packing volume is roughly appropriate. Thickness of the cup increased, but we used this new thickness when simulating for mass saving cuts. Because the airframe is 5.88" ID, we want some tolerance between the OD of the cup and the ID of the airframe. On the Pathfinder vehicle, this was measured as ~0.25" in tolerance, bringing the required outer radius of the cup to be 2.815" and correspondingly the inner radius to be 2.69". Due to the need to maintain roughly the same packing volume as Pathfinder, the overall length of the cup must be adjusted to 15"

Resources

NASA, Buckling of Thin-Walled Circular Cylinders