HADES Piston Selection and Development

The Design Space

Our redesigned piston must have the same form factor as a McMaster piston to allow for easy descope. Given the team's Fall 2017 semester experience with tie-rod pistons, we elect to continue using this style.

DTEG Requirements

As of 1/4/2018, the latest edition of the Spaceport America Cup's Design Test and Evaluation Guide has the following requirements for SRAD pressure vessels. These requirements can be read in more detail here.

4.2.2 DESIGNED BURST PRESSURE FOR METALLIC PRESSURE VESSELS

4.2.4.1 PROOF PRESSURE TESTING

4.2.4.2 OPTIONAL BURST PRESSURE TESTING 

You can find a complete list of DTEG requirements that affect the Recovery system on the Hermes Recovery System page.

Desired Performance

The piston must be able to supply enough force at its operating pressure to break the shear pins with a 2x safety factor, which is the safety-critical guideline for parachute components presented by NASA (Section 3.3.1.5). As of January 4, 2018, we are designing for 180lbs of shear pins, and thus the piston must supply 360lbs. The same source (Section 3.3.1.6) dictates a design burst pressure factor of 2x the maximum design pressure, which aligns with DTEG requirement 4.2.2. [5] Thus, we expect the piston to burst when it supplies 720 lbs. Here, we make use of thin-walled pressure vessel theory [2], paraphrased below:

Neglecting end effects, the limiting factor will be the hoop stress in the piston bore:

  $//<![CDATA[ \begin{array}{l}\sigma_{hoop} = \frac{pR}{t}\end{array} //]]>$

Given Aluminum 6061-T6 as the material, which typically has a tensile yield strength of approximately 276 MPA (this analysis neglects the internal temperature of the piston due to the gas produced by the combustion of black powder. A transient thermal spike could degrade material properties when the piston is pressurizing, but we assume that the magnitude of energy released is negligible compared to the thermal mass of the aluminum). The tensile yield strength can be used to calculate the design burst pressure. For this preliminary analysis, the wall thickness is chosen to be a 0.25x reduction in that of the previously-qualified piston bore (part 6491K254 on McMaster):

$//<![CDATA[ \begin{array}{l}t_{new} = \frac{1}{4}*t_{6491K254} = \frac{1}{4}*0.25in = 0.0625 in\end{array} //]]>$

  $//<![CDATA[ \begin{array}{l}\sigma_{burst} = \sigma_{tensile \ yield} = 276*10^6 Pa \approx 40030 psi\end{array} //]]>$

Applying P = F/A where F is 720 lbs at burst and A is the area of bore, we find:

$//<![CDATA[ \begin{array}{l}\sigma_{burst} = \frac{F*r}{A*t}\end{array} //]]>$

Then, assuming a circular bore, area takes the form A = πr² and we can solve for the radius of the cylinder.

$//<![CDATA[ \begin{array}{l}r = \frac{F}{t*\sigma_{burst}*\pi}\end{array} //]]>$

Plugging in numbers, we find the minimum radius of the piston bore:

$//<![CDATA[ \begin{array}{l}r = \frac{720 lb }{0.0625 in * 40030 psi * \pi}\end{array} //]]>$

r_{bore, min} = 0.092 in

Now, we seek to find an upper bound on the possible piston radius. Another requirement of the piston is that it cannot break the shear pins prematurely due to an internal build-up of pressure caused by the altitude difference. Between 4,245 ft (the altitude of Truth or Consequences, NM) and 152,945 ft ASL (a simulated upper bound on performance as of January 4, 2018), the pressure difference is approximately (given by the 1976 Standard Atmospheric Calculator using no temperature offset) -86600 Pa ≈ 12.56 psi.

Applying a 2x safety factor to premature separation (again in accordance with safety-critical recovery components as dictated by NASA), we calculate the maximum allowable radius of the piston [5]:

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

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

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

$//<![CDATA[ \begin{array}{l}\sqrt\frac{0.5 * 180lb}{12.56 psi * \pi} = r_{bore}\end{array} //]]>$

r_{bore, max} = 1.51 in

Of course, an additional constraint on piston radius is the allowable space inside the Avionics Bay Coupler. The Team previously found that 6491K254, which had a 1in radius, was large and provided little room for Avionics to house its hardware, especially the batteries. Thus, a logical conclusion is to restrict the new piston geometry to radii below 1 in, which will provide an even larger safety factor on premature separation due to a pressure differential.

Geometry

Based on the calculations above, we conclude that the allowable bore-radius range is 0.092 in → 1 in. This range can be further refined to 0.25 in → 1 in because 0.5 in is the minimum typical bore diameter for tie rod air cylinders.

Tolerances

To create the bore, we plan to take an existing piece of hollow aluminum tube and turn it down to the proper outer radius (the inner radius can be achieved by drill and then reamer). The chosen wall thickness of 0.0625 is achievable within the 0.5 thousandths diameter tolerance of lathes on campus.

COTS Solutions

First, it is necessary to determine an appropriate COTS solution for the piston. Due to timeline constraints associated with the difficult task of engineering base plates (most notably, all of the required seals), it is logical to take an existing piston and modify it to meet our needs (i.e. changing the throw on the piston, making mass saving cuts, etc). In this investigation, we examined pistons between 0.5 in and ~1 in bore diameter.

Solution No. 1: 1691T104 

The first solution is a 0.5" diameter (0.25" radius) compact tie rod air cylinder with a 4" stroke. Because the coupling section is 4.5", we need a much larger throw than that to achieve an appropriate factor of safety. Thus, it is necessary to replace the bore with a longer one (and also the tie rods). This is also necessary because the 1691T104 piston has a composite bore, which adds safety complications.

Some notable challenges with this option are:

• • Rod end is internally threaded. We'd be making a new rod anyways, but there's always a question of compatibility...
  • Different port size than our current piston. Not a huge issue because we'd probably redesign our actuation system anyways.
  • Only two holes for mounting on each base plate–poor load distribution
    

This piston has 4 inches of throw... Assuming that everything but the bore and the tie rods are identical, it may make most sense to actually purchase a piston with much less throw, such as the 1691T69.

Solution No. 2: 4211K121

This piston has a 9/16" diameter with 304 Stainless Steel as the body material and a 4" stroke length. Some notable advantages of this option are:

• • It is compatible with a sensor (which would cost an additional ~$60) that we may be able to use to tell Avionics if the piston hasn't fired. Not sure if this is any huge advantage though. If the piston doesn't fire, then we're sorta out of luck at that point.

Disadvantages include:

• • Again, need to machine a new bore due to increased necessary throw length as well as bore material (we want to avoid having a steel pressure vessel).
  • Correspondingly need to machine a new rod and purchase new tie rods.

Again, it may make sense to go with a similar piston with less stroke length. 

Solution No. 3: 5036K121

This piston has a 3/4" diameter with 304 Stainless Steel as the body material and a 4" stroke length. Some notable advantages of this option are:

• • It will not rotate, which may provide some advantages against things unscrewing during deployment.

Disadvantages include:

• • Two rods, which means that it probably will weigh more.
  • Increased manufacturing difficulty associated with a diaphragm with two holes will need to mill instead of power tap it on the lathe–also may require a redesign of diaphragm mass saving cuts.
  • Again, need to machine a new bore due to increased necessary throw length as well as bore material (we want to avoid having a steel pressure vessel).
  • Correspondingly need to machine a new rod and purchase new tie rods.

Again, it may make sense to go with a similar piston with less stroke length.

Solution No. 4: 6453K119 or 6453K143

This piston has a 3/4" bore diameter made from aluminum and has a 5" or 5.5" stroke length, respectively. Some notable advantages of this option are:

• • The square end plates fit the form factor we have already used.
  • Stroke length is exactly what we need, so it is a complete COTS solution that requires no adjustment. We could make mass saving cuts, change rod material (which is currently 303 stainless steel).
  • It's port inlet is 1/8 NPT, which for what it's worth, we already have compatible fittings for 1/8 NPT. This shouldn't be a driving factor, just a perk.

Disadvantages include:

• Only has two bolt attachment holes to the end plate on the payload side.

Solution No. 5: 6453K153

This piston has a 1-1/8" bore diameter made from aluminum with a 5.5" throw length. Some notable advantages of this option are:

• • The square end plates fit the form factor we have already used.
  • Stroke length is exactly what we need, so it is a complete COTS solution that requires no adjustment. We could make mass saving cuts, change rod material (which is currently 303 stainless steel).

Disadvantages include:

• Only has two bolt attachment holes to the end plate on the payload side.

Solution No. 6: 6556K416

This piston has a 1-3/4" bore diameter made from aluminum with a 5.5" throw length. Some notable advantages of this option are:

• • Has 4 bolt holes on the payload size, which will lead to better load distribution.
  • The square end plates fit the form factor we have already used.
  • Stroke length is exactly what we need, so it is a complete COTS solution.

Disadvantages include:

• • Doesn't represent a large mass savings

Selection Visualization

To help visualize the different options, here are some of the possible pistons placed side by side:

The Decision

At this point in time, I think it makes most sense to move forward with Option 6453K153. Its bore radius is ~0.5 in, which is marks approximately the bottom 1/3 of the reasonable range.

Selected Piston Dimensions and Improvements

The relevant dimensions and properties of 6453K119 are enumerated in the table below:

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

Rod Improvements

The rod can be improved by making it out of aluminum instead of stainless steel. An estimate for mass savings is calculated below:

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