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.
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.
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:
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):
Applying P = F/A where F is 720 lbs at burst and A is the area of bore, we find:
Then, assuming a circular bore, area takes the form A = πr2 and we can solve for the radius of the cylinder.
Plugging in numbers, we find the minimum radius of the piston bore:
rbore, 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]:
rbore, 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.
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.
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.
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.
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:
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:
Disadvantages include:
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:
Disadvantages include:
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:
Disadvantages include:
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:
Disadvantages include:
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:
Disadvantages include:
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 I previously calculated. Things I will need to check are:
EDIT: After first deciding to use McMaster 6453K153, it became apparent that we cannot purchase a companion eye-nut. Although there are some workarounds, none are worthwhile in comparison to switching to 6556K377, which has a thread size of 3/8"-16. The bore size is only marginally larger.
The relevant dimensions and properties of 6556K377 are enumerated in the table below:
| Bore Diameter, Inner (in) | Bore Material | Stroke Length (in) | Rod Material | Rod Diameter (in) | Total Length (baseplate to baseplate; in) |
|---|---|---|---|---|---|
| 1-1/4 | Aluminum | 5.5 | 303 Stainless Steel | 3/8 | 7.75 |
Given a 4.5" coupling section, this gives us a 1" margin on separation distance.
The rod can be improved by making it out of aluminum instead of stainless steel. We can estimate the mass savings by knowing that the approximate piston rod volume is 0.911 in3, the density of 303 stainless steel is 0.289 lb/in3, and the density of 6061 aluminum is 0.0975 lb/in3. Given this information, replacing the steel rod with one made from aluminum will save approximately 0.174 lbs.
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 and the elastic modulus of aluminum is 10000 ksi.
Given the area moment of inertia for a circular cross section is:
Pcr,steel = 15,765 lb and Pcr,aluminum = 5,630 lb
As you can see, both steel and aluminum rods have large factors of safety on buckling due to piston force.
Here we calculate the precise burst factor of safety on our piston. Some details:
Pburst = 2115.007 lb/in2
The necessary pressure for a separation of 360 pounds is calculated as follows:
Psep = 362.17 lb/in2
This gives a ~5.8x factor of safety on burst.
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):
Given that we plan to use 180lb of shear pins, this provides a minimum of 14.4 factor of safety on premature separation due to internal pressure buildup.
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