Booster - Staging Cone

SCP002 (Staging Cone).PDF

SCP001 (Staging Cone Base).PDF 

Purpose

The Staging Cone serves as an attachment interface between the booster and the sustainer stages of Phoenix. After burn of out the booster motor, drag forces should be larger on the booster due to its larger freestream area causing the sustainer should passively separate from its resting position on the Staging Cone. Recovery soft goods are stored in the Staging Cone and are released when the piston separates the Staging Cone from the booster airframe. 

Requirements

1. Must interface with the Sustainer nozzle
2. Must withstand the weight of the Sustainer (during flight)
3. Must be able to be machined using tooling in the Deep (MIT Machine Shop)

Design Details

Left: Isometric view of the staging cone. Right: Cross-sectional view of the staging cone 

Materials:

Aluminum 6061-T6 Round Stock (Cone)

Aluminum 6061-T6 Tube Stock (Base)

#8-32 Fasteners (18-8 Steel)

Software Used:

SolidWorks 2019 (CAD and FEA)

Design and Analysis

Design Brief:

The Staging Cone is designed to be able to attach by way of shear pins to the booster airframe and to the sustainer by a geometrical fit. The upper cone (henceforth the cone section) of the Staging Cone is to be the exact geometry of the sustainer nozzle (expansion section) so that it sits properly with no tilt and such that the entire wall area inside the nozzle is in contact with the cone. This calls for fine, and currently unspecified, tolerances. If manufactured correctly, the top lip of the base section of the Staging Cone should also be in contact with the bottom of the sustainer nozzle, dividing the weight of the sustainer between the base and cone sections of the Staging Cone. The number of bolts being used to attach the cone and base sections was derived assuming worst case tolerances and all of the sustainer's weight is on the cone section. In the alternate extreme case where weight is only on the base lip, there is no force on the bolts.  

Hand Calculation Analysis:

The spreadsheet that completed these hand calculations can be found here: https://docs.google.com/spreadsheets/d/1kWIMJ8-9FpM9AI0ZJvyIqJiwlM8lQ-BzgPI3EAgFaO4/edit#gid=0. If you would like edit access, contact Max Kwon (maxkwonkorea@gmail.com or maxkwon@mit.edu) 

There were three failure modes that were taken into account when modifying the design of the Staging Cone. 

1) Exceeding the shear strength of the bolts

To run calculations on the shear strength of the bolts, it was assumed that all of the sustainer's weight would be on on the cone section and reacting against the bolts. This would yield the most conservative estimate. The forces accounted for on the cone were the weight of the sustainer under a maximum acceleration of 20 G's and drag force at Max-Q (from RASAero). To find the shear stress, this total force is this divided by the minor area of a bolt multiplied by the number of bolts to be used. To find the equivalent or von mises stress, this stress is then multiplied by the square root of 3. This comes from the equation of von mises stress under the condition of shear only. This von mises stress allows us to compare against the tensile strength of the bolt which is easier to find. 

2) Exceeding the bolt tear out strength of the aluminum 

To calculate the tear out stress from the bolts reacting against the aluminum of the base (smaller thickness), that same derived total sustainer force is then divided by the projected area of the bolt onto the walls of the hole. This is A = minor diameter * wall thickness. This area calculation was used knowing that there are more correct and conservative estimation methods but it was felt that this was sufficient and simple. After finding this stress, a stress concentration factor of Kt = 3 was multiplied. Without this, stress calculations will be severe underestimates. 

3) Exceeding the maximum moment the cone could impart on the sustainer 

To calculate the pure moment that would be imparted by the cone section onto the sustainer in the event of non-zero angle attack, a maximum angle of attack is specified. In the case of my calculations, it was 5 degrees. Flight conditions including velocity and dynamic pressure are specified at their maximum values (these values are coupled). Experimental data on the drag coefficient of a cylinder based on the Reynolds number of the flight was then used with a compressibility factor given that the rocket will be supersonic to find the drag on the projected area of the rocket. This force is then assumed to be concentrated at half the length of the rocket and a moment is calculated from there. 

This moment can then be used to find the stress on the cone after calculating the minimum second moment of area of the cone. We use the minimum since a pure moment does not have one reference position and therefore this minimum point is where failure would occur. The equation for a circular ring is posted below. Stress can be found using max_stress = M*r_max/I_min where r_max is the maximum distance away from the center line of the cone, M is the moment and I_min is the minimum second moment of area.

From this, it was found that 8 bolts would suffice, but is NOT the minimum. 

Output for 8 bolts:

Given: 

Status: Completed

Actual machining plan used:

• Used slightly over-size round stock for both parts
• Lathe speeds were 800 sfm, max 1500 rpm
• Holes drilled at 400 rpm
• See drawing for hole sizes
• Base:
  • Faced both ends and turned the OD to create reference surfaces
  • Chucked stock from OD
  • Drilled out thru-hole on the lathe with Todd's largest drill bit
  • Ran a program to turn the inside profile on the lathe
  • Turned MPT interfacing-end to final dimension
  • Chucked part in radial indexer on mill
  • Drilled all thru-holes, tapped the holes that needed threads
  • Spot faced the forward-facing holes to allow for bolts to sit flush
  • Chucked part from the ID with the forward facing direction in the positive z direction on the lathe
  • Ran a program to turn the outer profile
• Cone:
  • Faced both ends and turned the OD to create reference surfaces
  • Chucked stock from OD
  • Turned Base-interfacing side to final dimension
  • Drilled several holes in the inner diameter of various sizes to get as much material out by drilling as possible
  • Turned half of the inner profile of the inside with a large boring bar that would not vibrate
  • Chucked part vertically in the mill
  • Used 3/4" end mill to drill all the way through the inner profile
  • Chucked part back in the lathe
  • Used a smaller boring bar to turn the rest of the inner profile
  • Chucked part in the radial indexer
  • Drilled and tapped all thru-holes
  • Chucked part from the ID with the forward facing direction in the positive z direction on the lathe
  • Ran a program to turn the outer profile
  • Drilled and tapped thru-hole on the lathe

Problems

• Inner profile hard
  • Inner profile was really too deep to be turned on the lathe
  • Not sure if that would work better using CAM and a large end mill on the milling machine
  • Could also just make the inner profile easier to machine
• Radial indexing
  • Radial indexer in the Deep not precise, after one or two full rotations the holes no longer lined up as precisely
  • Perhaps do all holes in the same rotation, or do all operations on each hole before moving to the next hole
• Fit check
  • Burrs from drilling/tapping made fit checking difficult
  • Could drill/tap holes immediately after creating reference surfaces, then the machining process would take off the burrs

Changes from Demo II

The main design change from Demo II is that the Staging Cone (Phoenix) will be made in two separate pieces. This was done for the purpose of making machining faster and more practical. It may also have the unintended (but welcome) consequence of making the part cheaper. This is due to the fact that there is less material that has to be cut away since the smaller diameter cone is made from a separate piece of stock from the larger diameter base (booster airframe retention). 

Manufacturing

Preliminary Plan:

• Take both stock and face both sides on the lathe
• Turn outer profile (for both)
• Bore our inner profile (for both)
• Use Radial Indexer on the mill to drill holes (in both)

Testing

Loading Preliminary Plan: