Geometry and Structural Stability

Structures Division

Geometry and Structural Stability

Meghan Capra

2006-2007 F.A.S.T. Pallet

Copyright © 2002 Department of Mechanical Engineering, Colorado State University

ABSTRACT

The structure for a sounding rocket payload must be able to support all internal components and bracketing as well as survive extreme conditions while maintaining a very low mass. The ability to reduce overall mass while sustaining a rigid structure is critical to the success of an aerospace mission, due to (1) the calculated characteristic velocity of a mission and (2) the rigorous conditions during flight. Creating a suitable structure entails detailed investigation of different geometric designs. The results will be computer analyzed and experimentally tested, then integrated into a key component in the payload of a sounding rocket mission.

INTRODUCTION

The payload is all of the equipment needed to complete the research for the mission. Each payload is allotted a certain amount of mass, which must be maintained in order for the mission to be completed as calculated. The structure of a payload is crucial in order to protect all the internal components for any given task. Because of its importance the structure tends to account for a large portion of the total mass.

The FAST Pallet team needs a small case which will house all necessary components to successfully create an artificial space plasma bridge for a Japanese Aerospace Exploration Agency (JAXA) sounding rocket mission. Components for this mission consist of a large Xenon tank, PC boards, DC-DC converters, tubing/wiring, and most importantly a hollow cathode. All of these items are crucial to the success of the fast pallet and to the entire electron collection experiment on the sounding rocket. (For more information on the complete experiment see Appendix A).

The case for these components must fit within the mass and volume requirements given to CSU by JAXA. Structurally it must be able to support the mass of the internal components during the rigorous flight. These extreme conditions include temperatures in excess of 1000 C, and accelerations of 20g’s. This includes all of the static and dynamic loading caused by the tremendous forces at launch. The current design of this structure is focused on the static loading and will then later be analyzed with the dynamic forces. Currently three designs exist which will be analyzed for their mass, volume, and the maximum loading they can withstand.

Casing Design

Constraints – When Colorado State University (CSU) was awarded the FAST Pallet project, JAXA sent specifications which the team is expected to follow. This document specifies mass and volume requirements for the FAST Pallet. It is important that these constraints are followed because they can hinder an entire mission. Due to these conditions, the FAST Pallet team has set some design decisions for the casing (all preceding calculations are recorded in appendix B).

Mass & Volume - The sounding rocket that will be used for the tether experiment is classified as an S-310 (Figure 1). This rocket allows for a total payload of 110lbs, in which the FAST Pallet is allowed a maximum of 11lbs. It has been discovered that the internal components will take up approximately 6.61lbs of the allotted payload, which leaves ~4.4lbs for the case and all necessary bracketry. The rocket has a diameter of 12.21in, which the outer diameter of the case can be 10in. The rocket is circular which gives an area of 78.54in2. The payload is allowed a maximum height of 5.5in which gives a total volume of 432in3.

(Fig. 1), S-310 Sounding Rocket

Material - Aluminum is the material for the case specified by the design team. This was chosen mainly because of its low density. The team will make use of its laser welding compatibilities which allows for the welding of very thin materials in a very precise manor. Aluminum 6061-T6 can be obtained at very small thicknesses and has a relatively high Young’s modulus, which will give the necessary strength for the structure.

Loading - The case will be constrained at the base plate and will be structurally isolated from other payloads on the sounding rocket. Because of this the case is not required to support any additional loading on the top of it. Structure of the case will need to be able to support all necessary internal components for the pallet. The sounding rocket reaches a max acceleration of 21g’s. This acceleration on 6.62lbs equates to an internal load of 53668lbf.

Design Concepts – Three design concepts were generated incorporating ideas of maximum volume, minimum mass, and ease of manufacturability. All three designs have a base plate, top plate and a shell. The base plate is 0.25in thick, the top plate is 0.20in thick and the shell is 0.01in. There is also a lip of 0.15in between the edge of the plates and where the shell is welded into place. Each concept has a cutout in the side for the hollow cathode, with a base length of 3in and a max height of 3in. This area will be where a plasma bridge will be created from the sounding rocket to outer space. This creates an additional location for failure on the structure and will be analyzed in conjunction with other factors.

Circle – The circle concept (Figure 2) utilizes the maximum volume by filling the allotted capacity. The plates of the structure fill the given 10in diameter and reaches a height of 5.5in. This gives an internal volume of 373.2in3. The total mass of this case is 3.51lbs.

(Fig 2), Circle

Square –The square model (Figure 3) is a square peg in a round opening, basically a simple box which fits inside the allotted circular area. In order to generate a square with the maximum area within the 10” diameter circle two methods evolved. First the design started with the 2D plot of the circle then it was divided into four quadrants. From here either (1) a box could be drawn in each quadrant creating one square for the four smaller ones (Figure 4), or (2) a triangle could be drawn in which the hypotenuse is one side of the square (Figure 5).

(Fig 4)

(Fig 5)

The second choice allowed for an easier calculation of the maximum internal area, with a height of 5.5in the total internal casing volume is 252in3. The square concept has a total mass of 2.33lbs.

(Fig 3), Square

Hexagon – Creating the model for the hexagon (hex) was a bit of a cross between the square and the circle (Figure 6).

(Fig 6), Hexagon

It makes use of more of the entire area while sustaining flat surfaces. In order to generate the hex a similar a method similar to that for the square was used. A circle was drawn and then broken into six quadrants (Figure 7).

(Fig 7), Drawing

In each quadrant a triangle was drawn in which the hypotenuse is one side of the hex. This structure gives a total internal volume of 339.3in3, and a total mass of 3lbs.

Analysis & Testing

analysis – All three designs were modeled in Pro-Engineer. A rigid constraint was applied to the base plate and a uniform internal load was applied to the positive Z axis of the base plate (Figure 7).

(Fig 7), Base Plate (shown for circular concept)

This load mimics the total mass of internal components evenly dispersed across the plate. Analysis was done on all three concepts to (1) find where the maximum displacement takes place and its magnitude, (2) find maximum stress points and their magnitude and (3) the max strain energy. In order to do this yield strength for Aluminum 6061 was used to calculate the maximum pressure the material can sustain. From here the top surface area was used to determine the max force the material should be able to hold. Because the center of the top plate is not constrained it is expected that deformation will occur and the structure will not be able to support the max load the material alone can support. The question is whether the center of the top plate that will sink in or will the shell of the structure buckle first. In order to find the maximum force each design concept can support an iterative method was used, by starting first with the calculated max force and then decreasing the calculated mass by forty percent each run.

Circle –The circular design was analyzed using FEA in Pro-Engineer. Figure 8 shows a view of the case with all applied loads and constraints.

(Fig 8), Circle with applied loads and constraints

Analysis was run with twenty different loads. The deformation and the stresses were calculated and recorded in Table 1. The two yellow highlighted rows are those which stay within the limits of less than five hundredths of an inch. The maximum force the case can sustain is approximately 2250lbf. This gives a maximum deformation of 0.04in. This deformation takes place in the center of the top plate (Figure 9). The shell of the case is beginning to displace as well as seen at a zoomed in scale in Figure 10. Using Young’s modulus for aluminum it was calculated with a load of 2247lbs uniformly applied. This structure has a force to displacement ratio of 56175lb/in. The maximum stress location is at the connection of the top plate to the shell of the structure. At this point the stress maximum reaches magnitude of 35904lbf/in2. This means there is a large force being exerted on the connecting weld.

Table 1

Force(lbf) / Max displacement (in) / Max Stress
785399998 / 14731 / 1316622000
589049999 / 11048 / 987466500
294524999 / 5524 / 4952420000
147262500 / 2762 / 2468666000
73631250 / 1381 / 1234333000
36815625 / 690 / 617166600
18407812 / 345 / 308583300
9203906 / 173 / 154291600
4601953 / 86 / 77145820
2300977 / 43 / 38572900
1150488 / 22 / 19286450
575244 / 11 / 9643226
287622 / 5.39 / 4821613
143811 / 2.70 / 2410807
71906 / 1.35 / 1023385
35953 / 0.67 / 602706
17976 / 0.34 / 301345
8988 / 0.17 / 150676
4494 / 0.08 / 75337
2247 / 0.04 / 35904
1124 / 0.02 / 17944

(Fig 9), Deformation

(Fig 10), Shell Compression

Square – Using the same methods as in the circular concept the square was analyzed with FEA. Figure 11 shows the square design with all of the applied constraints and loads.

(Fig 11), Applied constraints

Table 2 shows the results of fifteen different tests runs.

Table 2

Force / Max deformation (in) / Max Stress
499799925 / 15044.0 / 13902270000
199919970 / 6017.6 / 5560907000
79967988 / 2407.0 / 2224363000
31987195 / 962.8 / 889745200
12794878 / 385.1 / 355898100
5117951 / 154.1 / 142359200
2047180 / 61.6 / 56943680
818872 / 5.32 / 22777470
327549 / 9.86 / 9110994
131020 / 3.94 / 3644409
52408 / 1.58 / 1457764
20963 / 0.63 / 583100.2
8385 / 0.252 / 233234.3
3354 / 0.101 / 93293.93
1342 / 0.04 / 37328.91

The last row shows the maximum force the square casing can sustain while maintaining a deformation of less than four hundredths of an inch. With the applied load of 1342lbs the square casing will be able remain in tact without buckling. The square design has a displacement ratio of 33550lb/in. The max deformation takes place in the center of the top plate where there are no supports. The shell also shows some deformation in the -Z direction as seen with the circular structure. The main stress concentration points are where the shell connects to the top plate at the corners. Additionally the cutout for the cathode is of some concern. Where the connection goes from a line into an arc stresses seem to be greater.

Hexagon – Using FEA again for the hexagon, maximum displacement and stress points were calculate (Table3). The hex structure followed the square and circle in that the center was the point of max deflection (Figure 11). The max applied load tested was 1656lbf, which resulted in a displacement of 0.07in. This gives a ratio of 23657lb/in. The maximum stress concentration exists in the corners (Figure 12). The stress reaches a max of 85603lbf/in2.

Table 3

Force / Max deformation (in) / Max Stress
616797241 / 25374 / 31883930000
246718896 / 10149 / 12753570000
98687559 / 4060 / 5101429000
39475023 / 1624 / 2040572000
15790009 / 650 / 816228600
6316004 / 260 / 326491500
2526401 / 104 / 130596600
1010561 / 41.6 / 52238660
404224 / 16.6 / 20895440
161690 / 6.65 / 8358197
64676 / 2.66 / 3343279.00
25870 / 1.06 / 1337291.00
10348 / 0.43 / 534916.40
4139 / 0.17 / 213956.30
1656 / 0.07 / 85603.23

(Fig 11), Displacement

(Fig 12), Max stress concentration

testing – Physical testing has not been done, however a testing procedure has been established.

Materials – Aluminum 6061-T6, variable masses that will cover surface area for all three casing designs.

Procedure – (1) Need scaled version of all three designs. Apply a series of different loads to the top of the structures. Measure each structure after proportional amount of time to the total length of a sounding rocket mission (14 min). Measure the deformation of the case in the Z direction, at the center of the top plate and in the shell. (2) Use scaled version of all designs and apply loads until failure for all three. Locate the placement of failure. Then test again to see if it is reproducible.

Conclusion

Results – After running complete analysis on all three structure designs the FAST Pallet team will use the circular concept. It has the best force to displacement ratio, which will allow the case to sustain additional unforeseen loads that may be encountered during flight. However, all three designs show a much smaller force to displacement ratio than what was calculated using Aluminums Young’s modulus, which a value of 1.11*107lbf/in. The circular configuration also shows the smallest max stress at 35904lbf/in2. Given this force and the surface area of the connection of the shell it was calculated that this area can withstand a direct applied force of 43742lbf. In addition the circular casing allows for the maximum use of the allotted volume given by JAXA. The center of the top plate of the structure will need additional support which can be obtained from the bracketing of the internal tank which will lay directly down the center of the case. An additional problem area is where the cutout is for the cathode. This will be counteracted by using the internal case for the cathode, which is built to thermally isolate it from other components. Use of physical testing will prove very valuable in making all final decisions and creating additional supports.