Project P07110-Vertical Test Stand Mechanical DesignAnalysis

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					Project P07110 - Vertical Test Stand
   Mechanical Design & Analysis
      Team Guide: Dr. Jeffrey Kozak
           Start Term: 2006-2




                   1
Contents

I    Mechanical Calculations                                                                                                                                                                3
1 Introduction                                                                                                                                                                               3

2 Initial Design Constants                                                                                                                                                                   3

3 Tapered Roller Bearing Assembly                                                                                                                                                            3
  3.1 Tapered Roller Bearings . . . . . . . . . . .                                 .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    3
  3.2 Bolts Holding Bearing Case Together . . . .                                   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    4
      3.2.1 Summary of Standard Bolt Preloads                                       .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    4
      3.2.2 Bolt Sizing . . . . . . . . . . . . . .                                 .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    5
  3.3 Shaft in Bearing Case . . . . . . . . . . . .                                 .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    5
      3.3.1 Initial Hand Calculations . . . . . .                                   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    5
      3.3.2 FEA Analysis of Shaft . . . . . . . .                                   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    6

4 Universal Joint                                                                                          8
  4.1 FEA Analysis on Modified Universal Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
  4.2 Shearing In Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Load Cell Connection to Rocket Assembly                                                                                                                                                   12
  5.1 Tension and Compression in Bolt . . . . . .                                   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   13
  5.2 Shear of Threads . . . . . . . . . . . . . . .                                .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   13
      5.2.1 One Thread Carries Load . . . . . .                                     .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   14
      5.2.2 20 Threads Carry Load . . . . . . .                                     .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   14

6 Frame                                                                                                  14
  6.1 Stress in Frame Uprights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
  6.2 Weld at Base of Frame Uprights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15


II   Risk Assessment                                                                                                                                                                        17
7 Risk Management Philosophy                                                                                                                                                                17

8 Standards for the Ranking of Hazardous Conditions                                                                                                                                         18

9 Standards for the Probability of a Hazardous Condition Occurring                                                                                                                          18

10 Hazards in the Design                                                                                                                                                                    19
   10.1 Frequent Hazards . .    .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   19
   10.2 Probable Hazards . .    .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   19
   10.3 Occasional Hazards .    .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   19
   10.4 Remote Hazards . .      .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   20
   10.5 Improbable Hazards      .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   20

11 Risk Management Summary                                                                                                                                                                  20




                                                                                2
Part I
Mechanical Calculations
1     Introduction
The responsibility of the P07110 - Vertical Test Stand Team is to create a design for a vertical test that
meets the requirements necessary of other teams in the METEOR project. The main purpose of the
vertical test stand is to provide accurate test data to the P07106 - Guidance and P07109 - Flying Rocket
teams so that they can design and optimize the rocket. To accomplish this the test stand will have to
safely constrain the rocket. This is necessary to prevent injury to people in the vicinity of the test stand
and damage to other testing equipment.
    This document outlines the design process and calculations for the vertical test stand that our team
is creating. At this point certain aspects of the design are contingent on the physical design of the actual
rocket, so the test stand team will be and has been working closely with the Flying Rocket team. The
current design will be subject to scrutiny and refinement because of the progressive nature of the design
process. In light of this, many of the intricate details of our test stand design have deliberately been left
vague in order to accommodate whatever needs that may arise from the Flying Rocket and Guidance
teams.
    Calculations are given in this report to justify and support our team’s design decisions. Some of the
factors of safety in the calculations are abnormally large because of the need to provide ease of assembly
and use of the final design. This data is purposely included though, to provide a record of and an
engineering justification for the vertical test stand design.


2     Initial Design Constants
The table below summarizes the initial a priori design specifications that the vertical test stand is being
tailored to. These constraints and guidelines were formed for two reasons. They provide a starting point
for our team’s calculations and serve to define the relationship that our project has with other projects
in the METEOR program.

                                     Specification                          Value
                               Maximum Rocket Diameter                     12 in
                                Maximum Rocket Length                      50 in
                                Estimated Plume Length                      3 ft
                                Maximum Rocket Thrust                     200 lbf
                          Maximum Rocket Weight (including fuel)           50 lbf
                            Maximum Lateral Force Expected                 25 lbf
                            Maximum Roll Moment Expected                 100 in-lbf


3     Tapered Roller Bearing Assembly


3.1    Tapered Roller Bearings
Two tapered roller bearings mounted in series provide freedom of roll movement; this is shown in figure 1
on the following page. Tapered bearings were selected because the shaft coming from the universal joint
will see a torque and an axial force. Since the axial force will change in direction depending on whether
the rocket is hanging from the stand or firing with an upward thrust, two bearings were used. In light
of the fact that the bore of the universal joint is 1 in., the bore of the tapered bearings were selected to
be 1 in.



                                                     3
                         Figure 1: Diagram of tapered roller bearing assembly.




    Elaborate engineering analysis was not done on the bearings because they will not support a con-
stantly rotating shaft. The supplier of the bearings gives dynamic load capacities of 1620 lbf in the radial
direction and 1040 lbf in the axial direction. Both of these values are well within any loading expected
to be placed on the bearings.

3.2     Bolts Holding Bearing Case Together
A bolt pattern, around the outer edge of the tapered roller bearing case, was decided as the method for
holding the top and bottom of the bearing case together. For engineering simplicity, it was also decided
to use a fastener going through the bearing case and terminated with a nut and washer. Figure 1 shows
how the bolts go though the bearing case. The design criteria chosen is to design the bolted joint so
that enough preload is developed in the bolts to prevent the three sections of the bearing case from
separating in any loading case apt to occur.
    At this point in the design, the only concrete loading data is that the maximum expected thrust of
the rocket is 200 lbf and the maximum weight of the fueled rocket will be 50 lbf . An unknown piece
of loading data is the weight of the testing apparatus connecting the rocket to the load cell. The total
load placed on the rocket will be the net sum of the three forces described above. Additionally, it can
be said that the rocket thrust will act in the opposite direction of both the weight of the rocket and the
testing apparatus. Therefore, if the combined weight of the rocket and testing apparatus are less than
the rocket thrust, the net force never exceed the magnitude of the thrust force. We feel that using the
maximum thrust force as the design load on our test apparatus because we feel it is very reasonable to
assume that the weight of the rocket and testing apparatus will not be greater in magnitude than the
rocket thrust.

3.2.1   Summary of Standard Bolt Preloads
The preloads (Fi ) obtainable for a standard reusable bolted joint containing are given in table 1 on the
    following page for fasteners ranging in size from #6 to 1/4 in. The decision to use stainless steel
fasteners is made up front because of the corrosion resistance that stainless steel provides. With this in


                                                     4
                              Table 1: Summary of developed bolt preloads.
                                        Size   At (in2 ) Fi (lbf )
                                       #6-32    .00909    231.8
                                       #6-40    .01015    258.8
                                       #8-32     .0140    357.0
                                       #10-24    .0175    446.3
                                       #10-32    .0200    510.0
                                       1/4”-20   .0318    810.9
                                       1/4”-28   .0364    928.2


mind, the proof strength (Sp ) of the stainless steel fasteners used is 34 ksi. This value was obtained by
using the relationship that the proof strength is generally equal to 85% of the tensile yield strength of
                                          the fastener material.

                            Fi = .75At Sp , At ≡ standard tensile stress area



3.2.2   Bolt Sizing
From table 1 it can be safely said that many of the bolt sizes given will satisfy the necessary requirements.
So that a symmetric clamping force is applied to the end plates of the bearing case, a bolt pattern of
4 bolts was selected. The size of the bolts selected are #10-24 because they provide a balance between
overall strength of the bolt and the bearing case. Using the the preload results obtained before, the final
total preload force holding the bearing case together is computed to be about 1785 lbf . If the net force
created by the rocket during testing is transferred as a thrust into the bearings, then the tendency of
this force will be to try to pull the bolted connection between the three components of the bearing case
apart. Our design case uses a design load, F, equal to the maximum thrust of the rocket. This leads to
a factor of safety, against separation of the components of the bearing case, of 8.9.
                                        ΣFi     1785 lbf
                                   n=       ⇒n=          ⇒ n = 8.9
                                         F       200 lbf

3.3     Shaft in Bearing Case
On the shaft inside the bearing case there is a shoulder that supports the weight of the rocket and any
thrust forces during the rocket firing. Stress concentrations occur at changes in diameters of shafts and
the bolt holes that connect the shaft to the universal joint. Initial hand calculations and then FEA
models were run on the shaft because of the stress concentrations.

3.3.1   Initial Hand Calculations
The hand calculations were done assuming a 200 lbf tensional load applied to the shaft. Only the tension
case was analyzed because common stress concentration factor charts only provide data for loading in
tension. In addition the tensional loading cases generally result in higher stress states. Figure 2 on the
following page shows the dimensions required for the shaft to fit in the bearing housing and the variables
that those dimensions correspond to in the stress concentration factor equations.



   The stress concentration in the shoulder region of the shaft is dependent on the ratio of the two
shaft diameters and the fillet radius between those diameters. These diameters and the fillet radius were




                                                     5
        Figure 2: Dimension schematic for hand calculation of bearing case shaft stress calculations.




determined from the confines of the bearings. Using figure A-15-7 in Mechanical Engineering Design the
value of the stress concentration factor was visually determined.
                   D    1.375 in              r    .050 in
                      =          = 1.375         =         = .050   ⇒       Kt,shoulder = 2.2
                   d1     1 in                d1     1 in
This stress concentration factor is then applied to the the basic formula for pure tensional stress in the
region of the minor diameter of the shaft.
                                      F         d1             200 lbf
                    σ = Kt,shoulder     , A = π( )2 ⇒ σ = 2.2 • 1 in 2 ⇒ σ = 560 psi
                                      A         2              π( 2 )
    Since there may be play in the drilled bolt holes at the end of the shaft, it is possible for only one
hole to carry the entire load placed on the shaft. Accordingly the calculation assumes this fact. The
stress concentration factor was again visually determined using figure A-15-1 in Mechanical Engineering
Design. In the formula below Amin refers to the minimum cross sectional area of the shaft at the hole
and this value was calculated to be approximately equal to .319 in2 .
                                      d2   .5 in
                                         =       = .5   ⇒   Kt,hole = 2.2
                                      d1    1 in
                                          F                200 lbf
                           σ = Kt,hole        ⇒ σ = 2.2 •          ⇒ σ = 1379 psi
                                         Amin             .319 in2

3.3.2     FEA Analysis of Shaft
Models were run for a 200 lbf force in compression and tension applied at the bolt connection closest to
the end of the shaft. The shoulder of the shaft was fixed. The material was chosen as AISI 304 stainless
steel shaft with a yield strength of 32 ksi.
    Figure 3 on the next page shows the results from the tension case. The maximum von Mises stress
in tension was 2756 psi, resulting in a factor of safety of 11.


    Figure 4 on the following page shows the results from the compression case. The maximum von Mises
stress in compression was 1509 psi, resulting in a factor of safety of 21.


    A third case, where a 100 in-lbf moment was applied to the bottom of the shaft, was also run to
simulate seizure of the taper bearings. Figure 5 on page 8shows this and the maximum von Mises stress
in this case was 5438 psi. In this case the resulting factor of safety was 6.




                                                        6
  Figure 3: FEA model of bearing shaft in tension.




Figure 4: FEA model of bearing shaft in compression.




                         7
                     Figure 5: FEA model of bearing shaft under 100 in-lbf torque.




4     Universal Joint
A Curtis universal joint was selected to provide freedom of lateral movement for the rocket. The 2 in.
universal joint comes with a 1 in. bore for mounting the shaft from the tapered roller bearing case
to the universal joint. The manufacturer of the universal joint gives maximum loads that the joint
can withstand. Additional analysis was also done on the universal joint because the design requires
modification of the stock universal joint.
    The manufacturer of the universal joint gives a static maximum torque rating of 22000 in-lbf and
a maximum axial force value of 25000 lbf . Both of these values are so large that they are not limiting
factors to the design. It is desired though to drill two holes into the universal joint to attach the shafts
however, so an FEA analysis was done on the modified universal joint.

4.1    FEA Analysis on Modified Universal Joint
Two FEA models were run on the modified universal joint yoke. One assumed a 200 lbf compression
loading and another assumed a 200 lbf load in tension. Both models used the constraint that the center
pin of the universal joint remained fixed. It is entirely possible for only one of the bolts between the
bearing case shaft and and the modified universal joint yoke, so the models were run with the 200 lbf
load applied to the hole closest to the opposite end of the universal joint. The force was placed at this
location because it is of importance to gain insight to the stress flow around the other hole in the shaft.
The yoke was assumed to be made out of alloy steel with a yield strength of 90 ksi.
    Results for the compression case are shown in figure 6 on the following page. In compression the
maximum von Mises stress in the part was 778 psi. This yields a factor of safety of 115.




                                                     8
Figure 6: FEA analysis for compression case.




                     9
                                 Figure 7: FEA analysis for tension case.




   Figure 7 shows results for the FEA model involving tension. The maximum von Mises stress for this
case is 2341 psi, resulting in a factor of safety of 38.



4.2    Shearing In Bolts
As explained in the previous section, the worst case scenario is for one of the bolts shown in figure 8 on
the following pageto be carrying the entire 200 lbf load. Another worst case scenario assumption is that
the loading was applied as a pure shear load over the minor area in the threaded portion of the bolt.



     SAE Grade 8 1/2”-20 bolts were selected for this joint. A fine thread series and Grade 8 rating were
selected for maximum strength. Figure 9 on the next page shows a free body diagram for the bolt as
analyzed. Since the bolt is in double shear, the total shear force being applied across each load bearing
section of the bolt is 100 lbf . The minor area of the bolt that the shear force is applied over is As =.1486
in2 . Using these conditions the shear stress in the bolt is calculated below.


                                       Fs         100 lbf
                                τs =      ⇒ τs =           ⇒ τs = 673 psi
                                       As        .1486 in2


                                                     10
            Figure 8: Bolts through universal joint.




Figure 9: Free body diagram for bolt through the universal joint.




                               11
                       Figure 10: Bolt connecting load cell to rocket assembly.




    The resultant shear force of 673 psi is very small. For calculating the resultant factor of safety
Distortion-Energy Theory was used to predict the shear yield strength based on the known tensile yield
strength. That relationship is that the shear yield strength is approximately equal to .577 times the
tensile yield strength. For a Grade 8 bolt the minimum yield strength in tension is 130 ksi. Now the
resultant factor of safety is calculated for the bolt to be 111.
                       Sy,s ≈ .577Sy,t ⇒ Sy,s = .577 • 130 ksi ⇒ Sy,s = 75.0 ksi
                                      Sy,s     75.0 ksi
                                 n=        ⇒n=          ⇒ n = 111
                                       τs      673 psi

5    Load Cell Connection to Rocket Assembly
The connection between the rocket assembly and the vertical load cell needs to be analyzed because
only the load cell only accepts one 1/2” bolt (location shown in figure 10). Therefore there is only one
point of connection ultimately holding the rocket up. In light of this fact the bolt and threads of this
connection were heavily analyzed.


    The load cell is threaded to accept a 1/2”-20 bolt as the member that actually connects the load to
be measured to the load cell. Therefore, the size of the bolt is a driven quantity. One design choice
that we could make was to specify a SAE Grade 8 bolt for this connection. This will provide maximum
possible strength. Table 2 on the next page provides a neat summary of the minimum strength values,
for Grade 8 bolts, used in our calculations.


                                                  12
                           Table 2: Strength properties of SAE Grade 8 bolts.
                                 Property         Minimum Allowable Value
                            Proof Strength (Sp )             120 ksi
                            Yield Strength (Sy )             130 ksi
                           Tensile Strength (St )            150 ksi




5.1    Tension and Compression in Bolt
For failure analysis purposes the bolt can be analyzed as it is carrying the net load entirely in tension
or compression on the standard tensile stress area (At ) of the bolt. From a stress analysis point of view,
one of the design targets in a bolted connection is to have maximum stress state in the bolt that is less
than the proof strength of the bolt. The load factor of an externally loaded bolt is generally calculated
as the ratio of the proof strength of the bolt to the stress state created in the bolt as the result of an
external load. In a bolted connection the net stress state in the bolt is made up of several different
factors. Those factors are the external load applied to the bolted connection (P), the fraction of the
external load carried by the bolt (C), and the preload force developed in the bolted connection (Fi ).
    Our postulation that the entire load could be carried in tension on the bolt area is a possible situation
because this could happen if the bolt was not tightened with a preload. In this case Fi =0, by definition,
and C=1 because the entire external load would be carried by the bolt. C can only be less than one in
cases where and elastic reaction force is developed in the members as a result of the clamping reaction
of the bolt. Taking into account the parameters of our design case, the general equation for the load
factor of a bolt can be simplified.
                                             S p At − F i     S p At
                                        n=                ⇒n=
                                                 CP             P
Our design case assumes an external load (P) of 200 lbf and the standard tensile stress area (At ) of a
1/2”-20 bolt is .1599 in2 . The final calculation for the load factor equals 95.

                                   S p At     120 ksi • .1599 in2
                              n=          ⇒n=                     ⇒ n = 95
                                     P             200 lbf

5.2    Shear of Threads
The other possible area of failure is if the internal threads of the hole that the bolt going through the
load cell shear off (strip). The bolt itself was selected to be SAE Grade 8, and the shaft material that
the bolt is going to thread into is going to be annealed AISI 304 stainless steel. Of the two thread
materials, the stainless steel has the lower tensile yield strength. The tensile yield strength (Sy,s ) of AISI
304 stainless steel is 40.0 ksi. Again using the Distortion-Energy Theory, the shear yield strength (Ss,y )
of AISI 304 stainless steel was approximately calculated to be 23.1 ksi.

                        Sy,s ≈ .577Sy,t ⇒ Sy,s = .577 • 40.0 ksi ⇒ Sy,s = 23.1 ksi

The other piece information needed for developing an analytical expression for the shear on the thread(s)
is the area that the shear force acts upon. This area is a function of the thread pitch (p), thread root
diameter (dr ), and percentage of engagement between the internal and external threads (wi ). For a UNF
1/2” thread the thread pitch is .05 in, the root diameter is .435 in, and the percentage of engagement is
80%. Using an expression for the circumference of the thread and the known values previously stated,
the area that the shear force acts on for a single thread (As ) is calculated to be .055 in2 .

                      As = πdr wi p ⇒ As = π • .435 in • .80 • .05 in ⇒ As = .055 in2




                                                      13
If the maximum permissible shear stress is set equal to the shear yield strength and the shear stress
equation is resolved for the external load (F) an expression for the maximum force (Fmax ) that the
thread(s) will support is derived. nt is the number of engaged threads in the joint.

                                              F
                                     τmax =      ⇒ Fmax = Sy,s nt As
                                              As
Two cases were explored in our analysis. The first case assumes that the entire load is carried by a single
thread and and the second case assumes that 1 in of tapped hole or 20 threads carry the load.

5.2.1    One Thread Carries Load
                 Fmax = Sy,s nt As ⇒ Fmax = 23.1 ksi • 1 • .055 in2 ⇒ Fmax = 1270 lbf
Using the design load (F) and the maximum load (Fmax ) an expression and value for the factor of safety
in this case is found to be 6.3.
                                       Fmax     1270 lbf
                                  n=        ⇒n=          ⇒ n = 6.3
                                        F       200 lbf

5.2.2    20 Threads Carry Load
The calculated factor of safety in this case is 127.

                Fmax = Sy,s nt As ⇒ Fmax = 23.1 ksi • 20 • .055 in2 ⇒ Fmax = 25410 lbf
                                       Fmax     25410 lbf
                                 n=         ⇒n=           ⇒ n = 127
                                        F        200 lbf

6       Frame
The vertical test stand design utilizes a frame to hang the rocket from and attach the sensors to. A
preliminary CAD model of the vertical test stand with the frame highlighted is presented in figure 11 on
the following page. All analysis done on the frame assumes that a very weak structural steel was used
in the construction of the frame. Using this approach allows the use of stronger materials for increased
factors of safety if necessary later on. The steel type for the calculations is AISI 1040 hot rolled steel.
The specified minimum yield strength of this steel is 42 ksi.



6.1     Stress in Frame Uprights
Three 6” X 25 lbf /ft wide flange I beams were selected to be the uprights for the frame. The design
proposal assumes that the two tallest uprights are roughly 9 feet high. With regards to analysis, the
main area of concern with the frame is that people or equipment could lean up against the frame. Forces
applied perpendicular to the web of the upright will result in higher bending stresses in the beam than
forces applied along the web of the beam. Analysis will focus on a force applied perpendicular to the web
because the stress will be higher. For the design case, a 400 lbf force was applied, as shown in figure 12
on page 16, to the top of the tall upright. The maximum bending stress was then found at the base of
of the beam.



   M is the resultant bending moment for a force, F, applied at a distance, d, from the plane of analysis.
Since the beam selected is a standard shape values for cmax and I were obtained from tables. cmax =3.040
in and I=17.1 in4 .
                       M = F × d ⇒ M = 200 lbf × 20 in ⇒ M = 4000 lbf • in



                                                       14
                  Figure 11: CAD model of test stand design with frame highlighted.




                         M cmax             4000 lbf • in × 3.040 in
                 σmax =           ⇒ σmax =                           ⇒ σmax = .711 ksi
                            I                       17.1 in4
A factor of safety against yielding can now be computed based on the yield strength of the steel and
maximum stress just calculated.
                                         Sy       42 ksi
                                   n=        ⇒n=          ⇒ n = 59
                                        σmax     .711 ksi

6.2    Weld at Base of Frame Uprights
To secure the frame uprights to the ground, it is desired to weld square plates to the bottom of the
frame uprights (see figure 13 on the following page). Since this weld is in a comparatively high stress
area, compared to the rest of the frame, it is desired to use a butt weld with complete joint penetration.
This will take more effort to construct, but will yield a weld with strength comparable to that of the
base metals.



    According to AISC (American Institute of Steel Construction) guidelines, weld joints subjected to
bending stresses should conservatively have a maximum stress at the weld that is no greater than 60%
of the minimum yield strength of the metal(s) in the weld joint. If materials of several different yield
strengths are present in the weld then the lowest yield strength among the individual materials should
be used. Most common filler metals for steel have higher yield strengths than than the minimum yield
strength of the steel used in the frame design, so the frame material is the limiting factor.

                  Sy,weld = .60 × Sy,min ⇒ Sy,weld = .60 × 42 ksi ⇒ Sy,weld = 25.2 ksi

    Since complete joint penetration is being used in the welds the area of the weld area is at least as
large as the cross section of the beam. Since there is no area reduction, the maximum stress calculated
in section 6.1 on the previous page is representative of the stress in the weld. With this a factor of safety
can be calculated for the weld.
                                        Sy,weld     25.2 ksi
                                  n=            ⇒n=          ⇒ n = 35
                                         σmax       .711 ksi


                                                     15
Figure 12: Force applied to beam for stress computation.




   Figure 13: Detail of plate welded to frame upright.




                           16
         Figure 14: Steel tube surrounding the rocket (concrete bunker not shown for clarity).




Part II
Risk Assessment
7    Risk Management Philosophy
Current and future rockets constructed by the METEOR project are all experimental devices. Sound
judgment and scientific knowledge is applied during the design of the rockets, however, there is still an
uncertainty in knowing what exactly is going to happen when a rocket engine fires. In light of this fact,
our team has come up with a plan that lists the risks present and then describes the measures being
taken to mitigate the risks. It should be noted that the safety analysis done by the vertical test stand
team builds on previous safety analysis done for the METEOR project. These shared safety measures
provide proven strategies for dealing with the hazards of rocket testing; which in turn brings on less new
risk.
    The basic mentality that our team has taken in developing the plan to manage the uncertainty in
rocket testing, is to have engineering and physical barriers in place to help contain the hazards. From an
engineering standpoint safety was built into the design and excess strength exists in the structural design.
Physical barriers are also present to help contain any uncontrolled occurrences that may occur during a
test. The first of those is a steel tube that surrounds the rocket, shown in figure 14, to help minimize
property damage inside the concrete building that testing is done within. The concrete building itself is
another safety measure. This structure was put in place by a previous METEOR team to help contain
the rocket during testing. Our test stand holds the rocket in the vertical orientation with the thrust
forcing the rocket upward. As a safety measure there is only a 2 inch diameter hole in the top of the
concrete bunker. As shown in figure 15 on the next page, this hole allows the 1 inch shaft that supports
the rocket to connect to the load cell, but will not allow the rocket to come out the top of the concrete
bunker.




                                                    17
                             Figure 15: Hole in the top of the concrete bunker.




8    Standards for the Ranking of Hazardous Conditions
Hazardous conditions are categorized based on the severity of the outcome experience for a particular
condition. The framework below shows the standardized categories, and the consequence criteria for
each category.

    Category   Description        Environmental Health and Safety Results
     I         Catastrophic       Could result in death, permanent total disability, loss exceeding
                                  $1,000,000, and/or irreversible severe environmental damage that
                                  violates law(s) or regulation(s).
     II           Critical        Could result in permanent partial disability, injuries or
                                  occupational illness resulting in the hospitalization of at least three
                                  personnel, loss exceeding $200,000 and less than $1,000,000,
                                  and/or reversible severe environmental damage that violates law(s)
                                  or regulation(s).
     III         Marginal         Could result in injury or occupational illness resulting in one or
                                  more lost work day(s), loss exceeding $10,000 and less than
                                  $200,000, and/or mitigatable environmental damage that does not
                                  violate and law(s) or regulation(s) where restoration can be
                                  accomplished.
     IV          Negligible       Could result in injury or illness not resulting in a lost work day,
                                  loss exceeding $2,000 and less than $10,000, and/or minimal
                                  environmental damage not violating any law(s) or regulation(s).


9    Standards for the Probability of a Hazardous Condition Oc-
     curring
The probability of each hazardous condition occurring is also rated according to a standardized scale.
That scale is described below.




                                                     18
                    Level         Description        General Probability of Occurrence
                     A             Frequent              Continuously experienced.
                     B             Probable                  Occurs frequently.
                     C            Occasional              Will occur several times.
                     D              Remote        Unlikely, but can be expected to occur.
                      E           Improbable    Unlikely to occur, but possible none the less.


10     Hazards in the Design
The hazards for this project were collected and are explored in detail in the following subsections. To
help with the ranking of the hazards, they were separated into groups based on their probability of
occurrence. Each subsection contains a different probability of occurrence.

10.1    Frequent Hazards

 Hazard              Category          Probability   Control                                      Residual Risks
 Bunker fills            IV                 A         Persons not allowed in bunker until           Equipment
 with smoke /                                        smoke clears after testing.                     Damage
 exhaust.

10.2    Probable Hazards
None

10.3    Occasional Hazards

 Hazard              Category          Probability   Control                                      Residual Risks
 Burning chunks         III                C         Floor of bunker is concrete and thus not         None
 of material is                                      flammable.
 ejected    from
 rocket during
 test.
 Coupling      to           III            C         Secure attachment will be checked for in      Equipment
 rocket loosens                                      pre-test inspection and the rocket will be     Damage
 or breaks.                                          contained in the concrete bunker.




                                                          19
10.4    Remote Hazards

 Hazard              Category    Probability   Control                                      Residual Risks
 Rocket plume           II           D         Flammable material will be cleared             Small Fire
 or       exhaust                              around the test stand and a NYS Vol-
 ignites      sur-                             unteer Firefighter will be present during
 roundings.                                    tests.
 Small animal           IV           D         Testing bunker is enclosed on 5 of 6 sides        None
 enters test                                   and this occurrence would not be detri-
 area.                                         mental to the test or any observers.
 Person enters          II           D         People will not be allowed into the bunker        None
 bunker while it                               until exhaust clears.
 is filled with
 smoke /
 exhaust.
 Failure of             III          D         Acceptable factor of safety exists in the      Equipment
 bolted                                        design and a load rated bolt is being           Damage
 connection at                                 used for the this connection. Rocket will
 load cell.                                    be contained within the concrete bunker.
 Connection to          IV           D         Rocket would be still held by the main         Equipment
 one or more of                                coupling. Furthermore the rocket would          Damage
 the lateral load                              be contained within the bunker.
 cells breaks.
 Rocket              II or III       D         Rocket will be well contained within the      Equipment
 becomes                                       bunker. If it exits through the port in      Damage, Small
 totally                                       the bunker for the exhaust, that will be         Fire
 unconstrained                                 facing away from the test observers.
 within the
 bunker.

10.5    Improbable Hazards

 Hazard              Category    Probability   Control                                      Residual Risks
 Tapered roller         IV           E         Bearings have load ratings well in excess         None
 bearing(s)                                    of what is expected. Our mechanical
 seize.                                        design also will withstand this
                                               occurrence.


11     Risk Management Summary
The major item of note from our risk assessment is that the residual risks present all concern damage to
property and life. While steps were taken during the design, and will be taken in the future during the
testing procedure to minimize damage to equipment and the environment the potential for damage still
does exist. Hopefully, any undesirable occurrence during testing would be contained by the steel tube
surrounding the rocket in order to cause as little damage as possible. In addition, the predominantly
wet and swampy land around the concrete bunker where the rocket is tested would serve to limit the
spread of a brush fire.




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