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This document has been prepared and approved by the following:
Prepared By: Aditya Vipradas Date: December 10, 2015
Student (ASU ID: 1209435588)
Approved By: <Instructor> Date: December 10, 2015
Instructor
Issue Date
Page
Affected
Content
Affected Reason for Revision
0000 December 10, 2015 All All Initial Release
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Contents
1.0 Introduction ................................................................................................................... 6
1.1 Scope .......................................................................................................................... 6
2.0 General Requirements .................................................................................................. 6
2.1 Item Definition.............................................................................................................. 6
3.1.1. System Interface Definition ................................................................................... 7
3.1.1.1. Filter Manifold Assembly Orientation..................................................................... 7
3.1.1.5. Mechanical Interface to Thrust Cone .................................................................... 7
3.2 Characteristics............................................................................................................. 8
3.2.1 Performance ......................................................................................................... 8
3.2.1.1 Life Requirements................................................................................................. 8
3.2.1.2 Fluid Operating Temperature Range..................................................................... 8
3.2.1.3 Pressure ............................................................................................................... 8
3.2.1.3.1 Rated Steady State Operating Pressure ........................................................ 8
High Pressure Circuit.......................................................................................................... 8
3.2.1.7 Factors of Safety................................................................................................... 9
3.2.1.7.1 Filter Manifold Factors of Safety (Excluding Instrumentation)......................... 9
a. Proof Pressure...................................................................................................... 9
b. Burst Pressure...................................................................................................... 9
3.2.2 Physical Characteristics.......................................................................................10
3.2.2.2 Weight .................................................................................................................10
3.2.4 Environmental Requirements...............................................................................11
3.2.4.1 Flight Environment...............................................................................................11
3.2.4.1.4 Random Vibration.........................................................................................11
3.2.4.1.5 Acceleration..................................................................................................12
3.0 Conclusions..................................................................................................................13
4.0 Abbreviations and Acronyms ......................................................................................16
Appendix A. Analysis Methodology..................................................................................18
Appendix B. Model Verification ........................................................................................25
Appendix C. Analysis Results - Operational Pressure......................................................27
Appendix D. Analysis Results - Proof Pressure................................................................29
Appendix E. Analysis Results - Burst Pressure ................................................................31
Appendix F. Analysis Results – Random Vibration...........................................................33
Appendix G. Analysis Results – Flight Acceleration .........................................................41
Appendix H. Results of Fillet Optimization (Final Part A)..................................................45
List of Figures
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Figure 3.1.1.2-1: Filter Manifold Assembly Analysis Model Geometry........................................ 7
Figure 3.1.1.2-2: Filter Manifold Assembly Analysis Model Fixed Surfaces................................ 8
Figure 3.2.4.1.4-2-3: Random Vibration Requirements ...........................................................11
Figure A-3-1: Geometric Representation of TVC Filter Manifold Assembly ...............................18
Figure A-3-2: Lumped Mass Representations of Fittings...........................................................19
Figure A-3-3: Fixed Boundary Condition Surfaces used in FE Analyses ...................................19
Figure A-3-4: TVC Filter Manifold Assembly Finite Element Mesh ............................................20
Figure A-3-5: Manifold Pressure Surfaces.................................................................................20
Figure A-3-6: Bowl Pressure Surfaces ......................................................................................21
Figure A-3-7: 7075-T652 Material Properties ............................................................................21
Figure A-3-8: 7075-T7351 Material Properties ..........................................................................22
Figure C-3-9: Global Model Peak Von Mises Stress, TVC Filter Manifold – Operational Pressure
(psi)...........................................................................................................................................27
Figure C-3-10: Global Model Peak Von Mises Stress,Filter Bowl – Operational Pressure (psi).28
Figure D-3-11: Manifold Von Mises Stress –Proof Pressure (psi)..............................................29
Figure D-3-12: Bowl Von Mises Stress - Proof Pressure (psi) ...................................................30
Figure E-3-13: TVC Filter Assembly Von Mises Stress – Burst Pressure (psi) ..........................31
Figure E-3-14: Bowl Von Mises Stress – Burst Pressure (psi)...................................................32
Figure F-3-15: TVC Filter Manifold Assembly – Mode 1 (1053.8 Hz).........................................33
Figure F-3-16: TVC Filter Manifold Assembly – Mode 2 (1058.2 Hz).........................................34
Figure F-3-17: TVC Filter Manifold Assembly – Mode 3 (3539.4 Hz).........................................34
Figure F-3-18: TVC Filter Manifold Assembly – Mode 4 (3887.2 Hz).........................................35
Figure F-3-19: TVC Filter Manifold Assembly – Mode 5 (3895.9 Hz).........................................35
Figure F-3-20: TVC Filter Manifold Assembly – Mode 6 (4000.2 Hz).........................................36
Figure F-3-21: Random Vibration Requirements.....................................................................36
Figure F-3-22: 3-Sigma Von Mises Stress of Manifold - Radial Random Vibration (psi) ............37
Figure F-3-23: 3-Sigma Von Mises Stress of Bowl - Radial Random Vibration (psi)..................38
Figure F-3-24: 3-Sigma Von Mises Stress of Manifold - Longitudinal Random Vibration (psi) ...38
Figure F-3-25: 3-Sigma Von Mises Stress of Bowl - Longitudinal Random Vibration (psi).........39
Figure F-3-26: 3-Sigma Von Mises Stress of Manifold – Tangential Random Vibration (psi).....39
Figure F-3-27: 3-Sigma Von Mises Stress of Bowl - Tangential Random Vibration (psi) ...........40
Figure G-3-28: 1g TVC Filter Manifold Von Mises Stress – Longitudinal Flight Axis (psi)..........41
Figure G-3-29: 1g Bowl Von Mises Stress – Longitudinal Flight Axis (psi).................................42
Figure G-3-30: 1g TVC Filter Manifold Von Mises Stress – Tangential Flight Axis (psi).............42
Figure G-3-31: 1g Bowl Von Mises Stress – Tangential Flight Axis (psi) ...................................43
Figure G-3-32: 1g TVC Filter Manifold Von Mises Stress – Radial Flight Axis (psi)...................43
Figure G-3-33: 1g Bowl Von Mises Stress – Radial Flight Axis (psi)..........................................44
List of Tables
Table 1.1-1: Analysis Results Top Level Summary .................................................................... 6
Table 3.2.1.3.1-1: Margin of Safety for Assembly Components under Operational Pressure...... 9
Table 3.2.1.7.1-1: Margin of Safety for Assembly Components under Proof Pressure ..............10
Table 3.2.1.7.1-3: Margin of Safety for Assembly Components under Burst Pressure...............10
Table 3.2.2.2-1: Fluid Mass Distribution Summary....................................................................10
Table 3.2.4.1.4-1: Fatigue Damage Ratios for Radial Random Vibration Profile........................12
Table 3.2.4.1.4-2: Fatigue Damage Ratios for Longitudinal Random Vibration Profile...............12
Table 3.2.4.1.4-3: Fatigue Damage Ratios for Tangential Random Vibration Profile .................12
Table 3.2.4.1.5-1: Margin of Safeties for Flight Acceleration – Longitudinal Flight Axis .............12
Table 3.2.4.1.5-2: Margin of Safeties for Flight Acceleration – Tangential Flight Axis................13
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Table 3.2.4.1.5-3: Margin of Safeties for Flight Acceleration – Radial Flight Axis ......................13
Table A1-1: Elastic Properties for TVC Filter Manifold Assembly Parts .....................................22
Table A1-2: Temperature Correction Factors for Yield and Ultimate Strength ..........................23
Table A1-3: Aluminum Strength Properties Used in the FE Analyses.......................................24
Table B1-2: Working Pressure Force Balance Check Run Results ..........................................25
Table B1-3: Proof Pressure Force Balance Check Run Results...............................................25
Table B1-4: Burst Pressure Force Balance Check Run Results...............................................25
Table B1-6: Acceleration Force Balance Check Run Results - Flight Coordinate System ........26
Table F1-1: Natural Frequencies for TVC Filter Manifold Assembly .........................................33
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1.0 Introduction
1.1 Scope
This report presents the structural assessment and analysis associated with the Thrust Vector
Control (TVC) Hydraulic Filter Manifold. A top level summary of the analytical results for the
specification requirements (show for critical assembly components) is provided in Table 1.1-1.
Table 1.1-1: Analysis Results Top Level Summary
2.0 General Requirements
2.1 Item Definition
The Filter manifold assembly is a collector and distributor of hydraulic fluid. The Filter manifold
assembly incorporates instrumentation for the TVC hydraulic system. The Filter manifold
assembly performs the following functions and includes the following features and interfaces:
1. It provides mechanical relief for over pressurization of the high pressure circuit in the
TVC hydraulic system.
2. It provides insoluble contaminant retention from pump case drain and system
hydraulic fluid by means of mechanical filters.
3. It provides a means of isolating and preventing backflow during the operation of
either the main hydraulic pump or the circulation pump.
4. It provides fluid interfaces for the TVC actuator supply and return.
5. It provides fluid interfaces for high pressure bleed and fill (TBR).
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6. A pressure switch for remote sensing of the supply hydraulic fluid is provided.
The filter manifold assembly is pressurized and operational while on the launch pad.
The filter manifold assembly is then depressurized during the first approximately
130 seconds of flight. The filter manifold assembly is then be pressurized and operational for the
remainder of the mission (approximately 470 seconds) up to T + 600 seconds. At the end of the
mission, the filter manifold assembly, along with the entire upper-stage of the vehicle, will burn
up as it descends through the atmosphere.
3.1.1. System Interface Definition
3.1.1.1. Filter Manifold Assembly Orientation
The coordinate frame used for the analysis is shown in Figure 3.1.1.2.4.
Figure 3.1.1.2-1: Filter Manifold Assembly Analysis Model Geometry
3.1.1.5. Mechanical Interface to Thrust Cone
The Filter manifold assembly shall interface with an upper stage thrust cone. In order to
replicate a representative mounting configuration for the finite element model , the geometric
source for the analytical model was imprinted with circular faces at the bottom of the mounting
tabs which were considered to be a fixed boundary condition representing a standoff with a
washer faced threaded fastener. Figure 3.1.1.6.1 shows the surfaces considered fixed in the
analysis model.
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Figure 3.1.1.2-2: Filter Manifold Assembly Analysis Model Fixed Surfaces
3.2 Characteristics
3.2.1 Performance
3.2.1.1 Life Requirements
3.2.1.2 Fluid Operating Temperature Range
The Filter manifold assembly shall be designed to operate throughout a temperature range of -
40 °F to +275 °F per SAE AS 5440 Type II hydraulic system.
3.2.1.3 Pressure
3.2.1.3.1 Rated Steady State Operating Pressure
High Pressure Circuit
This particular filter assembly consists of a single pressure circuit. This corresponds to the high
pressure circuit of multi-circuit designs. The high pressure circuit of the Filter manifold assembly
shall be fully functional and be capable of meeting the requirements within this document when
operating at a hydraulic fluid pressure of 3200 psig.
The Filter manifold assembly finite element model was run under operational pressure
conditions to show compliance with specification requirements. The stiffness matrix resulting
from the operational pressure static load condition was also used to pre-stress the modal
analysis used in the random vibration evaluation. A table of margin of safeties for the critical
components of the TVC Filter Assembly is shown in Table 3.2.1.3.1-1.
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Table 3.2.1.3.1-1: Margin of Safety for Assembly Components under Operational Pressure
Appendix C contains details of the analyses conducted to show compliance under operational
pressure conditions.
3.2.1.7 Factors of Safety
3.2.1.7.1 Filter Manifold Factors of Safety (Excluding Instrumentation)
The filter manifold assembly, excluding instrumentation, shall be designed to the minimum
structural factors of safety shown below:
a. Proof Pressure
All high pressure circuits shall withstand application of a proof pressure of 4,800 psig (1.5 times
system nominal operating pressure) without yield.
b. Burst Pressure
All high pressure circuits shall withstand application of an internal pressure of 8,000 psig (2.5
times system nominal operating pressure) without rupture.
Ambient Temperature, Pressure Test Environmental Correction Factor: For ambient
temperature proof/burst pressure tests, the test pressure shall be adjusted by the maximum
environmental correction factor (ECF). An ECF is a factor to account for the effect that the
environment has on the strength (Yield, Ultimate, and Fracture toughness) capability at test
conditions versus the limiting operating condition.
ECF = Strength Capability at Operating Condition/ Strength Capability at Test Condition
The Filter manifold assembly finite element model was run under proof pressure conditions to
show compliance with specification requirements. Appendix D contains details of the analyses
conducted to show compliance under proof pressure conditions. A table of margin of safeties
for proof for the critical components of the TVC Filter Assembly is shown in Table 3.2.1.7.1-1.
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Table 3.2.1.7.1-1: Margin of Safety for Assembly Components under Proof Pressure
The Filter manifold assembly finite element model was run under burst pressure conditions to
show compliance with specification requirements. Appendix E contains details of the analyses
conducted to show compliance under burst pressure conditions. A table of margin of safeties
for burst for the critical components of the TVC Filter Assembly is shown in Table 3.2.1.7.1-3.
Table 3.2.1.7.1-2: Margin of Safety for Assembly Components under Burst Pressure
3.2.2 Physical Characteristics
3.2.2.2 Weight
Following is the Status of Mass properties of the TVC Hydraulic Filter Manifold Assembly and
the associated components. The total predicted weight (dry) of the filter manifold assembly,
including the mass growth allowance factor is 6.457 lbm.
The total wet weight was 7.492 lbm. The additional 1.035 lbm fluid mass was distributed
among the bowl and manifold, according to the table 3.2.2.2-1 below.
Table 3.2.2.2-1: Fluid Mass Distribution Summary
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3.2.4 Environmental Requirements
NOTE: All instrumentation is considered part of the filter manifold assembly and therefore shall
meet the environmental requirements specified in this document.
3.2.4.1 Flight Environment
3.2.4.1.4 Random Vibration
Per specification GRC-TVC-SPEC-015, the requirements for the TVC Filter Manifold Assembly
under random vibration are shown in Figure 3.2.4.1.4-1 below.
Figure 3.2.4.1.4-2-3: Random Vibration Requirements
The TVC Filter Manifold Assembly finite element model was run under the random loading
profiles in Figure 3.24.1.4-1 to show compliance with specification requirements. Tables of
fatigue damage ratio, (FDR = n/N, where n is the required test cycles and N is the expected
cycles to failure) have been developed based on results from the random vibration analyses and
equivalent stress equations for Aluminum 7075-T6 contained in MMPDS-04 (Curves for 7075-
T652 and 7075-T7351 do not exist). For conservatism, an R=0 assumption was used in the
equivalent stress equation for the random vibration loading. Critical damping of 5% was used for
the analyses.
Appendix F contains details of the analyses conducted to show compliance under random
vibration conditions. A table of fatigue damage ratios for the critical components of the TVC
Filter Assembly is shown in Tables 3.2.4.1.4-4 through 3.2.4.1.4-6.
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Table 3.2.4.1.4-1: Fatigue Damage Ratios for Radial Random Vibration Profile
Table 3.2.4.1.4-2: Fatigue Damage Ratios for Longitudinal Random Vibration Profile
Table 3.2.4.1.4-3: Fatigue Damage Ratios for Tangential Random Vibration Profile
Note: a) If expected cycles are > 108
, 108
is substituted.
3.2.4.1.5 Acceleration
Per specification GRC-TVC-SPEC-015, the requirements for the TVC Filter Manifold Assembly
under flight vibration are shown below.
The TVC Filter manifold assembly finite element model was subjected to a flight vibration
environment of 6.22g’s in the flight longitudinal direction and 2.0g’s in both the radial and
tangential flight axes to show compliance with specification requirements. Table 3.2.4.1.5-1
through 3.2.4.1.5-3 shows the margin of safeties for the flight acceleration loading.
Table 3.2.4.1.5-1: Margin of Safeties for Flight Acceleration – Longitudinal Flight Axis
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Table 3.2.4.1.5-2: Margin of Safeties for Flight Acceleration – Tangential Flight Axis
Table 3.2.4.1.5-3: Margin of Safeties for Flight Acceleration – Radial Flight Axis
Appendix G contains details of the analyses conducted to show compliance under flight
acceleration conditions.
3.0 Conclusions
The given TVC Hydraulic filter assembly is analyzed against different loading conditions in order
to check whether it is qualified to put to the desired aerospace use. This assembly is analyzed
under normal operating pressure load, proof pressure load and burst pressure load conditions.
The normal operating pressure load is also associated with 6.22g longitudinal, 2g axial and 2g
radial accelerations. Moreover, the assembly is also simulated for the available longitudinal,
axial and radial PSD acceleration data.
Safety of this assembly is ensured by checking whether the stress values for operating, proof
and acceleration loads lie within the yield limits of the respective materials used at the operating
temperature and the burst stress values lie within the ultimate strength limit of these materials.
Thus, the positive Margin of Safety (MS) values indicate the safety of the bowl and the manifold
present in the filter. The assembly is also said to clear the random vibrations criteria if the
Fatigue Damage Ratio (FDR) calculated is found to be less than 1.
As a part of preprocessing steps, the manifold is fixed at the four mounting locations. The fuel in
the assembly is also modeled. The assembly is meshed with 0.2 in SOLID187 tetrahedral
elements. The mesh refinement size at the bowl fillet and manifold thread relief areas is
determined by doing a convergence study for the normal operating pressure load condition. This
is achieved by successfully refining the mesh by a factor of 2 and checking the stress values at
the peak von-Mises stress location. The results are said to converge if the last and the
penultimate stress results differ by less than 4%. The following convergence plot is obtained for
the normal operating pressure load conditions. As observed from the table, a percent difference
of 1.02% is obtained in the stress values for 0.025 in face sizing. Thus, this face sizing is used
in all the following simulations to obtain converging results. Convergence study with 4%
accuracy is also performed on all the pressure load conditions to ensure that the obtained stress
values are correct.
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Figure: Result convergence for the normal operating pressure load condition
Following observations are made for different analyses. Pressure balancing is performed for all
the pressure loads to ensure that the reaction forces are below 5 lbf at the fixed supports.
1. Normal operating pressure loading condition
The maximum von Mises stress values on the manifold and bowl are 25.48 ksi and 31.31 ksi
respectively. These values are lower than the yield limits of the respective materials of the
manifold and bowl (48.38 ksi and 39.36 ksi resp.) at 135 °C. Hence, the assembly clears the
normal operating pressure load criterion.
2. Proof pressure loading condition
The maximum von Mises stress values on the manifold and bowl are 37.76 ksi and 39.21 ksi
respectively. These values are obtained by implementing the “eresx,no” command and
increasing the number of time steps to increase the accuracy. These values obtained are then
found to be lower than the yield limits of the respective materials of the manifold and bowl
(48.38 ksi and 39.36 ksi resp.) at 135 °C. Hence, the assembly clears the proof pressure load
criterion.
3. Burst pressure loading condition
The maximum von Mises stress values on the manifold and bowl are 51.55 ksi and 39.30 ksi
respectively. These values are obtained by implementing the “eresx,no” command and
increasing the number of time steps to increase the accuracy. The command line prevents
Gauss point extrapolation. These values are then found to be lower than the ultimate strength
limits of the respective materials of the manifold and bowl (54.6 ksi and 46.8 ksi resp.) at 135
°C. Hence, the assembly clears the burst pressure load criterion. Under the burst pressure, the
components yield i.e. deform plastically but do not break. The MS values for all these conditions
are also greater than 0.
4. 6.22g axial acceleration loading condition
The maximum von Mises stress values on the manifold and bowl are 0.129 ksi and 0.158 ksi
respectively. These values are lower than the yield limits of the respective materials of the
manifold and bowl (48.38 ksi and 39.36 ksi resp.) at 135 °C. Hence, the assembly clears the
6.22g axial acceleration load criterion.
5. 2g lateral (Y) acceleration loading condition
The maximum von Mises stress values on the manifold and bowl are 0.015 ksi and 0.01 ksi
respectively. These values are lower than the yield limits of the respective materials of the
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manifold and bowl (48.38 ksi and 39.36 ksi resp.) at 135 °C. Hence, the assembly clears the 2g
lateral Y acceleration load criterion.
6. 2g lateral (Z) acceleration loading condition
The maximum von Mises stress values on the manifold and bowl are 0.044 ksi and 0.051 ksi
respectively. These values are lower than the yield limits of the respective materials of the
manifold and bowl (48.38 ksi and 39.36 ksi resp.) at 135 °C. Hence, the assembly clears the 2g
lateral Z acceleration load criterion. The MS values for all these conditions are also greater than
0.
7. Radial random vibrations loading condition
3 sigma stresses are considered for the random vibration loading conditions. A 5% damping
ratio is said to exist. 6 modes of the assembly are extracted to assist in the Mode-Superposition
analysis. The FDR values obtained for the manifold and bowl are 0.075 and 0.012 respectively
which are lower than 1. Hence, the assembly clears the radial random vibrations loading
criterion.
8. Longitudinal random vibrations loading condition
The FDR values obtained for the manifold and bowl are 0.078 and 0.012 respectively which are
lower than 1. Hence, the assembly clears the longitudinal random vibrations loading criterion.
9. Tangential random vibrations loading condition
The FDR values obtained for the manifold and bowl are 0.616 and 0.280 respectively which are
lower than 1. Hence, the assembly clears the tangential random vibrations loading criterion.
Hence, it is observed that the TVC Hydraulic Filter assembly is found to be safe for all the
loading criteria.
Further mesh refinement of the high stress faces would have given more accurate results. But
computational resource and power limitations did not allow further mesh refinement. A face
sizing of 0.025 in took approximately 20 minutes to solve. Further mesh refinements would have
taken way more time than this to solve.
Moreover, the obtained stress values have convergence of 1.02% (within 4% accuracy). Hence,
the von Mises stress values evaluated give a good estimate of the actual stress values
prevalent on the components. Thus, we do have confidence in the obtained stress values due to
the convergence criteria used.
Alternatives to get precise results:
1. In order to get more precise estimates, further, say two more, mesh refinements can be
performed and the corresponding stress values can be found out to verify the obtained
convergence.
2. Moreover, further convergence study should be performed on each load case simulated
in order to have a strong confidence in each of the stress result values.
3. Furthermore, experimental testing can be performed on 1 or 2 TVC Hydraulic Filters and
the simulation parameters can be tweaked according to the experimental results. This
would give more precise results which would mimic the experimental behavior more
closely.
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4. The exact geometry can considered for the analysis to get more accurate results. But
this would increase the usage of computational resources and would take more time to
simulate.
5. We have used bilinear material data here. Availability of more nonlinear data points
would help us perform a multilinear analysis that would give more precise results.
4.0 Abbreviations and Acronyms
Assy. Assembly
Do. Document
ICD Interface Control Drawing
IAW In Accordance With
No. Number
SDRL Supplier Data Requirements List
TVC Thrust Vector Control
FE Finite Element
MS Margin of Safety
NOP Normal Operational Pressure (= max. working pressure)
18. Donaldson Company, Inc
SDRL No.: USP-CM-007
Engineering Drawings & Associated Lists
Ares I TVC Filter Manifold Assy
18
Appendix A. Analysis Methodology
This appendix describes the analysis methodology used in creating the finite element
model representation of the TVC Filter Manifold Assembly. Figure A-1 shows a CAD
representation of the complete TVC Filter Manifold Assembly.
Figure A-3-1: Geometric Representation of TVC Filter Manifold Assembly
The first simplification made for analysis purposes was the representation used for the
fittings and transducers. The fittings and transducers were removed from the assembly
and substituted with lumped masses defined at their respective center of gravity
locations based on the CAD representation. These lumped masses were attached to
mass less plugs added to the manifold housing in the thread region of each
corresponding fitting or transducer as shown in Figure A-3. The external bowl was
included in the analysis model. Its internal assemblies were ignored for this study.
Figure A-3 shows a plot of the mass less plugs with attached lumped mass elements
(spheres – manifold housing hidden). Red surfaces represent the attachment surface
for each lumped mass where constraint equations are used to attach the lumped
masses to the manifold housing.
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Figure A-3-2: Lumped Mass Representations of Fittings
In order to replicate a representative mounting configuration for the finite element model,
the geometric source for the analytical model was imprinted with circular faces at the
bottom of the mounting tabs, which were considered to be a fixed boundary condition
representing a standoff with a washer faced threaded fastener. Figure A-4 shows a plot
of the fixed boundary surfaces.
Figure A-3-3: Fixed Boundary Condition Surfaces used in FE Analyses
The TVC Filter Manifold Assembly finite element model was meshed with 134015
second order tetrahedral finite elements (for static pressure analyses) having a total of
216659 nodes. Modal and random vibration meshes are not discussed. The mesh is
shown in Figure A-5.
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Figure A-3-4: TVC Filter Manifold Assembly Finite Element Mesh
Because the geometric topology of the manifold contains many small machining
features, the global level model was simplified to remove small wire tie drill holes and
spot face machined regions.
The primary loading environment which the TVC Filter Manifold Assembly is subject is
pressure. Pressure surface in the manifold are shown in Figure A-6
Figure A-3-5: Manifold Pressure Surfaces
Figure A-7 shows the pressure surfaces associated with the bowl.
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Figure A-3-6: Bowl Pressure Surfaces
The material properties used in the finite element model were obtained from MMPDS-04
for Aluminum 7075-T652 and Aluminum 7075-T7351. S-Basis material allowables were
used for Aluminum 7075-T652 as shown in Figure A-9.
Figure A-3-7: 7075-T652 Material Properties (Source: MMPDS-01)
B-Basis material allowables were used for Aluminum 7075-T7351 as shown in Figure A-
10 below.
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Figure A-3-8: 7075-T7351 Material Properties (Source: MMPDS-01)
Table A1-1 shows the Young’s Modulus, density and Poisson’s ratio material properties
assigned to the Manifold and Filter Bowl parts.
Table A1-1: Elastic Properties for TVC Filter Manifold Assembly Parts
The TVC Filter manifold assembly is required to operate throughout a temperature range
of -40 °F to +275 °F per SAE AS 5440 Type II hydraulic system. To satisfy this
requirement, the material allowables used to calculate margins of safety and fatigue
needed to have a temperature correction factor established for yield and ultimate
strength. Figure 3.7.6.1.1(d) from MMPDS-04 was used to determine the temperature
correction factor for yield strength (as shown below).
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Figure 3.7.6.1.1(c) was used to determine the temperature correction factor for ultimate
strength (as shown below). Table A1-2 shows the temperature correction factors used
in the specification analysis runs.
Table A1-2: Temperature Correction Factors for Yield and Ultimate Strength
(Source: MMPDS-01)
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Table A1-3 shows the yield strength, ultimate strength and tangent modulus for both
Aluminum 7075-T652 and 7075-T7351 for both room temperature and 275 F. The
values for 275 F were used in calculations of factor of safeties as well as fatigue damage
ratios.
Table A1-3: Aluminum Strength Properties Used in the FE Analyses
For fatigue evaluations of the TVC Filter Manifold Assembly a best fit S/N curve from
Figure 3.7.6.1.8(a) in MMPDS-04 was used in the calculations of fatigue damage ratios
(shown below).
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Appendix B. Model Verification
A series of mathematical check runs were conducted on the finite element model of the
(TVC) Hydraulic System Flight Filter Manifold assembly prior to running the specification
analyses.
Static Force Balance Check
A further mathematical model check was performed per NASA-HDBK-7005, Section
5.1.5.3 d: “…Loads (internal forces, stresses, relative displacements) resulting from a
steady translational or rotational physical acceleration should match those predicted by
the finite-element model using the corresponding inertia forces.” To satisfy this check,
the total force (external and internal) was summed at the fixed mounting feet locations,
and this was done for each static loading environment.
Force Balance for Pressure Cases
The force balance was taken for the working pressure case as shown in Table B1-2.
The force sum in each flight direction is reported.
Table B1-4: Working Pressure Force Balance Check Run Results
For the proof and burst cases, only the combined pressure loads were used to calculate
the total force sum. These are shown in table B1-3 and B1-4
Table B1-5: Proof Pressure Force Balance Check Run Results
Table B1-6: Burst Pressure Force Balance Check Run Results
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Force Balance for Acceleration and Pseudo-Static Environments
A static 1g inertia load was applied in the flight coordinate system. The results for these
cases were scaled from the 1g results for the margin calculations for these environments
and all subsequent combinations of same. Reaction forces due this loading environment
are shown in Table B1-6 (as a check to ensure that 1g reaction force = weight)
Table B1-7: Acceleration Force Balance Check Run Results - Flight Coordinate
System
Acceleration in X-direction
Acceleration in Y-direction
Acceleration in Z-direction
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Appendix C. Analysis Results - Operational Pressure
The Filter manifold assembly finite element model was run under operational pressure
conditions to show compliance with specification requirements. A pressure of 3200 psig
was applied to surfaces within manifold and bowl, as shown in Figures A-6 and A-7.
Figures C-11 and C-12 show the stresses for the manifold and bowl, respectively due to
operational pressure loading.
Figure C-3-9: Global Model Peak Von Mises Stress, TVC Filter Manifold –
Operational Pressure (psi)
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.
Figure C-3-10: Global Model Peak Von Mises Stress,Filter Bowl – Operational
Pressure (psi)
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Appendix D. Analysis Results - Proof Pressure
The Filter manifold assembly finite element model was run under proof pressure
conditions to show compliance with specification requirements. A static structural
analysis was run for the proof pressure condition with fixed boundary conditions at the
mounting tab locations as shown in Figure A-4. A pressure of 4800 psig was applied to
surfaces within the manifold and bowl as shown in Figures A-6 and A-7, respectively.
Stress results for the manifold are shown in Figure D-1.
Figure D-3-11: Manifold Von Mises Stress –Proof Pressure (psi)
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Figure D-8 shows the Von Mises Stresses under the proof pressure loading for the bowl.
Figure D-3-12: Bowl Von Mises Stress - Proof Pressure (psi)
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Appendix E. Analysis Results - Burst Pressure
The Filter manifold assembly finite element model was run under burst pressure
conditions to show compliance with specification requirements. A static structural
analysis was run for the burst pressure condition with fixed boundary conditions at the
mounting tab locations as shown in Figure A-4. A pressure of 8000 psig was applied to
surfaces within the manifold and bowl as shown in Figure A-6 and A-7. The maximum
stress in the manifold under this condition is shown in Figure E-1.
Figure E-3-13: TVC Filter Assembly Von Mises Stress – Burst Pressure (psi)
Figure E-8 shows the Von Mises Stresses under the burst pressure loading for the bowl.
.
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Appendix F. Analysis Results – Random Vibration
A random vibration analysis was performed per the specification summarized in
“TVC_Filter_Specs.pdf”. the analysis is a linear mode-superposition-based analysis, and
so a modal analysis extracting the first 6 modes (from 0 to 6000 Hz) was first performed.
The modes extracted, as well as participation factors are documented below.
Table F1-1: Natural Frequencies for TVC Filter Manifold Assembly
Figures F-1 through F-6 show the first six mode shapes corresponding to the
frequencies listed in Table F1-1
Figure F-3-15: TVC Filter Manifold Assembly – Mode 1 (1053.8 Hz)
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Figure F-3-20: TVC Filter Manifold Assembly – Mode 6 (4000.2 Hz)
Per specification GRC-TVC-SPEC-015, the requirements for the TVC Filter Manifold
Assembly under random vibration are shown in Figure F-21 below.
Figure F-3-21: Random Vibration Requirements
The random vibration specification given in Figure F-21 was applied in a random
vibration in ANSYS to each of the three global axes as follows: The radial direction was
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applied as a random base excitation in the Z-direction. The Longitudinal excitation was
applied in the X-direction, and the Tangential excitation was applied in the Y-direction.
Figures F-25 – F-34 show the 3-sigam von Mises stress results to these excitations in
each of the respective loading directions.
Figure F-3-22: 3-Sigma Von Mises Stress of Manifold - Radial Random Vibration
(psi)
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Figure F-3-23: 3-Sigma Von Mises Stress of Bowl - Radial Random Vibration (psi)
Figure F-3-24: 3-Sigma Von Mises Stress of Manifold - Longitudinal Random
Vibration (psi)
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Figure F-3-25: 3-Sigma Von Mises Stress of Bowl - Longitudinal Random Vibration
(psi)
Figure F-3-26: 3-Sigma Von Mises Stress of Manifold – Tangential Random
Vibration (psi)
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Figure F-3-27: 3-Sigma Von Mises Stress of Bowl - Tangential Random Vibration
(psi)
Tables of fatigue damage ratio, (FDR = n/N, where n is the required test cycles and N is
the expected cycles to failure) have been developed based on results from the random
vibration analyses and equivalent stress equations for Aluminum 7075-T6 contained in
MMPDS-04. For conservatism, an R=0 assumption was used in the equivalent stress
equation for the random vibration loading. Critical damping of 5% was used for the
analyses.
Tables of fatigue damage ratios for the critical components of the TVC Filter Assembly is
shown in Tables 3.2.4.1.4-1 thru 3.2.4.1.4-3.
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Appendix G. Analysis Results – Flight Acceleration
Per specification GRC-TVC-SPEC-015, the requirements for the TVC Filter Manifold
Assembly under flight vibration are shown below.
The TVC Filter manifold assembly finite element model was subjected to a flight
vibration environment of 6.22g’s in the flight longitudinal direction and 2.0g’s in both the
radial and tangential flight axes to show compliance with specification requirements.
The acceleration condition was linearly combined with the operating pressure condition
to best represent the flight environment.
In order to provide for a convenient basis for linear superposition of stresses resulting
from the static acceleration load and the operational pressure, a 1g acceleration loading
(in each orthogonal axis) was run.
Figure G-2 through G-3 show the 1g Von Mises stress for the manifold, bowl
components for the longitudinal flight axis.
Figure G-3-28: 1g TVC Filter Manifold Von Mises Stress – Longitudinal Flight Axis
(psi)
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Figure G-3-29: 1g Bowl Von Mises Stress – Longitudinal Flight Axis (psi)
Figure G-6 through G-7 show the 1g Von Mises stress for the manifold, F4 and F6 bowl
components for the tangential flight axis.
Figure G-3-30: 1g TVC Filter Manifold Von Mises Stress – Tangential Flight Axis
(psi)
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Figure G-3-31: 1g Bowl Von Mises Stress – Tangential Flight Axis (psi)
Figure G-10 through G-12 show the 1g Von Mises stress for the manifold, F4 and F6
bowl components for the radial flight axis.
Figure G-3-32: 1g TVC Filter Manifold Von Mises Stress – Radial Flight Axis (psi)
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Figure G-3-33: 1g Bowl Von Mises Stress – Radial Flight Axis (psi)
To show compliance with the flight axis acceleration requirement the peak Von Mises
Stress from the operational pressure were linearly superimposed as follows:
Peak Operational Pressure Stress + (6.22 x 1g Longitudinal Axis Stress)
Peak Operational Pressure Stress + (2.00 x 1g Tangential Axis Stress)
Peak Operational Pressure Stress + (2.00 x 1g Radial Axis Stress)
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Appendix H. Results of Fillet Optimization (Final Part A)
Figure H- 3-1 Response surface plot from step 23
Figure H- 3-2 Response surface plot from step 24
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Figure H- 3-3 Screen Capture showing the 3 candidate points from step 27