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CHAPTER 5 FINITE ELEMENT MODELING AND...
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CHAPTER 5
FINITE ELEMENT MODELING AND ANALYSIS OF A FLEX SEAL
The design methodology of a flexible joint in the preceding
chapter-3 has to be confirmed by Finite Element Analysis.
Convergence study has been performed refining the finite element
model to obtain accurate stress distribution for the specified loads.
Each elastomer and reinforcement are divided into minimum of three
layers across the thickness. Both the elastomer and reinforcement
are divided into a minimum of 40 radial divisions. The structural
analysis of the designed flex seal has been carried using Ansys 10.0
(general purpose FEA software). Initially an axi-symmetric model
(symmetric about Y-axis) of the seal and throat housing is considered,
then detailed 3D analysis of the flex seal along with the divergent is
considered for analysis. A nonlinear static analysis is carried out with
large displacement option and Mooney - Rivlin material model is
chosen for modeling the rubber material.
The seal is subjected to ejection load due to motor chamber
pressure and the vectoring load. The objective of the present finite
element analysis is to find the seal compression due to chamber
pressure, predominant stresses in the inner diameter of shims and
the flex seal spring torque. The analysis is also done to characterize
the thermal boot contribution to the total torque. The analysis is done
at 3 pressures separately to characterize the flex seal with and
without thermal boot to study the effect of pressure on the spring
torque.
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5.1 FINITE ELEMENT MODEL
(Configuration-D)
5.1.1 Axi-symmetric Analysis
The CAD model and Finite Element model for 2D case are
shown in Figure 5-1 and Figure 5-2 respectively. The model is meshed
with Plane 82 elements for metallic shims, end rings, throat housing.
The Plane 82 element has 8 nodes with 2 degrees of freedom at each
node. Isotropic material properties have been assigned to metal
(AFNOR 15CDV6 steel). The rubber pads have been meshed with
Hyper 74 elements. The Hyper 74 elements also have 8 nodes and 2
degrees of freedom at each node. The material properties are given in
Table 5-1.
5.1.2 3D Analysis
The CAD model and Finite Element model for 3D case are
shown in Figure 5-3 and Figure 5-4 respectively. The model is meshed
with Solid 45 elements for metallic shims, end rings, throat housing.
The Solid 45 element has 8 nodes with 3 degrees of freedom at each
node. Isotropic material properties have been assigned to metal
(AFNOR 15CDV6 steel). The rubber pads and the thermal boot are
meshed with Hyper 58 elements. The Hyper 58 elements also have 8
nodes and 3 degrees of freedom at each node.
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Figure 5-1: CAD model of flex seal – load case-1
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Figure 5-2: Finite Element model with loading and Boundary Condition–case-1
FIXED BOUNDARYCONDITION
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Figure 5-3: CAD model of flex seal – load case – 2 & 3
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Figure 5-4: FE model with loading and boundary condition – load case-2 & 3
FIXED BOUNDARYCONDITION
VECTORING LOAD
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Table 5-1: Material properties used in the analysis
5.2 LOADS
Finite element analysis has been carried out for three loading
conditions as given in Table 5-2. The load case-1 is carried out to
evaluate the seal compression. The stresses are maximum during
combined pressure and vectoring loads. The load case-2 is carried out
to have an initial estimate of stresses on the shims. The case-3 is
close to the material behavior as characterised and modeled for
validation. A pressure load of 5.3 MPa which is equivalent to the proof
ejection load of 2157 kN is arrived based on configuration and is
applied for load case-1 & 2. The estimated spring torque at
atmospheric pressure from equation 3-14 is 3.413 kN-m/degree
which gives a vectoring force of 27.64 kN for four degrees. The
vectoring force applied is arrived iteratively to get an angular
deflection of 4 degrees at 5.3 MPa pressure, which is 21.46 kN. The
Material Property Value
15CDV6
(Stress-Strain curve)
E 206 GPa
γ 0.3
Elastomer
C1 0.18 MPa
C2 0.1 MPa
γ 0.499
Thermal Boot
C10.000212
MPa
C2 0.0119 MPa
γ 0.499
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vectoring loads are symmetric with respect to the resultant plane of
actuation. Hence, only 1800 sector model of the nozzle is considered
for the analysis. The analysis for evaluating flex seal spring torque and
the stress on the shims are evaluated at three pressures. These
pressures are at 0.5 MPa which is minimum pressure required to
support the flex seal from sagging due to self weight, 4.02 MPa which
is equivalent to the average chamber pressure of the rocket motor and
5.3 MPa which is equivalent to Proof Pressure of the rocket motor for
load case-3. The Vectoring Loads obtained through FEA iteratively at
0.5 MPa, 4.02 MPa and 5.3MPa pressures are 24.37 kN, 22.43 kN &
21.46kN respectively.
Table 5-2: Load cases for FE analysis
5.3 BOUNDARY CONDITIONS
Fixed boundary condition has been applied at the aft end ring
pitch circle diameter as shown in Figure 5-2 and Figure 5-4.
5.4 FEA RESULTS
Table 5-3 gives the hoop stress in the shims for all the three load
cases. The empirical relations in literature give the stresses in the
Cases Type Loads Metal Elastomer
Case-1 2D Pressure load Linear Non-linear
Case-2 3DPressure &
Actuator loadsLinear Non-linear
Case-3 3DPressure &
Actuator loadsNon-linear Non-linear
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middle shim of the flex seal. Hence, all the comparisons are made with
middle shim.
Case-1:
The seal compression and hoop stress are shown in Figure 5-5
& Figure 5-6. The maximum seal compression is 10.8 mm as shown
in Figure 5-5. The Maximum hoop stress in the mid shim due to the
pressure load is -788 MPa by considering linear properties of metal.
The analysis is repeated with nonlinear properties of metal & and the
mid shim hoop stress is -598.1 MPa.
Case-2:
The hoop stress plot for the seal is shown in Figure 5-7. The
maximum stress is in middle shim and the value is -103.12 kgf/mm2
(-1011.2 MPa).
Case-3:
Figure 5-8 shows the hoop stress plot for the shims. The
maximum stress is in middle shim and the value is -85.95 kgf/mm2
(-842.7 MPa). The shims experience compressive stress in the inner
diameter and tensile stress in outer diameter. The difference in hoop
stress between case-2 & 3 as shown in Table 5-3 is mainly due to
consideration of linear and non-linear metal behavior. The difference
is significant where the stress levels are high i.e., shim 3, 4 & 5. The
shear stress in pads is found to be 1.25 MPa against shear stress
capability of 2.65 MPa (minimum).
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The analysis has been carried out at 0.5 MPa and 4.02 MPa also
for case-3. The results are tabulated in Table 5-4. The stresses on the
shims are maximum at maximum pressure and maximum vectoring
angle. The force required to deflect the nozzle for same vectoring angle
is maximum at lowest pressure i.e., 0.5 MPa. From all the above hoop
stress tables (Table 5-3 & Table 5-4), it is clearly evident that middle
shims are loaded to the maximum.
The von-Mises failure criterion is adopted for shims. The hoop
stress in the shims is dominant compared to other stress components
which are brought out in Table 5-5. From the considerations of
measurement of strains during testing and validation, strain gauges
are possible to be mounted on the inner diameter (ID) of the shims.
The shim can accommodate only uni-axial strain gauge, since the
thickness of the shim being very less which is in hoop direction.
The FEA results show the radial, axial, hoop and von-Mises
stresses at proof load. The von-Mises stresses at MEOP are separately
shown. The factor of safety on both yield strength and ultimate tensile
strength are worked out based on the minimum guaranteed material
properties (Yield strength = 835 MPa and Ultimate tensile strength =
980 MPa). From Table 5-5 the minimum factor of safety on yield
strength over von-Mises stress is 1.14 and on ultimate tensile strength
is 1.34 which meets the design requirements.
This methodology was used to carry out the structural analysis
of flex seals of five other configurations also and their results are
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tabulated in Table 5-6 to Table 5-10. From the trends observed in all
the flex seal designs, the middle shims are loaded to the maximum
extent and hence the minimum factor of safety is on the middle shim
only.
Table 5-3: Hoop stress (MPa) in shims for three load cases-
Configuration-D
LOCATIONCase 1
(5.3 MPapressure)
Case 2(5.3 MPa pressure
+ 21.46 kNVectoring Load)
Case 3(5.3 MPa pressure
+ 21.46 kNVectoring Load)
SHIM 1 -638.7 -743.6 -735.0SHIM 2 -736.9 -908.8 -788.0SHIM 3 -778.2 -988.3 -821.4SHIM 4 -788.0 -1011.2 -842.7SHIM 5 -769.4 -985.0 -805.6SHIM 6 -713.0 -899.5 -793.2SHIM 7 -588.0 -719.1 -691.3
Table 5-4: Hoop stress (MPa) at three pressures for load Case-3 -
Configuration - D
LOCATION0.5 MPa (24.37
kN vectoringload)
4.02 MPa (22.43kN vectoring load)
5.3 MPa (21.46kN vectoring
load)SHIM 1 -97.6 -503.9 -735.0SHIM 2 -125.7 -594.4 -788.0SHIM 3 -137.1 -631.3 -821.4SHIM 4 -139.5 -639.8 -842.7SHIM 5 -135.7 -624.9 -805.6SHIM 6 -124.0 -577.6 -793.2SHIM 7 -97.2 -464.1 -691.3
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Figure 5-5: Seal compression plot of flex seal – load case - 1
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Figure 5-6: Hoop stress plot of flex seal – load case – 1.
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Figure 5-7: Hoop stress plot of flex seal – load case - 2
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Figure 5-8: Hoop stress plot of flex seal – load case - 3
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Table 5-5: FEA stresses on shims (MPa) – Configuration – D (load case-3)
LOCATIONFEA STRESS AT PROOF LOAD von-Mises
stress onMEOP
FACTOR OF SAFETY ON
Radial Axial Hoopvon
Misesvon-Mises
stress on YSvon-Mises stress
on UTS
SHIM 1 -3.8 -0.6 -735.0 647.1 588.3 1.42 1.67
SHIM 2 11.9 -10.1 -788.0 753.4 684.9 1.22 1.43
SHIM 3 27.3 -18.5 -821.4 795.8 723.5 1.15 1.35
SHIM 4 40.6 -24.4 -842.7 806.5 733.2 1.14 1.34
SHIM 5 52.6 -27.8 -805.6 792.2 720.2 1.16 1.36
SHIM 6 66.5 -30.0 -793.2 742.6 675.1 1.24 1.45
SHIM 7 91.2 -32.9 -691.3 616.4 560.4 1.49 1.75
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Table 5-6: FEA stress Values (MPa) on shims for Configuration – A
LOCATIONFEA STRESS AT PROOF LOAD von-Mises
stress onMEOP
FACTOR OF SAFETY ON
Radial Axial Hoop von Misesvon-Mises
stress on YSvon-Mises
stress on UTS
SHIM 1 169.9 167.1 -528.4 523.2 475.6 1.76 2.06
SHIM 2 218.9 199.9 -634.8 625.4 568.6 1.47 1.72
SHIM 3 250.1 217.7 -690.0 679.8 618.0 1.35 1.59
SHIM 4 270.5 225.6 -747.9 736.8 669.9 1.25 1.46
SHIM 5 280.1 225.1 -729.1 719.7 654.3 1.28 1.50
SHIM 6 278.2 214.6 -718.3 709.8 645.3 1.29 1.52
SHIM 7 265.6 193.0 -686.0 679.2 617.5 1.35 1.59
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Table 5-7: FEA stress Values (MPa) on shims for Configuration – B
LOCATION
FEA STRESS AT PROOF LOAD von-Misesstress on
MEOP
FACTOR OF SAFETY ON
Radial Axial Hoop von Misesvon-Mises
stress on YSvon-Mises
stress on UTS
SHIM 1 233.2 224.1 -653.7 652.9 593.5 1.41 1.65
SHIM 2 290.3 271.3 -753.6 744.1 676.5 1.23 1.45
SHIM 3 320.2 290.1 -789.4 779.3 708.5 1.18 1.38
SHIM 4 331.4 295.8 -799.9 789.7 717.9 1.16 1.37
SHIM 5 327.2 288.9 -792.4 783.0 711.8 1.17 1.38
SHIM 6 307.4 268.6 -764.0 755.9 687.2 1.22 1.43
SHIM 7 263.5 228.2 -689.7 685.4 623.1 1.34 1.57
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Table 5-8: FEA stress Values (MPa) on shims for Configuration – C
LOCATION
FEA STRESS AT PROOF LOAD von-Misesstress on
MEOP
FACTOR OF SAFETY ON
Radial Axial Hoop von Misesvon-Mises
stress on YSvon-Mises
stress on UTS
SHIM 1 176.1 175.3 -624.3 619.3 563.0 1.48 1.74
SHIM 2 211.4 196.9 -702.9 693.9 630.8 1.32 1.55
SHIM 3 230.0 205.1 -730.0 720.6 655.1 1.27 1.50
SHIM 4 232.8 207.4 -736.3 726.9 660.8 1.26 1.48
SHIM 5 226.4 203.3 -724.8 716.2 651.1 1.28 1.51
SHIM 6 209.0 189.2 -688.2 680.7 618.8 1.35 1.58
SHIM 7 173.5 158.0 -602.9 599.3 544.8 1.53 1.80
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Table 5-9: FEA stress Values (MPa) on shims for Configuration – E
LOCATION
FEA STRESS AT PROOF LOAD von-Misesstress on
MEOP
FACTOR OF SAFETY ON
Radial Axial Hoop vonMises
von-Misesstress on YS
von-Misesstress on UTS
SHIM 1 235.5 229.6 -590.6 580.9 528.1 1.58 1.86
SHIM 2 283.5 264.5 -664.8 653.7 594.3 1.41 1.65
SHIM 3 308.8 279.7 -693.4 682.3 620.3 1.35 1.58
SHIM 4 318.1 282.9 -700.3 689.6 626.9 1.33 1.56
SHIM 5 314.6 275.8 -690.6 681.0 619.1 1.35 1.58
SHIM 6 296.7 256.2 -658.4 651.3 592.1 1.41 1.66
SHIM 7 257.6 213.2 -573.4 573.3 521.2 1.60 1.88
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Table 5-10: FEA stress Values (MPa) on shims for Configuration – F
LOCATION
FEA STRESS AT PROOF LOAD von-Misesstress on
MEOP
FACTOR OF SAFETY ON
Radial Axial Hoop vonMises
von-Misesstress on YS
von-Misesstress on UTS
SHIM 1 228.4 222.3 -614.2 605.1 550.1 1.52 1.78
SHIM 2 295.8 266.4 -714.7 703.6 639.6 1.31 1.53
SHIM 3 319.2 273.1 -734.3 723.8 658.0 1.27 1.49
SHIM 4 310.1 253.5 -709.7 701.4 637.6 1.31 1.54
SHIM 5 262.7 195.1 -602.7 602.9 540.5 1.54 1.81
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5.5 COMPARISON OF FEA RESULTS FOR SHIM STRESSES WITH
DESIGN FORMULAE
Hoop stress calculated from the empirical relations is for middle
shim. The comparison of stresses obtained from empirical relations
and finite element analysis for pressure and vectoring load are given
in Table 5-11 and Table 5-12.
5.5.1 Comparison of FEA results with Eq.(3-1) & Eq.(3-2)
From Table 5-11 and Table 5-12, the comparison of stresses in
middle shim for pressure load between Eq.(3-1) and FEA prediction
shows a variation between -9.4% to 57.4% which shows a large
spread. For vectoring loads the variation between Eq.(3-2) and FEA
prediction shows a variation upto -92.2% which indicates the formula
for vectoring load under predicts the stresses due to vectoring.
5.5.2 Comparison of FEA results with Eq.(3-4) & Eq.(3-5)
From Table 5-11 and Table 5-12, the comparison of stresses in
mid shim for pressure load between Eq.(3-4) and FEA prediction
shows a variation between +4.1% to -43.5%. For vectoring loads the
variation between Eq.(3-5) and FEA prediction shows a variation upto
-46.9% which indicates the formula again under predicts the stresses
due to vectoring.
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Table 5-11: Comparison of stress between FEA and empirical relations
– only pressure load
Configuration
StressEq.(3-1)
StressEq.(3-4)
FEA% VARIATIONEq.(3-1) AND
FEA
% VARIATIONEq.(3-4) AND
FEAA -461.2 -391.3 -375.9 22.7 4.1B -565.5 -349.3 -617.8 -8.5 -43.5C -649.5 -416.5 -526.4 23.4 -20.9D -545.1 -426.0 -598.1 -8.9 -28.8E -508.3 -332.2 -561.2 -9.4 -40.8F -894.1 -472.4 -568.1 57.4 -16.8
Table 5-12: Comparison of stress between FEA and empirical relations
– only vectoring load
Configuration
StressEq(3-2)
StressEq(3-5)
FEA % VARIATIONEq.(3-2) AND
FEA
% VARIATIONEq.(3-5) AND
FEAA -29 -197.5 -372 -92.2 -46.9B -31.1 -153.9 -181.4 -82.9 -15.2C -32.8 -168.2 -209.9 -84.4 -19.9D -23.5 -147.4 -244.6 -90.4 -39.7E -14.4 -79.9 -139.1 -89.6 -42.6F -22.1 -101.1 -166.2 -86.7 -39.2
5.6 THERMAL BOOT TORQUE EVALUATION – CONFIGURATION D
The thermal boot is designed as mentioned in the section 3.3.6.
No closed form solutions or empirical relations are available for
estimation of the boot torque. The spring torque contribution of boot is
assumed to be 30% for bellow boot configuration. The thermal boot is
made of nitrile rubber. Mooney-Rivlin material model is chosen for the
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thermal boot. The CAD model of the flex seal with boot is shown in
Figure 5-9. The finite element model with loading and boundary
condition for flex seal with boot is shown in Figure 5-10. The flex seal
spring torque estimated from FE analysis for all the three pressures
are given in Table 5-13. The vectoring load is iteratively arrived at to
deflect the nozzle by 40 which worked out to 28.52 kN at 5.3 MPa. The
percentage of thermal boot contribution works out to 33% as
estimated from FE analysis. The deformed shape of the boot is shown
in Figure 5-11.
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Table 5-13: FEA prediction of flex seal spring torque with and without boot
PARAMETERVECTORING
LOAD (kN)
TORQUE
(kN-m)*
BOOT CONTRI-
BUTION(%)
Maximum Sealtorque under
pressure(4 Deg, 0.5 MPa)
withoutboot 24.37 12.04
27.78with boot 31.13 15.38
MaximumSeal torque
under pressure(4 Deg,
4.02MPa)
withoutboot 22.43 11.08
31.97with boot 29.6 14.62
MaximumSeal torque
under pressure(4 Deg, 5.3MPa)
withoutboot 21.46 10.60
33.0with boot 28.52 14.09
* Torque = vectoring load x moment arm (0.494 m)
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Figure 5-9: CAD model of flex seal with thermal boot
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Figure 5-10: FE model of flex seal with thermal boot
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Figure 5-11: Deformed shape of flex seal with thermal boot
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5.7 CONCLUDING REMARKS
Axi-symmetric analysis has been carried out to estimate the seal
compression which is important in sizing the actuator stroke. 3D non-
linear analysis has been carried out to estimate the shim stresses and
compared with empirical formulae available in literature. Large
variations between results obtained by empirical relations and FEA
are observed. Analysis of flex seal with thermal boot has been carried
out to estimate the additional force / torque required to vector the
nozzle. To validate the design of the flexible joint, various acceptance
tests such as proof pressure test (PPT), null position test (NPT) and
Vectoring tests with ejection load simulations and pull tests have to be
carried out. The details of evolution of test plan, design and realisation
of test set ups are discussed in the next chapter.