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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.

110

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.

111

Figure 5-1: CAD model of flex seal – load case-1

112

Figure 5-2: Finite Element model with loading and Boundary Condition–case-1

FIXED BOUNDARYCONDITION

113

Figure 5-3: CAD model of flex seal – load case – 2 & 3

114

Figure 5-4: FE model with loading and boundary condition – load case-2 & 3

FIXED BOUNDARYCONDITION

VECTORING LOAD

115

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

116

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).

118

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

119

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

121

Figure 5-6: Hoop stress plot of flex seal – load case – 1.

122

Figure 5-7: Hoop stress plot of flex seal – load case - 2

123

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

135

Figure 5-10: FE model of flex seal with thermal boot

136

Figure 5-11: Deformed shape of flex seal with thermal boot

137

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.