Numerical Investigations on Characteristics of Stresses in U Shaped Metal Expansion Bellows.pdf

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Research ArticleNumerical Investigations on Characteristics of Stresses in U-Shaped Metal Expansion Bellows

S. H. Gawande,1 N. D. Pagar,2 V. B. Wagh,3 and A. A. Keste1

Department of Mechanical Engineering, M. E. Society’s College of Engineering, Pune, Maharashtra , IndiaDepartment of Mechanical & Materials echnology and Department of echnology, S.P. Pune University, Pune , IndiaDepartment of Mechanical Engineering, G.S.M. College of Engineering, Pune, Maharashtra , India

Correspondence should be addressed to S. H. Gawande; [email protected]

Received May ; Revised July ; Accepted August

Academic Editor: Yuanshi Li

Copyright © S. H. Gawande et al. Tis is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Metal expansion bellows are a mechanical device or absorbing energy or displacement in structures. It is widely used to dealwith vibrations, thermal expansion, and the angular, radial, and axial displacements o components. Te main objective o thispaper is to perorm numerical analysis to nd various characteristics o stresses in U-shaped metal expansion bellows as per therequirement o vendor and ASME standards. In this paper, extensive analytical and numerical study is carried out to calculatethe different characteristics o stresses due to internal pressure varying rom MPa to MPa in U-shaped bellows. Finite elementanalysis by using Ansys is perormed to nd the characteristics o U-shaped metal expansion bellows. Finally, the results o analytical analysis and nite element method (FEM) show a very good agreement. Te results o this research work could be usedas a basis or designing a new type o the metal bellows.

1. Introduction

Metal bellows are structural component in which a wavy shape is ormed on the surace o a circular tube to introduceelastic property. Expansion joints used as an integral parto heat exchangers or pressure vessels shall be designated toprovide exibility or thermal expansion and also to unctionas a pressure-containing element. Normally metal bellows areused as an expansion joint in shell and tube heat exchanger.

It deals with vibrations, thermal expansion, and angular,radial, and axial displacements o components. Its presentapplications are in AC equipment, industrial plants, hosepipes, vacuum systems, and aerospace equipment.

Limited amount o research work has been carried outby some researchers working in the area o the expansion

joint or shell and tube heat exchanger. Teir work has beenreported by perorming industrial survey (namely, Ala LavalIndia Ltd., Pune) and exhaustive literature review throughearlier published research work, journal papers, and technicalreports. Many design ormulae o bellows can be ound inASME code []. And the most comprehensive and widely accepted text on bellows design is the Standards o Expansion

Joint Manuactures Association, EJMA []. Number o pilotand test experiments have been perormed or analysis o AM steel bellows by Shaikh et al. []. As bellows areexposed to marine atmosphere or more than years whichleads to pitting effect, hence the determination o dynamiccharacteristics o beam nite elements by manipulatingcertain parameters on commercial sofware was done by Broman et al. []. In comparison with semianalytical, meth-ods have potential o considering axial, bending, and torsion

degrees o reedom at the same time, and the rest are modeledby nite elements in which experimental results are also

veried. Te effect o the elliptic degree o Ω-shaped bellowstoroid on its stresses is investigated by Li []. In addition,Becht IV [] has investigated the atigue behavior o expan-sion joint bellows. Te results o Ω-shaped bellows with ellip-tic toroid calculated stresses correspond to experiments. Teelliptic degree o Ω-shaped toroid affects the magnitude o internal pressure-induced stress and axial deection-inducedstress. It especially produces a considerable effect on thepressure-induced stress. o maintain the atigue lie o toroidbellows, during manuacturing process toroid elliptic degreemust be reduced. EJMA stresses or unreinorced bellows are

Hindawi Publishing CorporationInternational Journal of MetalsVolume 2015, Article ID 957925, 9 pageshttp://dx.doi.org/10.1155/2015/957925


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International Journal o Metals

evaluated by Becht IV []. Using linear axisymmetric shellelements parametric analysis is conducted. Finite elementanalysis is carried out using commercial code. Meridionalstresses due to internal pressure and displacement are accu-rate. Bellows-orming process is done afer evaluating effec-tive parameters by Faraji et al. []. FEM results are compared

with analytical solutions. Faraji et al. [] used a commercialFEM code, ABAQUS Explicit, to simulate manuacturingprocess o metal bellows. Forming o different shapes o tubu-larbellows using a hydroorming process is proposed by Kanget al. []. Te conventional manuacturing o metallic tubularbellows consists o our-step process: deep drawing, ironing,tube bulging, and olding. In their study, single-step tubehydroorming combined with controlling o internal pressureand axial eeding was proposed. Tese reviewed papersshow that there is need or rigorous analysis and ormingparameters o bellows. It is stated that the Ω-shaped bellowshave much betterability to endure high internal pressurethancommon U-shaped bellows. Metal bellows have wide appli-cations in piping systems, automotive industries, aerospace,

and microelectromechanical systems. Kang et al. [] havedeveloped a microbellows actuator using microstereo lithog-raphy technology. Numerous papers have dealt with variousaspects o bellows except or orming process. Broman et al.[] have determined dynamic characteristics o bellows by manipulating certain parameters o the beam nite elements.Jakubauskas and Weaver [] have considered the transverse

vibrations o uid-lled double-bellows expansion joints.Jha et al. [] have investigated the stress corrosion crackingo stainless steel bellows o satellite launch vehicle propellanttank assembly. Zhu et al. [] have investigated the effecto environmental medium on atigue lie or U-shapedbellows expansion joints. However, ew papers have shown

the manuacturing process o the metal bellows. Wang et al.[] have developed a new process or manuacturing o expansion joint bellows rom i-Al-V alloys with highdegree o spring back. Wang et al. [] have used gas pressureinstead o uid pressure, becausethe process was done in hightemperature ambient. Kang et al. [] have investigated theorming process o various shapes o tubular bellows usinga single-step hydroorming process. Lee [] has carried outparametric study on some o the orming process parameterso the metal bellows by nite element only. He has mentionedthat, in general, metal bellows are manuactured in ourstages: deep drawing, ironing, tube bulging, and olding.

From the literature survey, it is seen that a numbero researchers have worked on study and applications o different types o bellows under various working conditions,their comparison, and manuacturing processes, and ew areworking on atigue lie enhancement. But investigations onneed or selection o proper material o bellows or givenapplication, their proper design, stresses induction, atiguelie analysis, and prediction o ailure and investigationson various characteristics o different bellows and vibrationeffect are essential.

2. Problem Formulation and Objective

As per literature and industrial survey, it is seen that bellowsare one o the most important elements in the expansion joint

P

S1

S2S3

S4

Pressure

F : Stress directions in bellows.

and have the unction to absorb regular as well as irregularexpansion and contraction o the system. Bellows require

high strength and good exibility, which can be achievedby good design and proper manuacturing method. Tedesign reerred to rom EJMA requires proper congurationselection which makes it difficult. Te metal bellows aremanuactured with different methods like orming, hydro-orming, bulging, drawing, and deep drawing, which dependon applications. Te materials used or bellows are normally stainless steel; in rare cases Inconel and aluminum are alsoused. Different shapes o bellows are U-shaped, semitoroidal,S-shaped, at, stepped, single sweep, and nested ripple. Asper discussion with experts working in the same eld, itis observed that the concept o study in this paper needsdetailed understanding o proper design and investigationson selection o materials, shapes, vibration effect, joiningo bellows to shell, stresses, ow analysis, atigue lie anal-ysis, and prediction o ailure. Hence this work ocuses onselection o materials o bellows or the given application,their proper design, and determination o characteristics o stresses o bellows, atigue lie analysis, and prediction o ailure.

3. Determination of Characteristics of Stresses of Bellows by Analytical Analysis

Metal expansion bellows are a very distinctive component o a piping system. Tey must be designed strong enough to

accommodate the system design pressure as well as exibleenough to accept the design deections or a calculatednumber o occurrences, with a minimum resistive orce. Inorder to understand the static and dynamic behavior o metalexpansion bellows as shown in Figure , it is necessary tostudy the selection o materials o bellows or the given appli-cation, basic undamental, their proper design, and working.Te different mechanical properties and design parametersor bellows under consideration are shown in able .

Te design and analytical analysis o metal expansionbellows is perormed as per ASME standards. Figure showsthe direction o different stresses induced in metal expansionbellows. According to ASME standards, the circumerential


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: Different design parameters.

Design parameters Notations Specications

Expansion joint material SA-

Material UNS number S

Bellows design allowable stress

. N/mm2

Bellows ambient allowable stress . N/mm2Bellows yield stress . N/mm2Bellows elastic modulus at designtemp.

N/mm2Bellows elastic modulus at ambienttemp.

N/mm2Poisson’s ratio ] .

Bellows material condition Formed

Design cycle lie, required numbero cycles

req

Design internal pressure .N/mm2Design temperature or internalpressure

∘

C

Bellow type U-shaped

Bellows inside diameter . mmConvolution depth . mmConvolution pitch . mmExpansion joint opening perconvolution

Δ . mmotal number o convolutions Nominal thickness o one ply . mmotal number o plies End tangent length

. mm

Fatigue strength reduction actor .

membrane stress (1) in bellows tangent due to internalpressure is given as per

1= 12

× × × + × 2 × × + × × × + × × × × . ()

Te end convolution circumerential membrane stress (2)due to internal pressure based on the equilibrium considera-tions is as shown in Figure . Equation () represents the endconvolution circumerential membrane stress:

2, = 12 × + × + × × + × × + × , ()

where is mean diameter o bellows convolution and it isgiven as

=

+ + × . ()

S2

Pressure

F : Deection stresses acting on bellows.

Pressure

S4

Te convolutionwants to take

this shape

F : Meridional bending stress due to internal pressure.

Te intermediate convolution circumerential membranestress (2,) due to internal pressure is calculated by using theollowing equation:

2, = 12 × × . ()Te bellows meridional membrane stress (3) due to internalpressure is calculated based on the component o pressure inaxial direction acting on the convolution divided by the metalarea o root and crown by using the ollowing equation:

3 = 12 × × . ()Te bellows meridional bending stress (4) due to internalpressure as represented in Figure is given by (). Figure shows the variation o meridional bending stresses inducedin bellows:

4 = 12 × × 2 × × . ()

Te bellows meridional membrane stress(5) and meridionalbending stress (

6) due to deection are given by (). Figure


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Convolution shape beoredeecting

When the bellows compressesthe side walls bend to shorten

the bellows

Convolution shapeafer deecting

S6

F : Meridional bending stress due to deection.

Convolutions

Lt

Db

nt

w

qNq

F : Geometry o metal expansion bellows.

shows the representation o meridional bending stress due todeection. Consider

5

=

×

2

× Δ

2 × 3 × ,6 = 5 × × × Δ3 × 2 × , ()

where , , and are the actors or calculating 4, 5, 6respectively. is modulus o elasticity or bellows. Figure shows the metal expansion bellows under consideration inthis paper.

4. Numerical Simulation

In order to perorm numerical simulation, it is necessary

to develop solid model o metal expansion bellows. Hencemetallic expansion bellows is rst modeled in Creo. asshown in Figure , which is latest CAD sofware andmakes modeling easy and user riendly. Te model is thentranserred in IGES ormat and geometry is imported oranalysis to Ansys. sofware. Ten metal expansion bellowsis analyzed in Ansys. sofware.

.. Finite Element Procedure and Mesh Generation. Numer-ical simulation includes three stages o analysis as shown inFigure. First is preprocessing which involves modeling, geo-metric clean-up, element property denition, and meshing.Second step is solution o problem, which involves applying

Y

Z X0.00 80.00

(mm)

F : Solid model o metal expansion bellows.

Dening elements type

Dening real constants

Dening material properties

Meshing solid model

Importing model in IGES ormat

Load and boundary conditions

Solve or analysis

Plot o equivalent von-Mises stresses

Presentation o results

F : Stages o analysis.

boundary conditions on the model and then solution. Tirdstep is postprocessing, which involves analyzing the resultsplotted with different parameters like stresses and deorma-tion. Te objective in creating a solid model is to meshthat model with nodes and elements. Afer completing thesolid model, set element attributes and establishing meshingcontrols, which turn the Ansys program to generate the niteelement mesh. For dening the elements attributes, the userhas to select the correct element type.


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Y

Z

X0.00 80.00

(mm)

F : Meshed model o metal expansion bellows.

Figure shows the meshed model o metal expansionbellows. In this work, structural solid element node plane element was used as element type. Elastic analyses werecarried out on ull convolutions o the bellows with axisym-metric model. Te computational domain is divided into elements in thickness and elements in length. Tereore,the model with elements 10 × 200 is used in all analyses. Inthe present analysis, a U-shaped bellow named VLC ShellDia. mm is picked. Te bellows inside diameter is mmwith outside diameter o mm, thickness o . mm, pitcho . mm, and height o the convolution is . mm. Te

bellows is made o stainless steel SA- with the moduluso elasticity o GPa and Poisson’s ratio o .. In this work,the internal pressure in applied by applying the constraints.

5. Results and Discussions

.. Numerical Validations. Comparison test is perormed or verication o the results obtained by numerical method.For the given solid element, FEM stresses are evaluated.Te circumerential membrane stress at bellows tangent,intermediate and end convolution membrane stress, merid-ional membrane stress, and meridional bending stress dueto internal pressure o U-shaped bellows are calculated. Te

applied internal pressures are MPa, . MPa, . MPa, and MPa, respectively. In able , the results obtained romanalytical approach and numerical simulations are presented.Te meridional membrane stress and meridional bendingstress or various internal pressures are presented in able .Afer comparing the results, it is observed that the obtainedstresses by two approaches or U-shaped bellows are in goodagreement and show very closed match.

.. Comparison of Induced Design and Simulated Stressesof Metal Expansion Bellows. In the present work, numerical

values o stresses are used or evaluation o characteristicso metallic bellows. Initially, the circumerential membrane

: Analytic and FEA stresses due to internal pressure.

Stress Source Internal pressure (MPa)

. .

1 ASME . . . .FEA . . . .

2 ASME . . . .FEA . . . .2 ASME . . . .

FEA . . . .

3 ASME . . . .FEA . . . .

4 ASME . . . .FEA . . . .

stress is simulated or various internal pressures. As per

the requirement, the internal pressures selected were MPa,. MPa, . MPa, and MPa, respectively. Figure showscomparison o circumerential membrane stress induced inbellows tangent due to internal pressure o MPa. Similarplots are obtained or various pressures as MPa, . MPa,and . MPa. Comparison o different stresses or variouspressures is explained in Figures –. From Figure , itis seen that the circumerential membrane stress obtainedby both approaches shows considerable variation in inducedstress, but, as per design criterion, this is within acceptableagreement. Tis is an important membrane stress that runscircumerentially around the bellows. For saety, the valuemust be lower than the allowable stress or the bellows

material multiplied by thebellows longitudinal weld joint effi-ciency. Figure shows variation o intermediate convolutioncircumerential membrane stress due to internal pressure.From Figure , it is observed that the intermediate con-

volution circumerential membrane stress obtained by bothapproaches shows very closed match. Tis means that thestresses obtained by both approaches are in good agreement.

From Figure , it is seen that the end convolution cir-cumerential membrane stress obtained by both approachesshows considerable variation as pressure varies rom .MPato MPa, but as per design criterion this is within acceptablelimit. Te end convolution circumerential membrane stress

obtained by both approaches shows much closed match orpressure o MPa. Tis means thatthe stress obtained by bothapproaches is in good agreement.

Figure shows the variation o meridional membranestress due to internal pressure. It is seen that the merid-ional membrane stress obtained by both approaches showsconsiderable variation in induced stresses, but as per designcriterion this is within acceptable limit. From Figure , itis observed that the calculated meridional membrane stressas per ASME standard almost remains constant as pressure

varies rom MPa to MPa, but the simulated meridionalmembrane stress increases signicantly as pressure increasesrom MPa to MPa.


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Y

Z X

Y

Z X

57.676

61.858

56.524

54.689

86.416

80.534

3.5000.000 7.000

(mm)

103.14 max

91.677

80.217

68.758

57.298

45.83834.379

22.919

11.46

2.3322e − 9 min

103.14 max

91.677

80.217

68.758

57.298

45.838

34.379

22.919

11.46

2.3322e − 9 min35.00 70.000.00

(mm)

F : Simulated model o metal expansion bellows or internal pressure o MPa.

C i r c u m

f e r e n t i a

l m e m

b r a n e s t r e s s

( S 1 )

S1 (FEA)S1 (ASME)

0

30

60

90

120

150

180

1.12 1.5 21

Internal pressure (N/mm2)

F : Circumerential membrane stresses in bellows tangent.

S2I (FEA)

S2I (ASME)

1.12 1.5 21


0

10

20

30

40

50

60

I n t e r m e d i a t e c o n v o

l u t i o n

m e m


( S 2 I

)

70

F : Intermediate convolution circumerential membranestress.

Figure shows thevariation o meridional bending stressdue to internal pressure. It is seen that the meridional bend-ing stress obtained by both approaches shows considerable

variation in induced stresses, but as per design criterion this

S2E (FEA)

S2E (ASME)

1.12 1.5 21


0

30

60

90

120

150

E n

d c o n v o

l u t i o n c i r c u m

f e r e n t i a

l

m e m


( S 2 E

)

180

F : End convolution circumerential membrane stress.

S3 (FEA)

S3 (ASME)

1.12 1.5 21


0

10

20

30

40

50

60

70

M

e r i

d i o n a

l m e m


( S 3

)

F : Meridional membrane stress.

is within acceptable limit. From Figure again, it is oundthat the calculated meridional bending stress as per ASMEstandard almost remains constant as pressure varies rom MPa to MPa, but the simulated meridional bending stress


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S4 (FEA)

S4 (ASME)

1.12 1.5 21


0

30

60

90

120

150

180

M e r i

d i o n a

l b e n

d i n g s t r e s s

( S 4

)

F : Meridional bending stress.

53.939 max

47.946

41.953

35.959

29.966

23.973

17.98

11.986

5.9932

5.3846e − 10 min

Y

ZX

7.0003.5000.000

(mm)

29.681

34.558

30.392

33.131

42.36743.83

F : Stress distribution due to internal pressure o MPa.

increases signicantly as pressure increases rom MPa to MPa.

.. Stress Distribution due to Internal Pressure. Te internalpressure varying rom MPa to MPa was applied on con-sidered metal expansion bellows with boundary condition, asno (xed) displacement o the six sides o the bellows. Figures– show stress distribution in the metal expansion bellowsunder consideration or internal pressure o MPa, . MPa,. MPa, and MPa.

6. Conclusions

In this paper, analytical and simulation study or character-istics o U-shaped metallic bellows is conducted. Te resultsobtained as per ASME standards are compared with the FEAor stress distribution. Te design stresses and distributionsare compared or U-shaped bellows. Te main conclusion isthat the most destructive stress in bellows due to internalpressure is meridional bending stress and circumerentialmembrane stress. Te circumerential membrane stress isan important membrane stress that runs circumerentially around the bellows. For bellows unctional saety, this valuemust be lower than the allowable stress.

Notations

: Bellows design allowable stress: Bellows ambient allowable stress: Bellows yield stress: Bellows elastic modulus at design temperature: Bellows elastic modulus at ambient temperature]: Poisson’s Ratioreq: Design cycle lie, required number o cycles: Design internal pressure

: Bellows inside diameter

: Convolution depth: Convolution pitchΔ: Expansion joint opening per convolution: otal number o convolutions: Nominal thickness o one ply : otal number o plies: End tangent length: Fatigue strength reduction actor.Conflict of Interests

Te authors declare that there is no conict o interestsregarding the publication o this paper.


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65.536 max

58.255

50.973

43.691

36.409

21.845

14.564

7.2818

29.127

8.9223e − 12 min

Y

ZX

33.26632.359

32.523

32.124

53.02

31.736

34.444

5.0000.000 10.000

(mm)

F : Stress distribution due to internal pressure o . MPa.

88.23 max

78.427

68.623

58.82

49.017

29.41

19.607

9.8034

39.213

2.9266e − 10 min

YZ

X

4.0000.000 8.000

(mm)

45.168

48.633

45.415

47.488

70.263

61.465

F : Stress distribution due to internal pressure o . MPa.

103.14 max

91.677

80.217

68.758

57.298

34.379

22.919

11.46

45.838

2.3322e − 9 minY

Z X3.5000.000 7.000

(mm)

57.676

61.858

56.524

54.689

86.416

80.534

F : Stress distribution due to internal pressure o MPa.


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Acknowledgment

Authors would like to thank Mr. Umesh Ubarhande, Senior Manager (R& D, PEM) o Ala Laval India Pvt. Ltd., Pune, orhelping them in ormulating the problem and providing thenecessary input and guidance to achieve the objective.

References

[] ASME, “ASME boiler and pressure vessel code-section VIII,division ,” in Appendix —Pressure Vessel and Heat Exchanger Joints, ASME, New York, NY, USA, .

[] EJMA, Standards of Expansion Joint Manufacturers Association,Expansion Joint Manuacturers Association, New York, NY,USA, th edition, .

[] H. Shaikh, G. George, and H. S. Khatak, “Failure analysis o anAM steel bellows,” Engineering Failure Analysis, vol. , no., pp. –, .

[] G. I. Broman, A. P. Jönsson, and M. P. Hermann, “Determiningdynamic characteristics o bellows by manipulated beam nite

elements o commercial sofware,” International Journal of Pressure Vessels and Piping , vol. , no. , pp. –, .

[] . Li, “Effecto theelliptic degreeo Ω-shaped bellows toroid onits stresses,” International Journal of Pressure Vessels and Piping , vol. , no. , pp. –, .

[] C. Becht IV, “Fatigue o bellows, a new design approach,”International Journal of Pressure Vessels and Piping , vol. , no., pp. –, .

[] G. H. Faraji, M. M. Mashhadi, and V. Norouziard, “Evaluationo effective parameters in metal bellows orming process,” Journal of Materials Processing echnology , vol. , no. , pp.–, .

[] G. H. Faraji, M. K. Besharati, M. Mosavi, and H. Kashanizadeh,“Experimental and nite element analysis o parameters inmanuacturing o metal bellows,” Te International Journal of Advanced Manufacturing echnology , vol. , no. -, pp. –, .

[] B. H. Kang, M. Y. Lee, S. M. Shon, and Y. H. Moon, “Forming various shapes o tubular bellows using a single-step hydro-orming process,” Journal of Materials Processing echnology , vol. , no. –, pp. –, .

[] H.-W. Kang, I. H. Lee, andD.-W. Cho, “Developmento a micro-bellows actuator using micro-stereolithography technology,” Microelectronic Engineering , vol. , no. –, pp. –,.

[] V. Jakubauskas and D. S. Weaver, “ransverse natural requen-cies and ow induced vibrations o double bellows expansion

joints,” Journal of Fluids and Structures, vol. , no. , pp. –, .

[] A. K. Jha, V. Diwakar, and K. Sreekumar, “Stress corrosioncracking o stainless steel bellows o satellite launch vehiclepropellant tank assembly,” Engineering Failure Analysis, vol. ,no. , pp. –, .

[] Y. Z. Zhu, H. F. Wang, and Z. F. Sang, “Te effect o environ-mental medium on atigue lie or u-shaped bellows expansion joints,” International Journal of Fatigue, vol. , no. , pp. –,.

[] G. Wang, K. F. Zhang, D. Z. Wu, J. Z. Wang, and Y. D. Yu,“Superplastic orming o bellows expansion joints made o titanium alloys,” Journal of Materials Processing echnology , vol., no. –, pp. –, .

[] S. W. Lee, “Study on the orming parameters o the metalbellows,” Journalof MaterialsProcessing echnology , vol. -,pp. –, .


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Numerical Investigations on Characteristics of Stresses in U Shaped Metal Expansion Bellows.pdf