bolted flanged connection on a basis of …€¦ · effect and inverse flexion flange design ......

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BOLTED FLANGED CONNECTION ON A BASIS OF SHAPE MEMORY EFFECT AND INVERSE FLEXION FLANGE DESIGN Anatoly Efremov Consultant on Mechanical Engineering 9923 Osuna Rd., NE, Albuquerque, NM 87111 USA Email: [email protected] Phone: (505) 301-1448 Bolted Flanged Connection (BFC) includes bolts and gasket with cores manufactured from Shape Memory Alloy (SMA) and shape-memorized in advance to the compression (bolt cores) and “swelling” (gasket core). Temperatures of reverse martensitic phase transformation of the SMA are close to process temperatures of the assembly. The constrained shape recovery of bolt and gasket cores is combined with inverse flexion flange design that constitutes original type of the BFC with feature to inhibit flange rotation and creep of the bolts and gasket under conditions of a variety of operating temperatures and internal pressures relating to critical engineering structures such as reactors, steam generators, heat exchangers, piping systems, and others. Presented type of the BFC reveals significant increase of internal pressure and leak tightness that allow maximizing efficiency of pressure vessels and plant/piping systems used in fossil fuel and nuclear power generation, petroleum refining, petrochemicals, and other process industries. INTRODUCTION Structural integrity and leakage tightness of bolted flanged connections are ones of principal factors to ensure a safe and extended service life of critical engineering structures such as reactors, steam generators, boilers, heat exchangers, piping systems, and others that operate under critical process conditions including internal pressure and a variety of operating temperatures. From structural integrity point of view safe design of the BFCs has been solved and satisfactorily standardized by American Codes [1], but joint leakage events remain an unresolved problem and a main cause of bolts and/or gasket damage and failures [2-5]. Similar situation observes in other countries. The leakage problem is especially important for BFCs used in technological equipment of fossil fuel and nuclear power generation, petrochemicals, petroleum refining, and other process industries. For example, the reports of the US Electric Power Research Institute constantly underline significant concerns at many Nuclear Plants about leakages from BFCs with sheet and spiral-wound gaskets [4, 5]. In fact, the leakages from these connections have resulted in significant boric and corrosion damages of flanges, low alloy steel bolting, pipes and pressure vessel shells used in Pressurized Water Reactor (PWR) Plants. Each year, several PWR Plants experience forced outages to deal with leaks from steam generator primary and secondary manways [4]. Even Boiling Water Reactor (BWR) Plants operating at lower pressures and temperatures than PWR experienced the leakages and forced outages related to the use of non-reliable gasket materials and styles. Utilities with both PWR and BWR Plants continue to express an interest in cost-effective and reliable ways to reduce or exclude leakages from BFCs because, for example, piping systems leakages alone conservatively cost each process industry hundreds of millions of dollars annually in lost profits as a result of plant shutdown,

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Page 1: BOLTED FLANGED CONNECTION ON A BASIS OF …€¦ · EFFECT AND INVERSE FLEXION FLANGE DESIGN ... The pressure vessel has a blind cover 1 and base 2 with flange ... following example

BOLTED FLANGED CONNECTION ON A BASIS OF SHAPE MEMORY

EFFECT AND INVERSE FLEXION FLANGE DESIGN

Anatoly Efremov Consultant on Mechanical Engineering

9923 Osuna Rd., NE, Albuquerque, NM 87111 USA Email: [email protected]

Phone: (505) 301-1448

Bolted Flanged Connection (BFC) includes bolts and gasket with cores

manufactured from Shape Memory Alloy (SMA) and shape-memorized in advance to the compression (bolt cores) and “swelling” (gasket core). Temperatures of reverse martensitic phase transformation of the SMA are close to process temperatures of the assembly. The constrained shape recovery of bolt and gasket cores is combined with inverse flexion flange design that constitutes original type of the BFC with feature to inhibit flange rotation and creep of the bolts and gasket under conditions of a variety of operating temperatures and internal pressures relating to critical engineering structures such as reactors, steam generators, heat exchangers, piping systems, and others.

Presented type of the BFC reveals significant increase of internal pressure and leak tightness that allow maximizing efficiency of pressure vessels and plant/piping systems used in fossil fuel and nuclear power generation, petroleum refining, petrochemicals, and other process industries.

INTRODUCTION

Structural integrity and leakage tightness of bolted flanged connections are ones of principal factors to ensure a safe and extended service life of critical engineering structures such as reactors, steam generators, boilers, heat exchangers, piping systems, and others that operate under critical process conditions including internal pressure and a variety of operating temperatures.

From structural integrity point of view safe design of the BFCs has been solved and satisfactorily standardized by American Codes [1], but joint leakage events remain an unresolved problem and a main cause of bolts and/or gasket damage and failures [2-5]. Similar situation observes in other countries. The leakage problem is especially important for BFCs used in technological equipment of fossil fuel and nuclear power generation, petrochemicals, petroleum refining, and other process industries. For example, the reports of the US Electric Power Research Institute constantly underline significant concerns at many Nuclear Plants about leakages from BFCs with sheet and spiral-wound gaskets [4, 5]. In fact, the leakages from these connections have resulted in significant boric and corrosion damages of flanges, low alloy steel bolting, pipes and pressure vessel shells used in Pressurized Water Reactor (PWR) Plants. Each year, several PWR Plants experience forced outages to deal with leaks from steam generator primary and secondary manways [4]. Even Boiling Water Reactor (BWR) Plants operating at lower pressures and temperatures than PWR experienced the leakages and forced outages related to the use of non-reliable gasket materials and styles. Utilities with both PWR and BWR Plants continue to express an interest in cost-effective and reliable ways to reduce or exclude leakages from BFCs because, for example, piping systems leakages alone conservatively cost each process industry hundreds of millions of dollars annually in lost profits as a result of plant shutdown,

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production penalties, maintenance rework activities, and equipment repair or replacement [6, 7]. The introduction of improved manufacturing processes for spiral-wound gaskets and low-stress spiral-wounds, new gasket materials and styles, and other steps [8] could not essentially change the plant/piping leakage situation, and eliminating or excluding operating leakages remains one of the highest priorities in plant/piping reliability programs and one of the most important users’ problems. Obviously, conventional methods and recommendations based on the use of typical flange designs and “passive” gasket behavior which form the common manufacturers’ production cannot guarantee safe and extended operation of critical plant/piping systems. The conventional way to obtain a durable and leak-tight joint consists in the use of standardized flange designs combined with sophisticated types of gaskets. This approach should ensure a necessary leak tightness and safe extended service life of the BFCs used in critical engineering structures. However, the uncertainties begin during the first stages of the assemblage procedure when poor flange alignment, off-center gasket installation, uneven bolt tightening, non uniform gasket contact stress distribution across the gasket width due to flange rotation [9, 10], and other factors could distort the joint members that creates conditions favorable for early joint opening followed by leakage. The uncertainties continue and increase under critical operating conditions when high and cyclic internal pressures, elevated temperatures, flow-induced vibrations, integral flow of neutrons and chemical influences affect the bolt-flange-gasket system. These conditions are accompanying by creep-relaxation, fatigue, corrosion and embrittelment of bolts, gaskets and other joint members, so that thoroughly balanced connection may be disorganized that opens a way for leakages. The leakage consequences are difficult to estimate, but the fires, explosions, environmental pollution and huge material and financial losses are direct relatives of operating leakages. One of the main causes of leakage events is a “passive” behavior of conventional gaskets under operating conditions when nonlinear gasket response to the loading-unloading process combined with creep-relaxation of bolted fasteners and gaskets leads to load loss and unavoidable joint opening. The presented approach being initially experimentally studied almost two decades ago [11] is an attempt to examine and develop a new type of the BFC capable to eliminate or exclude flange rotation and creep of bolted fasteners and gaskets, and to overcome an inevitability of operating leakages providing extended service life of the BFCs used in critical engineering structures. 1. CONVENTIONAL RAISED FACE BFC

A part of a cross-section of a pressure vessel with conventional raised face BFC is shown in Fig. 1. The pressure vessel has a blind cover 1 and base 2 with flange rings 3 and 4 connected with bolts 5 and nuts 6 elastic gasket 7 being placed between adjacent flange surfaces.

The blind cover 1 is a simple supported and symmetrically loaded circular plate subjected to circularly distributed bolt preload forces F0 (Fig. 1b), and then to internal pressure p along with operating temperature T (Figs. 1a and 1c).

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The schematic bolt-gasket joint diagram [12, 13] is shown in Fig. 2 where axial nut displacement δ is a sum of bolt elongation δb and allowable gasket contraction [δ]g when these displacements are elastic. Internal pressure p causes an axial force P that is equal to:

,gb PPP −= (1) where Pb is the bolt force, and Pg is the gasket clamping force. On the other hand, axial force P is equal to:

),()( gb PPP ∆+∆= (2) where ∆(Pb) is the bolt force increase, and ∆(Pg) is the gasket clamping force decrease.

Action of axial force P leads to bolt elongation increase ∆(δb) and gasket contraction decrease ∆(δg), which are equal one another (See Fig. 2). The creep-relaxation of the bolts and gasket due to prolonged action of constant internal pressure p and elevated temperature T will lead to complete gasket compression loss accompanied by joint opening and leakage. This schematic example shows that creep-relaxation is one of the main causes of plant/piping leakage. For example, the BFC of a pipeline with 150 mm internal diameter operating under temperature T = 5000C and internal pressure

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p = 10 MPa, and having 12 bolts M30 manufactured from chromium molybdenum heat resistant steel can preserve only one third of its initial preload after one year of operation [14]. On the other hand, early leakage may occur under critical axial force Pmax leading to excessive bolt elongation and complete gasket unloading (See Fig. 2). In this case it is additionally necessary to take into consideration the flexibility of the blind cover that will decrease the clamping force on the gasket surface. The generic equation defining assembly deformations may be written as: ,][)( gcb δδδ =+∆ (3) where ∆(δb) is a bolt elongation due to force ∆(Pb) = (Pb – F0), δc is the blind cover deflection in the midpoint of gasket location due to internal pressure p1, and [δ]g is the safe allowable gasket contraction to prevent gasket crushing due to bolt preload. It follows from Fig. 2 that

.)()(

][)()(

0 b

g

g

bbbb P

Pand

FP

∆=∆=∆

δδδδ (4)

Blind cover deflection δc in the midpoint of gasket location may be easily calculated from the maximum deflection W1 of symmetrically loaded and simple supported circular plate [15] subjected to pressure p1 (See Fig. 1c) as: δc = ηW1, (5) where η= (b – c)/b, and

],ln)1(4)37()3(4[(16

)1(3 22213

2

1 dbddbp

EhdW νννν

+−+−+−

= (6)

where h is a cover thickness; ν, E are Poisson’s ratio and Young’s modulus of the cover material. If ν = 0.3, Eq. (3) is then written as:

gbb p

Ehbdcb

FP ][)ln68,003,173,1()()( 22

13

2

0

δβββδ=+−

−+

∆ (7)

where β = d/b. The creep-relaxation of the bolts and gasket due to prolonged action of constant internal pressure p1 and elevated temperature T will change the joint members’ behavior described by Eq. (7). To maintain extended service life of the assembly it will be necessary to reduce significantly internal pressure p1. The described situation will change significantly if the bolts include rigidly fixed internal cores manufactured from shape memory alloy (SMA) having temperature interval of reverse martensitic phase transformation close to operating temperature T of the assembly [16-18]. The operating temperatures of bolted joints used in critical engineering applications vary from cryogenic to high temperatures depending on specific operating conditions. For example, the space facilities such as propellant depots or in-space systems for cryogenic fluids handling and storage operate at cryogenic temperatures. The operating temperatures of the BFCs used in fossil fuel and nuclear power generation, petrochemicals, petroleum refining, and other process industries vary from dozens to hundreds degrees and usually they remain stable for given type of equipment, so that one needs to choose an appropriate SMA for specific technological equipment. The SMAs containing Fe, Cu, Al, Si, Sn, Ga, Mn, Ni, Ti, In, Zr, Hf, Pd, Pt,

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and other elements have a large temperature intervals of reverse martensitic phase transformation [19-22] corresponding to the recovery of previously obtained shape-memorized deformations. The shape-memorized deformations may be obtained in advance during the formation of stress-induced martensite under temperature of martensite state or under temperature higher than temperature of austenite state of the SMA while aging deformed and rigidly fixed work piece having necessary initial shape. The internal bolt cores are shape-memorized in advance to the compression to prevent the bolt elongation due to creep. The schematic bolt-gasket joint diagram during the bolt preload F0 shown in Fig. 3 is similar to the one of conventional BFC (See Fig. 2), but when operating temperature T and internal pressure p are applied, the behavior of the bolts becomes dramatically different from the mechanism described above. The bolt cores will attempt to recover their initial shape with appearance of reactive shape-recovering forces of compression [17] attributed to “negative creep effect”. These forces will block the bolt elongations ∆(δb) due to internal pressure and following creep-relaxation, so that the lengths of “negative creep bolts” remain stable (See Fig. 3).

The reactive shape-recovering forces depend on core size, specific SMA’s properties, magnitude of shape-memorized deformations, rigidity of opposed component parts of the assembly, process temperatures, and other factors. Now, the joint opening will depend on blind cover deflections due to internal pressure p2, and Eq. (3) will be rewritten as:

,][ gc δδ = (8) where δc is defined by Eq. (5) with appropriate value of W2 depending on p2 in accordance with Eq. (6). The ratio p2/p1 is obtained from following example calculation.

It is necessary to note that Eqs. (3) and (8) do not take into consideration an effect of flange rotation, and they can be used to define only approximate internal pressure p1

and p2 corresponding to joint opening. Moreover, real recovery of conventional gasket materials used in conventional types of the BFCs [13] does not surpass (40…50)% of the [δ]g. The opposite situation occurs with the BFC that includes “negative creep bolts” and “negative creep gasket” with cores manufactured from the same SMAs. These gaskets are quite different from conventional ones because the gasket cores are shape-memorized in advance to the “swelling” with possibility to develop high shape-recovering forces during constrained shape recovery, so that the gaskets initially compressed by bolt preload will follow the blind cover deflection during all time of assembly operation under temperature T of reverse martensitic phase transformation. This gasket feature defines its “active” behavior under critical operating conditions including high internal cyclic pressures and temperatures T.

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As an example, a triangular corrugated shape of gasket core manufactured from the SMA with protective envelope is shown in Fig. 4. It is schematic representation of

“negative creep gasket” before installation (See Fig. 4a) and after installation, i.e. in service under conditions of operating internal pressure p and temperature T (See Fig. 4b). The constrained shape recovery of the corrugation deformed by bolt preload generates the reactive shape-recovering stresses σsr that appear between contact surfaces of the flanges and gasket providing multiple tight, automatic and continuous seal due to “negative creep effect”. The original triangular corrugation of the gasket core is obtained in advance during the shape memory

formation under conditions of stress-induced martensite and rigidly fixed core followed by aging at temperature higher than temperature of austenite state of the SMA.

2. NEW TYPE OF BOLTED FLANGED CONNECTION A part of a pressure vessel with new type of the BFC is shown in Fig. 5a. This pressure vessel has a blind cover 1 and base 2 with flange rings 3 and 4 fastened with bolts 5 and nuts 6 elastic gasket 7 being placed between adjacent flange surfaces into hollow space 8. The flange rings 3 and 4 have a rigid contact support 9 that constitutes an inverse flexion flange design [11, 23, 24] excluding conventional flange rotation.

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The bolts 5 have rigidly fixed rectilinear cores 10 manufactured from SMA and shape-memorized in advance to the compression [16-18]. Temperature interval of reverse martensitic phase transformation of the SMA is close to operating temperature of the assembly.

The BFC has two annular joints between the cover 1 and base 2. The first annular joint is a rigid contact support 9 situated on outer end of flange rings 3 and 4. The elastic gasket 7 forms the second annular joint. The reactive shape-recovering forces [17] of the bolt cores due to their “negative creep effect” block the bolt elongations. Now, the joint opening will depend on blind cover deflections due to internal pressure p that is described by Eq. (8).

The blind cover of the assembly is a circular plate subjected to circularly distributed bolt preload forces F0 (See Fig. 5b), and then to internal pressure p and operating temperature T (See Figs. 5a and 5c). The cover having two annular supports becomes a continuous statically indeterminate circular plate (See Figs. 5b and 5c). It may be schematically represented as a plate with rigidly fixed end (See Fig. 5d). Rigidly fixed end of the plate combined with rigidly fixed bolt lengths excludes the flange rotation and constitutes rigidly fixed support (See Fig. 5c), so that Eq. (6) will be rewritten [15] to:

],2

ln75.0)2

[(4

))(1(3 22233

22

3 dbaddbap

bEhdcbW +

−−+−−

=ν (9)

where W3 is a maximum blind cover deflection corresponding to internal pressure p3. If ν = 0.3, Eq. (8) with δc = ηW3 is then written as:

,][)ln68.051.068.0()2

)(( 31

21

2122

3 gbEhbacbdp δβββ

=+−+

− (10)

where β1 = 2d/(a + b). 3. EXAMPLE CALCULATION

a. Raised face conventional type of the BFC. The cover and base of a pressure vessel (See Fig. 1a) are fastened by 24 sets

of bolts and nuts. The size of bolts is M30 with length Lb = 0.3 m. We assume that material of the cover and base is steel for machine structural

use. The bolts are manufactured from heat resistant steel. The Poisson’s ratio ν and Young’s modulus E are equal to ν = 0.3 and E = 2x105 MPa for both cover and bolt materials. E and ν remain unchanged and independent on operating temperature T.

The conventional spiral-wound asbestos filled gasket with 16 mm width, 4.6 mm thickness, 1200 MPa/mm average stiffness and maximum seating stress σmax = 180 MPa [13] has approximate value of allowable gasket contraction [δ[g = 0.15 mm = 15x10-5 m. Using Eq. (7) we compute the deformations of the joint members taking into consideration the following dimensions of the assembly that are among the most troublesome constructions such as heat exchangers (See Fig. 1a): a = 0.45 m, b = 0.4 m, c = 0.358 m, d = 0.35 m, and h = 0.08 m. Seating gasket clamping force ΣF0 is equal to: ΣF0 = σmaxAg, where σmax = 180 MPa = 180x106 N/m2 is a gasket maximum seating stress, Ag is a full gasket contact area that is equal to Ag = 0.016x3.14x2x0.358 = 0.036 (m2). The gasket clamping force is: ΣF0 = 180x106x0.036 = 6.48x106 (N).

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The bolt preload force F0 is equal to F0 = ΣF0/Z, where Z is a number of bolts, i.e. F0 = 6.48x106/24 = 270000 (N). Bolt elongation due to bolt preload force is equal to:

,0

b

bb EA

LF=δ

where Ab is a cross sectional area of the bolt with diameter Db = 0.03 m, i.e. Ab = πDb

2/4, and δb = 270000x0.3x4/2x1011x3.14x9x10-4 = 57x10-5 (m). Taking into consideration the Eqs. (2) and (4) we compute:

),(8.31015

)(1057][

)()( 5

5

bb

g

bbg P

xPxPP ∆=

∆=

∆=∆ −

δδ

and P = ∆(Pg) + ∆(Pb) = 3.8 ∆(Pb) + ∆(Pb) = 4.8 ∆(Pb), where axial force P is equal to:

,2

1

ZdpP π

=

and then bolt elongation force increase is :

).(248.4

)35.0(14.38.48.4

)(2

1

21 N

xp

ZdpPPb ===∆π

Using Eq. (4) we can calculate bolt elongation increase as:

).(1007.0270000248.4

1057)35.0(14.3)()(3

110

52

10 N

mpxxx

xpFP bb

b−

==∆

=∆δδ

We obtain from Eq. (7):

,][})08.0(102

)]4.0/35.0ln()4.0/35.0(68.0)4.0/35.0(03.173.1[()35.0(4.0)358.04.0(1007.0{ 311

22210

1 gxxxp δ=

+−−+−

or (0.07 + 0.175)10-10p1 (m3/N) = 15x10-5 (m),

and internal pressure corresponding to joint opening will be: p1 = 15x10-5/0.245x10-10 N/m2 = 6.12x106 N/m2 = 6.12 MPa (11) If the BFC includes “negative creep bolts” and conventional spiral-wound gasket described above, then internal pressure p2 corresponding to joint opening will be calculated with Eq. (8) as: p2 = 15x10-5/o.175x10-10 = 8.75x106 (N/m2) = 8.57 MPa. (12) Internal pressure corresponding to joint opening will be increased as much as: (p2 – p1)x100% / p1 = (8.57 – 6.12)x100% / 6.12 = 40%. It was noted above that this example calculation does not take into account the flange rotation.

b. New type of the BFC showing in Fig. 5a has the same dimensions and characteristics except the bolt and flange designs. The BFC has an inverse flexion flanges with bolts manufactured from heat resistant structural steel, but bolts have an internal hollow channels adapted to place and fix firmly rectilinear rods manufactured from SMA. This novel type of the BFC excludes the flange rotation due to internal pressure, and to maintain similar load conditions the bolt size is slightly increased for about Db = 0.033 m.

The rods are shape-memorized in advance to the compression, and temperatures of reverse martensitic phase transformation of the SMA are close to operating temperatures of the assembly, so that reactive shape-recovering forces having

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direction inverse to the direction of internal pressure p will block the bolt elongations (See Fig. 3). Interaction of reactive shape-recovering forces with rigid contact end of the cover constitutes rigidly fixed support, and using Eq. (10) we obtain:

,][]}4.045.0

35.02ln)4.045.0

35.02(68.0)4.045.0

35.02(51.068.0[)35.0()2

4.045.0)(358.04.0{()08.0(1024.0

2222311

3g

xxxxxp

δ=++

++

−+

or 0.0568x10-10p3 (m3/N) = 15x10-5 (m), and p3 = 15x10-5/0.0568x10-10 N/m2 = 26.4106 N/m2 = 26.4 MPa. (13) Obviously, the results presented by (12) and (13) relate to ideal situation when the bolt elongations are completely blocked, and internal pressure increase leads only to the blind cover deflection. Besides, the gaskets used in both cases are the same. In reality it is needed to take into consideration real behavior of the bolt cores from SMA. For example, if operating temperature is equal to T = 5250C it is necessary to introduce an appropriate rods from SMA having similar temperature of reverse martensitic phase transformation. Thermal investigation of flange, gasket and bolt temperatures [25] indicate that gasket and bolt materials can expect to see slightly lower temperatures, (15…20)0C lower than operating temperatures. The Ti50Ni5Pd45 SMA [26] has the following characteristics:

- Temperatures of direct martensitic phase transformation are Ms = 4860C (start) and Mf = 4670C (finish).

- Temperatures of reverse martensitic phase transformation are As = 5030C (start) and Af = 5090C (finish).

- The Young’s modules are Em = 4.5x104 MPa (martensite) and Ea = 5x104 MPa (austenite).

We additionally assume that initial temperature of the assembly is T0 = 200C, shape memorized deformation of the rod from SMA (recovered strain) is εr = 3% = 3x10-2, and coefficient of thermal expansion is α = 6x10-6 1/0C. The reactive shape-recovering forces due to constrained shape recovery of the rod from SMA are calculated with following equation [17]:

)],(ln)[()( 20

01

0

00 TAk

TkAkk

AkRTkTR s

s

s

−+++

++

+= (14)

where As < T < Af is a temperature interval of reverse martensitic phase transformation of the SMA,

,)(;;; 0002010 αTASERSackSabkcbk smEEE

E −====

and

,;; 0sf

r

fs

maE

as

afmsE AA

aMMEEc

MMEMEM

b−

−=−−

=−

−=

ε

where S = πDr2/4 is a cross-sectional area of the rod from SMA with diameter Dr.

If Dr = 10 mm the parameters above will be: a0 = -3x10-2/(509 - 503) = -5x10-3 (1/0C); bE = (486x4.5 – 467x5)104/(486 – 467) = -7.8x104 (MPa); cE = (5 – 4.5)104/(486 – 467) = 0.026x104 (MPa/0C); k0 = -7.8x104/0.026x104 = -300(0C); S = 3.14(0.01)2/4 = 785x10-7 (m2);

Page 10: BOLTED FLANGED CONNECTION ON A BASIS OF …€¦ · EFFECT AND INVERSE FLEXION FLANGE DESIGN ... The pressure vessel has a blind cover 1 and base 2 with flange ... following example

k1 = -7.8x1010(-5x10-3)785x10-7 = 30615 (N/0C); k2 = 0.026x1010(-5x10-3)785x10-7 = -102 [(N/0C)2]; R0 = 4.5x1010x78510-7(503 – 20)6x10-6 = 10237 (N). For temperature T = 5070C the reactive shape-recovering forces will be:

).(31878)]507503)(102(507300503300ln30615

50330010237)[507300()507( NR −=−−+

+−+−

++−

+−=

For temperature T = 5090C (reverse martensitic transformation is finished) we obtain:

).(47234)]509503)(102(509300503300ln30615

50330010237)[509300()509( NR −=−−+

+−+−

++−

+−=

The 24 sets of bolts with cores manufactured from Ti50Ni5Pd45 SMA can produce an additional bolt force of compression F = 47234x24 = 1133616 (N) due “negative creep effect” of the bolt cores, and to compensate this additional force it is necessary to apply internal pressure for about: ∆p = F/πd2 = 1133616/3,14(0.35)2 = 2947136 (N/m2), i.e. ∆p = 2.95 MPa. This pressure will be maintained all time of operation with simultaneous inhibition of flange rotation and creep relaxation of the bolts. With this internal pressure the deflection δc of the blind cover will be calculated similarly to (13) as: δc = 0.0568x2.95x106 x10-10 = 1.67x10-5 (m). The deflection δc of the blind cover of conventional raised face flanges (conditionally in absence of flange rotation) determined by (11) is: δc = 0.245x2.95x106x10-10 = 7.23x10-5 (m). The conventional spiral-wound asbestos filled gasket cited above has approximate value of allowable gasket contraction [δ]g = 15x10-5 m, but real recovery of gasket material reduces this value for about (40…50)%, that is to say that conventional BFC with raised face flanges can begin to leak under internal pressure ∆p = 2.95 MPa. This is just the point when new type of the BFC might be actively involved into loading process that is characterized by bolt elongation and further blind cover flexion. This process is described by Eq. (3) where δc = 1.67x10-5 (m) + 0.0568x10-10 p4 (m3/N). Due to static indeterminacy of the blind cover with given size (See Fig. 5) the gasket clamping force will be about 60% of total bolt force in comparison with statically determinate blind cover (See Fig. 1), that is to say that the bolt preload force has to be increased to maintain similar gasket loading conditions, i.e.: F0 =270000/0.6 = 450000 (N). Bolt elongation due to bolt preload is equal to:

),(1093.86])01.0()033.0[(10214.3

3.04500004)(

4 5221122

0 mxxx

xxDDE

LF

rb

bb

−=−

=−

δ

Using Eqs. (2) and (4) we compute:

),(8.51015

)(1093.86][

)()( 5

5

bb

g

bbg P

xPxPP ∆=

∆=

∆=∆ −

δδ and

P = ∆(Pg) + ∆(Pb) = 5.8∆(Pb) + ∆(Pb) = 6.8∆(Pb). Now, the bolt elongation will be:

).(10045.0244500008.6

1093.86)35.0(14.38.68.6

)()(

3

410

52

40

2

400 N

mpxxxxxp

ZFd

pF

PFP bbbb

b−

====∆

=∆δπδδ

δ

Finally we obtain from Eq. (3): p4(0.045 + 0.0568)10-10 (m3/N) + 1.67x10-5 (m) = 15x10-5 (m)’ p4 = 13.13x106 N/m2 = 13.13 MPa.

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Real total internal pressure for new type of the BFC will be: pt = ∆p + p4 = 2.95MPa + 13.13 MPa = 16.08 MPa. It was noted above that new type of the BFC includes “negative creep gasket”

with cores manufactured from the SMAs. This gasket has a very small initial stiffness, and for this reason the clamping force and bolt preload force will be decreased significantly but reactive shape-recovering forces due to “ negative creep effect” of the gasket core will ensure automatic, continuous and leak-tight contact between flange and gasket surfaces during all time of assembly operation. This “active” behavior of the gasket is quite different from conventional “passive” one [9, 10]. So, the allowable gasket contraction and internal pressure can be further increased specifically for critical BFC engineering applications.

CONCLUSION

Presented novel type of the BFC reveals significant increase of operating internal pressure in comparison with conventional raised face flanges and gaskets. The combination of the “negative creep effect” of the bolt and gasket cores with inverse flexion flange design excludes the flange rotation and creates continuous and leak-tight joint that can maximize process efficiency and extend the safe service life of critical engineering structures.

Application of advanced shape-memory materials with feature of “negative creep effect” should be considered as a new sealing philosophy based on “active” intervention of bolted fasteners and gaskets into critical processes.

REFERENCES

1. ASME Boiler and Pressure Vessel Code, Section VIII, American Society of

Mechanical Engineers, New York, 2004. 2. Merrick, E., and Marston, T., “Industry Response to the Issue of Bolting

Degradation and Failure in U.S. Commercial Nuclear Power Plants”, Transaction of the 8th International Conference on Structural Mechanics in Reactor Technology, Amsterdam, 1985, Vol. C, D, pp.397-402.

3. Anderson, W., ”Recent Bolting Degradation Experience in Primary Coolant System Components of PWR Plants”, Transaction of the 8th International Conference on Structural Mechanics in Reactor Technology, Amsterdam, 1985, Vol. C, D, pp.403-408.

4. Assembling Bolted Connections Using Spiral-Wound Gaskets: Sealing Technology and Plant Leakage Reduction Series, Electric Power Research Institute, Palo Alto, 1999, Report TR-111472, 240 p.

5. Assembling Bolted Connections Using Sheet Gaskets: Sealing Technology and Plant Leakage Reduction Series, Electric Power Research Institute, Palo Alto, 2001,Report 1000922.

6. Proceedings of the 1st International Conference on Sealing Technology and Plant Leakage Reduction, Electric Power Research Institute, Palo Alto, 1999, Report TR-113859.

7. EPRI’s Plant Leak Reduction Program: EPRI’s Fluid Sealing Technology Program, Electric Power Research Institute, Palo Alto, 2000, Report 1001198.

8. Semi-metallic Gasket Performance: Sealing Technology and Plant Leak Reduction Series, Electric Power Research Institute, Palo Alto, 2003, Report 1009213.

9. Bouzid, A.-H., and Derenne, M., “Analytical Modeling of the Contact Stress with Nonlinear Gaskets”, ASME J. Pressure Vessel Technology, 2004, Vol. 124, pp. 47-53.

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10. Bouzid, A., and Champliaud, H., “Contact Stress Evaluation of Nonlinear Gaskets Using Dual Kriging Interpolation”, ASME J. Pressure Vessel Technology, 2004, Vol. 126, pp. 445-450.

11. Efremov, A.I., “Evaluation of the Strength and Leak Tightness of Bolted Flanged Connection with Inversely Deformed Flanges”, Strength and Stability of Real Solids and Engineering Structures, Transaction of Kyrgyz Academy of Sciences, Frunze, ILIM, 1991, pp. 62-66 (in Russian).

12. Birguer, I. A., Shorr, B. F., and Yosilevich, G. B., “Calculation of the Strength of Machine Components”, MASHINOSTROENIE (Mechanical Engineering), Moscow, 1979, 702 p. (in Russian).

13. John H. Bickford, “An Introduction to the Design and Behavior of Bolted Joints”, Marcel Dekker, Inc., New York, 1995, 951 p.

14. Mechanical Engineering Reference Book, MASHGUIZ, Moscow, 1962, Vol. 3, 651 p. (in Russian).

15. Ansel C. Ugural, “Stresses in Plates and Shells”, New Jersey Institute of Technology, McGraw Hill: WCB, 1999, 400 p.

16. Efremov, A. I., “Plant Leakage Reduction Trough Creep Limitation of Gasketed Joints”, Proceedings of the 11th Nuclear Plant Performance Improvement Seminar, Austin, 2004 (CD-Rom).

17. Efremov A. I., “Creep Limitation of Bolted Fasteners and Gaskets”, Design and Analysis, Proceedings of the ASME Pressure Vessel and Piping Conference, Denver, 2005 (CD-Rom).

18. Efremov, A., “Method and Devices to Limit a Creep of Mechanical Fasteners”, The US Patent Application No.2005244245, 2005.

19. Shimizu, K., and Tadaki, T., “Shape Memory Alloys”, H. Funakubo, Ed., Gordon and Breach Science Publishers, New York, 1987, 275 p.

20. Firstov, G. S., Humbeeck, J. V., and Koval, Y. N., “High-temperature Shape Memory Alloys: Some Recent Developments”, Material Science and Engineering: A, 2004, 378, pp. 2-10.

21. Recarte, V., Perez-Landazabal, J. I., Rodriguez, P.P., Bocanegra, E. H., No, M. I., and San Juan, J., “Thermodynamics of Thermally Induced Martensitic Transformations in Cu-Al-Ni Shape Memory Alloys”, Acta Materiala, 1999, 52, pp. 3941-3948.

22. Segui, C., Pons, J., Cesari, E., Muntaselli, J., and Font, J., “Characterization of a Hot-rolled Cu-Al-Ni-Ti Shape Memory Alloy”, Materials Science and Engineering: A, 1999, 273-275, pp. 625-629.

23. Efremov, A., “Life Extension of Bolted Flanged Connection from a Design Peculiarity’s Point of View”, Proceedings of the ASME/JSME Pressure Vessel and Piping Conference, 2004, 471, pp. 67-69.

24. Efremov, A., “Flange Design Conception: Flanges of Inverse Flexion”, The US Patent Application No. 20060017233, 2006.

25. Brown, N., Derenne, M., and Bouzid, A.-H., “Determination of the Steady State Operating Temperature of Pressure Vessel Flange Components: Part 2 – Simplified Methods”, ASME Pressure Vessel and Piping Conference, 2000, 405, pp. 105-113.

26. Lindquist, P. G., and Wayman, C. M., “Shape Memory and Transformation Behavior of Martensitic Ti-Pd-Ni and Ti-Pt-Ni Alloys”, Engineering Aspects of Shape Memory Alloys, Butterworth-Heinemann, 1990, pp. 58-68.

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