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Toshimichi Fukuoka
Professor
e-mail: fukuoka@cc.kshosen.ac.jp
Tomohiro Takaki
Research Associate
e-mail: takaki@cc.kshosen.ac.jp
Department of Ocean Electro-Mechanical
Engineering,
Kobe University of Mercantile Marine,
5-1-1, Fukaeminami, Higashinada, Kobe, Japan
Finite Element Simulation of
Bolt-Up Process of Pipe Flange
Connections With Spiral Wound
Gasket
It is well known that a large amount of scatter in bolt preloads is observed when bolting
up a pipe flange connection, especially in the case of using a spiral wound gasket. In this
study, a numerical approach is proposed, which can simulate the bolt-up process of a pipe
flange connection with a spiral wound gasket inserted. The numerical approach is de-
signed so as to predict the scatter in bolt preloads and achieve uniform bolt preloads at
the completion of pipe flange assembly. To attain the foregoing purposes, the stress-strain
relationship of a spiral wound gasket, which shows highly nonlinear behavior, is identified
with a sixth-degree polynomial during loading and with an exponential equation during
unloading and reloading. Numerical analyses are conducted by three-dimensional FEM,
in which a gasket is modeled as groups of nonlinear one-dimensional elements.
关DOI: 10.1115/1.1613304兴
1 Introduction
Pipe flange connections are usually tightened with a number of
bolts. It is well known that achieving uniform bolt preloads in a
one-pass tightening operation is almost impossible. The primary
reason causing such a scatter in bolt preloads is ‘‘elastic interac-
tion’’ due to flange deformation occurring in the process of suc-
cessive bolt tightening 关1兴. However, most of the previous re-
search on pipe flange connections have dealt with the mechanical
behavior or the sealing performance 关2–10兴. There are few papers
studying the mechanics of the tightening process of pipe flange
connections and aiming at the establishment of a desirable tight-
ening procedure.
Elastic interaction occurring in the tightening process of a pipe
flange connection is significantly affected by the stiffness of each
component of the pipe flange connection, i.e., bolt-nut connec-
tions, flanges and a gasket. It is commonly recognized that gasket
stiffness has dominant effects because of its relatively low stiff-
ness. In the previous study, two types of numerical methods were
proposed 关11兴. One is to estimate the scatter in bolt preloads at the
completion of pipe flange assembly and the other is to achieve
uniform bolt preloads in the final state. In each case, a solid-metal
gasket is employed and bolts are tightened one by one.
In the meantime, spiral wound gaskets are more widely used
and have lower stiffness than solid-metal gaskets. In addition, the
stress-strain relationships exhibit high nonlinearity. Hence, the
scatter of bolt preloads caused by a spiral wound gasket is much
larger than by a solid-metal gasket. In actual practice, the process
of tightening each bolt one by one is usually repeated several
times to get uniform bolt preloads.
Bibel and Ezell have systematically conducted bolt-up tests of
pipe flange connections to investigate the elastic interaction 关12兴.
Using the mutual relationships experimentally determined among
the stiffness variation of each portion caused by successive bolt
tightening, they proposed a procedure to achieve uniform bolt
preloads in the final state 关13兴. From the practical point of view, it
is important to establish a numerical method, which can simulate
the bolt-up process in order to provide an effective tightening
guideline, since pipe flange connections are available in a wide
variety of shapes, sizes and materials. Weber and Bibel attempted
to compute the magnitudes of initial bolt preloads needed to attain
the uniform bolt preloads by FEM, for the case of the objective
pipe flange being tightened with a spiral wound gasket 关14兴.It
seems, however, that their numerical method does not necessarily
give satisfactory results, since numerical analyses are conducted
as linear elastic problems ignoring nonlinear behavior due to the
stress-strain relationships of a spiral wound gasket and the contact
conditions at the interface.
In this study, the stress-strain relationships of a spiral wound
gasket are initially identified in terms of two equations. A spiral
wound gasket has very low stiffness in the direction of compres-
sion. Since such a low stiffness significantly affects the tightening
characteristics of pipe flange connections, the objective gasket is
modeled as groups of nonlinear one-dimensional elements. Then,
a special computer code is developed to solve the following two
types of problems.
Problem 1. What magnitude of bolt preloads is retained in
the final state, when tightening bolts one by one with target bolt
preloads in an arbitrary order?
Problem 2. What magnitude of initial bolt preloads is needed
for achieving uniform bolt preloads in the final state?
Commonly used pipe flange connections are chosen as the sub-
ject of numerical calculations in order to show how the foregoing
problems are solved. Further, a guideline of pipe flange assembly
to be proposed by ASME 关15兴 is evaluated from the practical
point of view, by use of the numerical method presented here.
The validity of the numerical method proposed in this study is
substantiated by experiments, where the scatter in bolt preloads at
the completion of the tightening operation is compared between
numerical and experimental results. Further, it is examined to
what extent the initial bolt preloads obtained numerically could
achieve the uniform preloads in the final state.
2 Numerical Analysis
2.1 Incremental Method. Nonlinearity in numerical calcu-
lations arise from the material properties of the gasket and the
contact conditions involved. In this analysis, such a nonlinear
problem is replaced with a linear problem by using so-called in-
Contributed by the Pressure Vessels and Piping Division for publication in the
J
OURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received by the PVP
Division September 11, 2001; revision received April 4, 2003. Associate Editor: D.
R. Metzger.
Copyright © 2003 by ASMEJournal of Pressure Vessel Technology NOVEMBER 2003, Vol. 125 Õ 371
cremental method. The incremental rate in each step is determined
as the minimum value satisfying each of the following conditions:
1. Retaining the present contact conditions.
2. Gasket stress during the reloading process is not in excess of
the yield stress determined when the unloading started.
3. Increments of stress and strain do not exceed prescribed
values.
2.2 One-Dimensional Gasket Element. Spiral wound gas-
kets are manufactured by winding a preformed V-shaped metal
strip and a soft non-metallic filler together under pressure. As
shown in Fig. 1, a spiral wound gasket has a complicated con-
struction. The objective gaskets used here are reinforced with in-
ner and outer rings 共No. 596V, Nippon Valqua Co.兲, and the di-
mensions concerned are specified in JIS B 2404. The filler is made
of special asbestos fiber, and the metal strip and inner and outer
rings are made of stainless steel. Gasket stiffness in the thickness
direction is determined by conducting a compression test.
The stress-strain relationship of the objective gasket thus ob-
tained experimentally is plotted with the symbol ‘‘⫹’’ in Fig. 2.
Compression tests are executed under a mean strain rate of 0.001/
sec, and loading and unloading operations are repeated up to the
maximum strain of 0.3 with a strain increment of 0.03. By con-
sidering that the mechanical behavior of pipe flange connections
is largely influenced by the gasket stiffness, especially in the
thickness direction, a spiral wound gasket is modeled as groups of
one-dimensional nonlinear elements and those elements are incor-
porated into a three-dimensional finite element analysis. As shown
in Fig. 2, a hysteresis loop is formed between unloading and re-
loading curves. In the actual analyses, each reloading curve is
assumed to be identical with the unloading one for simplifying the
numerical calculations. The resulting stress-strain relationships are
identified as follows:
Loading.
⫽ 65.2•⫹ 27.3⫻ 10
2
•
2
⫺ 17.4⫻ 10
3
•
3
⫹ 32.1⫻ 10
4
•
4
⫺ 17.5⫻ 10
5
•
5
⫹ 28.8⫻ 10
5
•
6
¯ (1)
Unloading and Reloading.
⫽
␣
exp
共

兲
⫹
␥
¯ (2)
␣
⫽
y
exp
共

y
兲
⫺ exp
共

r
兲

⫽ 103.3• exp
共
⫺ 9.9•
y
兲
⫹ 63.6
␥
⫽⫺
␣
exp
共

r
兲
where
and
y
are in MPa.
y
and
y
represent the magnitudes
of strain and stress on the loading curve when unloading starts.
r
represents the residual strain when perfect unloading occurs from
the point (
y
,
y
), which can be approximated Eq. 共3兲.
r
⫽ 1.25•
y
2
⫹ 0.47•
y
¯ (3)
Identified values using the above equations are indicated by solid
lines in Fig. 2, which agree well with the measured ones.
2.3 Contact Problem. A numerical method to solve general
multi-body contact problems proposed in the previous paper 关16兴
is extended to analyze the bolt-up process of pipe flange connec-
tions as a three-dimensional contact problem. On the bearing sur-
face of bolt head, only two types of contact conditions such as
‘‘separation’’ and ‘‘stick’’ are treated, because it has been con-
firmed in preliminary calculations that the effects of friction coef-
ficients concerned are trivial. Contact conditions on the gasket
bearing surface are also judged in terms of ‘‘separation’’ and
‘‘stick’’ using the one-dimensional gasket element defined in the
previous section.
2.4 Global Stiffness Equation. A set of bolt-nut connec-
tions is treated as one elastic body without contact surface for
better computation efficiency. In addition, by regarding the whole
bolt-nut connections as one body, the objective pipe flange con-
nection can be reduced to a numerical model consisting of three
elastic bodies, i.e., the foregoing clustered bolt-nut connections,
flange and a gasket. The three bodies form two contact surfaces
such as the bearing surface of the bolt head and gasket bearing
surface. Thus, the global stiffness equation to be solved is as
follows:
冋
K
e
00K
eC1
0
0 K
f
0 K
fC1
K
fC2
00K
g
0 K
gC2
K
C1e
K
C1f
0 K
C1
0
0 K
C2 f
K
C2g
0 K
C2
册
冦
⌬u
e
⌬u
f
⌬u
g
⌬R
1
⌬R
2
冧
⫽
冦
⌬Q
e
⌬Q
f
⌬Q
g
␦
1
␦
2
冧
¯
(4)
Fig. 1 Configuration of spiral wound gasket
Fig. 2 Stress-strain relationship of spiral wound gasket
372 Õ Vol. 125, NOVEMBER 2003 Transactions of the ASME
where
关
K
e
兴
,
关
K
f
兴
, and
关
K
g
兴
are stiffness matrices for clustered
bolt-nut connections, flange and a gasket.
关
K
g
兴
is a diagonal ma-
trix in which each entry k
gi
represents the stiffness of a one-
dimensional gasket element. The global stiffness matrix is not
symmetric as shown in Eq. 共4兲.
关
K
g
兴
⫽
冋
k
g1
00 0
0 k
g2
00
00k
g3
0
000 k
gm
册
¯ (5)
In Eq. 共5兲, k
gi
is calculated as the product of the gradient of the
stress-strain curve, shown in Fig. 2, and the area relating to each
contact node on the gasket bearing surface, and m is the total
number of one-dimensional gaskets. Other matrices in Eq. 共4兲,
such as
关
K
C1e
兴
,
关
K
C2 f
兴
etc., are associated with contact condi-
tions. ⌬u
e
and ⌬Q
e
are increments of nodal displacement and
nodal force, respectively.
␦
i
and ⌬R
i
designate initial discrepancy
and increment of equivalent contact force at each contact surface,
where subscript i is used for identifying each contact surface, i.e.,
‘‘1’’ for the bearing surface of bolt head and ‘‘2’’ for the gasket
bearing surface. Hence, initial discrepancy represents a gap size or
depth of penetration at the mating surfaces.
Since the components of
关
K
e
兴
,
关
K
f
兴
, and other matrices located
in the lower half-triangle of Eq. 共4兲, such as
关
K
C1e
兴
,
关
K
C2 f
兴
etc.,
are kept constant during incremental calculations, these matrices
need to be decomposed only once at the first incremental calcula-
tion. Consequently, the numerical calculations can be conducted
with high computation efficiency.
2.5 Numerical Model. The numerical model treated here is
an integral pipe flange specified in JIS B 2238 with a nominal
diameter of 50 mm used under a nominal pressure of 40 K 共4
MPa兲. Figure 3 shows the corresponding finite element model.
Isoparametric eight-node brick elements are used here. For better
computation efficiency, one-half of the pipe flange connection is
modeled because of geometric symmetry. Finely meshed areas
represent the gasket bearing surface. The objective pipe flange
connection is tightened by eight bolts with metric coarse thread of
M16. Young’s modulus and Poisson’s ratio of flange, bolt and nut
materials are 200 GPa and 0.3, respectively.
2.6 Numerical Procedures. Bolt preloads are produced by
applying appropriate amounts of longitudinal displacement to the
symmetrical cross section of the bolt body shown in Fig. 3. Figure
4 illustrates the bolt number identified by the bolt-up sequence,
where bolts are tightened in accordance with a typical star pattern.
In the following, it is shown in detail how Problems 1 and 2 can
be solved by FEM. For simplicity, a flange connection tightened
with three bolts is used to explain the procedure.
Problem 1: Estimation of Scatter in Bolt Preloads. Figure 5
schematically shows the numerical procedure for Problem 1. In
each step, the objective bolt is tightened with the same magnitude
of preload F, though the applied longitudinal displacement u
j
is
different for each bolt.
Tightening bolt 1. A certain amount of displacement incre-
ment is applied in the longitudinal direction to the symmetrical
surface of bolt 1, and incremental calculations are repeated until
the prescribed value of bolt preload F is obtained. While tighten-
ing bolt 1, the displacements on the symmetrical surface of the
Fig. 3 Finite element model
Fig. 4 Bolt number corresponding to the bolt-up sequence
Journal of Pressure Vessel Technology NOVEMBER 2003, Vol. 125 Õ 373
other bolts are constrained in the longitudinal direction. u
1
desig-
nates the magnitude of applied displacement to generate the pre-
scribed bolt preload in bolt 1.
Tightening bolt 2. Next, an arbitrary amount of displacement
increment is applied to bolt 2, while the magnitude of u
1
deter-
mined in the previous step is kept unchanged. The longitudinal
displacements of the other bolts are constrained as well. u
2
is the
displacement determined following the same manner to bolt 1 for
generating the prescribed bolt preload F.
Tightening bolt 3. Finally, u
3
is calculated in the same man-
ner. At this point, the scatter in bolt preloads in the final state is
completely determined. F
31
, F
32
, and F
33
, shown in Fig. 5, rep-
resent the resulting bolt preloads thus obtained.
Problem 2: Aiming at Uniform Bolt Preloads. Figure 6 illus-
trates the numerical procedure for Problem 2. Unlike Problem 1,
the amounts of longitudinal displacement u
j
applied in each step
are identical. Then, the magnitudes of bolt preloads generated in
each bolt are different. They achieve the uniform bolt preloads in
the final state, as shown in the bottom most picture of Fig. 6.
Preliminary calculation. An arbitrary amount of longitudinal
displacement is applied to all bolts equally and simultaneously in
order to determine the magnitude of displacement u for creating
the target preload F.
Tightening bolt 1. First, a certain amount of displacement in-
crement is applied in the longitudinal direction to the symmetrical
surface of bolt 1, and incremental calculations are repeated until
the longitudinal displacement on the surface reaches u. While
tightening bolt 1, the displacements on the symmetrical surface of
the other bolts are constrained in the longitudinal direction. The
resulting value, F
11
, represents the initial preload to be applied to
bolt 1 for achieving the uniform bolt preloads in the final state.
Tightening bolt 2. Next, an arbitrary amount of displacement
increment is applied to bolt 2, while the magnitude of u
1
deter-
mined in the previous step is kept unchanged and the longitudinal
displacements of the other bolts are constrained as well. Incre-
mental calculations are repeated until the longitudinal displace-
ment on the symmetrical surface of bolt 2 reaches u. The resulting
value, F
22
, represents the initial bolt preload to be applied to
bolt 2.
Tightening bolt 3. Finally, the same procedure is repeated for
tightening bolt 3. It is therefore evident that unlike Problem 1, the
amount of initial preload necessary for each bolt is successively
determined in each step.
For a pipe flange connection clamped with eight bolts, Tables 1
and 2 give the magnitudes of longitudinal displacements to be
Fig. 5 Numerical procedure for Problem 1
Fig. 6 Numerical procedure for Problem 2
Table 1 Longitudinal displacements applied to the symmetri-
cal cross section of bolt body „Problem 1…
Bolt Number j
12345678
Bolt-Up Sequence k 1u
1
0000000
2u
1
u
2
000000
3u
1
u
2
u
3
00000
4u
1
u
2
u
3
u
4
0000
5u
1
u
2
u
3
u
4
u
5
000
6u
1
u
2
u
3
u
4
u
5
u
6
00
7u
1
u
2
u
3
u
4
u
5
u
6
u
7
0
8u
1
u
2
u
3
u
4
u
5
u
6
u
7
u
8
374 Õ Vol. 125, NOVEMBER 2003 Transactions of the ASME
applied to each bolt in each step necessary for analyzing Problems
1 and 2, respectively. It should be emphasized here that, in Prob-
lem 1, the preload scatter at the end of bolt-up operation is deter-
mined when the tightening of bolt 8 is completed. On the other
hand, in Problem 2, the initial preload of each bolt needed for
attaining uniform bolt preloads is determined successively at each
tightening process. The computer program developed here can
conduct the foregoing calculations automatically without any help
of the analyst.
3 Experimental Procedures
To confirm the validity of the numerical analyses proposed
here, variations of bolt stress during the bolt-up process are mea-
sured. The objective pipe flange is the same as that for the nu-
merical analyses. Eight bolts with metric coarse thread of M16 are
employed. The tightening sequence is shown in Fig. 4. Experi-
ments are conducted at room temperature. Two spanners are used
in the actual operation, one is for applying the torque to the nut,
and the other is to restrain the bolt head rotation. In order to avoid
a large amount of ‘‘open up’’ deformation at the flange interface,
which leads to a significant scatter in bolt preloads, all the bolts
are tightened ‘‘finger tight’’ a priori. The increase from this initial
state is regarded as the bolt stress. Two sheets of strain gages are
mounted to measure the bolt stress, each placed 180 degrees apart.
4 Estimation of Scatter in Bolt Preloads „Problem 1…
4.1 Variations in Bolt Stress. Table 3 shows how the bolt
stress of bolt j varies in the process of successive bolt tightening,
which corresponds to the tightening sequence shown in Table 1.
The figures in Table 3 are normalized values divided by the initial
bolt stress
i
.
i
is set to be 50 MPa here. The diagonal compo-
nents are found to be unity as a necessary consequence. The com-
ponents in the upper half-triangle are zero, except for the stress
value of bolt 2 when tightening bolt 1. The values in the 8th row
are particularly important. They represent the magnitudes of the
final bolt stress
f
which remain in each bolt at the end of the
bolt-up operation.
The scatter in final bolt preloads so obtained is shown in Fig. 7,
together with two experimental results. The ordinate indicates the
ratio of
f
to
i
and the abscissa shows the bolt number defined in
Fig. 4. Remarkable preload reductions are observed from bolt 1 to
bolt 4, which have been tightened in the early stage of the tight-
ening operation. Specifically, the preloads of bolts 1 and 2 are
found to be almost zero. It is considered that such preload reduc-
tions are caused by elastic interaction, since these four bolts are
tightened in advance of the neighboring two bolts, unlike the other
four bolts.
Figure 8 shows how the preload of bolt 1, which is tightened
first, varies with the progress of the bolt-up operation. The nu-
merical results correspond to the first column in Table 3. The
abscissa indicates the bolt-up sequence. From this figure, the
amount of preload of bolt 1 increases when tightening the three
bolts located on the other side, i.e., bolts 2, 6, and 7 and decreases
in other cases. It is predicted that the former phenomenon is
caused by so-called ‘‘open up’’ deformation on the flange inter-
face, which occurs when tightening the bolts apart from bolt 1.
From Figs. 7 and 8, numerical results are in fairly good agreement
with experimental ones. It follows that the validity of numerical
procedure proposed here is confirmed.
4.2 Contact Pressure Distributions on Gasket Bearing
Surface. It is shown in Fig. 9 how the contact pressure distribu-
tions along the outer edge of gasket bearing surface vary with the
progress of bolt-up operation. The bolt locations are also illus-
trated in Fig. 9. The abscissa indicates the circumferential coordi-
nate and the left end corresponds to the center of bolt 1. The
distribution patterns of contact pressure do not show conspicuous
changes after tightening bolt 3. It is observed that at the end of
bolt-up operation, the magnitudes of contact pressure significantly
vary in the circumferential direction with a similar shape to sine
curve.
5 Aiming at Uniform Bolt Preloads „Problem 2…
5.1 Variations in Bolt Stress. In this section, the amount of
initial bolt preloads required for creating uniform final preloads,
when tightening each bolt one by one, is calculated. Table 4 shows
Fig. 7 Scatter in bolt stresses at the completion of bolt-up
„Problem 1…
Table 2 Longitudinal displacements applied to the symmetri-
cal cross section of bolt body „Problem 2…
Bolt Number j
12345678
Bolt-Up Sequence k 1u0000000
2uu000000
3uuu00000
4uuuu0000
5uuuuu000
6uuuuuu00
7uuuuuuu0
8uuuuuuuu
Table 3 Variations of bolt stresses in the bolt-up process „Problem 1…
Bolt Number j
12345678
Bolt-Up Sequence k 1 1.000 0.517 0.000 0.000 0.000 0.000 0.000 0.000
2 1.365 1.000 0.000 0.000 0.000 0.000 0.000 0.000
3 0.998 0.556 1.000 0.000 0.000 0.000 0.000 0.000
4 0.536 0.099 1.681 1.000 0.000 0.000 0.000 0.000
5 0.103 0.225 1.134 1.072 1.000 0.000 0.000 0.000
6 0.206 0.000 0.935 0.418 1.308 1.000 0.000 0.000
7 0.425 0.000 0.222 0.643 1.356 0.515 1.000 0.000
8 0.069 0.000 0.273 0.159 1.230 0.481 1.230 1.000
Journal of Pressure Vessel Technology NOVEMBER 2003, Vol. 125 Õ 375
how the uniform bolt preloads are produced in the process of
successive bolt tightening, where the amounts of constraint dis-
placement given in Table 2 are used for generating bolt preloads.
The target bolt stress
t
is set to be 50 MPa. The figures in Table
4 are normalized values divided by
t
. The numerical results in
the 8th row, which correspond to the end of bolt-up, are not per-
fectly unity because of the loading histories due to contact condi-
tions and gasket nonlinearity. However, the deviations from the
unity are favorably less than 5%. It is therefore considered that the
numerical procedure based on the displacement control proposed
here is effective from the practical point of view. The diagonal
components in Table 4 give the normalized initial stresses of each
bolt to create uniform final preloads. Tightening operations are
conducted using the initial stresses stated above. Strain gages are
attached to each bolt in order to apply the target bolt stress pre-
cisely. Experimental results thus obtained are shown in Fig. 10,
where experiments were done twice. The ordinate indicates the
normalized bolt stress, as defined in the similar manner to Table 4,
and the abscissa shows the bolt number. The scatter in bolt stress
is found to be at most 10%, which is surprisingly small comparing
to the case of tightening all bolts with the same initial preload. It
is thus concluded that the numerical procedure proposed here is
valid for estimating the amount of initial preload of each bolt
needed for creating uniform bolt preloads in the final state.
5.2 Contact Pressure Distributions on Gasket Bearing
Surface. Figure 11 shows the numerical results of the variations
of contact pressure distributions in the circumferential direction
on the gasket bearing surface, in the similar manner to Fig. 9. It is
observed from this figure that contact pressure distributions when
bolt 4 is tightened are nearly uniform and show almost the same
values as those at the completion of whole tightening process.
This is because the stress levels of the four bolts, from bolts 1 to
4, are almost the same and about twice the target bolt stress
t
when the tightening of bolt 4 is completed, as shown in the 4th
row of Table 4. As a result, at the completion of the bolt-up
operation the contact pressure distributions in the circumferential
direction could be regarded uniform from the practical point of
view.
6 Discussions
If the numerical procedure proposed in the previous chapter
could be applied to actual bolt-up operations successfully, almost
uniform bolt preloads can be obtained through only one pass
bolt-up operation. However, it involves a great deal of difficulty
from the practical point of view. That is, it is essentially difficult
for practicing workers to execute the tightening operation follow-
ing the prescribed values as given in Table 4, since the bolt pre-
loads to be applied differ from bolt to bolt.
In the actual tightening, bolt-up operations are usually con-
ducted with several passes. Then, it is shown in the following how
the numerical procedure developed for solving Problem 1 could
Fig. 8 Variations of bolt stress of bolt 1 „Problem 1…
Fig. 9 Variations of contact pressure distributions „Problem 1…
Fig. 10 Experimental results of the scatter in bolt stress using
calculated initial bolt stress „Problem 2…
Table 4 Variations of bolt stresses in the bolt-up process „Problem 2…
Bolt Number j
12345678
Bolt-Up Sequence k 1 1.381 0.701 0.000 0.000 0.000 0.000 0.000 0.000
2 2.831 2.836 0.000 0.000 0.000 0.000 0.000 0.000
3 2.493 2.499 0.705 0.000 0.000 0.000 0.000 0.000
4 1.805 1.811 1.807 1.863 0.000 0.000 0.000 0.000
5 1.323 1.923 1.350 1.962 0.948 0.000 0.000 0.000
6 1.397 1.380 1.417 1.431 1.030 1.059 0.000 0.000
7 1.498 0.897 0.932 1.530 1.026 1.043 0.938 0.000
8 0.961 0.972 1.007 0.992 1.022 1.039 1.024 1.052
376 Õ Vol. 125, NOVEMBER 2003 Transactions of the ASME
be applied to evaluate the conventional bolt-up operation for
achieving lower scatter in bolt preloads. A guideline for pipe
flange assembly to be presented by ASME is examined here 关15兴.
The summary of the bolt-up guideline is as follows:
Install. Hand tighten, then ‘‘snug up’’ to 10–20 ft-lb.
Round 1. Tighten to 20–30% of target torque.
Round 2. Tighten to 50–70% of target torque.
Round 3. Tighten to 100% of target torque.
Round 4. Continue tightening the bolts, but on a rotational
clockwise pattern until no further nut rotation occurs at the Round
3 Target Torque value.
Round 5. Time permitting, wait a minimum of four hours and
repeat Round 4; this will restore the short-term creep relaxation/
embedment losses.
The numerical procedure for Problem 1 is applied to the fore-
going assembly guideline. It is shown in Fig. 12 how the scatter in
bolt stresses varies in the progress of the tightening process. The
ordinate represents the ratio of the bolt stress at each step
f
to the
target bolt stress
t
⫽ 100 MPa. The abscissa shows the bolt num-
bers defined in the figure. Since the effects of viscosity of the
gasket are not taken into account, the analyses corresponding to
Round 5 are omitted here. Rotational tightening in Round 4 is
repeated three times. A large amount of scatter is observed during
Rounds 1 to 3, and then the scatter gradually decreases when
Round 4 starts. The final scatter is found to be about 20% from the
results of Round 4–3.
Thus, it is considered that the numerical method proposed here
could be applied to evaluate a variety of tightening procedures for
pipe flange assembly.
7 Conclusions
A numerical approach based on FEM is proposed for precisely
simulating the bolt-up process of a pipe flange connection with a
spiral wound gasket inserted.
The following results are obtained.
1. The numerical approach proposed here can predict the scat-
ter in bolt preloads with high accuracy, when tightening a pipe
flange connection with a number of bolts successively in an arbi-
trary order.
2. The numerical approach also can estimate how much initial
bolt preloads are needed for achieving uniform preloads in the
final state.
3. To establish the foregoing numerical approaches, the stress-
strain relationship of a spiral wound gasket, which exhibits high
nonlinearity, is identified with a sixth-degree polynomial during
loading and with an exponential equation during unloading and
reloading.
4. A guideline for pipe flange assembly by ASME is examined
by use of the numerical method stated in 共1兲.
5. The validity of the numerical approaches presented here is
demonstrated by comparing numerical results with experimental
ones.
Nomenclature
j ⫽ bolt number
k ⫽ bolt-up sequence
k
gi
⫽ gasket element stiffness
关
K
e
兴
⫽ stiffness matrix for equivalent model of bolt
and nut
关
K
f
兴
⫽ stiffness matrix for pipe flange
关
K
g
兴
⫽ stiffness matrix for gasket
关
K
C1e
兴
,
关
K
eC1
兴
,
关
K
C1
兴
, etc. ⫽ matrices relevant to contact conditions
m ⫽ number of contact nodes of gasket bearing
surface
u ⫽ constrained displacement to create uniform
final loads in each bolt
u
j
⫽ constrained displacement of jth bolt to
tighten all bolts to the same initial value
␣
,

,
␥
⫽ components specifying unloading equation of
gasket
␦
i
⫽ initial discrepancy at each contact surface
⌬Q ⫽ nodal force increment
⌬R
i
⫽ equivalent contact force increment
⌬u ⫽ nodal displacement increment
r
⫽ residual strain of gasket
, ⫽ gasket stress and strain
f
⫽ bolt stress in the final state
i
⫽ initial bolt stress
t
⫽ target bolt stress
y
,
y
⫽ stress and strain on loading curve of gasket
Fig. 11 Variations of contact pressure distributions „Problem
2…
Fig. 12 Evaluations of the guideline for pipe flange assembly
proposed by ASME
Journal of Pressure Vessel Technology NOVEMBER 2003, Vol. 125 Õ 377
References
关1兴 Goddard, D. L., and Bibel, G. D., 1994, ‘‘Bolt Preload Variation During Torqu-
ing of a Bolted Flange Connection,’’ ASME PVP-Vol. 274, pp. 25–32.
关2兴 Bouzid, A., and Derenne, M., 1999, ‘‘A Simple Method for Analyzing the
Contact Stress in Bolted Flange Joints With Non-Linear Gaskets,’’ ASME
PVP-Vol. 382, pp. 103–111.
关3兴 Hwang, D. Y., and Stallings, N. M., 1994, ‘‘Finite Element Analysis of Bolted
Flange Connections,’’ Comput. Struct., 51, pp. 521–533.
关4兴 Jofriet, J. C., Sze, Y., and Thompson, J. C., 1981, ‘‘Further Studies of the
Interface Boundary Connections for Bolted Flanged Connections,’’ ASME J.
Pressure Vessel Technol., 103, pp. 204–245.
关5兴 Rao, D. G., Ramamurti, V., and Narayama, S., 1985, ‘‘Effect of Bolt Load on
the Deformation of a Taper Hub Flange,’’ Comput. Struct., 21共3兲, pp. 405–
412.
关6兴 Sawa, T., Higurashi, N., and Akagawa, H., 1991, ‘‘A Stress Analysis of Pipe
Flange Connection,’’ ASME J. Pressure Vessel Technol., 113, pp. 497–503.
关7兴 Kohmura, S., 1985, ‘‘Design of Aluminum Bolted Flange Connections. 共Part
1: Relationship Between Leak Properties and Gasket Loads in Integral Hub
Flanges兲,’’ Bull. JSME, 28共243兲, pp. 2181–2188.
关8兴 Water, E. O., and William, P. G., 1952, ‘‘Stress Conditions in Flanged Joints
for Low-Pressure Service,’’ Trans. ASME, 74共1兲, pp. 135–156.
关9兴 Rosshim, D. B., and Markl, A. R. C., 1943, ‘‘Gasket-Loading Constants,’’
Mech. Eng. 共Am. Soc. Mech. Eng.兲, 65, pp. 647–648.
关10兴 Bazargui, A., and Payne, J. R., 1984, ‘‘Progress in Gasket Testing—Milestone
Results,’’ ASME J. Pressure Vessel Technol., 106, pp. 93–103.
关11兴 Fukuoka, T., and Takaki, T., 2001, ‘‘Finite Element Simulation of Bolt-Up
Process of Pipe Flange Connections,’’ASME J. Pressure Vessel Technol., 123,
pp. 282–287.
关12兴 Bibel, G. D., and Ezell, R. M., 1996, ‘‘Bolted Flange Assembly: Preliminary
Elastic Interaction Data and Improved Bolt-up Procedures,’’Weld. Res. Counc.
Bull., 408, pp. 1–27.
关13兴 Bibel, G. D., and Ezell, R. M., 1992, ‘‘An Improved Flange Bolt-Up Procedure
Using Experimentally Determined Elastic Interaction Coefficients,’’ ASME J.
Pressure Vessel Technol., 114, pp. 439–443.
关14兴 Weber, E. M., and Bibel, G. D., 1994, ‘‘Flange Bolt-Up Simulation Using 3-D
Finite Element Modeling,’’ ASME PVP-Vol. 274, pp. 63–82.
关15兴 ASME, 2000, ‘‘Guidelines for Pressure Boundary Bolted Flange Joint Assem-
bly,’’ ASME PCC-1.
关16兴 Fukuoka, T., 1997, ‘‘Evaluation of the Method for Lowering Stress Concen-
tration at the Thread Root of Bolted Joints with Modifications of Nut Shape,’’
ASME J. Pressure Vessel Technol., 119, pp. 1–9.
378 Õ Vol. 125, NOVEMBER 2003 Transactions of the ASME
