background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
1/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Organization (S):
EDF/RNE/MTC, CISI
Manual of Reference
R7.04 booklet: Evaluation of the damage
Document: R7.04.10
Operator of calculation of wear
Summary:
This note presents three laws of wear which make it possible to evaluate the volume used starting from the quantities resulting from one
dynamic calculation carried out with the operator
DYNA_TRAN_MODAL
[U4.54.03] and the key word
SHOCK
.
·
The law of Archard,
·
Law KWU_EPRI,
·
Law EDF_MZ.
The coefficients of wear necessary for these calculations are provided by the user or specified in one
base data.
From worn volume and geometry of the contact, it is possible to calculate the depth of wear for
mobile or its obstacle.
An angular figure division of play authorizes the operator to calculate the sizes relating to wear by
sectors.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
2/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Contents
1 Introduction ............................................................................................................................................ 3
2 Laws of wear ............................................................................................................................................ 3
2.1 Law of wear
“ARCHARD”
................................................................................................................... 4
2.2 Law of wear
“KWU_EPRI”
................................................................................................................ 5
2.3 Law of wear
“EDF_MZ”
..................................................................................................................... 7
3 Data base ................................................................................................................................... 8
4 Relation between worn volume and the depth of wear ......................................................................... 11
4.1 Situation “BUNCH - BORING” ................................................................................................... 11
4.2 Situation “BUNCH - NOTCH SIMPLE” .................................................................................... 12
4.3 Situation “BUNCH - NOTCH DOUBLES” .................................................................................. 13
4.4 Situation “Tubes of steam generator - Bar antivibratory” .................................................... 13
4.5 Situation “Tubes of steam generator - Boring” ..................................................................... 16
4.6 Situation “Tubes of steam generator - Trifoliate” ....................................................................... 17
4.7 Situation “Tubes of steam generator - Quadrifoliate” ................................................................. 20
4.8 Situation “Tubes of steam generator - Tube of steam generator” ................................. 23
5 figure Division of play in sectors ......................................................................................... 23
6 Updating of the table ....................................................................................................................... 24
7 Bibliography ........................................................................................................................................ 24
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
3/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
1 Introduction
The evaluation of the damage by wear requires a thorough knowledge of the bodies in presence at the time
contact, loadings and kinematics. Investigations led to the Mechanical Department
and Technology of the Components make it possible to provide coefficients for laws of wear relative to
configurations of wear affecting the components of the nuclear thermal power stations. A transitory calculation by
modal recombination, using the operator
DYNA_TRAN_MODAL
[U4.54.03] allows to know
kinematics and the dynamics of the contact for telegraphic structures such as the control rods
and the tubes of steam generator which impact and slip against their guidance.
To calculate the power of wear, the module of postprocessing of the wear of Code_Aster
®
,
(
POST_USURE
[U4.67.03]), uses, in a node of shock, the result in generalized co-ordinates
(
tran_gene
) resulting from
DYNA_TRAN_MODAL.
It combines the normal forces and speeds of slip
according to the definite method in the following paragraph. From the knowledge of the power of wear, it is
possible to go up with the volumes used by using one of the laws of wear suggested in
POST_USURE
.
The coefficients to be used are to be defined by the user or to seek in an integrated data base
with the operator.
In the second time, the knowledge of the geometry of the structures intern nuclear thermal power stations
allows to calculate the depths of wear starting from worn volumes.
The operator
POST_USURE
allows to cut out the figure of play in sectors in order to affect several
coefficients of wear at the same area of shocks to take account of complex geometries. For example,
the contact on edge leads to matter losses more important than the contact conformel in the case
control rods.
The table generated by
POST_USURE
give the value of the volumes used for several values of time.
It can be used in input of the operator
MODI_OBSTACLE
to know the evolution of the figure of
play due to the wear of the mobile and the obstacle. That gives the possibility of carrying out iterative calculations which
couple the evolution of dynamics with the wear of the mechanisms.
2 Laws
of wear
In its initial form, the law of Archard [bib1] expresses, for a configuration of adhesive wear, in
slip, a relation between worn volume and of the quantities characteristic of the contact:
V
K F L
H
N
=
.
.
where
V
:
used volume,
K
:
coefficient of wear without dimension,
F
N
:
modulate normal force of contact, presumedly constant,
L
:
slipped length,
H
:
hardness.
The coefficient
K
is different for each involved body. It depends on the conditions
geometrical and thermodynamic at the time of the contact.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
4/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
It was shown that the law of Archard can be extended to other mechanisms, in slip dominating.
With the help of a redefinition of certain parameters, the preceding equation can be written:
V
K W
=
.
where
K
:
is equal to
K
H
,
W
:
is equal to
F L
N
.
.
W
with the dimension of a work. By convention, it is called “work of wear”.
If the normal force of contact varies in the course of time (for example, in a situation
impact-slips,
F
N
present very strong variations of short duration at the time of the shocks),
definition of
W
becomes:
W
F
V dt
N
T
T
T
=
0
1
where
W
:
work of wear,
F
N
:
modulate normal force during the contact,
V
T
:
modulate speed of slip during the contact,
T
0
:
moment of beginning of calculation,
T
1
:
moment of end of calculation.
Consequently, by analogy with the usual laws of mechanics, it is possible to define a “power
of wear " while posing:
P
F
V
N
T
=
where
P
: power of wear.
If a stationary regime is reached, the power of wear is supposed to be constant with
run from time. In order to ensure itself of this stationnarity, the interval [
T
0
,
T
1
] can be cut out in
several blocks in the operator
POST_USURE
[U4.67.03]. For each one of these blocks, it is appropriate of
to check that the power of wear evolves/moves little (in any rigor, the use of the laws of wear below
suppose that the power of wear is constant).
2.1 Law
of wear
“ARCHARD”
Law is of the linear type [bib1]:
V
K P T
=
where
V
:
volume of wear,
K
:
coefficient of wear,
P
:
power of wear,
T
:
interval of time.
The coefficient
K
is provided by the user or is taken in a data base (see [§3]). It is
different for the two involved bodies and depends on the geometrical conditions and
thermodynamic in the contact. The interval of time
T
used for the calculation of wear
does not correspond to the effective time of simulation but to the interval of time over which the user wishes
to evaluate wear.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
5/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
2.2
Law of wear '
KWU_EPRI
'
The step of the model consists in determining a coefficient of wear
K
, within the meaning of the law of Archard, in
taking into account the particular conditions of the studied contact [bib2].
Normal forces
F
I
()
NR are divided into 5 classes, as well as speeds of slip
V
J
(/)
m S.
One obtains 25 classes whose identification is indicated as follows:
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
3.1
3.2
3.3
3.4
3.5
4.1
4.2
4.3
4.4
4.5
5.1
5.2
5.3
5.4
5.5
0
F
max
V
max
F
I
V
J
For a given calculation, one determines the percentages obtained for each of the 25 classes.
The processing is done by applying suitable factor loadings for each class, which
give an account of its particular contribution in the total process of wear.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
6/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
In the case of the pure impacts (classes 1.1 to 1.5), the contribution of these classes is modelized in
calling upon a factor loading
m
H
ij
defined by:
m
K K
F
C
H
I
ij
=
1
3
where
m
H
ij
:
adimensional factor of intensity of impact-work hardening
K
1
:
dimensional coefficient of correction
K
:
experimental adimensional constant
C
:
experimental adimensional constant
F
I
:
average value of the normal force for the class ij
In the case of the slip (class 1.1 and classes 2.1 to 5.5), the contribution of these classes is
modelized by calling upon a factor loading
m
W
ij
defined by:
()
m
K F V
W
I
J
ij
=
2
2
where
m
W
ij
: adimensional factor of intensity of wear by slip
K
2
: dimensional coefficient of correction
F
I
: average value of the normal force for the class ij
V
J
: average value the speed of slip for the class ij
It is then necessary to calculate the percentages balanced for each class of the two categories
impact-work hardening and wear by slip:
P
m
p
H
H
ij
ij
ij
=
P
m
p
W
W
ij
ij
ij
=
where
p
ij
is the percentage of elements of the class ij.
What leads to a total factor of intensity of wear
()
W
P
P
P
W
H
W
ij
ij
ij
=
+
2
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
7/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
The total factor of intensity
W
is used as factor of correction of the coefficient of wear within the meaning of
the law of ARCHARD according to the expression:
K
K W W
KWU
R
R
=
/
V
K
P T
KWU
=
where
K
R
:
is the coefficient of wear of reference obtained in experiments for conditions of test
conventional in oscillating slip,
and
W
R
is the total factor of intensity evaluated for this same test.
2.3
Law of wear '
EDF_MZ
'
It is currently developed for the only case of the control rods.
The experience feedback shows that the kinetics of wear slows down with time
T
; a manner of holding
count observations is to express the volume used in the form:
(
)
V
S
S
N
E
S T
NT
=
-




-
+
-
0
1
where
S
0
is initial speed and
S
the speed of wear asymptotic (see
below),
N
is a parameter of the model.
Values of
N
and of
S
are deduced from the experience feedback.
Tests on simulators, of short duration compared to that of a cycle of operation of one
jet engine, show that the speed of initial wear
S
0
a law of the type follows:
()
S
WITH P
B
0
0
=
where
P
0
is the power of initial wear
With
B
and
are coefficients determined by tests on simulators
[bib4]
The experience feedback shows that the speed of wear reaches an asymptotic value
S
. The relation
the preceding one, observed on simulator is supposed to be valid for every moment of the phenomenon of wear.
That supposes a power of wear
P
who allows to reach
()
S
WITH P
B
=
, for the values
raised time
T
(typically, one or more cycles of operation).
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
8/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
The corresponding evolution of the volume used according to time is form:
Slope S
0
Slope S
V
T
Worn volume
V
calculated with aid the operator
POST_USURE
is written:
()
(
)
V
WITH P
S
N
E
S T
B
NT
=
-


-
+
-
0
1
where
V
: volume of wear,
P
0
: power of wear calculated by Code_Aster
®
,
With
S N
, B,
: coefficients of the model defined above.
This model is described in detail by the reference [bib4].
3
Base data
The materials are identified by a letter followed by alphanumerics. The codes are
indicated below with a usual name and between brackets, standard AFNOR.
A304L
:
Steel 304L (Z2 CN 18-9),
A304LNI
:
Steel 304L nitrided,
A304LCR
:
Chrome steel 304L,
A304LLC1C
:
Steel 304L covered with chromium carbide,
A316L
:
Steel 316L (Z2 NDT 17-12),
A347
:
Steel 347 (Z6 CNNb 18-11),
A405
:
Steel 405 (Z6 CA 13),
A42
:
Steel A42 (A 42),
Z10C13
:
Z10C13 (Z10 C13),
Z6C13
:
Z6C13 (Z6 C13),
I600
:
Inconel 600 (NC 15 Fe),
I600CR
:
Inconel 600 chrome,
I600TT
:
Inconel 600 treaty thermically,
I690
:
Inconel 690 (NC 30 Fe),
I690TT
:
Inconel 690 treaty thermically,
I800
:
INCOLOY 800 (Z5 NC 35-20),
I800CR
:
INCOLOY 800 chrome,
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
9/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
The tables below give the coefficients of wear for the mobiles and the obstacles for
several material couples (mat1 is the material of the variable component and mat2 that of the obstacle).
The empty boxes correspond to null coefficients. A certain number of situations is
currently envisaged without all the coefficients being available because this data base will be able
to be supplemented with the results of the tests carried out at Department MTC.
Tables of the coefficients for the control rods for the model of ARCHARD:
CONTACT
:
“GRAPPE_ALESAGE”
(cf [§4.1])
mat1
mat2
Coef_mobile
Coef_obst
References
A304L
A304L
2.6E15
3.7E15
[bib5]
A316L
A304L
4.2E15
4.1E15
[bib5]
A304LNI
A304L
0.1E15
4.1E15
[bib5]
A304LCR
A304L
0.1E15
5.5E15
[bib5]
A304LLC1C
A304L
0.1E15
5.5E15
[bib5]
CONTACT
:
“GRAPPE_1_ENCO”
and
“GRAPPE_2_ENCO”
(cf [§4.2] and [§4.3])
mat1
mat2
Coef_mobile
Coef_obst
References
A304L
A304L
30.E15
17.E15
[bib5]
A316L
A304L
40.E15
29.E15
[bib5]
A304LNI
A304L
1.E15
124.E15
[bib5]
A304LCR
A304L
1.E15
43.E15
[bib5]
A304LLC1C
A304L
1.E15
34.E15
[bib5]
Tables of the coefficients for the control rods for model EDF-MZ:
CONTACT
:
“GRAPPE_ALESAGE”
(cf [§4.1])
mat1
mat2
Coef_mobile
Coef_obst
References
A304L
A304L
With = 2.6E15
B = 1.
NR = 2.44E8
S = 1.14E16
With = 3.7E15
B = 1.
NR = 2.44E8
S = 1.14E16
[bib5] [bib6]
A316L
A304L
With = 11.E15
B = 1.61
NR = 2.44E8
S = 1.14E16
With = 4.1E15
B = 1.
NR = 2.44E8
S = 1.14E16
[bib5] [bib6]
CONTACT
:
“GRAPPE_1_ENCO”
and
“GRAPPE_2_ENCO”
(cf [§4.2] and [§4.3])
mat1
mat2
Coef_mobile
Coef_obst
References
A304L
A304L
With = 20.E15
B = 1.05
NR = 2.44E8
S = 1.14E16
With = 23.E15
B = 1.19
NR = 2.44E8
S = 1.14E16
[bib5] [bib6]
A316L
A304L
With = 500.E15
B = 1.78
NR = 2.44E8
S = 1.14E16
With = 490.E15
B = 1.91
NR = 2.44E8
S = 1.14E16
[bib5] [bib6]
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
10/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Tables of the coefficients for the steam generators for the model of ARCHARD:
CONTACT
:
“TUBE_BAV”
(cf [§4.4])
mat1
mat2
Coef_mobile
Coef_obst
References
I600
I600
1.2E13
[bib6]
I600TT
I600
4.5E14
[bib6]
I600TT
I600TT
1.4E15
[bib6]
I600
I600CR
7.2E14
[bib6]
I600TT
I600CR
9.1E16
[bib6]
I690TT
I600CR
1.2E15
[bib6]
I600
Z10C13
9.9E14
[bib6]
I600
A405
6.2E14
[bib6]
I690
A405
4.1E16
[bib6]
I600TT
Z6C13
9.2E15
[bib6]
I600
Z6C13
7.1E15
[bib6]
I690TT
Z6C13
7.7E15
[bib6]
I600
A347
1.0E13
[bib6]
CONTACT
:
“TUBE_ALESAGE”
(cf [§4.5])
mat1
mat2
Coef_mobile
Coef_obst
References
I690
Z10C13
6.0E17
[bib6]
I600
I600
1.6E13
[bib6]
I690
I600
5.2E14
[bib6]
I600
I600CR
2.2E15
[bib6]
I690
I600CR
4.4E15
[bib6]
I600
A42
2.2E15
[bib6]
CONTACT
:
“TUBE_3_ENCO”
(cf [§4.6])
mat1
mat2
Coef_mobile
Coef_obst
References
I600
Z10C13
2.5E16
[bib6]
I690
Z10C13
2.4E16
[bib6]
CONTACT
:
“TUBE_4_ENCO”
(cf [§4.7])
mat1
mat2
Coef_mobile
Coef_obst
References
I600
Z10C13
2.4E16
[bib6]
I690
Z10C13
8.2E17
[bib6]
I600
A405
6.5E14
[bib6]
I600TT
A405
1.4E15
[bib6]
I690
A405
7.8E15
[bib6]
I600
I800
1.3E15
[bib6]
I600TT
I800
3.6E16
[bib6]
I690TT
Z10C13
1.2E15
[bib6]
I600
I800CR
2.2E15
[bib6]
I600
A347
2.6E16
[bib6]
CONTACT
:
“TUBE_TUBE”
(cf [§4.8])
mat1
mat2
Coef_mobile
Coef_obst
References
I600
I600
1.8E13
[bib6]
I690
I690
1.0E12
[bib6]
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
11/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
The values indicated above correspond to averages of the values recorded in
references for temperatures as close as possible to the conditions ITEM. It should be noted that
reference [bib6] does not give a value of coefficient of wear for the antagonists.
4
Relation between worn volume and the depth of wear
From the power of wear, the operator
POST_USURE
calculate worn volumes then them
depths of wear. Geometrical relations between worn volumes and the worn depths
depend on the type of contact.
Are:
D
m
: worn depth of the mobile tube,
D
O
: worn depth of the obstacle,
R
m
: radius external of the mobile tube,
R
O
: interior radius of the obstacle,
L
: width of the obstacle,
: mobile angle/obstacle,
V
m
: worn volume of the mobile tube,
V
O
: worn volume of the obstacle.
4.1
Situation “BUNCH - BORING”
The key word used is “
GRAPPE_ALESAGE
“. The bunch is centered in a boring. The trace of wear has
a section in the shape of lunule [bib6]. Worn volume is brought back to a surface used in a section,
multiplied by the worn height
L
Worn volumes are written [bib3]:
()
(
)
()
(
)
()
(
)
()
(
)
()
()
()
()
V
L
R
R
V
L
R
R
R
R
R
R
m
m
O
O
m
O
=
-
-
-
=
-
-
-
=
=
2
2
2
2
2
2
2
2
sin
sin
sin
sin
sin
sin
sin
sin
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
12/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Variables
R,
and
are intermediate variables of calculation defined on the figure
below:
R
m
R
O
R
Nonworn mobile
Nonworn obstacle
Area of contact
after wear
A numerical solvor integrated into Code_Aster® allows to pass to solve this system of equations
coupled to 4 unknown factors,
R,
. The depths of wear are then given by the relations
following:
()
()
(
)
()
()
(
)
D
R R
R
R
D
R
R
R
R
O
T
T
m
O
O
= -
-
-
=
- -
-
cos
cos
cos
cos
4.2
Situation “BUNCH - NOTCH SIMPLE”
The key word used is “
GRAPPE_1_ENCO
“.
The card of guidance comprises only one notch. Worn volume is brought back to a surface used in
a section, multiplied by the worn height
L
.
Worn volumes are written [bib7]:
V
L
With D
B D
C D
D
V
H R D
m
m m
m m
m m
m
O
O
O
=
+
+
+
=



3
2
0 47
,
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
13/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
with [bib7]:
With
2
B
10,30
C
0
D
0
m
m
m
m
= -
=
=
=


,
,
76
83
These coefficients are founded the experience feedback. They apply only to the bunches of
order whose characteristics are:
·
diameter external of the pencil of bunch: 9,7 mm
·
internal diameter of the card of guidance: 10,5 mm
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
4.3
Situation “BUNCH - NOTCH DOUBLES”
The key word used is “
GRAPPE_2_ENCO
“.
The card of guidance is made of 2 notches diametrically opposite. Worn volume is brought back to
a surface used in a section, multiplied by a worn height
L
.
Worn volumes are written [bib7]:
V
L
With D
B D
C D
D
V
H R D
m
m m
m m
m m
m
O
O
O
=
+
+
+
=



3
2
0 94
,
with [bib7]:
With
2
B
20,60
C
1
D
0
m
m
m
m
= -
=
=
=


5 5
66
,
,
These coefficients are founded the experience feedback. They apply only to the bunches of
order whose characteristics are:
·
diameter of the pencil: 9,7 mm
·
diameter of the card: 10,5 mm
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
4.4
Situation “Tubes of steam generator - Bar antivibratory”
The key word used is “
TUBE_BAV
“.
Case 1:
The tube is presented vertically, the bar impacts perpendicular to the tube, one supposes that
bar does not wear.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
14/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
The depths of wear are written [bib3]:
D
R
V
L
D
m
m
m
O
=


=




1
2
3
4
0
13
2 3
Case 2:
The bar is presented tilted (angle
) compared to the tube, the bar impacts perpendicular to
tube, one supposes that the bar does not wear.
·
if
D
L
m
<
The depths of wear are written [bib3]:
D
R
V
D
m
m
m
O
=






=




1
2
15
8
0
15
25
·
if
D
L
m
The relations between worn volume and depths of wear are written [bib3]
:
(
)
V
R
D
D
L
D
m
m
m
m
O
=
-
-




=



8 2
15
0
52
52
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
Case 3:
The tube is presented vertically, the bar impacts perpendicular to the tube, one takes into account
the wear of the bar.
is an unknown factor to be determined.
The relations between worn volume and depths of wear are written [bib3]:
(
)
() ()
()
(
)
D
V
V
V
R
V
V
L
V
V
L
R
R
D
R
D
m
m
m
O
m
m
O
m
O
m
m
O
T
m
=
+






+






+
=
-
=
-
-






1
2
3
4
1
13
2 3
2
2
sin
cos
cos
A solvor integrated into
POST_USURE
allows to determine
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
15/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Case 4:
The bar is presented tilted (angle
) compared to the tube, the bar impacts perpendicular to
tube, one takes into account the wear of the bar.
is an unknown factor to be determined.
·
if
(
)
D
D
L
m
O
+
<
The relations between worn volume and depths of wear are written [bib3]:
(
)
() ()
()
(
)
()
D
V
V
V
R
V
V
V
V
L
R
R
D
R
D
L
m
m
m
O
m
m
O
m
O
m
m
O
m
m
=
+






+




+
=
-
=
-
-
+








1
2
15
8
1
2
15
25
2
2
sin
cos
cos
sin
A solvor integrated into
POST_USURE
allows to determine
·
if
(
)
D
D
L
m
O
+
The relations between worn volume and depths of wear are written [bib3]:
(
)
(
)
(
)
(
)
(
)
(
)
(
)
()
(
)
()
V
R
K
D
D
K
D
D
K
L
V
V
L
R
R
D
R
D
L
m
m
m
O
m
O
m
O
m
m
O
m
m
=
+
+
+
-
+
+ -




+
=
-
=
-
-
+






8
2
15
1
1
1
1
2
52
5 2
2
2
.
sin () cos ()
cos
sin
where
K
is the relationship between worn volumes of the bar and the tube (
K
V
V
O
m
=
)
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
. In the same way, a solvor
allows to determine
.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
16/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
4.5
Situation “Tubes of steam generator - Boring”
The key word used is “
TUBE_ALESAGE
“.
Case 1:
The tube is centered perfectly in an animated boring of a pure orbital movement which wears of
uniform manner on all the periphery in contact with the obstacle.
The worn depths are written [bib3]:
D
V
L R
D
V
L R
m
m
m
O
O
O
=
=



2
2
….
….
Case 2:
The tube is centered in an animated boring of a movement of impact-slips of the elliptic type which
conduit with the formation of traces of wear of the cylindrical type diametrically opposite on the tube and
having a section in the shape of lunule.
Worn volumes are written [bib3]:
()
(
)
()
(
)
()
(
)
()
(
)
()
()
()
()
V
L
R
R
V
L
R
R
R
R
R
R
m
m
O
O
m
O
=
-
-
-
=
-
-
-
=
=
2
2
2
2
2
2
2
2
sin
sin
sin
sin
sin
sin
sin
sin
system of equations coupled to four unknown factors to determine:
R,
()
()
(
)
()
()
(
)
D
R R
R
R
D
R
R
R
R
O
m
m
m
O
O
= -
-
-
=
- -
-
cos
cos
cos
cos
These formulas have the same origin as those of the paragraph [§4.1].
Case 3:
The tube, animated of a movement of impact-slips, presents this time a slope by report/ratio
with the support. One obtains two symmetrical traces of wear on the tube.
()
(
)
()
(
)
()
(
)
()
(
)
()
()
()
()
V
L
R
R
V
L
R
R
R
R
R
R
m
m
O
O
m
O
=
-
-
-
=
-
-
-
=
=
2
2
2
2
2
2
2
2
sin
sin
sin
sin
sin
sin
sin
sin
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
17/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
system of equations coupled to four unknown factors to determine:
R,
()
()
(
)
()
()
(
)
D
R R
R
R
L
D
R
R
R
R
L
O
m
m
m
O
O
= -
-
-
+
=
- -
-
+
cos
cos
sin ()
cos
cos
sin ()
2
2
These formulas have the same origin as those of the paragraph [§4.1].
4.6
Situation “Tubes of steam generator - Trifoliate”
The key word used is “
TUBE_3_ENCO
“.
That is to say an angle
characteristic of the isthmus of the trifoliate boring, defined by the figure below:
Case 1:
The initial contact is carried out against an edge of one of the isthmuses of trifoliate boring. The tube is supposed
centered perfectly compared to its obstacle. The trace of wear does not extend to the entire isthmus.
One does not take into account the wear of the obstacle.
The relations between worn volume and the depth of wear are written [bib3]:
(
)
V
L R
X
R
R
X
R
X R
R
D
D
D
m
m
m
O
O
O
m
m
m
O
=




-




+
-
+
+




=



-
-
2
0
2
1
2
1
2
sin
sin
tg
with
(
)
(
)
(
)
X
R
R
R
R
R
D
R
R
D
m
O
m
O
m
m
O
m
m
=
-
-
-
-
+
-
+
2
2
2
2 2
2
4
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
18/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Case 2:
Same assumptions as for case 1 except the position of the tube compared to the obstacle. One supposes
this time that the tube presents an angle of inclination
.
·
if
D
L
m
<
The relations between worn volume and the depth of wear are written [bib3]:
(
)
V
D
R
X
R
R
X
R
X R
R
D
D
D
m
m
m
m
O
O
O
m
m
m
O
=




-




+
-
+
+




=



-
-
6
0
2
1
2
1
2
sin
sin
tg
with
(
)
(
)
(
)
X
R
R
R
R
R
D
R
R
D
m
O
m
O
m
m
O
m
m
=
-
-
-
-
+
-
+
2
2
2
2 2
2
4
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
·
if
D
L
m
The relations between worn volumes and depths of wear are written [bib3]:
(
)
V
L V
V V
V
D
m
O
=
+
+
=



6
1
1
2
2
0
with
(
)
(
)
(
)
X
R
R
R
R
R
D
R
R
D
m
O
m
O
m
m
O
m
m
1
4
2
2
2
2 2
2
=
-
-
-
-
+
-
+
(
)
V
R
X
R
R
X
R
X R
R
D
D
m
m
O
O
O
m
m
m
1
1
1
1
2
1
2
1
2
=




-




+
-
+
+
-
-
sin
sin
tg
(
)
(
)
(
)
X
R
R
R
R
R
D
L
R
R
D
L
m
O
m
O
m
m
O
m
m
2
4
2
2
2
2 2
2
=
-
-
-
-
+
-
-
+
-
(
) (
)
V
R
X
R
R
X
R
X R
R
D
L
D
L
m
m
O
O
O
m
m
m
2
2
2
2
2
1
2
1
2
=




-




+
-
+
- +
-
-
-
sin
sin
tg
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
19/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Case 3:
The contact is carried out against an edge of one of the isthmuses of trifoliate boring. The tube is supposed
centered perfectly compared to its obstacle. One takes into account the wear of the obstacle.
is
an angle characteristic of the isthmus of trifoliate boring.
Worn volumes are written [bib3]:
(
) (
)
V
V
R
X
R
R
X
R
X R
R
D
D
D +d
V
R D
m
O
m
m
O
O
O
m
m
O
m
O
O
O
O
+
=




-




+
-
+
+
+




=



-
-
1
2
141
2
1
2
1
sin
sin
tg
.
2
with
(
)
(
)
(
)
X
R
R
R
R
R
D
D
R
R
D
D
m
O
m
O
m
m
O
O
m
m
O
=
-
-
-
-
+
+
-
+
+
2
2
2
2 2
2
4
Case 4:
The contact is carried out against an edge of one of the isthmuses of trifoliate boring. One supposes this time that
the tube presents an angle of inclination
compared to its obstacle. One takes into account wear
obstacle.
is an angle characteristic of the isthmus of trifoliate boring.
·
if
(
)
D
D
L
m
O
+
<
Worn volumes are written [bib3]:
(
) (
)
V
V
D
D
R
X
R
R
X
R
X R
R
D
D
D
D
V
R D
m
O
m
O
m
m
O
O
O
m
m
O
m
O
O
O
O
+
=
+




-




+
-
+
+
+
+




=



-
-
6
141
2
1
2
1
sin
sin
tg
.
2
with
(
)
(
)
(
)
X
R
R
R
R
R
D
D
R
R
D
D
m
O
m
O
m
m
O
O
m
m
O
=
-
-
-
-
+
+
-
+
+
2
2
2
2 2
2
4
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
.
·
if
(
)
D
D
L
m
O
+
Worn volume is written [bib3]:
(
)
V
L V
V V
V
V
R D
m
O
O
O
=
+
+
=
6
1
1
2
2
141
.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
20/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
with
(
)
(
)
(
)
X
R
R
R
R
R
D
D
R
R
D
D
m
O
m
O
m
m
O
O
m
m
O
1
4
2
2
2
2 2
2
=
-
-
-
-
+
+
-
+
+
(
) (
)
V
R
X
R
R
X
R
X R
R
D
D
D
D
m
m
O
O
O
m
m
O
m
O
1
1
1
1
2
1
2
1
=




-




+
-
+
+
+
-
-
sin
sin
tg
+
2
(
)
(
)
(
)
X
R
R
R
R
R
D
D
L
R
R
D
D
L
m
O
m
O
m
m
O
O
m
m
O
2
4
2
2
2
2 2
2
=
-
-
-
-
+
+
-
-
+
+
-
(
) (
)
V
R
X
R
R
X
R
X R
R
D
D
L
D
D
L
m
m
O
O
O
m
m
O
m
O
2
2
2
2
2
1
2
1
2
=




-




+
-
+
+
- +
+
-
-
-
sin
sin
tg
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
4.7
Situation “Tubes of steam generator - Quadrifoliate”
The key word used is “
TUBE_4_ENCO
“.
That is to say an angle
characteristic of the isthmus of quadrifoliate, definite boring in the same manner as with
paragraph [§4.6]:
Case 1:
The initial contact is carried out against an edge of one of the isthmuses of quadrifoliate boring. It is supposed
tube perfectly centered compared to its obstacle. One does not take into account the wear of the obstacle.
Worn volume is written [bib3]:
(
)
V
L R
X
R
R
X
R
X R
R
D
D
D
m
m
m
O
O
O
m
m
m
O
=




-




+
-
+
+




=
-
-
2
0
2
1
2
1
2
sin
sin
tg
with
(
)
(
)
(
)
X
R
R
R
R
R
D
R
R
D
m
O
m
O
m
m
O
m
m
=
-
-
-
-
+
-
+
2
2
2
2 2
2
4
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
21/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Case 2:
Same assumptions as for case 1 except the position of the tube compared to the obstacle. One supposes
this time that the tube presents an angle of inclination
.
·
if
D
L
m
<
The relations between worn volumes and depths of wear are written [bib3]:
(
)
V
D
R
X
R
R
X
R
X R
R
D
D
D
m
m
m
O
O
O
m
m
m
O
=




-




+
-
+
+




=



-
-
6
0
2
1
2
1
2
sin
sin
tg
with
(
)
(
)
(
)
X
R
R
R
R
R
D
R
R
D
m
O
m
O
m
m
O
m
m
=
-
-
-
-
+
-
+
2
2
2
2 2
2
4
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
·
if
D
L
m
The relations between worn volumes and depths of wear are written [bib3]:
(
)
V
L V
V V
V
D
m
O
=
+
+
=



6
1
1
2
2
0
with
(
)
(
)
(
)
X
R
R
R
R
R
D
R
R
D
m
O
m
O
m
m
O
m
m
1
4
2
2
2
2 2
2
=
-
-
-
-
+
-
+
(
)
V
R
X
R
R
X
R
X R
R
D
D
m
m
O
O
O
m
m
m
1
1
1
1
2
1
2
1
2
=




-




+
-
+
+
-
-
sin
sin
tg
(
)
(
)
(
)
X
R
R
R
R
R
D
L
R
R
D
L
m
O
m
O
m
m
O
T
m
2
4
2
2
2
2 2
2
=
-
-
-
-
+
-
-
+
-
(
) (
)
V
R
X
R
R
X
R
X R
R
D
L
D
L
m
m
O
O
O
m
m
m
2
2
2
2
2
1
2
1
2
=




-




+
-
+
- +
-
-
-
sin
sin
tg
A solvor integrated into
POST_USURE
allows to determine
D
m
according to
V
m
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
22/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
Case 3:
The contact is carried out against an edge of one of the isthmuses of quadifolié boring. The tube is supposed
centered perfectly compared to its obstacle. One takes into account the wear of the obstacle.
Worn volumes are written [bib3]:
(
)
V
V
R
X
R
R
X
R
X R
R
D
D
V
R D
m
O
m
m
O
O
O
m
m
m
O
O
O
+
=




-




+
-
+
+




=



-
-
1
2
188
2
1
2
1
2
sin
sin
tg
.
with
(
)
(
)
(
)
X
R
R
R
R
R
D
D
R
R
D
D
m
O
m
O
m
m
O
O
m
m
O
=
-
-
-
-
+
+
-
+
+
2
2
2
2 2
2
4
Case 4:
The contact is carried out against an edge of one of the isthmuses of quadrifoliate boring. One supposes this time
that the tube presents an angle of inclination
compared to its obstacle. One takes into account
the wear of the obstacle.
·
if
(
)
D
D
L
m
O
+
<
Worn volumes are written [bib3]:
(
) (
)
V
V
D
D
R
X
R
R
X
R
X R
R
D
D
D
V
R D
m
O
m
O
m
m
O
O
O
m
m
O
m
O
O
O
+
=
+




-




+
-
+
+
+




=



-
-
6
188
2
1
2
1
sin
sin
tg
.
+ D
.
O
2
with
(
)
(
)
(
)
X
R
R
R
R
R
D
D
R
R
D
D
m
O
m
O
m
m
O
O
m
m
O
=
-
-
-
-
+
+
-
+
+
2
2
2
2 2
2
4
·
if
(
)
D
D
L
m
O
+
Worn volumes are written [bib3]:
(
)
V
L V
V V
V
V
R D
m
O
O
O
=
+
+
=



6
1
1
2
2
188
.
with
(
)
(
)
(
)
X
R
R
R
R
R
D
D
R
R
D
D
m
O
m
O
m
m
O
O
m
m
O
1
4
2
2
2
2 2
2
=
-
-
-
-
+
+
-
+
+
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
23/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
(
) (
)
V
R
X
R
R
X
R
X R
R
D
D
D
m
m
O
O
O
m
m
m
O
1
1
1
1
2
1
2
1
=




-




+
-
+
+
-
-
sin
sin
tg
+
.
2
(
)
(
)
(
)
X
R
R
R
R
R
D
D
L
R
R
D
D
L
m
O
m
O
m
m
O
O
m
m
m
2
4
2
2
2
2 2
2
=
-
-
-
-
+
+
-
-
+
+
-
(
) (
)
V
R
X
R
R
X
R
X R
R
D
D
L
D
D
L
m
m
O
O
O
m
m
O
m
O
2
2
2
2
2
1
2
1
2
=




-




+
-
+
+
- +
+
-
-
-
sin
sin
tg
4.8 Situation `Tube of steam generator - Tube of generator of
vapeur'
The key word used is “
TUBE_TUBE
“. Following the rupture of a stopped tube, there can be contact between it
tube and one of its neighbors. The wear of the two tubes by accommodation of surfaces leads to the contact
with the creation of two plane surfaces. This assertion is confirmed by tests carried out on
machine of wear.
The worn depths are written [bib3]:
D
R
V
D
R
V
T
m
m
O
O
O
=








=












1
2
15
8
1
2
15
8
15
25
15
25
5
Division the figure of play in sectors
The user with the possibility of defining a figure division of play in angular sectors for
which it gives a type of contact (
GRAPPE_1_ENCO
…), a coefficient of wear and angles of beginning
and of end of cutting (these angles must be increasing between - 180° and +180°). Power of wear
for each sector is then calculated like the arithmetic mean over the moments, beforehand
cut out in blocks, of the product of the standards of the normal force of shock and the speed of slip
by holding account only contacts which take place in the angular sector concerned. From this
power, it is possible to define a volume used by multiplying the power of wear of the sector by
coefficient of wear of the sector and by an operating time given by the user. He is
also possible to calculate the depth of wear for this sector, by supposing that extension
angular of the defect that of the sector does not exceed where it is detected.
It is the key word
SECTOR
who allows to define the whole of these amendments.
It is not envisaged to check the total coherence of calculations carried out. In particular, a wear can
to be distributed on several sectors and in this case, the calculation depth of wear does not have any more a smell.
It is up to the operator to be ensured a posteriori of the validity of its results. A new calculation
with another cutting must be possibly carried out to obtain the value depth
of wear. This choice is not constraining because of the speed of postprocessing considered. Interest
to carry out these calculations in
CONTINUATION
is obvious, taking into account what precedes.
A particular case deserves a development. It is the case of the control rods for which
results of
POST_USURE
are used in input of the control
MODI_OBSTACLE
. In this case, it
a number of sectors is fixed at 10, as it is explained in the reference [bib8]. The operator
MODI_OBSTACLE
use data resulting from the experience feedback to calculate wears which
can extend on several sectors while setting out again from the worn volumes obtained using
POST_USURE
. In this case, worn depths of
POST_USURE
necessarily do not have
physical significance.
background image
Code_Aster
®
Version
4.0
Titrate:
Operator of calculation of wear
Date:
01/12/98
Author (S):
D. HARROWING, L. VIVAN
Key:
R7.04.10-A
Page:
24/24
Manual of Reference
R7.04 booklet: Evaluation of the damage
HT-22/98/015/B
6
Updating of the table
The operator
POST_USURE
extrapolate the worn volume obtained in a few seconds of simulation with
durations defined by the user (typically a few months, even a few years).
It restores a table which contains worn volumes and the depths of wear for all the sectors and
every moment defined by the user by cumulating them since the initial moment of simulation.
It is possible to give a table to be reactualized by using the key word
ETAT_INIT
. That allows
to hold of the evolution of the geometries related to wear:
·
Starting from a figure of play, the user carries out a dynamic calculation.
·
He obtains volumes and depths of wear at exit of
POST_USURE
.
·
Using geometrical considerations, it evaluates the evolution of the figure of play connected to this
wear thanks to the operator
MODI_OBSTACLE
.
·
It carries out a new dynamic calculation with the figure of play modified.
·
It deduces some from new sizes related to wear and cumulates them in the table result of
POST_USURE
.
By reiterating the process a certain number of times [bib9], it is possible to take into account the evolution
geometries according to wear and to deduce the impact from it from this phenomenon on dynamics from
studied system.
7 Bibliography
[1]
ARCHARD J.F. : “Contact and Rubbing off flat surfaces”. Newspaper off Applied Physics, vol.24,
p. 24, 1953
[2]
P.J. HOFFMANN, D.A. STEININGER, T. SCHETTLER: “PWR Steam Generator Tubes Fretting
and Fatigue Wear Phenomena and correlations ". HTD - Vol. 230/- vol. 9, Symposium one
Flow-Induced Vibration and Noise, Flight 1, ASME, 1992
[3]
F. GUEROUT: “Wear of the tubes of Steam generators: geometrical relations enters
worn volumes and depths ". HT.22/93-21A. EDF-DER. July 1993
[4]
Mr. ZBINDEN, V. DURBEC: “A kinetic model for impacts/sliding wear off pressurized toilets
reactor internal components: application to rod cluster control assemblies ". Communication
presented at the Symposium one Flow Induced Vibration, Congress ASME Pressurized Vessels and
Piping, Montreal, 22 to July 26, 1996. HT.22/90-028A. EDF-DER.
[5]
Mr. ZBINDEN, A. LINA, HARROWING D.: “Control rods and guides of bunches:
synthesis of the tests of wear carried out on simulators ERABLE1 and ERABLE2 of 1995 with
1997 ". HT.22/97-21A. EDF-DER. March 1998
[6]
F. GUEROUT, Mr. ZBINDEN: “Bibliographical Study of the models of wear. Review of
coefficients of wear available for the study of the damage of the tubes of Generators
vapors ". HT.22/93-56A. EDF-DER. November 1993
[7]
A. LINA, Mr. ZBINDEN: “Wear of the sheaths of pencils of control rods: Relations
between worn volume and depth of wear ". HT.22/95-06A. EDF-DER. September 1995
[8]
J. - D. GEORGES, HARROWING D.: “Improvement of operator POST_USURE of Code_Aster
: calculation of wear by angular sectors of the contact mobile-antagonist ". HT.22/97-010A.
EDF-DER. February 1997
[9]
V. TO MOW, HARROWING D.: “Control rods of the jet engines 1300MW. Calculations
of wear iterative with progressive wear of the antagonists on the model with two pencils.
Preliminary method and calculations ". HT.22/98-009A. EDF-DER. March 1998