A METHOD AND A DEVICE FOR ESTIMATING A THICKNESS OF A
CERAMIC THERMAL BARRIER COATING
Background of the invention
5 The invention belongs to the general field of
depositing ceramic thermal barrier coatings on hot parts
of gas turbines, such as turbojets, for example.
The invention relates more particularly to
estimating a thickness of a ceramic thermal barrier
10 coating that is to be deposited by physical vapor
deposition on a hot part of a gas turbine, such as a
stator guide vane or a rotor wheel blade of a highpressure
turbine.
The invention thus has a preferred, but nonlimiting,
15 application to the field of aviation.
In known manner, while a gas turbine is in
operation, its blades are subjected to relatively high
temperatures.
In order to avoid the blades deterioration, one
20 solution consists in coating the wall of a blade with a
thermal barrier constituted by a ceramic outer layer in
order to lower the temperature of the blade. A ceramic
commonly used for this purpose is zirconia Zr02, possibly
stabilized with yttrium. Such a ceramic thermal barrier
25 is typically formed by physical vapor deposition (PVD),
and more particularly by electron beam assisted PVD
(EBPVD) .
In the EBPVD technique, the wall of the blade is
coated by ceramic vapor condensing thereon in a vacuum
30 enclosure with a partial pressure of an inert or reagent
gas. The ceramic vapor is generated by evaporating
"target" bars of sintered ceramic that are bombarded by
an electron beam
Only the surface of the blade that is situated
35 facing the surfaces of the ceramic bars is coated with a
layer of ceramic by means of that method. Thus, in order
to be able to cover the entire profile of the blade, the
blade is placed in the vapor during EBPVD deposition on
support tooling that is driven with movement in rotation
or in oscillation relative to the "target" bars.
At present, the thickness of the ceramic ther.m~,a l
5 barrier coating that is to be deposited on the wall of
the blade is specified by a design office. This
I
specification takes account only of the maximum wall
j temperature that the blade can accept before
I
I
! deteriorating. However it does not take account of
i 10 technical constraints associated with actually depositing
I
the coating (e.g. the shape and the movements of the
tooling and of the target bars, etc.), such that the
coating thickness recommended by the design office cannot
always be obtained in practice.
15 As a result, several tests are generally carried out
on real parts in order to act in iterative manner to
define support tooling for the blade and to define
conditions for EBPVD deposition (e.g. movements of the
tooling, exposure times of the hot part to the radiation
20 from the target(s), etc.) making it possible to achieve a
coating thickness that is as close as hossible to the
thickness specified by the design office.
Such tests require both the fabrication and the use
of real parts such as blades and various pieces of blade
25 support tooling and also of parts for masking zones of
the blade that it is desired not to expose to the
radiation from the ceramic bars during EBPVD deposition.
Such tests also require the deposits made in this way to
be analyzed, including cutting up blades after
30 deposition, measuring deposits on various sections of the
blade, and comparing the deposit thicknesses obtained
with the specifications from the design office.
In general, at least three tests are needed to
achieve the specifications of the design office. It can
35 thus readily be understood that that constitutes a method
that is relatively expensive, both in terms of material
resources and in terms of the time needed for achieving a
thermal. barrier coating that is satisfactory compared
with the specifications.
Object and summary of the invention
5 The present invention serves in particular to remedy
those drawbacks by proposing an estimation method for
estimating the thickness of a ceramic thermal barrier
coating that is to be deposited by physical vapor
deposition from at least one target and onto a gas
10 turbine hot part mounted on support tooling, the method
comprising:
a step of digitally modeling the geometrical shape
of the hot part and its movements relative to said at
least one target;
15 a step of representing the hot part as modeled in
f?
this way as a surface mesh; and
a step of estimating, for at least one mesh
element of the hot part exposed to the radiation from the
target during deposition of the coating, a coating
20 thickness to be deposited on said mesh element at a given
instant, by using a radiation model modeling radiation
from the target and taking account of the position of
said mesh element at that instant relative to the target.
Correspondingly, the invent~on also proposes a
25 device for estimating the thickness of a ceramic thermal
barrier coating that is to be deposited by physical vapor
deposition from at least one target and onto a gas
turbine hot part mounted on support tooling, the device
comprising:
30 .means for digitally modeling the geometrical shape
of the hot part and its movements relative to said at
least one target;
.means for representing the hot part as modeled in
thls way as a surface mesh; and
35 .means for estimating, for at least one mesh element
of the hot part exposed to the radiation from the target
during deposition of the coating, a coating thickness to
be deposited on said mesh element at a given instant,
these means being suitable for using a radiation model
modeling radiation from the target and for taking account
of the position of said mesh element at that instant
5 relative to the target.
Preferably, deposition is performed by electron beam
assisted physical vapor deposition (EBPVD) that is
performed in conventional manner with the help of ceramic
targets such as bars or ingots of sintered ceramic.
10 The movements of the hot part relative to the target
relate to the parameters and/or elements that
characterize any movement of the hot part relative to the
target during PVD deposition. Thus, the digital modeling
of the movements of the hot part relative to the target
15 may consist in particular in characterizing one or more
axes of rotation of the hot part relative to the target,
together with the associated speed(s) of rotation. It
should be observed that the origin of the movement of a
hot part relative to the target may be any origin, for
20 example it may come from a movement of the support
tooling, of the target, etc.
Thus, the invention propo'ses a predictive digital
tool for quickly and easily dimensioning and
characterizing the deposition of a thermal barrier on a
25 hot part, while taking account of real industrial
constraints (shapes and movements of a hot part relative
to the target, masked portions of the hot part, etc.).
Naturally, it is possible to develop a man machine
interface (MMI) for this tool in order to facilitate use
30 of the thicknesses obtained.
In accordance with the invention, the physical
phenomena involved during thermal barrier deposition and
associated in particular with bombarding the target with
the electron beam and with generating molecules during
35 evaporation of the target are treated as radiation from
the target. Correspondingly, the portions of the hot
part exposed to the vapor (i.e. to the ceramic particles)
from the target are treated as portions exposed to
radiation from the target.
The to.01 proposed by the invention thus relies
advantageously on a radiation model modeling radiation
5 from the target, with a ray emitted by the target in that
model corresponding to a flux of ceramic particles
emitted by the target along that ray. By analyzing the
estimated thickness and by using digital models, the tool
makes it easy to adapt the tooling and its movements for
10 the purpose of achieving a deposit that is as close as
possible to the specifications of the design office.
This limits the amount of tests needed on real parts in
order to achieve this result.
The surface meshing of the hot part makes it
15 possible to calculate the thickness at different points
on the part, and at different instants. This makes it
possible to avoid the various operations of cutting up
real parts that were previously used in order to verify
results. Also, by means of the invention, it is possible
20 to access the thickness of the deposit at numerous points
on the hot part, thereby making it easier to analyze the
results.
Furthermore, having recourse to a digital model of
the hot part makes it possible to adapt to a wide variety
25 of hot parts. By way of example, such digital modeling
is made available by the CATIAO software developed by the
supplier Dassault Syst&mes and known in the field of
computer assisted design (CAD).
In an implementation, the method of the invention
30 further comprises:
a step of digitally modeling the geometrical shape
of said at least one target; and
a step of representing said at least one target as
modeled in this way as a surface mesh;
3 5 wherein the radiation model is defined for a mesh
element of said at least one target by:
r(e) = I , [ C O S ( ~ ) ] ~
where:
I(B) designates the intensity of a ray emitted by
the mesh element of said at least one target in a
direction at an angle 9 relative to the normal to said
5 mesh element (this intensity modeling the rate at which
ceramic particles are emitted by the target in the
direction 8); and
n and I. designate predetermined constants.
The invention thus makes use of a model that is
10 accurate and that also takes account of the shape of the
target. It should be observed that the constants n and I0
may be determined theoretically or experimentally.
In another implementation, the method of the
invention further comprises:
15 a step of digitally modeling at least one mask
suitable for preventing a zone of the hot part being
exposed to the radiation from said at least one target;
and
a step of representing said at least. one mask as a
20 surface mesh;
wherein the mesh elements of the 'hot parts that are
taken into consideration during the estimation step
comprise mesh elements that are not masked at the given
instant from said at least one target by mesh elements of
25 said at least one mask during deposition of the coating.
Modeling and representing masks as surface meshes
give greater flexibility in taking deposition constraints
into account. These masks may come from elements of the
tooling itself used for supporting the hot part during
30 PVD deposition (e.g. for a blade, the support tooling may
mask the platform of the blade and its base), or may
represent zones that it is desired not to expose to the
evaporation (i.e. to the radiation) from the target
during deposition (e.g. the trailing edge of the blade).
3 5 By means of the invention, it is thus also easy to
test various positions for the hot part on the support
tooling relative to the target by modeling appropriate
masks.
In an implementation, the method of the invention
further comprises:
5 a step of digitally modeling the support tooling
for supporting the hot part; and
a step of representing the support tooling as
modeled in this way as a surface mesh.
Modeling and surface meshing the tooling serve to
10 improve the accuracy with which the thickness of the
coating is estimated, and to make it easy to take account
of changes in the support tooling for the hot part.
In addition, the use of a digital tool as proposed
I
by the invention makes it easy to store support tooling
15 (with the associated movements) that has been tested and
verified relative to the specifications of the design
office (in the sense that such tooling is known to make
it possible to achieve the specifications of the design
office). This produces better traceability of the
20 intended verification tests. It is also easy to devise a
tooling catalogue suitable for constituting a knowledge
base for developing new tooling and new proposals for
movements of the tooling.
It should be observed that the surface meshing of
25 the support tooling as a surface mesh, given that the
tooling participates only in defining the masks of the
hot part, does not need to be as accurate as the surface
mesh representation of the hot part and/or where
appropriate, of the target.
3 0 In a variant implementation, during the estimation
step, account may also be taken of a loss factor
corresponding to rays that are emitted by said at least
one target during deposition but that do not reach the
hot part (in spite of there being no obstacle between the
35 target and the hot part, some ceramic particles do not
reach the hot part). Taking this loss factor into
account makes it possible to obtain an estimate for the
thickness of the coating that is closer to that defined
experimentally during tests performed on real parts.
In an implementation, the vari0u.s steps of the
estimation method of the invention are determined by
5 computer program instructions.
Consequently, the invention also provides a computer
program on a data medium, the program being suitable for
being performed in an estimation device, or more
generally in a computer, the program including
10 instructions adapted to performing steps of an estimation
method as described above.
The program may use any programming language, and
may be in the form of source code, object code, or code
intermediate between source code and object code, such as
15 in a partially compiled form, or in any other desirable
form.
The invention also provides a computer readable data
medium including instructions of a computer program as
mentioned above. ~ 2 0 The data medium may be any entity or device capable
i of storing the program. For example, the medium may
I comprise storage means, such as a read only memory (ROM),
for example a compact disk (CD) ROM or a microelectronic
circuit ROM, or indeed magnetic recording means, for
25 example a floppy disk or a hard disk.
Furthermore, the data medium may be a transmissible
medium such as an electrical or optical signal, which may
be conveyed via an electrical or optical cable, by radio,
or by other means. The program of the invention may in
30 particular be downloaded from a network of the Internet
type.
Alternatively, the data medium may be an integrated
circuit in which the program is incorporated, the circuit
being adapted to execute or to be used in the execution
35 of the method in question.
In another aspect, the invention also provides the
use of the method of the invention for estimating a
thickness of a ceramic thermal barrier coating that is to
be deposited by physical vapor deposition from at least
one target ,and onto a stator blade or a rotor blade of a
gas turbine.
5
Brief description of the drawings
Other characteristics and advantages of the present
invention appear from the following description made with
reference to the accompanying drawings, which show an
10 implementation having no limiting character. In the
figures :
Figure 1 shows, in its environment, support
tooling having a plurality of gas turbine blades mounted
thereon and suitable for use during EBPVD deposition;
15 Figure 2 shows a device in accordance with a
particular embodiment of the invention and suitable for
estimating the thickness of a thermal barrier coating
made of ceramic that is to be deposited on a blade
mounted on the tooling shown in Figure 1;
2 0 Figure 3 is in the form of a flowchart, and shows
a particular implementation of the main steps of a method
in accordance with the invention for estimating the
thickness of a thermal barrier coating made of ceramic,
as performed by the device of Figure 2;
2 5 Figure 4A shows digital models of the support
tooling and of the gas turbine blade shown in Figure 1,
represented by using a surface mesh of triangles;
Figure 4B shows a particular mesh for the target
shown in Figure 1;
30 Figure 4C shows a nonuniform mesh for the turbine
blade shown in Figure I;
Figure 5 shows a ray emitted by a mesh element of
the target towards a mesh element of the turbine blade;
and
3 5 Figure 6 shows thickness values for the thermal
barrier coating made of ceramic as obtained using the
method of the invention and compared with test results.
Detailed description of the invention
The presently described implementation concerns
estimating a thickness of a thermal barrier coating made
5 of ceramic that is to be deposited by electron beam
assisted physical vapor deposition (EBPVD) on a blade of
a gas turbine.
By way of example, this blade is a stator guide vane
or a rotor blade of a high-pressure turbine.
10 Nevertheless, this assumption is not limiting, and
the invention can be applied to determining the thickness
of a thermal barrier coating on other hot parts of a gas
turbine.
As described above, in order to proceed with the
15 EBPVD deposition of a ceramic thermal barrier on a gas
turbine blade, the blade is placed in a vacuum enclosure
with a partial pressure of inert or reagent gas. The
blade is then coated by condensation of ceramic vapor
generated by evaporating one or more ceramic sources by
20 electron bombardment. By way of example, the ceramic
sources may be sintered ceramic bars. In the meaning of
the invention, these are "targets" (for the electron
beam) .
In order to expose the entire profile of the blade
25 to the ceramic vapor emanating from the ceramic sources,
the blade is placed in support tooling that causes it to
move in rotation or in oscillation relative to the
sources while EBPVD deposition is taking place.
Since the principle of the EBPVD deposition is known
30 to the person skilled in the art, it is not described in
greater detail herein.
By way of example, Figure 1 shows, in its
environment, support tooling 1 suitable for use during
EBPVD deposition of a ceramic thermal barrier by one or
35 more target,sources 2 onto a plurality of high-pressure
turbine blades 3.
This support tooling 1 has an arm 4 terminated by a
fork having two parallel branches 5A and 5B. The
parallel branches 5A and 5B support transverse
cylindrical bars 6 on which the blades 3 are mounted.
5 The transverse bars 6 are caused to move in rotation
about their axes of revolution, thereby causing the
blades 3 to move relative to the targets 2 .
The targets 2 are positioned under the support
tooling 1 and clouds of ceramic vapor emanate therefrom
10 under the effect of electron bombardment (not shown).
The use of a plurality of targets 2 presents the
advantage of providing a vapor field that is more uniform
in the vicinity of the blades.
Each blade 3 is mounted on a transverse bar 6 and is
15 fastened thereto via its trailing edge, its platform, and
its root. It can thus immediately be understood that
these zones of the blade are masked by elements of the
tooling 1, as shown in Figure 1, so they are not exposed
to the emanations from the targets during EBPVD
20 deposition.
As mentioned above, the invention advantageously
proposes a predictive tool that makes it possible, at a
given instant, to estimate the thickness -e of the ceramic
thermal barrier coating deposited by EBPVD on one of the
25 gas turbine blades 3 mounted on the tooling 1.
In the presently described example, this Cool is in
the form of a computer program having instructions
adapted to performing steps of an estimation method of
the invention.
30 With reference to Figure 2, the program is stored in
an estimator device 7 in accordance with the invention,
and in this example having the hardware architecture of a
computer.
In particular, the device 7 comprises a processor 8,
35 a random access memory (RAM) 9, a ROM 10, a nonvolatile
memory 11, input/output means 12 (e.g. a mouse, keyboard,
etc.) and a screen 13 for viewing the thicknesses
estimated in accordance with the invention. The ROM 10
constitutes a data medium in accordance with the
invention that is readable by the processor 8 and on
which the above-mentioned program is stored.
5 With reference to Figure 3, there follows a
description of the main steps of the estimation method of
the invention, in a particular implementation in which
the steps are performed to estimate a thickness of
ceramic coating that is to be deposited by EBPVD on one
10 of the blades 3A of the plurality of blades 3 mounted on
the tooling 1 of Figure 1. It should be observed that
the invention enables this thickness to be estimated at
various points of the blade 3A.
In the presently described implementation, numerical
15 models Ml, M2, and M3 are initially established for the
support tooling 1, for the targets 2, and for the blade
I 3A, respectively (step El0).
i In this example, these digital models are in the
form of discrete data files stored in the nonvolatile
20 memory 11 of the device 7, and in particular they
describe the geometrical shapes of t.he tooling I, of the
targets 2, and of the blade 3A, together with their
positions in a predetermined reference frame ( X , Y , Z ) . In
other words, the discrete data constituting the digital
25 models MI, M2, and M3 corresponds to the coordinates of
various points representative of the tooling 1, 01 the
targets 2, and of the blade 3A in this predetermined
reference frame.
Techniques for obtaining such geometrical models are
30 themselves known. By way of example they may be
generated using computer assisted design tools such as
the CATIAO tool developed by the supplier Dassault
SystPmes.
In addition to defining the geometrical shapes of
35 the elements that they model, these models also include,
where appropriate, the characteristics of the movements
that apply to these elements.
Thus, the model MI includes the characteristics of
the movements performed by the transverse bars 6 of the
support tooling 1, namely the coordinates of the axis of
revolution of the bar 6 on which the blade 3A is mounted,
5 together with its speed of rotation about its axis.
In the presently described example, the targets 2
are stationary.
Likewise, the blade 3A is stationary relative to the
transverse bar 6. In other words, the blade 3A moves
10 relative to the targets 2 resulting solely from the
movement of the transverse bar 6 on which it is mounted.
Consequently, defining the movements of the transverse
bar 6 is also equivalent to defining the movements of the
blade 3A relative to the targets 2.
15 It should be observed that defining these movements
makes it possible at each instant to define the position
of a point on the blade 3A relative to the targets 2. 1 Once the models MI, M2, and M3 have been
established, the surfaces of the elements as modeled in
20 this way are represented as meshes (also referred to as
tiling) (step E20).
In known manner, surface mapping a domain consists
in subdividing the domain into a plurality of finite
dlscrete geometrical elements (or cells), such as for
25 example triangles, quadrilaterals, or other polyqons
Such a mesh advantageously serves to simplify Lhe digital
models MI, M2, and M3 in order to facilitate calculating
the thicknesses of the thermal barrier coating at various
points on the blade 3A.
3 0 This may be done in particular with the help of
known methods or software for making a mesh
representation and not described in detail herein, whlch
methods or software may be applled to the previouslyestablished
digital models MI, M2, and M3.
35 Figure 4A shows an example model 53 resulting from
representing the surface of the blade 3A as a mesh using
triangles and starting from the digital model M3. In
order to avoid overcrowding the figure, only a portion of
the model S3 is shown.
Each triangle constitutes a mesh element m - of the
model S3. Each mesh element m - of the model S3 is defined
5 by the coordinates of its vertices A, B, and C and of its
center 0 in the reference frame ( X , Y , Z ) .
Figure 4B shows an example model 52 resulting from
representing the surface of the target 2 as a mesh using
triangles and starting from the digital model M2. Each
10 triangle constitutes a mesh element m2 of the model S2.
Each mesh element m2 of the model S2 is defined by the
coordinates of its vertices A, B, and C and of its center
0 in the reference frame (X,Y, Z ) .
It should be observed that the fineness of the
15 surface mesh representation used (i.e. the size of the
cells making up the mesh) may vary from one element to
the other.
Thus, it is preferable to use a surface mesh that is
quite fine for the zone under study of the blade 3A and
20 for the targets 2, in order to make it possible to
estimate accurately the thickness of the coating at
various points on the blade.
In contrast, it is possible to use a coarser mesh
for the tooling 1, since the purpose of this mesh is to
25 characterize rather briefly the elements of the tooling
that, at a given instant, are masking zones of the blade
3A while it is being exposed to the emanations from the
targets 2. These elements constitute "masks" in the
meaning of the invention.
3 0 Also, the mesh representation that is used need not
necessarily be uniform. Thus, the fineness of the mesh
for a given element may be adapted as a function of the
zones of the blade that it is desired to study.
By way of example, Figure 4C shows a nonuniform mesh
35 S1 of the blade 3A in order to study a section at 50%,
the zone of the section 17 being represented by a mesh
that is much finer than for the remainder 16 of the part.
In the presently described implementation, the
invention also provides the possibility of defining one
or more masks (step E30) serving as screens between the
targets 2 and the blade 3A during EBPVD deposition in
5 order to prevent certain zones of the blade 3A being
exposed.
These masks may be defined in two stages (digital
modeling and representing the masks as surface meshes),
~ in a manner similar to above-described steps El0 and E20.
i 10 In the example shown in Figure 4A, two masks 14 and
1 5 are defined by cylinders and they are coarsely
represented with the help of triangles. In a variant,
other models may be envisaged, e.g. with the help of
parallelepipeds.
1 5 After representing the parts 1, 2, and 3 as surface
meshes on the basis of the models M I , M2, and M3 (leading
i to three respective mesh models S1, 52, and S 3 ) , and
where appropriate, after representing the masks 14 and 15
defined in step E30 as surface meshes, those mesh
20 elements of the blade 3A that are exposed at a given
instant -t to the emanations from the targets 2 are
identified. In other words, the mesh elements that are
identified are not masked at the instant -t by an element
of the support tooling 1 or by the masks 14 and 1 5 (step
25 E 4 0 ) .
For this purpose, the processor 8 of the device 7
acts at instant -t to evaluate the position of each mesh
element of the blade 3A relative to the target 2 with the
help of the coordinates of the centers of the mesh
30 elements of the blade 3A and of the centers of the mesh
elements of the target 2 as defined respectively in the
models S1 and 52.
Then, for each mesh element m of the blade 3A and
for each mesh element m2 of the targets 2, it searches to
35 discover whether one or more mesh elements of the tooling
1 or of the masks 14 and 15 lie on the trajectory of a
ray passing through the center of the mesh element -m and
the center of the mesh element m2. This search is based
on using geometrical techniques (for identifying whether
a line intersects a predetermined surface) that are
themselves known and that are not described in detail
5 herein.
In the description below, the mesh elements of the
blade 3A that are exposed to emanations from the targets
2 at instant -t are written me.
In the presently described implementation, for each
10 mesh me identified during step E40, the thickness e(m,) of
the thermal barrier coating deposited by the targets 2 on
that mesh at that instant is then estimated (step E50).
To do this, in accordance with the invention, the
physical phenomena that take place during deposition of
15 the thermal barrier coating are treated as radiation
coming from the targets 2.
Thus, a model of radiation from the targets 2 is
advantageously used for estimating the thickness e(m,).
Each mesh element m2 of a target 2 is characterized by
20 its center and it emits ceramic particles. The radiation
model used herein defines the intensity of the radiation
or the intensity of particle emission from each target 2
(i.e. the flow rate of particles emitted by the target)
as a function of the direction of particle emission.
25 Advantageously, this model makes it possible to take
account of the position of the mesh element me oL Lhe
blade 3A under consideration relative to the target at
the instant -t.
Naturally, if the targets are of different natures,
30 a different radiation model (e.g. having different
parameters) may be envisaged for each target. In the
presently considered example, only one radiation model is
used.
More precisely, this model relies on the assumption
35 that each mesh element m2 of a target 2 emits particles
at a rate I(@) along a direction at an angle 0 relative
to the normal to the mesh element m2 (and expressed as a
number of particles per square meter per second), as
given by the following equation (1):
I(6') = I,[c0s(6')]~
where -n and I. designate predetermined constants.
In other words, the rate at which particles emitted
5 by the mesh element m2 reach a mesh element me of the
blade 3A depends on the position of the mesh element me
relative to the mesh element m2 at instant -t.
The constant I. represents the mean volume of ceramic
that is evaporated by the targets 2 per unit surface
10 area. In the presently described implementation, 10 is
determined theoretically from the upward speed -v of the
ceramic (c') and from the density p of the ceramic
evaporated by the targets 2, using the following equation
15 Where NAV designates Avogadro's number and M,
designates the molar mass of the ceramic particles
emitted by the targets.
The exponent -n gives the shape oE the beam of
particles emitted by the target 2. In this example it is
20 determined experimentally, on the basis of tests
performed using the tooling 1: the tests consist in
placing test plates at various distances from the targets
2 in order to measure the rates at which particles reach
the plates. The results of the tests are compared with
25 the values given by the radiation model of equation (I),
so as to adjust the value of the constant -n. An average
taken over all of the tests serves to deduce the value of
the constant n used for modeling the target 2.
It should be observed that for simplification
30 purposes, the radiation model described herein assumes
that evaporation from a target is constant as a function
of time and uniform over the entire target (i.e. over
each mesh element). The inventors have observed that
these assumptions are true in practice and on average
over an EBPVD deposition cycle, in particular given the
movements imparted to the blade 3A by the tooling 1.
Naturally, other models that are more elaborate
could be envisaged in variant implementations in order to
5 take account of variations in evaporation as a function
of time and/or of evaporation being nonuniform over the
target.
Starting from the radiation model defined in
equation (I), the flux O,,,, of particles emitted by a mesh
10 element m2 of the target 2 of surface area - s towards a
mesh element me of the blade 3A of surface area s' can be
written using the following equation (3):
cos B, cosQz
ds ds'
r
where r specifies the distance between the center of an
elementary surface area ds' of the mesh element me from
15 the center of an elementary surface area ds of the mesh
element m2, 01 designates the angle at which the
elementary surface area ds of the mesh element m2 emits a
ray relative to the normal to the elementary surface area
ds of the mesh element m2, and 02 designates the angle at
20 which the elementary surface area ds' of the mesh element
me receives the same ray relative to the normal to the
elementary surface area ds' of the mesh element me.
Figure 5 shows the distance - r, and the emission and
the reception angles 01 and 02.
2 5 With a fine mesh for the targets 2 and for the blade
3A, - s and s' are small compared with the distance - r, such
that equation (3) can be approximated by the following
equation (4) :
cos 8, cos8,
= I,, c0sne1 s S'
rZ
where - r specifies the distance between the center of the
30 mesh element me from the center of the mesh element m2, 01
designates the angle at which the mesh element m2 emits a
ray relative to the normal to the mesh element m2, and 82
designates the angle at which the mesh element me receives
the same ray relative to the normal to the mesh element
me.
Since the total flux 0,' of particles radiated by the
target 2 to the surface area s' of the mesh me is equal to
5 the sum of all of the contributions from the surface
areas - s of the meshes m2 of the target on the surface
area s', the following equation (5) applies:
ms. = 1 @,+,.
S
The processor 8 thus evaluates the to-tal flux 0,' of
particles radiated by the target 2 from equations (4) and
10 (5). For this purpose, the angles 81 and 82 and the
distance -r are calculated by the processor 8 in known
manner from the coordinates of the centers of the mesh
elements m2 and me as defined by the mesh models S2 and
S3. The dimensions of the surface areas - s and s' are
15 predefined and known from the surface meshing step E20.
On the basis of the total flux 0,' as evaluated in
this way, the processor 8 calculates the mass Mdeposit that
is deposited at lnstant - t (i.e. after an exposure of
duration - t to the radiation from the targets) on the
20 surface area s' of the mesh element me under consideration
by using the following equation (6):
Mrn
MdeposLt = @s' - N~~
Thereafter it evaluates the thickness e(m,) nt the
coating deposited at the lnstant -t on the mesh element me
of surface area s' with the help of following equation
25 (7):
In the presently described implementation, during
the estimation step E50, the processor 8 also applies a
multiplicative loss factor y to the thickness e(m,)
representing rays that are emitted by the targets 2 but
30 that do not reach the blade 3A, including when there are
no masks impeding the passage of these rays (these rays
are models of ceramic particles emitted by the targets
but that do not reach the blade 3A). This factor y
varies as a function of the distance traveled by the ray,
and therefore as a function of the position of the blade
3A relative to the target. It may be determined
5 experimentally by performing tests on real parts, in a
manner similar to determining the exponent -n.
At the end of step E50, the thickness estimated by
the processor 8 for the mesh element me of the blade 3A at
instant -t is given by y x e(m,). This thickness
10 represents the thickness of the ceramic thermal barrier
coating that is to be deposited by the targets 2 on the
mesh element me of the blade 3A at instant -t.
For a given section of a blade (e.g. section at
50%), Figure 6 shows thermal barrier coating thickness
15 values as estimated with the help of the method of the
invention for various different curvilinear abscissa
values. These values are represented by curve C1. In
the example shown, n = 3.5 and y = 0.667 (deduced from
testing).
2 0 By way of comparison, this figure also shows a curve
C2 of thickness values obtained by real tests. It should
be observed that the curve Cl'is very close to the curve
C2. The differences observed between the two curves may
be explained in particular by the number of points taken
25 into consideration for constructing the curve C2 being
less than the number of points that were estimaLed with
the help of the method of the invention for the curve C1.
The digital tool proposed by the invention thus makes it
possible quickly and simply to estimate the coating
30 thickness at many more points than can be measured during
tests on a real part.
The invention thus makes it possible to obtain
easily and quickly the thickness of the ceramic thermal
barrier coating that is to be deposited at any point on a
35 hot part of a gas turbine, such as the blade 3A, taking
predetermined technical constraints into consideration.
These constraints (e.g. the shape and the movements of
the tooling, the presence of masks, etc.) can easily be
specified, e.g. by means of a man machine interface ( M M I )
constituting an interface with the digital tool of the
invention.
5 Similarly, it is possible to develop an MMI for
facilitating viewing and using the results (thermal
barrier coating thickness). For example, such an MMI
could show the variation in the thickness of the thermal
barrier coating at various points on the hot part as a
10 function of time, with the distribution of such
thicknesses on different sections of the hot part, or
indeed with the distribution of thicknesses over the
entire hot part, etc.
CLAIMS
1. An estimation method for estimating the thickness of a
ceramic thermal barrier coating that is to be deposited
by physical vapor deposition from at least one target (2)
5 and onto a gas turbine hot part (3A) mounted on suppor-t
tooling, the method comprising:
a step (El0) of digitally modeling the geometrical
shape of the hot part and its movements relative to said
at least one target;
10 a step (E20) of representing the hot part as
modeled in this way as a surface mesh;
a step (E10) of digitally modeling the geometrical
shape of said at least one target;
a step (E20) of representing said at least one
15 target as modeled in this way as a surface mesh; and
a step (E50) of estimating, for at least one mesh
element of the hot part exposed to the radiation from
said at least one target during deposition of the
coating, a coating thickness to be deposited on said mesh
20 element at a given instant by using a radiation model
modeling radiation from said at least 'one target and
taking account of the position of said mesh element at
that instant relative to said at least one target, said
radiation model being defined for a mesh element of said
25 at least. one target by:
I(6') = I, [cos(B)]"
where:
I(6) designates the intensity of a ray emitted by
the mesh element of said at least one target in a
direction at an angle 6 relative to the normal to said
30 mesh element; and
n and I. designate - predetermined constants.
2. A method according to claim 1 further comprising:
a step (E30) of digitally modeling at least one
35 mask (14, 15) suitable for preventing a zone of the hot
part being exposed to the radiation from said at least
one target; and
a step (E30) of representing said at least one
mask as a surface mesh; and
5 wherein the mesh elements of the hot part that are
taken into consideration during the estimation step
comprise mesh elements that are not masked at the given
instant from said at least one target by mesh elements of
said at least one mask during deposition of the coating.
10
3. A method according to claim 2 wherein at least one
mask comes from an element of the support tooling for
supporting the hot part.
15 4. A method according to claim 3 further comprising:
a step (E10) of digitally modeling the support
tooling for supporting the hot part; and
a step (E20) of representing the support tooling
as modeled in this way as a surface mesh.
2 0
5. An estimation method according to any one of claims 1
to 4, wherein during the estimation step (E50), account
is also taken of a loss factor corresponding to rays that
are emitted by said at least one target during deposition
25 but that do not reach the hot part.
6. A method according to claim 4 or claim 5, wherein the
fineness of the surface mesh varies between the hot part
(3A), the target (2), the mask (14, 15), and/or the
30 support tooling.
7. A method according to any one of claims 1 to 6,
wherein during the step (E20) of surface meshing the
modeled hot part, the part is subjected to nonuniform
35 surface meshing.
8. A computer program including instructions for
executing steps of the estimation method according to any
one of claims 1 to 7, when said program is executed by a
computer.
5
9. A computer-readable data medium storing a computer
program including instructions for executing steps of the
estimation method according to any one of claims 1 to 7.
10 10. The use of the method according to any one of claims
1 to 7, for estimating a thickness of a ceramic thermal
barrier coating that is to be deposited by physical vapor
deposition from at least one target on a rotor blade of a
gas turbine.
15
11. The use of the method according to any one of claims
1 to 7, for estimating a thickness of a ceramic thermal
barrier coating that is to be deposited by physical vapor
deposition from at least one target on a st.ator blade of
20 a gas turbine.
12. A device (7) for estimating the thickness of a
ceramic thermal barrier coating that is to be deposited
by physical vapor deposition from at least one target (2)
25 and onto a gas turbine hot part (3A) mounted on support
tooling, the device comprising:
.means for digitally modeling the geometrical shape
of the hot part and its movements relative to said at
least one target;
30 .means for representing the hot part as modeled in
this way as a surface mesh;
.means for digitally modeling the geometrical shape
of said at least one target;
.means for representing said at least one target as
35 modeled in this way as a surface mesh; and
.means for estimating, for at least one mesh element
of the hot part exposed to the radiation from said at
least one target during deposition of the coating, a
coating thickness to be deposited on said mesh element at ;
a given instant by using a radiation model modeling
radiation from said at least one target and taking
5 account of the position of said mesh element at that
instant relative to said at least one target, said !
radiation model being defined for a mesh element of said ;
at least one target by:
I(@) = I
where :
10 I ( 6 ) designates the intensity of a ray emitted by
the mesh element of said at,least one target in a
direction at an angle 6 relative to the normal to said
mesh element; and
n and I. designate - predetern'ined constants.