GENERAL TECHNICAL FIELD
The present invention relates to computer aided design.
More specifically, it relates a method for modeling a part, in 5 particular
a blading.
STATE OF THE ART
10 The requirement of constantly improving the performances of pieces
of equipment, in particular of aeronautical equipment, for example rotors of
turbine engines (i.e., the assembly formed with a hub on which are attached
blades extending radially, as visible in Fig. 1a), has today imposed the use
of computer modeling tools.
15 These tools give the possibility of assisting with the design of parts by
automatically optimizing some of their characteristics. For a blading (i.e., the
assembly formed with the blades of a turbine engine disc, one fragment of
which is illustrated in Fig. 1b), the principle is to determine an
aeromechanical and/or acoustic geometrical optimum of laws of a blade of
20 the blading, in other words of one or several curves describing the value of
a physical quantity (examples will be given later on) along a section or a
height of the blade, in a given environment, by executing a large number of
simulation computations.
For this, it is necessary to parametrize the law for which optimization
25 is sought, i.e., to make it a function of N input parameters. The optimization
then consists of varying (generally randomly) these different parameters
under a constraint, until their optimum values are determined for a
predetermined criterion. A “smoothed” curve is then obtained by
interpolation from determined passage points.
30 The number of computations required is then directly related (linearly
or even exponentially) to the number of input parameters of the problem.
2
Many methods for parametrization of a law exist and it is in particular
possible to distinguish two large categories:
- A discrete model: The law is defined by the position of a plurality
of points (in practice 5 to 10 for a law over the height, and 50 to
200 for a section), displaced one by one during optimizat5 ion;
- A parametric model: The law is defined via mathematical curves
known in the literature, such as Bézier curves or NURBS curves
(non–uniform rational B–splines).
10 It is desirable to use a large number of parameters for improving by
as much the quality of a law (this is a major challenge for the designs of
blades), but such an approach is rapidly limited by the capacity and the
resources of present processors.
Even by using expensive supercomputers, the time required for
15 modeling a single law is consequent.
Another problem, it is seen that in the presence of a large number of
parameters problems occur: The determined laws actually have a too large
number of passage points to be observed, and the first curves obtained are
abnormally “rippled” (this is what is called the Runge phenomenon) and
20 cannot be utilized as such. They have to be reworked until they are
sufficiently smooth, which further increases the time required for obtaining
results.
For all these reasons, the parametric representations (using
25 mathematical curves) are quasi exclusively used since it is noticed that they
require up to five times less parameters for modeling a law with equal
quality.
However, it is seen that even with high level parametric
representations, the number of required parameters for having a sufficient
30 modeling quality for the present standards remains a problem (about 10
parameters).
3
It would be desirable to find a way of parameterizing and optimizing
the laws of a blade (or of any other part) which is still more economical in
terms of use of computer resources, which gives the possibility of
maintaining or even increasing the modeling quality, and this while limiting
the risks of occurrence of “rippled” curves5 .
PRESENTATION OF THE INVENTION
The present invention proposes according to a first aspect, a method
10 for modeling a part, the method being characterized in that it comprises
performing, by data processing means of a piece of equipment, steps of:
(a) parameterizing a curve of class C1 representing the value of
a physical quantity characterizing said part as a function of a
position along at least one portion of the part, the curve being
15 defined by:
a. two end points defining the extent of said portion of the
part;
b. at least one intermediate point positioned between the
end points;
20 c. at least two Bézier curves connected at said intermediate
point;
the parameterization being applied according to one or
several parameters defining said intermediate point;
(b) determining optimized values of said parameters of said
25 curve;
(c) outputting the determined values on an interface of said
piece of equipment.
Bézier curves are parametric polynomial curves defined as
30 combinations of N+1 elementary polynomials, so–called Bernstein
Polynomials: a Bézier curve is defined by the set of points 􀀃􀏃􀭒􀭧􀭀􀬴􀀅􀭧􀭒􁈺􀂖􁈻􀎮􀀓􀭧􀇡􀂖􀗐
4
􁈾􀍲􀇡􀍳􁈿, the 􀀃􀀅􀭧􀭒􁈺􀂖􁈻􀵌􀵫􀭒 􀭧
􀵯􀂖􀭒􁈺􀍳􀵆􀂖􁈻􀭒􀬿􀭧 being the N+1 Bernstein polynomials of
degree N.
The points {P0, P1…PN} are called “implicit” control points of the curve
and are the variables by which a law of a blade may be modeled by a Bézier
curve5 .
These points are called “implicit” since a Bézier curve may be seen
as the whole of the barycenters of the N+1 control points weighted with a
weight equal to the value of the Bernstein polynomial associated with each
control point. In other words, these points act like localized weights
10 attracting the curve generally without it passing therethrough (except for the
first and the last points, respectively corresponding to t=0 and t=1, and
certain cases of alignment of points).
Generally, in the known modeling techniques of a law using a Bézier
curve, the end control points P0 and PN of the curve used are fixed (they
15 define the extent of the portion of a part, in particular a blade of blading, on
which modeling will be applied), but the other points {P1…PN–1} have mobile
coordinates forming the input parameters for the optimization algorithm.
The present modeling method proposes parameterization of a law not
20 via implicit control points of a complex Bézier curve, but only via connecting
points (so–called “intermediate user control points (UCP)”) of a plurality of
elementary Bézier curves.
Further, unlike the prior art which only proposed a definition of the
control points by their coordinates (x, y), the present method
25 advantageously proposes also the use of criteria for example related to the
tangents as additional input parameters.
In other words, instead of modeling a law via the sole positions of a
large number of implicit control points, up to five parameters of a small
number of explicit control points are used.
30 Figs. 2a and 2b illustrate this principle by comparing the control
points required in a known method and in the method according to the
invention. The applicant thus noticed that this novel technique gives the
5
possibility, with twice as less parameters (or even in certain cases 60%
less), of obtaining an equivalent modeling quality. The time and/or the
computing power required are therefore substantially reduced.
Moreover, independently of the number of parameters, the number of
control points is as for it reduced by a factor three or even 5 en four (since the
intermediate control points concentrate a larger number of parameters). The
problem of the undesirable “ripple” effect resulting from a too large number
of passage points of the curve is thus considerably resolved.
10 According to other advantageous and non–limiting features:
􀁸 The parameter(s) defining an intermediate point are selected from an
abscissa of the point, an ordinate of the point, an orientation of a tangent to
the curve at the point and two tension coefficients each associated with a
half–tangent to the curve at the point;
15 􀁸 the parameterization is also applied according to one or several
parameters defining at least one of the end points;
􀁸 the parameter(s) defining an end point is(are) selected from an abscissa
of the point, an ordinate of the point, an orientation of the tangent to the
curve at the point and a tension coefficient associated with a half–tangent to
20 the curve at the point;
􀁸 a tension coefficient associated with a half–tangent to the curve at an
intermediate or end point depends on a value of a second derivative of the
curve in the vicinity of the point;
􀁸 said curve is defined by K–1 intermediate points ordered according to
25 the travel of said part portion, and by K Bézier curves, with 􀀃􀀎􀵒􀍴;
􀁸 the first Bézier curve is defined on the interval comprised between the
end point associated with the beginning of said part portion and the first
intermediate point, the Kth Bézier curve is defined on the interval comprised
between the K–1th intermediate point and the end point associated with the
30 end of said part portion;
6
􀁸 􀀃􀀎􀵒􀍵􀀃, the single Bézier curve or the ith Bézier curves each being
defined on an interval comprised between the i–1th intermediate point and
the ith intermediate point;
􀁸 each Bézier curve is entirely determined by the points defining its
extremitie5 s;
􀁸 the part is selected from among blading, a turbine engine platform, a
rearview mirror, a fin, a fixed or rotary wing, a tail, a fuselage, a propeller, a
nozzle, a vein, a fairing, and a turbine;
􀁸 the part is a blade, the part portion being a portion of a blade of the
10 blading;
􀁸 said portion of a blading’s blade is a sectional portion of the blade of the
blading or a height portion of the blade of the blading;
􀁸 said physical quantity characterizing said blading is selected from the
thickness of the blading, the skeleton, the skeleton angle law of a section of
15 a blade of the blading, the maximum thickness law, the maximum thickness
position law, the sag and dihedral angles, the stacking law, the
upstream/downstream angles of the blade of the blading along the height.
According to a second aspect, the invention relates to a method for
20 manufacturing a part, the method comprising the steps:
- applying the method according to the first aspect so as to at
least model one portion of the part;
- manufacturing said part according to the modeling of at least
one portion of the obtained part.
25
According to a third aspect, the invention relates to a piece of
equipment for modeling a part characterized in that it comprises data
processing means configured in order to implement:
- a module for parameterization of a curve of class C1 representing the
30 value of a physical quantity characterizing said part as a function of a
7
position at least along one portion of the part, the module defining a
curve by:
o two end points defining the extent of said portion of the part;
o at least one intermediate point positioned between the end
5 points;
o at least two Bézier curves connected at said intermediate
point;
the parameterization being applied according to one or several
parameters defining said intermediate point;
10 - a module for determining optimized values of said parameters of said
curve;
- a module for outputting the determined values on an interface of said
piece of equipment.
15 According to a fourth and a fifth aspect, the invention respectively
relates to a computer program product comprising code instructions for
executing a method according to the first aspect of the invention for
modeling a part; and a storage means which is legible by a computer
equipment on which a computer program product comprises code
20 instructions for executing a method according to the first aspect of the
invention for modeling a part.
PRESENTATION OF THE FIGURES
25 Other features and advantages of the present invention will become
apparent upon reading the description which follows of a preferential
embodiment. This description will be given with reference to the appended
drawings wherein:
- Fig. 1a described earlier represents an exemplary turbine engine;
30 - Fig. 1b described earlier illustrates an exemplary blade for which the
method according to the invention is applied;
- Figs. 1c–1d illustrate a section of a blade of a blading;
8
- Figs. 2a–2b described earlier compare the parameterization of a
curve in a method of the prior art and in a method according to the
invention;
- Fig. 3 illustrates a system for applying the method according to the
inventio5 n;
- Fig. 4 illustrates a curve used by the method according to the
invention;
- Figs. 5a–5e are examples illustrating the application of the invention
for a thickness law on a blade of blading;
10 - Figs. 6a–6e are examples illustrating the application of the invention
for a skeleton angle law on a blade of blading.
DETAILED DESCRIPTION
15 Generally, it will be understood that the present method is preferably
intended for modeling a turbine engine part, in particular a blading (any
blading), but it is not limited either to this part nor even to the field of
aeronautics. Any “part”, i.e., any industrially manufactured element and for
which the design complies with external physical constraints (in particular of
20 the aeromechanical and/or acoustic type, but also of hydrodynamic type,
etc.), may be modeled and optimized by means of this method.
In the following of the present description, the example of a blade of
blading will be taken, but one skilled in the art will know how to transpose
the method for modeling for example:
25 - in the field of turbine engines, the veins (inner and outer walls of each
of the flows), 3D platforms (non–axisymmetrical design of the
platform of a single–block bladed disc or of the ferrule of a rectifier).
With reference to Fig. 1a, by moving from the inlet of the turbine
engine to the outlet, exemplary areas of the turbine engine were
30 successively shown, for which modeling with the present method is
particularly advantageous: a vein portion said to be with “a swan
neck” (i.e., the vein portion positioned between the outlet of the low
9
pressure compressor and the inlet of the high pressure compressor),
the turbine (at the outlet of the combustion chamber), and the nozzle
(at the outlet of the turbine);
- in the automotive field (in particular Formula One), the rearview
mirrors, the fins5 ;
- in the field of aeronautics, the airfoil of an airplane, the tails, the
fuselage, the blades of a helicopter, the empennage of the tail of a
helicopter, the propellers of an airplane;
- in the space sector, the ejection nozzle of a rocket engine (and more
10 widely a design of any type of nozzles);
- in the railway sector, the front and the rear of a train;
- in the field of hydrodynamics, the propellers used in water treatment
tanks, the propellers of a fan, the propellers of a ship, the blades of a
turbine of a dam;
15 - and many other parts in various fields such as the shape of
handlebars of a bicycle or motorcycle.
Generally, it will be understood that the present method is particularly
suitable for modeling any part intended to be mobile with respect to a
contacting fluid, and the shape of which has an influence on the
20 performances, in particular vehicle parts (in the broad sense: land, sea, air,
space, vehicles etc.), and rotary industrial parts (propellers, turbines, etc.).
In the field of turbine engines, the part 1 is preferentially selected from a
blading, a platform, a vein and a nozzle (of the turbine engine).
25 In Fig. 1b, the blading 1 has a plurality of blades 2 (the base of one
of them is seen) extending radially from a central disc portion. Fig. 1c
illustrates a detail of a blade 2 on which a “section” of the blade 2 was
identified, which extends from a leading edge BA towards a trailing edge
BF. By section, is meant a cross–section of the blade 2.
30 Fig. 1d more specifically illustrates this BA–BF section (the concave–
convex profile is noted). The “chord” should be noted, i.e., the straight line
which connects the extremities of the section. This chord will be used as this
10
will be seen later as a mark for locating the points along the section. In Fig.
1d a middle line, the “skeleton” of the blade 2 is also seen. Orthogonally to a
section, the “height” of the blade 2 is found. Several physical quantities of
the blade are also illustrated and will be described later on. As explained,
these quantities may be modeled along a section or a height of the blade 5 2.
Such blading is modeled, during its design, via a piece of computer
equipment 10 of the type of the one illustrated in Fig. 3. It comprises data
processing means 11 (one or several processors), data storage means 12
(for example one or several hard disks), interface means 13 (consisting of
10 input means such as a keyboard and a mouse or a tactile interface, output
means such as a screen for displaying results). Advantageously, the piece
of equipment 10 is a supercomputer, but it will be understood that an
application on various platforms is quite possible.
Many criteria may be selected as criteria to be optimized during the
15 modeling of a blade or of another part. As an example, in the case of a
blade, maximization of the mechanical properties such as the resistance to
mechanical stresses, frequency responses of the blade, displacements of
the blade, aerodynamic properties such as the yield, the pressure rise, the
throughput capacity or the pumping margin, etc. may be attempted.
20
Parameterization
A step (a), applied by the data processing means 11 under control of
an operator, is a first step for parameterizing a curve representing the value
25 of a physical quantity characterizing said blading 1 (or of any other part) as
a function of a position along at least one portion of a blade 2 of the blading
1 (generally a portion of the part), in particular a portion of a section or a
height of the blade 2. By “sectional portion”, is meant all or part of the space
extending from the leading edge BA to the trailing edge BF. By “height
30 portion”, is meant all or part of the space extending from the proximal
extremity to the distal extremity of the blade 2.
11
In the continuation of the present description, the example of the
section of a blade 2 will be taken, but it will be understood that the method is
transposable to any defined sub–space of the part.
As explained earlier, the position along the curve is expressed
according to the chord length (in abscissas), and more specifically 5 the
“standardized” chord length, i.e., expressed between 0 and 1 when one
crosses the blade 2, to be covered in order to attain the (orthogonal)
projection of this point on the chord. This in other words corresponds to the
x coordinates which a point of the section would have in an orthonormal
10 reference system in which the point BA would have (0,0) as coordinates,
and the BF point (0,1). For example, a point of the section associated with a
normalized chord length of “0.5” is on the perpendicular bisector of the
chord. It is noted that as the curve may extend only on one (continuous)
portion of the section of the blade 2, the associated function is defined on a
15 sub–interval of [0, 1].
However, it will be understood that the invention is by no means
limited to the expression of a curve representing the value of a quantity
versus a chord length, and that other marks are possible.
20 This curve representing the value of a physical quantity should be
understood as the modeling of a law of this physical quantity (as such it will
be designated as “modeling curve” in order to distinguish it from the Bézier
curves in terms of terminology). Said physical quantity may be any quantity
having an aeromechanical and/or acoustic meaning for the design of parts,
25 and mention will be made as non–limiting examples in the case of blading,
of:
- a function of the chord (sectional vision)
o Thickness law
o Skeleton angle law
30 - A function of the blade height (3D vision)
o Max thickness, position of the max thickness
o Sag and dihedral laws (BA, BF, …)
12
o Stacking law of the sections
o Upstream/downstream angle laws (􀈕1, 􀈕2)
Associated examples will be described later on.
In the case when the part 1 is a nozzle, the physical quantity may be
the section of the nozzle, which allows definition of the minimum 5 um section of
the nozzle, controlling the change in the effective Mach number in the
nozzle, etc. In the case of a vein, the physical quantity may be the section of
the vein, the section ratio (inlet section / outlet section), the slowing down
(which is the ratio between the outlet speed and the inlet speed. This
10 parameter inter alia gives the possibility of estimating the ease with which
the fluid will be able to follow the required angle variations).
The modeling curve is a regularity class of at least C1, i.e., it
corresponds to a continuous function and of at least one continuous first
derivative on its definition space (the portion of the part). The significance of
15 this condition will be seen further on. In practice, the obtained curve is C􀂒
piecewise (functions which may be indefinitely derived on each interval),
with continuity of the curve and of the derivative at the connections (the
intermediate control points). It will be understood that these are minimum
conditions and that the curve may quite be for example C􀂒 over the whole of
20 its definition space.
The curve is defined by means of its control points. Like in the prior
art, two end user control points UCP0 and UCPK are fixed and define the
extent of the portion of the part (i.e. the definition domain of the curve). The
modeling curve further comprises at least one intermediate user control
25 point UCPi, 􀝅􀗐􀛤􀍳􀇡􀜭􀵆􀍳􀛥 positioned between both of these two end points
UCP0 and UCPK.
The intermediate point(s) are “explicit” control points since the curve
passes through them. Indeed, the latter comprises at least two Bézier
curves connected at said intermediate point.
30 As this is seen in Fig. 4 for example, the modeling curve may only
consist of a sequence of Bézier curves, each extending between an end
13
point UCP0, UCPK and an intermediate point UCPi, or between two
intermediate points UCPi and UCPi+1.
In other words, all the (end or intermediate) user control points UCP0,
UCP1 … UCPK–1, UCPK of the curve are end control points P0, PN of a
Bézier curv5 e.
The fact that the curve is of class C1 imposes that each intermediate
point UCPi ensures continuity including on the derivative (same tangent).
As this will be seen in the examples, the use of a single intermediate
point UCP1 (and therefore of two Bézier curves) is sufficient for defining very
10 satisfactorily the curve representing a law. However, it will be understood
that the method may be generalized to the use of K–1 (with 􀀎􀵒􀍴)
intermediate points (UCPi, 􀝅􀗐􀛤􀍳􀇡􀜭􀵆􀍳􀛥) ordered according to the travel of
said part portion 1 (a blade 2 in the case of blading), i.e., K Bézier curves
(one between each pair of control points {UCPi; UCPi+1}).
15 In every case, the modeling curve comprises at least two “end”
Bézier curves, i.e., having as an extremity one of the two end user control
points UCP0 and UCPK : the first Bézier curve is defined on the interval
comprised between the end point UCP0 associated with the beginning of
said part portion 1 and the first intermediate point UCP1, and the Kth Bézier
20 curve (the other end curve) is defined on the interval comprised between the
K–1th intermediate point UCPK–1 and the end point UCPK associated with the
end of said part portion 1.
In the case of at least two intermediate points UCPi, in other words
when 􀜭􀵒􀍵, the modeling curve comprises «intermediate» Bézier curves:
25 the ith (􀗊􀝅􀗐􀛤􀍴􀇡􀜭􀵆􀍳􀛥) Bézier curves are each defined on the interval
comprised between the i–1th intermediate point UCPi–1 and the iith
intermediate point UCPi.
Parameters of a user control point
30
The processing parameterizes the modeling curve not according to
the parameters of the implicit control points of a Bézier curve, but according
14
to parameters of intermediate control points (and optionally end control
points) defining extremities of Bézier curves forming the modeling curve.
In particular, each Bézier curve may be entirely determined by the
UCP points defining its extremities. In other words, the parameters of the
UCP points (in terms of coordinates and of derivatives) 5 es) are used as
boundary conditions for computing with the data processing means 11 the
coordinates of the implicit control points of the different Bézier curves, which
are selected with a sufficient minimum degree in order to meet these
boundary conditions. Step (a) then comprises the definition of the implicit
10 points of the Bézier curves according to the parameters of the UCP points
forming their ends.
The parameter(s) defining an intermediate point UCPi is(are) thus
selected from among an abscissa of the point, an ordinate of the point, an
orientation of the tangent to the curve at the point and two tension
15 coefficients each associated with a half–tangent to the curve at the point.
Being aware that the curve is of class C1 (continuous derivative), the
orientation of the tangent should be the same on either side of an
intermediate point UCPi. On the other hand, the “length” of both half–
tangents may be different on either side of the point, a length which
20 expresses the propensity of each Bézier curve of “adhering” to the tangent
on either side of the point. This is what are the “tension coefficients”
mentioned earlier model.
Practically, each tension coefficient associated with a half–tangent to
the curve at an intermediate point depends on a value of a second
25 derivative of the curve in the vicinity of the point. Indeed, the value of the
second derivative in the vicinity of the control point expresses the “rate” with
which the curve moves away from the tangent.
And the fact that the modeling curve is not necessarily a class C2
allows discontinuities of a second derivative at the intermediate points.
30 In the case of a parameterized end point UCP0 or UCPK, the
parameter(s) defining this end point is(are) selected from an abscissa of the
point, an ordinate of the point, an orientation of the tangent to the curve at
15
the point and a tension coefficient associated with a half–tangent to the
curve at the point.
In other words, only the half–tangent in the definition domain of the
curve (the one on the right for UCP0 and the one on the left for UCPK) may
5 be taken into account.
It should be noted that all the parameters mentioned earlier are not
necessarily actually used (in particular for the end points). Indeed, in the
majority of the cases, one or several of these parameters (an abscissa of
10 the point, an ordinate of the point, an orientation of the tangent to the curve
at the point and two tension coefficients each associated with a half–tangent
to the curve at the point) have a predetermined value set by the user, and
are therefore not used as “variables” for the continuation of the method.
15 Examples
Figs. 5a–5e illustrate different curves which may be used for
modeling the law of a quantity called “skeleton angle law (􀈕)”, which
corresponds to the derivative of the skeleton of the section of the blade 2
20 (see Fig. 1d).
In Fig. 5a, the law is modeled by using a single intermediate point
UCP1, with a greater tension on the right as compared with on the left.
In Fig. 5b, the parameter taken into account is the coordinate y of the
intermediate point UCP1. Three instances of the curve corresponding to
25 three different values of this parameter are illustrated.
In Fig. 5c, the parameter taken into account is the orientation of the
tangent to the curve at the intermediate point UCP1 (in other words, the
value of the derivative at this point). Three instances of the curve
corresponding to the three different values of this parameter are illustrated.
30 In Fig. 5d, two parameters are taken into account, i.e., the tension
coefficients each associated with a half–tangent to the curve at the
16
intermediate point UCP1. Three instances of the curve corresponding to
three pairs of values for these parameters are illustrated.
Fig. 5e represents an alternative in which two intermediate points
UCP1 and UCP2 are used.
5
Figs. 6a–6e illustrate various curves which may be used for modeling
the law of another quantity called a “thickness law”, which simply
corresponds to the thickness of the blade 2 along the section.
In Fig. 6a, the law is modeled by using a single intermediate point
10 UCP1, with a horizontal tangent (local maximum).
In Fig. 6b, the parameter taken into account is the co–ordinate y of
the intermediate point UCP1. Three instances of the curve corresponding to
the three different values of this parameter are illustrated.
In Fig. 6c, the parameter taken into account is the coordinate x of the
15 intermediate point UCP1. Three instances of the curve corresponding to the
three different values of this parameter are illustrated. The adaptation of
both Bézier curves on either side of the intermediate point UCP1 is noted so
as to observe the conditions imposed by the parameters of this point.
In Fig. 6d, again both tension coefficients each associated with a
20 half–tangent to the curve at the intermediate point UCP1 are taken into
account. Three instances of the curve corresponding to the three pairs of
values for these parameters are illustrated. A curve is notably noted, for
which the coefficients are particularly unbalanced, whence a particularly
visible asymmetry of the curve.
25 Fig. 6e illustrates a highly advanced alternative in which three
intermediate points UCP1, UCP2 and UCP3 are used.
Optimization and output
30 According to a second step (b), the method comprises a step for
determining with the data processing means 11 optimized values (and if
17
possible optimum values) of said parameters of said curve. This is an
optimization step.
Many techniques for applying this step are known to one skilled in the
art, and for example it is simply possible to vary pseudo–randomly the
variable selected parameters while carrying out simulations for determini5 ng
these optimized values (i.e., for which the selected criterion is maximized) of
the parameters of the control points UCPi. The invention is however not
limited to this possibility.
In a last step (c), the determined values of the parameters are output
10 by the interface means 13 of the piece of equipment 10 for use, for example
by displaying the modeling curve in which the parameters are set to these
optimized values.
Alternatively, the interface means 13 may only display these
numerical values.
15
Manufacturing method and part
Once it is modeled, the part 1 may be manufactured. A method for
manufacturing a part 1 (in particular a blading) is thus proposed, the method
20 comprising the steps:
- Applying the method according to the first aspect so as to
model at least one portion of the part 1 (a portion of a blade 2
of the blading);
- Manufacturing said part 1 according to the modeling of said at
25 least one portion of the obtained part 1.
A blading 1 comprising a plurality of blades 2, thereby produced, may
be obtained. It has the desired optimum physical properties.
30 Equipment
18
The piece of equipment 10 (illustrated in Fig. 4) for applying the
method for modeling a part 1 comprises data processing means 11
configured so as to implent:
- a module for parameterizing a curve of class C1 representing the
value of a physical quantity characterizing 5 ng said part 1 as a fubnction
of a position along at least one portion of the part 1, the module
defining a curve by:
o Two end points UCP0, UCPK defining the extent of said portion
of the part 1;
10 o At least an intermediate point UCPi, 􀝅􀗐􀛤􀍳􀇡􀜭􀵆􀍳􀛥 positioned
between the two end points UCP0, UCPK ;
o At least two Bézier curves connected at said intermediate
point;
the parameterization being applied according to one or several
15 parameters defining said intermediate point;
- a module for determining optimized values of said parameters of said
curve;
- a module for outputting the determined values on an interface 13 of
said piece of equipment 10.
20
Computer program product
According to a fourth and a fifth aspect, the invention relates to a
computer program product comprising code instructions for executing (on
25 data processing means 11, in particular those of the piece of equipment 10)
a method according to the first aspect of the invention for modeling a part 1,
as well as storage means legible by a piece of computer equipment (for
example a memory 12 of this piece of equipment 10) on which is found this
computer program product.

I/We Claim:
1. A method for modeling a part (1), the method being characterized
in that it comprises performing, by data processing means (11) of a piece of
equipment (10), steps of5 :
(a) parameterizing a curve of class C1 representing the value of a
physical quantity characterizing said part (1) as a function of a
position along at least one portion of the part (1), the curve being
defined by:
10 a. two end points (UCP0, UCPK) defining the extent of said
portion of the piece (1);
b. at least one intermediate point (UCPi, 􀝅􀗐􀛤􀍳􀇡􀜭􀵆􀍳􀛥) positioned
between the end points (UCP0, UCPK);
c. at least two Béziers curves connected at said intermediate
15 point;
the parameterization being applied according to one or several
parameters defining said intermediate point;
(b) determining optimized values of said parameters of said curve;
(c) outputting determined values on an interface (13) of said piece of
20 equipment (10).
2. The method according to claim 1, wherein said parameter(s)
defining an intermediate point (UCPi) is(are) selected from an abscissa of
the point, an ordinate of the point, an orientation of the tangent to the curve
25 at the point and two tension coefficients each associated with a half–tangent
to the curve at the point.
3. The method according to one of claims 1 and 2, wherein the
parameterization is also applied according to one or several parameters
30 defining at least one of the end points (UCP0, UCPK).
20
4. The method according to claim 3, wherein the parameter(s)
defining an end point (UCP0, UCPK) is(are) selected from an abscissa of the
point, an ordinate of the point, an orientation of the tangent to the curve at
the point and one tension coefficient associated with a half–tangent to the
curve at the point5 .
5. The method according to one of claims 2 and 4, wherein a tension
coefficient associated with a half–tangent to the curve at an intermediate or
end point depends on a second derivative value of the curve in the vicinity
10 of the point.
6. The method according to one of claims 1 to 5, wherein said curve
is defined by K–1 intermediate points (UCPi, 􀝅􀗐􀛤􀍳􀇡􀜭􀵆􀍳􀛥) ordered along
the travel of said portion of the part (1), and K Bézier curves, with 􀜭􀵒􀍴.
15
7. The method according to claim 6, wherein the first Bézier curve is
defined on the interval comprised between the end point (UCP0) associated
with the beginning of said portion of the part (1) and the first intermediate
point (UCP1), the Kth Bézier curve is defined on the interval comprised
20 between the K–1th intermediate point (UCPK–1) and the end point (UCPK)
associated with the end of said portion of the part (1).
8. The method according to claim 7, wherein 􀜭􀵒􀍵, the ith Bézier
curve(s) (􀝅􀗐􀛤􀍴􀇡􀜭􀵆􀍳􀛥) each being defined on the interval comprised
25 between the i–1th intermediate point (UCPi–1) and the ith intermediate point
(UCPi).
9. The method according to one of claims 1 to 8, wherein each Bézier
curve is entirely determined by the points (UCP) defining its extremities.
30
10. The method according to one of claims 1 to 9, wherein the part (1)
is selected from a blading, a turbine engine platform, a rearview mirror, a fin,
21
a fixed or rotary wing, a tail section, a fuselage, a propeller, a nozzle, a vein,
a fairing and a turbine.
11. The method according to claim 10, wherein the part (1) is a
blading, the part portion (1) being a portion of a blade (2) of the 5 e blading.
12. The method according to claim 11, wherein said blade portion (2)
of blading (1) is a sectional portion of the blade (2) of the blading (1) or a
height portion of the blade (2) of the blading (1).
10
13. The method according to claim 12, wherein said characteristic
physical quantity of said blading (1) is selected from among the thickness of
the blading (1), the skeleton, the skeleton angle law of a section of the blade
(2) of the blading (1), the maximum thickness law, the position law of the
15 maximum thickness, the sag and dihedral angles, the stacking law, the
upstream/downstream angles of the blade (2) of the blading (1) along the
height.
14. A method for manufacturing a part (1), the method comprising the
20 steps:
- performing the method according to one of claims 1 to 13 so as to
model at least one portion of the part (1);
- manufacturing said part (1) according to the modeling of the at least
one portion of the part (1) obtained.
25
15. A piece of equipment (10) for modeling a part (1), characterized in
that it comprises data processing means (11) configured for implementing:
- a module for parameterization of a curve of class C1 representing
the value of a physical quantity characterizing said part (1) as a
30 function of a position along at least one portion of the part (1), the
module defining a curve by:
22
o two end points (UCP0, UCPK) defining the extent of said
portion of the part (1);
o at least one intermediate point (UCPi, 􀝅􀗐􀛤􀍳􀇡􀜭􀵆􀍳􀛥) positioned
between the end points (UCP0, UCPK);
o at least two Bézier curves connected at said intermediat5 e
point;
the parameterization being applied according to one or several
parameters defining said intermediate point;
- a module for determining optimized values of said parameters of
10 said curve;
- a module for outputting the determined values on an interface (13)
of said piece of equipment (10).
16. A computer program product comprising code instructions for
15 executing a method according to one of claims 1 to 13 for modeling a part
(1).
17. A storage means which is legible by a piece of computer
equipment, on which a computer program product comprises code
20 instructions for executing a method according to one of claims 1 to 14 for
modeling a part (1).