FR3147299A1 - Automated weaving process with optimized shed opening - Google Patents

Abstract

A method for automated weaving of a woven structure (30) by means of a weaving machine (1), comprising the insertion of a weft thread when opening a shed of warp threads, and preliminary steps of optimization, by an optimization tool (20), of an objective function having a first member evaluating a balance of said warp threads when opening the shed, and a second member evaluating constraints specific to the weaving machine (1). This optimization comprises the determination of a set of opening parameters minimizing, at least locally, said objective function, and this set of opening parameters is used to parameterize the weaving machine (1). Figure for the abstract: Fig. 1

Description

Automated weaving process with optimized shed opening FIELD OF THE INVENTION

The present invention relates to an optimization method for the automated weaving of woven structures, in particular three-dimensional woven structures.

A possible field of application for such woven structures is the aeronautical industry.

This is indeed looking for solutions to meet increasing environmental requirements, particularly with regard to reducing the consumption of fossil fuels. The use of lighter composite materials for the design of aircraft makes it possible in particular to reduce their consumption and therefore contribute to reducing the ecological impact.

Various parts of aircraft are affected by composite materials, for example fan blades in turbomachines.

Indeed, turbomachine blades must cope with significant mechanical and thermal constraints, in addition to meeting weight and size constraints. It has therefore been proposed to replace, on certain aircraft models, metal fan blades (typically titanium) with blades made of composite material based on woven 3D reinforcements. Such three-dimensional woven structures for fan blades have been proposed in several documents, such as French patent FR3085417.

But three-dimensional woven structures can find other applications in the aeronautical field (brake bars for landing gear, etc.) or in many other fields.

The production of three-dimensional woven structures involves the use of weaving machines, or looms. These allow the automation of the weaving itself, but require an upstream parameterization phase which is generally manual and tedious. This parameterization concerns in particular the definition of the positioning of each of the heddles in the high position (upper shed) and in the low position (lower shed).

Generally speaking, the design of a composite material with woven reinforcement is a complex task that requires, in particular, the pooling of diverse skills. In particular, it may require several iterations of exchanges between a design office that provides mechanical specifications of the woven structure and the textile production department that must produce the specified structure with the technical means available, in particular according to the specifications of the weaving machine.

A good quality woven structure is thus the result of an optimized compromise between the characteristics of the material requested (warp/weft ratio, volume fraction of fiber, etc.) and the constraints required by weaving (armors, count of available threads, position in the harness, etc.).

Once the geometry of the desired woven structure has been defined, it is necessary to ensure the correct setting of the weaving machine so that the weaving provides a good quality result. In particular, this involves defining the weaving speed, the advancement of the preform, the positioning of the heddles in high and low positions (high and low sheds, respectively).

Among all the parameters to be adjusted on a weaving machine, the shed opening is of critical importance.

Indeed, a correct shed opening is necessary so that the lance is inserted in the right place in the shed without impacting the warp threads. If this were not the case, the textile preform produced would not comply with the specifications. It is therefore necessary to open the shed sufficiently so that the weft threads are inserted in the right places between the warp threads.

In addition, it is necessary to ensure a good balance between the upper and lower sheds, so that the warp tension remains correct and also to avoid weaving errors. In other words, it is necessary to determine the shed opening, that is to say the high and low positions of each of the machine's eyelets.

It is therefore understandable that this phase of manually determining the shed opening parameters is long. It therefore implies a substantial extension of the production time. The time required to correctly define the shed opening can be estimated at around 1 week for a complex woven structure.

It can also involve human errors, which can penalize the quality of the structure produced or require a return to the parameterization phase, thus further extending the production time.

There is therefore a need to improve current state-of-the-art proposals.

The invention aims to automate at least part of the parameterization of the weaving machine in order to minimize the risk of errors and to speed up the production of the textile structure, once it has been specified by a design office.

This setting aims in particular to determine the crowd opening parameters (positions of the eyelets in high and low positions).

For these purposes, according to a first aspect, the present invention can be implemented by a method of automated weaving of a woven structure by means of a weaving machine, this method comprising the insertion of a weft thread when opening the shed of warp threads, and prior steps of optimizing an objective function having a first member evaluating a balance of said warp threads when said shed opening, and a second member evaluating constraints specific to said weaving machine, said optimization comprising determining a set of opening parameters minimizing, at least locally, said objective function, and said set of opening parameters being used to parameterize said weaving machine.

• ladite optimisation comprend de déterminer un optimum global de ladite fonction objectif en introduisant une perturbation aléatoire.
• ladite optimisation utilise un algorithme de Basin-hopping.
• lesdits paramètres d’ouverture définissent une première droite déterminant une ouverture supérieure de ladite foule, et une seconde droite déterminant une ouverture inférieure de ladite foule. D’une façon très générale, les paramètres d’ouverture de foule peuvent spécifier le positionnement des lices (et donc des œillets) en position supérieure et en position inférieure.
• ledit équilibre des fils de chaîne est évalué par des différences d’élongation entre les fils de chaîne d’une ouverture supérieure de ladite foule, et d’une ouverture inférieure de ladite foule.
• ledit second membre évalue une hauteur entre une ouverture supérieure et une hauteur inférieure de ladite foule.
• ledit second membre évalue des distances entre lesdits fils de chaîne et une lance de ladite machine à tisser et/ou un battant de ladite machine à tisser.

According to preferred embodiments, the invention comprises one or more of the following features which may be used separately or in partial combination with each other or in total combination with each other:

• said optimization comprises determining a global optimum of said objective function by introducing a random perturbation.
• said optimization uses a Basin-hopping algorithm.
• said opening parameters define a first straight line determining an upper opening of said shed, and a second straight line determining a lower opening of said shed. In a very general manner, the shed opening parameters can specify the positioning of the heddles (and therefore of the eyelets) in the upper position and in the lower position.
• said warp yarn balance is assessed by differences in elongation between the warp yarns of an upper opening of said shed, and of a lower opening of said shed.
• said second member evaluates a height between an upper opening and a lower height of said crowd.
• said second member evaluates distances between said warp threads and a lance of said weaving machine and/or a beater of said weaving machine.

According to another aspect, there is provided a computer program comprising instructions for implementing a method as previously described.

According to yet another aspect, there is provided a weaving tool comprising a weaving machine of a woven structure adapted for the insertion of a weft thread during the opening of a shed of warp threads, and a tool for optimizing an objective function comprising having a first member evaluating a balance of said warp threads during said shed opening, and a second member evaluating constraints specific to said weaving machine, said optimization comprising determining a set of opening parameters minimizing, at least locally, said objective function, and said set of opening parameters being used to parameterize said weaving machine.

Other features and advantages of the invention will become apparent from reading the following description of a preferred embodiment of the invention, given by way of example and with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying drawings illustrate the invention:
There schematically represents a context of use of the method according to embodiments.
There schematically represents an example of a weaving machine.

There represents a flowchart of an exemplary implementation of an automated weaving method of a three-dimensional woven structure according to the invention.

There schematically illustrates a linear modeling of the upper and lower openings of the crowd.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

There schematically illustrates a context of use of an automated weaving process.

In the example of this figure, a weaving machine (or loom) 1 produces a woven structure 30 which is typically a three-dimensional woven structure. This three-dimensional woven structure can be used as reinforcement for composite materials.

These composite materials can be used in particular in the aeronautics sector for fan blades in turbomachines, brake bars for landing gear, and, more generally, any type of thick three-dimensional textile preforms.

This woven structure can be a three-dimensional part with a high thickness, in particular with a thickness greater than 10 or 20 mm. The automatic shear opening optimization process is particularly advantageous for complex woven structures and in particular for three-dimensional parts with a high thickness.

The weaving machine 1 can use a set of parameters 43 provided by an optimization tool 20.

This optimization tool may be a computer or any information processing device including virtualized on a platform (for example of the “cloud computing” type), adapted to this specific optimization task. This adaptation may consist of the deployment of a specific software application.

The optimization tool 20 and the weaving machine 1 can communicate by means of telecommunications networks (not shown in the figure). This may be a local network, such as Ethernet, Wi-Fi, Bluetooth, etc., but these telecommunications networks may also include longer-distance networks, in particular in the case where the optimization tool is delocalized and, for example, transferred to a remote platform. These telecommunications networks may include a so-called “Internet” network.

The optimization tool can be based on data 41 provided by a design office and specifying the woven structure 30 to be produced, and on data provided 42 relating to the weaving machine 1.

Based on these data 41, 42, the optimization tool 20 can provide a set of parameters 43 to the weaving machine 1 which allow it to produce the woven structure 30 while minimizing weaving errors. These parameters 43 include the parameters fixing the opening of the shed in the weaving machine 1.

In addition, the optimization tool 20 makes it possible to avoid the manual setting of the shed opening, by automatically determining these. Once the specifications of the woven structure 30 to be produced are known, it is thus possible to trigger the production by the loom 1 of the woven structure 30 more quickly and with less risk of errors.

On the is schematically represented such a weaving machine 1. This diagram is extremely simplified and aims to explain the elements useful for understanding the automated weaving process presented.

Typically, a set of warp threads, 7a, 7b, 7c, 7d, are stretched between beams (not shown). In the example in the figure, the warp threads are stretched horizontally (low-warp loom), but they can also be stretched vertically (high-warp loom). In the example, the warp threads are unwound from a beam located on the right of the figure, and form a preform 2, on the left of the figure.

Each warp (or pick) thread, 7a, 7b, 7c, 7d, passes through an eyelet, respectively 5a, 5b, 5c, 5d, of a respective heddle 6a, 6b, 6c, 6d.

The heddles are typically made of wire or twine. They are mounted in frames, or blades, suspended from the harness 8 of the loom 1. Each frame, or blade, can be individually actuated in translation perpendicular to the plane of the warp threads.

In the example in the figure, only 4 warp yarns and 4 heddles are shown for clarity of the exposition and the figure, but it is obvious that a much larger number of yarns and heddles are present for the production of a woven textile.

By raising or lowering the heddles, the corresponding warp threads are moved up or down from their nominal horizontal positions.

So, on the , the heddles 6a and 6b are translated upwards, which spreads the warp threads 7a, and 7b upwards. The heddles 6c, 6d are translated downwards and spread the corresponding warp threads 7c, 7d downwards.

Thus, the whole of the warp threads, or shed, is divided into two parts: a part, or shed, high 10a, and a part, or shed, low 10b.

This opening of the shed allows a weft thread to be inserted using an insertion device such as a lance 9. This weft thread is inserted perpendicular to the warp threads.

A flap formed of upper (or upper flap) 12a and lower (or lower flap) 12b elements and a comb (not shown) can then pack the weft thread against the previous weft threads in order to form the weft line 3 of the preform 2. The weft line is called the zone between this last inserted weft thread and the start of the beam around which the preform 2 can be wound.

This process is iterated over time: at each time, a different set of heddles can be raised and lowered, according to an ordering dependent on the type of woven structure being produced: plain, twill, satin, etc. At each opening, a weft thread is inserted. Preform 2 is therefore formed by interlacing a succession of weft threads with the sheet of warp threads.

In addition, in the case of a three-dimensional woven structure, binding threads are inserted in order to hold the different woven layers together.

This preform 2 forms a woven textile 30.

This woven structure can then be used to form a composite material, for example by embedding it in a matrix material.

It is proposed to automatically determine the opening of the shed, i.e. the angles formed by the warp threads 7a, 7b, 7c, 7d with the horizontal plane, when the heddles are translated upwards and downwards. In other words, determining the opening of the shed amounts to determining the excursion of the heddles upwards and downwards.

As previously stated, these angles should be large enough so that the lance 9 does not risk hitting the warp threads 7a, 7b, 7c, 7d. But they should not be too large so that, on the one hand, these warp threads do not risk hitting the leaves 12a, 12b and, on the other hand, to avoid imbalances in the tension of the warp threads between the upper and lower sheds.

There illustrates a flowchart of an exemplary implementation of the automated weaving method 100.

In a step 110, the optimization tool 20 is provided with data 41 specifying the woven structure 30 to be produced, and with provided data 42 relating to the weaving machine 1.

In a step 120, the optimization tool 20 can determine an objective function.

An objective function is a function that serves as a criterion for determining a solution to an optimization problem. It associates a value with an instance of an optimization problem. The goal of the optimization problem is then to minimize or maximize this function, ideally to find a global optimum.

This objective function has a first member evaluating a balance of the warp threads during warp opening. This balance corresponds to that between the upper and lower sheds.

It also includes a second member evaluating constraints specific to the weaving machine.

The problem is thus formulated as an optimization (of the first member) under constraint (second member) in which we seek to determine a set of opening parameters minimizing, at least locally, this objective function.

The opening parameters are chosen to allow one-to-one parameterization of the loom.

Also, the parameters are chosen to form a relatively restricted optimization space in order to seek an understanding of the combinatorics of the problem and the precision of adjustment of a loom.

Considering these elements, it was chosen to make the hypothesis that the opening of the upper sheds 10a and lower sheds 10b form a linear configuration in the depth of the harness 8. This makes it possible to model the shed opening by two independent straight lines (one for the upper shed and one for the lower shed) and by the positioning of the preform in height.

The upper shed is the set of warp threads that are “open upwards”, i.e. passing through raised heddle eyelets in the upper half of the harness, and the lower shed is the set of warp threads that are “open downwards”, i.e. passing through lowered eyelets in the lower half of the harness.

In other words, the upper crowd corresponds to the upper opening of the crowd, and the lower crowd corresponds to the lower opening of that same crowd.

Each straight line can be modeled by two parameters, for example a vertical position of the corresponding eyelet on a given rail (for example of the rail closest to the face), and a slope coefficient.

There illustrates this modeling.

In this figure, preform 2 has 3 planes, or layers, of preform P ₀ , P ₂ , P ₂ .

Each plane corresponds to a warp thread belonging to the upper shed and a warp thread belonging to the lower shed. Each plane therefore corresponds to a row of heddles in the depth of the harness.

A wire can be modeled in a high position and a low position, and the optimization then aims to minimize the maximum difference between the high and low positions of this wire.

According to one embodiment, a set of insertions can be considered. In this set, some threads will always remain in the high shed, others in the low shed, and others will occupy the high shed and the low shed. The optimization can be implemented only for these latter threads: it can then be sought to minimize the maximum gap between the high and low positions of these threads alone.

The re-entry is defined by the user: the user can specify the positioning of the warp threads of the preform in relation to the positions available on the upper and lower rights.

Thus, point A in the figure is the end of two warp threads, one coming from the upper shed and passing through eyelet B, and the other coming from the lower shed and passing through eyelet C.

• y_S: ordonnée de l’œillet le plus haut, correspondant à la lisse H₀la plus proche de la façure ;
• a_S: coefficient directeur
• x_iet x₀: abscisse de, respectivement, un œillet dans i de la foule supérieure, et de l’œillet d’ordonnée y_S.

The line defining the upper crowd can be written: y _S +a _S (x _i -x ₀ ), with

• y _S : ordinate of the highest eyelet, corresponding to the H ₀ rail closest to the face;
• a _S : slope coefficient
• x _i and x ₀ : abscissa of, respectively, an eyelet in i of the upper shed, and of the eyelet of ordinate y _S .

• y_I: ordonnée de l’œillet le plus bas, correspondant à la lisse H₀la plus proche de la façure ;
• a_I: coefficient directeur

The line defining the lower crowd can be written: y _I +a _I (x _i -x ₀ ), with

• y _I : ordinate of the lowest eyelet, corresponding to the H ₀ rail closest to the face;
• a _I : slope coefficient

y ₀ can be the ordinate, or height, of the preform. For example, it can be the vertical position of the midplane of preform 2.

Optimizing the crowd opening therefore comes down to finding the optimized values for this 5-tuple vector [y ₀ , y _S , a _S , y _I , a _I ].

Thus, thanks to the proposed modeling, the number of crowd opening parameters (initially 2 parameters per eyelet) is reduced to 5 parameters.

Knowing these opening parameters defining two lines, we can directly determine the translations to be carried out for each rail in order to obtain this opening.

As seen previously, the objective function can be formulated as the balance between the upper shed and the lower shed of the warp threads during the insertion of a weft thread (i.e. during shed opening).

This balance can be estimated by the differences in elongation between the warp threads of the upper shed and the lower shed.

More precisely, we can model this balance by considering each pair of wires starting from the same level of the line of figure 3.

For example, we can consider the lengths AB and AC.

We can write that these lengths L _AB , L _AC are

And [Math. 2]

More generally, for each pair i of warp threads arriving at the fabric line, we can consider the lengths of the segments L_If, L_Ii :

• x_i, y_iles coordonnées du point en ligne de façure où arrive le couple de fils de chaîne,
• x_Hi, y_Siles coordonnées de l’œillet où passe la fil de chaîne de la foule supérieure, et
• x_Hi, y_Iiles coordonnées de l’œillet où passe la fil de chaîne de la foule inférieure, et

with

• x _i , y _i the coordinates of the point on the line of the fashion where the pair of warp threads arrives,
• x _Hi , y _If the coordinates of the eyelet where the warp thread of the upper shed passes, and
• x _Hi , y _Ii the coordinates of the eyelet where the warp thread of the lower shed passes, and

The eyelets moving vertically, they have the same abscissa x _Hi in the upper and lower crowds.

According to one embodiment, the balance of the warp threads during the opening of the shed can be estimated by means of these thread elongations, for example by considering the maximum of the differences between two threads of a pair of warp threads:

The equilibrium objective, obj _E , is therefore evaluated by the maximum, for any warp i, of the difference between the two warp threads of the pair.

These chains can be those modeled, that is to say taken into account in the modeling, because it is possible, according to one embodiment, to exclude from the modeling chains which remain in the upper or lower crowd during a set of insertions.

The objective function also includes constraints, including constraints specific to the weaving machine. These constraints are applied to all the threads.

Generally speaking, these constraints aim to avoid collisions between the warp threads and obstacles (throw 9, upper 12a and lower 12b flaps), as well as to respect a maximum height between the upper shed and the lower shed.

The first constraint, c ₀ , corresponds to the shed height, that is, the maximum vertical distance between the eyelets of the upper shed 10a and the eyelets of the lower shed 10b.

This constraint can be expressed:

For a chain i if the gap between the eyelets (y _Si -y _Ii ) is less than a threshold F _max , then the constraint c _0,i is zero. This threshold depends on the type and geometry of the harness. It is physically the maximum displacement admissible by the rails.

Other constraints aim to avoid collision between the warp threads and obstacles in the loom elements, in particular the rapier and the beater.

According to one embodiment, its obstacles are modeled by circles, that is to say by a point and a radius. It is then sufficient, for each obstacle, to compare a distance between the warp threads and the centers with respect to the radius, with a safety margin. For the leaf, we distinguish its upper part 12a (modeled by a first circle), and its lower part 12b (modeled by a second circle).

It can be predicted that each constraint is zero if the warp thread passes on the right side of the obstacle and at a sufficient distance, and equal to the distance between this warp thread and the obstacle.

For example, for the upper leaf 12a, we can write:

• d_i,1: distance entre le fil de chaîne i et le battant supérieur 12a. On peut supposer que cette distance d_{i ,1}est signée par les différences en abscisses.
• α représente une marge de sécurité. On peut proposer α=1.1
• R₁est le rayon du battant supérieur.

with :

• d _i,1 : distance between the warp thread i and the upper clapper 12a. We can assume that this distance d _{i ,1} is signed by the differences on the abscissa.
• α represents a safety margin. We can propose α=1.1
• R ₁ is the radius of the upper leaf.

For lance 9, we can define a criterion c ₂ concerning the upper crowd and another criterion c ₃ concerning the lower crowd.

For example, we can write:

• d_i,2: distance entre le fil de chaîne i de la foule supérieure et la lance 9. On peut supposer que cette distance d_i,2est signée par les différences en abscisses.
• α représente une marge de sécurité. On peut proposer α=1.1
• R₂est le rayon de la lance 9.

with :

• d _i,2 : distance between the warp thread i of the upper shed and the lance 9. We can assume that this distance d _i,2 is signed by the differences on the abscissa.
• α represents a safety margin. We can propose α=1.1
• R ₂ is the radius of the lance 9.

For the lower crowd, we can for example write:

• d_i,3: distance entre le fil de chaîne i de la foule inférieure et la lance 9. On peut supposer que cette distance d_i,3est signée par les différences en abscisses.
• α : une marge de sécurité. On peut proposer α=1.1
• R₂: le rayon de la lance 9.

with :

• d _i,3 : distance between the warp thread i of the lower shed and the lance 9. We can assume that this distance d _i,3 is signed by the differences on the abscissa.
• α: a safety margin. We can propose α=1.1
• R ₂ : the radius of the lance 9.

A fifth constraint may concern the lower leaf 12b and its relative position with respect to the warp threads of the lower shed 10b. This is in some way the symmetrical criterion of criterion c _1,i .

For example, we can write:

• d_i,4: distance entre le fil de chaîne i et le battant inférieur 12b. On peut supposer que cette distance d_i,4est signée par les différences en abscisses.
• α représente une marge de sécurité. On peut proposer α=1.1
• R₄est le rayon du battant inférieur 12b.

with :

• d _i,4 : distance between the warp thread i and the lower clapper 12b. We can assume that this distance d _i,4 is signed by the differences on the abscissa.
• α represents a safety margin. We can propose α=1.1
• R ₄ is the radius of the lower leaf 12b.

It can be noted that the constraints c _1,i and c _3,i on the one hand and c _2,i and c _4,i on the other hand follow different directions because the distances are signed by the difference on the abscissa.

The constraints c _1,i , c _2,i , c _3,i and c _4,i are zero if the unsigned distance is greater than the radius of the corresponding obstacle plus a margin (of 10% in the examples above with α=1.1).

When inserting a weft thread (which therefore involves opening the shed), the overall stress can be expressed as the sum of the stresses previously described for all the warp threads.

Thus, this global constraint c can be written:

The optimization phase can consider an objective function with a first member evaluating a balance of the warp threads during the opening of the shed, and a second member c evaluating the constraints.

This objective function f(ν) can for example then be written:

k is a hyperparameter of the optimization process and can be set by the user. It influences the relative importance of the constraints with respect to the optimization of the crowd balance. It is a penalty factor normally linked to the geometry of the problem. It can be between 10 and 200.

represents the desired 5-tuple vector. In other words, we are looking for an optimization of the objective function f( in the space of possible.

As seen previously, this 5-tuple is defined by = [y ₀ , y _S , a _S , y _I , a _I ]. The 5-tuple of opening parameters providing this optimum can then be used to parameterize weaving machine 1.

Step 130, in Figure 3, consists of searching for a pair which minimizes the objective function f( .

A production step, 140, of the woven structure can then be implemented using the weaving machine 1. To do this, the parameters determined by the optimization tool 20 can be used.

More precisely, in this step 140, the 5-tuple value of the opening parameters which corresponds to this objective function f( minimized can be used to set the shed opening of the weaving machine 1. The weaving machine 1 can produce the woven structure by inserting a weft yarn when opening the shed of the warp yarns according to these opening parameters. .

Different algorithms can be used to determine an optimum ( . It should be noted that a global optimum is not necessarily necessary: indeed, it is important to obtain a good crowd opening, which respects the constraints c and achieves a good balance obj _E of the upper and lower crowds, but it may be unimportant whether or not there are better solutions in the space of .

An algorithm giving a local minimum can be considered.

Preferably, one can seek to avoid blockages in the local minima of the objective function and use, for example, a random perturbation algorithm to avoid such blockages.

One possible algorithm is “Basin-hopping”.

This algorithm is based on a global optimization technique that iterates by performing a random perturbation of the coordinates, performing a local optimization, and accepting or rejecting new coordinates based on a minimized function value. It is particularly well suited for obtaining global optimizations in a high-dimensional space.

This algorithm was introduced in Wales, David J.; Doye, Jonathan P.K. (1997-07-10). "Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms". The Journal of Physical Chemistry A. 101 (28): 5111–5116. arXiv:cond-mat/9803344

The Basin-hopping algorithm is available in libraries and can therefore be easily used. For example, for use in Python, one can access an available implementation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.basinhopping.html#scipy.optimize.basinhopping

Obviously, once again, other existing or future algorithms can be considered to implement this optimization phase.

Of course, the present invention is not limited to the examples and the embodiment described and shown, but is defined by the claims. It is in particular susceptible of numerous variants accessible to those skilled in the art.

Claims (10)

Automated weaving method (100) of a woven structure (30) by means of a weaving machine (1), comprising the insertion of a weft thread when opening a shed of warp threads, and prior steps (110, 120, 130) of optimizing an objective function having a first member evaluating a balance of said warp threads when said shed opening is carried out, and a second member evaluating constraints specific to said weaving machine, said optimization comprising determining a set of opening parameters (43) minimizing, at least locally, said objective function, and said set of opening parameters being used to parameterize said weaving machine. Method according to the preceding claim in which said woven structure (30) is a reinforcement for composite materials. Method according to one of the preceding claims, in which said optimization comprises determining a global optimum of said objective function by introducing a random perturbation. Method according to the preceding claim, wherein said optimization uses a Basin-hopping algorithm. Method according to one of the preceding claims, in which said opening parameters define a first straight line determining an upper opening of said shed, and a second straight line determining a lower opening of said shed. Method according to one of the preceding claims in which said balance of the warp threads is evaluated by differences in elongation between the warp threads of an upper opening (10a) of said shed, and of a lower opening (10b) of said shed. A method according to one of the preceding claims, wherein said second member evaluates a height between an upper opening and a lower height of said shed. Method according to one of the preceding claims wherein said second member evaluates distances between said warp threads and a lance (9) of said weaving machine (1) and/or a beater (12a, 12b) of said weaving machine (1). Computer program comprising instructions for, when executed by a processor, implementing a method according to one of the preceding claims. Weaving tool comprising a weaving machine (1) of a woven structure (30) adapted for the insertion of a weft thread when opening a shed of warp threads, and an optimization tool (20) of an objective function comprising having a first member evaluating a balance of said warp threads when said shed opening, and a second member evaluating constraints specific to said weaving machine, said optimization comprising determining a set of opening parameters (43) minimizing, at least locally, said objective function, and said set of opening parameters being used to parameterize said weaving machine (1).