Automated weaving method with optimized shed opening

Abstract

Method for the automated weaving of a woven structure (30) by means of a weaving machine (1), comprising the insertion of a weft thread during the opening of a shed of warp threads, and prior steps of optimization, by an optimization tool (20), of an objective function having a first member evaluating the balance of said warp threads during the shed opening, said balance of the warp threads being 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, and a second member evaluating constraints specific to the weaving machine (1). This optimization comprises the determination of a set of opening parameters that, at least locally, minimize said objective function, and this set of opening parameters is used to set the parameters of the weaving machine (1).

Description

Automated weaving process with optimized shed opening

[0001] FIELD OF THE INVENTION

[0002] The present invention relates to an optimization method for the automated weaving of woven structures, in particular three-dimensional woven structures.

[0003] A possible field of application for such woven structures is the aeronautical industry.

[0004] The latter is indeed looking for solutions to meet growing environmental demands, particularly with regard to reducing fossil fuel consumption. The use of lighter composite materials for aircraft design allows, in particular, to reduce their consumption and therefore contribute to reducing the ecological impact.

[0005] Various parts of aircraft are affected by composite materials, for example fan blades in turbomachines.

[0006] Indeed, turbomachine blades must cope with significant mechanical and thermal constraints, in addition to satisfying 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.

[0007] But three-dimensional woven structures can find other applications in the aeronautical field (brake bars for landing gear, etc.) or in many other fields.

[0008] The creation of three-dimensional woven structures requires the use of weaving machines, or looms. These allow for the automation of the actual weaving process, but require an upstream configuration phase that is generally manual and tedious. This configuration involves defining the positioning of each of the warps in the upper position (upper shed) and in the lower position (lower shed).

[0009] Generally speaking, the design of a woven-reinforced composite material 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 for the woven structure and the textile production department that must produce the specified structure with the available technical resources, particularly depending on the specifications of the weaving machine.

[0010] A good quality woven structure is thus the result of an optimized compromise between the characteristics of the material required (warp / weft ratio, fiber volume fraction, etc.) and the constraints required by weaving (weaves, count of available threads, position in the harness, etc.).

[0011] Once the geometry of the desired woven structure has been defined, it is necessary to ensure the correct settings of the weaving machine so that the weaving produces a good quality result. This involves, in particular, defining the weaving speed, the advancement of the preform, and the positioning of the heddles in the high and low positions (high and low sheds, respectively).

[0012] Among all the parameters to be adjusted on a weaving machine, the shed opening is of critical importance.

[0013] 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 conform to 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.

[0014] Furthermore, it is important to ensure a good balance between the upper and lower sheds, so that the warp tension remains correct and weaving errors are avoided. In other words, it is necessary to determine the shed opening, that is, the upper and lower positions of each of the machine's eyelets.

[0015] We therefore understand that this phase of manually determining the crowd opening parameters is long. It therefore implies a substantial extension of the production time. We can estimate the time required for the good definition of the shed opening at around 1 week for a complex woven structure.

[0016] It can also involve human errors, which can penalize the quality of the structure produced or require a return to the configuration phase, thus further extending the production time.

[0017] There is therefore a need to improve current state-of-the-art proposals.

[0018] SUMMARY OF THE INVENTION

[0019] The invention aims to automate at least part of the configuration of the weaving machine in order to minimize the risk of errors and to accelerate the production of the textile structure, once it has been specified by a design office.

[0020] This setting aims in particular to determine the opening parameters of the shed (positions of the eyelets in high and low positions).

[0021] For these purposes, according to a first aspect, the present invention can be implemented by a method for automated weaving of a woven structure by means of a weaving machine, this method comprising the insertion of a weft thread during the opening of the shed of warp threads, and prior steps of optimizing an objective function having a first member evaluating a balance of said warp threads during said shed opening, said balance of the warp threads being evaluated by differences in elongation between the warp threads of an upper opening of said shed, and of a lower opening of said shed, 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.

[0022] 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 woven structure is a reinforcement for composite materials; - 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 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.

[0023] According to another aspect, there is provided a computer program comprising instructions for implementing a method as previously described.

[0024] 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 having a first member evaluating a balance of said warp threads during said shed opening, said balance of the warp threads being evaluated by differences in elongation between the warp threads of an upper opening of said shed, and of a lower opening of said shed, 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.

[0025] Other characteristics and advantages of the invention will appear on reading the following description of a preferred embodiment of the invention, given by way of example and with reference to the appended drawings.

[0026] BRIEF DESCRIPTION OF THE FIGURES

[0027] The accompanying drawings illustrate the invention: Figure 1 schematically represents a context of use of the method according to embodiments. Figure 2 schematically represents an example of a weaving machine. Figure 3 represents a flowchart of an example of implementation of an automated weaving method of a three-dimensional woven structure according to the invention. Figure 4 schematically illustrates a linear modeling of the upper and lower openings of the crowd.

[0028] DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0029] Figure 1 schematically illustrates a context of use of an automated weaving process.

[0030] 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.

[0031] 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.

[0032] This woven structure can be a three-dimensional piece with a high thickness, in particular with a thickness greater than 10 or 20 mm. The automatic shedding opening optimization process is particularly advantageous for complex woven structures and in particular for three-dimensional pieces with a high thickness.

[0033] The weaving machine 1 can use a set of parameters 43 provided by an optimization tool 20.

[0034] This optimization tool can be a computer or any information processing device including virtualized on a platform (for example of the type "cloud computing"), adapted to this specific optimization task. This adaptation may consist of the deployment of a specific software application.

[0035] 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, moved to a remote platform. These telecommunications networks may include a so-called “Internet” network.

[0036] 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.

[0037] Based on these data 41, 42, the optimization tool 20 can provide a set of parameters 43 to the weaving machine 1 which allows 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.

[0038] Furthermore, the optimization tool 20 makes it possible to avoid manual configuration 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 production of the woven structure 30 by the loom 1 more quickly and with less risk of errors.

[0039] Figure 2 schematically shows such a weaving machine 1. This diagram is extremely simplified and aims to explain the elements useful for understanding the automated weaving process presented.

[0040] 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.

[0041] 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.

[0042] The heddles are typically made of wire or string. They are mounted in frames, or blades, suspended from the harness 8 of the loom 1. Each frame, or blade, can be individually operated in translation perpendicular to the plane of the warp threads.

[0043] In the example in the figure, only 4 warp threads and 4 heddles are shown for clarity of exposition and figure, but it is evident that a much larger number of threads and heddles are present for the production of a woven textile.

[0044] By raising or lowering the heddles, the corresponding warp threads are moved up or down from their nominal horizontal positions.

[0045] Thus, in Figure 2, the heddles 6a and 6b are translated upwards, which separates the warp threads 7a and 7b upwards. The heddles 6c, 6d are translated downwards and separate the corresponding warp threads 7c, 7d downwards.

[0046] 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.

[0047] 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.

[0048] 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 zone between this last inserted weft thread and the start of the beam around which the preform 2 can be wound is called the weft.

[0049] 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 the interlacing of a succession of weft threads with the sheet of warp threads.

[0050] In addition, in the case of a three-dimensional woven structure, binding threads are inserted to hold the different woven layers together.

[0051] This preform 2 forms a woven textile 30.

[0052] This woven structure can then be used to form a composite material, for example by embedding it in a matrix material.

[0053] 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.

[0054] As stated previously, 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 flaps 12a, 12b and, on the other hand, to avoid imbalances in the tension of the warp threads between the upper and lower sheds.

[0055] Figure 3 illustrates a flowchart of an exemplary implementation of the automated weaving method 100.

[0056] In a step 110, the optimization tool 20 is provided with the data 41 specifying the woven structure 30 to be produced, and with provided data 42 relating to the weaving machine 1.

[0057] In a step 120, the optimization tool 20 can determine an objective function.

[0058] 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.

[0059] This objective function has a first member evaluating a balance of warp threads during warp opening. This balance corresponds to that between the upper and lower sheds.

[0060] It also includes a second member evaluating constraints specific to the weaving machine.

[0061] 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.

[0062] The opening parameters are chosen to allow one-to-one parameterization of the loom.

[0063] 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.

[0064] Taking these elements into account, it was chosen to make the assumption that the opening of the upper 10a and lower 10b sheds 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 the height.

[0065] 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.

[0066] 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.

[0067] 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 direction coefficient.

[0068] Figure 4 illustrates this modeling.

[0069] In this figure, preform 2 has 3 planes, or layers, of preform Po, P2, P2.

[0070] 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.

[0071] A wire can be modeled in the high position and in the low position, and the optimization then aims to minimize the maximum difference between the high and low positions of this wire.

[0072] According to one embodiment, we can consider a set of insertions. In this set, some threads will always remain in the high shedding, others in the low shedding, and others will occupy the high shedding and the low shedding. We can implement the optimization only for these last threads: we can then seek to minimize the maximum difference between the high and low positions of these threads alone.

[0073] The tuck-in 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.

[0074] 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.

[0075] The line defining the upper crowd can be written: ys+as(xi-xo), with - ys: ordinate of the highest eyelet, corresponding to the Ho rail closest to the face; - as: slope coefficient - Xi and xo: abscissa of, respectively, an eyelet in i of the upper crowd, and of the eyelet of ordinate ys.

[0076] The line defining the lower crowd can be written: yi+ai(xi-xo), with - yi: ordinate of the lowest eyelet, corresponding to the rail Ho closest to the face; ai: slope coefficient

[0077] yo can be the ordinate, or height, of the preform. For example, it can be the vertical position of the midplane of preform 2.

[0078] Optimizing the crowd opening therefore comes down to finding the optimized values ​​for this 5-tuple vector [yo, ys, as, yi, ai].

[0079] Thus, thanks to the proposed modeling, the number of crowd opening parameters (initially 2 parameters per eyelet) is reduced to 5 parameters.

[0080] 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.

[0081] 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).

[0082] This balance can be estimated by the differences in elongation between the warp threads of the upper and lower sheds.

[0083] More precisely, we can model this balance by considering each pair of wires starting from the same level of the line of figure 3.

[0084] For example, we can consider the lengths AB and AC.

[0085] We can write that these lengths LAB, LAC are

[0086] [Math. 1]

[0087] And [Math. 2]

[0088] More generally, for each pair i of warp threads arriving at the fabric line, we can consider the lengths of the segments Lsi, Lu:

[0089] [Math. 3]

[0090] with - Xi, yi the coordinates of the point in the line of the fabric where the pair of warp threads arrives, - XHi, ysi the coordinates of the eyelet where the warp thread of the upper shed passes, and - XHi, yii the coordinates of the eyelet where the warp thread of the lower shed passes, and

[0091] The eyelets moving vertically, they have the same abscissa XHi in the upper and lower sheds.

[0092] 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:

[0093] [Math. 4] (diffi = \L si - L u \ \obj E = maXi(_diffi)

[0094] The equilibrium objective, objE, is therefore evaluated by the maximum, for any warp i, of the difference between the two warp threads of the pair.

[0095] 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.

[0096] The objective function also includes constraints, particularly constraints specific to the weaving machine. These constraints are applied to all the threads.

[0097] Generally speaking, these constraints aim to avoid collisions between the warp threads and obstacles (throw 9, upper 12a and lower 12b beaters), as well as to respect a maximum height between the upper shed and the lower shed.

[0098] The first constraint, co, corresponds to the shed height, that is to say the maximum vertical distance between the eyelets of the upper shed 10a and the eyelets of the lower shed 10b.

[0099] This constraint can be expressed:

[0100] [Math. 5] c0,i = max y si - y u - F max ,- 0)

[0101] For a chain i, if the distance between the eyelets (ysi-yii) is less than a threshold Fmax, then the stress co.i is zero. This threshold depends on the type and geometry of the harness. It is physically the maximum displacement admissible by the rails.

[0102] Other constraints aim to avoid collision between the warp threads and obstacles in the loom elements, in particular the rapier and the beater.

[0103] 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).

[0104] We can predict 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.

[0105] For example, for the upper leaf 12a, we can write:

[0106] [Math. 6]

[0107] with: di,i: distance between the warp thread i and the upper beater 12a. We can assume that this distance di,i is signed by the differences in abscissa. a represents a safety margin. We can propose a=1 .1 Ri is the radius of the upper leaf.

[0108] For lance 9, we can define a criterion C2 concerning the upper crowd and another criterion C3 concerning the lower crowd.

[0109] For example, we can write:

[0110] [Math. 7]

[0111] with : - di,2: distance between the warp thread i of the upper shed and the lance 9. We can assume that this distance di,2 is signed by the differences on the abscissa. - a represents a safety margin. We can propose a=1 .1 - R2 is the radius of the lance 9.

[0112] For the lower crowd, we can for example write:

[0113] [Math. 8] c 3 i= max d l 3 - « x R2,- O)

[0114] with : - di,3: distance between the warp thread i of the lower shed and the lance 9. We can assume that this distance di,3 is signed by the differences on the abscissa. - a: a safety margin. We can propose a=1.1 - R2: the beam of the lance 9.

[0115] A fifth constraint may concern the lower 12b flap 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 ci.

[0116] For example, we can write:

[0117] [Math. 9]

[0118] with : - di, 4: distance between the warp thread i and the lower beater 12b. We can assume that this distance di,4 is signed by the differences on the abscissa. - a represents a safety margin. We can propose a=1 .1 - R4 is the radius of the lower leaf 12b.

[0119] It can be noted that the constraints eu and C3j on the one hand and C2j and C4j on the other hand follow different directions because the distances are signed by the difference in abscissa.

[0120] The constraints eu, C2,i, C3,i and C4,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 a=1 .1 ).

[0121] 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.

[0122] Thus, this global constraint c can be written:

[0123] [Math. 10]

[0124] The optimization phase can consider an objective function with a first member obj Eevaluating a balance of the warp threads during the opening of the shed, and a second member c evaluating the constraints.

[0125] This objective function f(v) can for example then be written:

[0126] [Math. 11] / (v) = obj E (y) + k. c(y)

[0127] k is a hyperparameter of the optimization process and can be set by the user. It influences the relative importance of constraints with respect to crowd balance optimization. It is a penalty factor normally related to the geometry of the problem. It can be between 10 and 200.

[0128] v represents the desired 5-tuple vector. In other words, we are looking for an optimization of the objective function f(v) in the space of possible v.

[0129] As seen previously, this 5-tuple is defined by v = [yo, ys, as, yi, ai]. The 5-tuple of opening parameters providing this optimum can then be used to parameterize the weaving machine 1 .

[0130] Step 130, in Figure 3, consists of searching for a pair v,f(y) which minimizes the objective function f(v).

[0131] A production step, 140, of the woven structure can then be implemented by means of the weaving machine 1. To do this, the parameters determined by the optimization tool 20 can be used.

[0132] More precisely, in this step 140, the 5-tuple value of the opening parameters v which corresponds to this minimized objective function f(v) can be used to parameterize the opening of the shed 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 v.

[0133] Different algorithms can be used to determine an optimum (v, (v)). 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 objE of the upper and lower crowds, but it may be unimportant whether or not there are better solutions in the v space.

[0134] An algorithm giving a local minimum can be considered.

[0135] 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.

[0136] One possible algorithm is “Basin-hopping”.

[0137] This algorithm is based on a global optimization technique that iterates by randomly perturbing the coordinates, performing local optimization, and accepting or rejecting new coordinates based on a minimized function value. It is particularly well suited for achieving global optimizations in a large-dimensional space.

[0138] This algorithm was introduced in Wales, David J.; Doye, Jonathan PK (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

[0139] 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

[0140] Obviously, once again, other existing or future algorithms can be considered to implement this optimization phase.

[0141] 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

Claims

1. A method of automated weaving (100) of a woven structure (30) by means of a weaving machine (1), comprising inserting 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, said balance of the warp threads being 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, 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.

2. Method according to the preceding claim in which said woven structure (30) is a reinforcement for composite materials.

3. Method according to one of the preceding claims, wherein said optimization comprises determining a global optimum of said objective function by introducing a random perturbation.

4. Method according to the preceding claim, wherein said optimization uses a Basin-hopping algorithm.

5. 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.

6. 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.

7. A method according to one of the preceding claims wherein said second member evaluates distances between said warp threads and a rapier (9) of said weaving machine (1) and / or a beater (12a, 12b) of said weaving machine (1).

8. A computer program comprising instructions for, when executed by a processor, implementing a method according to one of the preceding claims.

9. Weaving tool comprising a weaving machine (1) of a woven structure (30) adapted for the insertion of a weft thread during the opening of a shed of warp threads, and an optimization tool (20) of an objective function having a first member evaluating a balance of said warp threads during said shed opening, said balance of the warp threads being 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, 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).

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