Method for optimizing the nesting of two blanks within a planar strip extending in the longitudinal direction

Abstract

A first object of the present invention is to provide a computerized method for determining the best nesting of blanks in a strip in order to optimize the material usage and to determine the associated material usage. Solving the material usage optimization problem involves at least three different variables (two rotational angles of the blank and one lateral offset amount), and thus potentially involves optimizing a material usage function over a very large set of combinations. This causes long computation times, which can be a serious obstacle to the implementation of material usage optimization methods. Therefore, a second object of the present invention is to provide a computerized method for accelerating the computerized determination of the best blank nesting and the associated material usage for material usage optimization.

Description

Technical Field

[0001] The present invention relates to the manufacture of cut-out shapes, and more particularly to the manufacture of shapes cut from a rectangular planar strip of material that generally extends in a longitudinal direction.

Background Art

[0002] In many material manufacturing processes of materials that are generally planar, the continuous nature of the manufacturing process suggests that the final manufactured product is generally in the form of a long strip that extends in a longitudinal direction and has an elongated rectangular shape. This applies, for example, to the production of flat sheet metals such as flat steel products or flat aluminum products. This also applies to the pulp and paper industry, or when manufacturing fabrics and textiles. The strips mentioned above are often adjusted in the form of coiling the strips into a coil shape in order to efficiently store or transfer the strips.

[0003] One common approach to using the material in subsequent shaping processes is to cut out a shape having a predetermined contour from the strip. For example, a metal blank can be cut out in the case of a metal strip, or fabric or textile can be cut out in the fashion industry. In the case of a metal strip, this operation is called blanking, and the resulting product is called a metal blank, that is, a generally planar metal piece having a predetermined contour suitable for use in subsequent shaping processes. This operation can be performed, for example, by punching, water jet cutting, oxy cutting, or laser cutting.

[0004] Hereinafter, the term "blank" is used for simplicity, but as will be readily understood, the application field of the present invention is not limited to metal materials only.

[0005] The pattern, hereinafter referred to as nesting in this specification, followed when blanks are placed in a strip affects the material usage of the blanking operation. The term "material usage" as used in this description and the claims corresponds to the material components of the blanking operation and can include several different aspects listed below, although this list is not exhaustive: - Environmental aspect: For example, if the raw material production process emits CO2, it may be interesting to optimize the material usage during the blanking operation to reduce the total CO2 emissions. - Productivity aspect: Optimizing the material usage means that a shorter time required to produce the raw material is optimized. - Industrial feasibility aspect: The blank nesting pattern determines the required width of the strip in the longitudinal direction, and the required width of the strip, in itself, can have an impact on the industrial feasibility of the raw material strip (a very large width or a very narrow width may not be feasible). - Cost aspect: Optimizing the material usage means that less raw material is used, and thus the material cost incurred is reduced.

[0006] In the present invention, the configuration is as follows: a strip from which a first blank and a second blank are cut, each blank having a predetermined contour. Each blank has a degree of freedom of rotation about an axis perpendicular to the upper and lower surfaces of the strip, and the second blank has a degree of freedom for being arranged so as to have a specific lateral offset amount compared to the first blank, and the first blank itself is positioned close to the edge of the strip. The longitudinal arrangement of two consecutive blanks relative to each other determines a nesting pattern, which will then be repeated as long as the strip extends longitudinally. In the present invention, a cost function is associated with the arrangement of the two blanks in the strip, and the cost is a function of at least the orientation of each blank and the lateral offset amount between the blanks.

Summary of the Invention

Problems to be Solved by the Invention

[0007] A first object of the present invention is to provide a computer-implemented method for determining the best nesting of blanks in a strip in order to minimize the amount of material used. Solving the optimization problem involves three different variables (two rotation angles of the blank and one lateral offset amount), and thus potentially involves optimizing the material usage function over a very large set of combinations. This causes long computation times, which can be a serious obstacle to the implementation of the method. Therefore, a second object of the present invention is to provide a computer-implemented method for accelerating the optimization method.

Means for Solving the Problems

[0008] By providing a computer-implemented method for minimizing material usage and an accelerated method of said method, the present invention enables the best nesting pattern of two blanks in a strip and the associated material usage to be determined automatically, quickly, and in an error-proof manner. This improves the productivity of blanking design. Further, this also enables the method to be executed for many different sets of blanks, thereby enabling the nesting of a huge number of blank shapes and the investigation of material usage in a minimal amount of time.

[0009] The object of the present invention is achieved by providing a method for computer-implemented optimization of the nesting of two blanks in a strip for minimizing material usage according to claim 1, optionally including the features from claims 2 to 19. The object of the present invention is further achieved by providing a computer program according to claim 19 and a computer-readable storage medium according to claim 20.

[0010] Next, the present invention will be described in detail and illustrated by way of example without introducing any constraints, with reference to the accompanying drawings.

Brief Description of the Drawings

[0011]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6A

Figure 6B

Figure 7A

Figure 7B

[0012] Referring to FIG. 1, in the present invention, the longitudinal direction refers to the main direction in which the strip 1 extends, and the transverse direction refers to the direction perpendicular to the longitudinal direction in the plane. Further, the strip 1 extends over a limited width between two parallel edges 2 and 3 in the transverse direction Y and extends over a width W in said direction.

[0013] The strip 1 has an upper side and a bottom side, also referred to as the upper surface and the bottom surface. All the attached drawings are two-dimensional top views and only the upper side is visible. The distance between the upper surface and the bottom surface is specified as the thickness of the strip. The thickness can be measured, for example, using a micrometer, with the spindle and anvil of the micrometer placed on the upper surface and the bottom surface.

[0014] In the following description and claims, the terms longitudinal and horizontal have the same meaning, and the terms transverse and vertical have the same meaning. The terms "left" and "right" are used in the following description and claims and refer to relative positions that are further rearward and along the longitudinal direction, respectively, i.e., along the direction marked by the "X" arrow in FIG. 1. The terms "upward" (and "above", "higher than", etc.), "downward" (and "below", "lower than", etc.) are used in the following description and claims and refer to relative positions that are further rearward and along the transverse direction, respectively, i.e., along the direction marked by the "Y" arrow in FIG. 1.

[0015] Referring to FIG. 1, a first blank A having a first contour and a second blank B having a second contour are cut from strip 1.

[0016] Blank B is laterally offset from blank A by a lateral offset amount dy, and the lateral offset amount dy is defined as the difference in the lateral rise between the lowermost points in the lateral direction of blank contour B and blank contour A. The lateral offset amount dy is expressed in mm.

[0017] Blank A and blank B each form an angle α and β with respect to a given direction in the plane of strip 1. In the present invention, by convention, the angles α and β are defined with respect to the longitudinal direction. The angles α and β are expressed in degrees (degree).

[0018] Referring to FIG. 1, blank A has a height dymax(α) measured in the lateral direction, and this height depends on angle α. The maximum height value dymax is defined as the maximum value of dymax(α) for all possible values of α included between 0° and 360°.

[0019] Next, a computer-implemented method for nesting blanks A and B in the strip and then determining the optimal values (α, β, dy) that minimize the resulting material usage will be described: - Step 1.1 consists of the step of preparing blank contours A and B. - Step 1.3 includes calculating the value of the quantity Material(α, β, dy) for several values of α, β, and dy, and determining the minimum value, MinMaterial, of the quantity Material(α, β, dy), where Material(α, β, dy) corresponds to the amount of material obtained when nesting the blank contours in the rectangular strip, blank contour A is oriented using angle α, blank contour B is oriented using angle β, and dy is the difference in the lateral lift amount between the lowest point of blank A and the lowest point of blank B. - Step 1.4 consists of outputting MinMaterial and the combination (α optimal , β optimal , dy optimal ) such that Material(α optimal , β optimal , dy optimal ) = MinMaterial to the user. - Step 1.5 consists of arranging the first blank A in the strip using angle α optimal , the first blank B using angle β optimal and the lateral offset amount dy optimal , arranging the next (second) blank A to be laterally aligned with the first blank A using angle α optimal , and arranging the next (second) blank B using angle β optimal and the lateral offset amount dy optimal , and repeating the pattern along the strip, for example as long as it extends in the longitudinal direction.

[0020] In step 1.3, the quantity Material(α, β, dy) preferably corresponds to the amount of material obtained while minimizing the amount of material for the optimal longitudinal spacing between blank A and blank B, i.e., the spacing that minimizes the amount of material given that α, β, and dy have fixed (not necessarily optimal) values.

[0021] The longitudinal interval between Blank A and Blank B is defined, for example, by two pitches Δ1 and Δ2, where Δ1 is the distance between the left end of Blank A in the longitudinal direction and the left end of the adjacent Blank B on its right, and Δ2 is the distance between the left end of Blank B and the left end of the adjacent Blank A on its right.

[0022] Therefore, the quantity Material(α,β,dy) corresponds to the pitches Δ1(α,β,dy) and Δ2(α,β,dy) that minimize the material usage for given values of α, β, and dy.

[0023] Δ1(α,β,dy) can be determined iteratively, for example, in the combination (α,β,dy) under consideration (and similarly for Δ2), by gradually moving Blank B towards Blank A in the longitudinal direction until Blank B touches or is about to touch Blank A. Δ1(α,β,dy) and Δ2(α,β,dy) can also be determined directly (instead of being optimized iteratively) using an explicit and rapid calculation method that will be further described later.

[0024] In either case, as presented above, in the method according to the invention, minimization of the material usage is carried out by partitioning: - On the one hand, the optimization of the values of α, β, and dy, - And on the other hand, the optimization of the longitudinal intervals Δ1, Δ2, which is carried out separately (i.e., for each set (α,β,dy)).

[0025] Instead of performing a global optimization in the five - dimensional coordinate space (α, β, dy, Δ1, Δ2), it is beneficial to separate these two sub - optimizations from each other. In practice, for a given set (α, β, dy), that is, by setting the values of α, β, and dy, it is convenient to adjust Δ1 and Δ2 (iteratively or directly) to minimize the material usage: can it be achieved efficiently from a computational perspective? Further, more generally, from a numerical perspective, the split "three - dimensional plus two - dimensional optimization" is easier to achieve than a complete, entangled five - dimensional optimization.

[0026] In addition, as mentioned above, once the values of α, β, and dy are set, the optimal longitudinal spacing (i.e., the calculation of Δ1(α, β, dy) and Δ2(α, β, dy)) can be directly determined (thanks to a specific method), thereby further accelerating the nesting optimization.

[0027] The method for nesting two blanks described herein can include the following step 1.2: providing a material usage function Material(α, β, dy). This material usage function can take the form of a computer sub - program, routine, or other function that returns the value of Material(α, β, dy) given the values of α, β, and dy.

[0028] For discretizing the problem, an angular accuracy ε in degrees of an angle angle and a distance accuracy ε in mm dy can be provided. For example, ε angle = 1° and ε dy = 1 mm. Step 1.3 includes calculating MinMaterial as the minimum value of all Material(α, β, dy) values over all combinations of (ε angle *i, ε angle *j, ε dy *k), where i, j, and k range from 0 to 360 / ε angle+1, 360 / ε angle +1, and dymax / ε dy is an integer included between +1. Note further that this detailed discretization can be different from the above example: this is because the discrete values of α, β, dy can belong to a lattice of values (points) that are not necessarily rectangular (different from the above example), and the step between two discrete values can potentially be non-uniform.

[0029] In any case, in the above-exemplified discretization scheme, i, j, and k range from 0 to, respectively, 360 / ε angle +1, 360 / ε angle +1, and dymax / ε dy +1, but do not take all possible integer values. In other words, the quantity Material(α, β, dy) does not need to be evaluated for all integer values from 0 to, respectively, 360 / ε angle +1, 360 / ε angle +1, and dymax / ε dy +1 to determine MinMaterial. Specifically, in the acceleration method for performing step 1.3 presented later, the quantity Material(α, β, dy) is evaluated for only some of the integer values included between 0 to, respectively, 360 / ε angle +1, 360 / ε angle +1, and dymax / ε dy +1 (to avoid redundancy in calculations).

[0030] In a particular embodiment, step 1.3 of the method described above further includes the determination of pitches Δ1(α optimal , β optimal , dy optimal ) and Δ2(α optimal , β optimal , dy optimal ), where Δ1(α optimal , β optimal , dy optimal ) is the distance between the left end of A blank in the longitudinal direction and the left end of the adjacent B blank on its right, and Δ2(α optimal , β optimal , dyoptimal ) is the distance between the left end of the B blank and the left end of the adjacent A blank on its right.

[0031] In certain embodiments, step 1.5 of the method described above further includes the use of Δ1(α optimal , β optimal , dy optimal ) and Δ2(α optimal , β optimal , dy optimal ), and step 1.5 comprises, in the strip, arranging the first blank A at an angle α optimal , the first blank B at an angle β optimal and a lateral offset amount dy optimal relative to the first blank A, and a longitudinal offset amount Δ1(α optimal , β optimal , dy optimal ), arranging the next blank A at an angle α optimal to be laterally aligned with the first blank A, and a longitudinal offset amount Δ2(α optimal , β optimal , dy optimal ) towards the first blank B, and repeating the pattern along the strip as long as it extends longitudinally.

[0032] In the remainder of the following description, MinMaterial is also referred to as "substantially optimal", and (α optimal , β optimal , dy optimal ) is also referred to as "substantially optimal combination".

[0033] For example, ε angle = 1°, and ε dyWhen dymax is, for example, 500mm which is a common value in the dimensions of a steel blank and =1mm, the number of possible combinations of (α,β,dy) that need to be calculated is 360*360*500 = 64800000. Performing calculations for such a huge number is costly in terms of computer usage and becomes an obstacle to the implementation of this method, especially in situations where it is necessary to consider several blank shapes.

[0034] The inventors noticed that calculating Material(α,β,dy) over the entire range of possible combinations of (α,β,dy) in step 1.3 would lead to many redundant calculations for combinations that are far from the best combination. Taking this into account, the inventors developed a method to accelerate step 1.3 of the method described above by performing several iterations of calculating Material(α,β,dy) for a smaller number of possible combinations of (α,β,dy). In each iteration, the combination of (α,β,dy) with the lowest material usage is selected, and each subsequent iteration is performed using points adjacent to the selected point. Overall, this makes it possible to significantly reduce the number of combinations of (α,β,dy) required to calculate the function Material(α,β,dy). In the following description and claims, this method is designated as an acceleration method.

[0035] The number of iterations of the acceleration method is indicated by N, and N is an integer greater than or equal to 2.

[0036] The acceleration method includes the following steps: - Step 2.1: Selecting the combination of (α,β,dy) with the lowest Material(α,β,dy) value from only a part of the possible combinations of (α,β,dy) in step 1.3 of claim 1. - Step 2.2: Iteration from k = 1 to N - 1: Select the combination of (α, β, dy) with the lowest Material(α, β, dy) value from the combination of (α, β, dy) selected in the previous step and at least a part of the neighboring combinations of (α, β, dy), where the neighboring combination of (α, β, dy) is the combination (α + X * u k *ε angle , β + Y * v k *ε angle , dy + Z * w k *ε dy ), where X, Y, and Z can each take the value -1, 0, or +1, and u k , v k , and w k are integers greater than or equal to 2, and u k <u k- 1, v k <v k- 1, and w k <w k- 1. Repeat this step. - Step 2.3: Determine the accelerated minimum material usage MinMaterialAcc as the minimum value of Material(α, β, dy) from the combination of (α, β, dy) selected in the previous step and at least a part of the neighboring combinations of (α, β, dy) (α + X * u N *ε angle , β + Y * v N *ε angle , dy + Z * w N *ε dy ), where X, Y, and Z can each take the value -1, 0, or +1, and u N , v N , and w N are integers greater than or equal to 1, and u N <u N-1 , v N <v N-1 , and w N <w N-1 . This step. - Step 2.4: Material(α optimal_acc , β optimal_acc , dyoptimal_acc ) = MinMaterialAcc, the acceleration minimum material usage MinMaterialAcc and the values α optimal_acc , β optimal_acc , dy optimal_acc Outputting to the user.

[0037] Thanks to the acceleration method described above, the number of calculations of Material(α, β, dy) can be significantly reduced, which leads to a significant reduction in the calculation time. Note that a method for accelerating Step 1.3 based on gradually selecting points and then more precisely exploring the points adjacent to them can be implemented in a way different from the above example. For example, instead of corresponding to the paralepidid (similar to a rectangle) area of the adjacent area in the above example, the vicinity of each selected point can correspond to a spherical or nearly spherical area around this point.

[0038] Selecting a set of possible combinations (α, β, dy) reduced in Step 2.1 is a matter of compromise. In fact, if the number of possible combinations to be selected is very large, the speed of the acceleration method will decrease. On the other hand, if the number of possible combinations is very low, there is a risk that the final result MinMaterialAcc will deviate significantly from the substantial optimal result of the non-accelerated method. In fact, the acceleration method depends on testing a first set of points and then testing the points adjacent to them, where the distance between the points becomes smaller as the iteration progresses. If the initial set of combinations is very small and the space between two combinations is very large, there is a risk that the substantial optimal combination will be far from the initial set of combinations and will then not be reached even by exploring the adjacent points.

[0039] In a specific embodiment, the possible combinations of (α, β, dy) in Step 2.1 are combinations of (ε angle *C*i, ε angle *D*j, ε angle *E*m), where C, D, and E are fixed integers strictly greater than 1, and i, j, and m range from 0 to 360 / (εangle *C)+1, 360 / (ε angle *D)+1, and dymax / (ε dy is an integer that takes on all integer values between *E)+1. In other words, the initial set of combinations is a regular grid within the space of all possible combinations of (α, β, dy). Advantageously, this allows for the optimization of the space between the initial combinations of (α, β, dy), thereby making it less likely to miss the substantial optimal combination when using the acceleration method.

[0040] In certain embodiments, the acceleration method further includes an initial step of providing a tolerance threshold T% that is strictly greater than 0% and strictly less than 100%. Then, from the combination of (α, β, dy) selected in the previous step and at least a portion of the adjacent combinations of (α, β, dy), the combination of (α, β, dy) with the lowest Material(α, β, dy) value is selected by T%, and the selection process of iterative step 2.2 is performed. Advantageously, this allows for the implementation of a reproducible method for each selection step, which is also well-suited for encoding in the form of a computer program. Selecting the relevance threshold is also a matter of compromise. As T% increases, more points will be carried over to the next step, and thus more calculations will be involved in the next step. However, on the other hand, if the relevance threshold T% is too low, there is a risk of missing the substantial optimal combination when applying the acceleration method.

[0041] In certain embodiments, iterative step 2.2 of the acceleration method is u k = u k-1 / 2, v k = v k-1 / 2, and w k = w k-1It is characterized by being 1 / 2. In other words, in each iteration, the distance between the neighboring point and the selected point of the previous iteration is 1 / 2 of the distance during the previous iteration. Advantageously, this makes it possible to obtain a very good compromise between the need to extensively investigate the possible candidate combinations in the first iteration and the need to finely tune the set of possible candidates with a very high resolution in the last iteration.

[0042] In a specific embodiment, the acceleration method is such that all neighboring (α, β, dy) combinations of the (α, β, dy) combination selected during the previous step are used, that is, all combinations (α + X * u k * ε angle , β + Y * v k * ε angle , dy + Z * w k * ε dy ) are used, where X, Y, and Z take all values of -1.0 and +1 and are used in steps 2.2 and 2.3. Advantageously, this makes it possible to systematically check all neighboring combinations of the combination selected in the previous step, thereby minimizing the risk of missing the substantial optimal combination.

[0043] In a specific embodiment, the acceleration method is further characterized in that u N = 1, v N = 1, and w N = 1. In other words, the neighboring points in step 2.3 of the acceleration method are located to the immediate right of the selected point in the last iteration of step 2.2 at distances of ε angle , ε angle , and ε dy for α, β, and dy respectively. Advantageously, this makes it possible to investigate possible candidates with a very fine mesh in the last iteration, thereby minimizing the risk of missing the optimal result.

[0044] In an example of nesting steel blanks of different shapes in a steel strip, the inventors used the combination of the embodiments described above and different N values and T% values applied to various examples of industrial blank profiles A and B to perform several trials in order to determine the best N value and T% value, thereby enabling a very high calculation speed and ensuring that a substantial optimal combination is found.

[0045] The inventors discovered that it is possible to reach a substantial optimal value using the following specific combination of the embodiments described above: · ε angle = 1°, ε dy = 1 mm, and N = 5, · The acceleration method further includes an initial step that provides a tolerance threshold T% of 1%. Then, by selecting the combination of (α, β, dy) having the lowest Material(α, β, dy) value of 1% from the combination of (α, β, dy) selected in the previous step and at least a part of the combination of the neighboring (α, β, dy), the selection process of iterative step 2.2 is performed. · The possible combinations of (α, β, dy) in step 2.1 are the combinations of (ε angle *C*i, ε angle *D*j, ε dy *E*m), where C = D = E = 2 N-1 is. · u k = u k-1 / 2, v k = v k-1 / 2, and wk = w k-1 / 2. · u N = 1, v N = 1, and w N = 1 (this is actually the result of the two embodiments listed above). · All neighboring combinations of (α, β, dy) selected during the previous step are used, i.e., all combinations (α + X * u k * ε angle , β + Y * v k * εangle , dy + Z * w k * ε dy ) is used, where X, Y, and Z take all of the values -1, 0, and +1 and are used in Steps 2.2 and 2.3.

[0046] Table 1 below describes the investigations described above for steel blanks in the case of N = 5 and different values of T% (1%, 0.5%, 0.4%, and 0.3%):

[0047] [Table 1]

[0048] Trials were conducted using 18 different configurations of blank contours A and B. The number of points given in the second column reflects the total number of vertices of blanks A and B when numerically representing the blank contours as the form of sets of vertices joined by straight edges. This number indicates the complexity of the blank shape and thus the amount of time required to calculate Material(α,β,dy) for a given combination. A larger number of points results in a longer basic calculation of Material(α,β,dy) and thus a longer time required to find MinMaterialAcc. The third column gives the results of MinMaterial (here denoted as "MinMat" for the substantial optimum of the non-accelerated method). Along with the time required to implement the accelerated method, the results of MinMaterialAcc (denoted as "MinMatAcc" in the table) are given for each tested T%, and the calculations were performed on a standard portable computer. As shown, the calculation time for T% = 1% remains at a very reasonable time, and the values of MinMaterialAcc are the substantial optimum MinMaterial in all cases. Decreasing the tolerance threshold T% reduces the possible combinations selected in each iteration in step 2.2, thereby also shortening the calculation time. However, the resulting MinMaterialAcc is not always the substantial optimum MinMaterial. Cases deviating from the substantial optimum are highlighted in gray in the table. The inventors found that for N = 5, in the configuration where this method is applied to a general steel blank for the manufacture of automotive parts, for example, T% = 1 is a very good compromise between the calculation time and reaching the best solution to the optimization problem.

[0049] In certain embodiments, each calculated Material(α,β,dy) value for a given combination of (α,β,dy) is stored such that it can be retrieved at any time when the calculation is required. For example, each calculation result is stored in a hash table, where the index key is a label named after α, β, and dy, such as the string "α_β_dy". Advantageously, this makes it possible to avoid calculating the material usage for a given combination more than once, thereby reducing the total calculation time.

[0050] In certain embodiments, the function dymax(α) is defined as the height measured in the lateral direction of blank A when blank A is oriented at an angle α. At a given value of α, dymax(α) corresponds to the maximum value of dy, beyond which blanks A and B cannot contact each other under any circumstances. Nesting blanks A and B with dy > dymax(α) is generally not optimal with respect to material usage, and in particular, the amount of scrap generated by the blanking operation is an important factor. In certain embodiments, the present acceleration method is implemented using only combinations having dy < dymax(α). Advantageously, this avoids performing potentially wasteful calculations, and thus the calculation time is reduced without the risk of missing the substantially optimal combination.

[0051] Figures 2 and 3 are simplified graphical representations of certain embodiments of the acceleration method using a case where only two variables are considered. This simplification makes it possible to represent the method in a two-dimensional space instead of the three-dimensional space required for the combination of α, β, and dy, and is done for clarity. The problem space is represented using a set of Cartesian coordinates X1, X2. The accuracies of the two variables are ε1 and ε2.

[0052] In Figures 2 and 3, the number of selected iterations is N = 4. The relevance threshold T% is 25%. The corresponding number of iterations and the steps within the iteration are shown above each graph.

[0053] Referring to the upper left of FIG. 2, in this particular example, the initial possible combinations for step 2.1 are of the type of combinations (ε1*C*i, ε2*D*j), where C = D = 2 N-1 = 2 4-1 = 8. Since there are 16 initial combinations, the total number of combinations selected in the upper right graph representing the end of step 2.1 is 25% * 16 = 4 combinations.

[0054] The example depicted is the case where u k = u k-1 / 2 and v k = v k-1 / 2. Referring to the lower left of FIG. 2, the combinations adjacent to iteration 1 of step 2.1 are located at a distance of ε1 * 8 / 2 = ε1 * 4 in the X1 direction and ε2 * 4 in the X2 direction, which are the combinations selected at the end of step 2.1. These graphs also show the situations that can occur when generating adjacent combinations, that is, indicating that some of the selected points can have common adjacent points. This applies, for example, to the example of the point indicated by reference label 4. In a particular embodiment, the present acceleration method will be programmed so that, as previously explained, the material usage of these points is not calculated twice (for example, by using a hash table that associates the material usage results with those combinations).

[0055] Another possible situation is shown by the combinations with reference label 5: these combinations are located at the edges of the space defined by all combinations in the X1, X2 coordinate system, and thus have a more limited number of adjacent points.

[0056] Referring to the lower right of FIG. 2, 25% of the points with the lowest material usage are selected from a total of 20 points, and a total of 20 * 25% = 5 points are selected.

[0057] Referring to the upper left of FIG. 3, in iteration 2 of step 2.2, the distance between adjacent points has decreased to ε1*4 / 2 = ε1*2 and ε2*2. As a result, the sum of the previously selected combination and the adjacent combination is 39. Referring to the upper right of FIG. 3, from these 39 points, 25%*39 = 9 combinations with the lowest material usage are selected.

[0058] Referring to the lower left of FIG. 3 depicting step 2.3, the distance between adjacent points is ε1*2 / 2 = ε1 and ε2, that is, this is the case when u N = v N = 1. This results in a total of 78 combinations, from which the minimum material usage value is MinMaterialAcc, enabling the determination of the optimal combination (see the lower right of FIG. 3).

[0059] In summary, the acceleration method for the simplified graphic representations in FIGS. 3 and 4 requires the calculation of the material usage function for the following number of combinations: - Step 2.1: 16 combinations - Iteration 1 of step 2.2: 20 - 4 = 16 combinations (the number of adjacent combinations - the number of previously selected combinations - the material usage of the previously selected combinations was previously calculated and stored in the previous step) - Iteration 2 of step 2.2: 39 - 5 = 34 combinations - Step 2.3: 78 - 9 = 69 combinations.

[0060] Overall, this acceleration method involves calculating the material usage function for 16 + 16 + 34 + 69 = 135 combinations. When using the non-acceleration method, the total number of possible combinations is 26*26 = 676. Therefore, in this simplified case with one less variable than the actual three-dimensional problem of the present invention and a small number of possible values of the variable (for example, when the angular accuracy is 1°, the number of angular values is 26 instead of 360 in this simplified example), this acceleration method can already significantly reduce the amount of calculation to be performed to 1 / 5.

[0061] In certain embodiments, the material usage function Material(α,β,dy) is related to the cost of the blanking operation. The cost can be, for example, a monetary cost or an environmental cost (CO2 emissions), or a combination of both. The value of the material usage takes into account the cost of the material, the scrap ratio, and the cost of the scrap if a scrap buy-back market is available, and the following factors are employed to calculate the material usage for a given combination of (α,β,dy) in this embodiment: · The pitch Δ1(α,β,dy) already mentioned, · The pitch Δ2(α,β,dy) already mentioned, · The scrap ratio Scrap(α,β,dy) defined as the ratio of the scrap generated by the blanking process to the total amount of strip material used, · The strip thickness t defined above as the distance between the top and bottom of the strip, where t is expressed, for example, in mm, · The material cost per unit weight Cost_Material, expressed, for example, in currency / ton, · The cost of scrap per unit weight Cost_Scrap, expressed, for example, in currency / ton, in cases where scrap material can be bought back, such as in the steel industry where scrap is remelted, · The material density ρ defined as the ratio between the weight and volume of the material, where ρ is usually expressed in kg / m 3 as.

[0062] Then, the following equations: M_Sec = ρ * t * W * (Δ1(α,β,dy) + Δ2(α,β,dy)) Material(α,β,dy) = Cost_Material * M_Sec - Cost_Scrap * %Scrap(α,β,dy) * M_Sec can be used to calculate Material(α,β,dy).

[0063] In a particular embodiment, the material cost Cost_Material depends on the width W of the strip. In fact, it is provided in the form of a database Cost_database including a set of p elements (Width_range j , Cost_Material j ), where p is an integer greater than or equal to 2, j is an integer included between 1 and p, where Width_range j is a width range having a value of the minimum strip width and a value of the maximum strip width, and Cost_Material j is the material cost per unit weight when the width W of the strip is included in Width_range j .

[0064] Variable costs according to the strip width can occur when the industrial cost for producing the strip actually depends on the width. For example, the industrial cost can increase with the width when an increase in width is associated with a decrease in productivity. For example, the material cost can increase with the width when a material of large width can only be produced in a determined industrial facility, thereby entailing a significant increase in logistics costs.

[0065] As mentioned above, the pitches Δ1(α,β,dy) and Δ2(α,β,dy) here correspond to the optimal pitch between consecutive blanks and make it possible to minimize the material usage (for given values of α, β, and dy). These pitches are preferably calculated using the following direct calculation method suitable for any polygonal-shaped blank (i.e., any blank whose contour includes straight edges): - Place blank A in the X, Y coordinate system such that the leftmost point of blank A is located at X = 0 and the lowermost point of blank A is located at Y = 0, and place blank B such that the leftmost point of blank B is located at X = 0 and the lowermost point of blank B is located at Y = dy. - In the X, Y coordinate system, a discrete set of vertices {A1,...,A P} and {B1,...,B qProvide a numerical representation of the contours of blank A and blank B, where p and q are integers greater than or equal to 3, and the vertices are joined by straight edges. - For each vertex A i calculate the distance dA i defined as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank A at the Y value of vertex A i A, and calculate the maximum internal lateral distance dAA i defined as the maximum value of all dA - For each vertex B i calculate the distance dB i defined as the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank B at the Y value of vertex B i B, and calculate the maximum internal lateral distance dBB i defined as the maximum value of all dB - For each vertex A i located at a Y value where at least one point of the contour of blank B exists i calculate the directed distances dA i B and dBA i respectively defined as the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank A, and the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank B at the Y value of vertex A i - For each vertex B i located at a Y value where at least one point of the contour of blank A exists i calculate the directed distances dAB i and dB i A respectively defined as the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank A, and the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank B at the Y value of vertex B i - All dA i B and dAB​​I Calculate the directed distance dAB defined as the maximum value of the values of all dB i A and dBA I Calculate the directed distance dBA defined as the maximum value of the values of - Δ1 is defined as the longitudinal pitch between the left end of the A blank and the left end of the adjacent B blank to the right thereof, and set Δ1 to the value dBA. - Δ2 is defined as the pitch between the left end of the B blank and the left end of the adjacent A blank to the right thereof. When dAB + dBA ≥ dAA and dAB + dBA ≥ dBB, set Δ2 to dBA. When dAB + dBA < dAA and dAA ≥ dBB, set Δ2 to dAA - dBA. When dAB + dBA < dBB and dBB > dAA, set Δ2 to dBB - dBA.

[0066] This method for determining dAA, dAB, dBB, and dBB, and thus Δ1 and Δ2, is shown in FIGS. 6A to 7B for a simple example, where blank A is rectangular and blank B is triangular (similar to FIG. 1). The blank contours of A and B are represented by vertices A1, A2, A3, A4, and B1, B2, B3 joined by straight edges, respectively. Each vertex A i is identified by its coordinates (XA i , YA i ), and each vertex B i is identified by its coordinates (XB i , YB i ).

[0067] For example, in the case of FIG. 6A, dA2A and dA4A are equal to 0, while dA3A and dA1A have equal values, so dAA = dA3A = dA1A. On the other hand, in FIG. 6B, dBB = dB2B.

[0068] Value dA i B and dAB i In the case of FIG. 7A representing the directed vectors corresponding to, dAB is equal to dAB2. Value dB i A and dBA iIn the case of FIG. 7B representing the oriented vector corresponding to, dBA becomes equal to dBA3.

[0069] In certain embodiments, the width W of the coil takes into account a width tolerance W_tol, typically expressed in mm. This further affects the value of the width W used to calculate the scrap cost and the blanking cost. The width tolerance corresponds, for example, to the accuracy that the strip production line can achieve with respect to the width. In order to ensure that blanks A and B fit into the strip even when the width of the strip produced is at the lower end of the width tolerance spectrum, it is necessary to aim for a strip width W that at least corresponds to the minimum width required to fit blanks A and blank B into the strip by adding the width tolerance W_tol. This configuration is shown in FIG. 5, where a margin of W_tol / 2 is left on either side of strip 1.

[0070] In certain embodiments, when nesting blanks A and B in the strip and thus also when calculating the scrap ratio and the material usage, a blanking tolerance Blank_tol, typically expressed in mm, is taken into account. The blanking tolerance corresponds to the accuracy of the tool used to cut the blank in the strip. In order to ensure that there is no overlap between the blanks when cutting the blanks from the strip, the distance between two adjacent blanks should not be less than 2*Blank_tol (in practice, each blank is cut with an accuracy of Blank_tol, and the risk of overlap can be completely avoided only by taking into account the blanking tolerance of each individual blank and providing the distance between two adjacent blanks). This is also shown in FIG. 5.

[0071] In certain embodiments, as shown in FIG. 6, the blanking tolerance is taken into account in the cost optimization method described above. This is done by first geometrically expanding blanks A and B by an amount of Blank_tol before applying the blank nesting method.

[0072] In certain embodiments, the method described above is applied to a configuration such that the blank B has exactly the same contour as the blank A. This is a very common case, and in fact, there is only one blank shape cut from the strip 1. In certain embodiments where the blank contour A = blank contour B, the directions of A and B with respect to the longitudinal direction in the optimization method described above are the same. In other words, the problem space contains only points of [α, β, dy] such that α = β or α = β + 180° mod 360° (mod indicates the modulo operator). This corresponds to situations where, for example, the direction of the blank within the strip has a technical impact on subsequent processes, which, for example, in the case of steel, the material is anisotropic and thus behaves differently when cut at different angles with respect to the longitudinal direction. For example, this applies when processing by stamping steel blanks from a strip with anisotropic properties. This enables the blanks A and B to have the same behavior in subsequent processes. Furthermore, this enables reducing the number of points within the problem space and thus making the cost optimization more rapid.

[0073] In certain embodiments, the method described above is applied to a configuration such that the blanks A and B have the same contour and dy = 0, that is, the problem space consists of only two dimensions corresponding to the angles α and β.

[0074] In certain embodiments, the method described above is applied to a configuration such that the blanks A and B have the same contour, dy = 0, and α = β, that is, the problem space consists of only one dimension corresponding to the angle α.

[0075] In certain embodiments, the method described above is applied to a configuration in which blank B has a mirror contour of blank A. This is a common case, for example, in the automotive industry, where many parts exist on both sides of the vehicle as right and left parts, which are generally mirror images of each other.

Claims

1. A computer-implemented method for nesting two blanks A and B within a rectangular strip, the strip generally extending in a longitudinal direction X and having a transverse direction Y, the method comprising: 1.1 / preparing two-dimensional blank contours for A and B; 1.3 / calculating values of a quantity Material(α, β, dy) for several values of α, β, and dy, and determining a minimum value, MinMaterial, of the quantity Material(α, β, dy), where Material(α, β, dy) corresponds to the amount of material used when nesting the blank contours in the rectangular strip, the blank contour A is oriented using an angle α, the blank contour B is oriented using an angle β, and dy is the difference in the transverse rise between the lowest point of blank A and the lowest point of blank B; 1.4 / Material(α ｏｐｔｉｍａｌ , β ｏｐｔｉｍａｌ , dy ｏｐｔｉｍａｌ ) = MinMaterial, the minimum value of Material(α, β, dy) shown as MinMaterial and α ｏｐｔｉｍａｌ , β ｏｐｔｉｍａｌ , dy ｏｐｔｉｍａｌ values to the user 1.5 / In the strip, the angle α ｏｐｔｉｍａｌ is used to form the first blank A, and the angle β ｏｐｔｉｍａｌ and the lateral offset amount dy ｏｐｔｉｍａｌ are used to form the first blank B. The next blank A is aligned horizontally with the first blank A using the angle α ｏｐｔｉｍａｌ , and the next blank B is arranged using the angle β ｏｐｔｉｍａｌ and the lateral offset amount dy ｏｐｔｉｍａｌ , and the pattern is repeated along the strip A computer-implemented method including the above.

2. The computer-implemented method according to claim 1, further comprising: 1.2 / providing a function Material(α, β, dy).

3. The desired angular accuracy ε expressed in degrees of an angle ａｎｇｌｅ and the desired distance accuracy ε expressed in mm ｄｙ being given, the blank A has a maximum height dymax in the lateral direction, and step 1.3 is executed by calculating the minimum material usage value MinMaterial as the minimum value of all Material(α, β, dy) values over all combinations of (ε ａｎｇｌｅ *i, ε ａｎｇｌｅ *j, ε ｄｙ *k), where i, j, and k are integers included between 0 and, respectively, 360 / ε ａｎｇｌｅ +1, 360 / ε ａｎｇｌｅ +1, and dymax / ε ｄｙ +1, a computer-implemented method according to claim 1 or 2

4. The computer-implemented method according to any one of claims 1 to 3, wherein in step 1.5, the pattern is repeated along the strip as long as it extends in the longitudinal direction.

5. The quantity Material(α, β, dy) corresponds to the amount of material obtained for an optimal longitudinal spacing (Δ １ , Δ ２ ) between blank A and blank B, and given fixed values of α, β, and dy, the optimal longitudinal spacing minimizes the amount of material used, the computer-implemented method according to any one of claims 1 to 4.

6. The computer-implemented method according to any one of claims 1 to 5, wherein step 1.3 is accelerated using an acceleration method, according to which several iterations of the calculation of Material(α, β, dy) are performed, each iteration being executed for a limited number of possible combinations of (α, β, dy), in each iteration, the combination of (α, β, dy) having the lowest material usage is selected, and each subsequent iteration is performed using points adjacent to the selected point in the (α, β, dy) space.

7. The acceleration method comprises: 2.1 / selecting a combination of (α, β, dy) having the lowest Material(α, β, dy) value from only a part of the possible combinations (α, β, dy) of step 1.3 of claim 1; 2.2 / N is an integer of 2 or more, and the following iteration is performed from k = 1 to N - 1, that is, from the combination of (α, β, dy) selected in the previous step and at least a part of the combination of the neighboring (α, β, dy), select the combination of (α, β, dy) having the lowest Material(α, β, dy) value, where the neighboring combination of (α, β, dy) is the combination (α + X * u ｋ *ε ａｎｇｌｅ , β + Y * v ｋ *ε ａｎｇｌｅ , dy + Z * w ｋ *ε ｄｙ ), where X, Y, and Z can each take a value of -1, 0, or +1, and u ｋ , v ｋ , and w ｋ are integers of 2 or more, and u ｋ < u ｋ－１ , v ｋ < v ｋ－１ , and w ｋ < w ｋ－１ ; repeat this step 2.3 / Determine the accelerated minimum material usage amount MinMaterialAcc as the minimum value of Material(α,β,dy) from at least a part of the combination of (α,β,dy) selected in the previous step and the combination of the neighboring (α,β,dy) (α + X * u Ｎ * ε ａｎｇｌｅ , β + Y * v Ｎ * ε ａｎｇｌｅ , dy + Z * w Ｎ * ε ｄｙ ), where X, Y, and Z can each take the value -1, 0, or +1, and u Ｎ , v Ｎ , and w Ｎ are integers greater than or equal to 1, and u Ｎ < u Ｎ－１ , v Ｎ < v Ｎ－１ , and w Ｎ < w Ｎ－１ . 2.4 / Material(α ｏｐｔｉｍａｌ＿ａｃｃ , β ｏｐｔｉｍａｌ＿ａｃｃ , dy ｏｐｔｉｍａｌ＿ａｃｃ ) = MinMaterialAcc, the accelerated minimum material usage MinMaterialAcc and the values α ｏｐｔｉｍａｌ＿ａｃｃ , β ｏｐｔｉｍａｌ＿ａｃｃ , dy ｏｐｔｉｍａｌ＿ａｃｃ output to the user The computer-implemented method according to claims 6 and 3, including the above.

8. The possible combinations of (α, β, dy) in step 2.1 are the combinations of (ε ａｎｇｌｅ *C*i, ε ａｎｇｌｅ *D*j, ε ｄｙ *E*m), where C, D, and E are fixed integers strictly greater than 1, and i, j, and m are integers taking all integer values from 0 to 360 / (ε ａｎｇｌｅ *C)+1, 360 / (ε ａｎｇｌｅ *D)+1, and dymax / (ε ｄｙ *E)+1, respectively, the computer-implemented method according to claim 7.

9. Further including an initial step of providing a tolerance threshold T% that is strictly greater than 0% and strictly less than 100%, and selecting a combination of (α, β, dy) having a minimum Material(α, β, dy) value from the combination of (α, β, dy) selected in the previous step and at least a part of the combinations of the neighboring (α, β, dy), the selection process of iterative step 2.2 is performed, the computer-implemented method according to claim 7 or 8.

10. Iterative step 2.2 is u ｋ = u ｋ－１ / 2, v ｋ = v ｋ－１ / 2, and wk = w ｋ－１ / 2, further characterized in that, a computer-implemented method according to any one of claims 7 to 9.

11. Step 2.3 and 2.3 are further characterized in that all combinations of adjacent (α, β, dy) of the (α, β, dy) selected during the previous step are used, i.e., all combinations (α + X * u ｋ * ε ａｎｇｌｅ , β + Y * v ｋ * ε ａｎｇｌｅ , dy + Z * w ｋ * ε ｄｙ ) are used, where X, Y, and Z take all values of -1, 0, and +1, and the computer-implemented method according to any one of claims 7 to 10, used in steps 2.2 and 2.

3.

12. u Ｎ = 1, v Ｎ = 1, and w Ｎ = 1, the computer-implemented method according to any one of claims 7 to 11.

13. ε ａｎｇｌｅ = 1°, ε ｄｙ = 1 mm, N = 5, and T% = 1%, further characterized by the method according to claims 7, 8, 9, 10, 11, and 12.

14. Further including an initial step of providing a blanking tolerance Blank_tol, and the method further includes, between steps 1.1 and 1.2 of claim 1, geometrically expanding blanks A and B by Blank_tol, and then applying subsequent steps to the expanded blank contours of the resulting blanks A and B, the method according to any one of claims 1 to 13.

15. Given the values of α, β, and dy, Providing an X, Y coordinate system parallel to L, T, and arranging blank A within the X, Y coordinate system such that the leftmost point of blank A is located at X = 0 and the lowermost point of blank A is located at Y = 0, and arranging blank B such that the leftmost point of blank B is located at X = 0 and the lowermost point of blank B is located at Y = dy, Within the X and Y coordinate systems, providing a numerical representation of the contours of blanks A and B consisting of discrete sets of vertices {A １ ,..., A Ｐ} and {B １ ,..., B ｑ}, where p and q are integers greater than or equal to 3, and the vertices are joined by straight edges, For each vertex A ｉ at the Y value of vertex A ｉ a distance dA ｉ is calculated as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank A, ｉ and the maximum internal lateral distance dAA defined as the maximum value of all dA For each vertex B ｉ a distance dB ｉ is defined as the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank B at the Y value of vertex B ｉ B is calculated, and the maximum internal lateral distance dB B ｉ defined as the maximum value of all dB B is calculated For each vertex A located at a Y value at which at least one point of the contour of the blank B exists ｉ calculate, for the vertex A ｉ at the Y value of the vertex A, the directed distances dAiB and dBA defined respectively as the difference between the maximum X value taken by the contour of the blank B and the minimum X value taken by the contour of the blank A, and ｉ at the Y value of the vertex A, the difference between the maximum X value taken by the contour of the blank A and the minimum X value taken by the contour of the blank B ｉ as For each vertex B located at a Y value at which at least one point of the contour of blank A exists ｉ calculate, as the difference between the maximum X value taken by the contour of blank B and the minimum X value taken by the contour of blank A at the Y value of vertex B ｉ and, as the difference between the maximum X value taken by the contour of blank A and the minimum X value taken by the contour of blank B at the Y value of vertex B ｉ respectively, the directed distances dAB ｉ and dBA ｉ ​ All dA ｉ B and dAB Ｉ Calculate the directed distance dAB defined as the maximum value of the values of ｉ A and dBA Ｉ Calculate the directed distance dBA defined as the maximum value of the values of, Δ １ is defined as the longitudinal pitch between the left end of the A blank and the left end of the adjacent B blank on its right, and Δ １ is set to the value dBA, Δ ２ is defined as the pitch between the left end of the B blank and the left end of the adjacent A blank on its right, and when dAB + dBA ≥ dAA and dAB + dBA ≥ dBB, Δ ２ is set to dBA, and when dAB + dBA < dAA and dAA ≥ dBB, Δ ２ is set to dAA - dBA, and when dAB + dBA < dBB and dBB > dAA, Δ ２ is set to dBB - dBA to determine an optimal longitudinal spacing (Δ １ , Δ ２ ) between the blank A and the blank B, the method according to claim 5 or any one of claims 6 to 14 dependent on claim 5.

16. The method according to any one of claims 1 to 15, wherein blank B has a contour that is exactly the same as blank A.

17. The method according to claim 16, wherein dy = 0 and α = β.

18. The method according to any one of claims 1 to 9, wherein blank B has a mirror image contour of blank A.

19. A computer program including instructions for causing a computer to execute the method according to any one of claims 1 to 18 when the program is executed by the computer.

20. A computer-readable storage medium including instructions for causing a computer to execute the method according to any one of claims 1 to 18 when executed by the computer.

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