Method for optimizing nesting of two blanks in longitudinally extending flat strip

Abstract

A first object of the invention is to provide a computerized method for determining an optimal 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 rotation angles and one lateral offset of the blank), and therefore potentially involves optimizing the material usage function over a very large combination set. This results in a high computational time, which may be a serious obstacle to implement material usage optimization methods. It is therefore a second object of the present invention to provide a computerized method for computerized determination acceleration for optimal blank nesting for material usage optimization and associated material usage.

Description

Technical Field

[0001] The present invention relates to the manufacture of cut-out shapes, and in particular to the manufacture of shapes cut from a generally rectangular flat strip of material extending in a longitudinal direction. Background Art

[0002] In many material manufacturing processes of typically flat materials, the continuous nature of the manufacturing process means that the final manufactured product is in the form of a long strip, typically extending in a longitudinal direction and having an elongated rectangular shape. This is the case, for example, in the production of flat metal sheets such as flat steel products or flat aluminum products. This is also the case in the pulp and paper industry or when manufacturing fabrics and textiles. Such strips are often conditioned by winding them into a coil shape so that they can be stored and transported efficiently.

[0003] A common way to use the material in a subsequent conversion process is to cut shapes with a predetermined contour from the strip. For example, a metal blank may be cut in the case of a metal strip, or a cutout of a fabric or textile in the fashion industry. In the case of a metal strip, this operation is called blanking, and the subsequent product is called a metal blank, i.e. a generally flat piece of metal with a predetermined contour, which is suitable for use in a subsequent conversion process. This operation can be performed, for example, by punching, water jet cutting, oxygen cutting or laser cutting. Summary of the invention

[0004] For the sake of simplicity, the term blank will be used hereinafter, but, as will be readily understood, the field of application of the invention is not limited to metallic materials.

[0005] The pattern in which the blanks are positioned in the strip (hereinafter referred to as nesting) influences the material usage of the blanking operation. The term "material usage" as used in the present description and claims corresponds to the material component of the blanking operation and may include several different aspects listed below, which list is not comprehensive:

[0006] - Environmental aspects: For example, if the production process of raw materials emits CO 2 , it would be interesting to optimize the material usage during the blanking operation to reduce the overall CO 2 emission,

[0007] - Productivity: Optimizing material usage means that the time spent on producing raw materials is also optimized,

[0008] - industrial feasibility aspects: the blank nesting pattern determines the necessary width of the strip in the longitudinal direction, which itself can have an impact on the industrial feasibility of the raw material strip (very large widths or very narrow widths may not be feasible),

[0009] - Cost: Optimizing material usage means using less raw material and therefore incurring less material costs.

[0010] In the present invention, the arrangement is as follows: a strip from which a first blank and a second blank are cut, each blank having a predetermined profile. Each blank has the freedom to rotate about an axis perpendicular to the top and bottom surfaces of the strip, and the second blank has the freedom to be positioned with a certain lateral offset compared to the first blank, which is itself located near the edge of the strip. The positioning of two consecutive blanks relative to each other in the longitudinal direction will determine a nesting pattern, which is then repeated as long as the strip extends in the longitudinal direction. In the present invention, a cost function is associated with the positioning of the two blanks in the strip, the cost being a function of at least the orientation of each blank and the lateral offset between the blanks.

[0011] The first object of the present invention is to provide a computer-implemented method for determining the optimal nesting of blanks in a strip so as to minimize material usage. Solving the optimization problem involves three different variables (two rotation angles of the blank and a lateral offset), and therefore potentially involves optimizing the material usage function over a very large set of combinations. This results in high computational time, which can be a serious obstacle to implementing the method. Therefore, a second object of the present invention is to provide a computer-implemented method for accelerating the optimization method.

[0012] By providing a computer-implemented method for minimizing material usage and by providing an acceleration method of said method, the present invention enables the automatic determination of the optimum nesting pattern of two blanks in a strip and the associated material usage in a fast and error-proof manner. This increases the productivity of blanking designs. In turn, this also enables the method to be performed on many different sets of blanks, thereby enabling the nesting and material usage of a large number of blank shapes to be studied in a minimum amount of time.

[0013] The object of the invention is achieved by providing a method according to claim 1 for computer-implemented optimization of the nesting of two blanks in a strip to minimize the material usage, the method optionally comprising the features of claims 2 to 19. The object of the invention is also achieved by providing a computer program according to claim 19 and a computer-readable storage medium according to claim 20. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The present invention will now be described and explained in detail by way of example without introducing limitations, with reference to the accompanying drawings:

[0015] - Figure 1 is an overview of the configuration of the nesting of two blanks in the strip,

[0016] - Figure 2 and Figure 3 is a simplified graphical description of the acceleration cost minimization method,

[0017] - Figure 4 and Figure 5 represents a specific embodiment of the invention in which the blanking tolerance and the width tolerance of the strip are taken into account in the calculation of the cost,

[0018] - FIG. 6A to FIG. 7B is a graphical representation of the calculation method used to determine the optimum longitudinal spacing between blanks. DETAILED DESCRIPTION

[0019] In the present invention, reference is made to Figure 1 , the longitudinal direction refers to the main direction of extension of the strip 1, and the transverse direction refers to the perpendicular direction in the plane to the longitudinal direction. The strip 1 also extends along the transverse direction Y with a limited width between the two parallel edges 2 and 3, and extends along the said direction with a width W.

[0020] The strip 1 has a top side and a bottom side, also referred to as the top surface and the bottom surface. All the figures are two-dimensional top views with only the top side visible. The distance between the top surface and the bottom surface is designated as the thickness of the strip. This thickness can be measured, for example, using a micrometer, the spindle and anvil of which are placed on the top surface and the bottom surface.

[0021] In the attached 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" will be used in the subsequent description and claims to refer to further rearward and further along the longitudinal direction (i.e., along the direction from Figure 1 The terms "upper" (and "above", "higher", etc.), "lower" (and "below", "lower", etc.) will be used in the subsequent description and claims to refer to further rearward and further in the lateral direction (i.e., along the direction indicated by the arrow "X" in FIG. 1 ), respectively. Figure 1 relative positioning of the components (in the direction marked by the “Y” arrow in the figure).

[0022] Reference Figure 1 , a first blank A having a first contour and a second blank B having a second contour are cut out from the strip 1 .

[0023] The blank B is offset in the transverse direction from the blank A by a transverse offset dy, which is defined as the transverse elevation difference between the lowest points in the transverse direction of the blank profile B and the blank profile A. The transverse offset dy is expressed in mm.

[0024] The blanks A and B form angles α and β respectively with a given direction in the plane of the strip 1. In the present invention, as a convention, the angles α and β are defined with reference to the longitudinal direction. The angles α and β are expressed in degrees.

[0025] Reference Figure 1 , the blank A has a height dymax(α) measured in the transverse direction, which depends on the angle α. The maximum height value dymax is defined as the maximum value of dymax(α) for all possible values ​​of α comprised between 0° and 360°.

[0026] A computer-implemented method for determining the optimal (α, β, dy) for nesting blanks A and B in a strip while minimizing subsequent material usage will now be described:

[0027] - Step 1.1 comprises providing a blank contour A and a blank contour B.

[0028] - step 1.3 comprises calculating the value of the quantity Material(α,β,dy) for several values ​​of α, β and dy in order to determine a minimum value MinMaterial of the quantity Material(α,β,dy), Material(α,β,dy) corresponding to the amount of material obtained when said blank profiles are nested in a rectangular strip, blank profile A being oriented at an angle α, blank profile B being oriented at an angle β, and dy being the difference in transverse elevation between the lowest point of blank A and the lowest point of blank B, the minimum value of Material(α,β,dy),

[0029] - Step 1.4 includes outputting MinMaterial and combination to the user (α optimal ,β optimal ,dy optimal ), so that Material(α optimal ,β optimal ,dy optimal )=MinMaterial.

[0030] - Step 1.5 consists in placing the first blank A in the strip at an angle α optimal Positioning, the first blank B at an angle β optimal and lateral displacement dy optimal Positioning, placing the subsequent (second) blank A at an angle α optimal and positioned transversely aligned with the first blank A, and the subsequent (second) blank B is positioned at an angle β optimal and lateral displacement dy optimal The pattern is positioned and repeated along the strip, for example, as long as the strip extends longitudinally.

[0031] In step 1.3, the quantity Material(α, β, dy) preferably corresponds to the material usage obtained for the optimal longitudinal spacing between blanks A and B, i.e. for the spacing that minimizes the material usage when α, β and dy have fixed (and not necessarily optimal) values.

[0032] The longitudinal spacing between blank A and blank B is, for example, composed of two pitches Δ 1 and Δ 2 Specify, Δ 1 is the distance in the longitudinal direction between the left end of the A blank and the left end of the adjacent B blank to its right, and Δ 2 It is the distance between the left end of the B blank and the left end of the adjacent A blank on its right.

[0033] Given the values ​​of α, β, and dy, the quantity Material(α,β,dy) corresponds to the pitch Δ that minimizes the amount of material used. 1 (α, β, dy) and Δ 2 (α,β,dy).

[0034] For the considered combination (α, β, dy), Δ can be iteratively determined by gradually moving blank B towards blank A in the longitudinal direction, for example until blank B touches or almost touches blank A. 1 (α,β,dy)(and for Δ 2 Δ can also be determined directly (rather than iteratively optimized) using the explicit fast calculation method described further below. 1 (α, β, dy) and Δ 2 (α,β,dy).

[0035] In summary, as presented above, in the method according to the invention, the minimization of the amount of material is carried out by splitting as follows:

[0036] - On the one hand, the optimization of the values ​​of α, β, and dy,

[0037] - and on the other hand a longitudinal spacing Δ 1 , Δ 2 The last one is performed separately (i.e. for each set (α, β, dy)).

[0038] Separate these two sub-optimizations from each other instead of 1 ,Δ 2 ) is beneficial to perform global optimization in the 5-dimensional space of . In fact, for a given set (α, β, dy), once the values ​​of α, β and dy are set, adjusting Δ 1 and Δ 2It is convenient to minimize the amount of material used (either iteratively or directly): this can be done efficiently from a computational point of view. And, more generally, from a numerical point of view, a split "3D plus 2D optimization" is easier to do than a full, entangled 5D optimization.

[0039] Furthermore, as mentioned above, once the values ​​of α, β and dy are set, it is straightforward to determine (thanks to a specific approach) the optimal longitudinal spacing (i.e., Δ 1 (α, β, dy) and Δ 2 (α, β, dy) calculation), which further speeds up the nested optimization.

[0040] The method for nesting two blanks described herein may include the following steps 1.2: providing a material usage function Material(α, β, dy). The material usage function may be in the form of a computer subroutine, routine, or other function that returns the value of Material(α, β, dy) given the values ​​of α, β, and dy.

[0041] To discretize the problem, an angular accuracy ε expressed in degrees is provided angle and distance accuracy ε in mm dy For example, ε angle = 1°, and ε dy =1mm. Step 1.3 then involves calculating MinMaterial as (ε angle *i,ε angle *j,ε dy The minimum value of all Material(α,β,dy) values ​​on all combinations of i, j, and k), where i, j, and k are included between 0 and 360 / ε respectively. angle +1, 360 / ε angle +1 and dymax / ε dy However, it may be noted that the detailed discretization may differ from the above example: the discrete values ​​of α, β, dy may belong to a value grid (of points) that is not necessarily rectangular (contrary to the above example), and the step size between two different values ​​may be non-constant.

[0042] In summary, in the above exemplary discretization scheme, it can be noted that i, j and k do not necessarily have to be included between 0 and 360 / ε respectively. angle +1, 360 / ε angle +1 and dymax / ε dy +1. In other words, to determine MinMaterial, there is no need to include all possible integer values ​​between 0 and 360 / ε respectively. angle +1, 360 / ε angle+1 and dymax / ε dy The quantity Material(α, β, dy) is evaluated for all integer values ​​between 0 and 360 / ε respectively. In particular, in the acceleration method for performing step 1.3 presented below, for angle +1, 360 / ε angle +1 and dymax / ε dy Only a portion of the integer values ​​between α and β + 1 are evaluated for the quantity Material(α, β, dy) (to avoid redundancy in the calculation).

[0043] In a specific embodiment, step 1.3 of the above method further comprises determining the pitch Δ 1 (α optimal ,β optimal ,dy optimal ) and Δ 2 (α optimal ,β optimal ,dy optimal ), so that Δ 1 (α optimal ,β optimal ,dy optimal ) is the distance in the longitudinal direction between the left end of the A blank and the left end of the adjacent B blank on its right side, Δ 2 (α optimal ,β optimal ,dy optimal ) is the distance between the left end of the B blank and the left end of the adjacent A blank on its right.

[0044] In a specific embodiment, step 1.5 of the above method further comprises using Δ 1 (α optimal ,β optimal ,dy optimal ) and Δ 2 (α optimal ,β optimal ,dy optimal ), so that step 1.5 comprises: placing the first blank A in the strip at an angle α optimal Positioning, the first blank B at an angle β optimal and a lateral offset dy compared to the first blank A optimal and longitudinal offset Δ 1 (α optimal ,β optimal ,dy optimal ) positioning, the subsequent blank A is positioned at an angle α optimal is aligned transversely with the first blank A and with a longitudinal offset Δ toward the first blank B 2 (α optimal ,β optimal ,dyoptimal ) are positioned and the pattern is repeated along the strip as long as the strip extends longitudinally.

[0045] In the remainder of the description below, MinMaterial will also be referred to as the “true optimal”, and (α optimal ,β optimal ,dy optimal ) is called the "truly optimal combination".

[0046] If, for example, as a typical value for the dimensions of a steel blank, ε angle =1°, ε dy = 1 mm, and dymax is, for example, 500 mm, the number of possible (α, β, dy) combinations that need to be calculated will be 360*360*500=64.8 million. Performing such a large number of calculations is expensive in terms of computer use and hinders the implementation of the method, especially when several blank shapes need to be considered.

[0047] The inventors have discovered that calculating Material(α, β, dy) for the entire range of possible (α, β, dy) combinations in step 1.3 results in many redundant calculations for combinations that are far from the optimal combination. With this in mind, the inventors have developed a method for accelerating step 1.3 in the above-described optimization method by performing several iterations of the Material(α, β, dy) calculation for a smaller number of possible (α, β, dy) combinations. In each iteration, the (α, β, dy) combination with the lowest material usage is selected, and each subsequent iteration is performed using the neighboring points of the selected point. Overall, this enables a significant reduction in the number of (α, β, dy) combinations for which the function Material(α, β, dy) needs to be calculated. In the accompanying description and claims, this method will be designated as an accelerated method.

[0048] The number of iterations of the acceleration method is represented by N, which is an integer equal to or greater than 2.

[0049] The acceleration method includes the following steps:

[0050] - step 2.1: selecting the (α, β, dy) combination having the lowest Material (α, β, dy) value from only a portion of the possible combinations (α, β, dy) of step 1.3 of claim 1,

[0051] - Step 2.2: Repeat the following iterations, where k=1 to N-1: Select the (α, β, dy) combination with the lowest Material (α, β, dy) value from the (α, β, dy) combination selected at the previous step and at least a portion of its adjacent (α, β, dy) combinations, where the combination adjacent to (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 of -1, 0, or +1, and u k 、v k and w k is an integer equal to or greater than 2, and where u k k -1, v k <v k -1, and w k <w k -1,

[0052] - Step 2.3: Determine the accelerated minimum material usage MinMaterialAcc as the (α, β, dy) combination selected in the previous step and its adjacent (α, β, dy) combination (α+X*u N *ε angle ,β+Y*v N *ε angel ,dy+Z*w N *ε dy ), where X, Y and Z can each take values ​​of -1, 0 or +1, and u N 、v N and w N is an integer equal to or greater than 1, and where u N N-1 , v N <v N-1 , and w N <w N-1 ,

[0053] - Step 2.4: Output the accelerated minimum material usage MinMaterialAcc and the value α to the user optimal_acc , β optimal_acc ,dy optimal_acc , so that Material(α optimal_acc ,β optimal_acc ,dy optimal_acc )=MinMaterialAcc.​​

[0054] Thanks to the above acceleration method, the number of Material(α,β,dy) calculations can be greatly reduced, resulting in a greatly reduced calculation time. It can be noted that the method for accelerating step 1.3 based on gradually selecting points and then exploring their neighborhood more finely can be implemented differently from the above example. For example, the neighborhood of each selected point can correspond to a spherical or almost spherical area around the point, rather than a parallelepiped (rectangular-like) neighborhood corresponding to the above example.

[0055] The selection of the reduced set of possible combinations (α, β, dy) in step 2.1 is a matter of compromise. In fact, if the number of possible combinations selected is very large, the accelerated method will be slower. On the other hand, if the number of possible combinations is very small, there is a risk that the final result MinMaterialAcc will be far from the true optimal result of the non-accelerated method. In fact, the accelerated method relies on testing the first set of points, and then testing their neighbors as the distances between the points become smaller and smaller as the iterations proceed. If the initial set of combinations is too small, with a large space between two combinations, there is a risk that the true optimal combination will be far away from the initial set of combinations and will never be reached when exploring the neighboring points subsequently.

[0056] In a specific embodiment, the possible (α, β, dy) combinations of step 2.1 are (ε angle *C*i,ε angle *D*j,ε dy *E*m) combination, where C, D and E are fixed integers strictly greater than 1, and where i, j and m are 0 and 360 / (ε angle *C)+1,360 / (ε angle *D)+1 and dymax / (ε dy *E)+1. In other words, the initial set of combinations is a regular grid in the space of all possible (α, β, dy) combinations. Advantageously, this allows the space between the initial (α, β, dy) combinations to be optimized, which makes it less likely that the true optimal combination will be missed when using the acceleration method.

[0057] In a particular embodiment, the acceleration method further comprises an initial step of providing a tolerance threshold T% strictly greater than 0% and strictly less than 100%. The selection process of iterative step 2.2 is then performed by selecting T% (α, β, dy) combinations with the lowest Material (α, β, dy) values ​​from the (α, β, dy) combination selected at the previous step and at least a portion of its adjacent (α, β, dy) combinations. Advantageously, this allows a repeatable method to be implemented for each selection step - it is also very suitable for encoding in the form of a computer program. The selection of the correlation threshold is also a matter of compromise. The higher T%, the more points will be transferred to the subsequent steps, and therefore more calculations will be involved at the subsequent steps. However, on the other hand, if the correlation threshold T% is too low, there is a risk of missing the truly optimal combination when applying the acceleration method.

[0058] In a particular embodiment, the iterative step 2.2 of the acceleration method is characterized by the fact that: k =u k-1 / 2,v k =v k-1 / 2 and wk=w k-1 / 2. In other words, at each iteration, the distance between the neighboring points and the selected point of the previous iteration is half the size as during the previous iteration. Advantageously, this allows a very good compromise to be obtained between the need to extensively investigate possible candidate combinations in the first iterations and the need to fine-tune the set of possible candidates at a very high resolution in the last iterations.

[0059] In a particular embodiment, the accelerated method is further characterized by the fact that all adjacent (α, β, dy) combinations of the (α, β, dy) combination 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 ), where X, Y and Z take all the values ​​-1, 0 and +1. Advantageously, this allows to systematically check all neighboring combinations of the combination selected at the previous step, minimizing the risk of missing the true optimal combination.

[0060] In a particular embodiment, the acceleration method is further characterized by the fact that: N =1, v N =1 and w N = 1. In other words, for α, β and dy, the neighboring points in step 2.3 of the acceleration method are ε angle , ε angle and εdy The distance is just next to the point selected in the last iteration of step 2.2. Advantageously, this allows to investigate possible candidates with a very fine grid in the last iteration, thereby minimizing the risk of missing the optimal result.

[0061] In the case of nesting steel billets of different shapes in steel strips, the inventors have performed several experiments using the above-mentioned embodiments and combinations of different N and T% values ​​applied to different examples of industrial billet profiles A and B to determine the optimal N and T% values, thereby allowing a very high calculation speed and ensuring that the truly optimal combination is found.

[0062] The inventors have discovered that the true optimum can be achieved using the following specific combination of the above embodiments:

[0063] ·ε angle =1°, ε dy =1mm, and N=5,

[0064] The accelerated method further comprises an initial step of providing a tolerance threshold T% of 1%. The selection process of iterative step 2.2 is then performed by selecting the (α, β, dy) combination having the 1% lowest Material (α, β, dy) value from the (α, β, dy) combination selected at the previous step and at least a portion of its neighboring (α, β, dy) combinations,

[0065] The possible (α, β, dy) combinations in step 2.1 are (ε angle *C*i,ε angle *D*j,ε dy *E*m) combination, and C=D=E=2 N-1

[0066] ·u k =u k-1 / 2,v k =v k-1 / 2 and wk=w k-1 / 2,

[0067] ·u N =1, v N =1 and w N =1 (this is actually the result of the two implementations listed above),

[0068] All adjacent (α, β, dy) combinations using the (α, β, dy) combination selected during the previous step, i.e. all combinations (α+X*u k *ε angle ,β+

[0069] Y*vk *ε angle ,dy+Z*w k *ε dy ), where X, Y, and Z take all the values ​​-1, 0, and +1.

[0071] Table 1 below lists the above investigations on steel blanks for the case of N=5 and for different values ​​of T% (1%, 0.5%, 0.4% and 0.3%):

[0072]

[0073]

[0074] The test was conducted using 18 different configurations of blank profiles A and B. The number of points given in the second column reflects the sum of the number of vertices of blank A and blank B when the blank profile is represented digitally in the form of a set of vertices connected by straight edges. This number indicates the complexity of the shape of the blank, and therefore indicates the amount of time spent by Material (α, β, dy) for a given combination. The more points there are, the longer the basic calculation of Material (α, β, dy), and therefore the longer it takes to find the time spent by MinMaterialAcc. The third column gives the result of MinMaterial (the true optimum of the non-accelerated method, marked here as "MinMat"). For each T% value tested, the MinMaterialAcc result (marked as "MinMatAcc" in the table) and the time required to perform the accelerated method are given, and the calculation is performed on a standard portable computer. As can be seen, the calculation time for T% = 1% is still very reasonable, and the MinMaterialAcc value is the true optimal MinMaterial in all cases. When reducing the tolerance threshold T%, the computation time decreases, since fewer possible combinations are selected at each iteration in step 2.2. However, the resulting MinMaterialAcc is not always the true optimal MinMaterial. The deviations from the true optimum are highlighted in grey in the table. The inventors have found that for N=5, in the configuration of applying the method to a typical steel blank for manufacturing, for example, automotive parts, T%=1% is a very good compromise between computation time and reaching the best solution to the optimization problem.

[0075] In a particular embodiment, each calculated Material(α,β,dy) value for a given (α,β,dy) combination is stored in a manner 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 tag named α, β, dy, such as the string "α_β_dy". Advantageously, this allows avoiding calculating the material usage for a given combination more than once, thus reducing the overall calculation time.

[0076] In a particular embodiment, the function dymax(α) is defined as the height of blank A measured in the transverse direction when A is oriented at an angle α. For a given value of α, dymax(α) corresponds to the maximum value in dy beyond which blank A and blank B can no longer contact each other. In terms of material usage, nesting blank A and blank B with dy > dymax(α) is generally not optimal, especially when the amount of scrap generated by a blanking operation is an important factor. In a particular embodiment, the acceleration method is only executed using combinations with dy < dymax(α). Advantageously, this avoids performing potentially useless calculations and thus reduces the calculation time without the risk of missing the true optimal combination.

[0077] Figure 2 and Figure 3 is a simplified graphical description of a particular embodiment of the acceleration method using the case of considering only two variables. This simplification allows representing the method in a 2D space instead of the 3D space required for α, β, dy combinations, and this simplification is made for clarity. The problem space is represented by a set of Cartesian coordinates of X 1 、X 2 . The accuracies of the two variables are ε 1 and ε 2 .

[0078] In Figure 2 and Figure 3 , the number of selected iterations is N = 4. The correlation threshold T% is 25%. The corresponding iteration number and step within the iteration are indicated at the top of each figure.

[0079] Referring to Figure 2 the upper left side, in this particular example, the initial possible combinations for step 2.1 are combinations of type (ε 1 *C*i, ε 2 *D*j), and C = D = 2 N-1 = 2 4-1 = 8. Since there are 16 initial combinations, the total number of selected combinations in the upper right side figure representing the end of step 2.1 is 25% * 16 = 4 combinations.

[0080] The example depicted is one in which uk =u k-1 / 2 and v k =v k-1 / 2. Figure 2 , lower left, the adjacent combination at iteration 1 of step 2.1 is located at the X of the combination selected at the end of step 2.1 1 ε in the direction 1 *8 / 2=ε 1 *4 and X 2 ε in the direction 2 *4. These figures also illustrate the fact that some of the selected points may have common neighbors when generating neighbor combinations. This is the case, for example, with the points indicated by reference numeral 4. In a particular embodiment, the acceleration method will be programmed in such a way that the material usage of these points is not calculated twice, as previously explained (e.g., by using a hash table to associate the material usage results with their combinations).

[0081] Another possible situation is illustrated by the combinations with reference numeral 5: these combinations are located in the region indicated by X. 1 , X 2 All combinations of coordinate systems are on the edge of the defined space, and therefore have a more finite number of neighbors.

[0082] Reference Figure 2 On the lower right side, the points with the lowest material usage of 25% are selected from a total of 20 points, and a total of 20*25%=5 points are selected.

[0083] Reference Figure 3 On the upper left side, in step 2.2 iteration 2, the distance between adjacent points drops to ε 1 *4 / 2=ε 1 *2 and ε 2 *2. This results in a total of 39 previously selected combinations and adjacent combinations. Figure 3 On the upper right side, among these 39 points, 25%*39=9 combinations with the lowest material usage are selected.

[0084] Reference Figure 3 Lower left, depicting step 2.3, with the distance between neighbors being ε 1 *2 / 2=ε 1 and ε 2 , that is, this is when u N =v N = 1. This yields 78 total combinations where the minimum material usage value is MinMaterialAcc and allows the optimal combination to be determined as well (see Figure 3 lower right).

[0085] In conclusion, Figure 3and Figure 4 The accelerated method described in the simplified graphical representation would require computing the material usage function for the following number of combinations:

[0086] -Step 2.1: 16 combinations

[0087] - Step 2.2 Iteration 1: 20-4=16 combinations (number of adjacent combinations - number of previously selected combinations - material usage of previously selected combinations already calculated and stored at the previous step).

[0088] - Step 2.2 Iteration 2: 39-5 = 34 combinations

[0089] - Step 2.3: 78-9 = 69 combinations

[0090] In general, the accelerated method involves calculating the material usage function for 16+16+34+69=135 combinations. The total number of possible combinations when the non-accelerated method is used is 26*26=676. Thus, in this simplified case involving one less variable than the actual 3-dimensional problem of the present invention and a small number of possible values ​​for the variable (e.g., 26 instead of 360 values ​​for the angle in the simplified example when the angle accuracy is 1°), the accelerated method has already reduced the amount of calculations to be performed very significantly by a factor of five.

[0091] In a particular embodiment, 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 (CO 2 In this embodiment, the material usage value takes into account the material cost, scrap rate and scrap cost (if a scrap buy-back market is available) - the following elements are used to calculate the material usage for a given (α, β, dy) combination:

[0092] The spacing Δ mentioned previously 1 (α,β,dy),

[0093] The spacing Δ mentioned previously 2 (α,β,dy),

[0094] Scrap rate Scrap(α,β,dy), which is defined as the ratio between the scrap generated by the blanking process and the total amount of strip material used,

[0095] Strip thickness t, which is defined above as the distance between the top and bottom sides of the strip, t being expressed, for example, in mm,

[0096] The material cost per unit of weight Cost_material, for example in currency / ton,

[0097] In cases where the scrap material can be bought back, such as is the case in the steel industry where the scrap is remelted, the cost of the scrap per unit weight Cost_Scrap, e.g. expressed in currency / tonne,

[0098] Material density ρ, which is defined as the ratio between the weight and volume of a material. ρ is usually expressed in kg / m 3 express.

[0099] Material(α,β,dy) can then be calculated using the following formula:

[0100] M_Sec=ρ*t*W*(Δ 1 (α,β,dy)+Δ 2 (α,β,dy)

[0101] Material(α,β,dy)

[0102] =Cost_material*M_Sec-Cost_scrap*%Scrap(α,β,dy)

[0103] *M_Sec

[0104] In a particular embodiment, the material cost Cost_material depends on the width W of the strip and is actually provided in the form of a database Cost_database, which includes a set of p elements (Width_range j ,Cost_material j ), p is an integer equal to or greater than 2, and j is an integer included between 1 and p, wherein Width_range j is a width range with minimum and maximum strip width values, and Cost_material j When the strip width W is included in Width_range j The material cost per unit of weight.

[0105] Variable costs according to the width of the strip may occur when the industrial costs of producing the strip do depend on the width. For example, if an increase in the width is associated with a lower productivity, the industrial costs may increase with the width. For example, if large-width material can only be produced in certain industrial facilities, the material costs may increase with the width, resulting in higher logistics costs.

[0106] As mentioned before, the spacing Δ 1 (α, β, dy) and Δ 2(α, β, dy) here corresponds to the optimal spacing between consecutive blanks, so that the material usage (given the values ​​of α, β and dy) can be minimized. These spacings are preferably calculated using the following direct calculation method, which is suitable for any polygonal blank (that is, for any blank whose contour includes straight edges):

[0107] - positioning blank A in an X, Y coordinate system so that the leftmost point of blank A is at X=0 and the lowest point of blank A is at Y=0, and positioning blank B so that the leftmost point of blank B is at X=0 and the lowest point of blank B is at Y=dy,

[0108] - In the discrete vertex set {A 1 ,…,A P} and {B 1 ,…,B q} provides a numerical representation of the contours of blanks A and B in the X, Y coordinate system composed of, p and q are integers greater than or equal to 3, and the vertices are connected by straight edges,

[0109] -For each vertex A i Calculate the distance dA i A, the distance dA i A is defined as the i The difference between the maximum X value taken by the profile of blank A and the minimum X value taken by the profile of blank A at the Y value of dA is calculated and is defined as the difference between the maximum X value taken by the profile of blank A and the minimum X value taken by the profile of blank A at the Y value of dA i The maximum internal lateral distance dAA of the maximum value in A,

[0110] -For each vertex B i Calculate distance in dB i B, the distance in dB i B is defined as the vertex B i The Y value of the blank B is the difference between the maximum X value taken by the profile of the blank B and the minimum X value taken by the profile of the blank B, and the calculation is defined as all dB i The maximum internal lateral distance dBB of the maximum value of B,

[0111] - For each vertex A there is at least one point of the contour of the blank B at the Y value i , calculate the directional distance dA i B and dBA i , the directional distance dA i B and dBA i They are defined as i 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 iThe difference between the maximum X value taken from the profile of blank A and the minimum X value taken from the profile of blank B at the Y value of

[0112] - For each vertex B at the Y value of at least one point on the profile of blank A i , calculate the oriented distance dAB i and dB i A, where the oriented distances dAB i and dB i A are respectively defined as the difference between the maximum X value taken from the profile of blank B and the minimum X value taken from the profile of blank A at the Y value of vertex B i , and the difference between the maximum X value taken from the profile of blank A and the minimum X value taken from the profile of blank B at the Y value of vertex B i .

[0113] - Calculate the oriented distance dAB defined as the maximum value among all dA i B and dAB I values, and calculate the oriented distance dBA defined as the maximum value among all dB i A and dBA I values.

[0114] - Δ 1 is defined as the spacing in the longitudinal direction between the left end of blank A and the left end of the adjacent blank B on its right. Set Δ 1 to the value dBA.

[0115] - Δ 2 is defined as the spacing between the left end of blank B and the left end of the adjacent blank A on its right. If dAB + dBA ≥ dAA and dAB + dBA ≥ dBB, then set Δ 2 to dBA; if dAB + dBA < dAA and dAA ≥ dBB, then set Δ 2 to dAA - dBA; if dAB + dBA < dBB and dBB > dAA, then set Δ 2 to dBB - dBA.

[0116] This way of determining dAA, dAB, dBB, and dBB and then Δ 1 and Δ 2 is shown in FIG. 6A to FIG. 7B for a simple example where blank A is rectangular and blank B is triangular (as in Figure 1 ). The blank profiles of A and B are respectively composed of vertices A 1 , A 2 , A 3 , A 4 and B 1, B 2 , B 3 Each vertex A i By its coordinates (XA i ,YA i ) and each vertex B i By its coordinates (XB i ,YB i ) logo.

[0117] For example, in Fig. 6A In the case of 2 A and dA 4 A is equal to 0, and dA 3 A and dA 1 A has the same value, so dAA = dA 3 A=dA 1 A. And for Figure 6B , dBB=dB 2 B.

[0118] In the representation with the value dA i B and dB i The corresponding directional vector Fig. 7A In the case of dAB, dAB is equal to dAB 2 . In the expression with the value dB i A and dBA i The corresponding directional vector Figure 7B In this case, dBA will be equal to dBA 3 .

[0119] In a particular embodiment, the width W of the coil takes into account a width tolerance W_tol, which is usually expressed in mm. This in turn affects the width value W used in the calculation of the scrap costs and the blanking costs. The width tolerance corresponds, for example, to the precision that can be achieved in the strip production line in terms of width. In order to ensure that the blanks A and B will fit into the strip even when the width of the manufactured strip is at the lower end of the width tolerance range, it will be necessary to target a strip width W that corresponds at least to the minimum width required in the blanks A and B to fit into the strip with the width tolerance W_tol added. This configuration is Figure 5 , where a margin of W_tol / 2 is left on both sides of the strip 1 .

[0120] In a particular embodiment, a blanking tolerance Blank_tol, usually expressed in mm, is taken into account when nesting the blanks A and B in the strip and therefore also when calculating the scrap rate and the material usage. The blanking tolerance corresponds to the precision of the tool used to cut the blanks in the strip. In order to ensure that there is no overlap between the blanks when they are cut from the strip, the distance between two adjacent blanks should not be less than 2*Blank_tol (in fact, each blank is cut with a precision of Blank_tol, and the risk of overlap can only be completely avoided by providing a distance between two adjacent blanks taking into account the blanking tolerance of each individual blank). This is also Figure 5 Shown in.

[0121] In a particular embodiment such as that shown in Figure 6, 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 a Blank_tol factor and then applying a blank nesting method.

[0122] In a particular embodiment, the above method is applied to a configuration in which blank B has exactly the same profile as blank A. This is a very common case in which there is actually only one blank shape to be cut from the strip 1. In a particular embodiment in which blank profile A = blank profile B, the orientation of A and B relative to the longitudinal direction is the same in the above optimization method. In other words, the problem space contains only [α, β, dy] points, where α = β or α = β + 180° mod 360° (mod represents the modulus operator). This corresponds to the case where, for example, the orientation of the blank within the strip has a technical impact on the subsequent process - for example in the case of steel, when the material is anisotropic and therefore will behave differently if cut at different angles to the longitudinal direction. This is the case, for example, when processing is performed by stamping a steel blank from a strip with anisotropic properties. This allows the same behavior in the subsequent process of blanks A and B. This also allows a smaller number of points in the problem space and therefore a faster cost optimization.

[0123] In a particular embodiment, the above method is applied to a configuration in which blanks A and B have the same profile and in which dy=0, ie the problem space consists of only two dimensions corresponding to the angles α and β.

[0124] In a particular embodiment, the above method is applied to a configuration in which blanks A and B have the same profile, dy=0 and α=β, ie the problem space consists of only one dimension corresponding to the angle α.

[0125] In a particular embodiment, the above method is applied to a configuration where blank B is a mirror image profile of blank A. This is a very common situation, for example in the automotive industry, where many parts exist on both sides of the vehicle as right-hand and left-hand parts that are often mirror images of each other.

Claims

1. A computer-implemented method for nesting two blanks A and B in a rectangular strip extending generally in a longitudinal direction X and having a transverse direction Y, the method comprising the steps of: 1.1 / Provide the two-dimensional blank contours of A and B, 1.3 / calculating the value of the quantity Material(α,β,dy) for several values ​​of α, β and dy to determine a minimum value MinMaterial of said quantity Material(α,β,dy), Material(α,β,dy) corresponding to the amount of material obtained when said blank profile is nested in said rectangular strip, blank profile A being oriented at an angle α, blank profile B being oriented at an angle β, and dy being the difference in transverse elevation between the lowest point of blank A and the lowest point of blank B, the minimum value of Material(α,β,dy), 1.4 / Output the minimum value of Material(α,β,dy) and the value α, which is recorded as MinMaterial, to the user optimal , β optimal ,dy optimal , so that Material(α optimal ,β optimal ,dy optimal ) = MinMaterial, 1.5 / In the strip, the first blank A is placed at an angle α optimal Positioning, the first blank B at an angle β optimal and lateral displacement dy optimal Positioning, placing the subsequent blank A at an angle α optimal and positioned transversely aligned with the first blank A and the subsequent blank B at an angle β optimal and lateral displacement dy optimal Position and repeat the pattern along the strip.

2. The computer-implemented method of claim 1 , further comprising: 1.2 / Provide function Material(α,β,dy).

3. The computer-implemented method of claim 1 or 2, wherein: Given the desired angular accuracy ε expressed in degrees angle and the required distance accuracy ε in mm dy In the case where the blank A has a maximum height dymax in the transverse direction, step 1.3 calculates the minimum material usage value MinMaterial as (ε angle *i,ε angle *j,ε dy *k), where i, j, and k are included between 0 and 360 / ε respectively. angle +1, 360 / ε angle +1 and dymax / ε dy Integer between +1.

4. A 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 the strip extends longitudinally.

5. The computer-implemented method according to any one of claims 1 to 4, wherein: The quantity Material(α, β, dy) corresponds to the amount of material obtained for the optimal longitudinal spacing (Δ1, Δ2) between blanks A and B, which minimizes the material usage given fixed values ​​of α, β and dy.

6. A computer-implemented method according to any one of claims 1 to 5, wherein: An acceleration method is used to speed up step 1.3, according to which several iterations of Material(α,β,dy) calculation are performed, each iteration is performed for a finite number of possible (α,β,dy) combinations, and at each iteration the (α,β,dy) combination with the lowest material usage is selected, and each subsequent iteration is performed using neighboring points of the selected point in the (α,β,dy) space.

7. The computer-implemented method of claims 6 and 3, wherein: The acceleration method The following steps are involved: 2.1 / selecting the (α, β, dy) combination with the lowest Material (α, β, dy) value from only a portion of the possible combinations (α, β, dy) of step 1.3 of claim 1, 2.2 / Repeat the following iterations, where k=1 to N-1, where N is an integer equal to or greater than 2: Select the (α, β, dy) combination with the lowest Material (α, β, dy) value from the (α, β, dy) combination selected at the previous step and at least a portion of its adjacent (α, β, dy) combinations, where the combination adjacent to (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 is an integer equal to or greater than 2, and wherein u k k-1 、v k <v k-1 And w k <w k-1 ,​ 2.3 / The accelerated minimum material usage MinMaterialAcc is determined as the (α, β, dy) combination selected in the previous step and its adjacent (α, β, dy) combination (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 is an integer equal to or greater than 1, and wherein u N N-1 、v N <v N-1 And w N <w N-1 ,​ 2.4 / Output the accelerated minimum material usage MinMaterialAcc and value α to the user optimal_acc , β optimal_acc ,dy optimal_acc , so that Material(α optimal_acc ,β optimal_acc ,dy optimal_acc )=MinMaterialAcc.

8. The computer-implemented method of claim 7, wherein: The possible (α, β, dy) combinations in step 2.1 are (ε angle *C*i,ε angle *D*j,ε dy *E*m) combination, where C, D and E are fixed integers strictly greater than 1, and where i, j and m are integers between 0 and 360 / (ε angle *C)+1,360 / (ε angle *D)+1 and dymax / (ε dy *E)+1.

9. A computer-implemented method according to claim 7 or 8, further comprising an initial step of providing a tolerance threshold T% strictly greater than 0% and strictly less than 100%, and wherein, The selection process of iterative step 2.2 is performed by selecting T% (α, β, dy) combinations having the lowest Material (α, β, dy) values ​​from the (α, β, dy) combination selected at the previous step and at least a portion of its neighboring (α, β, dy) combinations.

10. A computer-implemented method according to any one of claims 7 to 9, wherein: The iterative step 2.2 is also characterized by the fact that: k =u k-1 / 2, v k =v k-1 / 2 and wk=w k-1 / 2.

11. A computer-implemented method according to any one of claims 7 to 10, wherein: Steps 2.2 and 2.3 are also characterized by the fact that all adjacent (α, β, dy) combinations of the (α, β, dy) combination 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 ), where X, Y, and Z take all the values ​​-1, 0, and +1.

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

13. The method according to claims 7, 8, 9, 10, 11 and 12, further characterized in that The following facts: angle =1°、ε dy =1mm, N=5 and T%=1%.

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

15. A method according to claim 5 or any one of claims 6 to 14 as appended thereto, comprising: Given the values ​​of α, β and dy, the optimal longitudinal spacing (Δ1, Δ2) between blank A and blank B is determined by the following steps: - providing an X, Y coordinate system parallel to L, T, wherein blank A is positioned in said X, Y coordinate system so that the leftmost point of blank A is at X=0 and the lowest point of blank A is at Y=0, and blank B is positioned so that the leftmost point of blank B is at X=0 and the lowest point of blank B is at Y=dy, - In the discrete vertex set {A1,…,A P } and {B1,…,B q } provides a numerical representation of the contours of blank A and blank B in the X, Y coordinate system composed of, p and q are integers greater than or equal to 3, and the vertices are connected by straight edges, -For each vertex A i Calculate the distance dA i A, the distance dA i A is defined as the i The difference between the maximum X value taken by the profile of blank A and the minimum X value taken by the profile of blank A at the Y value of dA is calculated and is defined as the difference between the maximum X value taken by the profile of blank A and the minimum X value taken by the profile of blank A at the Y value of dA i The maximum internal lateral distance dAA of the maximum value in A, -For each vertex B i Calculate distance in dB i B, the distance in dB i B is defined as i The Y value of the blank B is the difference between the maximum X value taken by the profile of the blank B and the minimum X value taken by the profile of the blank B, and the calculation is defined as all dB i The maximum internal lateral distance dBB of the maximum value of B, - For each vertex A there is at least one point of the contour of the blank B at the Y value i , calculate the directional distance dA i B and dBA i , the directional distance dA i B and dBA i They are defined as i 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 i The difference between the maximum X value taken by the profile of blank A and the minimum X value taken by the profile of blank B at the Y value of - For each vertex B there is at the Y value of at least one point of the contour of the blank A i , calculate the directional distance dAB i and dB i A, the directional distance dAB i and dB i A is defined as i 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 and at vertex B i The difference between the maximum X value taken by the profile of blank A and the minimum X value taken by the profile of blank B at the Y value of -Calculation is defined as all dA i B and dAB I The directional distance dB is the maximum value among the values, and the calculation is defined as all dB i A and dBA I The directional distance of the maximum value in dBA, -Δ1 is defined as the distance in the longitudinal direction between the left end of the A workpiece and the left end of the B workpiece adjacent to the right side of the A workpiece, and Δ1 is set to the value dBA. -Δ2 is defined as the distance between the left end of the B workpiece and the left end of the A workpiece adjacent to the right side of the B workpiece. If dAB + dBA ≥ dAA and dAB + dBA ≥ dBB, then Δ2 is set to dBA; if dAB + dBA < dAA and dAA ≥ dBB, then Δ2 is set to dAA - dBA; if dAB + dBA < dBB and dBB > dAA, then Δ2 is set to dBB - dBA.

16. The method according to any one of claims 1 to 15, wherein: The workpiece B has exactly the same profile as the workpiece 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: The workpiece B has a mirror image profile of the workpiece A.

19. A computer program comprising instructions that, when the program is executed by a computer, cause the computer to perform the method according to any one of claims 1 to 18.

20. A computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 18.

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