Method to optimize the nesting of two blanks within a longitudinally extending flat strip

21:

• A computer implemented method for a nesting of two blanks A and B within a rectangular strip, the strip extending in a longitudinal direction X and having a transverse direction Y, the method comprising the following steps:
• step 1.1 providing 2-dimensional blank contours defining blank contour A and blank contour B;
• step 1.3 computing a value of a quantity Material(α, β, dy) for several values of a, R and dy to determine a minimum value, MinMaterial, of the quantity Material(α, β, dy), Material(α, β, dy) corresponding to a material usage obtained when nesting blank contour A and blank contour B in the rectangular strip, blank contour A being oriented with an angle α, blank contour B being oriented with an angle β and dy being a difference in transversal elevation between a lowest point of blank A and a lowest point of blank B, a minimum value of Material(α, β, dy);
• step 1.4 outputting to a user the minimum value of Material(α, β, dy), noted MinMaterial, and values αoptimal, βoptimal, dyoptimal, wherein Material(αoptimal, βoptimal, dyoptimal) equals MinMaterial;
• and
• step 1.5 positioning in the strip a first blank A with an angle αoptimal, a first blank B with an angle βoptimal and a transverse offset dyoptimal, a following blank A with the angle αoptimal and in transverse alignment of the first blank A and a following blank B with the angle βoptimal and the transverse offset dyoptimal and repeating the pattern along the strip.

27:

• The computer implemented method according to claim 26 wherein the accelerated method includes the following steps:
• step 2.1 selecting the (α, β, dy) combinations having the lowest Material(α, β, dy) values out of only part of the possible combinations (α, β, dy) of step 1.3 according to claim 21;
• step 2.2 repeating the following iteration for k=1 to N-1, wherein N is an integer equal to or greater than 2, selecting the (α, β, dy) combinations having the lowest Material(α, β, dy) values out of the (α, β, dy) combinations selected at the previous step and at least part of their neighboring (α, β, dy) combinations, wherein a neighboring combination to (α, β, dy) is the combination (α+X*uk*εangle, β+Y*vk*εangle, dy+Z*wk*εdy), wherein X, Y and Z can each take on the values −1, 0 or +1, wherein uk, vk and wk are integers equal to or greater than 2 and wherein uk<uk-1, vk<vk-1 and wk<wk-1;
• step 2.3 determining an accelerated minimum material usage MinMaterialAcc as being the minimum value of Material(α, β, dy) out of the (α, β, dy) combinations selected at the previous step and at least part of their neighboring (α, β, dy) combinations (α+X*uN*εangle, β+Y*vN*εangle, dy+Z*wN*εdy), wherein X, Y and Z can each take on the values −1, 0 or +1, wherein uN, vN and wN are integers equal to or greater than 1 and wherein uN<uN-1, vN<vN-1 and wN<wN-1;
• and
• step 2.4 outputting to a user the accelerated minimum material usage MinMaterialAcc and the values αoptimal_acc, βoptimal_acc, dyoptimal_acc, wherein Material(αoptimal_acc, βoptimal_acc, dyoptimal_acc) equals MinMaterialAcc.

34:

• The computer implemented method according to claim 21 further including:
• an initial step of providing a blanking tolerance Blank_tol;
• in between steps 1.1 and 1.2 of claim 21 a step of geometrically inflating blanks A and B by a factor of Blank_tol;
• and
• then applying the subsequent steps to the resulting inflated blank contours of blank A and blank B.

35:

• The computer implemented method according to claim 25 including, given the value of α, of β, and of dy,
• determining the optimal longitudinal spacing (Δ1, Δ2) between blank A and blank B, by
• providing a X, Y coordinate system parallel to L, T, where blank A is positioned in the X, Y coordinate system so that a furthest left point of blank A is located at X=0 and a lowest point of blank A is located at Y=0 and blank B is positioned that a furthest left point of blank B is located at X=0 and a lowest point of blank B is located at Y=dy;
• providing a numerical representation of the contours of blank A and blank B in the X, Y coordinate system consisting of discrete sets of vertices {A1, . . . , AP} and {B1, . . . Bq}, p and q being integers greater than or equal to 3, the vertices being joined by straight edges;
• computing for each vertex Ai a distance dAiA being defined as a difference between a largest X value taken by the contour of blank A and the a X value taken by the contour of blank A at the Y value of vertex Ai and calculating a largest inner transverse distance dAA defined as a maximum value of all dAiA;
• computing for each vertex Bi the distance dBiB being defined as the difference between a largest X value taken by the contour of blank B and a smallest X value taken by the contour of blank B at the Y value of vertex Bi and calculating a largest inner transverse distance dBB defined as a maximum value of all dBiB;
• computing for each vertex Ai located at a Y value for which at least one point of the contour of blank B is present oriented distances dAiB and dBAi defined respectively as a difference between the largest X value taken by the contour of blank B and a smallest X value taken by the contour of blank A at the Y value of vertex Ai and as a difference between the largest X value taken by the contour of blank A and the smallest X value taken by the contour of blank B at the Y value of vertex Ai;
• computing for each vertex Bi located at a Y value for which at least one point of the contour of blank A is present oriented distances dABi and dBiA defined respectively as a difference between the largest X value taken by the contour of blank B and the smallest X value taken by the contour of blank A at the Y value of vertex Bi and as the difference between the largest X value taken by the contour of blank A and the smallest X value taken by the contour of blank B at the Y value of vertex Bi;
• computing an oriented distance dAB defined as a maximum value of all dAiB and dAB1 values, and computing an oriented distance dBA defined as the maximum value of all dBiA and dBA1 values;
• Δ1 being defined as a pitch in the longitudinal direction between a left extremity of an A blank and a left extremity of its right-hand neighboring B blank, setting Δ1 to the value dBA;
• and
• Δ2 being defined as a pitch between the a extremity of a B blank and a left extremity of its right-hand neighboring A blank, setting Δ2 to dBA if dAB+dBA≥dAA and dAB+dBA≥dBB, setting Δ2 to dAA−dBA if dAB+dBA<dAA and dAA≥dBB, setting Δ2 to dBB−dBA if dAB+dBA<dBB and dBB>dAA.