Metal sheet forming limit determination method and forming limit determination system, and computer program
A metal sheet includes a forming test step that forms a test specimen with an arbitrary lattice or a pattern for strain analysis while capturing an image of the surface, analyzing images obtained during the forming to measure the strain, and storing the strain in time series from the start of the forming to the occurrence of fracture to construct a strain database; and a forming limit analysis step includes setting, an evaluation point sequence for acquiring a strain distribution in the vicinity of a portion where fracture has occurred, extracting strain corresponding to the position of the evaluation point sequence in an arbitrary forming step from the strain database, calculating an approximation strain curve corresponding to the position of the point sequence, determining, the difference between the strain based on the approximation strain curve and analyzing the images, and determining a forming limit based on the obtained approximation error.
1 . A metal sheet forming limit determination method comprising a forming test step and a forming limit analysis step for a metal sheet,
wherein:
the forming test step comprises
a step of preparing a test specimen of a metal sheet with an arbitrary lattice or a pattern for strain analysis displayed on the surface,
a step of forming the test specimen while capturing an image of the surface of the test specimen with the lattice or the pattern for strain analysis displayed on the surface,
a step of analyzing images captured sequentially during the forming to measure strain generated in the metal sheet, and
a step of storing the measured strain in time series from a start of the forming to occurrence of fracture to construct a strain database, and that
the forming limit analysis step comprises
a step of setting, on the test specimen, an evaluation point sequence for acquiring a strain distribution in the vicinity of a portion where fracture has occurred,
a step of extracting, from the strain database, the strain at a position of the evaluation point sequence in an arbitrary forming step,
a step of calculating, from the extracted strain, an approximation strain curve corresponding to the position of the evaluation point sequence,
a step of determining, as an approximation error, a difference between the strain at the position of the evaluation point sequence based on the calculated approximation strain curve and strain at the position of the evaluation point sequence measured by analyzing the images, and
a step of determining a forming limit based on the obtained approximation error.
2 . The metal sheet forming limit determination method according to claim 1 , wherein
the approximation strain curve is a polynomial function.
3 . The metal sheet forming limit determination method according to claim 1 , wherein
the step of determining a forming limit comprises determining that necking has occurred in a forming step in which the approximation error has exceeded a predetermined threshold and determining, as the forming limit, strain at the evaluation point sequence on the metal sheet in the forming step or one step earlier than the forming step.
4 . The metal sheet forming limit determination method according to claim 1 , wherein
the step of determining a forming limit displays the approximation strain curve, and a strain distribution in the vicinity of the evaluation point sequence.
5 . The metal sheet forming limit determination method according to claim 1 , wherein
the forming test step comprises performing forming tests for a plurality of test specimens having different shapes, and the forming limit analysis step comprises determining a forming limit for each test specimen to obtain a forming limit line.
6 . A computer program for executing the metal sheet forming limit determination method according to claim 1 , wherein
the computer program uses a computer to function as a forming test means and forming limit analysis means.
7 . A metal sheet forming limit determination system comprising a forming test machine, a strain measuring device, and a forming limit analysis device,
wherein:
the forming test machine is configured to perform press forming by, while clamping a test specimen of a metal sheet with an arbitrary lattice or a pattern for strain analysis displayed on the surface between a die and a blank holder, pressing a central portion of the test specimen with a tip end of a punch that is fitted into a forming test portion in a central hole of the die through a central hole of the blank holder, and comprises an image-capturing means for capturing an image of the surface of the test specimen during the press forming; that
the strain measuring device comprises an image analysis unit that analyzes images of the surface of the test specimen obtained by the image-capturing means to acquire a strain distribution, a strain measurement unit that calculates strain from the obtained strain distribution, and a strain data accumulation unit that stores strain in time series from a start of the forming to occurrence of fracture to construct a strain database; and that
the forming limit analysis device comprises
a strain extraction unit that sets, on the test specimen, an evaluation point sequence for acquiring a strain distribution in the vicinity of a portion where fracture occurs, and extracts the strain at a position of the evaluation point sequence in an arbitrary forming step from the strain database of the strain data accumulation unit,
a strain curve approximation unit that calculates from the extracted strain an approximation strain curve corresponding to the position of the evaluation point sequence,
an approximation error analysis unit that determines, as an approximation error, a difference between the strain at the position of the evaluation point sequence based on the calculated approximation strain curve and strain at the position of the evaluation point sequence measured by analyzing the images, and
a forming limit determination unit that determines a forming limit based on the obtained approximation error.
8 . The metal sheet forming limit determination system according to claim 7 , wherein
the forming test machine has a drive plate interposed between the test specimen and the punch.
9 . The metal sheet forming limit determination system according to claim 7 , further comprising a display device that displays the approximation strain curve, and a strain distribution in the vicinity of the evaluation point sequence.