Forming simulation method, forming simulation apparatus, forming simulation program, and recording medium
View Patent ↗The present invention provides a press forming simulation method using a finite element method for a sheet metal, in which a deformation state of a pressing tool is represented with high accuracy by superimposing at least one natural mode, for the surface shape of the pressing tool, in a no-load state.
1. A press forming simulation method using a finite element method for a sheet metal, the method comprising:
calculating a deformation state of a surface shape of a pressing tool with a computer by superimposing at least one natural mode on the surface shape, in a no-load state, using a formula:
z
(
x
,
y
)
=
z
0
(
x
,
y
)
+
∑
i
=
0
n
a
i
w
i
(
ξ
,
η
)
where x, y, and z are coordinates in a Cartesian coordinate system, z 0 is a coordinate of the surface shape before deformation, w i is an i-th order natural mode, a i is a weight coefficient for the i-th order natural mode, and n is the maximum order of the i-th order natural mode and the i-th order natural mode is shown by non-dimensional coordinates (ξ,η); and
visually displaying the surface shape of the pressing tool based on the results of the calculation on a display.
2. The press forming simulation method according to claim 1 ,
wherein the at least one natural mode is selected from the group consisting of a rigid body displacement mode, a rigid body rotation mode, a first order bending deformation mode, and a first order torsional deformation mode.
3. The press forming simulation method according to claim 1 ,
wherein a weight coefficient of the at least one natural mode is sequentially changed in accordance with a forming load.
4. The press forming simulation method according to claim 1 ,
wherein a weight coefficient of the at least one natural mode is determined in advance from a deformation amount in a pressing test that applies a predetermined forming load.
5. A press forming method based on the press forming simulation methods of any one of claims 1 to 4 .
6. A formed product that is pressed on the basis of the press forming simulation methods of any one of claims 1 to 4 .
7. A press forming simulation apparatus using a finite element method for a sheet metal, the apparatus comprising:
a computer processor configured to calculate a deformation state of a surface shape of a pressing tool by superimposing at least one natural mode on the surface shape, in a no-load state, using a formula:
z
(
x
,
y
)
=
z
0
(
x
,
y
)
+
∑
i
=
0
n
a
i
w
i
(
ξ
,
η
)
where x, y, and z are coordinates in a Cartesian coordinate system, z 0 is a coordinate of the surface shape before deformation, w i is an i-th order natural mode, a i is a weight coefficient for the i-th order natural mode, and n is the maximum order of the i-th order natural mode and the i-th order natural mode is shown by non-dimensional coordinates (ξ,η); and
a display unit which displays the surface shape of the pressing tool based on the results of the calculation.
8. The press forming simulation apparatus according to claim 7 , wherein the at least one natural mode is selected from the group consisting of a rigid body displacement mode, a rigid body rotation mode, a first order bending deformation mode, and a first order torsional deformation mode.
9. The press forming simulation apparatus according to claim 7 or 8 , wherein a weight coefficient of the at least one natural mode is sequentially changed in accordance with a forming load.
10. The press forming simulation apparatus according to claim 7 or 8 , wherein a weight coefficient of the at least one natural mode is determined in advance from a deformation amount in a pressing test that applies a predetermined forming load.
11. A press forming simulation computer program product embodied on a non-transitory computer readable media using a finite element method for a sheet metal, the computer program product comprising:
first computer-readable program code to calculate a deformation state of a surface shape of a pressing tool by superimposing at least one natural mode on the surface shape, in a no-load state using a formula:
z
(
x
,
y
)
=
z
0
(
x
,
y
)
+
∑
i
=
0
n
a
i
w
i
(
ξ
,
η
)
where x, y, and z are coordinates in a Cartesian coordinate system, z 0 is a coordinate of the surface shape before deformation, w i is an i-th order natural mode, a i is a weight coefficient for the i-th order natural mode, and n is the maximum order of the i-th order natural mode and the i-th order natural mode is shown by non-dimensional coordinates (ξ,η); and
to visually display the surface shape of the pressing tool based on the results of the calculation on a display.
12. The press forming simulation computer program product according to claim 11 ,
wherein the at least one natural mode is selected from the group consisting of a rigid body displacement mode, a rigid body rotation mode, a first order bending deformation mode, and a first order torsional deformation mode.
13. The press forming simulation computer program product according to claim 11 ,
wherein a weight coefficient of the at least one natural mode is sequentially changed in accordance with a forming load.
14. The press forming simulation computer program product according to claim 11 ,
wherein a weight coefficient of the at least one natural mode is determined in advance from the deformation amount in a pressing test that applies a predetermined forming load.