Note: Descriptions are shown in the official language in which they were submitted.
AMM62013-05-21 . .
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DESCRIPTION
[Title of Invention] METHOD FOR DESIGNING MATERIAL TO BE
SUBJECTED TO CYLINDER FORMING AND PRODUCT FORMED BY
PERFORMING CYLINDER FORMING
[Technical Field]
The present invention relates to a method for designing
a metal material in which a spring back angle in cylinder
forming can be controlled to a specified value and a product
formed by performing cylinder forming.
[Background Art]
A cylindrically formed product which is manufactured by
performing cylinder forming in which a metal material is
formed by performing bending forming (hereinafter, called
cylinder forming) is used for a food container, a medical
device, a metal container, an equipment part and so forth.
For example, in the case of a three-piece can which consists
of an end, a body and a bottom end, a cylinder product
formed by performing cylinder forming is used for the body.
In general, spring back occurs due to elastic recovery
when a metal material (a metal sheet) is subjected to
cylinder forming and then unloaded, which results in a
change in the shape of the cylinder. Therefore, when
cylinder forming is performed, it is necessary to determine
the conditions under which cylinder forming is performed in
consideration of spring back in advance.
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Nowadays, there is a tendency to require reduction of
the thickness (hereinafter, also called thickness reduction)
of a metal material in order to reduce material cost.
However, there is a problem in that thickness reduction
causes an increase in a spring back angle, which makes it
impossible to achieve a specified shape of a cylinder, that
is, a specified lapping width. Here, a spring back angle is
defined in terms of an amount of change in a bending angle
from the loaded state to the unloaded state in bending
forming. In addition, a lapping width is, as illustrated in
Fig. 1, defined in the following manner in terms of a
distance between one edge and another of the metal sheet
which is made into the shape of a cylinder by performing
cylinder forming: a lapping width has a value of 0 in the
case where both edges butt each other, a positive value in
the case where both edges are separated by a gap and a
negative value in the case where both edges overlap each
other.
Since a change in lapping width due to thickness
reduction hampers the succeeding processes (such as a
process in which a metal sheet is made into the body of a
three-piece can by welding the edges of the metal sheet), it
is necessary to prevent a change in lapping width due to
thickness reduction. Therefore, in the case where a thick
metal material is replaced by a thin metal material in a
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cylinder forming process, it is necessary to readjust
forming conditions or remodel a forming apparatus, which is
an obstacle to the improvement of productivity and the
reduction of cost.
Therefore, if a metal material can be designed so that
a specified shape of a cylinder (lapping width) can be
obtained even if the thickness of the material is reduced,
it is not necessary to readjust forming conditions or
remodel a forming apparatus. That is to say, it is
necessary to design a metal material with which a spring
back angle equivalent to that of a metal material before the
thickness is changed can be obtained even after the
thickness has been changed.
Incidentally, if it is assumed that a material which is
used for forming is an elastic-perfectly plastic solid which
does not exhibit work-hardening behavior, a spring back
angle can be theoretically calculated by the following
equation (2) (refer to Non Patent Literature 1):
A0/0 - 3(YP=r)/(E-t)-4[(YP-r)/(E=t)]3 === (2),
where, AO: spring back angle (degrees), 0: bending angle
(degrees), r: radius of curvature of bending (mm), t:
thickness (mm), YP: yield strength (MPa) and E: Young's
modulus (MPa).
Therefore, it is appropriate that designing a metal
material having the required mechanical properties (a
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Young's modulus and a yield strength) which are calculated
by the equation (2) in accordance with a target thickness
and a target spring back angle.
However, as Non Patent Literature 2 reports that, the
theoretical equation (2) does not necessarily correctly
replicate experimental findings. Moreover, although Non
Patent Literature 2 proposes an empirical equation regarding
a stainless steel sheet, since the target metal material is
limited to a stainless steel sheet, it cannot be said that
it is suitable for a wide variety of metal materials and
there is a problem left from the viewpoint of versatility.
[Citation List]
[NPL 1] Baba and Hashida: Tetsu-to-Hagane (The bulletin
of The Iron and Steel Institute of Japan), vol. 49(3) (1963).
p. 507.
[NPL 2] Sugimoto, Hukui, Mitsui, Watanabe and Nakamura:
Tetsu-to-Hagane, vol. 66 (1980), S 976.
[Summary of Invention]
[Technical Problem]
The present invention has been completed in view of the
situation described above. The inventors found a new method
for calculating a spring back angle which occurs when metal
materials having a wide variety of mechanical properties and
thicknesses are formed by performing cylinder forming, and
an object of the present invention is to provide a method
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for designing a metal material having a material quality
(mechanical properties) with which a specified spring back
angle can be achieved by using this calculating method and a
formed product which is manufactured by performing cylinder
forming from the metal material which is designed by using
the designing method.
[Solution to Problem]
The subject matter of the present invention will be
described as follows.
[1] A method for designing a material to be subjected
to cylinder forming, the method including, in the design of
a metal material to be subjected to cylinder forming in
which the metal material is formed by performing bending
forming, calculating the yield strength YP, the Young's
modulus E and the thickness t of the metal material on the
basis of equation (1) below so that a spring back angle AO
becomes a specified value when cylinder forming is performed
under conditions of a radius of curvature of bending r of 5
mm or more and a bending angle 0 of 90 degrees or more and
180 degrees or less and designing the metal material so that
the metal material has the calculated yield strength YP and
Young's modulus E:
A0/0 = -5.52[(YP=r)/(E.t)]2+4.13(YP-r)/(E=t) === (1),
where, AO: spring back angle (degrees), 0: bending angle
(degrees), YP: yield strength (MPa), E: Young's modulus
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(MPa), t: thickness (mm), r: radius of curvature of bending (mm).
[2] A method for manufacturing a cylindrically formed product, comprising:
- subjecting the metal material designed by the method according to item [1],
to
cylinder forming, in which the metal material is formed by performing bending
forming.
[Advantageous Effects of Invention]
According to the present invention, a metal material with which a spring back
angle can be controlled to a specified value can be easily designed and there
is a large
contribution to the improvement of productivity and the reduction of cost of a
cylinder
forming process.
[Brief Description of Drawings]
[Fig. 1] Fig. 1 is a schematic diagram illustrating a lapping width.
[Fig. 2] Fig. 2 is a diagram illustrating the relationship between /10/0 and
(YP=r)/(E=t).
[Description of Embodiments]
In the case where metal materials having the same mechanical properties and
different thicknesses are subjected to cylinder forming under the same
conditions, the
spring back angles of the materials vary each other depending on the
thicknesses and
thus it is difficult to achieve a specified lapping width (the shape of a
cylinder). Therefore,
in the case where cylinder forming is performed _______________________
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,
in a practical production site, it is necessary to remodel
the forming apparatus every time a thickness is changed or
to change forming conditions in accordance with the
thickness, which hampers productivity. In order to solve
this problem, it is thought to be effective to change a
material to one having different mechanical properties
depending on thickness. That is to say, in the case where
thickness is changed from t1 to t2, a formed product can be
obtained without change in lapping width after cylinder
forming has been performed, if a metal material having
mechanical properties with which a spring back angle
equivalent to that of a metal material having a thickness of
t1 is achieved is used.
In order to realize this, it is necessary to clarify
the influence of various factors such as the thickness and
mechanical properties of a metal material and forming
conditions on a spring back angle. Therefore, firstly, the
present inventors conducted investigations regarding what
kinds of factors among the various factors have an influence
on the spring back angle, and, as a result, confirmed that
such kinds of factors are a bending angle, a radius of
curvature of bending, a thickness, a yield strength and a
Young's modulus.
Secondly, an empirical equation which represents the
relationship between a spring back angle and such kinds of
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factors was derived by quantitatively evaluating the
influence of each of the factors by observing the spring
back angles when bending forming was performed under the
conditions in which each of the factors were varied. The
details will be described hereafter.
As described above, usually, when a metal material is
unloaded after having been subjected to bending forming, the
shape of the material changes slightly from the shape in the
loaded state due to elastic recovery. This phenomenon is
called spring back. A spring back angle AO (degrees) is
represented by equation (3) in the case where a bending
angle 0 (degrees) changes into 0' (degrees) due to spring
back. In addition, in bending forming, the relationship
represented by the equation (4) below is obtained in the
case where a radius of curvature of a plane at which there
is no change in strain in the circumferential direction
changes from r (mm) to r' (mm).
AO = 0 - 0' === (3)
A0/0 = (l/r - 1/r')/(1/r1) === (4)
In the case where there is the plane at which there is
no change in strain in the circumferential direction at the
position of the center in the thickness direction as stated
above, the equation (5) below holds regarding the change in
curvature due to unloading by using equation (4).
A0/0 = (Mr)/(E1) === (5),
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where, M is a bending moment (MPa-mm3) and I is an area
moment of inertia (mm4).
According to the theory of a beam in simple flexure,
since a bending moment is represented by equation (6) below,
equation (7) is derived by substituting equation (6) into
equation (5) described above. Incidentally, in the case
where it is assumed that a metal material is an elastic-
perfectly plastic solid which does not exhibit work
hardening behavior, since n (work hardening coefficient) - 0,
equation (2) described above is derived from equation (7).
However, it is not reasonable to assume n = 0 in an actual
metal material and the value of n varies depending on the
kind of metal material.
[Equation 1]
M=
El{ 3 (2r = YP\ 1-n 1¨ n ( 2r -YP)3
= = = (6)
r 2+n Et 2+n Et )
[Equation 2]
A8 3 (2r = YP\i-n1¨ n r 2r = YP)3
- = = = = (7)
E=t 2+12 Et )
According to Non Patent Literature 2 above, it was
found that there is a correlation between A0/0 and
(YP-r)/(E.t), and equation (8) is derived. However, since
the target metal material is limited to a stainless steel
sheet, the range of a factor with which A0/0 is determined
is narrow (0<(YE"r)/(E.t) ...c_(:).11), which results in a lack of
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versatility.
AO/0 = 1.9[(YE"r)/(E¨t)] '62 === (8)
Therefore, the present inventors observed a spring back
angle by actually performing bending forming with a wide
variety of metal materials (an aluminum sheet, a copper
sheet, a stainless steel sheet and a steel sheet) and
thickness conditions, where the radius of curvature of
bending was in the range of 5 mm or more, the bending angle
was in the range of 90 degrees or more and 180 degrees or
less and the thickness was in the range of 0.1 mm or more
and 2.0 mm or less. This is because these ranges can
sufficiently satisfy the requirements for practical use of
these materials in the fields of a food container, a medical
device, a metal container, an equipment part and so forth,
which means that there is versatility.
Fig. 2 illustrates investigation results regarding the
relationship between AO/0 and (YP=r)/(E¨t). In the figure,
0 denotes the result of this observation. A regression
equation which correctly replicates these observation
results was derived and equation (1) described above was
obtained (refer to the solid line in the figure). This
equation (1) can be applied to the range in which
(YE"r)/(E-t) is 0.33 or less and which is much wider than
the application range described in Non Patent Literature 2.
That is to say, this equation (1) can be applied to a wide
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variety of metal materials and, by using this equation,
mechanical properties (YP and E) with which a specified
spring back angle can be achieved can be calculated in
accordance with a specified thickness. Then, it is
appropriate that a metal material having the calculated
mechanical properties is designed. In addition, a thickness
with which a specified spring back angle can be achieved can
be calculated for a metal material having specified
mechanical properties. Moreover, it is possible to
calculate a spring back angle from a specified thickness and
specified mechanical properties. Incidentally, in Fig. 2, A
denotes the observed data in Non Patent Literature 2 and
dotted lines denote equation (8) and theoretical equation
(2).
In the case where the thickness of a metal material to
be subjected to cylinder forming is reduced, a procedure in
which a metal material is designed so that a spring back
angle is not changed (a lapping width is not changed) even
if a thickness is changed will be described hereafter.
Firstly, a spring back angle AO before a thickness is
changed is observed. A test piece having arbitrary
dimensions is subjected to bending forming under the
conditions of, for example, a radius of curvature of bending
of 12.7 mm and a bending angle of 180 degrees. Then, a
bending angle 0' of the test piece in the unloaded state is
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observed and a spring back angle AO is calculated by using
equation (3) described above. This procedure may be omitted
in the case where a spring back angle AO exists as stored
data.
By substituting the spring back angle AO and the bending
angle 0 (=1800) obtained as described above into equation
(1), the value to be taken by the ratio of a yield strength
to a Young's modulus (YP/E) is determined, since a radius of
curvature of bending r and a thickness t are already known
on the right-hand side of the equation. Then, in
consideration of the specification of a metal material to be
subjected to cylinder forming, a yield strength YP and a
Young's modulus E are determined from the YP/E obtained as
described above, and then a metal material having these
mechanical properties is designed. Incidentally, in the
design of a metal material, a metal material having the
mechanical properties described above may be selected from a
database of a metal material, or a new material may be
designed in accordance with the YP and E as indexes in the
case where the database cannot be found.
As another embodiment of the present invention, the
case where the mechanical properties of a metal material to
be subjected to cylinder forming are changed will be
described hereafter. Firstly, a metal material is subjected
to bending forming and a spring back angle is observed
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before the mechanical properties of the metal material are
changed. Then, a thickness t is calculated by using
equation (1) using the spring back angle described above, a
yield strength YP and a Young's modulus E which are
specified in advance and the conditions of bending forming
(a radius of curvature of bending and a bending angle). The
lapping width which is the same as that of the metal
material before the mechanical properties of the metal
material is changed can be achieved by forming the metal
material having this thickness and these mechanical
properties by performing cylinder forming.
According to the present invention, as described above,
in the case where required properties (a thickness and
mechanical properties) of a metal material are changed, a
specified lapping width can be achieved after cylinder
forming has been performed, firstly by making the spring
back angle of the metal material clear before the change,
and then, by determining the properties of the metal
material one after another under conditions in which
equation (1) is satisfied.
[EXAMPLES]
Under conditions in which the thickness of a metal
material to be subjected to cylinder forming was reduced, a
metal material with which a lapping width equivalent to that
of a metal material before the thickness was reduced can be
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achieved was designed. Firstly, in the case where the
specifications of a steel sheet before the thickness was
reduced were t = 0.153 mm, YP = 400 MPa, E = 206000 MPa, AO
= 96 degrees, 0 = 180 degrees, r = 12.7 mm and lapping width
was -10.5 mm or more and -9.0 mm or less (the mean value: -
9.6 mm) and where the thickness was reduced to t = 0.117 mm,
an example in which the optimization of a yield strength YP
was investigated in order to keep a spring back angle
constant will be described. The result that the object is
satisfied with a YP of about 310 MPa was obtained by
substituting AO = 96 degrees, E = 206000 MPa and t = 0.117
mm into equation (1).
On the basis of this result, two kinds of steel sheets
which had a thickness of 0.117 mm and different yield
strengths YP's were made, then 10 test pieces of 165.4 mm x
136.5 mm were cut out of each steel sheet, and then cylinder
forming was performed under the same conditions as before
the thickness was reduced. The observation results of a
lapping width after cylinder forming had been performed are
given in Table 1. The criteria for judging whether or not
the product was satisfactory, regarding whether the same
lapping width as before the thickness was reduced was
achieved, was decided so that the case where the observed
lapping width was within the range of -10% or more and +10%
or less of the mean lapping width of the material before the
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thickness was reduced was judged to be satisfactory in
consideration of the variability of a lapping width. The
mean value of the lapping width after cylinder forming had
been performed on a steel sheet (No. 2) having YP = 300 MPa
was -10.5 mm, which means that a lapping width equivalent to
that of the metal material before the thickness was reduced
was achieved in consideration of the variability of lapping
width. On the other hand, the mean value of the lapping
width after cylinder forming had been performed on a steel
sheet (No. 3) having YP = 362 MPa was +5.0 mm, which means
that a lapping width equivalent to that of the metal
material before the thickness was reduced was not achieved.
[Table 1]
Wrapping
Thickness YP E r 0 AO Saticfactory
No. Width Note
(mm) (Mpa) (Mpa) (mm) (degrees) (degrees)
or Not
(mm)
1 0.153 400 206000 12.7 180 96.0 -9.6
Conventional Material
2 0.117 300 206000,12.7 180 94.5 -10.5 0 Example
3 0.117 362 206000 12.7 180 105.0 4-5.0
Comparative Example
Secondly, in the case where the specifications of a
steel sheet before the thickness was reduced were t = 0.242
mm, YP = 310 MPa, E = 206000 MPa, AO = 54.3 degrees, 0 = 180
degrees, r = 12.7 mm and lapping width was -12.0 mm or more
and -8.0 mm or less (a mean value: -10.0 mm) and where the
thickness was reduced to t = 0.226 mm, an example in which
the optimization of a Young's modulus was investigated in
order to keep a spring back angle constant will be described.
The result that the object is satisfied with an E of about
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230000 MPa was obtained by substituting AO = 54.3 degrees,
YP = 310 MPa or more and 320 MPa or less and t = 0.226 mm
into equation (1).
On the basis of this result, two kinds of steel sheets
which had a thickness of 0.226 mm and different Young's
moduli E's were made, then 10 test pieces of 165.4 mm x
136.5 mm were cut out of each steel sheet, and then cylinder
forming was performed under the same conditions as before
the thickness was reduced. The observation results of a
lapping width after cylinder forming had been performed are
given in Table 2. The criteria for judging whether or not
the product was satisfactory, regarding whether the same
lapping width as before the thickness was reduced was
achieved, was decided so that the case where the observed
lapping width was within the range of -10% or more and +10%
or less of the mean lapping width of the material before the
thickness was reduced was judged to be satisfactory in
consideration of the variability of a lapping width. The
mean value of the lapping width after cylinder forming had
been performed on a steel sheet (No. 2) having E = 231000
MPa was -10.5 mm, which means that the lapping width
equivalent to that of the metal material before the
thickness was reduced was achieved in consideration of the
variability of lapping width. On the other hand, the mean
value of the lapping width after cylinder forming had been
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performed on a steel sheet (No. 3) having E = 214000 MPa was
-2.4 mm, which means that a lapping width equivalent to that
of the metal material before the thickness was reduced was
not achieved.
[Table 2]
Thickness YP 0 6,0 Wrapping Saticfactory
No. Width Note
(mm) (Mpa) (Mpa) (mm) (degrees) (degrees)
or Not
(mm)
1 0.242 310 206000 12,7 180 54.3 -
10.0 , Conventional Material
2 0.226 319 231000 12.7 180 53.5 -10.5 0
Example
3 0.226 319 214000 12.7 180 57.9 -2.4 x
Comparative Example
Although, in the examples described above, the cases
where one of a yield strength and a Young's modulus was
fixed and the other was optimized in order to reduce a
thickness were described, both may be changed. In addition,
although in the examples described above, the cases where a
yield strength or a Young's modulus was optimized in order
to keep the spring back angle (lapping width) unchanged
before and after a thickness was reduced were described, the
spring back angle may be changed to a certain value.
Moreover, a spring back angle can be calculated in the case
where a thickness is changed while a yield strength and a
Young's modulus are kept unchanged. Alternatively, a
thickness with which a specified spring back angle can be
achieved while a yield strength and a Young's modulus are
kept unchanged can be calculated.
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