U.S. patent application number 13/994103 was filed with the patent office on 2013-12-12 for method for designing material to be subjected to cylinder forming and product formed by performing cylinder forming.
This patent application is currently assigned to JFE STEEL CORPORATION. The applicant listed for this patent is Katsumi Kojima, Yusuke Nakagawa, Mikito Suto, Masaki Tada, Yoichi Tobiyama. Invention is credited to Katsumi Kojima, Yusuke Nakagawa, Mikito Suto, Masaki Tada, Yoichi Tobiyama.
Application Number | 20130327116 13/994103 |
Document ID | / |
Family ID | 46244807 |
Filed Date | 2013-12-12 |
United States Patent
Application |
20130327116 |
Kind Code |
A1 |
Suto; Mikito ; et
al. |
December 12, 2013 |
METHOD FOR DESIGNING MATERIAL TO BE SUBJECTED TO CYLINDER FORMING
AND PRODUCT FORMED BY PERFORMING CYLINDER FORMING
Abstract
An object of the present invention is to provide a method for
designing a metal material having mechanical properties with which
a specified spring back angle can be achieved after any one of
metal materials having a wide variety of mechanical properties and
thicknesses has been formed by performing cylinder forming and a
product formed by using the method. 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 so that a spring back
angle .DELTA..theta. 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 .theta. 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.
Inventors: |
Suto; Mikito; (Chiba,
JP) ; Kojima; Katsumi; (Hiroshima, JP) ;
Nakagawa; Yusuke; (Chiba, JP) ; Tada; Masaki;
(Hiroshima, JP) ; Tobiyama; Yoichi; (Chiba,
JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Suto; Mikito
Kojima; Katsumi
Nakagawa; Yusuke
Tada; Masaki
Tobiyama; Yoichi |
Chiba
Hiroshima
Chiba
Hiroshima
Chiba |
|
JP
JP
JP
JP
JP |
|
|
Assignee: |
JFE STEEL CORPORATION
Tokyo
JP
|
Family ID: |
46244807 |
Appl. No.: |
13/994103 |
Filed: |
December 13, 2011 |
PCT Filed: |
December 13, 2011 |
PCT NO: |
PCT/JP2011/079273 |
371 Date: |
August 27, 2013 |
Current U.S.
Class: |
72/368 |
Current CPC
Class: |
B21D 5/00 20130101; B21C
37/06 20130101; B21D 51/10 20130101; B21D 5/015 20130101 |
Class at
Publication: |
72/368 |
International
Class: |
B21C 37/06 20060101
B21C037/06 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 14, 2010 |
JP |
2010-277923 |
Claims
1. A method for designing a material to be subjected to cylinder
forming, the method comprising, 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 .DELTA..theta. 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 .theta. 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:
.DELTA..theta./.theta.=-5.52[(YPr)/(Et)].sup.2+4.13(YPr)/(Et) (1),
where, .DELTA..theta.: spring back angle (degrees), .theta.:
bending angle (degrees), YP: yield strength (MPa), E: Young's
modulus (MPa), t: thickness (mm), r: radius of curvature of bending
(mm).
2. A product formed by performing cylinder forming, the product
being manufactured by performing cylinder forming in which the
metal material designed by using the method according to claim 1 is
subjected to bending forming.
Description
TECHNICAL FIELD
[0001] 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
[0002] 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.
[0003] 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.
[0004] 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.
[0005] 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 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.
[0006] 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.
[0007] 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):
.DELTA..theta./.theta.=3(YPr)/(Et)-4[(YPr)/(Et)].sup.3 (2),
[0008] where, .DELTA..theta.: spring back angle (degrees), .theta.:
bending angle (degrees), r: radius of curvature of bending (mm), t:
thickness (mm), YP: yield strength (MPa) and E: Young's modulus
(MPa).
[0009] Therefore, it is appropriate that designing a metal material
having the required mechanical properties (a 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.
[0010] 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
[0011] [NPL 1] Baba and Hashida: Tetsu-to-Hagane (The bulletin of
The Iron and Steel Institute of Japan), vol. 49(3) (1963), p.
507.
[0012] [NPL 2] Sugimoto, Hukui, Mitsui, Watanabe and Nakamura:
Tetsu-to-Hagane, vol. 66 (1980), S 976.
SUMMARY OF INVENTION
Technical Problem
[0013] 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 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
[0014] The subject matter of the present invention will be
described as follows.
[0015] [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 .DELTA..theta. 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 .theta. 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:
.DELTA..theta./.theta.=-5.52[(YPr)/(Et)].sup.2+4.13(YPr)/(Et)
(1),
[0016] where, .DELTA..theta.: spring back angle (degrees), .theta.:
bending angle (degrees), YP: yield strength (MPa), E: Young's
modulus (MPa), t: thickness (mm), r: radius of curvature of bending
(mm).
[0017] [2] A product formed by performing cylinder forming, the
product being manufactured by performing cylinder forming in which
the metal material designed by using the method according to item
[1] is subjected to bending forming.
Advantageous Effects of Invention
[0018] 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
[0019] FIG. 1 is a schematic diagram illustrating a lapping
width.
[0020] FIG. 2 is a diagram illustrating the relationship between
.DELTA..theta./.theta. and (YPr)/(Et).
DESCRIPTION OF EMBODIMENTS
[0021] 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 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 t.sub.1 to
t.sub.2, 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
t.sub.1 is achieved is used.
[0022] 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.
[0023] Secondly, an empirical equation which represents the
relationship between a spring back angle and such kinds of 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.
[0024] 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 .DELTA..theta. (degrees) is represented by
equation (3) in the case where a bending angle .theta. (degrees)
changes into .theta.' (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).
.DELTA..theta.=.theta.-.theta.' (3)
.DELTA..theta./.theta.=(1/r-1/r')/(1/r') (4)
[0025] 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).
.DELTA..theta./.theta.=(Mr)/(EI) (5),
[0026] where, M is a bending moment (MPamm.sup.3) and I is an area
moment of inertia (mm.sup.4).
[0027] 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 = EI r { 3 2 + n ( 2 r YP Et ) 1 - n - 1 - n 2 + n
( 2 r YP Et ) 3 } ( 6 ) [ Equation 2 ] .DELTA..theta. .theta. = 3 2
+ n ( 2 r YP E t ) 1 - n - 1 - n 2 + n ( 2 r YP E t ) 3 ( 7 )
##EQU00001##
[0028] According to Non Patent Literature 2 above, it was found
that there is a correlation between .DELTA..theta./.theta. and
(YPr)/(Et), 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 .DELTA..theta./.theta. is determined is narrow
(0<(YPr)/(Et).ltoreq.0.11), which results in a lack of
versatility.
.DELTA..theta./.theta.=1.9[(YPr)/(Et)].sup.0.62 (8)
[0029] 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.
[0030] FIG. 2 illustrates investigation results regarding the
relationship between .DELTA..theta./.theta. and (YPr)/(Et). In the
figure, .largecircle. 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 (YPr)/(Et) 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 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, .DELTA. denotes the
observed data in Non Patent Literature 2 and dotted lines denote
equation (8) and theoretical equation (2).
[0031] 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.
[0032] Firstly, a spring back angle .DELTA..theta. 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 .theta.' of the
test piece in the unloaded state is observed and a spring back
angle .DELTA..theta. is calculated by using equation (3) described
above. This procedure may be omitted in the case where a spring
back angle .DELTA..theta. exists as stored data.
[0033] By substituting the spring back angle .DELTA..theta. and the
bending angle .theta. (=180.degree.) 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.
[0034] 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 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.
[0035] 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
[0036] 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 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, .DELTA..theta.=96 degrees, .theta.=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
.DELTA..theta.=96 degrees, E=206000 MPa and t=0.117 mm into
equation (1).
[0037] 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.times.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 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-US-00001 TABLE 1 Wrapping Thickness YP E r .theta.
.DELTA..theta. Width Saticfactory No. (mm) (Mpa) (Mpa) (mm)
(degrees) (degrees) (mm) or Not Note 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 .smallcircle. Example 3 0.117 362 206000 12.7 180 105.0 +5.0
x Comparative Example
[0038] 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, .DELTA..theta.=54.3 degrees, .theta.=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 230000 MPa was obtained by substituting
.DELTA..theta.=54.3 degrees, YP=310 MPa or more and 320 MPa or less
and t=0.226 mm into equation (1).
[0039] 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.times.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 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-US-00002 TABLE 2 Wrapping Thickness YP E r .theta.
.DELTA..theta. Width Saticfactory No. (mm) (Mpa) (Mpa) (mm)
(degrees) (degrees) (mm) or Not Note 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 .smallcircle. Example 3 0.226 319 214000 12.7 180 57.9
-2.4 x Comparative Example
[0040] 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.
* * * * *