- Email: [email protected]
Further investigation of the fine-blanking process employing large deformation theory
Journal of Materials Processing Technology 66 (1997) 258-263
Further investigation of the fine-blanking process em deformation theory T.C. Lee *, L.C. Chan, B.J. Wu ManuJhcturt~~g Enginwring
Department,
Hong Kong Polytechnic
Unicrrsity.
Hong Kong, Hong Kong
Accepted 30 October 1996
Abstract Fine-blanking is a special forming process in which the material is subjected to a complicated stress condition. Although some researchers have studied the theoretical deformation of the process, there still exists a lot of uncertainty to be clarified. This paper presents a direct application of large deformation theory in two-dimensional deformation to axi-symmetrical deformations. It is convenient to measure the coordinates of the deformed grid pattern and determine the mechanical parameters such as the rigid-body rotation and the directions and magnitudes of the principal strains. Therefore, a further and practical investigation, employing large deformation theory, of the fine-blanking process is presented in this paper, using the measured data after analysis. In this investigative work, it is revealed that when the clamping force increases the rigid body rotation increases. Also, when the die clearance decreases the rigid-body rotation increases. As a result, it is indicated that the rigid-body rotation does significantly affect the strain and the quality of the sheared edges of fine-blanked parts. 0 1997 Elsevier Science S.A. Keywords: Fine-blanking:
Large deformation
theory; Metal forming
1. introduction The fine-blanking process uses triple-action tooling elements: a punch, a blank holder (stripper) with an indented Vee-ring, and a counter-punch or ejector. In fine-blanking, a shearing operation without cracks is realized by the pure shearing of material under a high compressive stress state. In trying to restrict the deformation to within a narrow zone, the die clearance should be very small, i.e. approaching to zero. In the fine-blanking process, the sheet metal is clamped on both sides of the shearing line by the stripper and the counter-punch, with the Vee-ring surrounding the shearing line being pressed into the sheet metal. Good blanked parts should have square- and cleansheared edges without cracks, as well as minimum die-roll on the sheared surface. Several papers on the fine-blanking process have been published, but reports on the mechanism of fine-blanking are relatively rare. These studies are all based on the Levy-Mises small
*Correspondingauthor. Fax: + 852 23625267; e-mail: [email protected] 0924-0136/97/S17.000 1997 Elsevier Science S.A. All rights reserved. PU SO924-0136(96)02537-X
plasticity theory [l-5]. The authors either performed experiments, or applied Slip-Line-Field theory and the Finite-Element method to study the fincblanking process. These previous research works have produced some significant results on the stuldy of the fine-blanking mechanism. Owing to the complex stress and strain state of the sheared deformation zone, there are further aspects still to be studied. For irrstance, the way the blank-holding force affects, quantitatively, the strain distribution has not yet been established. Under such circumstances, a further and practical investigation of the fine-blanking process using Large Deformation theory will be presented here to explore such features. deformation
2. Large deformation analysis Large deformation with Green’s and Cauchy’s strain tensors is usually used for analysis, which involves second degree of displacement gradients. In order to avoid complicated mathematics, homogeneous deformation proposed by Hsu is adopted [6], which describes
the state of strain not just by the normal strain and ponents but also by t tion of the ~ri~c~~a~ s
(7) where
E
and
-
E are the natural strainsin the most ed and most severely compressed hbre.
lied to sheet metal forming processes, such A large homogeneous is illustrated in Fig. 1, in initial undeformed configuration
For the general condition. mation is the QrO
the matrix for the deforCQS 4;
a e
roceeding form transformation. Provided that the deformation
from the
cos 4
(1)
0)
[xl = IAWI
If two successive deformations take piace, a transformation represented by Eq. (I), followed by another transformation such as: x;’ = h, ,_X;+ 6,2x; x; = b,,x; + i?,,x; 1
(3)
can be considered, being equivalent matrix form transformation, thus:
to an overall sffine
x;’ = c, ,s, + C,$-~
wo-by-two matrix the restriction in
which contains t ependent variables. In order to find the link bet een matrix (8) and matrix (9), matrix uration which Ige de whilst matrix ost general deformation. and can be the result of a matrix link (8) plus a rotation. Thus: fl I I
@17
i a11 lQ,l%, + IPI%, cos L1) - sin w\. = CQSw J i sin w X
sinh E 1sin 24
cash E + sinh E ‘~0s 24 sinh E *sin 29 r
cash E -
sinh E . cos 21$ 1
(10)
Solving Eq. (10) we get: (4)
x; = cz,x, + c22s21
(81
(9)
where x, and sz are the coordinates of a particle in the undeformed body, x’, and xi are the corres coordinates of the same particle after deformations referred to the same coordinate axes, and u,,s are constants. More succinctly, the transformation in Eq. (1) can be represented in matrix form as follows:
tan W = (tr,, - LI,$(Llf, + U,JUZ,+ 1) cash E = sqr?{(a:, +a,+,,
+ l)“+(a,,
-cI,~)‘&}/~G
Eqs. (I), (3) and (4) become: sin 24, = 2a,,[nz,(u:, (5)
the relationships between the c and the a and b values being determined by the rules of matrix multiplication. Matrix (2) represents the general linear transformation, which changes an initial configuration. For incompressibility of the material a restriction must be imposed on the. matrix corresponding to the condition that the area (or volume) of the body remains unchanged, i.e.: jAI= I
4
is homogeneous:
x; = CI,,x, + (L,zXz x; = f&,x, + U2$2 1
In matrix notation,
-sin
sin f$
/sqrt([(nf,
+ aL) + a,,] + ~~~11~~ + 1J2+ (czz,- ~~,#~f,l
[(a:, + a,,a,, + 1)’+ (az, - u&1:,
- 4dlI
Y
(6)
Thus of the four elements in matrix (2) only three are independent. In all two-dimensional deformations, the easiest to visualize is the pure shear. Obviously, the matrix for this deformation is:
0
al2
(1,W all
Fig. I. Two-dimensional
x
finite deformation.
(11)
260
T.C. Lee et al. /Jownal of Materials Processing Teho~ogy 66 (1997) 258-263
Table I The experimental condition
End
15, 25, 34, 44 0.3, 0.5, 0.7, 1.0
Clamping pressures ( x 1000 kg/mm* (T,)) Clearances per side (“h x material thickness)
Fig. 2. The experimental sequence.
Any two-dimensional deformation may be factored into either a pure shear and a rotation, or a simple shear plus a rotation, or in some other way, all the different ways of factoring being equally valid. However, in order to simplify the actual measrrement, direct application of the above equations is the most suitable choice. For plane strain deformation, the above equation of two-dimensional deformation, ignoring the deformation in the thickness direction, can be applied directly. For axi-symmetrical deformation, it is usually permitted to ignore circumferential strain in actual application under the condition that the ratio of the diameter of the punch to thickness of the blank is large. Thus, the above equation can also be applied directly. The equivalent strain is equal to: B= sqrt(2 x (CT+ E$+ &)/3)
(12)
When ignoring circumferential strain, the equivalent strain is directly proportional to the principal strain.
3. Discussion on the experiments and results In this study, the experiments had been performed and were described in the following paragraphs clearly. Firstly, the square cold-rolled steel SPCC (low-carbon steel) blanks of thickness 4.5 mm were cut into 2 symmetrical portions. 0.4 mm by 0.4 mm grid patterns were then photo-etched onto the cut surface of the specimens, the etched line width being about 0.05 mm. The two separated pieces were then bound together and put into a special gauge for centering, and the test carried out on a fine-blanking press. Fig. 2 presents a schematic drawing of a specimen with the grid pattern imprinted upon it, The configuration of the blanked parts is a circular piece. All of the blanked specimens are 48 mm in diameter. A Toolmaker’s microscope with 30 times enlargement is used to observe and measure the deformed grid patterns on the meridian plane of the sample. The measured data of grid coordinates are substituted into Eqs. (1) and (8) with the developed
computer programme; then the rigid-body rotation, the direction of the principal axes and the principal strains are calculated for that observed area. In order to study the effect of the fine-blanking process parameters on these mechanical variables, four different die clearances and clamping pressures were chosen. The experimental conditions for the specimens are tabulated in Table 1. The measured and calculated grid coordinate system is shown in Fig. 3. In the radial direction, a total of 12 lines from the sheared edge, and 11 lines from the contacted punch face in the thickness direction of the blanked part, were marked and measured. Owing to the severity of the deformation near to the sheared surface, the grid coordinates of the first row and column could not be measured. Therefore, the grid coordinates measurement had to begin from the second row and column. A typical stress state of the deformation zone in fine-blanking is shown in Fig. 4, the material being mainly subject to shearing stress. Owing to the experimental method of one-step deformation, the degree of deformation as reflected by the grid pattern on the meridian plane is severe, especially for those grids near to the sheared edge. Due to the non-homogeneous deformation on the cutting edge, the computed results based on these grids have relatively unstable errors, especially for those principal strains. It is thus necessary to select grids at a distance from the sheared edge, the extrapolation method then being used to estimate the strain distribution situation of the sheared edges. The experimental results are shown in Figs. 5-12. In Fig. 5, the values of the principal finite tensile strain direction (4 + w) [4] near to the sheared edge are equal
[Die
10 8
El ii?
6
.$
4
4
2 J= K=l
Face]
II 11 11 11 11 I I I \ I I I II I_ I I I _ [Punch Face1
3_ 5
7
>X
9
11
Fig. 3. The measurement and computation coordinate system.
‘61 Clearance
[FunchO Face]
'.' * 1.5 2 25 3 Fx1aric8 km the FlJndl Face
3s 4 (mm)
iDie
Face1
Fig. 6. The principal strains distribution. Fig. 4. The stress state
to about 45’, this result being close to the ~~a~~tat~ve analysis of previous researchers into the fine-b~a~k~~~g process [2] and hence further confirms that the fineblanking process is one of ?ure shear deformation. Fig. 6 shows the distribution of pri~lcipai strains over the thickness direction of the blanked part at the K= 4 section, i.e. at about 1.2 mm from the s edge. The strain value near to the punch face is greater than that near to the die face, this result agreeing with those of previous study by FE and micro-hardness measurement. Furthermore, it is found that the principal strains increase when the die ciearance decreases. IIn this experiment, more severe deformation occurs when the die clearance is 0.3% of the material thickness. Fig. 7 shows the distribution of rigid-body rotation over the thickness direction of the blanked par? (K= 4 section), i.e. at about 1.2 mm from the sheared edge, contrasting with the principal strain distribution which is found to be greater at a position near to the die face. Fig. 8 indicates the distribution of principal strain for different stripper-holding pressures. When the stripper-holding - pressure increases, the strain first in_ creases, but then decreases, which implies that the
degree of straining first increases then decreases during the increase in compressive stress. Fig. 9 indicates that the rigid body rotation changes with different stripier-folding pressures. When the stripper pressure increases, the rigid-body rotation first increases to a ~art~c~~a~ value, but then decreases. Fig. 10(a) and (b) illustrate the principal strain and the distribution of rigid-body rotation along the radial direction of the blanked part at the j= 10 section, i.e. at about 3.6 mm from the punch face. Their values all increase with decreasing distance from the sheared edge. Furthermore, the closer to the sheared edge. the more severe are the changes. Fig. 11 shows the results of the micro-hardness experiment under different die clearances at the K= 1 section, i.e. at the sheared edge. When the die clearance is small, the hardness is high, this experiment result matching well with the principal strain computation results in Fig. 6. Fig. 12 shows the situation of the hardness variation under different stripper-holding pressures. This experimental result agrees with the computation results obtained using Large Deformation theory.
*NTfClearance
0
0.5
1
Distance
1,5 2 25 3 95 4 from Shear Edge (mm)
Fig. 5. The direction of principal strains in fine-blanking.
0
1 (5 2 25 3 3.5 4 [email protected]~mmm
0.5
Fig. 7. The rigid body rotation
in fine-blanking.
T.C. Lee et al. /Journal of Materials Processing TechtloB~gy66 (1997) 258-263
262
Pressure at 0.3% 0.12
arance
0.1
I
Or)8
”
0
(1
0.5
1
1.5
2
Oislmw from Ming 0
c.5
1
1.5
2
25
3
3.5
25
3
35
4
Edge (mm!
4
Gistarm Can the Fun& Face 0nmI
Fig. 8. The principal strains in fine-blanking.
4. Conclusions Due to the severe straining of the sheared edges in fine-blanking, the strain gradient is so large that the hypothesis of homogeneous deformation in the grid elements can hardly be satisfied. The calculated principal strains at the sheared boundary are spurious, consequently they can be determined only from the strain-distribution condition of the neighbouring regions. As a result of the present study, the following conclusions can be drawn. 1. The size of the grid elements should be as small as possible when applying Large Deformation theory to the fine-blanking process; otherwise, a large calculation error is found. 2. The distribution of principal strain increases significantly in the punch face compared to that in the die face. 3. Rigid-body rotation plays a very important role in fine-blanking. It is distributed over the thickness direction of the blanked part and is opposite to that of strain. The greater the gradient of the rigid-body rotation, the greater the strain that will be obtained. 4. The principal strains and the distribution of rigidbody rotation along the radial direction are similar: the
of 0
’
0.5
1
*.,l..
1.5
Distanm hw
2
Wmo
‘.
2.5
*
3
3.5
’
4
Edi% fml
Fig. 10. (a) The rigid body rotation in fine-blanking. strains in fine-blanking.
(b) The prinicpal
closer to the sheared edge, the more rapidly the values increase. 5. The principal strain is greater when the die clearance is smaller. 6. When the stripper-holding pressure increases, the principal strain first increases but then decreases. This is the same for the rigid-body rotation, which also increases to a particular value but decreases in its later stages.
Acknowledgements
The authors wish to thank all related people for their assistance in the experimental work and the equipment
5
2.5 2 1.5
0
0.5
1
1.5
2
Wl&?tce from lh
2.5
3
3.5
4
DimFew
Fig. 9. The rigid body rotation in fine-blanking.
;&--a5
'lace]
1
1.5
2
25
3
3.5
4
Facej
Oistanwlromthll~ F8cahml
Fig. Il. Change of sutiace hardness in fine-blanking.
563
PI
Fig. 12. Change of surFace hardness in fine blanking.
ong Kong ~ro~~~t~v~ty Council and The support of Hong Kong Polytechnic University.
T. Nakagawa and T. Marda. ExperimentaP in:estigatiori 011fine blanking, Sci. P~?L’KY I.P.C.R.. 62 11968) 65-~8O. R. JohimSton. B. Fogg and A.W.J. Chisholml. An inves~igalion into the fine blankinp process. PRK.. sr111Mai he Tool Drsip Oxford, 1969,pp. Cc0911 . ~irmii?~hm. .%p. 1968. $ergamon. 39?- 410. W. oni, F. Rotter land A. Krapoth, Feischnciden Dicker Blecbe-Experiment und Theorie. bldusrrie-All-_rrr. I7.2.:106 (14) (1984) 24-B. G.Q. Tu, P.F. Cheng. R.N. Li, J.W. Niu, X.G. Zhang. Recent dsvelopment of fine blanking technology in China. PRK &/I brr. Cot$ T~~c/znoi~~~~ c!f’Pluusriciry. Clli~~. 199.3, pp. 746-250. T.C. Lee and L.C. Chan, Straining behaviour in blanking process--fine blanking vs convemional blanking. J. Mccrfer-.Prtw.s~. ( 1995) 1OS 1I I. TLTl~ml.. 48 T.C. Hsu, A study of large deformations by m,ltrin algebra. J. Srrc~br dnal., I (4) (1966) 313-320. R. Sowerby, J.L. Duncan and E. Chu, The modelling of sheet metal stampings. pizf. J. ,21&f. &i.. 3 (7) (1986) 415 -431).
Further investigation of the fine-blanking process em deformation theory T.C. Lee *, L.C. Chan, B.J. Wu ManuJhcturt~~g Enginwring
Department,
Hong Kong Polytechnic
Unicrrsity.
Hong Kong, Hong Kong
Accepted 30 October 1996
Abstract Fine-blanking is a special forming process in which the material is subjected to a complicated stress condition. Although some researchers have studied the theoretical deformation of the process, there still exists a lot of uncertainty to be clarified. This paper presents a direct application of large deformation theory in two-dimensional deformation to axi-symmetrical deformations. It is convenient to measure the coordinates of the deformed grid pattern and determine the mechanical parameters such as the rigid-body rotation and the directions and magnitudes of the principal strains. Therefore, a further and practical investigation, employing large deformation theory, of the fine-blanking process is presented in this paper, using the measured data after analysis. In this investigative work, it is revealed that when the clamping force increases the rigid body rotation increases. Also, when the die clearance decreases the rigid-body rotation increases. As a result, it is indicated that the rigid-body rotation does significantly affect the strain and the quality of the sheared edges of fine-blanked parts. 0 1997 Elsevier Science S.A. Keywords: Fine-blanking:
Large deformation
theory; Metal forming
1. introduction The fine-blanking process uses triple-action tooling elements: a punch, a blank holder (stripper) with an indented Vee-ring, and a counter-punch or ejector. In fine-blanking, a shearing operation without cracks is realized by the pure shearing of material under a high compressive stress state. In trying to restrict the deformation to within a narrow zone, the die clearance should be very small, i.e. approaching to zero. In the fine-blanking process, the sheet metal is clamped on both sides of the shearing line by the stripper and the counter-punch, with the Vee-ring surrounding the shearing line being pressed into the sheet metal. Good blanked parts should have square- and cleansheared edges without cracks, as well as minimum die-roll on the sheared surface. Several papers on the fine-blanking process have been published, but reports on the mechanism of fine-blanking are relatively rare. These studies are all based on the Levy-Mises small
*Correspondingauthor. Fax: + 852 23625267; e-mail: [email protected] 0924-0136/97/S17.000 1997 Elsevier Science S.A. All rights reserved. PU SO924-0136(96)02537-X
plasticity theory [l-5]. The authors either performed experiments, or applied Slip-Line-Field theory and the Finite-Element method to study the fincblanking process. These previous research works have produced some significant results on the stuldy of the fine-blanking mechanism. Owing to the complex stress and strain state of the sheared deformation zone, there are further aspects still to be studied. For irrstance, the way the blank-holding force affects, quantitatively, the strain distribution has not yet been established. Under such circumstances, a further and practical investigation of the fine-blanking process using Large Deformation theory will be presented here to explore such features. deformation
2. Large deformation analysis Large deformation with Green’s and Cauchy’s strain tensors is usually used for analysis, which involves second degree of displacement gradients. In order to avoid complicated mathematics, homogeneous deformation proposed by Hsu is adopted [6], which describes
the state of strain not just by the normal strain and ponents but also by t tion of the ~ri~c~~a~ s
(7) where
E
and
-
E are the natural strainsin the most ed and most severely compressed hbre.
lied to sheet metal forming processes, such A large homogeneous is illustrated in Fig. 1, in initial undeformed configuration
For the general condition. mation is the QrO
the matrix for the deforCQS 4;
a e
roceeding form transformation. Provided that the deformation
from the
cos 4
(1)
0)
[xl = IAWI
If two successive deformations take piace, a transformation represented by Eq. (I), followed by another transformation such as: x;’ = h, ,_X;+ 6,2x; x; = b,,x; + i?,,x; 1
(3)
can be considered, being equivalent matrix form transformation, thus:
to an overall sffine
x;’ = c, ,s, + C,$-~
wo-by-two matrix the restriction in
which contains t ependent variables. In order to find the link bet een matrix (8) and matrix (9), matrix uration which Ige de whilst matrix ost general deformation. and can be the result of a matrix link (8) plus a rotation. Thus: fl I I
@17
i a11 lQ,l%, + IPI%, cos L1) - sin w\. = CQSw J i sin w X
sinh E 1sin 24
cash E + sinh E ‘~0s 24 sinh E *sin 29 r
cash E -
sinh E . cos 21$ 1
(10)
Solving Eq. (10) we get: (4)
x; = cz,x, + c22s21
(81
(9)
where x, and sz are the coordinates of a particle in the undeformed body, x’, and xi are the corres coordinates of the same particle after deformations referred to the same coordinate axes, and u,,s are constants. More succinctly, the transformation in Eq. (1) can be represented in matrix form as follows:
tan W = (tr,, - LI,$(Llf, + U,JUZ,+ 1) cash E = sqr?{(a:, +a,+,,
+ l)“+(a,,
-cI,~)‘&}/~G
Eqs. (I), (3) and (4) become: sin 24, = 2a,,[nz,(u:, (5)
the relationships between the c and the a and b values being determined by the rules of matrix multiplication. Matrix (2) represents the general linear transformation, which changes an initial configuration. For incompressibility of the material a restriction must be imposed on the. matrix corresponding to the condition that the area (or volume) of the body remains unchanged, i.e.: jAI= I
4
is homogeneous:
x; = CI,,x, + (L,zXz x; = f&,x, + U2$2 1
In matrix notation,
-sin
sin f$
/sqrt([(nf,
+ aL) + a,,] + ~~~11~~ + 1J2+ (czz,- ~~,#~f,l
[(a:, + a,,a,, + 1)’+ (az, - u&1:,
- 4dlI
Y
(6)
Thus of the four elements in matrix (2) only three are independent. In all two-dimensional deformations, the easiest to visualize is the pure shear. Obviously, the matrix for this deformation is:
0
al2
(1,W all
Fig. I. Two-dimensional
x
finite deformation.
(11)
260
T.C. Lee et al. /Jownal of Materials Processing Teho~ogy 66 (1997) 258-263
Table I The experimental condition
End
15, 25, 34, 44 0.3, 0.5, 0.7, 1.0
Clamping pressures ( x 1000 kg/mm* (T,)) Clearances per side (“h x material thickness)
Fig. 2. The experimental sequence.
Any two-dimensional deformation may be factored into either a pure shear and a rotation, or a simple shear plus a rotation, or in some other way, all the different ways of factoring being equally valid. However, in order to simplify the actual measrrement, direct application of the above equations is the most suitable choice. For plane strain deformation, the above equation of two-dimensional deformation, ignoring the deformation in the thickness direction, can be applied directly. For axi-symmetrical deformation, it is usually permitted to ignore circumferential strain in actual application under the condition that the ratio of the diameter of the punch to thickness of the blank is large. Thus, the above equation can also be applied directly. The equivalent strain is equal to: B= sqrt(2 x (CT+ E$+ &)/3)
(12)
When ignoring circumferential strain, the equivalent strain is directly proportional to the principal strain.
3. Discussion on the experiments and results In this study, the experiments had been performed and were described in the following paragraphs clearly. Firstly, the square cold-rolled steel SPCC (low-carbon steel) blanks of thickness 4.5 mm were cut into 2 symmetrical portions. 0.4 mm by 0.4 mm grid patterns were then photo-etched onto the cut surface of the specimens, the etched line width being about 0.05 mm. The two separated pieces were then bound together and put into a special gauge for centering, and the test carried out on a fine-blanking press. Fig. 2 presents a schematic drawing of a specimen with the grid pattern imprinted upon it, The configuration of the blanked parts is a circular piece. All of the blanked specimens are 48 mm in diameter. A Toolmaker’s microscope with 30 times enlargement is used to observe and measure the deformed grid patterns on the meridian plane of the sample. The measured data of grid coordinates are substituted into Eqs. (1) and (8) with the developed
computer programme; then the rigid-body rotation, the direction of the principal axes and the principal strains are calculated for that observed area. In order to study the effect of the fine-blanking process parameters on these mechanical variables, four different die clearances and clamping pressures were chosen. The experimental conditions for the specimens are tabulated in Table 1. The measured and calculated grid coordinate system is shown in Fig. 3. In the radial direction, a total of 12 lines from the sheared edge, and 11 lines from the contacted punch face in the thickness direction of the blanked part, were marked and measured. Owing to the severity of the deformation near to the sheared surface, the grid coordinates of the first row and column could not be measured. Therefore, the grid coordinates measurement had to begin from the second row and column. A typical stress state of the deformation zone in fine-blanking is shown in Fig. 4, the material being mainly subject to shearing stress. Owing to the experimental method of one-step deformation, the degree of deformation as reflected by the grid pattern on the meridian plane is severe, especially for those grids near to the sheared edge. Due to the non-homogeneous deformation on the cutting edge, the computed results based on these grids have relatively unstable errors, especially for those principal strains. It is thus necessary to select grids at a distance from the sheared edge, the extrapolation method then being used to estimate the strain distribution situation of the sheared edges. The experimental results are shown in Figs. 5-12. In Fig. 5, the values of the principal finite tensile strain direction (4 + w) [4] near to the sheared edge are equal
[Die
10 8
El ii?
6
.$
4
4
2 J= K=l
Face]
II 11 11 11 11 I I I \ I I I II I_ I I I _ [Punch Face1
3_ 5
7
>X
9
11
Fig. 3. The measurement and computation coordinate system.
‘61 Clearance
[FunchO Face]
'.' * 1.5 2 25 3 Fx1aric8 km the FlJndl Face
3s 4 (mm)
iDie
Face1
Fig. 6. The principal strains distribution. Fig. 4. The stress state
to about 45’, this result being close to the ~~a~~tat~ve analysis of previous researchers into the fine-b~a~k~~~g process [2] and hence further confirms that the fineblanking process is one of ?ure shear deformation. Fig. 6 shows the distribution of pri~lcipai strains over the thickness direction of the blanked part at the K= 4 section, i.e. at about 1.2 mm from the s edge. The strain value near to the punch face is greater than that near to the die face, this result agreeing with those of previous study by FE and micro-hardness measurement. Furthermore, it is found that the principal strains increase when the die ciearance decreases. IIn this experiment, more severe deformation occurs when the die clearance is 0.3% of the material thickness. Fig. 7 shows the distribution of rigid-body rotation over the thickness direction of the blanked par? (K= 4 section), i.e. at about 1.2 mm from the sheared edge, contrasting with the principal strain distribution which is found to be greater at a position near to the die face. Fig. 8 indicates the distribution of principal strain for different stripper-holding pressures. When the stripper-holding - pressure increases, the strain first in_ creases, but then decreases, which implies that the
degree of straining first increases then decreases during the increase in compressive stress. Fig. 9 indicates that the rigid body rotation changes with different stripier-folding pressures. When the stripper pressure increases, the rigid-body rotation first increases to a ~art~c~~a~ value, but then decreases. Fig. 10(a) and (b) illustrate the principal strain and the distribution of rigid-body rotation along the radial direction of the blanked part at the j= 10 section, i.e. at about 3.6 mm from the punch face. Their values all increase with decreasing distance from the sheared edge. Furthermore, the closer to the sheared edge. the more severe are the changes. Fig. 11 shows the results of the micro-hardness experiment under different die clearances at the K= 1 section, i.e. at the sheared edge. When the die clearance is small, the hardness is high, this experiment result matching well with the principal strain computation results in Fig. 6. Fig. 12 shows the situation of the hardness variation under different stripper-holding pressures. This experimental result agrees with the computation results obtained using Large Deformation theory.
*NTfClearance
0
0.5
1
Distance
1,5 2 25 3 95 4 from Shear Edge (mm)
Fig. 5. The direction of principal strains in fine-blanking.
0
1 (5 2 25 3 3.5 4 [email protected]~mmm
0.5
Fig. 7. The rigid body rotation
in fine-blanking.
T.C. Lee et al. /Journal of Materials Processing TechtloB~gy66 (1997) 258-263
262
Pressure at 0.3% 0.12
arance
0.1
I
Or)8
”
0
(1
0.5
1
1.5
2
Oislmw from Ming 0
c.5
1
1.5
2
25
3
3.5
25
3
35
4
Edge (mm!
4
Gistarm Can the Fun& Face 0nmI
Fig. 8. The principal strains in fine-blanking.
4. Conclusions Due to the severe straining of the sheared edges in fine-blanking, the strain gradient is so large that the hypothesis of homogeneous deformation in the grid elements can hardly be satisfied. The calculated principal strains at the sheared boundary are spurious, consequently they can be determined only from the strain-distribution condition of the neighbouring regions. As a result of the present study, the following conclusions can be drawn. 1. The size of the grid elements should be as small as possible when applying Large Deformation theory to the fine-blanking process; otherwise, a large calculation error is found. 2. The distribution of principal strain increases significantly in the punch face compared to that in the die face. 3. Rigid-body rotation plays a very important role in fine-blanking. It is distributed over the thickness direction of the blanked part and is opposite to that of strain. The greater the gradient of the rigid-body rotation, the greater the strain that will be obtained. 4. The principal strains and the distribution of rigidbody rotation along the radial direction are similar: the
of 0
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Fig. 10. (a) The rigid body rotation in fine-blanking. strains in fine-blanking.
(b) The prinicpal
closer to the sheared edge, the more rapidly the values increase. 5. The principal strain is greater when the die clearance is smaller. 6. When the stripper-holding pressure increases, the principal strain first increases but then decreases. This is the same for the rigid-body rotation, which also increases to a particular value but decreases in its later stages.
Acknowledgements
The authors wish to thank all related people for their assistance in the experimental work and the equipment
5
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Fig. 9. The rigid body rotation in fine-blanking.
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Fig. Il. Change of sutiace hardness in fine-blanking.
563
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Fig. 12. Change of surFace hardness in fine blanking.
ong Kong ~ro~~~t~v~ty Council and The support of Hong Kong Polytechnic University.
T. Nakagawa and T. Marda. ExperimentaP in:estigatiori 011fine blanking, Sci. P~?L’KY I.P.C.R.. 62 11968) 65-~8O. R. JohimSton. B. Fogg and A.W.J. Chisholml. An inves~igalion into the fine blankinp process. PRK.. sr111Mai he Tool Drsip Oxford, 1969,pp. Cc0911 . ~irmii?~hm. .%p. 1968. $ergamon. 39?- 410. W. oni, F. Rotter land A. Krapoth, Feischnciden Dicker Blecbe-Experiment und Theorie. bldusrrie-All-_rrr. I7.2.:106 (14) (1984) 24-B. G.Q. Tu, P.F. Cheng. R.N. Li, J.W. Niu, X.G. Zhang. Recent dsvelopment of fine blanking technology in China. PRK &/I brr. Cot$ T~~c/znoi~~~~ c!f’Pluusriciry. Clli~~. 199.3, pp. 746-250. T.C. Lee and L.C. Chan, Straining behaviour in blanking process--fine blanking vs convemional blanking. J. Mccrfer-.Prtw.s~. ( 1995) 1OS 1I I. TLTl~ml.. 48 T.C. Hsu, A study of large deformations by m,ltrin algebra. J. Srrc~br dnal., I (4) (1966) 313-320. R. Sowerby, J.L. Duncan and E. Chu, The modelling of sheet metal stampings. pizf. J. ,21&f. &i.. 3 (7) (1986) 415 -431).