chapter 6 forming besides blanking, bending and deep drawing, there are other forming methods in...
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Chapter 6 Forming
Besides blanking, bending and deep drawing, there are
other forming methods in stamping, such as local forming,
bulging, flanging, necking, sizing and spinning. All these
methods are generally called forming processes.
Chapter 6 Forming6. 1 Local forming
6.2 Bulging
6.3 Flanging
6.4 Necking
6.5 Sizing
6.6 Spinning
6. 1 Local forming
When drawing cylindrical part with flange (see Fig. 6.1),
the deformation resistance in the flange zone would increase with
increasing the flange diameter df for the same cylinder diameter d,
and it would be more difficult for the material in the flange zone to
flow into the die and be deformed. As the ratio of df /d reaches a
certain value, only little material in the flange zone would flow
into the cylinder zone, and the forming occurred in the cylinder
zone is mainly due to thickness thinning under biaxial tension.
Such forming process is called local forming.
Fig. 6.1 Cylindrical part with flange
The ratio df /d is an important index to differ local forming and
deep drawing with flange. This value varies with the hardening
condition of material, the geometric dimension of die and also the
blank holding force. Generally df /d=3 is taken as the approximate
critical value. When df /d>3, local forming takes place; when df
/d<3, deep drawing takes place. It is difficult to differ these two
processes strictly for usually there is a state of intermediate
deformation existed.
1.Deep drawing: dp/D>mL=0.5 2. Deep drawing—bulging: dp/D<mL=0.5 ~ 0.253. bulging : dp/D<0.25
According to the demand of workpiece, various shapes can be
made by local forming, such as rib (see Fig. 6.2), bulge, word and
flower. These processes not only enhance workpiece rigidity, but
also play a role in product decoration. As a result, it has a wide
application.
Fig. 6.2 Part with ribs
1 0
0
100L L
L
0. 70 0. 75% ( - )
During local forming, the material in the deformation zone
undergoes biaxial tension, its limit percentage deformation can
be approximately related to the percentage elongation, that is:
limit= (6-1)
where, δlimit is the limit percentage deformation of local forming
in %; δ is the allowable percentage elongation of material under
uniaxial tension in %; L0, L1 are the lengths before and after
deformation in mm (see Fig. 6.3a).
Due to non-uniform deformation during local forming,
coefficient 0.70~0.75 is adopted in Equation 6.1, which is
determined by the shape of local forming, with larger value for
ball-shaped rib and smaller value for trapezoidal rib.
(a) pre-forming (b) final formingFig. 6.3 Pressing bulge
If the calculation result meets the condition stated above,
then forming can be done in one pass; otherwise, an intermediate
hemispherical shape should be made first (see Fig. 6.3).
The types and sizes of the rib, the distance between the ribs
and also between the rib and the workpiece edge are listed in Table
6.1. If the distance between the rib and the edge in local forming is
less than (3~3.5) t (t: blank thickness), the edge material would
shrink inward during deformation, and a trimming process would
be necessary after forming with a trimming allowance set up
beforehand.
Examples R H D or B r α
(3~4) t (2~3) t (7~10) t (1~2) t
- (1.5~2) t ≥3h (0.5~ 1.5) t 15°~30°
Table 6.1 Types and sizes of the rib
Table 6.1 Types and sizes of the rib
Examples D (mm) L (mm) l (mm)
6.5 10 6
8.5 13 7.5
10.5 15 9
13 18 11
15 22 13
18 26 16
24 34 20
31 44 26
36 51 30
43 60 35
48 68 40
55 78 45
Usually, the local forming force is determined according to
the experimental data. When forming rib by rigid die, the
following equation can be used to calculate the approximate
pressure.
bP KLt (N) (6-2)
where, K is a coefficient (K=0.7~1.0), depending on the width
and depth of the rib, with larger value for the narrow and deep rib
and smaller value for the wide and shallow rib; L is the perimeter
of rib in mm; t is the blank thickness in mm; σb is the ultimate
tensile strength of material in MPa.
During the forming and sizing of thin material (t<1.5mm)
and small parts (F<2000mm2) with rigid die, the following
equation can be used to calculate the pressure. 2P KFt (N) (6-3)
where, K is a coefficient, for steel, K=300~400, and for cupper,
K=200~250; F is the area of the local forming region in mm2; t
is the blank thickness in mm.
6.2 Bulging
The process of expanding a hollow or tubular blank into a
curved-surface part is called bulging. By this process, various parts
with complex shapes can be made (see Fig. 6.4).
Fig. 6.4 Bulging part
Bulging can be performed by various methods. A rigid
sectional punch is usually used in mechanical bulging (see Fig.
6.5). When the slide block of press moves downwards, the
sectional punch is expanded outward along the conical surface of
the core, which causes a bulging deformation of the blank in radial
direction.
Fig. 6.5 Bulging with a rigid sectional punch
After deformation, the sectional punch is returned back to the
initial position with the aid of lower ejector and spring, then the
workpiece can be taken out. In this method the structure of die is
complex, the deformation of bulging is non-uniform and it is
difficult to produce a part with high size accuracy and complex
shape through this process.
Using liquid, gas, rubber or paraffin wax as pressure-
transferring medium, the soft die bulging can be realized. By this
method, the deformation of the material is uniform, the accurate
geometry shape can be obtained more easily. So this process can
be used to produce complex hollow part, especially corrugated
pipes and other parts used in aeronautic and astronautic engine.
Medium and large parts can be bulged by liquid, gas or shock
wave produced in exploding. The hydro- bulging die, as shown in
Fig. 6.6, is used in double action crank press, and the rigid die is
separable. Fig. 6.6 (a) shows that the liquid should be injected into
the blank before forming and poured out after forming, so the
productivity of this method is low. Fig. 6.6(b) shows that adding a
rubber bag into the punch may simplify the process.
(a) method of infecting liquid (b) method of adopting a rubber bag
Fig. 6.6 Hydro-bulging die
Using rubber as pressure-
transferring medium, the rigid punch
can also be left out (see Fig. 6.7). The
structure of this kind of die is simple,
and its forming effect is nice. Because
the polyurethane rubber is of higher
strength than natural rubber and with
fine oil-resistant capability, its life is ten
times higher than natural rubber.
Therefore the polyurethane rubber is
widely used in recent years. Fig. 6.7 Rubber-bulging die
PVC plastic is also a kind of pressure-transferring medium
with high quality, mainly consists of polyvinyl chloride resin,
plasticity intensifier and stabilizing agent. At present, both
elasticity and strength of the polyurethane rubber are better than
that of PVC, but on the long term, the PVC may be more popular
than polyurethane rubber due to its low cost and simple
synthesization.
During bulging, the material is subjected to tangential
tension; its limit percentage deformation is restricted by the
allowable percentage elongation of the material in the maximum
deformation zone. A coefficient K is usually denoted to express
the bulging extent in practice.
max
0
dK
d (6-4)
where, dmax is the maximum diameter of workpiece in bulging
zone after forming in mm; d0 is the original diameter of blank in
mm.
Generally, the relationship between the bulging coefficient K and the allowable percentage elongation of material [ ] is:
max 0
0
1d d
Kd
or 1K
Because the deformation conditions and the states of stress
and strain in bulging are not exactly the same as those of uniaxial
tension, the data of allowable percentage elongation of the material
[ ] cannot quote simply from that of uniaxial tension test, and
should be determined by special technological experiment. Some
data of allowable percentage elongation [ ] and limit bulging
coefficient are listed in Table 6.2.
MaterialThickness
(mm)Allowable percentage
elongation [δ](%)
Limit bulging coefficient
K
Aluminum LF21
0.5 25 1.25
1.0 28 1.28
1.5 32 1.32
2.0 32 1.32
BrassH62 0.5~1.0 35 1.35
H68 1.5~2.0 40 1.40
Mild carbon
steel
08 F 0.5 20 1.20
10, 20 1.0 24 1.24
Stainless steel
1Gr18Ni9Ti
0.5 26 1.26
1.0 28 1.28
Table 6.2 Experimental data of bulging coefficients
In favor of metal flowing and decreasing the thickness
reduction of blank in deformation zone during bulging, usually the
two ends of blank are unfixed, and may shrink freely. Therefore
the shrink amount should be considered in determining the blank
height. The calculation of the blank for the bulging workpiece is as
follows (see Fig.6.8):
Blank diameter: max0
dd
K (6-5)
Blank length: 0 [1 (0.3 0.4) ]L L b
(mm)
(mm) (6-6)
where, L is the generatrix length of the workpiece in mm; b is the trimming allowance, generally equals to 5~15mm; δ is the maximum elongation in circumferential direction; coefficient 0.3~0.4 represents the effect of the height reduction due to the tangential elongation.
The soft die bulging is widely used in practice. The pressure
per unit area p is related to the shape, thickness and mechanical
properties of bulging workpiece. It is known from Fig. 6.8, both
the curvature in circumferential direction and the tangential tensile
stress σ1 in all workpiece cross-section are variational, and both
the curvature and the tensile stress σ2 in generatrix direction are
also variational. But usually the curvature of workpiece generatrix
is small, in practice, only σ1 is taken into account and σ2 is
omitted.
After simplifying, we obtain:
1max
2tp
d
An annular strip with unit width in the maximum deformation
zone dmax is analyzed (see Fig. 6.9), from the equilibrium
equations of the half annular strip, we obtain:
max1
0
sin . 22
dp a da t
Fig. 6.8 Bulging workpiece and stressesFig. 6.9 Balance condition of the half annular strip of bulging
In order to have the material be plastically deformed, σ1
must be greater than or equal to the yield stress σs. Considering
the work hardening effect of the material, substituting σs by the
ultimate strength σb, we obtain the equation for calculating the
pressure per unit area during soft die bulging:
max
2b
tp
d (6-7)
The symbols in above equation are shown in Fig. 6.9. The
pressure per unit area of the soft die bulging calculated by
Equation 6.7 is usually smaller than the actual one, and it should
be modified in practice.
6.3 Flanging
Flanging is a forming process to presses the edge of the hole
or the external edge of the workpiece into vertical straight wall
(see Fig. 6.10). The 3-D part with complex shape and high
rigidity can be produced by flanging. This process can be used to
take place of deep drawing and bottom cutting processes to
produce the hollow bottomless parts.
Flanging can be classified into internal and external edge
flanging according to different states and characteristics of stress
and strain at the workpiece edge. Based on the thickness
variation along the vertical straight wall section, the internal
edge flanging is sub-classified into flanging without thinning
(conventional flanging) and flanging with thinning. There are
two kinds of external edge flanging: the outer curve flanging
(the upper one shown in Fig. 6.10b) and the inner curve flanging
(the lower one shown in Fig. 6.10b)
(a) internal edge flanging (b) external edge flangingFig. 6.10 Internal and external edge flanges
6.3.1 Internal edge flanging
1. Deformation characteristics of the internal edge flanging
The hole diameter of the blank before flanging is d0, the
deformation zone is the annular area with the inside and outside
diameter d0 and D. The material in the deformation zone is in the
biaxial tensile stresses state. The tangential tensile stress σθ is the
largest principal stress and the radial tensile stress σr caused by the
friction between the blank and die is a bit smaller (see Fig. 6.11).
The value of the stress varies in the whole deformation zone.
The hole edge is in the state of uniaxial tensile stress in tangential
direction, and the value of the stress is the maximum. The
tangential tensile strain also varies in the deformation zone. It
reaches the maximum value at the edge of the inner hole and
decreases rapidly with the distance from the hole edge increases
(see Fig. 6.12).
Fig. 6.11 Stress state in the deformation Fig. 6.12 Distributions of stress and strainzone of the internal hole flanging during circular hole flanging
The percentage deformation is expressed by the ratio m of
the hole diameter before flanging d0 to the diameter after flanging
D (if taking into account the blank thickness, the diameter is
measured refering to the center line of the blank thickness), that is:
0dm
D (6-8)
m is called flanging coefficient. Obviously, the larger the m, the
smaller would be the percentage deformation; and vice versa. The
minimum coefficient without crack occurring is called limit
flanging coefficient. The limit flanging coefficient is related to
many factors as follows:
(1) Plasticity of the material
The better the plasticity of the material, the smaller would
be the limit flanging coefficient. The relationship between m
and the percentage elongation of material δ or the area
reduction φ is as follows:
0
0 0
11 1
D d D
d d m
that is, 1(1 )m , or 1m
The coefficients of the circular hole flanging for various
materials at the first pass are listed in Table 6.3.
Blank material after annealingFlanging coefficient m
m0 mmin
Tinplate 0.70 0.65
Soft copper
t=0.25~2.0mmt=3.0~6.0mm
0.720.680.75
0.78
Brass H62 t=0.5~6.0mm 0.68 0.62
Aluminum t=0.5~5.0mm 0.70 0.64
Hard aluminum alloy 0.89 0.80
Titanium alloy
TA1 (Cold) 0.64~0.68 0.55
TA1 (300~400 )℃ 0.40~0.50
TA5 (Cold) 0.85~0.90 0.75
TA5 (500~600 )℃ 0.7~0.65 0.55
Stainless steel, High temperature alloy 0.69~0.65 0.61~0.57
Table 6.3 Flanging coefficients of various materials
When a small crack is allowed in the flanging wall, mmin can be
used; but usually m0 is used. The blank should be annealed before
flanging.
The high surface quality of the hole edge means no crack, burr
and work hardening existed before flanging. Such situation is
beneficial to the flanging process, so enable the limit flanging
coefficient to be taken a bit smaller. Such hole is usually made by
drilling instead of punching.
(2) Status of the hole edge
(3) Relative thickness of the material
0
td The relative thickness of the material is the ratio of the
material thickness t to the hole diameter before flanging d0. The
larger the relative thickness of the material, the larger would be
the absolute elongation of the material before fracture and results
in smaller flanging coefficient.
(4) Shape of the punch
The larger the roundness radius of punch, sometime even
turn to spherical (parabolic or conical shape), the more beneficial
would be the flanging deformation. In such situation, the flanging
hole is stretched smoothly and gradually, thus reducing the
possibility of the fracture at the hole edge.
The limit flanging coefficient of the mild carbon steel is listed in
Table 6.4. It is shown that the type of the punch, the manufacturing
method of the hole and also the relative thickness of the material
have certain influence on the limit flanging coefficient.
Table 6.4 Limit flanging coefficient of mild carbon steel
Relative thickness of the material ( ) 0
td
Shape of flanging punch
Method of the hole
manufacturing
100 50 35 20 15 10 8 6.5 5 3 1
Spherical
Burringafter drilling
0.70 0.60 0.52 0.45 0.40 0.36 0.33 0.31 0.30 0.25 0.20
Punching 0.75 0.65 0.57 0.52 0.48 0.45 0.44 0.43 0.42 0.42 -
Cylindrical
Burringafter drilling
0.80 0.70 0.60 0.50 0.45 0.42 0.40 0.37 0.35 0.30 0.25
Punching 0.85 0.75 0.65 0.60 0.55 0.52 0.50 0.50 0.48 0.47 -
For noncircular hole flanging (see Fig. 6.13), the flanging
line is a curve with changing curvature or even a straight line. With
the same flanging heights, the small the curvature radius, the larger
would be both the tangential tensile stress and strain, and vice versa.
There is only bending deformation occurred near die roundness.
When there is both curved and straight lines existed in one
workpiece, the flanging deformation in the curved zone may extend
to the straight zone, and decrease the tangential elongation
deformation in the curved zone.
Fig. 6.13 Noncircular hole flanging
Thus the limit flanging coefficient to be adopted can be a bit
smaller than that for circular hole flanging. The limit flanging
coefficient of noncircular hole can be obtained from Table 6.5, or
calculated as follows:
0'
0180
mam
where, m’ is the limit flanging coefficient of the noncircular hole
flanging; m is the limit flanging coefficient of the circular hole
flanging obtained from Table 6.4; a is the center angle of the
curvature zone.
Table 6.5 Limit flanging coefficient of noncircular hole (mild carbon steel)
Relative thickness of the material ( )0
tdCenter angle
of curvature α (°) 50 33 20 12.5~8.3 6.6 5 3.3
180~360 0.80 0.60 0.52 0.50 0.48 0.46 0.45
165 0.73 0.55 0.48 0.46 0.44 0.42 0.41
150 0.67 0.50 0.43 0.42 0.40 0.38 0.375
135 0.60 0.45 0.39 0.38 0.36 0.35 0.34
120 0.53 0.40 0.35 0.33 0.32 0.31 0.30
105 0.47 0.35 0.30 0.29 0.28 0.27 0.26
90 0.40 0.30 0.26 0.25 0.24 0.23 0.225
75 0.33 0.25 0.22 0.21 0.20 0.19 0.185
60 0.27 0.20 0.17 0.17 0.16 0.15 0.145
45 0.20 0.15 0.13 0.13 0.12 0.12 0.11
30 0.14 0.10 0.09 0.08 0.08 0.08 0.08
15 0.07 0.05 0.04 0.04 0.04 0.04 0.04
0 Bending
The above equation is suitable for α≤180°. When α>180°, the
influence of the straight zone is weak, its limit flanging coefficient
could refer to that of the circular hole flanging. In the case of short
straight line or without straight line, the limit flanging coefficient
can be calculated directly by the circular hole flanging.
2. Technological calculation of the internal hole flanging
As shown in Fig. 6.14, during technological calculation of
flanging, the diameter of the pre-punched hole d0 should be
calculated according to the workpiece diameter D, and then
checking the flanging height H. During flanging, the material
mainly undergoes tangential tensile deformation, the thick-ness
reduces but and the radial deformation is small. Therefore in
technological calculation, the diameter of the pre-punched hole
can be calculated approximately according to the principle of the
constant length on the neutral surface of bending workpiece.
Fig. 6.14 Flat blank flange
It is proved in practice that the error of this calculation
method is acceptable. The two kinds of flanging, the flat blank
flanging and the deep drawing blank flanging, are discussed as
follows.
When flanging in flat blank (see Fig. 6.14), the diameter of
the pre-punched hole d0 is calculated as follows:
0 1 [ ( ) 2 ]2
td D r h (6-9)
As 1 2D D r t
h H r t
Substituting them into Equation 6.9, and simplifying, the
expression of the flanging height H can be obtained:
0 0.43 0.722
D dH r t
(6-10)
or 0(1 ) 0.43 0.722
dDH r t
D
= (1 ) 0.43 0.722
Dm r t (6-11)
According to Equation 6.11, the allowable maximum flanging
height Hmax for the limit flanging coefficient mmin is:
max min(1 ) 0.43 0.722
DH m r t (6-12)
During forming, the deformation caused by tangential tensile
stress in the deformation zone makes the flanging height to
decrease, and the deformation caused by radial tensile stress makes
the flanging height to increase.
Those factors, such as percentage deformation, characteristics
of the die and property of the blank material, may change the
flanging height also. Generally, the effect of the tangential tensile
stress is more conspicuous, therefore the actual flanging height is a
bit less than the value obtained by calculating the developed height
of the bends. But this deviation is very slight, so it is not considered
in ordinary calculation. Only in the case of strict demand is given for
the flanging height, the above factors are taken into account to
determine the diameter of the pre-punched hole, or just to modify
the hole diameter through die tryout.
If the height of the part H>Hmax, it is difficult to form the part
by flanging in one pass. In such case, the deep drawing process is
carried out first. A hole is punched on the bottom of the drawn
workpiece, and then flanging is done (see Fig. 6.15).
Fig. 6.15 Punching and flanging on the bottom of drawn workpiece
So, the maximum flanging height should be calculated first,
and then to determine the deep drawing height. As shown in Fig.
6.15, the flanging height h is:
0 ( ) ( )2 2 2 2
D d t th r r
0(1 ) 0.572
dDr
D (6-13)
Substituting the limit flanging coefficient mmin into Equation
6.13, the limit flanging height hmax can be calculated as:
max min(1 ) 0.572
Dh m r (6-14)
The diameter of the pre-punched hole d0 is:
0 mind m D
Or, according to Equation 6.13, d0 can be calculated as:
0 1.14 2d D r h (6-15)
Hence, the deep drawing height h1 is:
1 maxh H h r t (6-16)
The deep drawing height before flanging h1, the diameter of
the pre-punched hole d0 and the flanging height h can be
calculated based on the hole diameter D after flanging (calculated
by the thickness center line), the workpiece height H, the
roundness radius r and the blank thickness t.
If the workpiece is difficult to be flanged in one pass, it can
be flanged in several passes, but the intermediate annealing
operation is necessary. The flanging coefficient should be 15~20%
larger than that of the previous pass.
3. Calculation of the flanging force
Usually, the flanging force is small. Using ordinary
cylindrical punch, the flanging force can be approximately
calculated by following equation:
0 31.1 ( )P D d t (N) (6-17)
where, D is the diameter after flanging in mm (calculated by the
thickness center line); d0 is the diameter of the pre-punched hole
in mm; t is the blank thickness in mm; σs is the yield strength of
material in Mpa.
The roundness radius of the flanging punch and the
clearance between the punch and die has great influence on the
flanging process and force. Increasing the roundness radius of
punch can decrease the flanging force rapidly. Comparing with
the small roundness radius of punch, the flanging force can
decrease about 50% when using a spherical punch. Increasing the
clearance between the punch and die properly, the flanging force
can also be decreased.
4. Design of the flanging die
The roundness radius of punch r should be as large as
possible, or to adopt the shape of sphere or parabola. Generally,
for the punch with a flat bottom, r≥4t. Fig. 6.16 shows some
punch shapes of the internal circular hole flanging. In view of
deformation convenience, the parabola shape ranks first, and the
flat bottom the last. But, in view of punch manufacturing, the
order is reversed.
The structure of the flanging die is similar to that of deep drawing. The shape and size in the working portion of die influence not only the flanging force, but also the flanging quality directly.
Fig. 6.16 Punch shapes of the circular internal hole flanging
The roundness radius of die has little influence on flanging,
and may equal to the roundness radius of workpiece.
The large clearance between the punch and die is beneficial
to flanging. If there is no demand on perpendicularity for the
hole edge of the workpiece, the clearance can be selected as
large as possible. If there is a high perpendicularity demand,
the clearance should be selected a bit smaller than the initial
blank thickness t. The single-sided clearance Z between the
punch and die is usually determined as:
0.85Z t (6-18)
Z can also be determined according to table 6.6.
Table 6.6 Clearance between punch and die for flanging (mm)
Material thickness 0.3 0.5 0.7 0.8 1.0 1.2 1.5 2.0
Flanging with a flat blank 0.25 0.45 0.6 0.7 0.85 1.0 1.3 1.7
Flanging after deep drawing - - - 0.6 0.75 0.9 1.1 1.5
The thinning of the vertical side after flanging can be
calculated as follows:
' 0dt t t m
D (6-19)
where, t’ is the thickness at the end zone of the vertical side after
flanging in mm; t is the blank thickness in mm; d0 is the
diameter of the pre-punched hole in mm; D is the diameter after
flanging in mm; m is the flanging coefficient.
5. Flanging with thinning
The thickness in the vertical zone of the workpiece is
naturally thinned accompanying the tensile stress occurred
during conventional flanging. In the case of workpiece with
large height H, the method of the compelling thinning can be
used by decreasing the clearance between the punch and die to
improve productivity and save raw material. This method is
called flanging with thinning.
During flanging with thinning, the material in the
deformation zone undergoes tensile deformation under the
pressure of punch first, the diameter of the hole increases
gradually, then the material undergoes extrusion deformation
caused by the clearance between the punch and die which is less
than the blank thickness, and the blank thickness is thinned
obviously. Workpiece with higher straight zone can be obtained
by flanging with thinning.
The final result of this process is the thinning in the vertical
zone of the workpiece. Therefore the percentage deformation can
be expressed by thinning coefficient k:
1tKt
(6-20)
where, t1 is the thickness in the vertical zone of the workpiece after
flanging with thinning in mm; t is the blank thickness before
flanging with thinning in mm.
The thinning coefficient of one pass flanging can be selected
as: K=0.4~0.5
The total force in this process is much greater than that of
conventional flanging. The increasing of the flanging force is
proportional to the percentage thinning.
Fig. 6.17 is an example of flanging with thinning. The blank
thickness is 2 mm, the thickness in the vertical zone of the
workpiece after flanging with thinning is 0.8 mm. It is shown that a
step punch is adopted in the process. The vertical zone of the
workpiece is thinned gradually after passing through different steps.
The distance between the steps should be greater than the
workpiece height to guarantee the next thinning doesn’t start until
the present thinning completes.
(a) workpiece (b) punch Fig. 6.17 Flanging with thinning
6.3.2 External edge flanging
The external flanging is also a process widely used in industry.
There exist two types: inner curve flanging and outer curve
flanging, as shown in Fig. 6.18 respectively.
(a) outer curve flanging (b) inner curve flanging Fig. 6.18 External edge flanging
Both the states of the stress and strain in the external edge
flanging with inner curve are the same as those of the internal hole
flanging. The deformation zone undergoes mainly tangential
tensile deformation. Its limit percentage deformation is mainly
restricted by the tensile failure in the edge zone. During outer
curve flanging, except bending near the roundness radius at the
bottom of the vertical zone, the vertical zone undergoes tangential
compressive stress and radial tensile stress. It results in tangential
compressive and radial tensile deformation. Among them the
tangential compressive stress and strain are the principals.
In fact, the deformation characteristics of the outer curve
flanging are the same as those of deep drawing. It can be regarded
as asymmetrical deep drawing along an unclosed curvilinear
edge. Its limit percentage deformation is mainly restricted by the
instability of the material in deformation zone.
The blank shape of the external flanging for the inner curve
flanging can be calculated referring to internal hole flanging; and
for the outer curve flanging, can be calculated referring to shallow
drawing.
6.4 Necking
Necking is a forming process to reduce the diameter of the
opening end of the hollow or tube part, as shown in Fig. 6.19.
Fig. .19 Necking of hollow part
During necking, the material in the deformation zone
undergoes mainly tangential compressive stresses but also axial
compressive stress, the blank diameter is reduced and both the
wall thickness and the height are inereased. The tangential
compressive stress trends to cause instability in the deformation
zone. Meanwhile, in the non-deformation zone the same
phenomena may occur due to necking pressure P. Therefore, to
prevent Instability is the main objective in necking forming. Its
limitpercentage deformation is mainly determined by the
compressive strength or the stability of the side wall.
The necking percentage deformation is expressed by the
necking coefficient m:
dm
D (6-21)
where, d is the diameter after necking in mm; D is the diameter
before necking in mm.
The necking coefficient m is usually related to the material,
thickness and surface quality of the blank, and also the type of
the die. The average necking coefficients m for various
materials and different supporting methods are listed in Table
6.7.
Table 6.7 Average necking coefficient m
Material
Supporting methods
No supportingOutside supporting
Inside and outside supporting
Mild steel 0.70~0.75 0.55~0.60 0.30~0.35
Copper H62, H68 0.65~0.70 0.50~0.55 0.27~0.32
Aluminum, LF21 0.68~0.72 0.53~0.57 0.27~0.32
Hard Al. (anneal) 0.73~0.80 0.60~0.63 0.35~0.40
Hard Al. (quench) 0.75~0.80 0.68~0.72 0.40~0.43
There are three kinds of supporting. The first one is non-
supporting (see Fig. 6.20). Its die structure is simple, but the
stability of blank during necking is bad. The second one is outside
supporting (see Fig. 6.21 a). Its die structure is complex than the
previous one, but the stability is good, and the necking coefficient
can be selected a bit smaller. The third one is inside and outside
supporting (see Fig. 6.21 b). Its die structure is more complex
than the formers, but its stability is the best, and the allowable
necking coefficient can be still smaller.
(a) outside supporting die (b) inside and outside supporting die Fig 6.21 Supporting types of the necking die
Fig. 6.20 Simple necking die
If the necking coefficient of the workpiece is less than the
value listed in Table 6.7, then this workpiece needs to be necked
in several passes. The necking coefficient of the first pass is
usually 5~10% less than the average one. Due to the influence of
work hardening, the coefficient of necking in subsequent passes is
usually 5~10% greater than the average one. The calculation of
the multi-pass necking is as follows:
Calculate the total necking coefficient: 0nd
mD
where, dn is the workpiece diameter after n passes necking in mm;
D is the blank diameter in mm.
The average necking coefficient m of each pass is
determined according to Table 6.7, then the diameter after and
before successive necking pass can be calculated, that is:
1 2
1 1
n
n
dd dm
D d d
Hence, the necking number n is:
0lg lg lg
lg lgnm d D
nm m
(6-22)
The necking coefficient is different with different material
thickness. With the increasing of the material thickness, the anti-
instability capacity increases. Therefore the necking coefficient
can be selected a bit smaller.
Table 6.8 Variations of average necking coefficient m with different material thickness
MaterialMaterial thickness (mm)
~0.5 >0.5~1.0 >1.0
Copper 0.85 0.80~0.70 0.70~0.65
Steel 0.85 0.75 0.70~0.65
Taking copper and steel as examples, the variation of the
necking coefficient with material thickness is listed in Table
6.8.
6.5 Sizing
Sizing is one of the finishing processes. There exist two
kinds of sizing. In the levelling process, the unevenness and
deflection of the blank or blanking workpiece is planished. In
the sizing process, bended and deep drawn workpiece or
workpiece formed by other process is reformed into final correct
shape.
1. Levelling
According to different blank thickness and surface
demand, levelling can be done by the die with plain surface or
toothed surface.
For thin and soft workpiece on which indentation is
unallowable, the die with plain surface is usually used. In order
to avoid the influence of the guidance accuracy of press slide-
block on levelling, it is better to use floating punch or die (see
Fig. 6.22). When the die with plain surface is used, due to the
influence of the material springback, the levelling result is bad
for high strength material.
(a) floating punch (b) floating dieFig. 6.22 Levelling with plain surface dieed
For thick workpiece, the die with toothed surface is usually
used. There are two kinds of tooth: fine and coarse. In the case of
fine-toothed die (see Fig. 6.23), the tooth depth h=(1~2) t, the
tooth space l=(1~1.2) t, it is suitable for workpiece with
indentation on its surface allowable. In the case of coarse-toothed
die (see Fig. 6.24), h=t, the addendum width b=(0.2~0.5) t,
l=(1~1.2) t, it is suitable for the thin workpieces of aluminum,
copper and brass, and the indentation on the workpiece surface
doesn’t allowable. For either fine-toothed or coarse-toothed die,
the upper tooth and the lower tooth should be staggered by each
other.
Fig. 6.23 Tooth shape of fine-tooth die Fig. 6.24 Tooth shape of coarse-tooth die
The levelling force is calculated as follows:
(N)
P Fq (6-23)
where, F is the projective area to be levelled in mm2; q is the
levelling force per unit area in Mpa, usually between 50~200
Mpa.
2. Sizing
After bending, deep drawing or other forming processes, the
shape and size of the workpiece is close to the finished product,
but the roundness radius may be a bit larger, or the accuracy of
the size or shape at some places is not good, then the sizing is
proceeded to meet the demand of the product completely. The
structure of the sizing die is approximately the same as the
forming die used in previous pass.
For bended part, the upset sizing method is used (see Fig.
6.25). By this method, besides the compressive stress in the
vertical surface of workpiece, there exists compressive stress in
longitudinal direction also. Therefore the workpiece is subjected to
the state of triaxial compressive stresses, and a good sizing results
can be obtained under small plastic percentage deformation.
The only difference is that the tolerance grade and surface
finish demand on the working portion of die are much higher,
and the roundness radius and the clearance between the punch
and die are a bit smaller. With different shapes and demands of
workpieces, the sizing methods adopted are also different.
For deep drawn part with a flange, the section to be sized may
include the flange surface, the sidewall, the bottom and the
roundness radius of the internal and external convex. The die
structure is shown in Fig. 6.26.
For cylindrical deep drawn part, the sizing die with a
clearance Z varying between (0.9t ~0.95 t) is usually used. Such
sizing can also be carried out simultaneously together with the last
deep drawing process.
Fig. 6.25 Sizing of bended partFig. 6.26 Sizing of the deep drawn part with a flange
The sizing force can be calculated as follows:
P Fq (N) (6-24)
where, F is the projective area of sizing in mm2; q is the sizing
force per unit area (or stress), usually, q=150~200 Mpa.
6.6 Spinning
Metal spinning is an indispensable component of advanced
manufacturing technology, which is widely used in aeronautic,
spaceflight, shipbuilding, automobile and mechanical
industries etc. Parts close to final shape (near net forming) can
be produced by metal spinning.
6.6.1 Classification of spinning technology
Traditional definition of the metal spinning technology is
that a continuous and local plastic forming occurs in the blank
to form an axis-symmetrical hollow part by means of roller
feeding and mandrel rotational movements, it is a kind of
advanced manufacturing technology with little chip or without
chip.
Spinning mainly includes conventional spinning and
power spinning (spinning with thinning). Conventional
spinning is defined as a process whereby the shape, size and
characteristics of the blank are significantly changed but with
only slight changing in wall thickness. Power spinning is
defined as a process whereby not only the shape, size and
characteristics of the blank are significantly changed, but also
the wall thickness. Power spinning is divided into shear
spinning (conical part) and flow forming (tubular part).
According to whether the directions of metal flowing and
roller feeding are the same or not, flow forming is divided into
forward and backward spinning (see Table. 6.9).
Table 6.9 Classification of spinning technology
Types Figures
Conventional spinning
Power spinning
Conical part spinning with thinning
Tubular part flow
forming
(Forward spinning)
(Backward spinning)
6.6.2 Conventional spinning
1. Technical process
During spinning, a local plastic deformation zone is
engendered under the roller. The advantage of local deformation is
that the power required during spinning is considerably lower as
compared to the conventional press forming machines, thus
enabling smaller equipment and tools to be used.
Fig. 6.27 shows the stress states in the working portion with
different directions of roller feeding. When the roller moves
towards the edge of the blank, the blank is subjected to radial
tensile stress and tangential compressive stress.
(a) (b)Fig. 6.27 Stress states during conventional spinning
The tensile stress produces a flow in the direction along the
mandrel and causes thinning, which is compensated by the
thickening effect due to the compressive stress (see Fig. 6.27 a).
When the roller traverses in the reverse direction toward the
center of rotation, build-up of metal occurs in front of the roller.
This causes tangential and radial compressive stress in the zone
between the roller and mandrel. As a result, the material is forced
to displace towards the mandrel (see Fig. 6.27b).
2. Processing parameters
There are numerous processing parameters that contribute to
a successful spinning product. Some of the more significant
processing parameters and their effects on conventional spinning
are discussed below.
(1) Feed rate
Feed rate is defined as the ratio of the roller feed to the
rotational speed of the spindle. As long as the feed rate remains
constant, the roller feed and the spindle rotational speed can be
changed without any significant effect on the quality of the product.
Maintaining an acceptable feed rate is vital as too high feed rate
generates too high force that may lead to cracking, and in contrast,
too low feed rate would cause excessive material flow, which
unnecessarily reduces productivity and unduly thins the wall.
(2) Roller path
The roller path is particularly important to the quality of
the spun part. Different roller paths such as linear, concave,
convex, involute and quadratic, etc. have different influences on
the deformation of the blank. The tendency of buckling,
wrinkling and cracking can be avoided by selecting correct
roller path.
(3) Roller shape
It is imperative to design the roller carefully as it directly
affects the shape, wall thickness and dimensional accuracy of the
spun part. Although roller diameter has little effect on the final
product quality, too small roller roundness radius may lead to
higher stress, and ultimately, lead to poor thickness uniformity.
Fig. 6.28 shows examples of different shapes of roller.
Fig.6.28 Different shapes of spinning roller
(4) Spinning ratio
Spinning ratio is defined as the ratio of blank diameter to
mandrel diameter. The higher the spinning ratio, the more difficult
would be the spinning process. If the spinning ratio is too large, the
remaining material cross section is no longer able to transmit the
very high radial tensile stresses generated in the wall. This may
lead to circumferential splitting along the transition from the flange
to the wall.
The spinning ratio is at its upper limit when the wrinkling in
the flange becomes so large that it cannot be removed in the
subsequent spinning passes.
6.6.3 Shear spinning
The process without changing the external diameter of the
blank, but with the wall thickness thinned significantly to
manufacture various axis-symmetrical cone-shaped thin-walled
parts is called shear spinning or conical parts spinning with
thinning. The blank can be a circular or square plate or a pre-
produced workpiece.
In shear spinning, the required wall thickness is achieved by
controlling the clearance between the roller and mandrel so that the
material is displaced axially, parallel to the axis of rotation. Under
local plastic deformation, the material can be deformed in greater
percentage deformation with lower forming forces as compared to
other processes. In many cases, only a single-pass is required to
produce the final part with net shape. Moreover due to work
hardening, significant improvement in mechanical properties can
be achieved.
A schematic diagram of the shear spinning process is
shown in Fig. 6.29. The workpiece thickness is reduced from t0
to t by a roller moving along the matrix of the cone-shaped
mandrel with half angle α. During shear spinning, the material is
displaced parallel to the rotational axis of the mandrel, as shown
in Fig.6.30. The principal deformation process is assumed to be
a process of pure shearing in plane strain state, and hence the
name ’shear spinning’ is given. The thickness of any section of
the workpiece along the axial direction keeps the same before
and after shear spinning.
Fig. 6.29 Principle of shear spinning Fig. 6.30 Idealized shear forming process
The inclined angle of the mandrel (sometimes called half-
cone angle) determines the reduction of the wall thickness. The
greater the angle, the less would be the reduction of the wall
thickness.
The workpiece thickness t is calculated from the blank
thickness t0 and the inclined angle of the mandrel α (sine law):
0 sint t (6-25)
When the sine law is followed strictly, the workpiece can be
spun without failure or defects. In contrary, if the sine law is not
strictly followed, the stresses involved in the process are not
confined solely to the localized area being worked, and the
remainder of the workpiece does not keep stress-free.
When the blank thickness is eanger than that calculated by sine
low, or the clearance between the mandrel and roller is set smaller
than that calculated by sine law (over-reduction), the workpiece
thickness would be t<t0sinα. In such process, the material will build
up gradually in front of the roller, causing the vertical unspun flange
to lean forward towards the headstock. In contrary, if the blank
thickness is smaller than that calculated by sine low, or the clearance
is larger than that calculated by sine low (under-reduced), the
workpiece thickness would be t>t0sinα. In such process, the flange
would lean backward and would likely to wrinkle. Fig. 6.31
illustrates the effects of deviation from the sine law.
Fig. 6.31 Variations of the flange shape when the blank thickness follows or deviates from Sine Law
6.6.4 Flow forming
Flow forming, also known as tube spinning, is a technique
closely allied to shear forming. In this process, as shown in Fig.
6.32, the metal is displaced axially along a mandrel, while the
internal diameter remains constant. It is usually employed to
produce cylindrical components. Most modern flow forming
machines employ two or three rollers, and their design is more
complex as compared to that of conventional and shear spinning
machines.
Fig. 6.32 Forward and backward flow forming
The shape of the blank can be a cylinder or a cup. The
blanks can be pre-produced by spinning, deep drawing or
forging plus machining to improve the dimensional accuracy.
1.Technical process In flow forming, as shown schematically in Fig. 6.33, the
blank is fitted into the rotating mandrel, the rollers press the blank alone the axial direction and the metal is deformed at the contacting zone. In this way, the wall thickness is thinned and the length of the workpiece increased.
Fig. 6.33 Principle of flow forming (deformation zone and forces)ν-Feed speed
The metal flow beneath the roller consists of axial and
circumferential flow. If the circumferential contact length is
much longer than the axial contact length, and the axial plastic
flow is in dominating situation, a sound product would be
produced. In contrary, if the circumferential flow is in
dominating situation, the flow in the axial direction would be
restrained, so metals would pile up in front of the rollers and
cause defects.
According to the constant volume condition, and
neglecting the tangential flow, the workpiece length can be
calculated as follows:
L1= L00 1 0
1 1 1
( )
( )
t d t
t d t
(6-26)
where L1 is the workpiece length; L0 is the blank length; t1 is the
workpiece thickness; t0 is the blank thickness and d1 is the
internal diameter.
2. Forward and backward flow spinning
In flow forming, especially in flow forming of tubes, there are
two methods to be employed, namely forward and backward flow
forming. These two methods are classified in accordance to the
direction of axial flow in the process, as shown in Fig. 6.32.
In forward flow forming, the material flows in the same
direction with that of the traversing rollers. The blank is held
between the mandrel and tailstock, and the blank should have a
base or internal flange to allow the tailstock to clamp against.
During this process, the portion that has not been worked is driven
ahead of the rollers. This method is typically suitable for making
high precision thin walled cylinders, such as rocket motor cases,
hydraulic cylinders, high-pressure vessels and launcher tubes.
For blanks without a base or internal flange, backward flow
forming can be employed. In this case, the blank is pushed onto
the mandrel and is held against the headstock. During flow
forming, the spun material flows towards the unsupported end of
the mandrel opposite to the moving direction of the roller.
Backward flow forming is especially suitable for the blank with
too low ductility to accommodate tensile stresses, such as blanks
made by special casting and welding.
Forward flow forming is usually less productive as
compared to the backward method for the roller should travel
over the total length of the workpiece. In addition, the workpiece
length with forward method is restricted by the mandrel length
and the slide stroke of the machine.
The forward method is normally preferred, because in the
backward method the worked material is more susceptible to
distortion like bell mouthing at the free end and loss straightness.
Moreover, backward flow spinning is normally prone to non-
uniform dimension across the length of the product.
In most cases, flow forming is carried out with more than
one roller. Most modern machines employ the three-roller
configuration mainly to achieve a better balance of loads for
producing precision parts. Normally, the three rollers are spaced
circumferentially at 120° apart, providing a uniform load
distribution to prevent the mandrel being deflected from the
center line. Furthermore, the rollers can be offset or staggered at
a particular distance in the axial and radial direction to improve
dimensional accuracy and surface finish.
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