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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