1. 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.

2. Chapter 6 Forming 6. 1 Local forming 6.2 Bulging 6.3 Flanging
6.4 Necking
6.5 Sizing
6.6 Spinning

3. 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.

4. 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.

5. 1.Deep drawing: dp/D>mL=0.5
2. Deep drawing—bulging: dp/D<mL=0.5～0.25
3. bulging : dp/D<0.25

6. 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

8. 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:
(6-1)
limit=
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).

9. (a) pre-forming (b) final forming
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 forming
Fig. 6.3 Pressing bulge

10. 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.

11. Table 6.1 Types and sizes of the rib
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°

12. 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 18 11 22 26 16 24 34 20 31 44 36 51 30 43 60 35 48 68 40 55 78 45

13. 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.
(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.

14. During the forming and sizing of thin material (t<1
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.
(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.

15. 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

16. Bulging can be performed by various methods
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

17. 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.

18. 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

19. 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

20. 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.

21. 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.
(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.

22. Generally, the relationship between the bulging coefficient K and the allowable percentage elongation of material [ ] is: or
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.

23. Table 6.2 Experimental data of bulging coefficients
Material
Thickness (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
Brass
H62
0.5~1.0 35
1.35
H68
1.5~2.0 40
1.40
Mild
carbon steel
08 F 20
1.20
10, 20 24
1.24
Stainless steel
1Gr18Ni9Ti 26
1.26

24. 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):
(6-5)
Blank diameter:
(mm)
(6-6)
Blank length:
(mm)
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.

25. The soft die bulging is widely used in practice
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.

26. 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:
After simplifying, we obtain:

27. Fig. 6.9 Balance condition of
the half annular strip of bulging
Fig. 6.8 Bulging workpiece and stresses

28. 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:
(6-7)
The symbols in above equation are shown in Fig 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.

29. 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.

30. 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)

31. (a) internal edge flanging (b) external edge flanging
Fig Internal and external edge flanges

32. 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).

33. The value of the stress varies in the whole deformation zone
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).

34. zone of the internal hole flanging during circular hole flanging
Fig Stress state in the deformation Fig Distributions of stress and strain
zone of the internal hole flanging during circular hole flanging

35. 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:
(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:

36. (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:
, or
that is,
The coefficients of the circular hole flanging for various materials at the first pass are listed in Table 6.3.

37. Table 6.3 Flanging coefficients of various materials
Blank material after annealing
Flanging coefficient m m0
mmin
Tinplate
0.70
0.65
Soft copper
t=0.25~2.0mm
t=3.0~6.0mm
0.72
0.68
0.75
0.78
Brass H62
t=0.5~6.0mm
0.62
Aluminum
t=0.5~5.0mm
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
TA5 (500~600℃)
0.7~0.65
Stainless steel, High temperature alloy
0.69~0.65
0.61~0.57

38. 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.
(2) Status of the hole edge
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.

39. (3) Relative thickness of the material
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.

40. 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
Shape of flanging punch
Method of the hole manufacturing
100 50 35 20 15 10 8
6.5 5 3 1
Spherical
Burring
after 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
0.48
0.44
0.43
0.42 -
Cylindrical
0.80
0.50
0.37
0.35
0.85
0.55
0.47
Relative thickness of the material ( )

41. For noncircular hole flanging (see Fig. 6
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.

42. Fig. 6.13 Noncircular hole flanging

43. 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:
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.

44. Table 6.5 Limit flanging coefficient of noncircular hole (mild carbon steel)
Center 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
0.44
0.42
0.41
150
0.67
0.43
0.40
0.38
0.375
135
0.39
0.36
0.35
0.34
120
0.53
0.33
0.32
0.31
0.30
105
0.47
0.29
0.28
0.27
0.26 90
0.25
0.24
0.23
0.225 75
0.22
0.21
0.20
0.19
0.185 60
0.17
0.16
0.15
0.145 45
0.13
0.12
0.11 30
0.14
0.10
0.09
0.08 15
0.07
0.05
0.04
Bending
Relative thickness of the material ( )

45. The above equation is suitable for α≤180°
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.

46. 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.

47. Fig 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.

48. When flanging in flat blank (see Fig. 6
When flanging in flat blank (see Fig. 6.14), the diameter of the pre-punched hole d0 is calculated as follows:
(6-9) As
Substituting them into Equation 6.9, and simplifying, the expression of the flanging height H can be obtained:
(6-10)

49. or =
(6-11)
According to Equation 6.11, the allowable maximum flanging height Hmax for the limit flanging coefficient mmin is:
(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.

50. 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.

51. 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 Punching and flanging on the bottom of drawn workpiece

52. 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:
(6-13)
Substituting the limit flanging coefficient mmin into Equation 6.13, the limit flanging height hmax can be calculated as:
(6-14)

53. The diameter of the pre-punched hole d0 is:
Or, according to Equation 6.13, d0 can be calculated as:
(6-15)
Hence, the deep drawing height h1 is:
(6-16)

54. 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.

55. 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:
(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.

56. 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.

57. 4. Design of the flanging die
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.
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 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.

58. Fig. 6.16 Punch shapes of the circular internal hole flanging

59. 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:
(6-18)
Z can also be determined according to table 6.6.

60. 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
0.85
1.3
1.7
Flanging after deep drawing -
0.75
0.9
1.1
The thinning of the vertical side after flanging can be calculated as follows:
(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.

61. 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.

62. 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.

63. 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:
(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

64. 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 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.

65. (a) workpiece (b) punch Fig. 6.17 Flanging with thinning

66. 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 respectively.
(a) outer curve flanging (b) inner curve flanging
Fig External edge flanging

67. 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.

68. 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.

69. 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
Fig. .19 Necking of hollow part

70. 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.

71. The necking percentage deformation is expressed by the necking coefficient m:
(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.

72. Table 6.7 Average necking coefficient m
Material
Supporting methods
No supporting
Outside 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
Hard Al. (anneal)
0.73~0.80
0.60~0.63
0.35~0.40
Hard Al. (quench)
0.75~0.80
0.40~0.43

73. There are three kinds of supporting
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 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 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.

74. Fig Simple necking die
(a) outside supporting die (b) inside and outside supporting die
Fig 6.21 Supporting types of the necking die

75. 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:
where, dn is the workpiece diameter after n passes necking in mm; D is the blank diameter in mm.

76. 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:
Hence, the necking number n is:
(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.

77. Taking copper and steel as examples, the variation of the necking coefficient with material thickness is listed in Table 6.8.
Table 6.8 Variations of average necking coefficient m
with different material thickness
Material
Material thickness (mm)
~0.5
>0.5~1.0
>1.0
Copper
0.85
0.80~0.70
0.70~0.65
Steel
0.75

78. 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.

79. 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.

80. (a) floating punch (b) floating die
Fig Levelling with plain surface dieed

81. For thick workpiece, the die with toothed surface is usually used
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.

82. Fig. 6. 23 Tooth shape of fine-tooth die Fig. 6
Fig Tooth shape of fine-tooth die Fig Tooth shape of coarse-tooth die

83. The levelling force is calculated as follows:
(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.

84. 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.

85. 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 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.

86. 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.
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

87. Fig Sizing of the deep
drawn part with a flange
Fig Sizing of bended part

88. The sizing force can be calculated as follows:
(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.

89. 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.

90. 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.

91. 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).

92. 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)

93. 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 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.

94. Fig. 6.27 Stress states during conventional spinning
(a) (b)
Fig Stress states during conventional spinning

95. 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 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).

96. 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.

97. (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.

98. (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.

99. Fig.6.28 Different shapes of spinning roller
(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 shows examples of different shapes of roller.
Fig.6.28 Different shapes of spinning roller

100. (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.
(5－23)

101. 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.

102. 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.

103. A schematic diagram of the shear spinning process is shown in Fig. 6
A schematic diagram of the shear spinning process is shown in Fig 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 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.

104. Fig. 6. 29 Principle of shear spinning Fig. 6
Fig Principle of shear spinning Fig Idealized shear forming process

105. 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):
(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.

106. 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 illustrates the effects of deviation from the sine law.

107. Fig. 6.31 Variations of the flange shape
when the blank thickness follows or deviates from Sine Law

108. 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.

109. Fig. 6.32 Forward and backward flow forming

110. The shape of the blank can be a cylinder or a cup
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.

111. Fig. 6.33 Principle of flow forming (deformation zone and forces)
ν-Feed speed

112. 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.

113. According to the constant volume condition, and neglecting the tangential flow, the workpiece length can be calculated as follows:
(6-26)
L1= L0
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.

114. 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
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.

115. 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.

116. 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.
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.

117. In most cases, flow forming is carried out with more than one roller
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.

118. Thank You ！