1. Chapter 5 DRAWING Main contents: Deformation feature of drawing;
Mechanic analysis of drawing;
Problems arising in drawing;
Drawing of cylindrical work-piece;
Drawing of other revolving work;
Drawing of boxes;
Other drawing methods ;
Assistant procedures of drawing.

2. Key points &Difficult point
Problems arising in drawing;
Drawing of cylindrical work-piece.
Difficult parts:
Mechanic analysis of drawing

3. New words deep drawing/深拉深, blank holder/压边圈,
cylindrical/圆柱形的，cup/杯形件， conic /锥形的,
box-shaped/盒形的，rectangular/矩形的
ironing drawing/变薄拉深,flange/凸缘, wrinkle/起皱
axisymmetric geometry/轴对称几何图形,
die radius/凹模圆角半径, radial/径向的,
punch corner radius/凸模圆角半径, redundant/多余的
longitudinal/纵向的，relative thickness of material/相对厚度，
drawing ratio/拉深比， blank diameter/毛坯直径,
number of successive draws/ 拉深次数，
add for trimming/修边余量

4. §5.1 Deformation features of drawing
Deep drawing is the process by which a punch is used
to force sheet metal to flow between the surfaces of a
punch and a die. A flat sheet is formed into a cylindrical-,
conical-, or box-shaped part.
1. Types
2. Deformation feature
3. Stress and strain state

5. 1. Types a)Pure drawing: without a reduction in the thickness
b)Ironing drawing: with a reduction in the thickness

6. 2. Deformation feature Grid method: Damage sites: bottom radius
Thickness: upper becomes thicker
lower becomes thinner
Hardening: upper serious
bottom light
Changes in grid:
bottom no change
wall from sector to rectangle

7. 3. Stress and strain state
Four parts:
deformation zone(the flange) D-d
transition zone -2 die radius
force transmitting zone-the wall
transition zone-2 punch corner radius
non-deforming zone-the bottom

8. §5.2 Mechanic analysis of drawing
Stress analysis of deformation zone
Stress distribution in deformation zone
Varying law of maximum radial stress and maximum tangential stress
Stress analysis of transmitting zone of wall

9. 1. Stress analysis of deformation zone
Equations of equilibrium
Plastic condition
Boundary condition
when

10. 2. Stress distribution in deformation zone
Characteristic point: ,

11. 3.Varying law of maximum radial stress and maximum tangential stress
similar with hardening law
4. Stress analysis of transmitting zone of wall

12. §5.3 Problems arising in drawing
Wrinkle
Fracture
Hardening

13. 1. Wrinkle 1.1 Generate deformation zone 1.2 Affecting factors
Relative thickness t/D0↑,wrinkle↓
Deformation degree m=d/D0↓,wrinkle ↑

14. 1. Wrinkle 1.3 Preventing measures drawing ring(blank holder)
taper die : make flange small
reverse drawing

15. 1. Wrinkle
1.4 Conditions of no wrinkles
Flat die: t / D0≥(0.09~0.17)(1-m)
Taper die: t / D0≥0.03(1-m)

16. 2. Fracture 2.1 Stress analysis of cylindrical surface
flange deformation resistance
friction caused by drawing ring
die radius friction resistance
die radius bending resistance
sum:
efficient tension strength in the wall

17. 2. Fracture 2.2 Condition of no fracture 2.3 Affecting factors
1) deformation degree: m↑fracture↓
2) properties of materials: σb↑fracture↓
3) size of parts : d , t ↑fracture↓
4) radius of die and punch: rp ,rd↑frature↓
5) lubrication: benefit and harmful

18. §5.4 Drawing of cylindrical work-piece
1. Blank
2. Drawing coefficient
3. Number of drawing
4. Drawing force and drawing power
5. Features of subsequent drawing
6. Determination of drawing die size
7. Homework

19. 1. Blank
Principle: constant surface area

20. 2. Drawing coefficient 2.1 Definition and meaning
m=d / D0 (or dn / dn-1)
an index measuring deformation degree of drawing
2.2   Limit drawing coefficient [m]
The maximum drawing coefficient where no wrinkle and no fracture occur.
2.3   Affecting factors
Material:
Die : Z↑Rd↑Rp↑,[m]↑
Drawing condition: blank holder, Hardening[m1]<[m2]<…<[mn]; lubrication

21. 3. Number of drawing m<[m1] need more than one time drawing
Examples
n=log dn / m1D0 / log mn+1

22. 4. Drawing force and drawing power
4.1   blank-holding force
Q = A p
4.2   drawing force
theoretical formula F=Aσρ
empirical formula F=kπdtσb
4.3   choose press
F = Fl + Q
4.4 drawing power

23. 5. Features of subsequent drawing
Inhomogeneous of blank thickness and mechanical properties ;
Constant deformation zone ;
Maximum drawing force occurs in later period ;
Fracture occurs in the later period ;
Wrinkle is not serious, because the subsequent drawing is more stable than the first drawing ;
Drawing coefficient is large, because of hardening .

24. 6. Determination of drawing die size
6.1   punch rp , dp ,(p93)
die rd ,Dd ,
blank holder
6.2   clearance Z
6.3   structure of die and punch

25. Homework
The workpiece shown in Fig.1 is made of 08 carbon steel sheet with the thickness of 2mm (1.5mm).
Calculate the blank diameter before drawing, the number of operation, dimension of work piece after each operation, and the force need
Judge whether a blank holder is needed and choose the press.

26. Homework
Fig.1 Final workpiece

27. §5.5 Drawing of other revolving works
Cylindrical works with flange
Cylindrical works with steps
Taper works
Spherical works

28. 1. Cylindrical works with flange
1.1 Blank(5 parts):constant surface area
1.2 Drawing coefficient
relative flange diameter, relative height and relative radius.
1.3 Wide flange( )
features
drawing principle
drawing method
calculation procedure
1.4 narrow flange

29. 2. Cylindrical works with steps
Drawing coefficient
Number of drawing
drawing methods for multi-drawing

30. 3. Taper works 3.1 Blank: constant surface area
3.2 Deformation region: plane under flange, die radius, free surface between clearance
3.3 Drawing coefficient
3.4 The effect of the work-piece shape on the drawing process
relative height(h/d2),
relative taper top radius(d1/d2),
relative thickness(t/d2)

31. 4. Spherical works 4.1 deformation zone four parts:
plane deformation zone under flange (curved surface)
--drawing
contact region rd
free surface(varying)
plastic deformation region(contact with the top of punch)
--bulging
4.2 drawing coefficient
4.3 drawing methods

32. §5.6 Drawing of boxes square and rectangular boxes
1. Features of drawing
deformation region and the stress state
2. Blank(shape and size)
3. Limited deformation degree of first drawing
4. Drawing of high box
5. Punch and die

33. §5.7 Other drawing methods
1.  Ironing
2.  Flexible die forming
3.  Locally-heated or locally-cooled drawing
4. Progressive drawing with sheet

34. §5.8 Assistant procedures of drawing
Lubrication(position and function)
Annealing(in process and stress-relief)
Pickling(remove scale and dirts)