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.

Key points &Difficult point

Key points: Problems arising in drawing; Drawing of cylindrical work-piece.

Difficult parts: Mechanic analysis of drawing

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

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 Deformation features of drawing

1. Types

a)Pure drawing: without a reduction in the thickness

b)Ironing drawing: with a reduction in the thickness

Grid method: Damage sites: bottom radiusThickness: upper becomes thicker lower becomes thinnerHardening: upper serious bottom lightChanges in grid: bottom no change wall from sector to rectangle

2. Deformation feature

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

3. Stress and strain state

)(),(),();(),(),( tt

)(),(),();(),(),( tt

)(),();( t

)(),();(),(),( tt

)(),(),();(),( t

§5.2 Mechanic analysis of drawing

1. Stress analysis of deformation zone

2. Stress distribution in deformation zone

3. Varying law of maximum radial stress and

maximum tangential stress

4. Stress analysis of transmitting zone of wall

Equations of equilibrium

Plastic condition

Boundary condition

when

1. Stress analysis of deformation zone

0 xF0 yF

dR

Rd

)(

s )(

tRR 0

2. Stress distribution in deformation zone

, maxmax,61.0 RRt

maxmax,)9.0~7.0( RRt

Characteristic point:

3.Varying law of maximum radial stress and maximum tangential stress

similar with hardening law

bBmA )/1(maxmax

maxmax

WM e )1)(( max

4. Stress analysis of transmitting zone of wall

§5.3 Problems arising in drawing

1. Wrinkle

2. Fracture

3. Hardening

1.1 Generate

deformation zone

1.2 Affecting factors

Relative thickness t/D0↑,wrinkle↓

Deformation degree m=d/D0↓,wrinkle ↑

1. Wrinkle

maxmax

1. Wrinkle

1.3 Preventing measures

drawing ring(blank holder)

taper die : make flange small

reverse drawing

1.4 Conditions of no wrinkles

• Flat die: t / D0≥(0.09~0.17)(1-m)

• Taper die: t / D0≥0.03(1-m)

1. Wrinkle

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

max

)/(2 tdQM

eM )( max

)2/( trt dbW

WM e )1)(( max

WbK k

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

K

§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

1. Blank

Principle: constant surface area

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

][,)/(/ mdDtnrbs

3. Number of drawing

m<[m1] need more than one time drawing

Examples

n=log dn / m1D0 / log mn+1

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

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 .

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

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.

Fig.1 Final workpiece

Homework

§5.5 Drawing of other revolving

works

Cylindrical works with flange Cylindrical works with steps Taper works Spherical works

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 procedure1.4 narrow flange

drdHddDdm F /44.3/4/1/ 0

4.1/ dd F

2. Cylindrical works with steps

Drawing coefficient

Number of drawing

drawing methods for multi-drawing

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)

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

§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

§5.7 Other drawing methods

1.  Ironing

2.  Flexible die forming

3.  Locally-heated or locally-cooled drawing

4. Progressive drawing with sheet

§5.8 Assistant procedures of drawing

Lubrication(position and function) Annealing(in process and stress-

relief) Pickling(remove scale and dirts)