Key takeaways:1. Deep drawing is a highly technical metal forming process that requires careful control of multiple factors, including material properties, die geometry, and applied forces, to prevent common defects such as wrinkling and tearing at the flange and the 'dangerous section' respectively, with the quality of the final product heavily reliant on the precise calibration of blank holder force and the optimization of die design. 2. The success of deep drawing is largely determined by the material's ability to withstand the stresses of the process, with factors like the material's hardening index, yield ratio, and the drawing coefficient playing pivotal roles in the material's deformation behavior, emphasizing the necessity for materials with specific mechanical properties to achieve the desired shape without failure. 3. Calculations for the deep drawing process are rooted in principles of shape similarity and equal surface area, where the initial blank's dimensions are strategically determined to ensure that the final drawn part maintains structural integrity and meets design specifications, highlighting the importance of detailed pre-process planning in achieving efficient and effective deep drawing operations.

**The definition of deep drawing**

Deep drawing is a processing method that uses a drawing die to press the flat blank into various open hollow parts or process the manufactured hollow parts into other shapes of hollow parts under the pressure of a press.

The mold for deep drawing is been called deep drawing die.

Types of deep drawing parts

- a) Deep drawing of axisymmetric rotating parts
- b) Box parts
- c) Asymmetric drawing parts

Deep drawing parts with more complicated shape

**Analysis of Deep Deformation Process**

**Analysis of Deep Deformation Process**

**1.1 Deep deformation process and characteristics**

**1.1 Deep deformation process and characteristics**

Deep drawing is the process of plastic flow of materials

How to process a round flat blank into an open hollow part without a mold?

Before deep drawing:

a=a=……=a

b=b=……=b

Material thickness t

After deep drawing:

a<a_{1}<a_{2}<a_{3}<a_{4}<a_{5}

b_{1}=b_{2}=… …=b

The thickness of the material varies along the height, and the mouth thickens.

h＞（D—d）/2

Changes before and after grid deep drawing.

Forces on the grid during deep drawing

Change of sheet thickness in height direction

Deep deformation characteristics:

- The material under the die has little change during the drawing process. The deformation is mainly concentrated in the (D-d) circular ring portion on the die plane, which is the main deformation area of the drawing.
- The deformation in the deformation zone is uneven. Under the combined action of tangential compressive stress and radial tensile stress, the metal is compressed in the tangential direction, and the more it compresses at the mouth, the more it extends in the radial direction, and the more the mouth is elongated.
- The thickness varies from place to place in the height direction, and the thickness at the mouth of the drawn part increases most.

**1.2 State and distribution of stress and strain of billet during deep drawing**

**1.2 State and distribution of stress and strain of billet during deep drawing**

- Stress-strain state

Take the first deep drawing of a straight-walled cylindrical part with a blank holder as an example.

Subscripts 1, 2, and 3 represent the radial, thick, and tangential stresses and strains of the billet, respectively.

- Stress-strain distribution

1) Ignore the stress in the thickness direction and do not consider work hardening

2) Solve two unknowns from the two equations of plastic deformation condition and force equilibrium condition

Stress in deformation zone

The value range of R: [r ~ R_{t}], σ1 and σ3 are changing every moment in the drawing process

Stress σ1 and σ3 distribution in deformation zone

When Rt = 0.61R_{0}, |σ_{1}|=|σ_{3}|

Variation of σ_{1max} and σ_{3max} during deep drawing

σ_{1max} reaches the maximum value during drawing when R_{t} = (0.7 ~ 0.9) R_{0}

**Deep drawing quality analysis and control**

**Deep drawing quality analysis and control**

The main quality issues in the drawing process:

- Wrinkling in the deformation area of the flange
- Rupture of dangerous section

**2.1 Wrinkl****ing**

**2.1 Wrinkl**

**ing**

- The concept and cause of wrinkling

Wrinkling refers to the phenomenon that uneven wrinkles are formed in the deformation area of the flange along the tangential direction during deep drawing deformation.

- Factors affecting wrinkling

- Mechanical properties of materials
- Relative thickness of flange material
- Degree of deformation
- Geometry of the working part of the die: conical die is not easy to wrinkle

In general: the larger the flange width, the thinner the thickness, the smaller the elastic modulus and the hardening modulus of the material, the weaker the resistance to instability, and the easier it is to wrinkle.

- Measures to prevent wrinkles

The most effective measure to prevent deep wrinkling in actual production is to use a blank holder ring and apply a suitable blank holder force Q

A few important conclusions about wrinkling:

(1) Wrinkling law: It has been proved in practice that wrinkles are most likely to occur during the first drawing of a straight-walled cylindrical part: the initial stage of deep drawing

(2) Anti-wrinkle measures: use blank holder ring to apply appropriate blank holder force

(3) Wrinkling position: the main deformation area of deep drawing (flange deformation area)

**2.2 ****D****rawing breakage-the key to deepening success**

**2.2**

**D**

**rawing breakage-the key to deepening success**

**The concept of drawing breakage and its causes**

When the tensile stress of the cylinder wall exceeds the tensile strength of the material of the cylinder wall, the drawn part will rupture at the tangent of the bottom corner and the cylinder wall-the “dangerous section”.

Mainly depends on:

- Tensile stress in the force transfer zone of the cylinder wall
- Tensile strength of the tube wall force transmission zone

**Factors affect drawing breakage**

(1) sheet mechanical properties

(2) drawing coefficient m

(3) the corner radius of the die

(4) friction

(5) blank holder force

**Measures to prevent cracking**

- Use materials with large hardening index and small yield ratio for deep drawing;
- Properly increase the radius of the convex and concave corners of the drawing;
- Increase the number of deep drawing;
- Improve lubrication.

Practice proves:

In the first deep drawing of the straight-walled cylindrical part, the most likely time for the crack to occur is in the initial stage of deep drawing.

**Deep drawing process calculation**

**Deep drawing process calculation**

**3.1 Calculation of Drawing Process for Straight Wall Rotating Parts**

**3.1 Calculation of Drawing Process for Straight Wall Rotating Parts**

- Calculation of drawing process for cylinders without flange

(1) Determination of the shape and size of the blank

The basis for determining the shape and size of the blank:

__Shape similarity principle__: The shape of the blank before drawing of the rotating body part is similar to the shape of the cross-section of the workpiece after drawing.

According to this, the shape of the blank used for the cylindrical part is circular

__Principle of equal surface area__: If the thickness of the material before and after drawing is unchanged, the surface area of the blank before drawing and after drawing are approximately equal.

Calculation steps of blank size:

1) Determine the margin for trimming.

2) Calculate the surface area of the drawn part.

- The deep drawing is divided into several simple geometries.
- Find the surface area ofeach simple geometry.
- Adding the surface area ofeach simple geometry is the total surface area of the part.

3) According to the principle of equal surface area, find the diameter of the blank.

Calculation formula of blank size

1) Check the table 5-2 to get the trim margin △h

Table: Trim allowance for non-flanged parts

Deep drawing height H | Deep drawing height H/d | |||

>0.5~0.8 | >0.8~1.6 | >16~2.5 | >2.5~4 | |

≤10 | 1 | 1.2 | 1.5 | 2 |

>10~20 | 1.2 | 1.6 | 2 | 2.5 |

>20~50 | 2 | 2.5 | 3.3 | 4 |

>50~100 | 3 | 3.8 | 5 | 6 |

>100~150 | 4 | 5 | 6.5 | 8 |

>150~200 | 5 | 6.3 | 8 | 10 |

>200~250 | 6 | 7.5 | 9 | 11 |

>250 | 72 | 8.5 | 10 | 12 |

2) Calculate surface area

The simplified blank diameter is:

Note: When the sheet thickness t<1mm, all dimensions are substituted with the marked dimensions, otherwise the midline dimensions are substituted.

(2) Determination of drawing coefficient

1) The concept of drawing coefficient

Relationship between drawing coefficient and drawing deformation

That is, the size of m can indirectly reflect the amount of tangential deformation.

The important conclusion of the deep drawing coefficient:

- The drawing coefficient can indicate the degree of drawing deformation. The smaller the drawing coefficient, the greater the drawing deformation. When the drawing coefficient is less than a certain value, the drawing part will be pulled apart, so there is a limit drawing coefficient .
- Ultimate drawing coefficient [m
_{n}]: The minimum drawing coefficient that keeps the drawing from breaking. - When performing the drawing process calculation and mold design, always reduce the drawing coefficient value as much as possible in order to reduce the number of drawing times.

2) Factors affecting the limit drawing coefficient

① Material

② The relative thickness of the sheet is large, and [m] can be reduced.

③ In terms of mold (small ultimate drawing coefficient)

- Large die clearance
- Convex and concave die with large corner radius
- Smooth mold surface
- Conical die

④ Deepening working conditions

- Whether to use blank holder
- Lubricating
- Deep drawing times

The overall influence law: Any factor that can increase the strength of the dangerous section of the tube wall force transmission zone and reduce the tensile stress in the tube wall force transmission zone will reduce the limit drawing coefficient, and vice versa.

3) Determination of the limit drawing coefficient

Table 5-3 and Table 5-4 are the limit drawing coefficients for each drawing of flangeless cylindrical parts.

Table: The limit stretching ratio of the cylindrical part with flanging (08, 10, 15Mn, and H62).

Deep drawing coefficient | Relative thickness t/D*100 | |||||

2~1.5 | 1.5~1 | 1~0.6 | 0.6~0.3 | 0.3~0.15 | 0.15~0.08 | |

m1 | 0.48~0.50 | 0.5~0.53 | 0.53~0.55 | 0.55~0.58 | 0.58~0.60 | 0.60~0.63 |

m2 | 0.73~0.75 | 0.75~0.76 | 0.76~0.78 | 0.78~0.79 | 0.79~0.80 | 0.80~0.82 |

m3 | 0.76~0.78 | 0.78~0.79 | 0.79~0.80 | 0.80~0.81 | 0.81~0.82 | 0.82~0.84 |

m4 | 0.78~0.80 | 0.80~0.81 | 0.81~0.82 | 0.82~0.83 | 0.83~0.85 | 0.85~0.86 |

m5 | 0.80~0.82 | 0.82~0.84 | 0.84~0.85 | 0.85~0.86 | 0.86~0.87 | 0.87~0.88 |

Table: The ultimate drawing coefficient of cylindrical parts without blank holder (08, 10 & 15Mn)

Relative thickness t/D*100 | Deep drawing coefficient for each time | |||||

m1 | m2 | m3 | m4 | m5 | m6 | |

1.5 | 0.65 | 0.80 | 0.84 | 0.87 | 0.90 | – |

2.0 | 0.60 | 0.75 | 0.80 | 0.84 | 0.87 | 0.90 |

2.5 | 0.55 | 0.75 | 0.80 | 0.84 | 0.87 | 0.90 |

3.0 | 0.53 | 0.75 | 0.80 | 0.84 | 0.87 | 0.90 |

>3 | 0.50 | 0.70 | 0.75 | 0.78 | 0.82 | 0.85 |

In order to improve process stability and part quality, deep drawing coefficients slightly larger than the limit drawing coefficient [m_{n}] should be used in actual production for deep drawing.

(3) Determination of drawing times

When [m_{total}]> [m_{1}], the drawing part can be drawn at one time, otherwise multiple drawing times are required.

There are several ways to determine the number of deep drawing:

- Table lookup method (Table 5-5)
- Prediction method
- Calculation method

Steps to calculate the number of deep drawing methods:

1) Check the limit drawing coefficient [m_{n}] of each time from Table 5-3 or Table 5-4.

2) Calculate the ultimate diameter of each drawing in turn, that is,

ｄ_{1}＝[ｍ_{1} ]Ｄ；

ｄ_{2}＝[ｍ_{2} ]ｄ_{1}；

…；

ｄ_{ｎ}＝[ｍ_{ｎ}]ｄ_{ｎ}－１；

3) When d_{n}≤d, the number of calculations n is the number of deep drawing.

4) Determination of the size of the drawing process

1) Diameter of semi-finished product

From Tables 5-3 and 5-4, the limit drawing coefficient [m_{n}] of each drawing is found, and it is appropriately enlarged and adjusted to obtain the actual drawing coefficient m_{n}.

The principles of adjustment are:

１）Ensure that m_{total}＝ｍ_{1}ｍ_{2}…ｍ_{ｎ}＝

２）Make ｍ_{1}＜ｍ_{2}＜…ｍ_{ｎ}＜1

Finally, calculate the diameter of each process according to the adjusted drawing coefficient:

ｄ_{1}＝ｍ_{1}Ｄ；ｄ_{2}＝ｍ_{2}ｄ_{1}；…；ｄ_{ｎ}＝ｍ_{ｎ}ｄ_{ｎ}－１=d

Amplification factor k

When calculating the diameter of the semi-finished product according to the above method, it is necessary to repeatedly try to take the values of m_{1}, m_{2}, m_{3}, …, m_{n}, which is cumbersome. In fact, the limit drawing coefficient can be enlarged by an appropriate multiple k.

In the formula, n is the number of deep drawing.

2) Round bottom corner radius r_{n}

The fillet radius r_{n} at the bottom of the cylinder is the fillet radius r_{p} of the deep drawing die of this process.

The determination method is as follows:

In general, except for the deep drawing process, r_{pi} = r_{di} is preferable.

For the last drawing process:

When the fillet radius of the workpiece r≥t , then r_{pn} = r;

When the fillet radius of the workpiece is r <t, then r_{pn}> t is taken. After the drawing is finished, r is obtained through the shaping process.

3) Calculation of process part height H_{i}

According to the principle that the surface area of the process parts after drawing is equal to the surface area of the billet, the following formula for calculating the height of the process parts can be obtained.

Before the calculation, the bottom corner radius of each work piece should be determined.

H_{i} is solved by the calculation formula of the blank diameter:

Deep drawing process calculation example

Example 4.1 Find the blank size of the cylindrical part shown in the figure and the dimensions of each drawing process. The material is 10 steel, and the sheet thickness is t = 2mm.

Solution:

Because t> 1mm, it is calculated according to the thickness and diameter of the plate.

(1) Calculate the diameter of the billet

According to the size of the part, its relative height is

Check the table 5-2 to get the cutting margin

Billet diameter is

Substitute the known conditions into the above formula to obtain D = 98.2mm, here D = 98mm

(2) Determine the number of deep drawing

The relative thickness of the blank is:

According to Table 5-1, the blank holder ring can be used or not, but for insurance, the blank holder ring is still used for the first drawing.

Table: Using a binder ring (flat die cavity)

Stretching Method | First stretch | Subsequent stretches | ||

（t/D）×100 | m1 | （t/D）×100 | m_{n} | |

Using a Flanging Ring | <1.5 | <0.60 | <1 | <0.80 |

Optional use of a flanging ring | 1.5~2.0 | 0.6 | 1~1.5 | 0.8 |

Without a flanging ring | >2.0 | >0.60 | >1.5 | >0.80 |

According to ｔ/Ｄ＝2.0％, check the table 5-3 to get the ultimate drawing coefficient for each drawing process：[ｍ_{1} ]＝0.50，[ｍ_{2} ]＝0.75，[ｍ_{3} ]＝0.78，[ｍ_{4} ]＝0.80，…

Table: Limit drawing coefficient of blank holder for cylindrical parts (08, 10, 15Mn and H62)

Corner radius | Relative thickness of sheet t/D*100 | |||||

2~15 | 1.5~1 | 1~0.6 | 0.6~0.3 | 0.3~0.15 | 0.15~0.08 | |

m1 | 0.48~0.50 | 0.5~0.53 | 0.53~0.55 | 0.55~0.58 | 0.58~0.60 | 0.60~0.63 |

m2 | 0.73~0.75 | 0.75~0.76 | 0.76~0.78 | 0.78~0.79 | 0.79~0.80 | 0.80~0.82 |

m3 | 0.76~0.78 | 0.78~0.79 | 0.79~0.80 | 0.80~0.81 | 0.81~0.82 | 0.82~0.84 |

m4 | 0.78~0.80 | 0.80~0.81 | 0.81~0.82 | 0.82~0.83 | 0.83~0.85 | 0.85~0.86 |

m5 | 0.80~0.82 | 0.82~0.84 | 0.84~0.85 | 0.85~0.86 | 0.86~0.87 | 0.87~0.88 |

Therefore,

ｄ_{1}＝[ｍ_{1} ]Ｄ＝0.50×98ｍｍ＝49.0ｍｍ

ｄ_{2}＝ [ｍ_{2} ]ｄ_{1}＝0.75×49.0ｍｍ＝36.8ｍｍ

ｄ_{3}＝ [ｍ_{3} ]ｄ_{2}＝0.78×36.8ｍｍ＝28.7ｍｍ

ｄ_{4}＝ [ｍ_{4} ]ｄ_{3}＝0.8×28.7ｍｍ＝23ｍｍ

At this time,

ｄ_{4}＝23ｍｍ＜28ｍｍ, so it should be drawn 4 times.

Table: The coefficient K1 value for the first draw of cylindrical parts (steel grades 08 to 15)

Relative thickness（t/D_{0}）×100 | First-time deep drawing coefficient (m_{1}) | |||||||||

0.45 | 0.48 | 0.50 | 0.52 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | |

5.0 | 0.95 | 0.85 | 0.75 | 0.65 | 0.60 | 0.50 | 0.43 | 0.35 | 0.28 | 0.20 |

2.0 | 1.10 | 1.00 | 0.90 | 0.80 | 0.75 | 0.60 | 0.50 | 0.42 | 0.35 | 0.25 |

1.2 | 1.10 | 1.00 | 0.90 | 0.80 | 0.68 | 0.56 | 0.47 | 0.37 | 0.30 | |

0.8 | 1.10 | 1.00 | 0.90 | 0.75 | 0.60 | 0.50 | 0.40 | 0.33 | ||

0.5 | 1.10 | 1.00 | 0.82 | 0.67 | 0.55 | 0.45 | 0.36 | |||

0.2 | 1.10 | 0.90 | 0.75 | 0.60 | 0.50 | 0.40 | ||||

0.1 | 1.10 | 0.90 | 0.75 | 0.60 | 0.50 |

Table: The coefficient K1 value for the first draw of cylindrical parts (steel grades 08 to 15)

Relative thickness（t/D_{0}）×100 | Second-time deep drawing coefficient (m_{2}) | |||||||||

0.7 | 0.72 | 0.75 | 0.78 | 0.80 | 0.82 | 0.85 | 0.88 | 0.90 | 0.92 | |

5.0 | 0.85 | 0.70 | 0.60 | 0.50 | 0.42 | 0.32 | 0.28 | 0.20 | 0.15 | 0.12 |

2.0 | 1.10 | 0.90 | 0.75 | 0.60 | 0.52 | 0.42 | 0.32 | 0.25 | 0.20 | 0.14 |

1.2 | 1.10 | 0.90 | 0.75 | 0.62 | 0.52 | 0.42 | 0.30 | 0.25 | 0.16 | |

0.8 | 1.00 | 0.82 | 0.70 | 0.57 | 0.46 | 0.35 | 0.27 | 0.18 | ||

0.5 | 1.10 | 0.90 | 0.76 | 0.63 | 0.50 | 0.40 | 0.30 | 0.20 | ||

0.2 | 1.00 | 0.85 | 0.70 | 0.56 | 0.44 | 0.33 | 0.23 | |||

0.1 | 1.10 | 1.00 | 0.82 | 0.68 | 0.55 | 0.40 | 0.30 |

(3) Determination of the size of each drawing process

The diameter of each process part is

ｄ_{1}＝k[ｍ_{1 }]Ｄ＝1.051185×0.50×98ｍｍ＝51.51ｍｍ

ｄ_{2}＝k[ｍ_{2 }]ｄ_{1}＝1.051185×0.75×51.51ｍｍ＝40.61ｍｍ

ｄ_{3}＝k[ｍ_{3 }]ｄ_{2}＝1.051185×0.78×40.61ｍｍ＝33.30ｍｍ

ｄ_{4}＝k[ｍ_{4 }]ｄ_{3}＝1.051185×0.80×33.30ｍｍ≈28ｍｍ

The radius of the fillet at the bottom of each process part takes the following values:

ｒ_{1}＝8ｍｍ，ｒ_{2}＝5ｍｍ，ｒ_{3}＝4ｍｍ，ｒ_{4}＝4ｍｍ

The height of each process part is ……

(4) Process part sketch

- Drawing process calculation of flanged cylindrical parts

The flanged cylindrical part can be regarded as a semi-finished product when the flangeless cylindrical part is drawn to a certain point in the middle and stopped.

Same drawing as flangeless tube:

- Deformation characteristics are the same.
- The quality problems that occur during the drawing process are similar.

(1) Classification and deformation characteristics of flanged cylindrical parts

1) Narrow flange cylindrical parts

Narrow flange cylinder:

Drawing method and process calculation method are the same as those of flangeless cylindrical parts

2) Wide flange cylindrical parts

**d**_{f}**/d＞1.4**

Drawing method and process calculation are different from flangeless cylindrical parts

(2) Deep drawing method of wide flange cylindrical part

**d**_{f}**/d＞1.4**

Special reminder:

Regardless of the drawing method, the flange size must be obtained during the first drawing. The height of the punch entering the cavity must be strictly controlled.

(3) Process calculation of wide flange cylindrical parts

1) Determination of the blank size of the wide flange

Blank unfolding: calculated according to the blank calculation method for flangeless cylindrical parts, that is, the blank surface area is calculated according to the principle of equal surface area.

When r_{p}=r_{d}=r，

d_{f} contains trim margin △d_{f}

2) Deformation of wide flanged cylindrical parts

The degree of deformation of wide flanged cylindrical parts cannot be measured only by the drawing coefficient

The number of drawing times is determined according to the drawing coefficient and the relative height of the parts.

- It is impossible to judge the partof deep drawing and the degree of deformation based on the deep drawing coefficient.
- The first ultimate drawing factor is smaller than that of a flangeless tube. Wide flanges have their own drawing coefficients, see table 5-7
- The drawing coefficient of a wide flanged cylindrical part depends on three relative ratios of dimensions: df/d (relative diameter of the flange), h/d (relative height of the part), r/d (relative fillet radius ).

Table 5-7 First limit drawing coefficient of wide flange

(3) Judge whether it can be pulled at once

Judging from the drawing coefficient and relative height, find the total drawing coefficient m and the total relative height h/d, find out the limit drawing coefficient [m_{1}] and relative height [h_{1}/d_{1}] that are allowed for the first time, and compare: m_{total}> [m_{1}], h/d≤[h_{1}/d_{1}], it can be pulled out at one time, otherwise multiple deep drawing is required.

(4) Determining the number of deep drawing: it can still be calculated by using the extrapolation algorithm.

(5) Determination of the size of the semi-finished product

3．Deep drawing of stepped cylindrical parts

Deformation characteristics:

The deep drawing of the stepped part is basically the same as that of the cylindrical part, and each step is equivalent to the drawing of the corresponding cylindrical part.

(1) Judge whether it can be deep-drawn at one time

Judging by the ratio of the part height h to the minimum diameter d_{n}.

If h/d_{n}≤[h_{1}/d_{1}], it can be pulled out once, otherwise it can be drawn multiple times. [h_{1}/d_{1}] can be found in Table 5-5

Table: Maximum relative height h1/d1 of wide flange cylindrical parts for first stretching (08, 10 steel)

Unit:mm

Relative diameter d_{convex}/d | Relative thickness of sheet t/D×100 | ||||

<2~1.5 | <1.5~1.0 | <1.0~0.5 | <0.5~0.2 | <0.2~0.06 | |

≤1.1e | 0.75~0.90 | 0.65~0.82 | 0.50~0.70 | 0.50~0.62 | 0.45~0.52 |

>1.1~1.3 | 0.65~0.80 | 0.56~0.72 | 0.45~0.60 | 0.45~0.52 | 0.40~0.47 |

>1.3~1.5 | 0.58~0.70 | 0.50~0.63 | 0.42~0.54 | 0.40~0.48 | 0.35~0.42 |

>1.5~1.8 | 0.48~0.58 | 0.42~0.53 | 0.37~0.44 | 0.34~0.39 | 0.29~0.35 |

>1.8~2.0 | 0.42~0.51 | 0.36~0.46 | 0.32~0.38 | 0.29~0.34 | 0.25~0.30 |

>2.0~2.2 | 0.35~0.45 | 0.31~0.40 | 0.27~0.33 | 0.25~0.29 | 0.22~0.26 |

>2.2~2.5 | 0.28~0.35 | 0.25~0.32 | 0.22~0.27 | 0.20~0.25 | 0.17~0.21 |

>2.5~2.8 | 0.22~0.27 | 0.19~0.24 | 0.17~0.21 | 0.15~0.18 | 0.13~0.16 |

>2.8~3.0 | 0.18~0.22 | 0.16~0.20 | 0.14~0.17 | 0.12~0.15 | 0.10~0.13 |

Table: The maximum relative height (h/d) for flangeless cylindrical deep-drawn parts.

Deep drawing time (n) | Relative thickness of the blank t/D×100 | |||||

2~1.5 | <1.5~1 | <1~0.6 | <0.6~0.3 | <0.3~0.15 | <0.15~0.08 | |

1 | 0.94~0.77 | 0.84~0.65 | 0.70~0.57 | 0.62~0.5 | 0.52~0.45 | 0.46~0.38 |

2 | 1.88~1.54 | 1.60~1.32 | 1.36~1.1 | 1.13~0.94 | 0.96~0.83 | 0.9~0.7 |

3 | 3.5~2.7 | 2.8~2.2 | 2.3~1.8 | 1.9~1.5 | 1.6~1.3 | 1.3~1.1 |

4 | 5.6~4.3 | 4.3~3.5 | 3.6~2.9 | 2.9~2.4 | 2.4~2.0 | 2.0~1.5 |

5 | 8.9~6.6 | 6.6~5.1 | 5.2~4.1 | 4.1~3.3 | 3.3~2.7 | 2.7~2.0 |

Note:

- 1. The larger h/d ratio is applicable for the initial forming process with larger die fillet radii, ranging from r
_{di}= 8t when t/D_{0}× 100 = 2-1.5, to r_{d}= 15t when t/D_{0}× 100 = 0.15-0.08. The smaller ratio applies to smaller die fillet radii [r_{d}= (4–8)t]. - The number of drawing stages listed in the table is suitable for deep-drawn parts made of 08 and 10 grade steel.

(2) Determination of deep drawing method for stepped pieces

1) When the ratio of the diameter of any two adjacent steps (d_{n}/d_{n}-1) is greater than the limit drawing coefficient of the corresponding cylindrical part, each step forms a step, from the large step to the small step the number of deep times is the number of steps.

2) If the ratio of the diameters of two adjacent steps (d_{n}/d_{n}-1) is less than the limit drawing coefficient of the corresponding cylindrical part, the drawing method is based on the wide flange part, which is drawn from the small step to the large step.

Drawing method of shallow stepped piece

**3.2 Drawing Process Calculation of Non-Straight Wall Rotating Body Parts**

**3.2 Drawing Process Calculation of Non-Straight Wall Rotating Body Parts**

- Drawing characteristics of non-straight wall rotating body parts

Deep drawing characteristics of non-straight wall rotating body parts:

(1) When the non-straight wall rotating body part is deepened, the flange portion below the blank holder ring and the suspended portion in the die opening are deformation regions.

(2) The drawing process of non-straight wall rotating body parts is a combination of drawing deformation and bulging deformation.

(3) Bulging deformation is mainly located in the vicinity of the bottom of the punch die

Wrinkling has become a major problem to be solved in the drawing of such parts. Especially the wrinkling of the suspended part-the inner wrinkle

Measures to neither wrinkle nor break

- Increase flange size
- Increase the friction coefficient under the blank holder
- Increase blank holder force
- Use drawbead
- Back draw

- Deep drawing of spherical parts

The drawing coefficient is constant and cannot be used as a basis for process design.

m=0.707

Drawing method for spherical parts

- When t / D> 3%, a simple bottomed die without a blank holder can be used for one-time drawing
- When t / D = 0.5% ~ 3%, deep drawing die with blank holder is used for deep drawing
- When t / D <0.5%, a concave die with deep drawing ribs or reverse deep drawing die is used

- Deep drawing of parabolic parts

Deep drawing is more difficult than spherical parts

Common drawing methods are:

(1) Shallow paraboloid (h/d <0.5 ～ 0.6). Because its height-to-diameter ratio is nearly spherical, the drawing method is the same as that of spherical parts.

(2) Deep paraboloid (h/d> 0.5 ～ 0.6). Its deepening difficulty has increased. At this time, in order to make the middle part of the blank close to the mold without wrinkling, a mold with deep drawing ribs is usually used to increase the radial tensile stress.

Deep drawing of deep paraboloids

- Deep drawing of conical parts

Deepening method depends on：h/d2，α

Deep drawing method of cone

(1) For shallow conical pieces (h / d2 <0.25 ～ 0.30, α = 50 ° ～ 80 °), it can be drawn at one time

(2) For medium conical pieces (h / d2 = 0.30 ～ 0.70, α = 15 ° ～ 45 °), the drawing method depends on the relative material thickness:

1) When t / D> 0.025, the blanking ring can be used for one-time drawing.

2) When t / D = 0.015 ～ 0.20, it can be drawn at one time, but measures such as blank holder ring, deep drawing ribs and adding process flanges are required.

3) When t / D <0.015, it is easy to wrinkle because the material is thin. It is necessary to use a blank holder mold and draw it twice.

(3) For highly tapered parts (h / d2> 0.70 ～ 0.80, α≤10 ° ～ 30 °), adopt:

1) Step transition deep drawing method

2) Stepwise deep drawing of cone surface

Deep forming method of high-cone piece

**3.3 Calculation of deep drawing process of flangeless box**

**3.3 Calculation of deep drawing process of flangeless box**

The box-shaped part is a non-rotating body part. When deep drawing is deformed, the rounded part is equivalent to the deep drawing of cylindrical part, and the straight edge part is equivalent to bending deformation.

Before deformation:

Δl_{1}=Δl_{2}=Δl_{3}

Δh_{1}=Δh_{2}=Δh_{3}

After deformation:

Δh_{1}＜Δh_{1}′＜Δh_{2}′＜Δh_{3}′

Δl_{1}＞Δl_{1}′＞Δl_{2}′＞Δl_{3}′

Drawing features of box-shaped parts:

(1) The material in the flange deformation zone is subject to the combined effect of radial tensile stress and tangential compressive stress, resulting in radial deformation and tangential compression deep deformation. The distribution of stress and strain is uneven, with the rounded corners being the largest and the straight edges being the smallest.

(2) The amount of deformation of the straight edge and the fillet in the deformation area is different.

(3) The degree of mutual influence between the straight edge portion and the rounded corner portion varies with the shape of the box.

**3.4 Deep drawing process force calculation and equipment selection**

**3.4 Deep drawing process force calculation and equipment selection**

- Blank holding force and blank holding device

(1) Blank holding force

The blank holding force Q is provided by a blank holding device provided in a mold.

The blank holding force Q generated by the blank holder should be as small as possible on the premise of ensuring that the deformation area does not wrinkle.

The required blank holder force for deep drawing parts of any shape: **Q = Aq**

In the formula:

- A- the projected area of the blank under the blank holder
- q- Pressing force per unit area,
**q = σ**_{b}**/ 150**

Blank holder force for straight wall cylindrical parts

Deep drawing of straight wall cylindrical parts for the first time:

Deep drawing of straight wall cylindrical parts in the subsequent process:

(2) Blank holder

The function of the blank holder is to prevent wrinkling in the deep deformation zone.

Depending on the source of the blank holder force, there are two types of blank holder devices:

- Elastic blank holder: used for single-acting punch, blank holder force is provided by spring, rubber, air cushion, nitrogen spring, etc.
- Rigid blank holder: used for double action punch, blank holder force is provided by outer slider.

Elastic blank holder

Application example of elastic blank holder

7–blank ring

Rigid blank holder on double action press

4–blank ring

- Calculation of drawing force

For cylindrical, elliptical, box-shaped parts, the drawing force is:

- F
_{i}– drawing force of the i-th drawing, the unit is N; - L
_{s}– perimeter of workpiece section (according to material thickness center), unit is mm; - K
_{p}– For deep drawing of cylindrical parts, K_{p}= 0.5 ~ 1.0; For deep drawing of oval parts and box-shaped parts, K_{p}= 0.5 ~ 0.8; For deep drawing of other shapes, K_{p}= 0.7 ~ 0.9. When the drawing approaches the limit, K_{p}takes a large value; otherwise, it takes a small value.

- Deep drawing equipment selection

For single-acting presses, the nominal pressure of the equipment should meet:

**F**_{E }**> F**_{i }**+ Q**

For double-acting presses, the tonnage of the equipment should meet:

**F**_{inner}** > F**_{i}

**F**_{outer}** > Q**

Pay attention:

When the drawing working stroke is large, especially when the blanking drawing is combined, the process force curve should be below the allowable pressure curve of the press slider.

In actual production, the nominal pressure F_{pressure} of the press can be determined by the following formula:

- Shallow drawing: ΣF ≤ （0.7~0.8）F
_{press} - Deep drawing: ΣF ≤ （0.5~0.6）F
_{press}

**Deep drawing process design**

**Deep drawing process design**

**4.1 Deep drawing process analysis**

**4.1 Deep drawing process analysis**

The processability of the drawn part refers to the adaptability of the drawn part to the drawing process.

The analysis of whether a deep-drawn part is suitable for deep drawing is mainly based on the structural shape, size, dimensioning, accuracy and material selection of the deep-drawn part, which is a requirement for product design from the perspective of product processing.

- Deep drawing shape

(1) The shape of the drawn part should be as simple and symmetrical as possible, and it should be drawn as soon as possible. Try to avoid sharp shape changes.

2) Shape error of the drawn part

- Drawing height

The height dimension of the drawn parts should be reduced as much as possible, and drawn as far as possible.

- Deep drawing flange width

Flange of flanged straight wall cylinder

The diameter should be controlled at:

d_{1} + 12t ≤ d_{f} ≤ d1+25t

Wide flange straight wall cylinder:

d_{f} ≤ 3d_{1}, h_{1} ≤ 2d_{1}

The flange width of the drawn part should be as consistent as possible and similar to the contour shape of the drawn part.

- Fillet radius of drawn parts

Rounded corners of bottoms and walls, flanges and walls of drawn parts

The radius should satisfy:

r_{p1} ≥ t, r_{d1} ≥ 2t, r_{c1} ≥ 3t

Otherwise, plastic surgery procedures should be added.

- Punching design for deep drawing

- Distance between punched holes on the flange of the drawn part: ≥5t
- Distance between punched holes on the side wall of the drawn part: h
_{d}≥ 2d_{h}+ t - The hole position on the drawing part should be set on the same plane as the main structural surface (flange surface), or the hole wall should be perpendicular to this plane

The hole in the drawing part is usually punched after the drawing is finished.

- Dimensioning of deep-drawn parts

- Material thickness should not be marked on the cylinder wall or flange
- For the mouth size that requires fit, the depth of the fit part should be marked
- The fillet radius at the junction of the cylinder wall and the bottom surface should be marked on the side of the smaller radius
- Radial dimensions should only be marked with external or internal dimensions according to the requirements of use

Ladder height dimensioning

- Material selection for deep drawing parts

Requires:

- Better plasticity.
- Smaller yield ratio σ
_{s}/σ_{b} - Large plastic strain ratioγ
- Small plastic strain ratio anisotropy coefficient Δγ

**4.2 Deep**** draw****ing process arrangement**

**4.2 Deep**

**draw**

**ing process arrangement**

1) If it is a shallow drawn part that can be formed in one drawing, the blanking drawing composite process is used to complete it.

2) For high-drawing parts, single-step stamping can be used when the batch size is not large; when the batch size is large and the size of the deep-drawn parts is not large, progressive drawing with strip can be used.

3) If the size of the drawn part is large, usually only single-step stamping can be used.

4) When the drawing parts have higher accuracy requirements or need to draw a small fillet radius, it is necessary to add a shaping process after the drawing is finished.

5) The trimming and punching processes of deep-drawn parts can usually be completed in combination.

6) Except that the bottom hole of the drawing part may be compounded with blanking and drawing, the holes and grooves of the flange part and side wall part of the drawing part must be punched out after the drawing process is completed.

7) If other forming processes (such as bending, flipping, etc.) are required to complete the shape of the drawn part, other stamping processes must be performed after the drawing is finished.

Features of subsequent deep drawing:

- Different blanks
- Deformation zone changes differently
- Different drawing force changes
- Rupture occurs at different times
- Deformation zones have different stability
- Different drawing factors
- The drawing method can be different

**Deep drawing die design**

**Deep drawing die design**

**5.1 ****Deep ****Drawing ****die ****type and typical structure**

**5.1**

**Deep**

**Drawing**

**die**

**type and typical structure**

- Deep drawing die for the first time

(1) Simple drawing die without blank holder

(2) Drawing die with blank holder

1) Formal drawing die

2) Inverted deep drawing die

(3) Blanking and drawing composite die

(4) Deep drawing die with rigid blank holder

- Subsequent deep drawing dies

(1) Positive drawing die

1) No blank holder

2) With blank holder

(2) Reverse deep drawing die

1) No blank holder

2) The blank holder is on the upper die

3) The blank holder is in the lower die

Simple drawing die for the first time without blank holder

First formal drawing die with blank holder

First reverse deep drawing die with blank holder

Blanking and drawing composite die

First drawing die for double action press

- Subsequent deep drawing die

(1) Positive drawing die

1) Each subsequent formal drawing die without blank holder

2) Subsequent inverted drawing die with blank holder

(2) Reverse deep drawing die

1) Reverse drawing die without blank holder

Double-action press forward and reverse drawing principle

**5.2 Deep**** drawing**** mold part design**

**5.2 Deep**

**drawing**

**mold part design**

- Structural design of male and female working parts
- Determination of fillet radius
- Determination of the die clearance
- Determination of working part size and tolerance

- Deep drawing structure of convex and concave die working parts

(1) One-time drawing of convex and concave die working structure without blank holder

Multi-drawing convex and concave die working part structure without blank holder

(2) Deep drawing convex and concave die working part structure with blank holder

- The working dimensions of drawing convex and concave die

- Fillet radius
- Deep drawing die clearance
- Working part size and tolerance

(1) Corner radius of convex and concave die

1) The influence of the fillet radius of the die:

- Deep drawing force
- Drawing die life
- Deep drawing quality

Need to meet: r_{di}≥2t

2) Fillet radius r_{p}

In the middle steps, take r_{pi} equal r_{di}, that is: r_{pi} = r_{di}

The last deep drawing:

- When the workpiece fillet radiusr≥t , take r
_{pn}=r - When the workpiece fillet radiusr<t, take r
_{pn}>t

Finally, the corner radius r of the workpiece is obtained.

(2) Gap between convex and concave die c

Gap size affects:

- Deep drawing force
- Drawing die life
- Deep drawing quality

**C = t**_{max}** + K**_{c}**t**

(3) Lateral dimension of the working part of the convex and concave die

For the first and intermediate deep drawing in multiple deep drawing, it is preferable to:

For one deep drawing or the last deep drawing in multi deep drawing,

Deepak AVery very informative

MachineMfgyes, we will continue to publish good articles like this.

Sijin SureshHi I need bar chair base metal sheet die design. Please check item image at i.is.cc/1b39aPEE.jpg

ShaneOur sales team will contact you soon.

Kris KidambiHi Shane

Need a quote for stage wise die design for a deep draw part. Please contact me at [email protected]. I can send you part drawings and other details.

Thanks and regards

Kris

ShaneOur sales team will contact you asap.

ZahraHi Shane,

Very useful article, I just couldn’t find the other tables. Just Table-7 is shown.

Irfan HabibThe mentioned tables 5.2, 5.3, 5.4, 5.4 are not present in the document I see only Table 5.7

ShaneWill update it.

ShaneI want to learn more. What books should I look for?

Excellent name by the way

DrDaruShane, which book is the image of the Stress-strain state from? Thanks, nice article.

Juan ZShane, any recommended literature to go deeper into this topic?

ShaneSearch for keywords directly in our blog, and you will find many other excellent articles for you to learn.

Karl WinklerNice technical information. I teach a class on rubber bushing design. In the class I discuss outer metal forming. This can be a stamped deep drawn tube as you show above except the bottom is cut out so it forms a tube with a flange at the top. Material is steel and aluminum. I believe I am in the correct section for this type of forming? I would like to learn a bit more about this process and the types of presses that can be used in the manufacture of bushing outer metals. I would be happy to send you a print to look at if you can help me understand this better.

Thanks,

RobertHi! Could you upload the missing tables?

Thank you

ShaneLet me know the details.

RobertTables:

5-1 blank holder ring,

5-2 trim margin,

5-3, 5-4 limit drawing coefficient,

5-5 determining number of deep drawing.

If it’s problematic to upload it, I’ll be thankful if you send it to my email address.

[email protected]

ShaneThe original form could not be found, so the data in the most relevant form to the content of the article has been updated.

RobertThank you so much. Everything what had been missed appeared again.

It’s the best article about deep drawing I have ever found.

ShaneThank you!