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The technology of deep drawing parts

The technological property of drawing parts refers to the adaptability of drawing parts to the drawing process, which is a technological requirement for the design of drawing products from the perspective of deep drawing processing. The drawing parts with good process property can simplify the structure of the drawing die, reduce the times of drawing and improve the production efficiency. The technology of drawing parts mainly considers the structure shape, size, precision and material selection of drawing parts.

Tolerance level of deep drawing parts

The dimensional accuracy of general drawing parts should not be too high, which should be below IT13 level and not higher than IT11 level. If the tolerance level is high, the shaping process can be added to meet the size requirements. Due to the uneven deformation of the drawing parts, the thickness of the upper and lower walls can vary up to (1.2~0.75)t, and t is the thickness of the sheet metal. For constant thin drawing, the requirement of wall thickness tolerance should not exceed the rule of wall thickness variation in drawing process.

Dimensions and shapes of deep drawing parts

• When designing the drawing parts, it is not allowed to mark the internal and external dimensions at the same time. The dimensions on the product drawing should indicate that the external dimension or internal dimension must be ensured. For deep drawing parts with steps, the dimension in the height direction should be based on the bottom. If the upper part is based on the bottom, the height dimension is not easy to guarantee. The fillet radius of the joint between the wall and the bottom can only be marked in the inner shape.

• The shape of deep drawing parts should be as simple and symmetrical as possible and should be formed at one time. The change of axisymmetric drawing parts in the circumferential direction is uniform, the die processing is easy, and its processability is the best. Try to avoid using very complex and asymmetric drawing parts, and try to avoid sharp contour changes. For semi-open or asymmetric hollow parts, it should be possible to combine them for deep drawing, and then cut them into two or more parts, as shown in Figure 1-1, so as to improve the stress condition during deep drawing.

• The size ratio of each part of the deep drawing piece should be appropriate. The design of wide flange and large depth drawing parts (i.e., flange diameter d_f＞3 d, h≥2 d) should be avoided as far as possible because these parts need more times of drawing and intermediate annealing. The outline of the flanges of the drawing parts should be similar to that of the drawing parts. The width of the flange should be consistent. Inconsistency not only makes it difficult to draw and increase the number of working procedures, but also needs to expand the margin of trimming and increase metal consumption.

• There is a concave drawing piece on the flange surface, as shown in Fig. 1-2. The concave axis below is consistent with the drawing direction, so it can be pulled out. If the axis of the concave is perpendicular to the drawing direction, it can only be pressed out during the final correction.

• When there are holes in the bottom or flange of the drawing piece, the distance between the hole edge and the side wall should be a≥r_D + 0.5t (or a≥r_P + 0.5t), as shown in Fig. 1-3.

• Under the premise of ensuring the assembly, the side wall of the drawing part should be allowed to have a certain slope. When multiple drawing is required, the inner and outer surfaces of the drawing parts shall be allowed to have marks generated in the drawing process on the premise of ensuring the necessary surface quality. Unless the parts have special requirements, only by shaping or shaping methods to remove marks.

Height of the deep drawing piece

When designing the drawing part, the height should be minimized so that it may be completed by one or two drawing processes. For various shapes of drawing parts, using a process can be drawn conditions as follows.

• See Table 1-1 for the height of a single drawing of the cylinder.

• The condition for a drawing of box-shaped parts is that when the radius of the rounded corner of the box-shaped part r=(0.05~0.20)B (B is the width of the short side of the box-shaped part), the height of the drawing part h＜(0.3~0.8) B.

• For flange parts, the condition of a pull is that the ratio of the diameter of the cylindrical part of the parts to the blank d/D≥0.4.

The fillet radius of the deep drawing piece

The radius of the fillet between the flange of the drawing piece and the wall of the cylinder should be r_D≥2t. In order to facilitate the smooth drawing, r_D≥(4~8)t is usually taken. When r_D≤2t, the shaping procedure should be added.

The radius of the fillet between the bottom of the drawing part and the wall of the cylinder should be r_P≥2t. In order to facilitate the smooth drawing, r_P≥(3~5)t is usually taken. When the parts require r_P＜t, it is necessary to increase the shaping process.

Material selection of deep drawing parts

Materials used for deep drawing generally require good plasticity, low flexural strength ratio, large plate thickness directivity coefficient and small plate plane directivity.

Deep drawing process calculation of cylindrical parts

The calculation of drawing process includes the determination of blank size, the determination of drawing times and the calculation of semi-finished product size.

Calculation of blank size of simple rotary deep drawing parts

To determine the trimming margin

Due to the anisotropy of the sheet material, the center of the wool and the convex and concave die can not completely coincide in the actual production, so the mouth of the drawing part can not be very neat. Usually, there is a trimming process to cut the irregular part. For this reason, trimming allowance should be left in advance when calculating the blank size. The trimming allowance for cylindrical parts and flange parts is shown in Table 1-2 and Table 1-3 respectively.

Calculate the surface area of parts

In order to facilitate the calculation, the parts are solved into several simple geometries, and their surface areas are calculated respectively and then added together. The parts shown in Fig. 1-4 can be regarded as composed of straight wall part 1 of cylinder, ball table part 2 formed by arc rotation and circular plate 3 at the bottom.

The total area of the workpiece is the sum of the surface area A1 of the straight wall of the cylinder, the surface area A2 of the ball table and the surface area A3 of the bottom circular plate.

A₁ = πd ( H-r )                             ( 1-1 )

A₂ = π/4 [ 2πr ( d-2r ) + 8r² ]                      ( 1-2 )

A₃ = π/4 ( d-2r)²                            ( 1-3 )

π/4 D² = A₁ + A₂ + A₃ = ∑A_i                       ( 1-4 )

W formule
d—the middle diameter of the cylinder part of the drawing piece, mm;
H—the height of the drawing piece,mm;
r—the radius of the fillet at the fillet of the workpiece center line, mm;
D—blank diameter,mm.

To find the blank size

To find the diameter of the blank D is

For Equation (1-5), if the thickness of the blank t＜1 mm, then the outer diameter and the outer height or the internal size are used to calculate. If the thickness of the blank t≥1 mm, each size should be substituted into the middle line size of the part thickness for calculation. For the commonly used rotary deep drawing parts, the calculation formula of blank diameter can be obtained by referring to relevant manuals.

Calculation of bad wool size of complex rotary deep drawing parts

The blank size of the drawing workpiece with complex shape can be calculated by using the Kurikin rule, that is, the area of the rotating body obtained when the bus of any shape rotates around the axis is equal to the product of the length of the bus and the circumference of the center of gravity rotated around the axis, as shown in Fig. 1-5.

That is, the surface area of the rotating body is

A=2πR_xL                              ( 1-6 )

Since the area before and after drawing is equal, the blank diameter D is

πD²/4 = 2πR_xL                           ( 1-7 )

W formule
A—area of the rotating body, mm²;
r_x—the distance between the centroid of the bus of the rotating body and the axis of rotation (called the radius of rotation), mm;
D—billet diameter, mm;
L—the length of the bus of the rotating body, mm.

According to Equation (1-6), the diameter of billet can be calculated as long as the length of the bus bar of the rotating body and the rotation radius of the centroid are known. Find the length of the bus and centroid position of the method has the analytical method, drawing analytic method, drawing method 3, can refer to the relevant information to understand.

Determine the number of deep drawing

Concept and significance of deep drawing coefficient

The degree of deformation in głębokie rysowanie can be expressed by the ratio of the height and diameter of the drawing piece. The smaller the ratio, the smaller the degree of deformation can be formed in a single drawing. Large ratios require two or more deep drawing to form. But when designing the drawing process and determining the necessary number of drawing processes, the drawing coefficient is usually used as the basis of calculation.

The drawing coefficient refers to the ratio of the diameter of the cylindrical part after drawing to the diameter of the blank (or semi-finished product) before drawing, as shown in Fig. 1-6, namely:

The first drawing coefficient              m₁=d₁/D

The second drawing coefficient           m₂=d₂/D

……

Nth drawing coefficient                 m_n=d_n/D

W formule
D—blank diameter,
D₁、d₂、……、d_n—the median diameter of the cylinder after each drawing.

The ratio between the middle diameter d_n of the drawing piece and the blank diameter D is called the total drawing coefficient, that is, the drawing coefficient required by the drawing piece, which is expressed by m.

m = d_n/D = d₁ /D*d₂/d₁*d₃/d₂*……*d_n-1/d_n-2*d_n/d_n-1= m₁m₂m₃……m_n-1m_n                  (1-9)

From the above, it can be seen that the total drawing coefficient m represents the change rate of blank diameter before and after drawing, and its value is always less than 1. It reflects the size of the tangential compression deformation of the outer edge of the billet during the drawing. The smaller the drawing coefficient, the larger the diameter difference before and after drawing, the larger the “extra triangle” area to be transferred, and the greater the drawing deformation.

On the contrary, the degree of deformation is smaller. Therefore, it can be used as an index to measure the degree of deformation in deep drawing. But if in deep drawing process, the value of m is too small, can make the deep drawing parts or severe variable thin ultra poor, wrinkling and fracture, therefore the boundaries of the decrease of the m has an objective, the boundaries are compared.in force area of the largest tensile stress equal to the effective tensile strength of the dangerous section of deep drawing coefficient, is called the limit drawing coefficient.

The limit drawing coefficient value is generally obtained by experimental method under certain drawing conditions, as shown in Table 1-4 and Table 1-5.

In order to prevent the defects of wrinkling and cracking in the process of drawing, it is necessary to reduce the deformation degree of drawing and increase the drawing coefficient, so as to reduce the possibility of wrinkling and cracking. The drawing coefficient expresses the difficulty degree of the drawing process, and the number of drawing can be determined if the limit drawing coefficient allowed for each drawing is known.

The determination of the number of deep drawing

The times of deep drawing can only be estimated roughly and finally determined by process calculation. There are several methods to preliminarily determine the number of deep drawing for flangeless cylinder parts.

• Recursion method

If the relative height t/D of the blank of the cylindrical part is known, the drawing times can be directly traced out from Table 1-4 or Table 1-5 the limit drawing coefficients m₁、m₂、m₃、… 、m_n, and then calculate the diameter d₁ of the first drawing, and calculate from the diameter d₁ of the first drawing to the diameter d_n of the nth drawing.

D₁=m₁D; d₂=m₂D₁; …; d_n=m_nD_n-1                          (1-10)

Until the obtained d_n is not greater than the required diameter of the drawing piece, then n is the number of drawing. In this way, not only the number of drawing can be found, but also the diameter of the semi-finished product obtained by the intermediate process can be known.

• Calculation method

If a blank with a diameter of D is finally drawn into a drawing piece with a diameter of dn, the number of drawing n can also be approximated by the following empirical formula.

lgd_nC= (n-1) Igm_n + lg (m₁D)
n=1 + [ lgd_n – lg (m₁D) ]/ Igm_n (1-11)

In the formula, mn—the average value of each drawing coefficient after the second time.

The n calculated by formula (1-11) is usually not an integer. In order to make the drawing process easier and avoid the occurrence of pulling and cracking, the smaller integer value should not be rounded, but the larger integer value should be chosen, so that the actual selected drawing d.coefficients are slightly larger than the preliminary estimated value.

• The look-up table method

The drawing times of flangeless cylindrical parts can also be directly found out by referring to the known relative height h/d of the drawing parts and the relative height t/D of the blank in Table 1-6.

Calculate the size of process parts

The dimensions of the working parts include the diameter of the semi-finished product d_n, the radius of the rounded corner at the bottom of the cylinder r_n and the height of the cylinder wall h_n. After the number of drawing is determined, the diameter and height of working parts should be determined after adjusting the drawing coefficient in order to produce a greater degree of drawing deformation under allowable conditions.

Determine the diameter d_n of process parts

After the number of drawing is determined, the requirement of safe drawing without cracking has been met. According to the calculation diameter d_n should be equal to the diameter d of the drawing piece, on the premise of m₁-m₁’≈m₂-m₂’≈…≈m_n-m_n’, the drawing coefficient of each time should be adjusted to make the drawing coefficient m₁、m₂、…、m_n is greater than the limit drawing coefficient m₁’、m₂’、…、m_n’.

Determine the height of working parts

According to the principle that the surface area of working parts is equal to that of billet after deep drawing, the following formula for calculating the height of working parts can be obtained. Before calculating the height of the working procedure parts after each drawing, the radius of the fillet at the bottom of each working procedure part should be determined. The height of each working procedure part can be calculated by the formula of the blank diameter.

h_n = 0.25 (D²/d_n – d_n) + 0.43 r_n/d_n (d_n + 0.32r_n)                   (1-12)

W formule
h_n—the height of the workpiece after the nth deep drawing, mm;
D – blank diameter, mm;
D_n—Diameter of workpiece after the nth deep drawing, mm;
r_n—the fillet radius at the bottom of the semi-finished product during the nth drawing, mm.

calculation of drawing force and blank holder force

Calculation of drawing force

The drawing force calculated from theory is not convenient in practical application, and because the influencing factors are more complex, the calculated result is often different from the actual drawing force, so the empirical formula is often used to calculate the drawing force in production. The drawing force of cylindrical workpiece can be calculated by the following empirical formula.

When using blank holder for deep drawing:

The first deep drawing                   F= πd₁tσ_bk₁                             (1-13)

After the second time             F_n= πd_ntσ_bk_n (n=2、3、…、i)                     (1-14)

Without blank holder for deep drawing:

The first deep drawing                   F= 1.25π (D – d₁) tσ_b                        (1-15)

After the second time             F_n= 1.3π (d_i-1 – d_i) tσ_b (n=2、3、…、i)               (1-16)  

W formule
F—drawing force;
σ_b—the tensile strength of the material, MPa;
t—material thickness, mm;
D—blank diameter, mm;
D₁…d_n—the middle diameter of each drawing process, mm;
k₁, k₂—correction coefficient, see Table 1-7.

Calculation of blank holder force

Blank holding conditions

The main method to solve the wrinkle problem in deep drawing is to use anti-wrinkle blank holder, and the blank holder force should be appropriate. If the degree of deformation of the drawing is relatively small and the relative thickness of the blank is relatively large, the blank holder is not required because it will not wrinkle. The use of blank holder for deep drawing can be determined by the conditions in table 1-8.

When it is determined that a blank holder is required, the size of the blank holder force must be appropriate. If the blank holder force is too large, it will increase the pull force of the blank into the die, and it is easy to crack the workpiece. If it is too small, it can not prevent the wrinkling of the convex edge and can not play the role of blank holder, so the size of the blank holder force should be as small as possible under the condition of no wrinkling.

Calculate the blank holder force

In mold design, it is usually to make the blank holder force F_ciśnienie slightly greater than the minimum value needed for wrinkle-proof effect, that is, under the premise of ensuring that the blank flange deformation zone is wrinkle-free, as far as possible to choose a small blank holder force, and according to the following empirical formula for calculation.

Total blank holder force: F_ciśnienie =Ap (1-17)
The first drawing of cylindrical parts: F_ciśnienie = π/4 [D² – (d₁ + 2r_die1)² ]p (1-18)
The subsequent deep drawing of cylindrical parts:
F_ciśnienie = π/4 [d_n-1² – (d_n + 2r_{die n-1})² ]p (1-19)

W formule
A—the projection area of billet under the press ring, mm²;
P—unit blank holder force, MPa, as shown in Table 1-9;
D—blank diameter, mm;
D₁、d₂、… 、d_n—the diameter of the workpiece for the first and subsequent times, mm;
r_die1、r_die2、… 、r_{die n}—Fillet radius of each deep drawing die, mm.

In production, the blank holder force F_{blank holder} in one drawing can also be selected by 1/4 of the drawing force.

F_{blank holder}=0. 25F₁ (1-20)

Theoretically, the reasonable blank holder force should change with the wrinkling trend. The BHF increases when the wrinkling is severe and decreases when the wrinkling is not severe, but it is very difficult to achieve this change.

Selection of nominal pressure of press

For single acting presses, the nominal pressure should be greater than the total process pressure. The total process pressure is the sum of the drawing force F_drawing and the blank holder force F_{blank holder}.

F_{acting press}＞F_drawing+F_{blank holder} (1-21)

For double acting press, the relationship between the nominal pressure of inner and outer sliders and the corresponding drawing force Fn and the blank holder force F should be considered respectively.

F₁＞F_drawing F₂＞F_{blank holder} (1-22)

W formule
F_{acting press}—Nominal pressure of the press;
F₁—Nominal pressure of inner slider;
F₂—nominal pressure of outer slider;
F_drawing—drawing force;
F_{blank holder}—blank holder force.

When selecting the nominal pressure of the press, attention must be paid to the process force curve under the allowable pressure curve of the press slider when the drawing stroke is large, especially when the blanking and drawing composite die is used. The specification of the press cannot be determined simply according to that the sum of the blanking force and the drawing force is less than the nominal pressure of the press. Otherwise the press may be overloaded and damaged due to the premature occurrence of the maximum impact pressure, as shown in Fig. 1-7.

We should consider the work done by the press in the compound stamping forming of blanking and deep drawing, and consider whether the press motor can be loaded.

Edge mounting device

At present, there are two main types of pressure mounting devices commonly used in production.

Elastic edge pressing device

This kind of device is often used in ordinary punch, usually there are three kinds: rubber edge pressing device as shown in Fig. 1-8 (a), spring edge pressing device as shown in Fig. 1-8 (b), air cushion edge pressing device as shown in Fig. 1-8 (c). The variation curve of the pressure force of these three flanging devices is shown in Fig. 1-9. In addition, nitrogen spring technology is also gradually used in the mold.

With the increase of tensile depth, the flange of the edge is required part is decreasing, so the pressure on the edge is gradually reduced, from Fig. 1-9 can be seen the rubber and spring edge pressing device. The actual pressure force is exactly the opposite of the pressure force needed, and increases with the increase of tensile depth, especially with the rubber pressure ring. This can increase the drawing force, resulting in parts breaking, so rubber and spring structures are usually used only for shallow drawing.

However, these two kinds of edge pressure device structure is simple, it is convenient to use in small and medium-sized press, as long as the spring specification and rubber brand and size are correctly selected, can reduce its adverse impact. The spring should be selected with a large total compression amount, and the pressure increases slowly with the compression amount. Rubber should be selected with soft rubber, and the relative compression amount should be guaranteed to be not large.

The pressure force of rubber is increasing rapidly with the compression amount, so the total thickness of rubber should be larger, it is suggested that the total thickness of rubber should not be less than 5 times the drawing stroke. The edge pressure effect of air cushion type edge pressure device is good, and the pressure force is basically not changed with the work stroke, but its structure is complex, manufacturing, use and maintenance department is relatively difficult.

Rigid edge pressing device

As shown in Fig. 1-10, the rigid edge pressing device is used for double acting press, convex die is installed on the inner slider of the press, and the edge pressing device is installed on the outer slider. In the process of drawing, the outer slider remains motionless, so its rigid edge pressure force does not change in the bearing process, the drawing effect is good, and the mold structure is simple.