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# basic formulas

By Virginia Martinez,2014-05-31 06:08
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basic formulas

Bending Force Calculation

V-Type and U-Type Bending without pressure pads below:

V-Type Bending with V-shaped pressure pad below (coining):

U-Type Bending with pressure pad below:

L-Type Bending or 90 degree bending: Tutorial on Bending Force Calculation

Calculate the bending force required for the above forming:

First, calculate C. From the L/C table in the reference notes above, as L=8t, then C=1.33. 111Accordingly, applying the numbers into the equation: 22P=C* (B*t*σ)/L = 1.33*(100*1*30)/8= 498.75 ? 500 kg 11B

Therefore, the required bending force is about 500 kgf.

Key Factors in Draw Forming

? Raw Material Selections for Draw Applications:

Choice and condition of the actual raw material to draw is important. In certain applications,

such as deep draw, specially formulated material may be required. Besides the grain size and

shape, the tolerance and composition of the raw material may affect the final part.

? Determining the Correct Amount of Material:

Blank development or the amount of raw material it will take to make the draw and carry the

part. Too much material means excessive scrap and can prevent the tool from drawing

properly.

? Metal Reduction:

Stock thickness is critical to the tool's ability to draw the metal. If the typical part require 3

draw operations to complete, but if the material has a low thickness to blank diameter ratio,

another draw may be required.

? Material Control:

Raw material control is the method by which the part will be carried or transferred through the

die. The determining factors are part geometry, material thickness, depth of draw, material

consumption, burr direction, annealing, production rate, and ejection.

? Tool Steel Selection:

This can relate back to the actual raw material of the part.

? Lubricants Selection:

Lubricants must be compatible with the metal being formed, the tool itself as well as the

environment.

Blank Size Calculation for Draw Forming or Draw

Stamping

Most textbooks teach that there are 2 ways of determining the blank size for a draw stamped part. They

are namely, algebraic method through centerline of stock using either the surface area or weight of the

part, and the graphical method of calculating blank size. The example below shows how to find the

blank size for a deep drawn can using the surface area algebraic method:

Most draw forming design and simulation softwares come with modules to calculate the blank based on

the stamped part data automatically. If further examples of different drawn components and the equations for calculating the blank sizes are useful as tutorial questions and answers purpose, email us.

These equations have been extracted from various sources.

Metal Reduction Rates

Draw forming a metal part is basically a series of reduction steps from the blank to the first draw, to the

second draw, and so on. The reduction rate is calculated as follows:

R=100(1-d/d) iii-1

R: i-th reduction in percentage id: Diameter of the part after the i-th draw reduction id: Diameter of the blank before the first draw reduction 0

As the actual draw forming of the same part would differ based on the different quality of the raw

materials, tooling coatings and lubricants, most die design experts agree that the metal reduction rates

available today merely serve as a guide based on past experience. During the assembly and

troubleshooting of the draw die, the toolmaker will still need to make finer adjustments.

Blanks with equal surface dimensions but different metal thickness have different outcomes when

subject to the same draw reduction rates. Thinner metal is more difficult to draw consistently when

compared to thicker metal. It is recommended that metal thickness to blank diameter ratio (t/d) should

be above 0.25.

Recommended maximum rates of reduction for round deep drawn parts are as follows: ststndndrdMaterial Thickness Blank-1 Draw (%) 1-2 Draw (%) 2-3 Draw (%)

0.010 27 18 17

0.015 32 20 19

0.020 35 21 20

0.025 39 22 21

0.030 42 23 22

0.035 44 26 24

0.040 46 28 25

0.045 47 28 25

0.050 47 29 26

0.055 48 29 26

0.060-0.125 48 30 27

The general maximum cupping reduction rates for different metals are as follows:

0.125-0.250 47 28 26 Aluminum alloys => 45%

Copper => 45%

Brass => 50%

Bronze, Tin => 50%

Low Carbon Steel => 45%

Austenitic Stainless Steel => 50%

Zinc => 40%

Component Design and Function

# Design of Blank Holder and Blank Holding Force

The design of the blank holder is important as it affects the rate of flow of the sheet metal during draw forming. The examples below shows the effect of insufficient blank holder force during the draw stamping of a can, causing either wrinkling of the flange or the side walls.

The punch and die clearances are arranged so that the metal is lightly drawn between them. This removes any creases which tend to form during the drawing operation. However, if we were to draw cup-shaped components with larger depth to diameter ratio from thinner metal, then puckering or wrinkling of the flange as shown above is likely to occur round the edge of the blank rim outside the die. This puckering is caused by the local thickening of material round the edge setting off hoop stress forces in the material.

This puckering may be sufficient to prevent the metal flowing smoothly through the die and the punch may tear the bottom out of the component. Even if the tensile strength of the metal allowed it to be forced through the die, it would be impossible to 'iron out' all the pucker marks.

The solution to this problem is to add a blank-holder to the deep draw tools. The blank-holder basically presses the blank rim material outside the die, and provides a tensile force opposing the compressive hoop stress within the blank rim. This allows the metal under the blank-holder to thicken uniformly

around its annular rim and progressively between the die mouth and the outside of the blank.

When using double action presses that have mechanically operated blank holders, the setting of the blank-holder force is usually determined empirically. This is done by drawing the shell progressively deeper using blanks of the same diameter while progressively lowering the blank holder until the surface of the drawn shell is smooth and free from wrinkles. The pressure of the blank holder on the blank increase during the drawing operation as the edge thickness of the blank increases under the effect of the hoop compression forces set up.

In cases when it is not possible to exert sufficient force on the blank-holder to prevent wrinkling, or there may be problems with lubrication of the blank itself, the tool may be designed with an entry bead to the die.

The minimum blank holding force for the various stamping materials are listed below for your reference: 2 Mild Steel t<0.5mm ==> 0.25~0.30 kg/mm2Mild Steel t>0.5mm ==> 0.20~0.25 kg/mm 2Aluminum ==> 0.03~0.07 kg/mm 2Copper ==> 0.08~0.14 kg/mm 2Brass ==> 0.11~0.21 kg/mm 2Stainless Steel (18-8) => 0.40~0.45 kg/mm 2Bronze ==> 0.20~0.25 kg/mm 2Aluminum Alloy ==> 0.14~0.70 kg/mm

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