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Multiple draw

5.4
Draw sequence
Fig. 1
draw sequence
① - ③ drawing stage d0 blank diameter d1-3 inner diameter
h1-3 drawn part heights s0 initial sheet thickness

The blank diameter d0 is reduced to the final diameter dn in several deep drawings. It is important to ensure in each drawing stage that the permissible maximum draw ratio βn max is not exceeded.

The draw ratio βn is defined as the ratio of the initial circumference to the circumference of the respective drawing stage. Usually the diameters d n always refer to the inside diameter of the drawn part. The reciprocal of βn is called the drawing modulus mn.

The drawing ratios of common materials are listed in the drawing ratios table.

Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} \beta_{\color{myred}n}~~=\frac{d_{\color{myred}n}}{d_{\color{myred}n+1}}
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} \beta_{\color{myred}ges}=\prod_{\color{myred}0}^{\color{myred}n}\beta_{\color{myred}n}
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} h_{\color{myred}n}=\frac{d_{\color{myred}0}^{\color{myred}2}-d_{\color{myred}n}^{\color{myred}2}}{4\cdot d_{\color{myred}n}}
Draw ratioβ0=2 
β1=1.32 
β2=1.25 
β3=2 
βges=6.6 
Clear heighth1=123.75mm 
h2=186.55mm 
h3=247.25mm 
h4=532mm 
Blank diameterd0 = 330mm
Diameter punchd1 = 165mm
d2 = 125mm
d3 = 100mm
d4 = 50mm
Calc 1
Multiple draw ratios Train sequence
Eqn. 4
\require{color}\definecolor{myred}{RGB}{255,0,0} n=\frac{\ln\left(\beta_{\color{myred}ges}\right)-ln\left(\beta_{\color{myred}1}\right)}{\ln\left(\beta_{\color{myred}n}\right)}
Numbern1.47 
Draw ratioβges = 2.5
β1 = 1.8
βn = 1.25
Calc 2
number of draw stages

A rough calculation of the required number of draw stages is given by the total draw ratio, the draw ratio of the first draw and the draw ratio of the nth draw.2738

Werkstoff
Zug 1
β0 100
Zug 2
β1 100
AlMg 3 weich
2
1.5
AlMg 3 halbhart
2
1.4
1.4301
2
1.25
DC 04
2
1.3

The limiting drawing ratio β100 refers to a punch diameter of 100 mm. If there are deviations from this diameter, this ratio must be corrected in order to correctly calculate the maximum draw ratio.8

8
Oehler; KaiserSchnitt-, Stanz- und ZiehwerkzeugeSpringer VerlagBerlin19937. Auflage
27
Herold, G.; Kluge, M. EFB-Forschungsbericht Nr. 61: Simulation des Formstempeltiefziehens im WeiterschlagEuropäische Forschungsgesellschaft für Blechverarbeitung e. V. Hannover1994
38
RomanowskiHandbuch der StanzereitechnikTechnik Verlag BerlinBerlin19684. Auflage
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