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5
Round Drawn Parts
5.2
Predraw
5.2.2
Drawing punch Partial forces and total force
203 Articles  2254 Elements

Drawing punch Partial forces and total force

5.2.2
Designations deep drawing
Fig. 1
Designations deep drawing
dA Flange diameter d0 blank diameter d1 punch diameter h drawn part height pn blank holder blankholder pressure s0 wall thickness rM drawing ring radius μ1 coefficient of friction of friction sheet metal / blankholder μ2 coefficient of friction of friction sheet metal / drawing die μ3 coefficient of friction of friction sheet metal / drawing ring radius

When deep-drawing rotationally symmetrical sheet metal parts, five partial forces act on the drawing predraw :

  • Fidis the ideal forming force required for lossless forming in the forming zone.
  • Fb the bending force required to bend the sheet around die radius rM.
  • FRB/N is the frictional force acting between the sheet metal and the blankholder.
  • FRB/Z is the frictional force acting between the sheet metal and the drawing die.
  • FRB/ZR is the frictional force acting between the sheet metal and the rounding of the die rM.
Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}ges}=F_{\color{myred}id}+F_{\color{myred}b}+F_{\color{myred}R\;B/N}+F_{\color{myred}R\;B/Z}+F_{\color{myred}R\;B/ZR}
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} \sigma_{\color{myred}Z}=\frac{F_{\color{myred}ges}}{d_{\color{myred}1}\cdot\pi\cdot s_{\color{myred}0}}
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}id}=d_{\color{myred}1}\cdot\pi\cdot s_{\color{myred}0}\cdot k_{\color{myred}fm}\cdot\ln\left(\frac{d_{\color{myred}A}}{d_{\color{myred}1}}\right)
Eqn. 4
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}b}=\pi\cdot d_{\color{myred}1}\cdot s_{\color{myred}0}\cdot\frac{k_{\color{myred}fi}\cdot s_{\color{myred}0}}{4\cdot r_{\color{myred}M}}
Eqn. 5
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}R\;B/N}=\mu_{\color{myred}1}\cdot\frac\pi4\cdot\left(d_{\color{myred}A}^{\color{myred}2}-d_{\color{myred}1}^{\color{myred}2}\right)\cdot p_{\color{myred}N}
Eqn. 6
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}R\;B/Z}=\mu_{\color{myred}2}\cdot\frac\pi4\cdot\left(d_{\color{myred}A}^{\color{myred}2}-d_{\color{myred}1}^{\color{myred}2}\right)\cdot p_{\color{myred}N}
Eqn. 7
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}R\;B/ZR}=\left(e^{\color{myred}\mu_{\color{myred}3}\cdot\frac\pi2}-1\right)\cdot\left(F_{\color{myred}id}+F_{\color{myred}R\;B/N}+F_{\color{myred}R\;B/Z}\right)
Total force punchFges=38.86kN 
Tensile stressσZ=123.68MPa 
Ideal forming forceFid=24.73kN 
Bending forceFb=6.87kN 
Friction force blank to blankholderFR B/N=0.27kN 
Friction force blank to drawringFR B/Z=0.27kN 
Friction force die radiusFR B/ZR=6.71kN 
Diameter flangedA = 130mm
Diameter punchd1 = 100mm
Sheet thicknesss0 = 1mm
Average work hardeningkfm = 300MPa
Superior yield stresskfi = 350MPa
Die radiusrM = 4mm
Blankholder Pressurpn = 1MPa
Coefficient of frictionμ1 = 0.05
μ2 = 0.05
μ3 = 0.15
130
Calc 1
Partial forces according to Siebel and Panknin935

The coefficients of friction can vary depending on the surface properties of the tool and the sheet metal.

The average work hardening kfm and the superior yield stress kfi are calculated using the deformation limits φ1 and φ2 and using the flow curves. The natural strain φ2 should be used for kfi.

An estimation of the maximum total force on the punch can be made using the following simplification:

Eqn. 8
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}max}\approx F_{\color{myred}ges}\left(d_{\color{myred}A}\approx0,77\cdot D_{\color{myred}0};k_{\color{myred}fm}\approx1,3\cdot R_{\color{myred}m}\right)
9
Siegert, K. / Blechumformung / Springer Vieweg / Berlin / 2015 / …
35
Strackerjahn, W. / Die Voraussage des Versagensfalls beim Tiefziehen rechteckiger Teile / Dissertation / Hannover / 1982 / …
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