Free bending

16.4

In contrast to die or stamping bending, in which the workpiece is pressed into the tool with high pressure until it rests, the tools used in free bending only function as a means of transferring forces or bending moments to the workpiece.

The dimensional accuracy of the free bending is rather unsatisfactory compared to the precision of the stamping with a V-die. Fluctuations in spring back and other disturbing influences such as deviations in wall thickness have a relatively strong effect on the bend angle and bend radius.*

Free bending
Fig. 1
Free bending*
lB bending length εa elongation outer fiber rM die radius rSt punch radius s0 sheet sheet thickness ub bending gap
Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} F_{\color{myred}St\;max}=\frac{k_{\color{myred}fm}\cdot s_{\color{myred}0}^{\color{myred}2}\cdot l_{\color{myred}B}}{4\cdot(r_{\color{myred}M}+r_{\color{myred}St}+s_{\color{myred}0})}\cdot\xi
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} \xi=\frac{\cos\left(\frac{\mathrm\pi}2-arc\cos\left(\frac{r_{\color{myred}M}+r_{\color{myred}St}+s_{\color{myred}0}}{r_{\color{myred}M}+r_{\color{myred}St}+u_{\color{myred}b}}\right)\right)+\mu\cdot\sin\left(\frac{\mathrm\pi}2-arc\cos\left(\frac{r_{\color{myred}M}+r_{\color{myred}St}+s_{\color{myred}0}}{r_{\color{myred}M}+r_{\color{myred}St}+u_{\color{myred}b}}\right)\right)}{\sqrt{\left(\frac{r_{\color{myred}M}+r_{\color{myred}St}+u_{\color{myred}b}}{r_{\color{myred}M}+r_{\color{myred}St}+s_{\color{myred}0}}\right)^{\color{myred}2}-1}+\mu\cdot\frac{s_{\color{myred}0}}{2\cdot\left(r_{\color{myred}M}+r_{\color{myred}St}+s_{\color{myred}0}\right)}}
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} \varphi_{\color{myred}m}=\ln(1+\frac{\varepsilon_{\color{myred}a}}2)=\ln\left(1+\frac1{4\cdot c+2}\right)
Eqn. 4
\require{color}\definecolor{myred}{RGB}{255,0,0} c=\frac{r_{\color{myred}M}}{s_{\color{myred}0}}
Eqn. 5
\require{color}\definecolor{myred}{RGB}{255,0,0} u_{\color{myred}b}>s_{\color{myred}0}\;,\;u_{\color{myred}b}\leq s_{\color{myred}0}+\sqrt{0,2\cdot s_{\color{myred}0}}
Max. punch forceFSt max=0.47kN 
Coefficientξ=1.57 
Medium natural strainφm=0.118 
Bending factorc=1.5 
Die radiusrM = 1mm
Punch radiusrSt = 3mm
Sheet thicknesss0 = 2mm
Bending gapub = 2.1mm
Bending lengthlB = 3mm
Average work hardeningkfm = 600MPa
Coefficient of frictionμ = 0.15
Calc 1
bending force
The tensile strength Rm can be used as an approximation for kfm.
By using a flow curve and the mean degree of deformation φm
more precise values for kfm can be determined.
*
Siegert, K.BlechumformungSpringer ViewegBerlin2015
*
Kluge, SiegfriedProzesse der BlechumformungCarl Hanser VerlagMünchen2020
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