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Effects on the deep drawing diagram in micro forming

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Abstract

The limits of the processing window for deep drawing, collected in a deep drawing diagram, are affected by material behavior, process parameters and size effects. A size effect, more specific a density effect, explains the changes in forming behavior of foils with respect to the forming limit, denoted by the limiting drawing ratio. It is shown that it occurs in so called Tiffany structures. The changes in the tribology in deep drawing have an influence on the clamping limit of the processing window. The changes are induced by changes of the drawing speed. They can be explained by the lubricant pocket model only if one takes the temperature dependence of the viscosity of the lubricant into account.

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Abbreviations

μ:

Coefficient of friction from Coulombs law

μeff :

Effective coefficient of friction from numerical identification using the formula by Storoshew

μff(p):

Coefficient of friction as function of contact pressure, given by the so called friction function

μH :

Coefficient of friction for hydrodynamic contact

μS :

Coefficient of friction for solid contact

μT :

Total coefficient of friction

A0 :

Macroscopic contact cross section area (mm2)

AL :

Liquid contact area (mm2)

AS :

Solid contact area (also: real contact area) (mm2)

d:

Diameter (mm)

dB,0 :

Initial blank diameter (mm)

dp :

Punch diameter (mm)

F:

Force (N)

FB :

Blank holder force (N)

FH :

Normal force transferred by hydraulic medium (N)

FN :

(Total) normal force (N)

FP :

Punch force (N)

FS :

Normal force on solid contact (N)

lp :

Punch travel distance during forming process (mm)

p:

(Contact) pressure (N/mm²)

pB :

Blank holder pressure (N/mm²)

pB,0 :

Initial blank holder pressure (N/mm²)

pL :

Lubricant pressure (N/mm²)

pS :

Pressure of solid contact (N/mm²)

r:

Radius (mm)

rD :

Drawing radius (edge radius of drawing ring) (mm)

rP :

Punch radius (radius between bottom and mantle) (mm)

s0 :

Sheet thickness (mm)

T:

Temperature (K)

T0 :

Temperature at viscosity η0 (K)

v:

Velocity (m/s)

vP :

Punch speed (m/s)

α:

Viscosity temperature index

β:

Drawing ratio (ratio of blank diameter to punch diameter)

βmax :

Limiting drawing ratio

ΔdD :

Drawing clearance (mm)

η:

Viscosity (m²/s)

η0 :

Viscosity at temperature T0 (m²/s)

ρ:

Density (g/cm³)

φmax :

Maximum strain

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Acknowledgments

The author is grateful for the financial support of the Deutsche Forschungsgemeinschaft (DFG) of the projects B1 and B3 of the Collaborative Research Center SFB 747, where the results were obtained. The author also thanks for support by Dipl.-Ing. S. Grünenwaldand Dr.-Ing. Z. Hu whilepreparingthismanuscript.

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  1. BIAS–Bremer Institut für angewandte Strahltechnik, Klagenfurter Straße 2, 28359, Bremen, Germany

    F. Vollertsen

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Correspondence to F. Vollertsen.

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Vollertsen, F. Effects on the deep drawing diagram in micro forming. Prod. Eng. Res. Devel. 6, 11–18 (2012). https://doi.org/10.1007/s11740-011-0355-5

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