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Some aspects of sheet-metal forming using impact loading through water columns

An analysis is presented that allows the estimation of pressure and deflection when sheet metals are free formed by a water column subjected to impact by a falling mass

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Abstract

This paper reports on work carried out on the free forming of 50.8-mm-diam low-carbon-steel sheet specimens using a water column as the energy-transmilling medium.

A ‘simple’ theory is presented that allows an estimation of the pressure variation, within the water column, with time to be made. The energy is supplied from a falling weight that impacts a punch testing on the top surface of the water column. The large mass of the falling weight relative to the mass of the water column allows an energy balance to be made between the kinetic energy of the weight and the strain energy absorbed by the column.

Experimental results are presented that show the theroy to be capable of providing a reasonable estimation of pressure variation.

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Abbreviations

A :

cross-sectional area of water column (or bar)

C :

linear stiffness of water column (or bar)

C′:

volumetric stiffnes

C ′ a :

apparent volumetric stiffnes

E :

Young's modulus

F :

force between punch and upper surface of water column

K :

bulk modulus of water

M :

mass of failling weight plus punch

M 1 :

mass of falling weight

M 2 :

mass of punch

P :

pressure in water column

R :

radius of water column

T :

time duration of impact

V :

volume of water column

V d :

velocity of falling weight just before impact

V 0 :

velocity of falling weight and punch combined at impact

ΔV :

change in volume of water column

ΔV′ :

volume generated by deforming sheet

ΔV a :

apparent change in volumen of water column

α:

amplitude of vibration of water-column upper surface

c :

velocity of sound in stransmitting medium

d :

initial sheet thickness

f :

length of water column (or bar)

t :

time

x :

displacement of water-column upper surface

x′:

polar deflection of sheet

μ:

mass ratio: falling weight plus stationary punch relative to weight of water column

ϱ:

density

ω:

natural angular frequency of mass-spring system

\(\sigma _f \) :

stress at fixed end

\(\sigma _o \) :

stress generated at the impact surface at impact

\(\sigma _y \) :

yield stress of sheet

References

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Authors and Affiliations

  1. Department of Production Technology, Brunel University, Uxbridge, Middx., U.K.

    R. J. Grieve (Lecturer)

  2. Department of Mechanical Engineering, Kenva Polytechnic, P.O. Box 52428, Nairobi, Kenya

    N. W. Wambugu (Lecturer)

Authors
  1. R. J. Grieve
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  2. N. W. Wambugu
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Grieve, R.J., Wambugu, N.W. Some aspects of sheet-metal forming using impact loading through water columns. Experimental Mechanics 21, 302–308 (1981). https://doi.org/10.1007/BF02325770

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  • DOI: https://doi.org/10.1007/BF02325770

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