3 Fundamentals of press design

Basic terms
in which � 1 is deformation in one principle axis and � 2 and � 3 in the
other two principle axes. This equation will give, for example, the
amount of compression in a body with height h (Fig. 2.2.1). � is calculated
from the compression relative to the starting measurement e or
from the relative deformation
h1 – h0
Δh
ε1 = = ,
h h
0 0
in which h 0 stands for the height of the body before compression and
h 1 the final height of the body after compression:
h1
ϕ1= ln = ln 1
+ ε
h
0
( )
In accordance with the law of volume constancy, according to which
the volume is not altered by the deformation process (Fig. 2.2.1), the
sum of all deformation values is always equal to zero:
l 0
F
b 0
h 0
ϕ + ϕ + ϕ =
1 2 3 0
V= l b h = V = l b h
0 0 0 0 1 1 1 1
Fig. 2.2.1 Dimensional changes in frictionless upsetting of a cube
Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998
l 1
b 1
h 1
27