Chapter 3 - Rolling of metals

The forces acting in the vertical direction are balanced by the specific roll
pressure p. Taking the equilibrium of forces in the vertical direction results in
a relationship between the normal pressure and the radial pressure.
p =
pr
( 1m µ tanθ
)
The relationship between the normal pressure and the horizontal
compressive stress σσσσ x is given by the distortion energy criterion of
yielding for plane strain.
2
σ 1 −σ
3 = σ o = σ
3
p σ
…Eq.14
Suranaree University of Technology Tapany Udomphol
Jan-Mar 2007
'
o
'
− σ x = o
…Eq.15
Where p is the greater of the two compressive principal stresses.