Chapter 3 - Rolling of metals

Theory of cold rolling
A theory of rolling is aimed at expressing the external forces, such as
the rolling load and the rolling torque, in terms of the geometry of the
deformation and the strength properties of the material being rolled.
Assumptions
1) The arc of the contact is circular – no elastic deformation of the roll.
2) The coefficient of friction is constant at all points on the arc of contact.
3) There is no lateral spread, so that rolling can be considered a problem
in plain strain.
4) Plane vertical section remain plane: i.e., the deformation is
homogeneous.
5) The peripheral velocity of the rolls is constant
6) The elastic deformation of the sheet is negligible in comparison with the
plastic deformation.
7) The distortion-energy criterion of yielding, for plane strain, holds.
2
σ 1 −σ
3 = σ o = σ
3
Suranaree University of Technology Tapany Udomphol
Jan-Mar 2007
'
o
Yield stress in plane
strain condition