The objective of this thesis is to gain a good understanding of the chatter phenomenon
incorporating the dynamic rolling model and mechanical system model of a rolling
stand in cold rolling. Although such systems have received great attention in the
academic literature, research to-date has not covered dynamic characteristics of the
multiple rolling body-bearing-support system due to its complexity and nonlinearities.
In this thesis, a steady-state rolling process model that includes the work hardening and
work roll flattening effect was developed based on the homogeneous deformation
theory with the relaxation of conventional assumptions. A dynamic model of the rolling
process was then formulated by taking into account multiple nonlinearities such as the
change in friction coefficient, rolling speed, roll gap (strip thickness) reduction and
reduction rate with respect to time. In linearisation of rolling force variations as stiffness
and damping coefficients, negative gradient of friction coefficient was introduced to
identify the negative damping effect in the dynamic roll gap. Also, dynamic rolling
force components were included in the analysis by the linearisation of variations of the
strip thickness and rolJing speed at exit side and of variations of reduction rate with
respect to time.
ln addition, a mechanical system model was derived through the inclusion of the
support bearings and surface contact between rolls. For the backup roll, a journal
bearing model was introduced to examine oil-film thickness change and a tapered roller
bearing model was adopted to model the work roll motion. In order to explain dynamics
in the surface contact between the backup roll and work roll, Hertzian contact theory is
incorporated into the mode-coupling theory. Finally, by coupling the dynamic rolling
process 1nodel with a mechanical system model including support bearings and surface
contact, a 6DOF mill vibration model for the analysis of vibrations symmetric to the ro11
gap was developed.
In determination of stability in the derived cold rolling stand chatter model, stability
analyses were performed through the change in the friction coefficient and rolling speed
at a given friction gradient. Many different aspects of stability threshold curves (STC)
have been obtained from the eigenvalues analysis of the system characteristic equation.
Influences of 10 rolling parameters such as the friction gradient, strip width, roll radius,
exit thickness, strain and strain-rate exponent, roll offset, bearing viscosity, length and
clearance on mill stability were thoroughly investigated. With the linearised stiffness
and damping coefficients at the given operating conditions, transient studies were
executed to prove the validity of the presented model.
Finally, in order to understand the effects of tension variations from the adjacent mill
stand, three different tension models were applied into the dynamic roll gap. By so
doing, the mill stability has been determined through the inclusion of transient
characteristics in the dynamic roll gap. In light of observation from the practical mill
configuration, simulation results suggest that chatter arises as the rolling speed increases
and friction coefficient decreases under the steady-state rolling conditions. When
tension variation applied, instability occurs as the inter-stand distance decreases and a
strip feed-in speed variation frequency matches to one of the system natural frequencies.