Investigation into dynamics of a rolling body-bearing-support system in a cold rolling stand
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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.
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