Investigation of the Influence of Deformation, Force, and Geometric Factors on the Roll Gripping Capacity and Stability of the Rolling Process

Abstract

This research developed a complex physical and mathematical model of the flat rolling theory problem. This model takes into account the influence of many parameters affecting the roll’s gripping capacity and the overall stability of the entire rolling process. It is important to emphasize that the method of the argument of functions of a complex variable does not rely on simplifying assumptions commonly associated with: the linearized theory of plasticity; or the decoupled solution of stress and strain fields. Furthermore, it does not utilize the rigid-plastic material model. Within this method, solutions are developed based on the complete formulation of the system of equations in terms of stresses and strains, incorporating constitutive relations, thermal effects, and boundary conditions that define a well-posed problem in the theory of plasticity. The presented applied problem is closed in nature, yet it accounts for the effects of mechanical loading and satisfies the system of equation. For this purpose, such factors as roll geometry, physical and mechanical properties of the rolled metal (including its fluidity, hardness, plasticity, and structure heterogeneity), rolling speed, metal temperature, roll lubrication, and many other parameters that can influence the process have been taken into account. Based on the developed mathematical model, a new, previously undescribed force factor significantly affecting the capture of metal by rolls and the stability of the rolling process was identified and investigated in detail. This factor is associated with force stretching of metal in the lagging zone—the area behind the rolls, where the metal has already left the deformation zone, but continues to experience residual stress. It was shown that this stretching, depending on the process parameters, can both contribute to the rolling stability and, on the contrary, destabilize it, causing oscillations and non-uniformity of deformation. The qualitative indicators of transient regime stability have been determined for various values of the parameter α. Specifically, for α = 0.077, the ratio f/α ranges from 1.10 to 1.95; for α = 0.129, the ratio f/α ranges from 1.19 to 1.95; and for α = 0.168, the ratio f/α ranges from 1.28 to 1.95.