Applying mathematical models and numerical methods is crucial for describing and simulating the metal cold-rolling process, wherein the accurate prediction of rolling force is an effective way to improve the quality of rolled sheets. This paper considers key influencing parameters such as friction lubrication, stress, tension, and roll-flattening radius during the rolling process and establishes a calculation model for the friction coefficient and roll-flattening radius. By considering the coupling effect of the dynamic roll gap on rolling force, a rolling force model for non-steady-state friction lubrication during the rolling process is obtained. The correctness of the proposed model is verified by comparing it with industrial measurement results. The influences of the friction coefficient, stress, tension before and after rolling, and roll-flattening radius on rolling force are quantitatively studied. The results show that the rolling force increases with an increase in the friction coefficient. When the friction coefficient exceeds 0.2, the rate of increase slows down, approaching dry friction conditions. The rolling force increases linearly with stress but decreases with increasing tension before and after rolling. The rolling force model, considering the roll-flattening radius, provides numerical calculation results that are closer to an industrial measured rolling force. This work contributes to a better understanding of the mechanism behind the improvement of the cold rolling process.

To reveal the influence of surface morphology characteristics in mixed lubrication on the contact characteristics of the rolling interface, a random three-dimensional rough surface model based on Gaussian distribution theory was established. The model utilizes the finite element method (FEM) to simulate the regular contact and tangential sliding behavior of micro-asperities at the rolling interface in mixed lubrication conditions. The connection bearing capacity of models with varied roughness in mixed lubrication was studied. Furthermore, the effect of various sliding and normal indentation amounts on the normal and friction stress was investigated. The simulation result reveals that the roughness of the surface influences the distribution of the lubricating oil film. The lubricating oil layer between the interfaces with a lower roughness has a higher bearing capacity due to its more uniform distribution of peaks and valleys. An increase in the normal indentation amount raises the friction stress and normal stress. In contrast, an increase in sliding lowers the normal pressure, substantially impacting the fluctuation of the friction coefficient dramatically. Finally, the random three-dimensional rough surface model is verified by comparing it with the experimental data in the related literature.

This study comprehensively utilizes the mixed lubrication theory and rolling deformation theory to establish a finite element stiffness contact model that considers the surface texture characteristics of the rolling interface. The dynamic explicit finite element analysis is used to obtain the deformed solid, and the turbulent equation is used to control the fluid boundary conditions. The bidirectional Fluid-Structure Interacton (FSI) ansysis is used to study the influence of surface roughness, surface textures, and rolling parameters such as rolling speed on the distribution of oil film pressure and contact characteristics during the rolling process. The results confirm that transverse texture reduces the friction coefficient and dynamic pressure by enhancing the trapping effect of rough peaks and facilitating the entrainment of the fluid film. Under the same textural conditions, the contact area decreases with increasing roughness while the friction coefficient increases. As the rolling speed increases, the rolling pressure decreases to a certain extent, and the contact area ratio will decrease; Lubricants with higher viscosity can effectively reduce the friction and rolling force at the rolling interface. We believe that the insights obtained from the numerical simulations provided in this reaserch will lay a theoretical foundation for subsequent research on plate shape control.