# Establishment and Numerical Analysis of Rolling Force Model Based on Dynamic Roll Gap
## 1 Introduction
[10] used the three-dimensional elastic-plastic finite element approach to simulate the working process of cold rolling, considering the elastic deformation of the roll, the plastic deformation of the rolling piece, and the pressure between the work roll and the backup roll, according to the numerical simulation, and the rolling force along the width distribution of rolling stock, and discussed the location of rolling force peaks under different rolling conditions. [PERSON] et al. [11] adopted the differential element method to establish the strip's finite element equation of plastic deformation of plastic deformation, they numerically simulated the flattening process of work rolls in the cold rolling process. [PERSON] et al. [12] used numerical methods to fit the roll shape curve after elastic flattening of work rolls, and established a new Hitchcock roll flattening radius calculation formula to increase the rolling force calculating model's precision. The authors of [13; 14] used sensors to measure the normal force and friction force of the rolling interface in the process of cold aluminum rolling; many experimental data demonstrated that the normal force and friction force changed nonlinearly with time, and discussed the influence of various friction coefficients on the aspect ratio of aluminum. [PERSON] et al. [15] developed a rolling force model to examine the plastic deformation of strips, talked about the impact of the rolling force's relationship to the ratio of extremely high pressure to extremely low pressure, and evaluated the precision of the model's calculated results using data from experiments. [PERSON] et al. [16] established an elastic-plastic multi-station finite element model of the TCR process considering work-hardening effects using a segmented modeling strategy, data transmission technology, and unit mesh partitioning technology; the effects of rolling force on the strip crown and flatness at each stand are investigated quantitatively using the developed FE model, revealing the influence of rolling force on the shape of strip, including the strip crown and flatness, demonstrates the importance of studying rolling force models. Although the mathematical model for calculating rolling force in cold rolling mills has been extensively studied, the research results remain limited due to the complexity of the dynamic roll gap in the cold rolling process and the constraints associated with solving mathematical and physical models. This paper proposes a new rolling force model, based on the existing Bland-Ford-Hill rolling-force calculation formula, to establish a more accurate rolling-force calculation equation. The model considers the internal correlation mechanism among the roll, strip, and lubrication friction in the cold rolling process and comprehensively considers the influence of multiple parameters, including strip stress, tension, unsteady lubrication friction, and roll-flattening radius. In the following sections, the theoretical basis of rolling-force modeling, the model-establishment process, and the numerical analysis results will be comprehensively elaborated. This research achievement will provide new insights and strategies for understanding and managing rolling force, thus having important practical significance for optimizing the cold continuous rolling process.