Modelling lateral spread in wire flat rolling

A mathematical model for wire rolling is developed, focusing on predicting the lateral spread. This provides, for the first time, an analytic model of lateral spread without any fitting parameters. The model is derived directly from the governing equations, assuming a rigid, perfectly plastic material and exploiting the thinness of the wire (in thickness and width) relative to the roller size. Results are compared against experiments performed on stainless steel wire using 100mm diameter rolls, demonstrating accurate predictions of lateral spread across a wide range of wire diameters (2.96mm-7.96mm) and reduction ratios (20%-60%), all without the need for fitting parameters. Since the model requires only seconds to compute, the model's valid range is explored for varying roll diameter, wire diameter, and reduction ratio, and their effects on the resulting lateral spread characterized. The model can serve as a robust tool for validating FE results, guiding process design, and laying the foundation for future improved models. Matlab code to evaluate the model is provided in the supplementary material.