Modelling Lateral Spread in Wire Flat Rolling

TL;DR

Addresses the problem of predicting lateral spread $W_t$ in wire flat rolling. The authors develop a leading-order asymptotic, plane-stress model for a rigid-perfectly plastic wire under Coulomb friction, with two geometric simplifications; predictions agree with stainless-steel experiments and FE data without fitting parameters and compute in seconds. The study demonstrates that $W_t$ is determined by inputs $d_0$, $R$, and $\mu$ through the reduced geometry and is robust across $d_0 in [2.96,7.96]$ mm and reductions 20–60%. This work provides a fast, parameter-free tool for process design, FE validation, and sets the stage for incorporating 3D effects and material anisotropy in future models.

Abstract

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.

Figures (10)

• Figure 1: A diagram of wire flat rolling process; the wire initially has a circular cross-section with diameter $d_0$ and is flattened to a barrel shape cross section with the lateral spread $W_t$ and the contact width $W_c$. Adapted from Figure 1 of carlsson1998contact.
• Figure 2: A diagram of the model; the region of interest extends from point A to the roll gap exit. At A, the cross-section is approximated as a square with the same area as the initial round wire, transitioning into a rectangular approximation during rolling with the same area as the real bulged cross section.
• Figure 3: Lateral spread for stainless steel wires with different diameters, $\hat{d}_0$, and reduction ratios, $\hat{d}_0/(2\hat{h}_1)$ from different methods; experimental data, empirical equation \ref{['eq:kaztotalwidth2']} from kazeminezhad2005width, empirical equation from Kobayashi \ref{['eq:kobayashi']}, and the current model. Other parameters used are $(\hat{R}, \mu)=( 50\, \mathrm{mm}, 0.25)$.
• Figure 4: Effect of friction coefficient on lateral spread. Results are plotted from different methods; experimental data, FE simulations vallellano2008analysis, empirical equation \ref{['eq:kaztotalwidth2']} from kazeminezhad2005width, empirical equation from Kobayashi \ref{['eq:kobayashi']}, and the current model.
• Figure 5: The initial wire length, along with the final experimental and predicted length for different samples. Each sample is labelled according to its initial wire diameter and the ratio of initial diameter to final thickness (for instance, "2.96--1.25" refers to a wire with an initial diameter of 2.96 mm and a reduction ratio of 1.25). Other parameters used are $(\hat{R}, \mu)=( 50\, \mathrm{mm}, 0.25)$.