Mathematical model of neutral line on the contact zone in alloyed bar rolling by the round-oval-round pass sequence

For determining the neutral line on the contact zone to determine the relative slip condition between the contact surface of rolling pieces and the roll, the contact boundary curve was proposed by obtaining the radius of flow line and the bite angle of points on the contact boundary based on the flow line method, and then the contact surface was discretized as flow line elements to build a novel analytic model to reconstruct the geometry of contact surface. Moreover, the velocity of flow lines on the contact surface along the direction of X-axis was derived by the condition of steady-state incompressible flow, and the function of neutral line was obtained by determining the neutral radius and the neutral angle of the points on the neutral line. In addition, the three-dimensional rectangular coordinates of points on the neutral line were derived.Based on these mathematical models, the three dimensional geometry of contact surface and neutral line were drawn up by mathematical software. The validity of the theoretical model was verified by rolling experiments of alloyed bar and the numerical simulation by rigid-plastic FEM software. Compared with the experimental data and simulation results, the prediction error is acceptable and the results of the mathematical model is satisfying.