Novel Analytic Model for the Projected Contact Zone Based on the Flow Line Element Method in Alloyed Bar Rolling

Abstract

For obtaining the profile and the projected area of contact zone exactly during alloyed bar rolling by Round-Oval-Round pass sequence, the analytic model for the length contact and contact boundary curve were built firstly by considering the influence of the spread of the outgoing workpiece on the effective height of outgoing workpiece and roll mean radius, and then the contact surface was discretized by finite flow line elements. Moreover, the radius equation and bite angle equation of different flow lines were derived and they were all expressed as the function of the position angle, then any flow line on the contact surface can be determined since the position angle has been given. Finally, since the analytic equation for the projected area of contact surface was hard to be integrated directly, the analytic model was proposed by summing up the area of discretized parts on the contact surface. Based on the analytical model of contact boundary and flow line element, 3-dimension contact surface was rebuilt by mathematical software, and the validity of analytic model was examined by the bar rolling experiments and the numerical simulation of alloyed bar rolling by rigid-plastic FEM software. Compared with the existing models, the precision of the projecting area of contact zone was improved obviously. So, it can be applied in alloyed bar rolling to predict the projected area of contact zone and velocity of outgoing workpiece exactly.