Abstract: To improve the quality of hot rolling products， the width precision of the hot rolling strip must be guaranteed. Vertical mill is usually installed in the roughing trains to control the width in actual production processing， but the cross section of the strip formed as a dog-bone shape after vertical rolling. The symmetric and anti-symmetric parabola dog-bone function model and kinematically admissible velocity field in the vertical rolling are firstly proposed in present paper. Using the first variation principle of rigid-plastic material， analytical solutions of the total power functional and rolling force for the vertical rolling are obtained using variable upper limit integration. The error of the rolling force obtained above compared with that of FEM simulation result is within 3%， while is less than 6.3% compared with that obtained by Yun’s model. The precision can satisfy the requirement of production control using this anti-symmetric parabola model to predict the rolling force in a strip rolling plant.

Key words: vertical rolling force, anti-symmetric parabola, dog-bone model, analytical solution