The deformation characteristic of an ultra-heavy plate in thickness direction is described by introducing a parameter, called deformation penetration coefficient, and the rolling force model taking this parameter into account in the broadside stage is established. In this paper, the deformation penetration coefficient is defined as the ratio of the actual deformation depth to the overall plate thickness, which is shown as the function of the initial thickness, the pass reduction and the critical shape factor. Since the plate width speard can be neglected during broadside rolling, a two-dimensional velocity field is constructed by simplifying a classical three-dimensional velocity field. For the purpose of solving the problem of functional integration originated from the nonlinear Mises specific plastic power, the simplified velocity field is analyzed by the geometric approximation (GA) yield criterion, and the internal deformation power is obtained. Moreover, the friction power and the shear power are obtained by the inner product method of the strain vector and the mean velocity intergral method, respectively. The analytical solution of rolling force is obtained by the variational method, and its value for each pass is compared with the measured data from a domestic factory. The comparison result shows that the rolling force model in this paper has a high predictive accuracy, since the maximum error is less than 8.6%. The rolling parameter analysis shows that the deformation penetration coefficient, the pass reduction and the ratio of plate thickness to diameter affect the rolling force of the ultra-heavy plate apparently.
