In order to solve the problem of establishing the rolling force model, which is caused by the nonlinear Mises specific plastic power, a novel yield criterion, called mean slope yield criterion, is constructed by averaging the slopes of yield loci of the Tresca criterion and Mises criterion. The yield criterion is a linear combination of the principal stress components, and its locus on the π-plane is an irregular dodecagon which intersects the Mises circle. For verification, the yield criterion was rewritten by introducing the Lode stress parameter and compared with the experimental data, and a good consistency is achieved. Meanwhile, a three-dimensional velocity field whose horizontal component satisfies the elliptic distribution from the entrance to the exit is proposed. Based on these achievements, the energy analysis of the velocity field is carried out with the derived yield criterion, and the expression of the internal deformation power is derived. Also, the friction power and shear power are derived in terms of the velocity field. Ultimately, the analytical solutions of rolling torque, rolling force, and the stress state coefficient are obtained through the minimization of the total power. By comparison, it is shown that the theoretical rolling torques and rolling forces coincide well with the measured ones since both the maximum errors are only 13.77%.

为了解决由非线性米塞斯比塑性功率引起的建立轧制力模型的问题，通过对特雷斯卡准则和米塞斯准则的屈服轨迹的斜率求平均值，构造了一种新的屈服准则，称为平均斜率屈服准则。标准。屈服准则是主要应力分量的线性组合，其在π平面上的轨迹是与米塞斯圆相交的不规则十二边形。为了验证，通过引入Lode应力参数重写屈服准则，并与实验数据进行比较，获得了良好的一致性。同时，提出了一个三维速度场，其水平分量满足从入口到出口的椭圆分布。基于这些成就，根据导出的屈服准则对速度场进行能量分析，导出内部变形能力的表达式。同样，根据速度场得出摩擦力和剪切力。最终，通过使总功率最小化，获得了轧制扭矩，轧制力和应力状态系数的解析解。通过比较，可以看出，理论轧制扭矩和轧制力与实测轧制扭矩和轧制力非常吻合，因为两个最大误差仅为13.77％。通过最小化总功率获得应力状态系数。通过比较，可以看出，理论轧制扭矩和轧制力与实测轧制扭矩和轧制力非常吻合，因为两个最大误差仅为13.77％。通过最小化总功率获得应力状态系数。通过比较，可以看出，理论轧制扭矩和轧制力与实测轧制扭矩和轧制力非常吻合，因为两个最大误差仅为13.77％。