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给出一种以非线性流线（除边界流线）描述的轴对称变薄拉深初始流动模型，通过总功率的极小化确定最佳动许可速度场。建立多模变薄拉深任一凹模出口拉应力的一般上限解。提出摩擦因子的试验测试方法并给出其计算公式。凹模出口拉应力和变薄拉深力的理论解与试验结果良好吻合。
An initial flow model of axisymmetric thinning and drawing with nonlinear flow line (except the boundary flow line) is given. The optimal moving velocity field is determined by the minimization of total power. The general upper limit solution of tensile stress at the exit of any die with multi-mode thinning is established. The test method of friction factor is proposed and its calculation formula is given. The theoretical solution of the die exit tensile stress and the thinning draw force are in good agreement with the experimental results.