为保证复杂异形截面环件直径达到预计目标尺寸时其孔型填充情况同时符合实际工艺要求，建立了一种环件二维轴对称多步胀形有限元模型，综合运用二维上限元法与二维有限元方法提出了等效矩形截面环件的计算方法，并利用二维上限元法计算等效矩形截面环件胀形过程速度场，然后通过二维轴对称有限元软件求解当前胀形步环件孔型填充情况。以钛合金机匣环件为例，采用二维轴对称有限元软件求解时间只需5～15 min,与三维有限元环件轧制模拟结果相比，环件截面填充率和内外径尺寸精度误差均在10%以内。通过环件二维轴对称多步胀形有限元模拟计算，可大幅减少环件轧制工艺设计与优化时间，提高生产效率。

To ensure that the filling of the hole pattern meets practical process requirements when the diameter of a complex-shaped cross-section ring reaches its target dimension, a two-dimensional axisymmetric multi-step expansion finite element model was developed for the ring. The calculation method for an equivalent rectangular cross-section ring was proposed by comprehensively applying the two-dimensional upper bound method and the two-dimensional finite element method. The expansion velocity field of the equivalent rectangular cross-section ring was calculated using the two-dimensional upper bound method. Subsequently, the filling condition of the hole pattern in the current expansion step was solved using a two-dimensional axisymmetric finite element software. Take titanium alloy casing ring as an example, the computation time with the two-dimensional axisymmetric finite element software was reduced to 5-15 min. Compared to the three-dimensional finite element simulation of ring rolling, the errors of the filling rate of the ring cross-section and the accuracy of the inner and outer diameters are within 10%. The two-dimensional axisymmetric multi-step expansion finite element simulation can significantly reduce the time required for the design and optimization of ring rolling processes, thereby improve production efficiency.