薄壁管材等曲率矫直临界曲率半径力学建模

薄壁管材等曲率矫直临界曲率半径作为重要的工艺参数,直接决定了设备结构和产品质量。而目前现场仍沿用经验图表结合人工经验和反复试矫对其进行估定,亟待建立针对性的力学模型以指导生产,为此从旋转壳体大挠度几何方程出发,基于J₂形变理论和能量理论,运用里茨法建立了薄壁管材等曲率矫直塑性失稳时的临界弯矩,以此确定了临界曲率半径模型,并给出了数值解法。应用ANSYS/LS-DYNA进行了有限元动态仿真试验,结果表明模型是近似正确的,通过仿真对比分析证明了轴向起皱先于截面畸变是薄壁管材等曲率矫直塑性失稳的主要模态。

MODELING OF THE CRITICAL RADIUS FOR STRAIGHTENING THIN-WALLED TUBES WITH EQUAL CURVATURES

The critical curvature-radius, as the main technical parameter in strengthing, decides the structure of equipment and the quality of products for straightening thin-walled tubes with equal curvature. However, it is usually carried out based on experiential data and charts by skilled labourers, whose art is based on long experience and experiments, and as such a specialized mathematical model is immediately necessary. Therefore, applying the large deflection strain-displacement relations of the shell of revolution, the mechanical model of the critical bending-moment for equal curvature straightening is presented by the Ritz method, based on J₂ deformation theory and energy methods. Then the critical radius is subsequently derived and it is also shown how to solve for it synchronously. In order to certify whether it is correct, several dynamic simulations were performed in ANSYS/LS-DYNA, and the results have shown that the model is approximately correct. By comparison of the simulations' results it is shown that wrinkling on the compression side of the tube occurs before buckling and is the principal failure mode when straightening plastically-unstable thin-walled tubes with equal curvature.