几何内蕴量对拉伸模具工作面力学性能的影响

曲率、度规不变量、凸凹性等几何内蕴量的不均匀分布直接影响模具的力学性能。本文研究了曲率与变形能、曲率与摩擦耗损功、度规不变量与热辐射、凸凹分布与辐射热通量等几何内蕴量与力学量之间的关系。结果表明:复杂曲面表面高斯曲率的不连续分布将导致表面的变形能、摩擦耗损功出现相应的不连续分布;型面上沿拉伸方向截面线的法曲率越小,摩擦耗损功越大;型面上的热通量会随着拐点数量的增加而增加。这些结果为模具表面优化设计提供了新的理论依据。

Effects of Geometric Intrinsic Quantities upon the Mechanical Properties on the Surfaces of Deep Drawing Dies

The mechanical properties on the active surfaces of the molds or dies will be directly influenced by non-uniform distribution of the geometric intrinsic quantities such as curvature, metric invariant, and convexity-concavity of the surfaces. This paper shows an investigation made on the relationship between such geometric intrinsic quantities and the mechanical quantities. The results demonstrate that discontinuity of Gaussian curvature will lead to discontinuity of deformation and frictional dissipative energy. The frictional dissipative energy will increase with the decrease of the normal curvature on the deep-drawing path. The heat flux will increase with the increase of inflection points on the surface. These provide novel references for optimal design of the molds and dies.