基于复杂接触摩擦的圆柱体镦粗的上限解

为了提高计算圆柱体镦粗单位镦粗力上限解的精度,提出了一种基于复杂接触摩擦圆柱体镦粗的上限解法.根据翁克索夫等人提出的镦粗时接触面上摩擦切应力按照库仑摩擦定律、最大摩擦定律及线性分布摩擦定律的组合分布,利用上限法求得了圆柱体镦粗时单位镦粗力上限解,该解和主应力法解析解完全相同,比通常假设接触面上摩擦切应力为某一常数或按库仑摩擦定律分布的上限解要精确得多,同时还指出了圆柱体镦粗时按库仑摩擦定律求单位镦粗力上限解的适用条件.

Upper-Bound Solutions of the Cylinder Upsetting Based on the Complicated Contact Friction

In order to improve the accuracy of the upper-bound solutions of the unit upsetting force of the cylinder upsetting, a new method for solving the upper-bound solutions of the cylinder upsetting based on the complicated contact friction was proposed. Based on the combination distributions for frictional shear stresses according to Coulomb friction law, the maximum friction law and the linear distribution friction law on the dieworkpiece interface during upsetting proposed by E. P. Unksov et al, the upper-bound solutions of the unit upsetting force for the cylinder upsetting were derived. The solutions are identically equal to the analytical solutions in the slab method. They are more accurate than the upper-bound solutions obtained by using the conventional upper-bound method, in which the constant friction or Coulomb friction law on the interfaces is assumed. Simultaneously, the suitable condition for solving the upper-bound solutions of the unit upsetting force for the cylinder upsetting according to Coulomb friction law was also proposed.