平辊轧制非局部摩擦问题及近似求解

An Analysis and Approximate Solution for Strip Steel Rolling Problem with Nonlocal Friction

在平辊轧制塑性加工问题中,为了考虑金属材料表面微凸结构对模具与加工件接触区域上的非局部摩擦效应,采用Oden等提出的非局部摩擦定律代替经典的库仑摩擦定律,利用工程法建立了平辊轧制问题的积微分形式的力平衡方程.在简化的情况下,采用摄动法得到近似的解析解,所得到的接触面压应力分布值与库仑摩擦定律下的值很接近,表明本文方法和结果是可靠有效的.

The nonlocal friction law proposed by Oden et al is adoptded in this paper in order to consider the nonlocal friction effect of the asperities on the contact surface between the die and the workpiece for the strip steel rolling problem.The equilibrium equation with the integral-differential form is obtained by using the engineering method and solved approximately by using the perturbation method.The normal stress distribution obtained when nonlocal friction law is adopted is slightly different from the one with the classical coulomb law of friction.And the nonlocal effect of the asperities on the contact surface stress distribution is shown here.