关于滑移线场α族线与x轴夹角ω的探讨

The principle of angle ω between α line and axis x when using slippage line method to solve the forming force

本文综合分析了滑移线法求解变形力时α线与x 轴夹角ω在汉基应力方程中的几种形式, 提出了α线与x轴夹角ω以及汉基应力方程中ωab 的确定原则。即对于两点 A、B, 确定α线与x 轴夹角ω原则是满足|ωab | =|ωa-ωb|<π,在确定A、B两点的ωa 和ωb 时应该遵循的原则是: (1) ωa 和ωb 同时沿逆时针或顺时针; (2) |ω|<π。如果条件 (1) 不能满足|ωab|<π, 则采用条件 (2) 来满足|ωab|<π。

It is analysized that forms of angle ω between α line and axis x in Hencky stress equation when using slippage line method to solve forming force. Confirmation principle of angle ω between α line and axis x is put forward. Between two points A and B, the confirmation principle of angle ω between α line and axis x is ｜ω ab ｜=｜ω a-ω b｜<π. In order to agree with the result of ｜ω ab ｜=｜ω a-ω b｜<π, ω a and ω b must agree with the conditions that are: (1) ω a and ω b are at the same direction (clockwise or anticlockwise);(2)｜ω｜<π. If condition (1) could not agree with ｜ω ab ｜<π,so using condition(2)to agree ｜ω ab ｜<π.