塑压接触平面上之长程滑动与短程滑动(等倾陡线规律)

塑压接触面之质点滑动线称“摩擦线”。滑动现象有两种基本类型,一为“长程滑动”,摩擦线为质点之长程连续轨迹,如抽拔,挤压,冲压等塑性过程中之滑动;一为“短程滑动”,质点仅在摩擦线上滑动一微小距离,如锻,轧,压力实验等过程中之滑动(小压缩时)。过去对这两种滑动现象之规律未曾分别处理。本文将摩擦力接纯力学关系视为一切应力,即压应力p与摩擦应力τ,以边界平衡关系,相系于一应力函数F: τ=Fp, F=((l₁²p₁²+l₂²p₂²+l₃²p₃²)/(l₁²p₁+l₂²p₂+l₃²p₃)²)^1/2-1, p₁,p₂,p₃为内部主应力; l₁,l₂, l₃为p对p₁,p₂,p₃之夹角余弦。除视τ为p之函数τ=τ(p)外,对摩摩力之物理性质不作规定。在此基础上,以住意质点滑动之最小摩阻功为基本条件分析滑向规律,一如任意质点滑动之最小摩阻力条件之于“陡线规律”。如此,则问题类于古典变分问题,变分方程引出两结论:在短程滑动中,滑向规律为已知之陡线规律;在长程滑动中为以下将提出之“等倾陡线规律”。并得到几个有关重要推论。

LONG RANGE AND SHORT RANGE FRICTIONAL SLIP-LINES ON PLANE CONTACT SURFACE IN PLASTIC COMPRESSION (THE RULE OF ISOCLINIC GRADIENT)

In the recent years, the theory related to friction-lines has been independently developed both in Europe and here, according the information reached the author in 1956. These investigations are based on the condition of least frictional resistance at a point.In 1954, a variational equation (2a) on classical basis was given on a meeting for the related research. This equation was based on the frictional work at point. In as much as the condition of least force at a point has became acceptable, there seems no reason to object the condition of least work at a point, that is, the frictional work along the path of an element of area. Thus, the above equation are further investigated in this paper.For the case of short range slip occuring in processes such as plane forging under small reduction, the last term of this equation is zero, the rule of gradient follows. Therefore, the rule of gradient holds only for short range slip or instantaneous friction-lines.For long range slip, this equation leads to the "rule of isoclinic-gradient", (equation 9), which states that the gradient line of pressure (p) is the isoclinic curve for frictional force τ(Fig. 2). The angle of inclination (φ) changes along the pressure contour according equation (11), and along the friction-line according to equaiion (14). The function (τ) has the general nature of equation (16). Examples for long range slip is given in Fig. 3 and 4. Continuous divergent long range slip can only be generated by point or line-sourse in extrusion. The singularities in the case of short range slip are not real sourses.In this analysis, the frictional force is regarded as a shear stress on pure mechanical basis, without assuming its physical nature.For complete details of the paper, see10].