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塑压接触面上之摩擦力,在一定时间作用于一定曲线族之切线方向,此曲线族称为“摩擦线”,其理论意义为:摩擦线本身为塑压表面流动之方向规律;其实际意义为:加工压力之科学计算有赖于摩擦线。 在连续塑性变形过程中,接触面上质点之流动轨迹称为“长程滑线”,在塑压中一形状变为另一形状,长程滑线为始末形状间之表面变化规律。 本支为一系列研究(例如[1]至[3])之续,目的及结果有三: (1)证明前文中摩擦线、等压线与压力布三个微分方程不受摩擦物理方程之约束; (2)提出椭圆板摩擦线族之另一解; (3)开拓出决定直观摩擦线的方法,定出塑泥及铅椭圆板之一系列摩擦线族,并对理论与实验结果作了比较讨论。 金属摩擦线研究在进行中。 北京钢铁学院的温金珂先生在本文前一作者指导下作过一长方板的摩擦线,她的结果将在长方板摩擦线系统化研究中一并发表。

This paper is one of the developments of our previous investigations (forexample,). In a recent paper a set of general plane differential equations forfriction-lines and for pressure contours were obtained as:θ=angle (x, second principal stress);τ=unit frictional force. As shown in the chinese text, these two equations and the general curvilineardifferential equation (C) for pressure distribution all hold for any case of plasticfriction: P=unit pressure; h=thickness of the plate; f_2(ε)=strain function (see[2]); K=uniaxial yielding point; s=arc length of the complete friction-line.For the case of elliptical plates a set of solutions were obtained as shown in Fig1 of the chinese text, by taking θ as defined by the tangents of concentric ellipses.In this paper, we show that a second set of solutions can be deduced by taking θas defined by regular elliptic coordinates. As shown in Fig. 2 and Fig. 3, the new solutions for friction-lines and pressure contours are radii and circles, the pressuredistribution has a finite peak at the center. To check the validity of these theoretical results, experimental determinationof friction-lines was made for lubricated plates of lead and plastic mass by photo-graphic and isoclinic methods. The methods are obvious in the Fig. 4 to 17, andneed not be elabourated here. As Liu Shu-i has pointed out in a paper to be published soon, the surfacestream-lines and the instantaneous friction-lines are two different families of curvesobeying different laws-the rule of gradient for instantaneous friction-lines andLiu's rule of isoclinic gradient for stream-lines called long-rang friction-lines. Fig. 9 to 11 are surface stream-lines from which the instantaneous friction-lines were deduced by isoclinic method as shown in Fig. 12 to 17. Each figure forfriction-lines consists of two families: the isoclinics and the friction-lines (witharrows). Fig. 18 provides an indication of a no-slip point at the center of the plate. It appears that the theoretical solution of the last paper yields friction-lineswith curvatures greater than the experimental curves and the solution given in thispaper is close to the experimental curves only for ellipses with axial ratio not too farfrom unity. However, the solution of last paper mathematically holds, if the axialratio is replaced by an arbitrary constant. This will allow us to interpret moreexperimental facts on the basis of that solution. The case of bipolar plate is under investigation, we have obtained the dif-ferential equation for friction-lines as equation (D), its solution will be published inanother paper.tanφ={(y/x)([(a~2+y~2-x~2)~2-4x~2y~2](a~2+y~2+x~2)-4x~2(a~2+y~2-x~2)(a~2-y~2-x~2))/(4y~2(a~2+y~2-x~2)(a~2+y~2+x~2)+[(a~2+y~2-x~2)-4x~2y~2](a~2-y~2-x~2)); (y/x)(a~2+y~2+x~2)/(a~2-y~2-x~2); when(a~2+y~2-x~2)>0. when(a~2+y~2-x~2)=0. (y/x)([(a~2+y~2-x~2)-4x~2y~2](a~2+y~2+x~2)+4x~2(a~2+y~2-x~2)(a~2-y~2-x~2))/(-4y~2(a~2+y~2-x~2)(a~2+y~2+x~2)+[(a~2+y~2-x~2)~2-4x~2y~2](a~2-y~2-x~2));}(D) when(a~2+y~2-x~2)<0.α=constant in the equation of bipolar coordinates.