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正确表达塑性压力加工时接触面上的单位压力,不仅对正确计算总压力有影响,而且对金属纵向和横向的变形比、变形后的周界形状、工具和坯料合理形状的选择,等等,都有很大的影响。但是关于此一问题的文献资料,绝大部分将单位压力做一维表达p=p(x),显然,做为反映接触面上的单位压力分布规律是不全面的。将接触面上的单位压力进行二维表达的资料很少,而且还皆因公式繁杂、精度较差、应用不便而难以推广。本文根据接触面上金属质点的流动方式和摩察力规律,按照压力场与摩察力场的关系建立起单位压力分布的偏微分方程,再取变形体对称平面的平面变形条件做为边界条件,从而得出形式简便、适应性广的单位压力分布的二维表达式p=p(x,0)p(0,y)/p_(mzx)=p(x,y)。用园柱体和长方体的铅试件进行压缩试验。在接触面上刻有座标网格,通过对变形后网格变化的分析,利用本文公式,可以求出完全符合实验结果的粘着区、制动区和滑动区单位压力等压线的表达式。用本文公式和其他作者的公式计算总变形力,然后和试验时的实测值相比较。对比结果表明,本文公式所给出的计算值和实测值最接近,平均误差在±10％以内。还可以在本文的基础上维续发展,求出接触面上金属流动时的流线方程和宽展公式,以及周界受约束时(如模锻、在孔型中轧制等)的约束力规律。
Correctly expressing the unit pressure on the contact surface during plastic pressure machining not only affects the correct calculation of the total pressure, but also the deformation ratio in the longitudinal and transverse directions of the metal, the perimeter shape after deformation, the proper shape selection of tools and blanks, Have a great impact. However, the literature on this issue, the vast majority of the unit pressure to do one-dimensional expression p = p (x), obviously, as a reflection of the contact pressure distribution on the unit is not comprehensive. There is very little information about the two-dimensional expression of unit pressure on the contact surface, but also because of the complicated formula, poor accuracy and inconvenient application, it is difficult to popularize. In this paper, according to the flow pattern of metal particles on the contact surface and the law of friction force, the partial differential pressure equation is established according to the relationship between the pressure field and the friction force field. Then, the plane deformation condition of the symmetry plane of the deformation body is taken as the boundary condition , So as to obtain a two-dimensional expression of unit pressure distribution of simple form and wide adaptability, p = xp (x, 0) p (0, y) / p mzx = p (x, y). Compression tests were conducted on lead specimens of cylinders and rectangular parallels. Coordinate grids are engraved on the contact surface. Based on the analysis of the grid deformation after deformation, the expression of unit pressure isobars in the adhesion zone, braking zone and sliding zone can be obtained by the formula . The total deforming force is calculated using the formulas in this article and the formulas of other authors, and then compared with the measured values at the time of testing. The comparison results show that the calculated value given by the formula in this paper is the closest to the measured value and the average error is within ± 10%. But also on the basis of this article to continue the development of the contact surface to find the flow of metal streamline equation and the breadth of the formula, and the constraints of the perimeter (such as forging, rolling in the hole, etc.) the binding force law.