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190年前就已提出,对犁这样一种属于全人类具有长期广泛使用历史的重要工具,其曲面应该能用科学的标志——数学解析法来描述和设计。至今,国内外各种直元线、曲元线和其他设计法联同其参数选择仍然基本上属于经验式,因为都不能将所耕土壤的物理力学特性量、耕后要求达到的土垡状况、耕速阻力等工况与曲面形状曲面参数在设计中有机地联系起来。本文提出一种企图将这些因素联系起来的设计法。犁耕中土垡的运动仍用土垡剖面的翻转来描述。犁体曲面即为曲率在不断变化的土垡剖面底边线在翻转中扫描所成的空间曲面,其解析式为泛函ψ(x,y,z)=f_1(x)y~2+f_2(x)y+f_3(x)z+f_4(x)=0。土垡剖面底边任意点土粒在曲面上的运动迹线为以土垡剖面底边的底点为瞬时轴心,以从轴心至该任意点距离为半径的柱面与曲面的交线,其方程为(?)。通过对土粒在曲面上运动迹线的微分几何分析,建立了不同土壤在不同耕速下土垡合理翻转而阻力最小的几项曲面主要参数的选择判断式。导出了制作曲面时所需的各条样板曲线的方程式。最后规定了整个曲面设计的具体步骤。
It has been proposed 190 years ago that the plow should be able to be described and designed in terms of the scientific symbolic-analytic method of mathematics, an important tool that has a long and widespread history of belonging to mankind. So far, all kinds of straight line, curved line and other design methods at home and abroad still belong to empiricism together with their choice of parameters because neither the physical and mechanical properties of the cultivated soil, the soil conditions required for plowing , Tillage resistance and other conditions and surface shape and surface parameters in the design of organically linked. This article presents a design approach that attempts to relate these factors. Soil plowing in the soil movement is still used to describe the soil 垡 section of the flip. The plow body surface is the space surface that the curvature curves at the bottom edge of the changing soil 扫 section in the inversion. The analytical formula is ψ (x, y, z) = f_1 (x) y ~ 2 + f_2 x) y + f_3 (x) z + f_4 (x) = 0. The moving trace of soil particles on the curved surface at any point on the bottom of the soil profile is the instantaneous axis at the bottom of the bottom of soil profile and the intersection of the cylindrical surface and the curved surface whose radius is from the axis to the arbitrary point , The equation is (?). Based on the differential geometric analysis of the trajectories of the soil particles on the curved surface, the selection criteria of several surface parameters of the soil with reasonable tilting of the soil at different tillage velocities with the least resistance are established. The equations for the various sample curves needed to create the surface are derived. Finally, the entire surface of the specific design steps.