Kholodnyak Y. Variative discrete geometrical modelling of one-dimensional contours on the bases of basis triangles according to the given law of curvature change

The object of the research is variative discrete geometric modelling of curves arbitrary configuration which specified in the Cartesian coordinate system, with ensuring laws of change of differential-geometric characteristics. The purpose of the research is the development, algorithmic and program realization and practical application of the method of variable discrete geometric modelling of plane contours with ensuring laws of change provisions of tangents and values of the radiuses of curvature along the curve. During the studies used interpolation methods, numerical methods, methods of discrete modelling of plane contours. In the process of development of the method defined conditions, the fulfillment of which makes it possible to modelling of the second order of smoothness contour with monotonous change of radiuses of curvature and developed an algorithm of formation such contours; developed a method for forming of a contour of on areas that contain the point changes of increase and decrease of the radiuses of curvature and inflection points; proposed a scheme to ensure the continuity of the rate of change of the radiuses of curvature along the contour; designed surface of the blade of rotary machine and impeller of centrifugal single-stage pump. Ensuring laws of change of differential-geometric characteristics along the elements of carcass of surfaces makes it possible to improve the dynamic quality of the surfaces and reduce energy loss in the product. Results of the study adopted for the introduction on the foundry company "MELT"; LLC "Melitopol factory of turbocompressors"; PE "Tavriya Turbo Plus"; LLC "PPCF "Special hydraulic machines"; PPC "ROSTA"; LLC "PPC "CAD Center".