MODELING SURFACES ACCORDING TO SPECIFIED CONDITIONS BASED ON AN ARRAY OF POINTS

Abstract

The development of technology of design of computer models of surfaces defined by points array, and programs of their processing on the machines with computer numerical control (CNC). The main requirement to the surface of products which interact with the environment, is to ensure a given character of their flow. Functional quality of the surface is ensure by its geometric characteristics. Laminar nature of flow of surfaces can be provided by monotonous change of curvature values, torsion, radiuses of adjoining spheres along the curves that are part of the determinant of the surface. The initial points set and geometrical characteristics of the curve are the initial data for the formation of linear elements of carcass of surface. The methods of formation of plane and spatial curves with regular change of characteristics on the basis of an arbitrary points set is developed. At each site, which is bounded by successive points  the area within which are all the curves corresponding to the conditions of the problem is determined. The resulting curve, which is represented by a new point series consisting of an arbitrarily large number of points, it is considered formed when the area of its possible location is less than a predetermined value. Practical application of the proposed technology is demonstrated by the example of designing of surfaces inter scapular channel of impeller of the turbocharger and the working surface of the disk cutter for loosening the soil. The developed technology for the design of surfaces of complex technical products includes the creation of geometric models of surfaces and control programs for their processing on CNC machines. From the initial array of points allocated subset - point sets, on the basis of which the linear elements of the carcass of surface are formed. A computer model of the surface is created on the basis of discretely carcass the line represented by the families of longitudinal and transversal curves. The control program is created in the automated mode using the CAM-packets based on three-dimensional computer model which is formed in a package of three-dimensional parametric modeling SolidWorks.

Keywords: dynamic surface; carcass of surface; linear element of model; discretely represented curve; regular change of curvature and torsion