Modeling mated surfaces with the required parameters

Abstract

This paper has proposed improving the methods of circular and screw conversion, to be used in the design of cutting tools and toothing that include complex mated surfaces. Underlying the improvement of both methods is the construction of a mathematical base and the development of a computer subprogram, based on it, in the MATLAB system. During the research, the original screw-type curved surface and the curvilinear generatrix axis were formed on the basis of improved methods, taking into consideration the exclusion of interference at the design stage. A comprehensive solution to this problem is important for the manufacture of products by rolling. Given this, the original instrumental surface of the cutting tool takes into consideration the pairing condition between the article’s and tool’s points. The result, when designing gears and cutting tools using the proposed improved methods, assigns the curvilinear surface parametrically, represented by two-dimensional arrays characterizing its coordinates. To avoid interference at the design stage, it is necessary to analyze the intersection of the axis of the curvilinear generatrix with horizontal planes. That would make it possible, when machining an article, to avoid cutting, jamming, as well as the dangerous concentration of stresses. The accuracy and reliability of a wide range of articles in machines and machinery and other kinematic pairs also improve. The proposed improvement of circular and screw conversion methods to simulate curvilinear mated surfaces that exclude interference at the design stage is of practical interest in machine building

Formation of conjugate curved surfaces that exclude interference

“…This is the mathematical justification for rotating the coordinates of a given parametric surface (Fig. 3), which was more convenient [10] for obtaining the required curvilinear conjugate shapes of the product. The intersection of the axis of the curvilinear generatrix with horizontal planes is carried out according to formula (3).…”

“…In [10], studies were carried out on conjugate curved surfaces with a decrease in contact stresses to eliminate interference during gear operation. Modernized methods of circular and helical transformation made it possible to model the original curved surface to obtain the required curved conjugate shapes of the product.…”