R-functions and chevron surfaces in machine building

Abstract

In this article, was developed methodologies and constructed equations of different heat transfer surfaces of the fins, including Chevron with the help of R-functions theory. The resulting equations of surfaces have been implemented on a 3D printer. Ribbing not only increases the heat transfer surface, but also has a great influence on the hydrodynamics of the flow, and thus on the heat transfer coefficient. In experiments with various methods of finning of Fuel rod claddings were developed more favorable shape of the fins, the so-called Chevron and multi-zone. With the Chevron ribbing the entire surface of the shell is divided into four, six or eight sectors and adjacent sectors of the spiral are located symmetrically relative to the longitudinal axis. Because of the complexity and high cost of manufacturing Chevron transmission is used less frequently than helical, i.e. only in those cases when it is required to transmit high power and high speed, and the axial load of junk. On special machines V-wheels are made all of one piece. A disadvantage of the Chevron ribbing is the high complexity and cost of manufacturing. Thanks to the technology of 3D printing, these deficiencies can be remedied, because the benefits of using 3D printers is reducing the cost of production, reduction of terms of its appearance on the market, the modeling of objects of any shape and complexity, rapidity and high precision manufacturing, the use of different materials, including concrete, hydrogel, wood, metal, plastics, chocolate and even living cells. The article examines the technology of 3D printing. The analysis of the major representation schemes of models of continuous bodies, which revealed significant shortcomings. From the point of view of universality, one of the most promising functional representation, which is based on the use of language implicit mathematical functions with the structural features of the R-functions theory, developed by academician V. L. Rvachev. The analytical description of the designed objects enables to use symbolic geometrical parameters, complicated superposition of functions consequently allowing to change the design elements of these objects. The positivity feature of the built functions in the mid points of the object is convenient to 3D-printing implementing