Morozova A. Mathematical modeling of aviation industry objects surfaces and machine-building parts for 3D-printer implementation

The dissertation is devoted to the development of methods for three-dimensional geometric objects modeling and the implementation of the constructed equations of the surfaces of aviation industry objects and machine-building parts on a 3D-printer. The algorithms using R-functions have been developed for the phased construction of mathematical models of engineering objects, including screws with constant and variable twist pitch, screw swirls, pipes with local twist and twisted pipes of complex cross section. The method of obtaining equations of geometric objects with a translational and cyclic symmetry type in 3D, which was used to construct the equations of open and half-closed impellers of centrifugal pumps with radial and curved blades, is investigated. The methods have been developed for obtaining equations of UAV surfaces of various types using constructive means of the R-functions theory. The blending on the frame was used for inventting the UAV surface equations. The equations of the surfaces of launch vehicles and the model of the spacecraft are received. The constructed mathematical models of UAVs, engineering and aerospace objects are implemented on a 3D-printer at the A. Pidhornyi Institute of Mechanical Engineering Problems of the NAS of Ukraine. The reliability of the results obtained, their adequacy to the designed objects is confirmed by visualization both in the operating conditions of the RFPreview program and implementation on a 3D-printer. Analytical recording of designed objects makes it possible to use alphabetic geometric parameters, complex superpositions of functions, which, in turn, allows you to quickly change their structural elements. The positivity property of the developed functions at the internal points of the object is very convenient for 3D printing implementing. Keywords: R-functions theory, 3D-printing, 3D-modeling, 3D-printer, engineering details, aerospace objects, UAVs, augers, centrifugal pumps, vizualization, mathematical model, normalized equations, symmetry.