Mathematical 3D-modeling in the formation process of the overhauled surfaces in the repair industry

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V.V.Protsiv,, Dnipro University of Technology, Dnipro, Ukraine, email: This email address is being protected from spambots. You need JavaScript enabled to view it.

V.U.Grigorenko,, Dnipro University of Technology, Dnipro, Ukraine, email: gvu135gvu@

H.O.Veremei,, Chernihiv Polytechnic National University, Chernihiv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2022, (2): 124 - 128


Mathematical representation of the geometry of the overhauled valve seat surfaces in the shape-forming process in the auto repair industry.

The research methods were based on: the theory of cutting and metalworking scientific positions, theoretical foundations of the technology of mechanical engineering and overhaul repairs; the basics of technical operation and vehicle structure; provisions of standardization, technical measurements; means of mathematical modelling, statistics and programming.

The geometric 3D-model of the processing surfaces of valve seats has been presented, which is used in the overhaul process of these parts, which is basic in the general model of the shape-forming system, which allows controlling the shaping parameters with the required precision due to the structure of the model itself and introducing the results of processing particular models: interpolation (to assess the worn surfaces state) and optimization (for determining the volume of cut material and setting cutting conditions).

For the first time a particular mathematical 3D-model of the general shape-forming system has been developed, consisting of other particular mathematical models (interpolation and optimization), which gives a geometric representation of the processed valve seat surfaces within their overhaul in the auto repair industry.

Practical value.
The proposed mathematical 3D-model allows:

- implementing the shape-forming process adequately within the simultaneous boring of three inner conical surfaces by copying with a profile cutting plate, which provides the required parameters of precision and quality of processing during the valve seats overhaul;

- implementing the results of the flaw detection process of worn surfaces of valve seats with a complex-variable topography due to usage of the of roundness- and profile-diagrams and method based on an interpolation geometric 3D-model;

- introducing an optimization model to determine the optimal volumes of cut material and the rational cutting modes select.

The MathCAD software package has been developed, which allows having a graphical performance of the formed surface based on the interpolation model.

processed valve seat surfaces, shape-forming process and function, cutting modes in metalworking, precision and quality parameters of processing, valve seat overhaul


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