MATHEMATICAL MODELING AND SOLUTION ALGORITHMS OF GEOMETRIC PROBLEMS IN NUMERICALLY CONTROLLED MACHINES
DOI:
https://doi.org/10.5281/zenodo.18583934Keywords:
interpolation, numerical control, technological equipment, machining quality, technological process, geometric problem.Abstract
At present, strengthening the practical orientation of education in the training of specialists is one of the most
relevant scientific and practical challenges. This issue can be effectively addressed by systematically motivating the
educational process and integrating theoretical knowledge with practical application. The main objective of this study is to
scientifically demonstrate the practical application of knowledge acquired in mathematics and automation of technological
processes.
The article provides a detailed analysis of solving geometric problems on computer numerical control (CNC) machine
tools. Within the framework of the study, an interpolation algorithm ensuring the movement of machine working elements
is implemented, and the principles of its operation as well as methods for organizing motion along a specified trajectory
are examined. The scientific novelty of the research lies in substantiating the possibility of high-precision machining based
on accurate determination of cutting tool motion geometry and correct formulation of the geometric problem.
The practical significance of the work is determined by the development of a real CNC machining control program using
interpolation algorithms within the part coordinate system. The study employs general scientific and specialized research
methods, including observation, comparison, analysis, and synthesis. The obtained results demonstrate that the proposed
approach enhances productivity, improves machining accuracy, and reduces time consumption.
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