Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Research of Parametric Interpolation Approaches for Smoothing a Piecewise Linear Toolpath

Author(s):

Alexander Alexandrovich Zelensky

Candidate of Technical Sciences, Associate Professor,
Director of the Institute of Digital Intelligent Systems,
Moscow State University of Technology "STANKIN"

zelenskyaa@gmail.com

Tagir Khabibovich Abdullin

leading engineer, lecturer of the Department of
“Industrial Electronics and Intelligent Digital Systems",
Moscow State University of Technology "STANKIN"

everestultimate@yandex.ru

Vadim Viktorovich Dubovskov

leading engineer, lecturer of the Department of
“Industrial Electronics and Intelligent Digital Systems",
Moscow State University of Technology "STANKIN"

dtnt1121@gmail.com

Yuri Vladimirovich Ilyukhin

Doctor of Technical Sciences,
Professor of the Department of Robotics and Mechatronics,
Moscow State Technical University "STANKIN"

ilyv-2@mail.ru

Abstract:

The paper considers the basic methods of parametric interpolation of tool trajectory during contour machining of products having complex geometric surface shape. The paper applies an approach based on inserting cubic B-splines into the initial piecewise linear trajectory and implementing linear and parametric interpolation algorithms which allow increasing machining productivity. When there is no explicit analytical dependence spline parameters on its length of the corresponding trajectory segment parametric interpolation is performed. Therefore, numerical methods are used for formation of interpolated points along the curve, which have different accuracy of approximation of the spline parameter and have a significant impact on the quality of machining of the product due to the unstable feed rate. A number of numerical experiments have been conducted to select the most effective parametric interpolation algorithm for a trajectory that has a geometric continuity of G2. The best results are shown by the second-order Runge-Kutta algorithm with a compensating approximation scheme, which is the best choice for control systems of machine tools and industrial robots for high-precision and high-speed machining of parts with complex geometries.

Keywords

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