Simulation model of spline interpolation of piecewise linear trajectory for CNC machine tools

Ivanov V.M.
 pdf (362K)

In traditional CNC systems, each segment of a piecewise linear trajectory is described by a separate block of the control program. In this case, a trapezoidal trajectory of movement is formed, and the stitching of individual sections is carried out at zero values of speed and acceleration. Increased productivity is associated with continuous processing, which in modern CNC systems is achieved through the use of spline interpolation. For a piecewise linear trajectory, which is basic for most products, the most appropriate is a first-degree spline. However, even in the simplest case of spline interpolation, the closed nature of the basic software from leading manufacturers of CNC systems limits the capabilities of not only developers, but also users. Taking this into account, the purpose of this work is a detailed study of the structural organization and operation algorithms of the simulation model of piecewise linear spline interpolation. Limitations on jerk and acceleration are considered as the main measure to reduce dynamic processing errors. In this case, special attention is paid to the S-shaped shape of the speed curve in the acceleration and deceleration sections. This is due to the conditions for the implementation of spline interpolation, one of which is the continuity of movement, which is ensured by the equality of the first and second derivatives when joining sections of the trajectory. Such a statement corresponds to the principles of implementing combined control systems of a servo electric drive, which provide partial invariance to control and disturbing effects. The reference model of a spline interpolator is adopted as the basis of the structural organization. The issues of processing scaling, which are based on a decrease in the vector speed in relation to the base value, are also considered. This allows increasing the accuracy of movements. It is shown that the range of changes in the speed of movements can be more than ten thousand, and is limited only by the speed control capabilities of the actuators.

Keywords: piecewise linear trajectory, jerk, S-shaped speed curve, spline, processing scale, servo drive
Citation in English: Ivanov V.M. Simulation model of spline interpolation of piecewise linear trajectory for CNC machine tools // Computer Research and Modeling, 2025, vol. 17, no. 2, pp. 225-242
Citation in English: Ivanov V.M. Simulation model of spline interpolation of piecewise linear trajectory for CNC machine tools // Computer Research and Modeling, 2025, vol. 17, no. 2, pp. 225-242
DOI: 10.20537/2076-7633-2025-17-2-225-242
URL: http://crm-en.ics.org.ru/journal/article/3596/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Copyright © 2009–2025 Institute of Computer Science