Abstract
This work aimed to develop a thermal error compensation system for a three-axis computer numerical control (CNC) machine, a 20-year-old CNC milling machine. An interferometric laser was used to acquire the error measurements, and a compensation model was developed using a radial basis function neural network. The model was implemented directly via the machine programmable logic controller. The model was able to predict the observed errors under the acquired conditions (using supervised learning), replicating the trends in the errors. A further conclusion was that the model could differentiate between errors arising at room temperatures from thermal errors found during machine operation at higher temperatures. For practical validation, 360 data points were acquired and tested under conditions not used for model training. The neural network model was implemented directly in the controller of the CNC machine using ladder logic blocks as an extra routine accessed simultaneously during machine operation. The resulting calculus value was added as a correction value to the final axis position instantaneously, based on the instant axis position and instant temperatures at the bearings. The system was able to apply the corrections suggested by the model with a strong alignment between the real corrected positioning and the positioning predicted by the model. Preliminary results obtained under higher-temperature operating conditions indicated a reduction in the maximum thermal error up to 77.8%, and for room temperatures, the positioning errors were compensated at average rates of 33%.
Similar content being viewed by others
References
Bryan J (1990) International status of thermal error research. CIRP Ann 39:645–656
Abdulshahed AM, Longstaff AP, Fletcher S (2015) The application of ANFIS prediction models for thermal error compensation on CNC machine tools. Appl Soft Comput J 27:158–168
Yue HT, Guo CG, Li Q, Zhao LJ, Hao GB (2020) Thermal error modeling of CNC milling machining spindle based on an adaptive chaos particle swarm optimization algorithm. J Braz Soc Mech Sci Eng 42:427. https://doi.org/10.1007/s40430-020-02514-z
Liu K, Sun M, Wu Y, Zhu T (2016) Comparison of accuracy stability using a thermal compensator and grating ruler. J Braz Soc Mech Sci Eng 38:2403–2411. https://doi.org/10.1007/s40430-016-0491-0
Miao EM, Gong YY, Niu PC (2013) Robustness of thermal error compensation modeling models of CNC machine tools. Int J Adv Manuf Technol 69:2593–2603
Shi H, Jiang CP, Yan ZZ, Tao T, Mei XS (2020) Bayesian neural network-based thermal error modeling of feed drive system of CNC machine tool. Int J Adv Manuf Technol 108:3031–3044
Papananias M, McLeay TE, Obajemu O, Mahfouf M, Kadirkamanathan V (2020) Inspection by exception: a new machine learning-based approach for multistage manufacturing. Appl Soft Comput J 97:1067–1087
Mareš M, Horejš O, Havlík L (2020) Thermal error compensation of a 5-axis machine tool using indigenous temperature sensors and CNC integrated Python code validated with a machined test piece. Precis Eng 66:21–30
Zhou H, Hu P, Tan H, Chen J, Liu G (2018) Modelling and compensation of thermal deformation for machine tool based on the real-time data of the CNC system. Procedia Manuf 26:1137–1146
Reddy TN, Shanmugaraj V, Vinod P, Gopi Krishna S (2019) Real-time thermal error compensation strategy for precision machine tools. Mater Today Proc 22:2386–2396
Reddy TN, Shanmugaraj V, Prakash V, Gopi Krishna S, Narendranath S, Shashi Kumar PV (2014) Real-time thermal error compensation module for intelligent ultra precision turning machine (IUPTM). Procedia Mater Sci 6:1981–1988
Li ZJ, Zhao CY, Lu ZC (2020) Thermal error modeling method for ball screw feed system of CNC machine tools in X-axis. Int J Adv Manuf Technol 106:5383–5392
Deng Y, Liu J, Li D (2021) Development of a thermal compensator based on PLC for Fanuc CNC system. Int J Adv Manuf Technol 112:1885–1902
Liu J, Ma C, Gui H, Wang S (2021) Thermally-induced error compensation of spindle system based on long short term memory neural networks. Appl Soft Comput 102:1070–1094
De Oliveira LW, Campos Rubio JC, Duduch JG, Maciel de Almeida PE (2015) Correcting geometric deviations of CNC machine tools: an approach with artificial neural networks. Appl Soft Comput J 36:114–124
Buhmann MD (2003) Radial basis functions: theory and implementations. Cambridge University Press
Piret C, Hanert E (2013) A radial basis functions method for fractional diffusion and equations. J Comput Phys 238:71–81
Martínez CAT, Fuentes C (2017) Applications of radial basis function schemes to fractional partial differential equations, fractal analysis: applications in physics, Engineering and Technology. Fernando Brambila, IntechOpen DOI: https://doi.org/10.5772/67892
Broomhead D, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355
Skansi S (2018) Introduction to deep learning: from logical calculus to artificial intelligence. Springer. https://doi.org/10.1007/978-3-319-73004-2
Aggarwal C (2018) Neural networks and deep learning. Springer. https://doi.org/10.1007/978-3-319-94463-0
Cover TM (1965) Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Trans Electro Comput EC-14(3):326–334. https://doi.org/10.1109/PGEC.1965.264137
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Izabel Fernanda Machado.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
de Farias, A., dos Santos, M.O. & Bordinassi, E.C. Development of a thermal error compensation system for a CNC machine using a radial basis function neural network. J Braz. Soc. Mech. Sci. Eng. 44, 494 (2022). https://doi.org/10.1007/s40430-022-03812-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-022-03812-4