Abstract
Thermal error of machine tools has a huge influence on the accuracy of the workpiece. However, the nonlinearity of the thermal error limits the accuracy and robustness of the prediction model. With the rapid advancement in artificial intelligence, this paper presents a novel thermal error modeling method based on random forest. The model’s hyper-parameters are easy to be optimized by grid searching method integrating with cross validation. The temperature features are measured as the model input. Based on the out-of-bag data generated during modeling process, the proposed model itself can simultaneously evaluate the temperature feature importance through comparing the decrease in model’s the prediction accuracy after randomly shuffling the value of the target feature. Moreover, to enhance the model performance and reduce the measurement and computational cost, the method of selecting key temperature points are presented to exclude the redundant features through iteratively eliminating the least important feature and comparing the prediction accuracy under different feature combinations. Furthermore, the hysteresis effect between temperature and deformation is also considered. The method of determining the time lag is proposed through permuting the original time series of the target feature while keeping the remainder constant and comparing the resultant relative importance. A thermal error experiment validates the accuracy and robustness of the proposed model which can continuously maintain the prediction accuracy of over 90% in spite of varying operation conditions. Compared to conventional machine learning methods, the proposed model requires less training data, enables faster and more intuitive parameter tuning, achieves higher prediction accuracy, and has stronger robustness.
Similar content being viewed by others
References
Abdulshahed, A. M., Longstaff, A. P., Fletcher, S., & Myers, A. (2015). Thermal error modelling of machine tools based on ANFIS with fuzzy c-means clustering using a thermal imaging camera. Applied Mathematical Modelling, 39(7), 1837–1852. https://doi.org/10.1016/j.apm.2014.10.016
Abdulshahed, A. M., Longstaff, A. P., Fletcher, S., & Potdar, A. (2016). Thermal error modelling of a gantry-type 5-axis machine tool using a Grey Neural Network Model. Journal of Manufacturing Systems, 41, 130–142. https://doi.org/10.1016/j.jmsy.2016.08.006
Bardak, S., Bardak, T., Peker, H., Sözen, E., & Çabuk, Y. (2021). Predicting effects of selected impregnation processes on the observed bending strength of wood, with use of data mining models. BioResources, 16(3), 4891–4904. https://doi.org/10.15376/biores.16.3.4891-4904
Bardak, S., Tiryaki, S., Nemli, G., & Aydın, A. (2016). Investigation and neural network prediction of wood bonding quality based on pressing conditions. International Journal of Adhesion and Adhesives, 68, 115–123. https://doi.org/10.1016/j.ijadhadh.2016.02.010
Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
Fujishima, M., Narimatsu, K., Irino, N., & Ido, Y. (2018). Thermal displacement reduction and compensation of a turning center. CIRP Journal of Manufacturing Science and Technology, 22, 111–115. https://doi.org/10.1016/j.cirpj.2018.04.003
Geurts, P., Ernst, D., & Wehenkel, L. (2006). Extremely randomized trees. Machine Learning, 63(1), 3–42. https://doi.org/10.1007/s10994-006-6226-1
Grama, S. N., Mathur, A., & Badhe, A. N. (2018). A model-based cooling strategy for motorized spindle to reduce thermal errors. International Journal of Machine Tools and Manufacture, 132, 3–16. https://doi.org/10.1016/j.ijmachtools.2018.04.004
Hassani, V., Tjahjowidodo, T., & Do, T. N. (2014). A survey on hysteresis modeling, identification and control. Mechanical Systems and Signal Processing, 49(1–2), 209–233. https://doi.org/10.1016/j.ymssp.2014.04.012
Katherasan, D., Elias, J. V., Sathiya, P., & Haq, A. N. (2014). Simulation and parameter optimization of flux cored arc welding using artificial neural network and particle swarm optimization algorithm. Journal of Intelligent Manufacturing, 25(1), 67–76. https://doi.org/10.1007/s10845-012-0675-0
Kovac, P., Rodic, D., Pucovsky, V., Savkovic, B., & Gostimirovic, M. (2013). Application of fuzzy logic and regression analysis for modeling surface roughness in face milling. Journal of Intelligent Manufacturing, 24(4), 755–762. https://doi.org/10.1007/s10845-012-0623-z
Li, Y. X., Yang, J. G., Gelvis, T., & Li, Y. Y. (2006). Optimization of measuring points for machine tool thermal error based on grey system theory. The International Journal of Advanced Manufacturing Technology, 35(7–8), 745–750. https://doi.org/10.1007/s00170-006-0751-8
Li, Y., Zhao, W. H., Lan, S. H., Ni, J., Wu, W. W., & Lu, B. H. (2015). A review on spindle thermal error compensation in machine tools. International Journal of Machine Tools and Manufacture, 95, 20–38. https://doi.org/10.1016/j.ijmachtools.2015.04.008
Liu, H., Miao, E. M., Wei, X. Y., & Zhuang, X. D. (2017). Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm. International Journal of Machine Tools and Manufacture, 113, 35–48. https://doi.org/10.1016/j.ijmachtools.2016.11.001
Liu, J. L., Ma, C., & Wang, S. L. (2020). Data-driven thermally-induced error compensation method of high-speed and precision five-axis machine tools. Mechanical Systems and Signal Processing, 138, 106538. https://doi.org/10.1016/j.ymssp.2019.106538
Liu, J. L., Ma, C., Wang, S. L., Wang, S. B., Yang, B., & Shi, H. (2019). Thermal boundary condition optimization of ball screw feed drive system based on response surface analysis. Mechanical Systems and Signal Processing, 121, 471–495. https://doi.org/10.1016/j.ymssp.2018.11.042
Liu, K., Wu, J., Liu, H., Sun, M., & Wang, Y. (2021). Reliability analysis of thermal error model based on DBN and Monte Carlo method. Mechanical Systems and Signal Processing, 146, 107020. https://doi.org/10.1016/j.ymssp.2020.107020
Lo, C. H., Yuan, J. X., & Ni, J. (1999). Optimal temperature variable selection by grouping approach for thermal error modeling and compensation. International Journal of Machine Tools & Manufacture, 39(9), 1383–1396. https://doi.org/10.1016/S0890-6955(99)00009-7
Mayr, J., Jedrzejewski, J., Uhlmann, E., Alkan Donmez, M., Knapp, W., Härtig, F., Wendt, K., Moriwaki, T., Shore, P., Schmitt, R., Brecher, C., Würz, T., & Wegener, K. (2012). Thermal issues in machine tools. CIRP Annals, 61(2), 771–791. https://doi.org/10.1016/j.cirp.2012.05.008
Miao, E., Gong, Y., Niu, P., Ji, C., & Chen, H. (2013). Robustness of thermal error compensation modeling models of CNC machine tools. The International Journal of Advanced Manufacturing Technology, 69(9–12), 2593–2603. https://doi.org/10.1007/s00170-013-5229-x
Miao, E., Liu, Y., Liu, H., Gao, Z., & Li, W. (2015). Study on the effects of changes in temperature-sensitive points on thermal error compensation model for CNC machine tool. International Journal of Machine Tools and Manufacture, 97, 50–59. https://doi.org/10.1016/j.ijmachtools.2015.07.004
Mosallam, A., Medjaher, K., & Zerhouni, N. (2016). Data-driven prognostic method based on Bayesian approaches for direct remaining useful life prediction. Journal of Intelligent Manufacturing, 27(5), 1037–1048. https://doi.org/10.1007/s10845-014-0933-4
Nti, I. K., Adekoya, A. F., Weyori, B. A., & Nyarko-Boateng, O. (2021). Applications of artificial intelligence in engineering and manufacturing: A systematic review. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-021-01771-6
Ramesh, R., Mannan, M. A., & Poo, A. N. (2002). Support vector machines model for classification of thermal error in machine tools. International Journal of Advanced Manufacturing Technology, 20(2), 114–120. https://doi.org/10.1007/s001700200132
Świć, A., Gola, A., Sobaszek, Ł, & Šmidová, N. (2021). A thermo-mechanical machining method for improving the accuracy and stability of the geometric shape of long low-rigidity shafts. Journal of Intelligent Manufacturing, 32(7), 1939–1951. https://doi.org/10.1007/s10845-020-01733-4
Tan, B., Mao, X., Liu, H., Li, B., He, S., Peng, F., & Yin, L. (2014). A thermal error model for large machine tools that considers environmental thermal hysteresis effects. International Journal of Machine Tools and Manufacture, 82–83, 11–20. https://doi.org/10.1016/j.ijmachtools.2014.03.002
Tan, F., Yin, M., Wang, L., & Yin, G. (2017). Spindle thermal error robust modeling using LASSO and LS-SVM. The International Journal of Advanced Manufacturing Technology, 94(5–8), 2861–2874. https://doi.org/10.1007/s00170-017-1096-1
Tian, L., & Luo, Y. (2020). A study on the prediction of inherent deformation in fillet-welded joint using support vector machine and genetic optimization algorithm. Journal of Intelligent Manufacturing, 31(3), 575–596. https://doi.org/10.1007/s10845-019-01469-w
Xiang, S., Yao, X., Du, Z., & Yang, J. (2018). Dynamic linearization modeling approach for spindle thermal errors of machine tools. Mechatronics, 53, 215–228. https://doi.org/10.1016/j.mechatronics.2018.06.018
Yang, H., & Ni, J. (2003). Dynamic modeling for machine tool thermal error compensation. Transactions of the ASME Journal of Manufacturing Science and Engineering, 125(2), 245–254. https://doi.org/10.1115/1.1557296
Yang, H., & Ni, J. (2005). Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error. International Journal of Machine Tools and Manufacture, 45(4–5), 455–465. https://doi.org/10.1016/j.ijmachtools.2004.09.004
Yin, Q., Tan, F., Chen, H., & Yin, G. (2018). Spindle thermal error modeling based on selective ensemble BP neural networks. The International Journal of Advanced Manufacturing Technology, 101(5–8), 1699–1713. https://doi.org/10.1007/s00170-018-2994-6
Zhang, S., & Wong, T. N. (2018). Integrated process planning and scheduling: An enhanced ant colony optimization heuristic with parameter tuning. Journal of Intelligent Manufacturing, 29(3), 585–601. https://doi.org/10.1007/s10845-014-1023-3
Acknowledgements
This work is financially supported by the National Key R&D Program of China (Grant No. 2018YFB1701204).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhu, M., Yang, Y., Feng, X. et al. Robust modeling method for thermal error of CNC machine tools based on random forest algorithm. J Intell Manuf 34, 2013–2026 (2023). https://doi.org/10.1007/s10845-021-01894-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-021-01894-w