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Volume 13 | Issue 9 | Year 2026 | Article Id. IJME-V13I9P101 | DOI : https://doi.org/10.14445/23488360/IJME-V13I9P101

Thermal Error Prediction of a Three-Axis CNC Machine Tool using an Artificial Neural Network with Optimized Hidden-Neuron Architecture

Nguyen Trong Minh, Dang Duc Thuan

Received Revised Accepted Published
25 Jun 2026 05 Aug 2026 21 Aug 2026 26 Sep 2026

Citation :

Nguyen Trong Minh, Dang Duc Thuan, "Thermal Error Prediction of a Three-Axis CNC Machine Tool using an Artificial Neural Network with Optimized Hidden-Neuron Architecture," International Journal of Mechanical Engineering, vol. 13, no. 9, pp. 1-19, 2026. Crossref, https://doi.org/10.14445/23488360/IJME-V13I9P101

Abstract

Thermal errors are one of the major factors that affect the positioning accuracy of CNC machine tools and hence the quality of the manufactured products. Artificial Neural Networks (ANNs) have been extensively used for modeling the thermal errors, but the impact of hidden-layer architecture on the prediction accuracy remains insufficiently explored. In this study, a Neuron-Optimized Artificial Neural Network (NO-ANN) model is proposed for predicting the thermal positioning errors of a three-axis CNC machine tool. The effect of the hidden-layer neuron configuration was systematically examined to determine the optimal configuration to capture the nonlinear relationship between the thermal variations and positioning errors. The model performance was assessed by Coefficient of Determination (R2), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). The optimized architecture of 11 hidden neurons demonstrated the highest overall performance, with an R2 value of 0.998, RMSE of 1.3247 μm, and MAE of 0.6539 μm, and the model showed high accuracy in both training and testing sets, indicating its robustness and generalization ability. Compared with previously reported thermal error prediction models, the proposed NO-ANN achieved comparable or superior predictive accuracy while requiring only 11 hidden neurons, indicating reduced model complexity and improved computational efficiency. The results indicate that the systematic optimization of hidden-layer neurons can significantly improve the accuracy of thermal error prediction of ANNs, which can be used to effectively compensate for the thermal error in intelligent CNC machining systems.

Keywords

Artificial Neural Network, CNC machine tool, Hidden neuron optimization, Machining precision, Thermal error prediction.

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