A high-fidelity simulation with PINN-driven thermal reconstruction framework for real-time tool error prediction in air-cooled motorised spindles

Abstract In the context of Industry 4.0, manufacturing enterprises face challenges in achieving high production rates and part accuracy with machine tools employing high-speed motorised spindles. Thermal stability of the spindle-shaped by its intricate geometry, transient heat flow, and dynamic conditions-directly influences structural deformations and, in turn, affects the part’s accuracy. Several modelling approaches have been reported to predict tool deformation (TD) through thermal and thermo-mechanical routes. However, these models’ accuracy is limited by (i) the assumption of thermal parameters, and (ii) overlooking spindle cooling mechanisms. In addition, these models’ computational cost is high, hence unsuitable for real-time applications. To address these challenges, the present study proposes an advanced framework integrating high-fidelity multi-physics simulations (MPS) with physics-informed neural network (PINN) to enable faster computation. The MPS incorporates conjugate heat transfer to accurately capture coupled fluid-solid-thermal interactions, allowing precise temperature and deformation predictions under varying operating conditions. Although accurate, MPS is computationally intensive; this is addressed by integrating a PINN, reducing reliance on experimental datasets, lowering computational load, and ensuring strong generalisation to unseen conditions. Experimental validation of the proposed framework across spindle speeds of 10 000 rpm, 15 000 rpm, and 18 000 rpm reveals that the average MAE for temperature predictions at critical hotspots using the MPS is 0.45 °C, 0.60 °C, and 0.38 °C for the front bearing, rear bearing, and motor, respectively. Compared with the MPS, the MPS + PINN framework exhibited average MAEs of 1.15 °C, 0.95 °C, and 2.5 °C at the corresponding locations. The average root-mean-square-error for axial TD using the MPS is 2.42 µm, while the MPS + PINN approach yields 3.12 µm. Hence, the proposed framework demonstrated an accurate spindle performance estimation, reducing computational time by 92% and lowering hardware requirements, facilitating real-time implementation.