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AI-driven real-time thermal error prediction and compensation for hydrostatic rotary tables in large-scale CNC gear cutting machines
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DOI：10.1007/s00170-026-18683-5.png)
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Abstract
En 中文
Thermal displacement of hydrostatic rotary tables is a critical source of machining error in large-scale CNC gear-cutting machines, especially during long-duration operation under nonuniform thermal loading. This study proposes an FNN–PID thermal compensation framework for Z-axis thermal displacement prediction and hydraulic pressure-command correction. Eight PT100 temperature sensors were installed at representative oil-pad race, static-pressure oil cavity, and core shaft tip locations, while the Z-axis displacement response was measured and synchronized with the thermal data over a 4278 s continuous thermal loading cycle. The measured displacement signal was decomposed into a low-frequency thermal displacement trend and high-frequency residual disturbance, allowing the model to focus on the thermally governed component rather than random vibration or measurement noise. The synchronized thermal response showed clear spatial nonuniformity, with final temperature rises ranging from 20.88 °C to 24.21 °C and a mean spatial temperature spread of 8.52 °C. The optimized feedforward neural network accurately predicted the extracted Z-axis thermal displacement trend, achieving all-data R = 0.9972, R²=0.9943, RMSE = 0.1007 µm, and MAE = 0.0784 µm. Compared with an LSTM model trained on the same dataset, the FNN provided a more favorable balance between prediction accuracy and inference efficiency for real-time compensation. The predicted displacement trend was converted into PID-controlled hydraulic pressure commands for the six hydrostatic oil pockets. The compensated thermal-trend RMS decreased from 2.6804 µm to 0.1007 µm, corresponding to an overall RMS reduction of 96.24%. The calculated pocket-pressure commands remained smooth and bounded around the nominal 3.0 bar operating pressure, with mean values between 3.061 and 3.073 bar and a maximum command range of 0.106 bar. These results demonstrate that the proposed FNN–PID framework can provide accurate, computationally efficient, and hydraulically feasible Z-axis thermal displacement compensation for hydrostatic rotary-table systems.
Keywords:
Hydrostatic rotary table
Thermal error compensation
Z-axis displacement
Feedforward neural network
PID control
Hydraulic pressure command
CNC gear cutting
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