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Data-Driven Temperature Modelling of Machine Tools by Neural Networks: A Benchmark

C. Coelho, M. Hohmann, D. Fernández, L. Penter, S. Ihlenfeldt, O. Niggemann

TL;DR

This work addresses thermally induced errors in machine tools by shifting from direct error compensation to data-driven prediction of thermal fields. It introduces a modular framework with a neural-network temperature predictor that outputs high-resolution $T(\mathbf{x},t)$ and $q(\mathbf{x},t)$, plus swappable error computation and correction components to realise various error types. The approach relies on FEM-generated data under multiple initial conditions and employs a two-stage node reduction to minimize sensor requirements, followed by benchmarking six time-series NN architectures in specialised and generalised settings. Results demonstrate accurate, low-cost prediction of temperature and heat flux fields, with GRU and BiLSTM often delivering the best performance, while generalized heat-flux prediction remains more challenging and benefits from richer training data. Overall, the framework enables flexible, generalisable thermal error correction suitable for digital-twin workflows and real-time control, while highlighting the importance of dataset diversity and sensor placement for robust generalisation.

Abstract

Thermal errors in machine tools significantly impact machining precision and productivity. Traditional thermal error correction/compensation methods rely on measured temperature-deformation fields or on transfer functions. Most existing data-driven compensation strategies employ neural networks (NNs) to directly predict thermal errors or specific compensation values. While effective, these approaches are tightly bound to particular error types, spatial locations, or machine configurations, limiting their generality and adaptability. In this work, we introduce a novel paradigm in which NNs are trained to predict high-fidelity temperature and heat flux fields within the machine tool. The proposed framework enables subsequent computation and correction of a wide range of error types using modular, swappable downstream components. The NN is trained using data obtained with the finite element method under varying initial conditions and incorporates a correlation-based selection strategy that identifies the most informative measurement points, minimising hardware requirements during inference. We further benchmark state-of-the-art time-series NN architectures, namely Recurrent NN, Gated Recurrent Unit, Long-Short Term Memory (LSTM), Bidirectional LSTM, Transformer, and Temporal Convolutional Network, by training both specialised models, tailored for specific initial conditions, and general models, capable of extrapolating to unseen scenarios. The results show accurate and low-cost prediction of temperature and heat flux fields, laying the basis for enabling flexible and generalisable thermal error correction in machine tool environments.

Data-Driven Temperature Modelling of Machine Tools by Neural Networks: A Benchmark

TL;DR

This work addresses thermally induced errors in machine tools by shifting from direct error compensation to data-driven prediction of thermal fields. It introduces a modular framework with a neural-network temperature predictor that outputs high-resolution and , plus swappable error computation and correction components to realise various error types. The approach relies on FEM-generated data under multiple initial conditions and employs a two-stage node reduction to minimize sensor requirements, followed by benchmarking six time-series NN architectures in specialised and generalised settings. Results demonstrate accurate, low-cost prediction of temperature and heat flux fields, with GRU and BiLSTM often delivering the best performance, while generalized heat-flux prediction remains more challenging and benefits from richer training data. Overall, the framework enables flexible, generalisable thermal error correction suitable for digital-twin workflows and real-time control, while highlighting the importance of dataset diversity and sensor placement for robust generalisation.

Abstract

Thermal errors in machine tools significantly impact machining precision and productivity. Traditional thermal error correction/compensation methods rely on measured temperature-deformation fields or on transfer functions. Most existing data-driven compensation strategies employ neural networks (NNs) to directly predict thermal errors or specific compensation values. While effective, these approaches are tightly bound to particular error types, spatial locations, or machine configurations, limiting their generality and adaptability. In this work, we introduce a novel paradigm in which NNs are trained to predict high-fidelity temperature and heat flux fields within the machine tool. The proposed framework enables subsequent computation and correction of a wide range of error types using modular, swappable downstream components. The NN is trained using data obtained with the finite element method under varying initial conditions and incorporates a correlation-based selection strategy that identifies the most informative measurement points, minimising hardware requirements during inference. We further benchmark state-of-the-art time-series NN architectures, namely Recurrent NN, Gated Recurrent Unit, Long-Short Term Memory (LSTM), Bidirectional LSTM, Transformer, and Temporal Convolutional Network, by training both specialised models, tailored for specific initial conditions, and general models, capable of extrapolating to unseen scenarios. The results show accurate and low-cost prediction of temperature and heat flux fields, laying the basis for enabling flexible and generalisable thermal error correction in machine tool environments.

Paper Structure

This paper contains 24 sections, 19 equations, 5 figures, 29 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Thermal Errors in Machine Tools
  4. Types of Thermally Induced Errors
  5. Thermo-elastic Deformations
  6. Position Drift
  7. Orientation and Volumetric Errors
  8. Neural Networks for Time-series
  9. Recurrent Neural Networks
  10. Long-Short Term Memory
  11. Gated-Recurrent Unit
  12. Bidirectional Long-Short Term Memory
  13. Transformer
  14. Temporal Convolutional Networks
  15. Method
  16. ...and 9 more sections

Figures (5)

  • Figure 1: Process chain: from heat losses to errors at the TCP. Adapted from ihlenfeldt2020adjustment.
  • Figure 2: Schematic representation of the proposed thermal error compensation framework, consisting of three modules: (1) a temperature predictor to forecast temperature distributions given a known initial thermal field; (2) a swappable error computation module, which employs different strategies to compute various errors; (3) a swappable error correction module, which, given the error, computes the corresponding compensation.
  • Figure 3: Schematic representation of the temperature predictor training pipeline, consisting of: a machine tool digital twin is constructed via CAD and FEM simulations to generate thermal field and heat flux datasets under different initial conditions; through correlation analysis, the lower informative nodes are removed for NN training, minimising prediction error on retained nodes; for inference, disregarded node values are reconstructed using retained nodes.
  • Figure 4: Comparison of thermal fields of RUN1 by interpolating temperatures from 29 sensors predicted the specialised temperature predictor with different NN architectures, and ANSYS simulation.
  • Figure 5: Comparison of thermal fields of Run3 by interpolating temperatures from 29 sensors predicted using different NN architectures, generalised approach and ANSYS simulation, also used as displayer.

Theorems & Definitions (1)

  • Definition 1: Two-stage node selection strategy