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<p>In general, the tool center point (TCP) accuracy of machine tools can be enhanced by minimizing geometric error (GE) and tracking error (TE). However, five-axis machining for sculptured surfaces has led to increased dynamic error (DE), driven by vibrations and deformations under the real-time influence of machine dynamics and motion parameters. These characteristics in DE align closely with the core concept of digital twins, which involve real-time interactions between physical objects and their virtual models to map system state changes. Hence, a TCP trajectory prediction model (TTPM) of five-axis machine tools (FAMTs) is proposed to achieve precise trajectory prediction based on a digital twin, integrating DE with GE and TE. Firstly, a TCP dynamic error model (TDEM) is established to estimate DE considering multi-axis coupling and varying structural dynamics in FAMTs. Simultaneously, a forward kinematic model (FKM) is constructed using screw theory to account for GE and TE. Then, by integrating the TDEM and FKM, the proposed TTPM predicts TCP trajectories considering DE, GE, and TE. Finally, the TTPM is verified through the R-test. The results reveal that the proposed model exhibits an average deviation of 3.80 µm and a maximum deviation of 6.53 µm in high-speed and high-acceleration trajectories, resulting in a 14.81% improvement in root mean square error and a 22.13% enhancement in trajectory error prediction accuracy on average. The proposed model achieves high prediction accuracy with low computational cost and can be integrated into digital twin systems.</p>

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A high-fidelity TCP trajectory prediction model considering dynamic errors for digital twins of five-axis machine tools

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Shuo Liu,
  • Dun Lyu,
  • Luis Norberto López de Lacalle,
  • Jokin Munoa,
  • Gorka Aguirre

摘要

In general, the tool center point (TCP) accuracy of machine tools can be enhanced by minimizing geometric error (GE) and tracking error (TE). However, five-axis machining for sculptured surfaces has led to increased dynamic error (DE), driven by vibrations and deformations under the real-time influence of machine dynamics and motion parameters. These characteristics in DE align closely with the core concept of digital twins, which involve real-time interactions between physical objects and their virtual models to map system state changes. Hence, a TCP trajectory prediction model (TTPM) of five-axis machine tools (FAMTs) is proposed to achieve precise trajectory prediction based on a digital twin, integrating DE with GE and TE. Firstly, a TCP dynamic error model (TDEM) is established to estimate DE considering multi-axis coupling and varying structural dynamics in FAMTs. Simultaneously, a forward kinematic model (FKM) is constructed using screw theory to account for GE and TE. Then, by integrating the TDEM and FKM, the proposed TTPM predicts TCP trajectories considering DE, GE, and TE. Finally, the TTPM is verified through the R-test. The results reveal that the proposed model exhibits an average deviation of 3.80 µm and a maximum deviation of 6.53 µm in high-speed and high-acceleration trajectories, resulting in a 14.81% improvement in root mean square error and a 22.13% enhancement in trajectory error prediction accuracy on average. The proposed model achieves high prediction accuracy with low computational cost and can be integrated into digital twin systems.