APPLICATION OF TOPOLOGICALLY COMPLEX SURFACES IN DIGITAL TWINS OF CYBER-PHYSICAL MACHINE TOOLS

This paper presents an innovative mathematical modelling paradigm for intelligent CNC machine tools based on the Steiner Roman surface as a geometric core of digital twins. The use of this topological abstraction is investigated for analytical determination of the cutter-workpiece engagement (CWE) zone during multi-axis milling of free-form surfaces. An approach for detecting kinematic singularities and optimising cutting forces through invariants of the algebraic model is proposed. It is demonstrated that the transition from traditional solid B‑Rep models to compact analytical "physical models" dramatically reduces computational load, enabling compensation of elastic tool deformations directly on edge computing devices in real time. Lyapunov-based stability analysis guarantees convergence of the state estimates and adaptation of neural network weights for approximating uncertain dynamic disturbances. The proposed architecture is shown to comply with the international standards ISO 23218 (CNC systems and their integration) and ISO 23704 (cyber-physically controlled smart machine tool systems, CPSMT). A comparative analysis with a recent MTConnect-based digital twin implementation highlights the advantages of the continuous analytical CWE model for real-time force control.