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This study presents a novel application of the Transmission Line Matrix Method (TLM) for the modelling of the dynamic behaviour of non-linear hybrid systems for computer numerical control (CNC) machine tool drives. The application of the TLM technique implies the dividing of the ball-screw shaft into a number of identical elements in order to achieve the synchronisation of events in the simulation, and to provide an acceptable resolution according to the maximum frequency of interest. This entails the use of a high performance computing system with due consideration to the small time steps being applied in the simulation. Generally, the analysis of torsion and axial dynamic effects on a shaft implies the development of independent simulated models. This study presents a new procedure for the modelling of a ball-screw shaft by the synchronisation of the axial and torsion dynamics into the same model. The model parameters were obtained with equipments such as laser interferometer, ball bar, electronic levels, signal acquisition systems, etc. The MTLM models for single and two-axis configurations have been simulated and matches well with the measured responses of machines. The new modelling approach designated the Modified Transmission Line Method (MTLM) extends the TLM approach retaining all its inherent qualities but gives improved convergence and processing speeds. Further work since, not the subject of this paper, have identified its potential for real-time application.

Computer numerical control vertical machining centre feed drive modelling using the transmission line technique