Digital Twin Development of a Turning Machine for Designing a Stability Diagram

The turning machining system as an object of study and the dynamic phenomena that constitute the problem that leads to the occurrence of vibrations are presented. The definition of a vibration-free cutting mode is proposed according to the stability diagram simultaneously for two components of the cutting mode – depth and feed. The mathematical model reflects the machining system as a three-mass one in the form of oscillatory links interconnected by negative feedbacks for elastic displacements and positive feedbacks through the delay function. A mathematical model has been developed in the form of a digital twin, due to its representation in state variables, which allows for modeling by numerical methods. Such a model is the basis of the created software, which allows predicting the behavior of the machining system in time and frequency spaces depending on the initial parameters of the machining system and the cutting mode. To ensure adequacy, the model uses dynamic parameters obtained by experimental modal analysis methods. The created software allows you to design stability diagrams of the machining system in the coordinates “cutting depth – speed” and“feed – speed”. The design is carried out automatically according to the stability criterion, which is based on the analysis of the location of the frequency response hodograph on the complex plane. The adequacy of the developed mathematical model and the created procedures for automatic design of the stability diagram is experimentally confirmed by comparing theoretical results and the roughness of the machined surface. The developed digital model and software allow you to choose a vibration-free cutting mode, which guarantees the required quality of machining at maximum productivity.