Simulation Technique for Coupled Vibration Between Machine Tool Dynamics and Cutting Force: A Method by Simscape Multibody Model and Boolean Operation Between Tool and Workpiece Geometries

To improve the productivity of the machining process, it is crucial to minimize non-productive time during the manufacturing process. For instance, a significant amount of time is often spent troubleshooting issues on-site when machining failures occur, which reduces overall productivity as the machine remains idle during this period. Recently, using virtual environments constructed in computer systems to predict and resolve such problems has become increasingly popular. This approach, often referred to as a “digital twin,” can be highly effective in addressing issues. However, accurately predicting physical phenomena in a virtual environment can be challenging, requiring considerable effort to ensure the virtual model correctly represents real-world behavior. This study presents a technique for simulating coupled vibrations between machine tool dynamics and cutting forces using MATLAB/Simulink, a widely used commercial software. Machine tool dynamics are modeled with the “Simscape Multibody” function, which allows the construction of a multi-body dynamics model by defining mass, inertia, and constraint conditions. Cutting forces and machined surface geometry are calculated through Boolean operations between two geometric shapes represented by polygonal models. Self-excited chatter vibrations are simulated as an example of coupled vibrations, and actual cutting tests are conducted to validate the accuracy of the simulated results. A stability lobe diagram of the chatter vibrations is also generated based on measured and simulated frequency responses. The results demonstrate that the constructed model can accurately predict machining stability and cutting forces.