Prediction of position-dependent stability lobes based on reduced virtual model

The stability of a machining process is directly affected by the dynamic response between the tool and the workpiece. However, as the tool moves along the path, the dynamic stiffness of the machine tool changes. To determine the position-dependent dynamic stiffness accurately, a computationally efficient methodology based on a complex virtual model is presented. The virtual model is assembled using Finite Element Method and is effectively reduced via Component Mode Synthesis and transformation to a State-Space Multi-Input-Multi-Output system. Combination of these techniques allows time-efficient response simulations with significantly less computational effort than the conventional full Finite Element models. Furthermore, they describe the behaviour of the complex structure more accurately opposed to the commonly used models based on a simple 1 Degree-of-Freedom systems. The reduced model is used to simulate dynamic response of the structure to a cutting force during operation. A response is measured on an existing machine to modify the virtual model by incorporating fuzzy parameters, such as damping. The stability regions are calculated for variable positions, resulting in position-dependent lobe diagrams. The presented approach can be used to create a map of stable zones to predict and prevent unstable behaviour during operation