Receptance coupling for tool point dynamic prediction by fixed boundaries approach

• A new analytical model based on Timoshenko beam theory with the fixed boundary approach is proposed to perform the receptance coupling.
• The good results obtained by the analytical model with the methodology proposed by Park are confirmed.
• The influence of different parameters involved in the receptance coupling is studied.
• Stability diagrams are obtained with receptance coupling predictions and compared with experimental cutting tests.

The material removal capability of machines is partially conditioned by self-excited vibrations, also known as chatter. In order to predict chatter free machining conditions, dynamic transfer function at the tool tip is required. In many applications, such as high-speed machining (HSM), the problematic modes are related to the flexibility of the tool, and experimental calculation of the Frequency Response Function (FRF) should be obtained considering every combination of tool, toolholder and machine. Therefore, it is a time consuming process which disturbs the production. The bibliography proposes the Receptance Coupling Substructure Analysis (RCSA) to reduce the amount of experimental tests. In this paper, a new approach based on the calculation of the fixed boundary dynamic behavior of the tool is proposed. Hence, the number of theoretical modes that have to be considered is low, instead of the high number of modes required for the models presented up today. This way, the Timoshenko beam theory can be used to obtain a fast prediction. The accuracy of this new method has been verified experimentally for different tools, toolholders and machines.