Numerical Investigation of Bending-Critical Eigenmodes and Stable Operating Conditions in the Utilization of Slim Tool Extensions - The Influence of Resonance and Nutation Phenomena

State-of-the-art machining of complex integral workpieces requires the utilization of slim tool extensions in machine tools. Previous investigations indicate that resonant excitation of slim tool extensions at their bending-critical eigenfrequency can result in complex plastic deformation and subsequent failure. Significantly increased eccentricity of slim tool extensions’ mass causes an abrupt increase in the accumulated kinetic energy of potential fragments released in the event of a resonance catastrophe. This exceeds the retention capacity of standard safety guards by orders of magnitude. A novel approach for resolving this issue is to induce defined failure in slim tool extensions by means of design measures. Therefore, preliminary knowledge of the excitation conditions is essential. This paper presents findings from numerical analyses with specific focus on the interrelationship between resonance and the rotodynamic phenomenon of synchronous and asynchronous nutation. Modal and frequency response analyses on finite element models are conducted to determine bending-critical eigenfrequencies of slim tool extensions and tool holders along with their respective eigenmodes. The insights gained throughout these analyses facilitate a more profound comprehension of slim tool extensions’ behavior in the range of bending-critical eigenmodes and the associated limits of safe operation.The results obtained provide substantial evidence that, beyond the mere phenomenon of resonance, failure of slim tool extensions due to bending-critical excitation is caused by a complex resulting state of stress that cannot be attributed to mere bending. Furthermore, exemplarily conducted transient run-up simulations could demonstrate that a distinct relationship between invoked resonance and stress states can be reproduced in a non-linear time domain.