Extension of Tlusty׳s law for the identification of chatter stability lobes in multi-dimensional cutting processes

• Efficient calculation of limiting chip width for various cutting processes.
• Extension of applicability of Tlusty׳s law to milling.
• Effect of rotational direction on stability lobes in turning.
• Effect of structural coupling for torsional–axial chatter in drilling.
• Imaginary part of oriented transfer function determines stability in milling.

Chatter vibrations in cutting processes are studied in the present paper. A unified approach for the calculation of the stability lobes for turning, boring, drilling and milling processes in the frequency domain is presented. The method can be used for a fast and reliable identification of the stability lobes and can take into account nonlinear shearing forces, as well as process damping forces. The applicability of Tlusty׳s law, which is a simple scalar relationship between the real part of the oriented transfer function of the structure and the limiting chip width, is extended to milling and any other multi-dimensional chatter problem without neglecting the coupled dynamics. The given analysis is suitable for getting a deep understanding of the chatter stability dependent on the parameters of the cutting process and the structure. Basic examples based on experimental data of real machine tools include the dependence of the stability behavior on the rotational direction in turning, the effect of axial–torsional structural coupling in drilling, and the dynamics of slot milling.