Model generalizations
Machining vibrations - How can they be identified and addressed

Multi-mode unidirectional systems

The previous model extends quite naturally to systems with several decoupled modes. In practice, it is sometimes difficult to obtain all the associated parameters (frequencies, damping).

Multi-directional systems

Taking into account several directions (x, y, z) requires identification of the modal directions, the cutting force components and the chip regeneration pattern (since the regenerative effect may be strong in one direction and weak or even negligible in another, it is not sufficient to apply "x(t + T) - x(t)" indifferently to the different directions), which is far from obvious for a milling tool of any shape, for example.

Non-linear cutting laws...