Criticality of Hopf bifurcation in state-dependent delay model of turning processes

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Multiple mode analysis of the self-excited vibrations of rotary drilling systems (2009, result): “Thus, in contrast to the work on the self-excited vibrations of machine tools, where with few exceptions [20, 21] the delay is considered constant, the variation of the angular velocity affecting the bit due to the large torsional compliance of the drilling structure needs to be accounted for.”
The effect of serration on mechanics and stability of milling cutters (2010, methodology): “This may lead to the use of state-dependent delay models similar to the ones in [12,28].”
On the Global Dynamics of Chatter in the Orthogonal Cutting Model (2011, unknown): “By analysing when steady cutting is linearly unstable, we may thus identify combinations of technological parameters which the machinist should avoid [3–10].”
Galerkin projections for state-dependent delay differential equations with applications to drilling (2013, background): “Systems with state-dependent delays, though not as common as constant delay systems, nevertheless, arise in several important situations [23–26].”