Suppression of regenerative instability in a single-degree-of-freedom (SDOF) machine
tool model was studied by means of targeted energy transfers (TETs). The regenerative
cutting force generates time-delay effects in the tool equation of motion, which retained
the nonlinear terms up to the third order in this work. Then, an ungrounded nonlinear
energy sink (NES) was coupled to the SDOF tool, by which biased energy transfers from
the tool to the NES and efficient dissipation can be realized whenever regenerative
effects invoke instability in the tool. Shifts of the stability boundary (i.e., Hopf
bifurcation point) with respect to chip thickness were examined for various NES parameters.
There seems to exist an optimal value of damping for a fixed mass ratio to shift the
stability boundary for stably cutting more material off by increasing chip thickness;
on the other hand, the larger the mass ratio becomes, the further the occurrence of
Hopf bifurcation is delayed. The limit cycle oscillation (LCO) due to the regenerative
instability appears as being subcritical, which can be (locally) eliminated or attenuated
at a fixed rotational speed of a workpiece by the nonlinear modal interactions with
an NES (i.e., by means of TETs). Three suppression mechanisms have been identified;
that is, recurrent burstouts and suppressions, partial and complete suppressions of
regenerative instabilities in a machine tool model. Each suppression mechanism was
characterized numerically by time histories of displacements, and wavelet transforms
and instantaneous energies. Furthermore, analytical study was performed by employing
the complexification-averaging technique to yield a time-delayed slow-flow model.
Finally, regenerative instability suppression in a more practical machine tool model
was examined by considering contact-loss conditions.