Suppression of Machine Tool Chatter Using Nonlinear Energy Sink

Abstract

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.