Nonlinear Modeling and Dynamic Simulation Using Bifurcation and Stability Analyses of Regenerative Chatter of Ball-End Milling Process

A dynamic model for a ball-end milling process that includes the consideration of cutting force nonlinearities and regenerative chatter effects is presented. The nonlinear cutting force is approximated using a Fourier series and then expanded into a Taylor series up to the third order. A series of nonlinear analyses was performed to investigate the nonlinear dynamic behavior of a ball-end milling system, and the differences between the nonlinear analysis approach and its linear counterpart were examined. A bifurcation analysis of points near the critical equilibrium points was performed using the method of multiple scales (MMS) and the method of harmonic balance (MHB) to analyse the local chatter behaviors of the system. The bifurcation analysis was conducted at two subcritical Hopf bifurcation points. It was also found that a ball-end milling system with nonlinear cutting forces near its critical equilibrium points is conditionally stable. The analysis and simulation results were compared with experimental data reported in the literature, and the physical significance of the results is discussed

Triple-well potential with a uniform depth: Advantageous aspects in designing a multi-stable energy harvester

Analytical expressions for the bi- and tri-stable conditions of a multi-stable energy harvester (MEH) are derived on the basis of bifurcation analyses, and the associated multi-stable regions are characterized in a 2-D parametric space. It is found that a special boundary condition exists for a triple-well with a uniform depth (TU boundary condition), originating from a degenerate pitchfork bifurcation (DPF) point. Interestingly, the outermost well-to-well distance of the triple-well potential, when subjected to the condition that the maximum well depth is kept constant, becomes widest when the well depth is uniform. Accordingly, instead of investigating all possible parametric conditions, the design parameters for the optimal well configuration of the MEH can be sought most efficiently by simply tracing them on the TU boundary. A detailed examination of the potential well configurations along the TU boundary reveals that the most efficient energy harvesting from low-intensity ambient vibrations can be achieved on a TU boundary point, near the DPF point but inevitably a certain distance apart, by inducing an enlarged interwell motion. This investigation is experimentally validated.Published versio