Instability regimes and self-excited vibrations in deep drilling systems

peer reviewe

Aspects of non-smooth dynamics in models of percussion

peer reviewe

Non-smooth dynamics modeling of drill-string systems in heterogeneous formations

An extension of the drill-string dynamics model for drilling in heterogeneous rock formations is presented to study the heterogeneity effect on both the axial and torsional dynamics

An Alternative Approach to Model Milling Dynamics

In models for the dynamics of the milling process, the characterization of the chip thickness plays a central role. In this abstract, we develop an alternative model for the computation of the chip thickness. The chip thickness is computed using (i) a surface function describing the evolution of the milled surface and (ii) the information about the shape of the workpiece. Combining a partial differential equation (PDE) governing the surface function with the ordinary differential equations (ODE) governing the tool dynamics, a mixed PDE-ODE model formulation is proposed to describe the milling process dynamics. Compared with the classical delay differential equation (DDE) formulation for milling dynamics, this novel formulation is more accurate because less assumptions have been made to compute the chip thickness. Case studies show that the two formulations generally agree well with each other. However, a sizable difference on predicted limit cycles, characterizing the periodic tool motion, occurs when the axial depth of cut is relatively large. This PDE-ODE formulation brings a novel perspective for analyzing milling processes as well as a means to assess the validity of models that based on DDE formulation