The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the engagement and disengagement of the cutting tool into the workpiece material and tool breakthrough. Model parameters include the actual rigidity of the tool and workpiece holders, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations, which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. Calculated bifurcation diagrams make it possible to derive the relevant domain of user-specified system parameters along with the determination of optimal cutting conditions.

This paper proposes a dynamic model of cylindrical grinding with a tool owning specified distribution of abrasive grains. Cutting forces have been calculated, the surface geometry formed after a grinding wheel pass has been determined, the influence of the process dynamics on cutting forces and machined surface geometry has been taken into account, and the effects of cutting condit on vibrations being generated in the process of grinding have been investigated.

The nonlinear dynamics of a tool commonly employed in deep hole drilling is analyzed. The tool is modeled as a two-degree of freedom system that vibrates in the axial and torsional directions as a result of the cutting process. The mechanical model of cutting forces is a nonlinear function of cutting tool displacement including state variables with time delay. The equations of new surface formation are constructed as a specific set. These equations naturally include the regeneration effect of oscillations while cutting, and it is possible to analyze continuous and intermittent cutting as stationary and nonstationary processes, respectively. The influence of the axial and torsional dynamics of the tool on chip formation is considered. The Poincaré maps of state variables for various sets of operating conditions are presented. The obtained results allow the prediction of conditions for stable continuous cutting and unstable regions. The time domain simulation allows determination of the chip shape most suitable for certain workpiece material and tool geometry. It is also shown that disregarding tool torsional vibrations may significantly change the chip formation process.

In this work, a new three-dimensional approach to the numerical dynamics modeling of drilling processes with a special elastic device contributing to the tool's axial self-oscillations excitation on specified machining regimes is being proposed. The numerical model considers the possibility of self-oscillations excitation in the system due to the regeneration mechanism of cutting. Sufficient axial vibration amplitude causes fragmentation of chips, which significantly facilitates chip removal from the cutting zone and causes a positive influence on machining process quality. On the other side, in the device-tool-workpiece system along with the axial vibrations, lateral vibrations in other directions can be excited, which results in a distorted polygon-like shape of the drilled hole. Time realizations of device-tool system motion, machined surface configuration and the shape of the drilled hole were obtained for different machining regimes as simulation results. The proposed approach to the modeling and obtained results may be used in designing devices for vibratory drilling and to the rational machining regimes selection in the drilling of deep holes with application of such devices.