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.
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.
The paper is devoted for the analysis of the dynamics effect on the 5-axis milling process of flexible details. The integrated model of milling dynamics composed by block principle in the paper is presented. The model consist of: 1) dynamical model of tool; 2) dynamical model of machined detail based on Finite Element Method (FEM); 3) phenomenological model of cutting forces and 4) algorithm of geometry modeling for instant machined chip thickness calculation. Regeneration mechanism of cutting and calculation of the machined surface are into this algorithm embedded. The elaborated model is adapted for 5-axis processing of the profiled details with 3-D complex geometry. Alteration of workpiece dynamic characteristics while the allowance removal is considered by the special algorithm of FEM grid changing based on the results of cutting geometry modeling. The results of modeling give us opportunity determine cutting forces, estimate the machined surface quality, calculate the magnitude and the character of tool and detail vibrations under the specified cutting conditions. The conception of increasing the process quality and the machinability for 3-D shaped details machining is offered in the paper. Applying the specified efficient conditions the undesired dynamical effects can be excluded on the base of the results of multi-variant simulation for milling dynamics varying the technological parameters at the different region of the processing route.
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