Non-conservative oscillations of a tool for deep hole honing

The dynamics of a rotating tool, commonly employed in deep hole honing, is considered. A mathematical model of the process including a dynamic representation of tool, workpiece surface and honing stones interaction is suggested and analyzed. It is shown that interaction forces are non-conservative. The honing tool is modeled as a rotating continuous slender beam with a mandrel attached at an intermediate cross-section. The transverse oscillations of tool shaft cause variation in expansion pressure and change the interaction forces on the surface of the workpiece. The interaction forces are nonlinear and non-conservative in the general case including delayed functions. The expansion pressure of stones turns out to be a critical parameter in a honing process. Since the removal of stock increases linearly with pressure, the productivity can be improved by increasing expansion pressure, but in certain conditions may cause dynamic instability of the tool shaft. On the other hand, the lower expansion pressure and feed rates increase accuracy. Another source of shaft instability is due to the asymmetry of the tool that leads to discrepancy of the system stiffness in the transverse directions. As a result, under certain conditions unstable parametric vibrations may occur. Needless to say, the dynamic behavior of the tool can considerably influence the machined surface formation. In this study a model of honing surface formation is introduced and integrated into the model of process simulation. The system response is studied for different parameters in a non-dimensional form. Thus it is possible to analyze a set of real processes by applying the similarity conditions. The variation in the machined surface having various initial discrepancies from ideal cylinder is also analyzed.