Nonconservative oscillations of a tool for deep hole honing

The dynamics of rotating toot commonly employed in deep hole honing is considered. Mathematical model of a process including the dynamic model of tool and model of workpiece surface and honing sticks interaction is analyzed. It is shown that interaction forces are nonconservative. Honing tool is modeled as a continuous slender beam with a honing mandrel attached at intermediate cross section. Multi-stone tool rotates and has reciprocational motion in axial direction. Honing stones are expanded to the machined surface by special rigid mechanism that provides cutting of workpiece cylindrical surface. The tool vibrates in the transverse and axial directions. The transverse oscillations cause the variation of expansion pressure and change the interaction forces on the surface of the workpiece. Hence the vibrating tool shaft is under action of nonconservative forces depending on its position. The expansion pressure is a critical parameter in honing since its influence on process is different. The removal of stock increase linearly with pressure but the lowest expansion pressure and feed rate possible should be used to increase accuracy. The process productivity can be improved by increasing expansion pressure but may in a certain conditions cause a dynamic instability of tool shaft lateral oscillations. Another method of process productivity increasing is applying additional axial vibration of tool. In this case the tool passes more distance alone, the machined surface at the same time. But this method requires special machine tool with vibration actuator and additional research of system dynamic stability. Methods of vibratory process rational conditions evaluation are considered. The derived partial differential equations of rotating beam motion are reduced to a set of ordinary differential equations by the Galerkin approximation method. The derived differential equations with time periodic functions are numerically analyzed by Floquet method. The system response is studied for different technology and geometric parameters in non-dimensional form. That makes it possible to analyze a set of real processes applying the similarity conditions.