Dynamic modeling and simulation of a nonlinear, non-autonomous grinding system considering spatially periodic waviness on workpiece surface

In this study, nonlinear analyses are performed on a cylindrical traverse grinding process for a workpiece with a spatially periodic wavy surface in order to investigate its nonlinear, non-autonomous vibration characteristics. The wavy surface is often undesirably generated owing to chattering (Tobias, 1965) in rough machining processes (such as a turning or milling) conducted prior to fine surface finishing (grinding) processes. By considering the wavy surface in the modeling process of this study, the nonlinear behavior of the grinder can be considered and analyzed in a more general situation. The resulting governing differential equations of the grinding system appear to be Hill-type, non-autonomous, doubly regenerative delay differential equations. The nonlinear normal grinding force is properly expanded in a Taylor series by employing a restriction that the wavy pattern is much smaller than the initial depth of cut. Subsequently, analyses of the forced vibration model are completed using several numerical approaches such as time traces, phase planes, frequency spectra, projection planes and stroboscopic sections.The focal frequencies of interest for these investigations are near the frequency of natural oscillation, called the eigen-frequency, of the nonlinear autonomous grinding system. The spatial characteristics of the wavy surface significantly affect the dynamic behavior of the grinder, especially when the frequency of the excitation force that originated from the traveling of the grinding wheel on the wavy surface, is close to the eigen-frequency of the system. The resulting phenomena, called 1:1 forced synchronizations, appearing in the present grinding process are important because their influence on the machined surface quality is often significant. These 1:1 forced synchronization phenomena are thoroughly examined in this study. Due to the suppression of natural oscillation and phase locking, two different synchronization mechanisms can occur. The dependence of these mechanisms on the amplitude and wave length of the pattern on the workpiece surface is identified and discussed.