Nonlinear chatter with large amplitude in a cylindrical plunge grinding process

The phenomenon that the stable smooth grinding process coexists with chatter vibrations with large amplitudes in a cylindrical plunge grinding process is investigated in this paper. In the analyzed dynamic model, the workpiece and the grinding wheel involved in the grinding process are regarded as a slender hinged-hinged Euler–Bernoulli beam and a damped spring mass system, respectively, and the contact force between the two is treated as the main factor that affects the dynamic behaviors of the process. Called regenerative force, the contact force represents the interaction with regenerative effects between the workpiece and the wheel. To clarify the relation between the force and the dynamical behaviors in the grinding process, all the effects of the system parameters related to the interaction, such as the grinding stiffness, the rotation speeds of the workpiece and the wheel, on the dynamic motions of the process are studied. To this end, the eigenvalues analysis is firstly carried out to find the chatter-free-region, in which the smooth grinding process is stable and the chatter vibration may be absent. And then the nonlinear chatter vibrations when the values of concerned parameter leave the chatter-free region are predicted numerically. It is interesting that both the supercritical and subcritical Hopf bifurcations are found on the same boundary of the chatter-free region. As we know, there must be a zone in the chatter-free region where the stable smooth grinding process coexists with the chatter vibration when the subcritical one arises and the switching point between the supercritical and the subcritical ones is a Bautin bifurcation point mathematically. Thus, the Bautin bifurcation analysis is performed to scan the subregion in which the smooth grinding process is not unconditional stable anymore.