Generalized modeling of drilling vibrations. Part II: Chatter stability in frequency domain

A time domain model of the drilling process and hole formation mechanism is presented in Part I, and the general solution of drilling chatter stability in frequency domain is presented in this paper. The drill's flexibility in torsional, axial and lateral directions are considered in determining the regenerative chip thickness. Stability is modelled as a fourth order eigenvalue problem with a regenerative delay term. The critical radial depth of cut and spindle speed are analytically determined from the eigenvalues of the characteristics equation of the dynamic drilling process in frequency domain. The method is compared against the extensive numerical solutions in time domain which were presented in Part I, cutting experiments and previously published partial stability laws. The time domain model presented in Part I of the paper considers tool geometry dependent mechanics, all vibration directions and the true kinematics of drilling, while allowing for nonlinearities such as tool jumping out of cut and nonlinear cutting force models. It is shown that accurate prediction of drilling stability requires modeling of drill/hole surface contact stiffness and damping which is still a research challenge.