Enhanced dynamic modeling of chatter incorporating nonlinear Hertzian contact

Chatter during milling significantly hampers machining productivity, surface quality, and machine accuracy. This study introduces an analytical framework to enhance milling through the development of a Single Degree of Freedom model. The model integrates regenerative theory and Hertzian contact, incorporating factors such as cutting tool-workpiece interaction, tool geometry, and material properties. Solving a nonlinear delayed differential equation with quadratic and cubic terms, the model yields a stability criterion using the multiple scales approach. This criterion generates a Stability Lobes Diagram to predict chatter occurrence, distinguishing between stable and unstable cutting zones. Numerical verification via the Runge-Kutta method validates the model's efficacy. These results underscore the crucial role of natural frequency and damping ratio in ensuring milling stability.