The Parametric Resonance Instability in a Drilling Process

Abstract

This study investigates dynamic instability in a high-speed drilling process. A pretwisted beam is used to simulate the drill. The time-dependent nature of the thrust force and the drilling depth is considered in the equation of motion of the drill. A moving Winkler-type elastic foundation assumption is applied to the drill tip to approximate the time-varying boundary conditions in the drilling process. Galerkin’s method is used to formulate the characteristic equation in a discrete form. The variation of the instability regions of the drill system is solved and analyzed by employing the multiple-scales perturbation method. The numerical results indicate that the unstable regions suddenly enlarge and shift toward a lower frequency when the drill first contacts the work piece. The effects of the rotational speed, pretwisted angle, and thrust force of the drill on the variation of the dynamic instability in high-speed drilling are also studied and are found to be highly influential.