Dynamic instability in a high speed drilling process

The variation of dynamic instability in a high speed drilling process was investigated in this article. A pre-twisted beam is used to simulate the drill. The time dependent thrust force and drilling depth are considered in the equation of motion. A moving Winkler-Type elastic foundation assumption is employed to the drill tip to approximate the time varying boundary conditions in the drilling process. The Galerkin method is used to formulate the characteristic equation in a discrete form. The variation of instability regions of the drill system is solved and analyzed by employing the multiple scales perturbation method. Numerical results indicate that unstable regions are enlarged and shifted toward a lower frequency suddenly at the moment when the drill attaches the work piece. The effects of spinning speed, pre-twisted angle and thrust force of the drill on the variation of the dynamic instability in a high speed drilling process are also studied.