Instability of a cracked twisted beam with a time-dependent boundary

The crack effect on the instability of a twisted beam with a time-dependent boundary, a drill in the drilling process, is studied in this work. This work presents the drilling force from the two active parts of a twisted drill subjected to small fluctuations during the drilling process. This small drilling force fluctuation may lead the system into a dynamically unstable condition. In this work, the instability of a drill with drilling force fluctuations is focused to study as the drill has a crack. A moving Winkler-type elastic foundation is used to approximate the drilling process and the multiple scale method is employed to solve for the unstable regions. Numerical analysis indicates that the unstable regions are enlarged and shifted to a lower frequency suddenly as a drill with a crack bites into a workpiece. It is also observed that the crack depth, thrust force and rotation speed drastically change the dynamic instability of the drilling process.