Reconstructed drill-bit motion for sonic drillstring dynamics

Abstract

In tunnel excavation that integrates Resonant Sonic Head Drilling (RSHD) machine, one of the important stability problem to deal with is represented by the necessity to assign axial vibration amplitude induced by the RSHD to a resonant vibration mode. In general, a control law depends on system variables which are partially available for measurements. In drilling operation, the drillstring variables at the tip boundary aren’t easy, if not impossible, to be measured. The sonic drillstring infinite dimension dynamics, derived in this paper, will play an important role in PDE (Partial Derivative Equation) observer design for the drill bit motion. The well-posedness problem is addressed, and the designed PDE-observer stability is detailed using the resolvent method. The wave peak amplitude is determined from the resonant drillstring mode shape, and the system’s stability is analyzed around a practical frequency mode.