Modeling of Coupled Axial and Torsional Motions of a Drilling System

During drilling operations, rock-bit interactions may cause a wide range of undesirable system vibrations. The induced vibrations subsequently reduce drilling efficiency and increase fatigue loads acting on drill bit. In this paper, a coupled torsional and axial drilling model is proposed. It can be used to predict the vibrations including bit bounce and stick-slip. Instead of using finite element (FEM) approach, the drill pipe is accurately modeled based on wave propagation theory. This results in time-delay equations in time domain and significantly reduces the computational complexity associated with FEM. The axial and torsional motions are coupled by bit-rock interactions. Different rock-bit interaction conditions are considered based on bit rotation and contact with formation. Simulations are conducted using the proposed model to analyze the impact of different applied weights on bit and surface rotary speeds on the system vibrations. This information provides insights into optimization of drilling operation.