Modeling and Finite Element Analysis of Drill Bit Vibrations

Abstract

Drill bit vibrations are modeled using the Euler-Bernoulli beam theory. The model includes the most important properties of drill bits and of the drilling operation. These are: the drill bit cross sectional geometry, the drill helix angle, rotational speed of the drill bit, the thrust force, torque, and cutting forces generated during drilling. Equations of motion are derived in an inertial frame and then transformed to a rotating fluted frame for convenience in the solution. The transformed equations are discretized using finite element techniques. The finite element code developed is capable of solving the eigenvalue problem for various boundary conditions and drill cross sectional geometries. Finite element solutions are compared to known analytical, numerical, and experimental results from the literature and good agreement is obtained.